NTIA REPORT 79-25 

SPECTRUM RESOURCE 

ASSESSMENT 

IN THE 2.7-2.9 GHz BAND 

PHASE II: RADAR 

SIGNAL PROCESSING 

(REPORT N0.2) 

Robert L. Hinkle 

Robert M. Pratt 

JayS. Levy 

U.S. DEPARTMENT OF COMMERCE 

Juanita M. Kreps, Secretary 

Henry Geller, Assistant Secretary 

for Communications and Information 

AUGUST 1979 
ACKNOWLEDGEMENT 

The completion of this general investigation into the signal processing 

properties of the primary radars in the 2.7 to 2.9 GHz band and the 

Automated Radar Terminal System (ARTS-IliA ) required the contributions of' 

many individuals. In particular, the ASR-8 measurements made at Stapleton 

Airport, Denver, Colorado, were coordinated by Gerald J. Markey, Chief 

Frequency Engineering Branch, Federal Aviation Administration; and Larry 

Scofield, Supervisory Electronic Technician, Federal Aviation 

Administration . In addition, Robert B. Steves, Air Traffic Control (ATC) 

Systems Engineer, Texas Instruments Incorporated, contributed extensively to 

the completion of this investigation by providing both analytical and 

hardware experience in the signal processing properties of the ASR-7 and 

ASR-8 radars. Also, the generosity of Dr. Gerard V. Trunk, Naval Research 

Laboratory, Department of Defense, in technically reviewing the report was 

greatly appreciated. 

i ii 

: 
TABLE OF CONTENTS 

ACKNOWLEDGEMENT 

ABSTRACT 

SECTION 1 

INTRODUCTION 

BACKGROUND. 

Phase I 

Phase II. 

OBJECTIVE 

APPROACH. 

SECTION 2 

CONCLUSIONS AND RECOMMENDATIONS 

GENERAL 

GENERAL CONCLUSIONS 

PRIMARY RADAR CONCLUSIONS 

ARTS-IliA POST PROCESSING CONCLUSIONS 

GENERAL RECOMMENDATIONS . 

PRIMARY RADAR RECOMMENDATIONS 

ARTS-IliA POST PROCESSING RECOMMENDATIONS 

iv 

. iii 

. xxv 

. 1-1 

. 1- 2 

. 1-2 

. 1-3 

. 1-3 

.2- 1 

.2-1 

.2-2 

. 2-2 

.2-4 

.2-4·· 

.2- 5 

·, 

, . 

• 

' ' 

.. 
0 

SECTION 3 

PRIMARY RADAR SIGNAL PROCESSING 

INTRODUCTION ....... . 

GENERAL SYSTEM DESCRIPTION. 

Antenna and RF Waveguide. 

Receiver Unit . 

Processor Unit . . ... . 

ANTENNA AND RF WAVEGUIDE SYSTEM 

RECEIVER UNIT ... 

Receiver Front End. 

TR Limiter .... 

Sensitivity Time Control (STC) Attenuators. 

Antenna Pattern Switch. 

Passive Channel . . ~ 

Parametric Amplifier. 

Preselector Filter. 

Phase Shifter 

Mi xer . . . . 

Preamplifier. 

Normal Channel . . 

IF Amplifiers 

Envelope Detector 

Log-Normal Channel. . .. ' 

Log IF Bandpass Filter. 

Log IF Amplifier-Video Detector 

Moving Target Indicator (MTI) Channel 

IF Filter ......... . 

L i near-Li mHi ng Amp1 i fi er . . 

MTI Quadrature Phase Detector 

Low Pass Filter ...... . 

PROCESSOR UNIT ....... . 

Processor Unit Normal Channel 

Subtracter Anti -Log 

Noise . . . . . 

Desired Signal . 

Interference. . 

Normal Enhancer . . 

Feedback Integrator 

Binary Integrator . 

' . 

Normal Channel Wea ther Background . 

v 

. . 

.. 3- 1 

.3-2 

.3- 2 

.3-2 

. 3- 5 

.j-5 

. 3- 7 

. 3- 9 

.3-9 

.3-9 

.3-11 

. 3- 11 

.3-11 

. 3- 13 

.3- 13 

. 3- 13 . 3- 14 

.3-14 

. 3- 14 . 3- 16 . 3-22 

.3- 22 .. 3- 24 

. 3- 26 . 3- 27 

. 3- 29 

.. 3- 29 . 3- 30 

. 3- 33 

. 3- 33 . 3- 35 

.3- 35 . 3- 35 

.3- 35 . 3- 37 

.3- 38 

. 3- 43 

.3-52 
Processor Unit MTI Channel. 

MTI Cancellers ... 

Noise ..•..... 

Desired Signal . .. 

Interfering Signal. 

Rectifier . 

Combiner ... 

MTI Log-FTC . MTI Enhancer. 

Noise . . 

Desired Signal . 

Interference 

Processor Unit Al ignment/Di versi ty .Combiner 

MTI/Normal Alignment . . . . . . . • . • 

Output D/A Converter ........ . 

Weather Background Diversity Combiner 

SECTION ~ 

. . . 

ARTS-IliA SIGNAL PROCESSING 

INTRODUCTION. . • . . . . . . . . . . . .. . . 

RADAR DATA ACQUISITION SUBSYSTEM DESCRIPTION. 

Radar Extractor . . . . . . . . . 

Video Mul tiplexer Converter . 

Rank Order Detection Process. 

Rank Quantizer. 

Hit Processor . . 

Target Detection. . . . 

Clutter Moni tor Logic . 

Radar Micro Controller .. 

ARTS-IliA RDAS INTERFERENCE ANALYSIS ..... . 

Effect of Interference on the Probability of a Hit •. 

Effect of Interference on Probability of False Alarm. 

Probability of False Targ.et Hit Caused by Noise . 

Probability of False Target Hits Caused by Interference 

Probability of False Alarm Caused by Interference ... 

Interpretation of Interference Effects on False Alarms. 

Effect of Interference on Probability of Target Detection 

Probability of Target Hit Caused by a Target. 

Normal Channel . . . . . 

MTI Channel . . . . . . Interference Effect on Target Hit .. 

Interference Effect on Target Detection 

.3-54 

.3-54 . . 3-57 

.3-60 

.3-60 

. 3- 61 

.3-61 

. 3-63 

. 3 .. 65 

.3-65 

. 3-66 . 3-66 # • , • ••• 3-69 

... 3-69 .. . 3-69 

• 3-71. 

.~-1 

.. 4-1 . .• 4-3 

.~-3 

.4-3 

. · . 4-3 

.4-5 

.4-8 

.4-8 

.4-8 

. . 4-11 

. .. 4-13 . .4-15 

.4-15 

.4-16 .. 4-26 

.4-34 

.4-36 

.4-36 

. .4-37 

Interpretation of Interference Effects on Target Detection. 

. .. 4-38 

. 4-40 

.4-51 

.4-61 

vi 
Trade-Off Between Interference Suppression and ARTS-IIIA/RDAS 

Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Rank Quantizer Threshold Trade-Off .......... . ... . . 

Hit and Miss Count Threshold Trade-Off ........ . .... . Second Order Interference Effects . . . . • . . . . . . . . . . . . . . 

Interference Effect on Clutter Hit Probabiljty ... , ... . 

Interference Effect on Video Selectjon Control . . ..... . 

Interference Effect on MTI Channel Hit Count Threshold Control 

INTRODUCTION. . . . . . . 

MIXER TRANSFER PROPERTIES 

Noj se . . . . . . . . . . Desjred/Interfering Signal. 

SNR Transfer Properties 

IMAGE RESPONSE . . . . . 

APPENDIX A 

MIXER TRANSFER PROPERTIES 

APPENDIX B 

IF FILTER TRANSFER PROPERTIES 

INTRODUCTION 

IF SELECTIVITY. 

IF Selectivity Modeljng 

RECEIVER FREQUENCY-DEPENDENT- REJECTION CHARACTERICTICS. 

IF OUTPUT TIME WAVEFORM 

IF OUTPUT NOISE LEVEL . 

IF FILTER INR TRANSFER PROPERTIES 

vii 

.4- 62 

.4-62 

. 4- 67 

.4-69 

. 4-69 

.4- 70 

.4- 75 

.A-1 

.A-1 

. A- 1 

.A-3 

.A- 5 

.A- 5 

.B-1 

. B-1 

.B-2 

.B-7 

.B-9 

.B-18 

.B- 24 
APPEND'I.X C 

MTI CHANNEL TRANSFER PROPERTIES 

INTRODUCTION. 

PHASE DETECTOR TRANSFER PROPERTIES. 

Noise . . . . . . . . . Desired / Interfering Signal. . . 

Signal-Plus-Noise Distribution. 

MTI LOW PASS FILTER TRANSFER PROPERTIES 

Noise . . . . . . . . . . . 

Desired/ Interfering Signal .... 

MTI CANCELLER TRANSFER PROPERTIES 

Single Stage Canceller Transfer Properties. 

Noise ...... . 

Desired Signal . • ..... 

Interfering Signal ..... Double Stage Canceller Transfer 

Noise . . . . . . . Desired Signal . . . Interfering Signal .. . 

RECTIFIER . . . . . . . . 

Properties. 

DUAL MTI CHANNEL TRANSFER PROPERTIES. 

APPENDIX D 

INTEGRATOR TRANSFER PROPERTIES 

INTRODUCTION .... 

FEEDBACK INTEGRATOR 

Input Limiter Transfer Properties 

Feedback Integrator Loop Transfer Properties. 

Noise . . • . . 

Desired Signal. 

Interference. . 

v iii 

.C-1 

.C-1 

.C-1 

.C-6 

.C-8 

.C-9 

. C-11 

. C-11 

.C-13 

.. C-13 

.C-17 

.C-17 

.C-18 

.C-18 

.C-23 

.C-23 

.C-24 

.C-28 

.C-31 

.D-1 

.D-2 

.D-2 

• .D-4 

.D-4 

.D-6 

.D-20 
BINARY INTEGRATOR . . . . . FAA Integrator Modification 

Noise . . . .. Desired Signal. 

Interference. . 

INTRODUCTION . . ... . . . 

PROCESSOR UNIT DESCRIPTION. 

DESIRED SIGNAL ... 

INTERFERING SIGNALS 

NOISE . . . 

NORMAL CHANNEL SIMULATION 

Noise Di stri but ion. . . . 

S]gnal-Plus-Noise Distribution. 

N"ormaJ Channel ~nhancer . 

NormaJ Channel Alignment . 

MTI CHANNEL SIMULATION .. 

Noise Di str i buti on. . . . 

SignalTPlus-Noise Distr]bution. 

MTI Cancellers .. .. 

MTI Channel Enhancer . 

MTI Channel Al]gnment 

FEEDBACK ENHANCER 

OUTPUT DISPLAY . . 

INTRODUCTION. 

DERIVATION OF EQUATIONS 

• f 

APPENDIX E 

RADAR SIMULATION 

APPENDIX F 

Effect of Interference on Hit Probab]Jjty 

Propabi 1 i ty of False Target Hit . . . . . 

ix 

.D- 32 

.D- 32 .D-34 

.D- 41 

.D- 58 

.E- 1 

.E-1 

.E- 4 

.E- 6 

.E- 6 

.E-6 

.E-6 

.E- 6 

.E- 8 

.E-11 

. E-11 

. E-11 

. E- 11 .E- 12 

.E-15 

.E-15 

.E-15 

. E- 15 

.F-1 

.F-1 

.F- 1 

.F-5 
Probability of Target Hit ... 

COMPUTER PROGRAM DESCRIPTIONS .. 

Probability of False Alarm Program. 

Probability of Target Detection Program 

APPENDIX G 

SYSTEM CHARACTERISTICS 

INTRODUCTION .................. . 

APPENDIX H 

REFERENCES 

X 

.F-8 

.F-9 

.F-9 

.F-11 

... G-1 
LIST OF ILLUSTRATIONS 

FIQURE 

3-1 Block Diagram of Non-Diversity Radar Receivers ... 

3-2 Block Diagram of Frequency Diversity Radar Receivers 

3- 3 ASR- 8 RF System Simplified Block Diagram 

3-4 ASR-8 Diplexer Fil ter Characteristics. 

3- 5 ASR-8 Receiver Unit Block Diagram. 

3- 6 STC Waveform Generation ..... . 

~ 

. 3- 3 

. 3- 4 

.3- 6 

.3-8 

.3- 10 

.3-12 

3- 7 Typical IF Output Time Wavefore Responses for On-Tune and Off- Tune 

Pu 1 se s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3- 1 7 

3- 8 Signal-to-Noise Ratio Transfer Properties of a Linear Detector . 3- 19 

3-9 Signal-to-Noise Ratio Transfer Properties of a Square-Law 

Detector . . . . . . . . . . . ..... .3-20 

3- 10 Probability-Density Function for Noise Only and for Signal -PlusNoise at the Normal Channel Envelope Detector Output . 3-21 

3- 11 Logari thmic Amplifier-Detector Block Diagram . 3- 23 

3- 12 L..og Ampl Hi er Transfer Char act eri st i cs . 3- 25 

3- 13 Receiver Unit MTI I and MTI Q Channel. .3-28 

3- 14 Probability Density Function for Noise Only and for SignalPlus-Noise at the MTI Phase Detector Output. .3-31 

3~15 Processor Unit Normal Channel Block Diagram. . 3- 34 

3- 16 Log-FTC Block Diagram . . . . . . . . 3- 36 

3-17 Feedback Integrator Block Diagram . .3-39 

3- 18 Simulated Normal Channel Unintegrated Target Return Pulse Train 

for a SNR = 15 dB. . . . . . . . . . . . . . . . . . . . . . . 3-4 1 

3-19 Simulated Normal Channel Integrated Target Return Pulse Train 

for the Input Limiter Set at 1.0 Volts and a SNR = 15 dB ..... 3- 41 

xi 
3-20 Simulated Normal Channel Integrated Target Return Pulse Train 

for the Input Limiter Set at 0.5 Volts and a SNR = 15 dB ..... 3-4 2 

3-21 Simulated Normal Channel Integrated Target Return Pulse Train for 

the Input Limiter Set at 0.34 Volts and a SNR = 15 dB ....... 3-42 

3-22 Simulated Normal Channel Unintegrated Radar Output with 

Interference . . . . . .. 3-44 

3-23 Simulated Normal Channel Integrated Radar Output with 

Interference . . 

3-24 ASR-7 (AN/GPN-12) Binary Integrator Block Diagram. 

3-25 Hit/Miss Characteristic Curve for FAA Modified ASR-7 Enhancer. 

3-26 Simulated Binary Integrator Output for Target Return Pulse 

. 3-44 

.3-45 

. 3-4 7 

Train (ASR-7, AN/GPN-12) . . . . . . ..... . .. 3-50 

3-27 Simulated FAA Modified Binary Integrator Output for Target Return 

Pulse Train ( ASR-7). . . . . . . . . . . . . . . . . . 3- 50 

3-28 Simulated Normal Channel Uni ntegrated Target Return Pulse Train 

for a SNR = 15 dB. . .3-51 

3- 29 Simulated Normal Channel Integrated Target Return Pulse Train 

for a SNR = 15 dB. . . 3-51 

3- 30 Simulated Normal Channel Uni nt egrat ed Radar Output with 

Interference . . 3-53 

3-31 Simulated Normal Channel Integrated Radar Output with 

Interference . . . 3-5 3 

3-32 Weather Background Modes .3-55 

3-33 Processor Unit MTI Channel Block Diagram .3-56 

3-34 Canonical Form of Simulated ASR-7 MTI Canceller. .3-58 

3-35 Probabiljty Density Function for Noise Only and for Signal-PlusNoise at the MTI Canceller Output for a single Channel Double 

Stage Canceller. . . . . . . . ............. 3-62 

3-36 Probability Density Function for Noise Only and for Signal-PlusNoise at the MTI Canceller Output for a Dual Channel Double 

Stage Canceller (Simulated) . . . . . . . . . . . . . . .3- 64 

3-37 Simulated MTI Channel (Mode 1 and 2 CASC) Unintegrated Radar 

Output with Interference . . . . . . . . . . . . . . . . . . 3-67 

xii 
3-38 Simulated MTI Channel (Mode 1 and 2 CASC) Radar Feedback 

Integr ator Output with Interference for the Input Limiter Set at 

2. 0 Volts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3- 67 

3-39 Simulated MTI Channel (Mode 1 and 2 CASC) Radar Feedback 

Integrator Output with Interference for the Input Limiter Set at 

0. 34 Volts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6d 

3-40 Simulated MTI Channel (Mode 1 and 2 CASC) Radar Binary Integrator 

Output with Interference . . . . . . . . . . . . . . . . 3- 68 

3-41 Processor Unit Alignment/Diversity Combiner Block Diagram. 

4-1 Block Diagram of Radar Data Acquisition Subsystem . 

4- 2 Block Diagr am of Radar Extractor 

4- 3 Block Diagram of Rank Quantizer Logic. 

4- 4 Block Diagram of Hit Processing Logic. 

4- 5 Block Diagram of Target Detection. 

4- 6 Block Diagram of Clutter Monitor Logic 

4- 7 ARTS- IIIA/RDAS MTI Channel Hit Count Threshold Contr ol fo r 

Maintaining a Constant False Alarm Rate .. 

4- 8 ARTS- IIIA/RDAS Probability of False Target 

Received Interference (ASR- 7 Victim Radar, 

Quantizer Thr eshold 23) ......... . 

4- 9 ARTS- IIIA/RDAS Probability of False Target 

Received Interference (ASR- 7 Victim Radar, 

Quantizer Threshold 24) ....... . 

Hit Versus Rate 

Normal Channel, 

Hit Versus Rate 

Normal Channel, 

Hit Versus Rate 

of 

Rank 

of 

Rank 

4- 10 ARTS- IIIA/RDAS Probability of False Target of 

Received Interference (ASR- 7 Victim Radar, 

Quanti zer Threshold 23). . . . . . . . . . 

MTI Channel, Rank 

4- 11 ARTS- IIIA/RDAS Probability of False Target 

Received Interference (ASR- 7 Victim Radar, 

Quantizer Threshold 24). . . . . . . ... 

Hit 

MTI 

Versus Rate of 

Channel , Rank 

4- 12 ARTS- IIIA/RDAS Probability of False Target Hit Versus Rate of 

Received Interference (ASR- 8 Victim Radar , Normal Channel, Rank 

.3- 70 

.4- 2 

.4- 4 

. 4- 6 

. 4- 7 

. 4- 9 

.4-10 

.. 4- 12 

. 4-18 

.4- 19 

. 4- 20 

.4- 21 

Quantizer Threshold 23). . . . . . . . . . . . . . . . . . . 4- 22 

xiii 
4-13 ARTS-III/RDAS Probability of False Tar~et Hit Versus Rate of 

Received Interference ( ASR-8 Victim R:ad,ar, Normal Channel , Rank 

Quanti zer Threshold 24). . . . . . . . . . . . . . . . 4-23 

4-14 ARTS-IIIA/RDAS Probability of False Ta@get Hit Versus Rate of 

Received Interference (ASR-8 Victim Ra~ar, MTI Channel, Rank 

Quantizer Threshold 23) . . . . . . . . . . . . . . . . 4-24 

4-15 ARTS-IIIA/RDAS Probability of False Ta~get Hit Versus Rate of 

Receiv~d Interference (ASR-8 Victim R~d,ar, MTI Channel, Rank 

Quantizer Threshold 24). . . . . . . . . . . . . . . . . 4-25 

4-16 ARTS-IIIA/RDAS Probability of False A~arm Versus Probability of 

False Target Hit for Various Hit/Miss Count Threshold Parameter 

Combinations . . . . . . . . . . . . .. . . . . . . 4-31 

4-17 Probability of Target Hit Versus Signal-to-Noise Ratio for the 

ARTS-IIIA/RDAS connected to the ASR-7 or ASR-8 Radar Normal 

Channel (Rank Quantizer Thresholds 23 and 24) ........... 4-3~ 

4-18 Probability of Target Hit Versus Signal-to-Noise Ratio for the 

ARTS-IIIA/RDAS Connected to the ASR-7 Radar MTI channel (Rank 

Quantizer Thresholds 23 and 24). . . . . . . . . . .4-41 

4-19 Probability of Target Hit Versus Signal-to-Noise Ratio for the 

ARTS-IIIA/RDAS Connected to the ASR-8 Radar MTI Channel (Rank 

Quantizer Threshold 23 and 24) . . . . . . . . . . . . . . .4-42 

4-20 ARTS-IIIA/RDAS Probability of Target Hit Versus Rate of Received 

Interference (ASR-7 Victim Radar, Normal Channel, Rank Quantizer 

Threshold 23). . . . . . . . . . . . . ............ 4-43 

4-21 ARTS-IIIA/RDAS Probability of Target Hit Versus Rate of Received 

Interference (ASR-7 Victim Radar, Normal Channel, Rank 

Quantizer Threshold 24). . . . . . . . ............ 4-44 

4-22 ARTS-IIIA/RDAS Probability of Target Hit Versus Rate of Received 

Interference (ASR-7 Victim Radar, MTI CHannel, Rank Quantizer 

Thrsshold 23). . . . . . . . ... .. ..... .. ...... 4-45 

4-23 ARTS-III/RDAS Probability of Target Hit Versus Rate of Received 

Interference (ASR-7 Victim Radar, MTI CHannel, Rank Quantizer 

Threshold 24). . . . . . . . . . . . . ...... 4-46 

4-24 ARTS-IIIA/RDAS Probability of Target Hit Versus Rate of Received 

Interference ( ASR-8 Victim Radar, Normal Channel, Rank Quantizer 

Threshold 23). . . . . . . . . . . . . . ... ... . .. .. 4-47 

4-25 ARTS-IIIA/RDAS Probability of Target Hit Versus Rate of Received 

Interference (ARS-8 Victim Radar, Normal Channel, Rank Quantizer 

Threshold 24). . . . . . . . . . . . . . . . . . . . . . . . . . . 4- 48 

xiv 
4-26 ARTS-IIIA/RDAS Probability of Target Hit Versus Rate of Received 

Interference ( ARS- 8 Victim Radar, MTI Channel, Rank Quantizer 

Threshold 23). . . . . . . . . . . . . ............ 4-49 

4-27 ARTS-IIIA/RDAS Probability of Target Hit Versus Rate of Received 

Interference (ASR- 8 Victim Radar, MTI Channel , Rank Quantizer 

Threshold 24) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-50 

4-28 ARTS-IIIA/RDAS Probability of Target Detection Versus Probability 

of Target Hit for Rank Quantizer Threshold 23 and Various Hit/ 

Miss Count Threshold Parameters Combinations (Probability Scale) .4- 57 

4-29 ARTS-IIIA/RDAS Probability of Target Detection Versus Probability 

of Target Hit for Rank Quantizer Threshold 24 and Various Hit/ 

Miss Count Threshold Parameter Comb inations (Pr obability Scale) .. 4- 58 

4-30 ARTS-IIIA/RDAS Probability of Target Detection Versus Probability 

of Target Hit f or Rank Quantizer Threshold 23 and Various Hit/ 

Miss Count Threshold Parameter Combinations (Linear Scale) . 4- 61 

A-1 Radar Mixer Block Diagram. .A-2 

B-1 ASR-8 Normal IF Bandpass Filter Schematic. .B- 3 

B- 2 "Y" Parameter Equivalent Circuit for One IF Amplifier Stage Shown 

in Figure B-1. . . . B-4 

B-3 Simulated IF Output Time Wav eform Envelope .B-12 

B- 4 Simulated IF Output Time Waveform Envelope .B- 13 

B-5 Simulated IF Output Time Waveform Envelope .B- 14 

B- 6 Simulated IF Output Time Waveform Envelope .B-15 

B-7 Simulated IF Output Time Waveform Envelope .B-16 

B- 8 Simulated IF Output Time Waveform Envelope . B- 1 7 

B- 9 Simulated IF Output Time Waveform Envelope .B- 19 

B-10 Simulated IF Output Time Waveform Envelope .B- 20 

B-11 Simulated IF Output Time Wav eform Envelope .B- 21 

B- 12 Measured IF Output Time Waveform .B-22 

B- 13 Measured IF Output Time Waveform .B- 22 

B- 14 Measured IF Output Time Waveform .B- 22 

XV 
B-15 Simulated IF Output Phase Modulation for an Off-Tuned Pulse 

Signal . . . .B-23 

C- 1 Digital MTI Channel Block Diagram. .C-2 

C- 2 Inphase and Quadrature Digital MTI Channel Block Diagram .C- 3 

C- 3 Radar Coherent MTI Phase Detector. .C-4 

C-4 Probability Density Function for Noise Only and for Signal-PlusNoise at the MTI Phase Detector Output . . . . . .C-10 

C-5 Measured MTI Low Pass Filter Output Tjme Waveform. .C-12 

C-6 Measured MTI Low Pass Filter Output Time Waveform. .C-12 

C-7 Measured MTI Low Pass Filter Output Time Waveform. .C- 12 

C- 8 First-Order Nonrecursive Filter. . .C-14 

C-9 Canonical Form of First-Order Nonrecursive Filter. .C- 14 

C-10 Frequency Response for a Single Stage MTI Canceller. .C-16 

C-11 Measured Single Stage MTI Canceller Output Time Waveform. .C-16 

C-12 Second-Order MTI Filter with Feedback for Velocity Shaping .C-19 

C-13 Canonical Form of Second-Order Recursive Filter .. .C-19 

C- 14 Frequency Response for a Double Stage Canceller with Feedback. . C- 22 

C-15 Measured Double Stage MTI Canceller Response to an Interfering 

Pulse ( 1 and 2 CASC Mode). . . .C- 25 

C-16 Simulated Double Stage MTI Canceller Response to an Interfering 

Pulse ( 1 and 2 CASC Mode). . C-25 

C-17 Simulated Double Stage MTI Canceller Response to an Interfering 

Pulse (SCV-25 Mode). . . . . .C-26 

C-18 Simulated Double Stage MTI Canceller Response to an Interfering 

Pulse (SCV-30 Mode). . . . .C-26 

C- 19 Simulated Double Stage MTI Canceller Response to an Interfering 

Pulse (SCV-35 Mode). . . . . .C-27 

C- 20 Simulated Double Stage MTI CanceJler Response to an Interfering 

Pulse ( SCV -40 Mode) . . . . C-27 

xvi 
C-21 Probability Density Function for Noise Only and for Signal-Plus 

Noise at the MTI Canceller Output for a Single Channel Double 

Stage Canceller ................. . ........ C-29 

C-22 Probability Density Function of One-Sided Gaussian Distribution 

(Equation C-41). . . . . . . . . . . . . . . . . . . . . C-30 

C-23 Probability Density Function for Noise Only and for Signal-PlusNoise at the MTI Canceller Output for a Dual Channel Double Stage 

Canceller (Simulated) .............. ..... .. .. C-32 

C-24 Probability Density Function of Rayleigh Distribution 

(Equation C-44). . . . . . . 

D-1 Feedback Integrator Block Diagram. 

D-2 Canonical Form of Second-Order MTI Canceller Filter Showing Noise 

.C-34 

.D-3 

Carrel ation at MTI Channel Output. . . . .D- 7 

D-3a Simulated Normru Channel Unintegrated Target Return Pulse Train 

for a SNR : 3 dB . . . . D-11 

D-3b Simulated Normru Channel Integrated Target Return Pulse Train 

For a SNR : 3 dB ( V = 2. 0) . . . . . . . D-1 1 

D-4a Simulated Normru Channel Unintegrated Target Return Pulse Train 

for a SNR : 5 dB . . . . . . D- 12 

D- 4b Simulated Normru Channel Integrated Target Return Pul s~ Train 

for a SNR = 5 dB (V = 2.0). . . .D- 12 

D-5a Simulated Normal Channel Unintegrated Target Return Pulse Train 

for a SNR : 10 dB. . , . . D- 13 

D-5b Simulated Normal Channel Integrated Target Return Pulse Train 

for a SNR : 10 dB (V = 2.0) . .D-13 

D- 6a Simulated Normru Channel Unintegrated Target Return Pulse Train 

for a SNR = 15 dB. . . . . D-14 

D-6b Simulated Normal Channel Integrated Target Return Pulse Train 

for a SNR : 15 dB (V : 2.0) .D-14 

D-7 Simulated Normru Channel Integrated Target Return Pulse Train 

for a SNR: 15 (V = 1.0). .D- 15 

D-8 Simulated Normru Channel Integrated Target Return Pulse Train 

for a SNR : 15 (V = 0. 7). . . . D- 15 

D-9 Simulated Normru Channel Integrated Target Return Pulse Train 

for a SNR : 15 ( V = 0. 5) . . . . D- 16 

xvii 
D-10 Simulated Normal Channel Integrated Target Return Pulse Train 

for a SNR : 15 (V : 0.34) . ..... . . D-16 

D- 11 Measured ASR- 8 Normal Channel Integrated Output. .D-17 

D- 12 Measured ASR-8 Normal Channel Integrated Output . .D-17 

D-13 Measured ASR-8 Normal Channel Integrated Output . . .D-17 

D- 14 ASR- 7 Six Stagger Sequence . .D-22 

D- 15 ASR- 8 Four Stagger Sequence . .D-22 

D- 16 Simulated Feedback Integrator Output for Asynchronous Normal 

Channel Interference (V = 2.0, INR = 30 dB) ........... D-23 

D-17 Simulated Feedback Integrator Output for Asynchronous Normal 

Channel Interference (V = 1.0, INR = 30 dB) . . ....... .. D-23 

D- 18 Simulated Feedback Integrator Output for Asynchronous Normal 

Channel Interference (V = 0.34, INR = 30 dB) ... .. . .D-24 

D- 19 Measured ASR- 8 Integrator Output for Asynchronous Normal Channel 

Interference . . . . . . . . . . . . . . .D-25 

D-20 Measured ASR- 8 Integrator Output for Asynchronous Normal Channel 

Interference . . . . . . . . . . . . D-25 

D-21 Measured ASR-8 Integrator Output for Asynchronous Normal Channel 

Interference . . . . . . . . D- 25 

D-22 Simulated Normal Channel Unintegrated Radar Output with 

Interference . . . . . . . . . . .D-26 

D-23 Simulated Normal Channel Integrated Radar Output with 

Interference . . ... . .. D- 26 

D- 24 Simulated Feedback Integrator Output for Asynchronous MTI Channel 

Interference (V = 2.0, INR = 30 dB) . . . . . . . . . . .D-28 

D- 25 Simulated Feedback Integrator Output for Asynchronous MTI Channel 

Interference (V = 1. 0' INR : 30 dB) . . . . . . . . . . D-28 

D-26 Simulated Feedback Integrator Output for Asynchronous MTI Channel 

Interference (V = 1. 0' INR 30.0 dB) . . . . . . . . . .D-29 

D- 27 Measured ASR-8 Integrator Output for Asynchronous MTI Channel 

Interference . . .D-30 

xviii 
D-28 Measured ASR-8 Integrator Output for Asynchronous MTI Channel 

Interference . . . .D-30 

D-29 Measured ASR-8 Integrator Output for Asynchronous MTI Channel 

Interference ' .D-30 

D-30 Simulated MTI Channel (Mode 1 and 2 CASC) Unintegrated Radar 

Output with Interference . . . . . . . . . . . . . . . .. D- 31 

D-31 Simulated MTI Channel (Mode 1 and 2 CASC) Integrated Radar 

Output with Interference . . . . . . . . . . . . . . D- 31 

D- 32 ASR-7 ( AN /GPN- 12) Binary Integrator Block Diagram. .D-33 

D-33 FAA Modified ASR-7 Enhancer Block Diagram . . . .D- 35 

D-34 Hit/Miss Characteristic Curve for.FAA Modified ASR-7 ~nhancer. . D- 36 

D-35 Probability of Noise Causing a Binary 1 at the Threshold 

Comparator Output. . . . . . . . . . . . . . . . . .... D- 38 

D- 36 Probability of 1 at the Threshold Comparator Ou~put as a Function 

of the Signal - to- Noise Ratio at the Threshold Comparator Input for 

the Normal Channel . . . . . . . . . . . . . . . . . . . . . . . D- 4 4 

37 Probability of 1 at the Threshold Comparator Output as a Function 

of the Signal-to-Noise Ratio at the Threshold Comparator Input for 

a Single Channel MTI Canceller . . . . . . . . . . D- 4 6 

D-38 Simulated Binary Integrator Output for Target Return Pulse Train 

(ASR-7, AN/GPN-12) . . . . . . . . . . . . . . . D-50 

3~ Simulated FAA Modified Binary Integrator Output for Target Return 

Pulse Train (ASR-7). . . . . . . . . . . . . . . . .D-50 

D-40a Simulated Normal Channel Unintegrated Target Return Pulse Train 

for a SNR = 3 dB . . . . . . . . . . . . . . . . . D- 51 

D- 40b Simulated Normal Channel Integrated Target Return Pulse Train 

for a SNR = 3 dB. . . . . . . . . . . . . . . . . D- 51 

D-41a Simulated Normal Channel Unintegrated Target Return Pulse Train 

fo~ a SNR = 5 dB. . . . . . . . . . . . . . . . 0- 52 

D-41b Si mulated Normal Channel Integrated Target Return Pulse Train 

for a SNR = 5 dB. . D- 52 

D-42a S:i mul ated Normal Channel Unint egrated Target Return Pulse Train 

for a SNR = 10 dB .D- 53 

xix 
D-42b Simulated Normal Channel Integrated Target Return Pulse Train 

for a SNR = 10 dB . . . . . . . . . . D-53 

D-43a Simulated Normal Channel Unintegrated Target Return Pulse Train 

for a SNR = 15 dB . . . . . . . .D-54 

D-43b Simulated Normal Channel Integrated Target Return Pulse Train 

for a SNR = 15 dB . . . . . . . . D-5 4 

D-44a Simulated MTI Channel (Mode and 2 CASC) Unintegrated Target 

Return Pulse Train for a SNR = 3 dB . . . . . . . . . . . D-55 

D-44b Simulated MTI Channel (Mode 1 and 2 CASC) Integrated Target 

Return Pulse Train for a SNR = 3 dB . . . . . . .D-55 

D-45a Simulated MTI Channel (Mode 1 and 2 CASC) Unintegrated Target 

Return Pulse for a SNR = 10 dB . . . . . .D-56 

D- 45b Simulated MTI Channel (Mode 1 and 2 CASC) Integrated Target 

Return Pulse Train for a SNR = 10 dB. . . . .D-56 

D-46a Simulated MTI Channel (Mode 1 and 2 CASC) Unintegrated Target 

Return Pulse Train for a SNR = 20 dB. . . . . . . . . . . . . . D-57 

D-46b Simulated MTI Channel (Mode 1 and 2 CASC) Integrated Target 

Return Pulse Train for a SNR = 20 dB. . . . . . . . .. D-57 

D- 47a Simulated Normal Channel Unintegrated Radar Output with 

Interference. . . . . . . . . . . . . . . . . . .... D-59 

D- 47b Simulated Normal Channel Integrated Radar Output with 

Interference . . . . . . . . . . . . . . D-59 

D-48a Simulated MTI Channel (mode & 2 CASC) Unintegrated Radar 

Output with Interference . . . . .D-61 

D- 48b Simulated MTI Channel (mode & 2 CASC) Integrated Radar Output 

with Interference . . . . .D-61 

E-1 Block Diagram of Simulated ASR- 7 Processor Unj t. .E-2 

E- 2 Clock Timing and Desired Signal Characteristics for ASR-7 Radar .. E- 3 

E-3 ASR- 5 Interfering Signal Characteristics .E-7 

E- 4 ASR- 8 Interfering Signal Characteristics .E-7 

E- 5 AN/FPS- 90 Interfering Signal Characteristics . .E- 7 

XX 
E-6 Probability Density Function for Noise Only and for Signal-PlusNoise at the Normal Channel Envelope Detector Output .E-9 

E-7 ASR-7 (AN/GPN-12) Binary Integrator Block Diagram. . .E-10 

E-8 Probability Density function for Noise Only and for Signal-PlusNoise at the MTI Phase Detector Output . . . . . .E-13 

E-9 Canonical Form of Simulated ASR-7 MTI Canceller. .E-14 

E- 10 Feedback Integrator Block Diagram ... 

E- 11 Simulated PPI Display of Interference. 

F- 1 Modified Cumulative Distribution of Signal-Plus-Noise at ASR-7 

Radar MTI Channel Output for Various Signal-to- Noise Voltage 

.E-16 

.E-17 

Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F-6 

xxi 
L lSI OF T$BL ES 

TABLE ~ 

3-1 MTI Canceller Transfer Properties .. .3-59 

4-1 Time Intervals That Interfering Radar Pulses Overlap The 

Rank Quantizer Range Bin Sample Times For Various 

Combinations Of Interfering And Victim Radars ..... 4-17 

4-2 ARTS-IIIA/RDAS Probability Of False Target Hit When 

Connected To ASR-7 Radar That Is Receiving Interference 

From One Radar. . . . . . . . .......... 4-27 

4-3 ARTS-IIIA/RDAS Probability Of False Target Hit When 

Connected To ASR-7 Radar That Is Receiving Interference 

From One Radar. . . . . . . . .......... 4-28 

4-4 ARTS-IIIA/RDAS Probability Of False Target Hit When 

Connected To ASR-8 Radar That Is Receiving Interference 

From One Radar. . . . . . . . ......... . 4-29 

4-5 ARTS-IIIA/RDAS Probability Of False Target Hit When 

Connected To ASR-8 Radar That Is Receiving Interference 

From Three Radars Of The Same Type. . . . ..... 4-30 

4-6 ARTS-IIIA/RDAS Probability Of False Alarm For Typical 

Detection Parameters And Various Combinations Of 

Interfering And Victim Radars ............. 4-33 

4-7 Average Number Of Azimuth Change Pulse Since Initial Hit 

For A False Alarm To Occur ... ..... ...... 4-35 

4-8 ARTS-IIIA/RDAS Probability Of Target Hit When Connected To 

ASR-7 Radar That Is Receiving Interference From One 

Radar . . . . . . . . . . . . . . . . . . ....... 4-52 

4-9 ARTS-IIIA/RDAS Probabi lity Of Target Hit When Connected To 

ASR-7 Radar That Is Receiving Interference From Three 

Radars Of The Same Type . . . . . . . . . . . . . 4-53 

4-10 ARTS-IIIA/RDAS Probability Of Target Hit When Connected To 

ASR-8 Radar That Is Receiving Interference From One 

Radar. . . . . . . . . . . . . . . . . . . . . .. 4-54 

4-11 ARTS-IIIA/RDAS Probability Of Target Hit When Connected To 

ASR-8 Radar That Is Receiving Interference From Three 

Radars Of The Same Type . . . . . . . . . . . . . . . 4-55 

xxii 
4-12 ARTS-IIIA/RDAS Probability Of Target Detection For Typical 

Detection Parameters And Various Combinations Of 

Interfering And Victim Radars . . . ....... . 4-59 

4-13 ARTS-IIIA/RDAS Probability Of False Alarm When Connected 

To ASR-7 Radar (MTI Channel) That Is Receiving 

Interference From Three Radars Of The Same Type ..... 4-63 

4- 14 ARTS-IIIA/RDAS Probability Of False Alarm When Connected 

To ASR-8 Radar (MTI Channel) That Is Receiving 

Interference From Three Radars Of The Same Type ..... 4-64 

4-15 ARTS-IIIA/RDAS Probability Of Target Detection When 

Connected To ASR-7 Radar (MTI Channel) That Is 

Receiving Interference From Three Radars .... 4-65 

4-16 

4-17 

ARTS-IIIA/RDAS Probability Of Target Detection When 

Connected To ASR-8 Radar (MTI Channel) That Is 

Receiving Interference From Three Radars Of The 

Same Type ............ . 

ARTS-IIIA/RDAS Probability Of Clutter Hit When Connected 

To Victim Radr That Is Receiving Interference From 

Three Radars Of The Same Type . . . . . . . . . . . . . 

4-18 ARTS-IIIA/RDAS Probability Of Clutter Parameter 

Decrement And Increment Due To Interference Effect On 

.4-66 

.4-71 

Normal Channel Clutter Hits . . . . . . .4-74 

4-19 ARTS-IIIA/RDAS Probability Of MTI Hit Count Threshold 

And Sliding Window Isolated Hit Sum Change Due To 

Interference. . . . . . . . . 4-74 

C-1 MTI Canceller Transfer Properties . C-20 

C-2 Signal-To-Noise Improvement (In Decibels) Relative To 

Detection Of r2 + Q2 (Fluctuating Signal), Single 

Pulse . . . . . . .C-35 

D-1 Feedback Integrator Peak Signal - To-Noise Enhancement For 

Normal Channel . . . . . . . . . . . . . . . . .D-9 

D-2 Target Azimuth Shift Caused By Feedback Integration .D-19 

D-3 Probability Of Noise Causing The Integrator To Be In 

State Ej . . . . . . . . . . . . . . . .D-40 

D-4 Probability Of Noise Causing The Modified FAA Integrator 

To Be In State Ej . . . . . . . . . . . . ...... D-42 

x x i ii 
D-5 Probability Of Noise Causing The Integrator To Be In 

State E (Simulated) . . . . . . . . . D-4 3 

D-6 Probability Of Desired Signal Target Return Pulse Train 

Of 20 Pulses Causing The FAA Modified Integrator To Be 

In State E . . . . . . . . . D-48 

G- 1 ASR-5 System Characteristics .G-2 

G- 2 ASR-7 System Characteristics .G- 3 

G- 3 ASR- 8 System Characteristics .G-4 

G- 4 WSR- 57 System Characteristics .G- 5 

G-5 WSR-74S System Characteristics .G-6 

G- 6 AN / FPS- 6 System Parameters .G-7 

G-7 AN/GPN-20 System Charact eristics .G-8 

G- 8 AN/CPN-4 System Characteristics . . .G- 9 

G-9 AN/MPN-13 System Characteristics .G-10 

G-10 AN-TPN-24 System Characteristics .G- 11 

xxiv 
ABSTRACT 

The National Telecommunications and Information Administration (NTIA) in 

the Department of Commerce undertook a detailed program to investigate the 

signal processing properties of the primary radars in the 2.7 to 2.9 GHz 

band, and the Automated Radar Terminal System (ARTS- IliA) post processor 

planned for use by the Federal Aviation Administration on the Airport 

Surveillance Radars (ASRs). This investigation was the second investigation 

in a series of tasks undertaken by NTIA as part of a spectrum resource 

assessment of the 2 . 7 to 2.9 GHz band. The overall objective of the spectrum 

resource assessment was to assess the degree of congestion in the band in 

designated areas in the United States, and to promote more effective 

utilization of the band. 

The investigation into the signal processing properties of the primary 

radars and ARTS- IliA included the transfer properties of noise, desired 

signal, and asynchronous interference along with a detailed parametric 

analysis of the trade- offs to the desired signal performance in suppressing 

asynchronous interference . As a result of the investigation, it was 

concluded that all radars in the 2.7 to 2.9 GHz band have a very low duty 

cycle (less than 0.2%) thus permitting the use of signal processing 

techniques in the radars and post processors for suppression of interference 

to obtain more efficient utilization of the 2 . 7 to 2 . 9 GHz band. The use of 

integrators (enhancers) and other digital signal processing techniques along 

with the trend of displaying synthetic video on the Plan Position Indicator 

(PPI ) display provides the capability of suppressing asynchronous 

interference, while also permitting the enhancement of weak desired targets 

that are below the radar receiver system noise level. Also, with properly 

designed signal processing techniques, the trade-offs in suppressing the 

asynchronous inter ference (target azimuth shift, angular resolution, and 

desired signal sensititity) in low duty cycle radars are minimal. 

In summary, some spectrum conservation techniques can be used by the 

radiodetermination services in the 2.7 to 2.9 GHz band to obtain more 

efficient utilization of the spectrum. Also, the current hardware in the 

later model primary radars and the ARTS-IliA will suppress asynchronous 

interference with trade-offs to the desired signal performance. 

KEY WORDS 

Primary Radar 

ARTS-lilA 

Interference Suppression 

Signal Processing 

Simulation 

XXV 
SECTION 1 

INTRODUCTION 

BACKGROUND 

Dur ing the period of August 1971 through April 1973, the Interdepartment 

Radio Advisory Committee (IRAC) had under study the accommodation of 

Department of Defense (DoD), Federal Aviation Administration (FAA), and 

Department of Commerce (DoC) radar operations in the band 2.7- 2.9 GHz. A 

series of meeti ngs was held between the agencies (Summary Minutes of the 

Fi rst (October 1972) and Second (December 1972) OTP Meetings) to determine if 

new FAA air traffic cont r ol radars could be accommodated in this band without 

degrading their performance , and what impact these radars would have on the 

performance of existing radars in the band . An initial assessment of the 

problem (Maiuzzo , 1972) determined that the addition of new radars to the 

band could create a potential problem . To resolve the immediate problem of 

accommodating the new FAA Air Traffic Control Radars, the following actions 

were taken: 

a. The band 3.5- 3.7 GHz was reallocated by footnote to provide for 

co- equal primary Government use by both the Aeronautical Radionavi -

gation and Radiolocation Services. The footnote reads as follows : 

QllQ Government ground- based stations in the 

aeronautical radionavigation service may be authorized 

between 3.5-3 . 7 GHz where accommodation in the 2.7- 2.9 GHz 

band is not technically and/or economically feasible . 

Agencies were requested to cooperate to the maximum 

pr acticable to ensure on an area- by- area, case- by- case basis 

the band 2.7- 2 . 9 GHz is employed effectively. 

extent 

that 

b. The Spectrum Planning Subcommittee was tasked to develop a 

long- range plan for fixed radars with emphasis on the 2.7- 2.9 GHz 

and 3.5- 3.7 GHz bands. The SPS plan (SPS Ad Hoc Committee, 1974) 

was completed and approved by the IRAC. 

The Office of Telecommunicat~ons Policy (OTP) * subsequently tasked the 

Office of Telecommunications (OT) * to perform a spectrum resource assessment 

of the 2.7- 2.9 GHz band. The intent of this assessment was to provide a 

quantitative understanding of potential problems in the band of concern as 

well as to identify options available to spectrum managers for dealing with 

* OTP and OT have been reorganized into the National Telecommunications and 

Information Administration (NTIA) within the Department of Commerce. 

1-1 
these problems. One of the primary reasons for initiating the assessment was 

to ensure identification of problems during the early phases of design and 

planning rather than after-the-fact, i.e., after a system has been designed 

and hardware fabricated. By making these band assessments early, necessary 

actions can be taken to assure that appropriate communication channels are 

established between agencies whose systems are in potential conflict. This 

will enhance the early identification of solutions which are mutually 

satisfactory to all parties involved. 

A multiphase program to the solution of the 2 . 7-2.9 GHz Spectrum 

Resource Assessment task was undertaken by NTIA. 

Phase I - The first phase involved the identification of systems existing 

in and planned for the band in question, determination of available techn·ical 

and operational data for each system, identification of the potential 

interactions between systems, and the generation of a plan that leads to an 

overall assessment of the band•s potential congestion. A Phase I report 

(Hinkle and Mayher, 1975) for the 2.7-2.9 GHz Spectrum Resource Assessment 

was completed. 

Phase II - The second phase encompasses several tasks: 

1. A detailed measurement and model validation program in the Los 

Angel es and S.an Francisc.o .areas. The objective of this task .was to 

validate models and procedures used to predict .radar- to- radar 

interference, and assess the capability of predicting band 

congestion . This task was completed and the findings are given in 

a report by Hinkle, Pratt, and Matheson (1976). 

2. Investigation of the signal processing properties of primary 

radars in the 2 . 7-2 . 9 GHz band and the Automated Radar Terminal 

System (ARTS-IliA) to assess the capability of the radars to 

suppress asynchronous interference and the trade-offs in 

suppressing asynchronous signals. 

3. Investigation of the potential band congestion and band 

efficiency in eight designated congested areas (New York, 

Philadelphia, Atlanta, Miami, Chicago, Dallas, Los Angeles, and San 

Francisco) based on the technical findings of Tasks 1 and 2. 

4. Development of engineering and management aids to assist the 

frequency manager in determining if new radars can be accommodated 

in the 2.7 - 2.9 GHz band, and a methodology for assessing how 

efficiently the band is being utilized. 

This report is the second Phase II report in a series of reports related 

to the Spectrum Resource Assessment of the 2.7-2.9 GHz band. The nature of 

the 2.7-2 . 9 GHz spectrum resource problem requires a rigorou~·. analytical, and 

measurement investigation into the signal processing properties of the radars 

presently in and planned for the 2.7- 2.9 GHz band as well as the ARTS-IliA 

1-2 
post processor used in the FAA Terminal radars. This report contains the 

investigation of the signal processing properties of the radars and post 

processors to noise, desired signal, and interfering signals to access the 

capability of the equipment to suppress asynchronous signals and the 

trade-offs to the desired signal in suppressing asynchronous signals. This 

investigation was necessary to assure that the investigation of potential 

band congestion will be based on sound technical procedures. 

OBJECTIVE 

In order to promote effective use of the band, it is necessary to 

determine the electromagnetic compatibility of present and future radars 

planned for deployment in the 2.7-2.9 GHz band. The second task of the Phase 

II program encompassed a detailed investigation into the signal processing 

properties of the primary radars and ARTS-IliA post processor. The 

objectives of this extensive signal processing investigation were to: 

1. Determine the signal processing properties of radars presently 

operating or planned for the 2.7-2.9 GHz band and the terminal 

radar ARTS-IliA Radar Data Acquisition System (RDAS). 

2. Investigate the trade-offs to desired signal detection in 

suppressing asynchronous interfering signals, and determine methods 

to minimize these trade-offs: 

3. Determine methods of obtaining more efficient utilization of 

the band by using interference suppression techniques. 

APPROACH 

In order to accomplish the objectives related to the radar signal 

processing task, the following approach was taken: 

1. Conduct a preliminary investigation to determine the radar 

nomenclatures presentl~ operating in the band, and the new radars 

and post processors planned to be used. in the oand. 

2. Perform a cursory investigation into the operating modes (i.e., 

normal, log-normal, Moving Target Indicator (MTI), weather 

background, etc.), types of circuitry and processing techniques 

(analog or digital) used by radars in the band to determine the 

representative radars to be analyzed in detail. 

3. Perform a detailed signal processing investigation of the 

transfer properties of the representative radars to noise, desired 

signal, and interfering signals using analytical techniques, 

measurements, and simulation. 

1-3 
SECTION 2 

CONCLUSIONS AND RECOMMENDATIONS 

GENERAk 

The following is a summary of the conclusions and recommendations as a 

result of a detailed investigation into the signal processing properties of the 

primary radars in the 2 . 7 to 2.9 GHz band, and the Automated Radar Terminal 

System (ARTS- IliA) post processor planned for use by the Federal Aviation 

Administration (FAA) on the Airport Surveillance Radars (ASRs). The 

investigation included the signal processing properties of the primary radars 

and the ARTS-IliA to noise, desired signal, and asynchronous interference along 

with a detailed parametric analysis of the trade-offs to the desired signal in 

suppressing asynchronous interference. 

The signal processing of the primary radars was based primarily on the 

ASR- 7 (AN/GPN-12) and ASR- 8 radars which are late model digital processing type 

radars. However, the analysis is in general applicable to the older analog 

processing type radars in the 2.7 to 2.9 GHz band. The signal processing 

properties of the primary radars are discussed in Section 3 and Appendices A, 

B, C, D and E. 

The signal processing investigation of the ARTS-IliA included only the 

Radar Data Acquisition Subsystem (RDAS) since it is the portion of the 

ARTS- IliA which processes the 2.7 to 2.9 GHz radar signals. The signal 

processing properties of the ARTS-IliA are discussed in Section 4 and Appendix 

F. 

GENERAL CONCkUSIONS 

The following is a summary of general conclusions ~ as a result of the 

signal processing investigation: 

1. Radar signal processing techniques can be used to obtain more 

efficient spectrum utilization. These techniques may include 

the elimination of processing in the range-azimuth bin containing 

interference, the use of integration techniques, or variable 

thresholding techniques. With properly designed signal processing 

techniques, the suppression of asynchronous interference in low 

duty cycle radars will have minimal effects on target azimuth 

shift, angular resolution, and desired signal sensitivity. 

2 . Since a complete redesign of existing hardware would be required 

to obtain the full advantage of signal processing techniques for 

interference elimination, emphasis must be placed upon design 

standards for new equipment. 

3. The cost of realignment or retrofit of existing systems to 

2-1 
eliminate interference must be weighed against 

created by interference and the cost of other 

reduction techniques such as waveguide filtering. 

the problems 

interference 

PRIMARY RAQAR CONCLUSIONS 

The following conclusions on the sign·al 

primary radars in the 2.7 to 2.9 GHz ~nd 

measurements, analytical analysis, and simula~ion: 

processing properties of the 

are based on a combination of 

1. The investigation showed that the ASR-7 binary integrator and 

ASR-8 feedback integrators can suppress asynchronous interference 

in the Normal, Moving Target In~icato r (MTI), and log-FTC 

channels with minimal trade-offs in ~arget azimuth shift, angular 

resolution, and desired signal sensitivity. 

2 . The desired signal trade-offs in suppressing asynchronous 

interference are less for the FAA modified binary integrator than 

for the feedback integrator. 

3. In theory the feedback integrators 

(ASR-4, 5, 6, etc.) should also be 

asynchronous interference. 

in the 

capable 

analog radars 

of suppressing 

4. The primary radar MTI canceller circuitry produces several 

synchronous interfering pulses for each interfering asynchronous 

pulse. Therefore, asynchronous interference in the MTI channel 

has the potential to be enhanced by the feedback or binary 

integrator. Thus, if the integrator (enhancer) is not adjusted 

properly, the level of interference can be greater with the 

integrator on than with it off. 

5. When operating in the log-FTC mode with weather background 

displayed, interference could potentially be displayed on the 

PPI since the weather background channel does not have an 

integrator (enhancer). Since only the master channel of the 

frequency diversity radars provides the weather background video, 

proper choice of the master channel may eliminate the potential 

interference. 

ARTS-IliA POST PROCESSING CONCLUSIONS 

The following conclusions are based on a combination of analytical 

analysis and simulation. Wor~t-case interference and desired signal level 

assumptions were made, and consequently, the conclusions may be slightly 

pessimistic in regard to the impact of interference. The investigation 

considered the int erference effect on a per antenna rotation basis (as opposed 

to multiple antenna rotation tracking ability) with the ARTS-IliA interfaced 

with an ASR-7 or ASR-8 radar. A parametric range of interfering pulse widths 

2-2 
between 0 . 5 ~sec and 4.0 ~sec were considered in the investigation. 

Conclusions 1 through 7 are based on the Radar Data Acquisition Subsystem 

(RDAS) detection parameter combinations that FAA National Aviation Facility 

Ex peri mental Center ( NAFEC) recommended for ope rat i ona1 use (rank quanti zer 

threshold 23, hit count threshold 9, miss count threshold 3). 

1. For interference levels in currently congested U.S. terminal 

areas, the reduction in the probability of a target being 

detected in one antenna rotation would typically be less than 2.5 

percent. A congested area interference level is considered to 

consist of one radar interfering at a given time and interference 

coupling over 50 percent of the victim radar antenna rotation . 

2. If the level of congestion increases in the future to the point 

where a victim radar receives interference from three radars 

simultaneously over its entire antenna rotation, the probability 

of detection would be significantly decreased. The analysis 

indicated that for a worst-case combination of interfering and 

victim radars, the probability of target detection could be 

decreased by as much a~7 15 percent,_7 and the false alarm 

probability from 4.6 x 10 to 11.7 x 10 . 

3. Interference has a greater impact on the probability of 

detection and false alarm when the ARTS-IliA is connected to the 

radar MTI channel than when connected to the normal channel 

because the MTI circuits generate several synchronous 

interfering pulses for each asynchr~nous interference pulse at 

its input. For example, the wor~e-case (three continually 

interfering radars), reduction in probability of detection for 

the MTI channel was 15 percent while that for the normal channel 

was 5 percent . 

4. In general, the impact of interference oo the probability of 

target detection depends on the victim radar's range bin 

characteristics (width, hold, and sample time), and the 

interfering radar pulse width and PRF. For the case in which 

the interfering pulse width is less than the sum of the victim 

radar range bin width and hold time, the level of interference 

increases as a function of the interfering radar duty cycle. 

For the case in which the interfering pulse width is greater 

than the sum of the victim radar range bin width and hold time, 

the impact of interference is independent of the interfering 

radar pulse width and increases only with interfering radar PRF . 

5. Asynchronous pulse interference will not significantly affect 

the RDAS automatic video select (Normal or MTI channel) control 

function. The probability of an incorrect video channel select 

decision due to worst-case continual interference from three 

radars was found to be much less than 0.002. 

2-3 
6. Asynchronous pulse interference will not significantly affect 

the RDAS's automatic MTI hit count threshold control. The 

probability of an MTI hit count threshold change due to 

worst~~ase continual interference from three radars was found to 

be insignificant. 

1. A rank quantizer threshold of 23 gives superior desired 

signal detector performance and interference suppression performance over a rank quantizer threshold of 24. For a rank quantizer 

threshold setting of 23, the analysis indicated the optimum 

hit/miss count threshold which gives the maximum desired signal 

detection probabilities with or without interference is (9,4). 

GENERAL RECOHMENDATIONS 

1. An Ad Hoc committee consisting of Government agencies using 

radiodetermination services should be established to determine 

what standards should be adopted in regard to radar interference 

suppression techniques and the trade-offs in their utilization. 

The committee findings should then be incorporated in the 

technical standards of the NTIA Manual of Regulations and 

Procedures for Radio Frequency Management, and implemented at 

the systems review level and frequency assignment review level. 

2. All new radar systems and post processing systems include during 

the conceptual design stage of development, a performance evaluation in the presence of asynchronous interference , in addition to 

clutter and noise, in all designed modes of operation. 

3. All technical manuals used in the field on radars and post 

processors include instructions on how to suppress asynchronous 

interference while minimizing the trade-offs oi the desired 

signal performance. 

PRIMARY RADAR RECOHMENDAIIONS 

1. In order to ensure that an investigation into the accommodation 

of future planned radar systems in the 2.7 to 2.9 GHz band is 

based on sound technical procedures, a measurement program should 

be undertaken to: 

a. Investigate the operational capability of the feedback 

and binary integrators ( enhancers) to suppress 

asynchronous interference. 

b. Accurately determine the frequency/ distance separation 

requirements necessary for the new radars using 

filtered magnetrons, klystrons, or Traveling Wave Tube 

(TWT) transmitter output devices. 

2-4 
2. The accommodation of projected future radar deployments in 

corgested areas should then be investigated using the 

measurement results and findings in this report. 

3. In congested areas consideration should be given to equipping 

ASR-8 radars with the FAA modified binary integrator used in the 

ASR-7 radars. The binary integrator provides superior performance 

over the feedback integrator in minimizing the desired signal 

trade-offs while suppressing asynchronous interference. 

ARTS-IliA POST PROCESSING RECOMMENDATIONS 

1. Since a rank quantizer threshold setting of 23 provides 

significantly more interference suppression than a threshold 

setting of 24 without sacrificing over-all radar performance, 

it is recommended that a rank quantizer threshold setting 

of 23 be employed on operational ARTS-II!As. NAFEC has also 

recommended a rank quantizer threshold of 23 based on measurements on desired s1gnal performance. 

2. Measurements should be performed on the ARTS-lilA in 

congested u.s. areas to determine the particular hit/miss count 

threshold setting combinations that provide an optimum trade- off 

between target detection and interference suppression . 

2- 5 
SECTION 3 

PRIMARY RADAR SIGNAL PROCESSING 

INTRODUCTION 

This section discusses the signal processing properties of radar 

receivers in the 2.7 to 2.9 GHz band. 'A detailed discussion of the receiver 

signal processing properties to noise, desired signal, and asychronous 

interfering signals is given. Because of the types of services 

(aeronautical, radionavigation, meteorological, and radiolocation) provided by 

radars in the 2.7 to 2.9 GHz band, and number of nomenclatur~s, it was 

necessary to limit the signal processing investigation to the ASR-7 and ASR-8 

radars which are FAA radars used for aeronautical radionavigation. 

The ASR- 7 and ASR-8 are later 

processing after signal detection. 

selecting several modes of operation 

information. 

Normal Channel: 

Normal Video 

Enhanced Normal Video 

Normal Log-FTC Video 

Enhanced Normal Log-FTC Video 

model 

Both 

for 

radars 

radars 

display 

Normal LOG-FTC with Weather Background Video 

which use digital signal 

have the capability of 

of the received video 

Enhanced Normal LOG-FTC with Weather Background Video 

MTI Channel: 

MTI Video 

Enhanced MTI Video 

MTI Log-FTC Video 

Enhanced MTI Log-FTC Video 

MTI Log-FTC with Weather Background Video 

Enhanced MTI Log-FTC with Weather Background Video 

The weather background channel of the ASR-7 and ASR-8 ie very similar to the 

circuitry of the meteorological radars (WSR-57 and WSR-74S) in the 2.7 to 2.9 

GHz band. Therefore, an investigation of the ASR-7 and ASR-8 radar signal 

processing characteristics is also applicable to the meteorological radars in 

the band. Also both the normal and MTI channels of the ASR-7 and ASR-8 are 

very similar to the radiolocation height finding radar in the 2.7 to 2.9 GHz 

band. Therefore, an analysis of the ASR-7 and ASR-8 radars is generall¥ 

applicable to all radars in the 2.7 to 2.9 GHz band. Also since the trend in 

new radar systems is toward digital signal processing, the analysis of the 

ASR-7 and ASR-8 radars will be more applicable to other new radar systems 

3- l 
coming in the band. 

GENERAL SYSTEM DESCRIPTION 

Radar system characteristics of major aeronautical radionavigation, 

meteorological , and radiolocation radars in the 2.7 to 2 . 9 GHz band is given 

in Appendix G. As stated previously, this section will only investigate the 

signal processing properties of the ASR- 7 and ASR-8. However, the analysis 

is applicable . to other aeronautical radionavigation,. meteorological, and 

radiolocation radars in the 2.7 to 2.9 GH~ ~and as well as radars in other 

bands. 

In gene~al, ~ll radar ~eceivers in the 2.7 to 2.9 GHz band can be divided 

into three sections: antenna and RF waveguide, receiver unit, and processor 

unit. Figure 3-1 shows a typical radar sy~tem block diagram of a radar which 

only operates one channel at a time (non-diversity mode). Figure 3-2 shows a 

typical radar system block diagram of a radar which has frequency diversity 

capability (simultaneou3 dual channel operation) . Radars operating in the 

frequency diversity mode use one of the channels as a master channel for 

timing information to the slave channel. The two reflected signals from a 

target are separated in the diplexer and applied to the t wo receivers . Each 

signal is processed in its receiver and the t wo signals are realigned in time 

and additively combined in the video processor unit of the master channel 

before being displayed . The following is a general description of antenna 

and RF waveguide, receiver unit, and processor units of radars in the 2.7 to 

2 . 9 GHz band. 

Antenna and RF Waveguide 

Several different types .of antennas are used by radars in the 2.7 to 2.9 

GHz band. All the aeronautical radionavigation radars use a shaped beam 

reflector which produces a cosecant- squared elevation pattern. The antenna 

gain of the aeronautical radionavigation radars range between 31 and 34 dBi. 

The meteorological radars have parabolic dish antennas with a gain of 32 to 

38 dBi. The type of radiolocation radar antennas is varied with antenna 

gains between 32 and 39 dBi. Some of the later model radars have antennas 

with several horns. 

The RF waveguide system generally consists of rotary-joint, several 

couplers, waveguide switche3, circulators, and Transmit-Receiver (TR) 

limiters. Radars with frequency diversity capability also have RF diplexers. 

In general, the RF waveguide characteristics of all radars in the 2 . 7 to 2 . 9 

GHz band are similar, and therefore, the ·signal processing properties can be 

generalized. 

Receiver Unit 

The radar receiver ·unit includes all the analog circuitry between the 

receiver RF input and the detector output of the normal, MTI, and log normal 

radar channels. The receiver unit generally includes a parametric amplifier, 

3- 2 
w 

I 

w 

FROM 

ANTENNA 

r--------------------, 

I CHANNEL "A" I 

I . MTI I 

I l viDEO 

I ' NORMAL VIDEO I OUTPUT* RECEIVER VIDEO PPI j r oRM . LOG VIDEO PROCESSOR ; 

I I .1 I 

WAVEGUIDE 

SWITCH 

L _____________________ __j 

*Only one channel 

operates at a time 

..-.-------------------. 

I I 

I I I MTI - I VIDEO l ' NORMAL VIDEO 1 OUTPUT 

! RECEIVER VIDEO I ' NORM. LOG VID~~ PROCESSOR ; 

I I I 

I CHANNEL "B" l ____________________ _.J 

PPI 

Figure 3- 1. Block Diagram of Non-Diversity Radar Receivers 
w 

I 

I:-

FROM 

~TENNA 

r - -- -------------------~ 

CHANNEL "A" (MASTER) 

!~ MTI I I VIDEO I MTI Q - I OUTPUT . I - VIDEO a 

I RECEIVER NORMAL VIDEO PROCESSOR PPI 

I NORM. LOG VIDE_O 

I 

I .. I~ 

~---. r----------·-·--

HIGH POWI:R LOW POWER 30 MHZ SYNC ( f-) s IP~XER ~ DIPLEXER COHO CONTROL ~ c 

TIMING v 

M 

r----- ---.-,------.-... ----· I 

(PASSIVE I 

CHANNEL) I lflT I 

I MT I Q - VIDEO RECEIVER 

! NORMAL VIDEO PROCESSOR ' 

NORM . LOG VIDF.J:L 

I ' 

I 

L ------ :::__ ~_J_S~~) ____ j 

Figure 3-2 . Block Diagram of Fre quency Di versity Radar Receivers 
mixer, IF amplifier, and detectors. The newer radars have solid-state 

receiver units with the older radars being tube-type. The signal processing 

properties of the solid-state and tube-type radar receiver units are 

essentially the same. Since the ASR-7 and ASR-8 have normal, MTI, and log 

normal channels, the signal processing properties of the ASR-7 and ASR-8 

receiver units are generally applicable to all radars in the band. 

Processor Unit 

The radar processor unit includes all the circuitry between the detector 

outputs and the display unit. The processor unit generally includes the MTI 

cancellers, integrator (enhancer), Log Fast-Time-Constant (Log-fTC), and 

weather background circuitry. The newer radars have digital processor units 

where the detector output is A/D (analog-to-digital) converted, the signal 

processing done, and then D/A (digital-to-analog) converted for display. The 

older radars have analog processor units. The transfer properties of the 

analog and digital processor units can be treated identically with the 

exception of the quantization noise due to A/D conversion and roundoff and 

truncation inherent in digital processing. Therefore, the signal processing 

properties of the ASR-7 and ASR-8 (digital processor units) is generally 

applicable to all radars in the 2.7 to 2.9 GHz band. 

ANTENNA AND Rf WAVEGUIDE SiST~ 

The following is a discussion of the signal processing properties of the 

antenna and RF waveguide system of typical radars in the 2.7 to 2.9 GHz band. 

The discussion includes the hardware from the antenna feed horn output to the 

receiver unit input. The analysis does not include antenna gain, antenna 

patterns, or polarization discrimination. The antenna types and antenna 

gains of radars in the 2.7 to 2.9 GHz band are given in Appendix G. Antenna 

pattern measurement of several radars in the band are contained in a report 

by Hinkle, Pratt, and Matheson (1976). 

Several of the new radars in the band (ASR-8, AN/GPN-20, and AN/TPN-24) 

have multiple feedhorn antennas and diplexers in the waveguide to permit 

frequency diversity operation. These new radars have the more complex RF 

waveguide systems, and have all the waveguide components as the single-horn 

non-frequency diversity radars. Therefore, the ASR-o RF waveguide system, 

wnich has a normal and passive channel, and frequency diversity capability, 

was selected as being representative of radars in the 2.7 to 2.9 GHz band. 

Figure 3-3 shows a block diagram of the ASR-8 Rf waveguide system. The 

passive channel is used to receive reflected target energy during the first 

part of the receive period and consists of a rotary-joint, low-power 

diplexer, TR tube, and --waveguide couplers. The normal channel is used to 

transmit pulses and receive reflected target energy during the remainder of 

the receive period and consists of a rotary-joint, high-power diplexer, 

high-power waveguide switch, circulator, and waveguide couplers. Interfering 

signal power loss in the RF system may occur from insertion loss and, 

attenuation from the diplexer filter due to frequency separation between the 

3- 5 
TRANSMITTER DUMMY 

CHANNEL A LOAD Jl 

I ' I 

LOW PASS SIGNAL 

FILTER -- CIRCULATOR - COUPLER 

' RECEIVER 

CHANNEL A 

' TR LOW POWER 

LIMITER TERMINATION 

t 

SIGNAL 

Jl- COUPLER 

f 

LOW POWER 

DIPLEXER 

J 

SIGNAL 

Jl- COUPLER 

l 

TR LOW POWER 

LIMITER TERMINATION 

' TRANSMITTER RECEIVER 

CHANNEL B CHANNEL B 

' t 

LOW PASS f-.- SIGNAL 

FILTER CIRCULATOR - COUPLER 

1 I 

DUMMY Jl 

LOAD 

-

~ 

1--

-

I 

TWO PORT 

COUPLER 

~ 

WAVEGUIDE ....... SWITCH 

" 

HIGH POWER 

DIPLEXER -

INCIDENT PO WER Jl 

REFLECTED PO WER J2 

HIGH POWER 

DUMMY LOAD 

I I 

TWO PORT 

COUPLER - TO 

ANTENNA 

(PASSIVE CHANNEL) TO ANTEt-<'"NA 

- WAVEGUIDE f---.- HIGH POWER 

SWITCH DUMMY LOAD 

TWO PORT 

COUPLER 

l 

J2 REFLECTED POWER 

Jl INCIDENT P OWER 

Figure 3- 3. ASR- 8 RF System Simplified Block Diagram 

3-6 
• l 

l 

, 

interfering signal and victim receiver channel tuned frequency . The 

insertion loss is approximately 2 dB for both the passive and normal channel. 

Since the low- and high- power diplexer filter bandwidth is much wider than 

the interference spectrum bandwidth of radars in the 2.7 to 2.9 GHz band, the ' 

interfering signal peak power loss for a symetrical emission is given by: 

where : 

PriN = 

2 

PriN (BdTi) F6F 

4 

Interfering signal peak power level at diplexer input, in 

watts 

Interferi ng signal peak power level at qiplexer output, in 

watts 

f = Frequency separation between interferer carrier and victim 

receiver tuned frequency, in MHz 

Bd = Diplexer 3 dB bandwidth, in MHz 

Ti = Interferer transmitter pulse width, in sec 

F = Interfering signal emission spectrum level at r relative 

to level at carrier, in dB 

(3-1) 

Figure 3- 4 shows the selectivity of the ARS- 8 diplexer. The frequency 

selectivity characteristics of diplexer of radars in the 2.7 to 2.9 GHz band 

varies depending on the radar nomenclature. However, the peak power loss of 

an interfering signal due to frequency separation is essentially determined 

by the victim receiver IF selectivity characteristics since the IF bandwidth 

is much smaller than the RF waveguide diplexer bandwidth. 

RECEIVER UNIT 

The following is a discussion of the signal processing properties of the 

receiver unit of the ASR-7 and ASR-8 radars. All the radars in the 2 . 7 to 

2 . 9 GHz band have a receiver unit very similar to either the normal, log 

normal, or Moving Target Indicator (MTI) channel of the ASR-7 or ASR-8. Also 

the signal processing properties of the older tube-type receiver unit radars 

3-7 
0 r ' I 

Ill 

"0 

z -20 

H 

li:l 

U} 

z 

0 

0.. -30 

w U} 

00 

I ~ 

~ 

> 

H 

E-t 

o<:l; -40 ~ 

~ 

- 50 

I 

I 

-· \ 

I \ 

I \ I 

, 

I ~ 

v ' \ 

-10 - 60 

-80 - 60 -40 

- 20 0 20 10 60 80 6F IN 1-1Hz 

Figure 3-4 . ASR- 8 Diplexer Filter Characteristics 
and the newer solid-state receiver unit radars can be treated identical~y. 

In those cases where the ASR-7 or ASR-8 circuitry is significantly different 

from the other radars in the band, a discussion of the signal processing 

properties of other types of circuitry will be given. 

Figure 3-5 shows a block diagram of the receiver unit of the ASR- 8 radar. 

The radar receiver unit accepts either normal channel or passive channel 

S-band radar signals from the antenna and waveguide subsystems and provides 

either normal video, log- normal video, or MTI video to the processor unit. 

Receiver Front End 

Normal channel RF ener gy entering the rec~iver is first applied to the 

TR- limiter through the waveguide system. The TR-limiter is a passive device. 

Two diode limiters are used within the TR- limiter for reduction of spike 

leakage . Output from the TR-limiter is applied through a waveguide-to- coax 

adapter to the Sensitivity Time Control (STC) attenuator. The attenuator 

uses bias voltage- controlled RF attenuation of PIN diodes to provide a 

continuously variable 40 dB range of attenuation at frequencies of 2.7 to 2.9 

GHz. STC control voltages are provided to the attenuator from the processor 

unit. Using control voltages in steps 0 and +10 volts the attenuation 

provides linear attenuation throughout the input frequency band. Insertion 

loss is less than 0 . 6 dB at zero control voltage. Bias voltages of +15 and 

- 15 Vdc are supplied to the attenuator from the respective power supplies 

located in the module rack. RF energy from the STC attenuator is sent to the 

antenna pattern switch. The antenna pattern switch is a solid-state device 

using PIN diodes to switch RF from the normal beam to the passive beam. 

Switch control logic signals from the processor unit are converted to normal 

and passive drive signals in the switch driver assembly. The switch drive 

signals are used by the antenna pattern switch to perform the switching . 

Either normal or passive beam RF energy is coupled out to the parametric 

amplifier. 

TR Limiter 

The TR limiter protects the receiver from high level RF energy during the 

trans~itter pulse . Lower level energy whi ch might not have sufficient 

amplitude to ionize the TR tube directly is reflected by the limiter portion 

of the assembly. The effect of the TR limiter on an interfering signal would 

be to attenuate the interfering signal if it coincided with the transmitted 

"on" period. During the receive period the TR limiter has approxima tely a 

0.3 dB insertion loss. 

Sensitivity Time Control (STC) Attenuators 

High levels of reflected energy from ground clutter will saturate the 

receiver if not reduced in level before entering the parametric amplifier and 

the following receiver elements. The STC attenuators reduce this clutter as 

required at any particular site . The attenuators are controlled by signals 

from the processor unit. Two separate but identical function generators in 

3-9 
w 

I 

t-' 

0 

r-----------------------------------------:-

I tWR!-lAL ASR-8 RECEIVER UNIT I Clol\NNEL - l wruT 

TR STC LI~ITER ~ ATTF:NUATOR 

JNORN!\L Gl\I I CONT . 

I • I 

I S\H'l ('II S\VITCH 1\NlT~i:--!A 

- PARJ\METRIC lr RJ:S CLF.CTOR 

:CONTROL. DRIVER PATTER~ AHPLIFlL" - FILTER 

S\VITC!l 

.\f.SIVE Gl\T:~ T. 

l I 

IPt.SSIVC STC 

I SOL!, TOR - 1\TTENUl\TOR l Clll\!'~ i:L - INPUT NOR"l.AL N0RH.li..L --J ~ IF 

N1PLIFIER VIDEO I 

- I 

I 

I r- PRE- LOG .. ?I!ASE l't!XER ~ AMPLIFIER .... --.J LOG IF 

SHIFTER AMPLIFI ER VIDEO I 

t-- I 

I 

I 

l'ITI I J !.._. MTI 

STALO COHO MODULE f.lTI Q ~J - I 

L-----------------------------------------------_1 

Figure 3-5. ASR-8 Receiver Unit Block Diagram 
the processor are provided, one for the normal antenna beam and one for the 

passive antenna beam. Board- mounted switches permit selection of the initial 

attenuation (up to 40 dB), delay of initiation of the STC curve after the 

transmitter pulse up to 100 microseconds, and selection of the STC curve 

exponent from 1/R to 1/Rs. Receiver sensitivity control, using the RF 

attenuator, is digitally added to the STC function. Five values of preset 

receiver sensitivity can be selected by the radar control panel; the 

individual levels are preset using board - mounted switches. A 

digital-to- analog converter changes the composite digital STC and sensitivity 

control signal to an analog voltage to control the RF attenuator. Figure 3-6 

shows the STC characteristics of the ASR- 8. 

The STC function in some radars in the 2.7 to 2.9 GHz band is achieved by 

varying the IF amplifier gain as a function of time. However, the affect of 

STC circuitry on a desired or interfering signal is the same. That is, the 

STC attenuators will attenuate the signal level as a function of the radar 

receiver period in which the pulse arrives, generally eliminating low level 

interference in the center of the PPI scope. 

Antenna Pattern Switch 

The antenna pattern switch accepts signal drive current from the switch 

driver and connects the receiver to either the normal or passive channels. 

The switch uses fast- acting PIN diodes which allow channel switching to occur 

within 100 ns. The antenna pattern switch will reduce tne interfering signal 

power level when the interference is coupled in through the passive horn 

which has a higher tilt antle than the normal horn . The reduction in 

interfering signal power can be determined from the mainbeam antenna 

elevation patterns of the passive and normal horns. The affect of the 

antenna pattern switch in the interference is that from mainbeam antenna 

coupling of the victim receiver, the level of interference will be reduced in 

the center of the PPI display. When the interference is coupled in through 

the backlobe of the victim radar, the switching betwee~ passive and normal 

horn will not have a significant effect on the median interfering signal 

level . 

Passive Channel 

Passive channel RF energy enters the 

externally- connected TR- limiter. The energy 

isolator to the STC attenuator. Operation of 

identical to the normal STC attenuator. 

Parametric Amplifier 

receiver unit from an 

passes through a two-port 

the passive STC attenuator is 

The antenna pattern switch feeds the signals from the passive and normal 

channel to the parametric amplifier. The parametric amplifier provides 

low- noise amplification of RF energy prior to down conversion. The amplifier 

covers the entire radar frequency range of 2.7 to 2 . 9 GHz, and has a m~nLmum 

gain of 15 dB. Noise figure of the parametric amplifier is 1.25 dB maximum. 

3-11 
L.J 

I 

f-' 

N 

z 

0 

H 

H 

~ 

::::> 

z 

J,.U 

H 

H 

< 

r:.... 

p:: 

INITIAL VALUE 

ADJ 

RF VALUE ADJ 

TIME CONTROL 

ADJ 

I \ \ ~0 dB MAX OUTPUT 

SLOPE ADJ 

(1/Rn) 

" ' , . 

'· ' ............ ________ ..................... ..........__,_--::::...... 

PRFTG TlME 

Figure 3-6 . STC Waveform Generation 
Saturation, the signal level at whi ch the gain decreases 1.0 dB, occurs at an 

input power level of -30 dBm. 

Since this investigation only covers interference from radars in the 2 . 7 

to 2 . 9 GHz band, the parametric amplifier will not provide any 

Frequency-Dependent-Rejection to radars in the 2.7 to 2.9 GHz band. For 

analytical reasons, the parametric amplifier is assumed to be a linear 

amplifier with 0 dB gain . This assumption of linearity and 0 dB gain allows 

signal and noise to be treated separately. 

Preselector Filter 

The preselector filter prevents external signals not in the receiver 

passband from interfering with receiver operation. The preselector filter is 

composed of four direct-coupled cavities and has a 10 MHz passband at any 

selected frequency between 2.7 and 2 .9 GHz. The filter has 60 dB rejection 

at frequencies 50 MHz from the center of its passband. Four micrometer 

tuners are used to set the filter to any desired frequency from 2.7 to 2 . 9 

GHz. The insertion loss of the filter is approximately 0.6 dB. The effect 

of the preselector filter on an interfering signal will be to attenuate those 

signals whi ch fall outside the receiver passband. Since the interfering 

signal peak power loss as a function of frequency separation ) is mainly 

determined by the IF filter selectivity , the analysis of interfering signal 

peak power loss as a function of interfering signal frequency separation will 

be discussed in the IF filter section. 

Phase Shifter 

The phase shifter is used to vary the electrical length of the line 

between the preselector filter and mixer . Some power from the incoming 

signal is converted to the image frequency in the mixing process. This power 

propagates out the mixer input port toward the preselector. It is reflected 

from the preselector back to the mixer. The phase shifter adjusts the phase 

of the reflected image so that the IF signal voltage resulting from it is in 

phase with the IF voltage from the signal frequency. Mixer conversion loss 

is improved in this manner. The insertion loss of the phase shifter is 

approximately 0 . 3 dB. The phase shifter will change the phase of the 

interfering signal . 

Mixer 

RF to IF signal conversion of received signals is accomplished by m~x~ng 

the stable local oscillator (STALO) output signal with the amplified RF 

return signal . Mixing takes place in the crossbar mixer wh ile the 

preselector filter and phase shifter are also employed to improve conversion 

efficiency. The echo signal at frequency w0 or an interfering signal at 

frequency ~W mixes in the mixer with the STALO signal ( W0 +S0 ) where S0 is 

equal to 30 MHz. The main signal component produced is the difference 

between the two inputs, which is the IF frequency S0 . In addition to the IF 

frequency, harmonics of the STALO frequency and harmonics of the sum of the 

3-13 
STALO and input signal frequencies are produced. 

The STALO provides a reference RF signal between 2 . 67 and 2.93 GHz for 

the receiver signal mixer to down or up convert received signals to the 30 

MHz IF. A three- cavity tunable bandpass filter selects the desired STALO 

frequency and attenuates the adjacent frequencies by 30 dB or greater 

applying the output to a RF network . The RF network is a two-stage S-band 

transistor amplifier which provides +11 dBm gain to the output. The noise 

30 MHz away from the carrier is suppressed to near thermal noise. This 

precludes the STALO signal in the receiver mixer from having appreciable 

noise or spurious products at the intermedia·te frequency. 

It is shown in Appendix A that the signal- to- noise ratio (SNR) and 

interference- to- noise ratio (INR) at the mixer output is the same as at the 

mixer input. Thus the signal transfer ~roperties of the mixer can be 

expressed as: 

SN~0 (3-3) 

Preamplifier 

The preamplifier model provides low noise amplification of the IF signal. 

Outputs from the preamplifier are coupled to the normal, log normal, and MTI 

radar channels. The bandwidth of the preamplifier is approximately 10 MHz, 

same as the preselector . Therefore the interfering signal time waveform at 

the pr eamplifier output will be similar to that at the preselector output (if 

saturation does not occur) with the exception of the frequency conversion 

produced by the mixer. As previously mentioned the effect of the preamplifer 

10 MHz bandwidth on an interfering signal will be to attenuate those signals 

which fall outside the receiver passband. Since the interfering signal peak 

power loss as a function of frequency separation (AF) is mainly determined by 

the IF filter selectivity, the analysis of interfering signal peak power loss 

as a function of interfering signal frequency separation will be discussed in 

the IF filter section . 

Normal Channel 

The normal channel IF subassembly accepts the 30 MHz IF signal from the 

preamplifier module and provides IF amplification, video detection, and video 

amplification. The normal channel video amplifier output is a low-noise 

high- gain video signal supplied to the processor unit. 

IF Amplifiers 

The normal channel IF amplifiers consist of four wide- band symetrical 

limiter amplifiers followed by five IF passband filter stages. The overall 

3-14 
bandwidth of the IF stages is 1.2 MHz. Appendix B contains a detailed 

analysis of the ASR-8 IF selectivity and sign~~ tra~sfer properties. 

The relative IF filter selectivity response AdB(F) is derived in Appendix 

B, Equation B-19, and can be expressed as: 

where : 

and: 

= 

-20 log (1 + x2)5/2 

Frequency relative to the receiver IF tuned frequency B0 , 

in Hz 

Bs = IF amplifier stage 3 dB bandwidth, in Hz 

(3-4) 

Since the normal channel IF amplifier stages have a narrower bandwidth and 

sharper selectivity characteristics than the preceding receiver unit stages, 

a desired signal or interfering time response at the IF amplifier output is 

essentially governed by the normal channel IF selectivity characteristics. 

For an interfering signal, the peak power and time waveform response at 

the IF filter output is determined by the receiver IF selectivity 

characteristics, interfering signal emission spectrum, and frequency 

separation between the interfering signal carrier and the victim receiver 

tuned frequency. In general, the receiver front emd prior to the receiver 

normal channel input can be modeled as a linear receiver with 0 dB gain 

allowing tbe IF input inter·ference-to-noise ratio, (INR)rF·, to be expressed 1 

as (Equation B-37a): 

INRrF i 

where: 

1 idBm = Interfering signal peak power level at the receiver input , 

in dBm 

Receiver noise level, in dBm 

(3-5) 

The amplitude distribution of the noise at the IF input and output is 

3-15 
Gaussian. The IF output interference-to-noise ratio, INRI F

0

can be expressed 

as (Equation B-38 ) : 

INRIF 

0 

where: 

FDR 

FOR = Receiver Frequency Dependent Rejection, in dB 

(3- 6) 

The Frequency-Dependent-Rejection (FOR) of the interfering signal is 

determined by Equation B-21 and is discussed in detail in Appendix B. 

The interfering signal IF output time waveform can be expressed as an 

amplitude and phase modulated pulse given bt: 

where: 

VIF (t ) 0 Bp (t' ') cos [·eo t + 4Jo + lj>(t' ) ) 

B = Interfering signal voltage amplitude 

p(t' ) = Interfering signal amplitude modulation after IF filtering, 

value between 0 and 1 

60 = Reaeiver tuned IF frequency, in radians per second 

~o = Interfering ~ignal carrier phase angle 

t' = t - t 0 where t 0 is the delay t ime of the IF filter 

4J( t') = Interfering signal phase modulation after IF filtering 

(3- 7) 

The interfering signal IF output time response is a func tion of the 

interfering si gnal pulse width (T ) , frequency separation between t he 

interfering signal carrier and the victim receiver tuned frequen cy (6F) , and 

the receiver IF bandwidth (BrF) · A detailed discussion of an interferi ng 

signal IF output time response as a function of these parameters is given in 

Appendix B. Figure 3- 7 summarizes typical IF output time waveforms for 

different TB 1 F products and 6F' s. 

Envelope Detector 

The envelope detectors used in the normal channel of radars in the 2.7 to 

2.9 GHz band generally consists of a full-wave detector followed by a low 

pass filter and a video amplifier. The IF signal level at the detector i nput 

3- 16 

.. 
w 

I 

....... 

-....1 

~ 

'T'BIF< I 

'T'B ~I IF 

'T'a1

F>>1 

ll f : 0 llf~BIF M>>BIF 

Figure 3-7 . Typical IF Output Time Waveform 

Responses for On- Tune and Off-Tune 

Pulses 

ONE 

POSSIBLE 

THRESHOLD 

LEVEL 
is generally large enough for operation in the linear portion of the diode 

detectors. However, for completeness both the signal-to- noise transfer 

properties of a linear and square law detectors are given. 

Figure 3- 8 shows the signal- to- noise (SNR) transfer characteristics of a 

linear detector (R. Gannaway, 1965). The signal- to- noise (SNR) transfer 

characteristics of the square- law detector are shown in Figure 3- 9, and are 

given by (R. Gannaway, 1965 and Davenport and Root, 1958 ) : 

2 

(SNR) i 

1 + 2 (SNR)i 

(3 - 8) 

For small input signal- to- noise ratios (SNR; <10 dB), the linear and 

square- law detectors have similar transfer pro~erties. For large input 

signal- to- noise ratios (SNR; >10), the linear detector performance is better 

than the square-law detector. However, the collapsing loss for a linear 

detector is much greater than the collapsing loss for a square-law det~ctor. 

Thus the difference between the linear and square-law detector performance in 

the required detector input 'signal-to- noise ratio is less than a dB (Trunk, 

1972). The collapsin~ loss is the additional signal required to maintain the 

same probability of deeecti~n (Pd) and probability of false alarm (Pf a ) when 

noise along with the desired signal- plus-noise are integrated. Figures 3-8 

and 3-9 can ,also be used for the interference- to-noise (I~R ) transfer 

properties of a linear and square-law envelope detector, respectively. : 

The noise amplitude distribution at the linear detector output is 

Rayleigh distributed. The signal- plus-noise probability density func tion 

(PDF ) at the envelope detector output for a non-fluctuating target (Marcum 

Case 0) has a RjcP. distribution (1954) given by: 

- (v 2+A2) 

2o2 

o2 

(3- 9) p ( v , A) v e 

wher ~: 

10 ( = Modified Bessel function of the first kind of order zero 

A = Peak signal amplitude, in volts 

o = rms noise level, in volts 

The normal channel er.velope 

to investigate trade- offs 

The simulation of the radar 

Figure 3-10 shows the Rice 

signal-to-noise ratio. 

detector output signal- plus-noise was simulated 

in suppressing asychronous interfering si gnals. 

normal channel is discussed in Appendix E. 

PDF given by Equation 3-9 as a function of the 

3-18 
~ 

w o:l I 

1-' "d 1.0 ~ 

E-< 

:::::> 

0 

p:: 

z 

(/) 

40 v 

20 

/ 

/ 

v 

v 

30 

10 

0 I 

v 

I 

v 

' -10 

-20 

-10 0 10 20 30 40 50 

SNRIN(dB) 

Figure 3-8 . Signal-To-Noise Ratio Transfer Properties 

of a Linear Detector 
~ 

Ill 

'd 

-8 

:::> w 

I rr.o N 

0 :z 

Ul 

40 

v 

20 

10 

0 

/ 

/ 

/ 

/ 

v 

/ 

v 

v 

I I I 

1/ 

I 

. I 

j 

30 

-10 

-20 

-10 0 10 20 30 40 50 

SNRIN (dB) 

Figure 3-9 . Signal-to-Noise Ratio Transfer Properties 

of a Square-Law Detector 
VJ 

I 

N 

I-' 

4; 

> 

~ 

~ 

.~----------~--------~----------~----------~----------~ .R-15 Nc?ise _Level (cr ) = 0. 2 5 Volts 

Noise Onr 

2. S/N = 5 dB 

S/N = 15 dB 

/ 

S/N = 20 dB 

/ I 

1 . II i \ A I \ I I 't I I \ I I 

0 • [ £ >, I 4 ,<>, ">z I >._ ,< I I > I 

0 . 

Figure 3-10 . 

1. 2 . 3. 4. 

VOLTS 

Probabi lity-Density Function for Noise Only 

and for Sign~l Plus Noise at the Norma l 

Channel Lnvclope Detector Output . 

5 . 
The envelope detector video output ~ low-pass filtered and amplified. 

For the normal channel the low-pass filter handwidth is usually matched to 

the receiver normal channel IF bandwidth. Therefore, there is no improvement 

in the signal-to-noise ratio between the input and output of the normal 

channel low-pass filter. The low-pass filter output is amplified and sent to 

the video processor unit. 

Log-Normal Channel 

The log-normal channel IF subassembly accepts the 30 MHz IF signal from 

the preamplifier module and provides log IF amplification, video detection, 

and video amplification. The function of the log amplifier is to normalize 

the variances in precipitation clutter. The circuits operate on the 

principle that precipitation clutter, after being passed through a 

logarithmic response, has a noise variation a~out the average value that is 

independent of the average value. Filter circuits subtract out the average, 

leaving only the constant residue level. This level is adjusted to be equal 

to the receiver noise, thus totally eliminating precipitation clutter from 

the display. In the radar normal channel, the log function is performed by 

the log IF subassembly in the receiver unit. The filtering and subtraction 

is performed by the normdl/LOG-FTC assembly ' in the processor unit. In 

general, the normal log IF channel amplifies IF signals logarithmically so 

that small target amplitudes are amplified more than large target amplitudes, 

and suppresses precipitation clutter; thus allowing for possible detection of 

small targets in precipitation clutter. · 

The log IF amplifier also permits 

excess of 80 dB in some radars. 

WSR-57 and WSR-74S weather radars for 

dynamic range. 

a large radar receiver dynamic range in 

Log IF amplifiers are also used in the 

the purpose of achieving a large 

The ASR-7 and ASR-8 have a log IF bandpass filter followed by a chain of 

untuned amplifier-video detectors and a video amplifier (see Figure 3-11 ) . 

The gain of the string ·of amplifier-video detectors is such that the last 

stage in the string become3 overdriven with inherent noise signals and 

limiting commences. As the 30 MHz signal· amplitude increases, successive 

stages toward the first stage becomes overdriven and further limiting occurs. 

The net effect is that the video output increases as a function of the log of 

the input signal. The resultant video output is sent to both the weather 

channel and the subtracter antilog circuitry in the processor unit. The 

log-function begins at signal levels 20 dB below ' the rms npise level for the 

ASR-7 and ASR-8. Some radars (WSR-57 and WSR-74S) include the tuned bandpass 

filter circuits in the amplifier-video detector chain. Therefore, the log IF 

amplifier bandwidth becomes a function of the signal level. 

Log IF Bandpass Filter 

As with the normal channel IF bandpass filter, this log IF bandpass 

filter has a much narrower bandwidth and a sharper selectivity characteristic 

3-2 2 
w 

I 

N 

w 

STAGE 1 

LIMITING AMPLIFIERS 

STAGE N 

Figure 3- 1 1 . Logarithmic Amplifier-Detector Block Diagram. 
than the preceding receiver unit stages. Therefore, the desired signal or 

interfering signal time response at the log IF bandpass filter output is 

essentially governed by the log IF bandpass·filter characteristics. 

The desired and interfering signal oransfer properties of the log IF 

bandpass filter are !dentical to the normal. channel IF bandpass filter, and 

are discussed in detail in Appendix B and previously discussed in the radar 

normal channel section (Equations 3-5 through 3-7 and Figure 3-7 ) . 

Log IF Amplifier-Video Detector 

Figure 3-11 shows a typical block d~gram of the log IF amplifier and 

video detector hardware of the ASR-7 and AS~8 radars. The response of a log 

amplifier can be expressed as: 

Where the break 

approximately 

properties have 

given by: 

where: 

(3-10) 

point between the linear region and logarithmic region occurs 

where bei l. The signal-to-noise ratio (SNR) transfer 

been derived (Atlantic Research Corporation, 1974), and are 

( 3- ll ) 

ns + N ~ ln(l + 0.885 k.F) - 1/2 

( 

0.215 K2B ) 

(1 + 0 .885 k.F) 2 

nN z ln(l + 0 . 885 K) - l/2 

( 

0.215 K2 ) 

(1 + 0.885K) 2 

F(-l/2; l; -z) 

(1 + 0. 88 5 K) 2 

-z/2 

e [(l + z) I 0 (z/2) + zi1 (z/2)] 

B=(l+2.33 (S/N) 1 ) 

1 + (S/N)i 

z = (S/N) i 

Figure 3- 12 shows the signal-to-noise transfer characteristics for various 

Break Points (BP) in a logarithmic amplifier relative to the RMS noise input 

level. As previously mentioned the ASR-7 and ASR-8 have a BP = - 20 dB. 

3- 24 
60r-----~------~------~-------r------~------~------r-----~~-----, 

40 I I I I I I I J I 1 

Ill 

20 I 

I I 

"d 

~ 

8 

0 I' ~ \ \ \ \.....BP = 10 

/~ w 0 

BP = Linear-Logarithmic I ll:: 

Breakpoint in dB I \ \ '-BP = 0 

N z V1 (/) 

Relative to the RMS 

I 

Noise Input Level 

I 

\ BP= -1 -201/T 

I I I BP = -20 I -40 

~0 I 

~0 -1 0 0 10 20 30 40 50 60 70 

SNRrN(dB) 

Figure 3wl2 . Log Amplifier Transfer Characteristics 
The signal-to-noise ratio (SNR) transfer characteristics shown in Figure 3-12 

are also applicable to interfering signal transfer characteristics. 

The detectors in the log-normal channel are linear envelope detectors. 

Therefore, the signal-to-noise ratio (SNR) tra~sfer curve s~own in Figure 3-8 

can be used. 

Moving Target Indicator (MTI) Channel 

The ASR-& MTI receiver unit channel consists of IF filter, linear 

limiting amplifier, quadrature phase detector, and low pass filter amplifier 

circuits (Figure 3-13). The receiver unit MTI channel output feeds the 

digital cancelling circuits and other processing circuits in the processor 

unit. The function of the MTI receiver unit channel and processor unit is to 

reduce ground clutter return and stationary target echoes to system . noise 

level and to enhance moving target echoes~ on the PPI display. This is 

accomplished by using the phase difference between the transmitted pulse and 

reflected pulse. The COHO provides the basic timing and phase reference. 

One output from the COHO is mixed with an output from the STALO to produce 

the RF signal used to drive the transmitter amplifier. Another output from 

the COHO is applied to the phase detector in the MTI circuit. This output 

retains the phase of the transmitted signal. After down conversion to IF, 

the returned signal is amplified and applied to the phase detector. The 

phase detector output voltage is proportional to the phase difference between 

the transmitted (reference) signal and the returned signal. For stationary 

targets, the phase difference from pulse to pulse is always the same, causing 

the output voltage from the phase detector to be constant. For moving 

targets, the changing range from pulse to pulse causes a pulse-to-pulse 

change in phase. The output voltage from the phase detector varies from 

pulse-to-pulse rather than remaining constant as it does for stationary 

targets. The output from the phase detector, consisting of the return from 

both stationary and moving targets', is sent to the processor unit where the 

constant voltage is removed leaving only the fluctuating voltage caused by 

moving target echoes. The fluctuating voltage is applied to the PPI to 

provide the visual presentation of moving targets. In a MTI system employing 

a single phase detector and canceller the voltage fluctuations cause fading 

of parts of the visual display as the antenna scans past the moving target. 

To overcome this undesirable fading, the ASR-8 employs an "inphase" (I) and 

"quadrature" {Q) phase detector and digital canceller for each of these MTI 

channels. Because the phase detector output varies from a plus voltage 

through zero to a minus voltage as the relative phase between transmitted and 

received signals varies through 180 degrees, there are times when the return 

from a target produces a zero or near-zero output from the phase detector. 

If a second phase detector is used and supplied with a reference voltage 

delayed in phase 90 degrees from the reference voltage supplied to the first 

detector and the reflected voltage is divided and applied in phase to the 

signal inputs of each of the phase detectors, there is always a non-zero 

output from one of the detectors. If after cancellation, the two phase 

detector outputs are combined with the appropriate format, very little 

fluctuation will be present in the moving target voltage applied to the PPI. 

3-26 
A block diagram of the ASR-8 receiver unit MTI I and MTI Q channel is shown 

in Figure 3-13. 

IF Filter 

The ASR-8 MTI channel IF filter consists of eight cascaded synchronous 

single tuned stages with a 3 dB bandwidth of 5.0 MHz. The relative IF filter 

amplitude response ActB(F) is derived in Appendix B, and can be expressed as 

(Equation B-19): 

where: 

and: 

-20 log (1 + x2) 812 

~F = Frequency relative to the receiver IF tuned frequency 

in Hz 

B8 = IF amplifier stage 3 dB bandwidth, in Hz 

(3-12) 

Since the MTI IF filter has the narrowest bandwidth and sharpest 

selectivity characteristics, the interfering signal peak power loss as a 

funtion of off-tuning (Frequency-Dependent-Rejection, FOR) is essentially 

governed by the receiver IF selectivity characteristics, interfering signal 

emission spectrum and the frequency separation between the interfering signal 

and victim radar tuned frequency. Appendix B discusses in detail the signal 

transfer properties of an IF filter. In summary, the MTI channel IF filter 

transfer properties can be treated the same as the normal channel. That is 

the interference-to-noise ratio (INR) at the MTI channel IF input is given by 

Equation 3- 5, and the transfer properties of the MTI IF filter are given by 

Equation 3-6. Also the MTI channel IF output time waveform is given by 

Equation 3.7. 

Since the MTI channel uses a phase detector which is amplitude and phase 

sensitive, both amplitude and phase modulation of the interfering signal IF 

output time waveform are important. Appendix B discusses in detail both the 

amplitude and phase response of an IF filter to an interfering signal as a 

function of off-tuning. It is shown in Appendix B that when the interfering 

signal is off-tuned, tne IF filter causes a beat tone phase modulation during 

the steady state portion of the pulse equal to the off-tuning (Figure B-15). 

The affect of this beat tone phase modulation in relation to the MTI channel 

interfering signal processing properties will be discussed later. The 

3- 27 
l-•) 

I 

[\) 

CD 

PREAMPLIFIER 

OUTPtiT 

PHASE ~ DETECTOR 

AMPLIFIER 

IF & 1 

AMPLIFIER 1-- LIMITER ~ SINUSOIDAl 

RESTORER 

900 PHASE 

SHIFTER 

PHASE ~ DETECTOR 

Figure 3-13 . Receiver Unit MTI I and MTI Q Channel 

~ LOW PASS 

FILTER & 

At.WLTFIER 

- 30 MHz 

COHO 

LOW PASS 

f-.-- FILTER 

& 

AMPT.T li'TF.R 

~ 

TO 

.PROCESSOR 

UNIT 

TO 

PROCESSOR 

UNIT 
narrowband white noise at the IF filter output has a Gaussian amplitude 

distribution and a uniform phase angle distribution. 

Linear-Limiting Amplifier 

The output of the IF amplifier is amplified and limited by series-diode 

limiters. The setting of the limit level is adjustable (L = 35 to 42 dB 

SNR) by setting the bias voltage level on the diodes. When the signal at the 

limiter input exceeds the bias level the signal is limited. The MTI 

linear~limiting amplifier signal processing properties can be expressed as: 

(3-13) 

LNR for SNRi > LNR 

Equation 3-13 also applies to the interference-to-noise (INR) transfer 

properties of the linear-limiting amplifer . 

MTI Quadrature Phase Detector 

The ASR-8 has a quadrature phase detector. Most of the radars in the 

2.7-2.9 GHz band only have a single channel MTI phase detector. The 

quadrature MTI channel uses two phase detectors with the COHO signal into the 

two phase detectors being shifted by 90 degrees (see Figure 3-13). Both the 

single channel and quadrature channel MTI signal processing properties are 

discussed in detail in Appendix C. Since the inphase (I) and quadrature (Q) 

channel are identical except for the COHO being shifted by 90 degrees, it is 

sufficient to analyze the signal processing properties of only one phase 

detector. 

The phase detector output is a function of the phase difference between 

the amplified and limited received signal and the reference COHO signal. The 

output is a video pulse of polarity and amplitude which is a function of the 

received signal amplitude and the phase difference between the applied input 

signals. Appendix C contains a derivation of the signal-to-noise ratio (SNR) 

and the interference-to-noise ratio (INR) transfer properties of the MTI 

phase detector. The transfer properties of the phase detector can be 

expressed as (Equation C-15): 

SNRpdo 

Equation 3- 14 also applies to the interference-to-noise ratio 

properties. That is the SNR or INR at the phase detector output is 

the SNR or INR at the phase detectqr input. 

3-29 

(3-14) 

transfer 

equal to 
The noise probability density function at the phase detector output is 

Gaussian. This is due to the fact that the phase detector is amplitude as 

well as phase sensitive. The noise amplitude PDF at the input to the phase 

detector is Gaussian distributed, and the noise phase PDF is uniform 

distributed. Therefore, the noise amplitude PDF at the phase detector output 

is Gaussian. If one considers a fixed amplitude (non-fluctuating) desired or 

interfering signal at the phase detector inp~t, the signal-plus-noise at the 

phase detector output is given by: 

N (t) + A cos cp (3-15 ) 

where: 

N(t) = Noise amplitude which is Gaussian distributed, in volts 

A = Desired or interfering signal amplitude, in volts 

cp = Phase difference between received signal and COHO which is 

uniformly distributed 

Popoulis (1965) derives the probability density function for Equation 3-15 

which can be expressed as: 

p(v,A) = _1 /lT 

7TO ffTI 

e 

(3-16 ) 

dcp 

0 

where: 

o = rms noise level, in volts 

Equation 3-16 can not be written in closed form. The MTI channel phase 

detector output was si.mulated to investigate trade-offs in suppressing 

asychronous interfering signals. The simulation of the radar MTI channel is 

discussed in Appendix E. Figure 3-14 shows the PDF given by Equation 3-16 as 

a function of the signal-to-noise ratio. The PDF was obtained by simulation. 

Low Pa$s Filter 

The low pass filter in the MTI channel is used to reduce the MTI channel 

video noise level. The low pass filter bandwidth (BlpV is approximately 

equal to 1/T where T is the desired signal pulse widtn. The MTI channel IF 

bandwidth is always much greater than 1/ T (generally 5.0 MHz ) to produce a 

constant phase characteristic across the desired pulse. Therefore, a 

narrower low pass filter bandwidth will improve the video signal-to-noise 

ratio. The MTI channel low pass filters are usually several stages. The low 

pass filter frequency response can be expressed as: 

ALp(F) l (3-17 ) 

F n 

[l + j ( FL ) y ] 

3- 30 

,. 
< 

' 

!> 

w - I 0.. 

w 

....... 

-r---~.---~-----r-----r----,-----~----r----,-----r----~ 

RMS Noise Level (a) = 0 . 25 Volts 

2 . I I I ! I I I I : I I 

ftl) oise Only 

l. 

20 dB 

-5. 

l_~~~~~~~~~~~~~ -4. - 3 . -2 . - 1. 0 . l. 2 . 3 . ~~ 4 . 5 . 

Figure 3- 14 . 

VOLTS 

Probability Density Function for Noise Only 

and for Signal-Plus- Noise at the MTI Phase 

Detector Output. . 
where: 

FL = Low pass filter 3 dB cutoff frequency , in Hz 

n = Number of low pass filter stages 

y = ;21/ n_l 

The interfering signal low pass filter output time response, Vlpo(t) , can 

be obtained by multiplying in the frequency domain the low pass filter 

frequency response with the phase detector output interfering signal 

frequency spectrum, Vpdo(F~ and taking the •Fourier transform. That is: 

V lpo (t) = (3-18 ) 

Measurements made on an ASR-8 showed that as the interfering signal is 

off-tuned (AF), the signal level followed the low pass filter selectivity due 

to the sinusoidal modulation during the steady state portion of the pulse. 

However, for AF greater than 3 MHz, the off-tuned interfering signal response 

started to follow the interfering signal RF frequency spectrum, and the low 

pass filter interfering signal output response was caused by the phase 

modulation that occurs during the transient part (rabbit ear response 

occurring at the leading and trailing edge of the IF filter output response, 

see Figures B-10, B-11, B-13, and B-14) of the interfering signal time 

waveform. Figure C- 5 shows a photograph of the phase detector output time 

waveform of a 60 s pulse signal off-tuned 200 kHz. The measurement was made 

on an ASR-8 radar. The pulse width was set ?t 60 ~s to demonstrate the 200 

kHz sinusoidal modulation during the steady state portion of the pulse which 

is caused by the phase modulation produced by the IF filter transfer 

properties, and is equal to the off-tuned frequency ( AF). Figure C-6 shows a 

photograph of an ASR-8 low pass filter output of a .83 ~s pulse off-tuned 5 . 0 

MHz. Since the low pass filter interfering signal output response for 

off-tuned interference is due to the phase modulation which occurs during the 

transient portion of the IF filter response, the low pass filter output 

interfering signal time response changes from pulse-to-pulse. However, the 

average pulse amplitude appears to follow the interfering signal RF spectrum 

envelope as the interfering signal is off-tuned. Figure C- 7 shows a 

photograph of the low pass filter output for the same interfering signal 

parameters as in Figure C- 6. However, the phase modulation during the 

transient portion of the interfering signal did not cause a low pass filter 

output response. 

3- 32 
The signal-to-noise (SNR) transfer properties of the MTI low pass filter 

can be expressed as: 

BIF SNRlpi + 10 log Blpf 

(3-19 ) 

For a radar with a 5.0 MHz IF bandwidth and a 1.2 MHz low pass filter 

bandwidth, the noise power at the low pass filter output is given by: 

SNRlpi + 6.2 dB ( 3- 20) 

Therefore, the low pass filter increases the MTI channel signal-to-noise 

ratio by 6.2 dB. Equations 3-19 and 3-20 also apply to the 

interference-to-noise transfer properties of the MTI channel low pass filter. 

The affect of the MTI channel low pass filter on off-tuned interference is 

discussed in detail in Appendix C. 

PROCESSOR UNIT 

The following is a discussion of the signal processing properties of the 

processor units of the ASR-7 and ASR-8 radars. The function of the processor 

unit is to accept raw video from the receiver unit, condition the video 

depending on the operating mode desired, and present the video to a Pl a n 

Position Indicator (PPI) display for Air Traffic Control (ATC) purposes. The 

processor unit accepts as inputs normal, log-normal, and bipolar MTI video. 

Both the ASR-7 and ASR-8 have digital processor units. Some of the radars in 

the 2.7 to 2.9 GHz band have analog processing units. In general, the signal 

processing properties of the analog radars can in most cases, and for 

analytical simplicity, be modeled by the same operations as the digital 

signal processing units. The digital processing units will introduce some 

quantization, roundoff and truncation error. However, the error due to 

quantization, roundoff and truncation is generally very small and can be 

neglected in most cases. The following is a discussion of the signal 

processing properties of the processor unit normal, log-normal, and MTI 

channels to noise, desired signal, and asynchronous interference. 

Processor Unit Normal Channel 

A simplified block diagram of the processor unit normal channel is shown 

in Figure 3-15. The following types of normal video can be provided at the 

processor unit output for display on the PPI: 

Normal Video 

Enhanced Normal Video 

3- 33 
w 

I 

w 

.p-.. 

LOG NORMAL 

VIDEO I N 

NORMAL 

VIDEO I N 

r------------------------, 

I PROCESSOR UNIT NORNAL CHANNEL l 

I' I 

I \•JEATHER I I r BACKGROUND I r I ON/OFF 

I ·I I I 

' 

SUBTRACTER SELECT SWITCH SELECT S\'IITCII ! 

I ANTI-LOG ENHANCER 

r-t ON/OFF 

I LOG-FTC ON/OFF 

I 

I 

I 

I VIDEO NOJU.1AL 

; DELAY - ENHANCER 

---- I 

1 I 

1 · . . . I 

L-------------------------~ 

Figure 3-15 . Processor Unit Normal Channel Block Diagram 

NORMAL 

WEATHER 

BACKGROUND 

NORMAL 

LOG FTC 

VIDEO OUT 
Normal Log-FTC Video 

Enhanced Normal Log-FTC Video 

Normal LOG-FTC with Weather Background Video 

Enhanced Normal LOG-FTC with Weather Background Video 

The various normal channel modes are obtained by switching the Log-FTC and 

enhancer selection switches on or off. 

Sybtractor Anti-Log 

Radars in the 2.7 to 2.9 GHz band use Logarithmic Fast Time Constant 

(Log-FTC) or Logarithmic Constant False-Alarm Rate (Log-CFAR) circuits to 

remove precipitation clutter or residue. The circuits operate on the 

principle that precipitation clutter, after being passed through a 

logarithmic response, has a noise variation about the average value that is 

independent of the average value. Filter circuits subtract out the average, 

leaving only the constant residue level. This level is adjusted to be equal 

to the receiver noise, thus totally eliminating precipitation clutter from 

the display. 

Figure 3-16 shows a block diagram of the normal Log-FTC channel. In the 

radar normal channel, the log function is performed by the log IF module in 

the receiver unit. The filtering subtraction and anti-log functions are 

performed by the normal/Log-FTC assembly in the processor unit. The filter 

averages the log video over a certain time interval (8 to 12 range bins) to 

form an average value. The delay line delays the video signal of interest 

(one range-bin) so as to maintain coincidence with the averaging filter. The 

average video signal is then subtracted from the delayed video signal. A DC 

bias is then added to produce a positive mean and eliminate negative signals. 

The signal is then applied to an anti-log amplifier to return the signal to a 

linear function and eliminate the loss in detectability caused by logarithmic 

compression. 

Noise - The DC bias in the Log-FTC circuitry is adjusted so that the 

noise amplitude distributi~n after the logarithmic detection, subtraction and 

anti-log function are performed is approximately Raleigh at the Log-FTC 

circuitry output. 

Desired Signal - For the desired signal in the presence of noise only 

(no clutter), the detectability of the desired signal is only slightly 

degraded (1 or 2 dB) due to a small amount of the target energy falling in 

the adjacent range bins. In the presence of clutter, the desired signal 

level must be greater than the clutter in order for the signal to be 

detected. This is due to the fact that the signal must be greater than the 

average clutter signal in order to appear at the subtractor output. 

Interference The Log-FTC circuitry acts as 

discriminator for interfering signals with a pulse width 

system designed pulse width. Long pulse interference which 

range bins increases the average energy in the filter 

3- 35 

a pulse width 

greater than the 

covers several 

since the filter 
FILTER 

T 

IF SIGNAL 

LOGARITHMIC 

DETECTOR 

DELAY 

V dt~--~----------------------~--- (t T) -2 

SUB TRACTOR 

ANTILOG AMPLIFIER 

VIDEO TO DISPLAY 

Figure 3- 1 6. Log- FTC Block Diagram 

3- 36 
averages over several range bins. Therefore, long pulse interference acts 

somewhat like clutter, and the interfering signal level at the subtracter 

output is reduced. Measurements made on an ASR-8 radar showed that for 

interfering pulse widths greater than 2.0 sees the interference was 

suppressed. Thus, interference from height finding radars (AN/FPS- 6, 90), 

and weather radars operating in the 4.0 ~sec mode can be suppressed by 

operating in the Log-FTC mode. For CW type interference, the Log-FTC circuit 

reduces the interference down to the receiver noise level since the CW 

interference appears somewhat like clutter. However, the desired signal will 

not be detected unless the signal is above the CW interference. Therefore, 

for every dB the CW interference is above the receiver noise level the 

desired signal sensitivity will be reduced by that number of dB. 

Normal Enhancer 

The process of summing the echo pulses from a target is called 

integration. The following is a discussion of the transfer properties of 

integrators (enhancers) used by radars in the 2.7 to 2.9 GHz band. The 

discussion includes the integrator transfer properties of noise, desired 

signal, and asynchronous interfering signals. Also discussed are the 

trade-offs in the desired signal transfer properties of the enhancers in 

suppressing asynchronous interfering signals. 

Integrators are generally used in the primary radars for t wo reasons: 

1. To enhance weak desired targets for PPI display. 

2. To suppress asynchronous pulsed interference. 

The principle of the radar video integrator is that radar signal returns from 

a point target consist of a series of pulses generated as the radar antenna 

beam scans past the target, all the pulses from the target will occur in the 

same range bins in successive radar periods. It is this series of pulses 

from a target which permits integration of target returns to enhance the weak 

signals. The number of pulse returns (N) from a target depends upon the 

radar antenna beamwidth (BW), the rate of antenna rotation (RPM), the radar 

pulse repetition rate (PRF), and the target characteristics. The equation 

for the number of pulses from a point target is given by (Skolnik, 1962): 

N PRF BW (3-21) 

6 RPM 

where: 

PRF = Radar pulse repetition frequency, in PPS 

BW = Antenna 3 dB beamwidth, in degrees 

3-37 
RPM = Antenna scan rate, in rpm 

A range value of N for radars in the 2.7 to 2 . 9 GHz band is 12 to 20. The 

integrator will suppress asynchronous interference since the interfering 

pulses will not be separated in time by the radar period, and thus will not 

occur in the same range bin in successive periods (asynchronous with the 

system ). Therefore, the asynchronous interference will not add-up, and can 

be suppressed. 

All radars in the 2.7 to 2.9 GHz band employ post detection or 

noncoherent integrators. The types of post detection integrator employed in 

radars in the 2.7 to 2.9 GHz band can be categorized either as a feedback 

integrator or a binary integrator. Radars employing feedback integrators may 

be of analog (delay line) or digital (shift register) type. Only digital 

binary integrators are used. Appendix D contains a detailed discussion of 

the feedback and binary integrator transfer properties and the trade-offs in 

suppressing asynchronous interference. The transfer properties were 

investigated analytically and by simulating the noise, desired signal, 

interfering signals, and the feedback and binary integrator hardware. 

Appendix E contains a detailed discussion of the methods used to simulate the 

noise, desired signal, interfering signal, and the actual radar hardware 

simulated. 

Feedback Integrator Figure 3-17 shows a block diagram of a typical 

feedback integrator used by radars in the 2.7 to 2.9 GHz band. The feedback 

integrator consists of an input limiter, an adder, and a feedback loop with 

an output limiter and a delay equal to the time between transmitter pulses 

(1/PRF). The radar period delay for digital radars is achieved by clocking a 

shift register, and the actual integrator hardware is essentially represented 

in Figure 3-17 . Analog radars in the 2.7 to 2.9 GHz band generally use 

quartz delay lines, thus accomplishing the delay accoustically to reduce the 

size of the delay line . However, the inherent loss of quartz delay lines 

requires use of additional hardware, such as, modulators, attenuators, . 

amplifiers, detectors, and balancing circuits (AGC) to achieve integration. 

If the analog integrator balancing circuitry is aligned properly, the 

transfer properties of an analog integrator can, for analytical simplicity, 

be modeled by the operations shown in Figure 3-17. Digital integrators will 

also introduce some quantization, roundoff and truncation error. However, 

the error due to quantization, roundoff and truncation is generally very 

small and can be neglected in most cases. 

Prior to the input of the feedback integrator, signal processing 

circuitry is used to reduce the mean noise level at the input to the feedback 

integrator. This circuitry generally consists of an attenuator, subtracter, 

and bottom clipper so that the noise at the input to the feedback integrator 

will be positive. The function of this circuitry is to reduce the mean level 

of the noise at the integrator input to reduce the noise gain of the feedback 

integrator. Since the noise is being continually added by the feedback 

integr ator, the noise amplitude probability density function at the feedback 

integrator output by the central limit theorem is approximately Gaussian with 

3- 38 
w 

I 

w 

\0 

CiT) INPUT +I \ OUTPUT eol' t 

LHH'l'ER ' J LIMITER 

+ ....., ........ 

DELAY 

- K - To = 1/PRF 

Fiyurc 3-17 . Feedbu~k Integrator Block Diagram 
non-zero mean. 

It is shown in Appendix D (Equation D-10) that the signal-to-noise-ratio 

enhancement (SNRE) of the desired signal is given by: 

N 

20 log 10 [ (~=~ ) (3-22 ) 

where: 

N Number of target return pulses 

K = Integrator feedback constant 

Equation 3-22 is only a first order approximation of the signal-to-noise 

ratio enhancement of a feedback integrator since it assumes zero mean noise 

amplitude distribution and a constant desired signal level. The desired 

signal level actually· varies from pulse-to-pulse due to fluctuations in 

target returns (scintillation and antenna pattern modulation). Studies 

(Trunk, 1970) have been made which take into account pulse amplitude 

variations due to the antenna pattern modulation. Trunk concluded that the 

SNR enhancement of a feedback integrator could be reduced by as much as 1.6 

dB due to antenna beam shape pulse amplitude variations. The actual 

reduction in SNR enhancement due to the radar antenna pattern is between 0 

and 1.6 dB, and is also a function of the integrator input limiter limit 

level setting. It is shown in Appendix Dusing Equation 3-22 and measurement 

results that the optimum value of the feedback constant (K) is between .92 

and .94 for 20 pulses from a target (N = 20), and the signal-to-noise-ratio 

enhancement (SNRE) due to integration is approximately 10 to 12 dB. 

Figure 3-18 shows a simulated unintegrated target return pulse train for 

target azimuth shift and angular resolution reference. Figures 3-19 through 

3-21 show a simulated feedback integrator output of a target return pulse 

train for 20 pulses for an input limiter limit level setting of 1.0, 0.5, and 

0.34 volts. A detailed discussion of the radar simulation model is given in 

Appendix E. When a feedback integrator is used there are trade-offs in 

target azimuth shift and angular resolution. A comparison of Figure 3-18 

with Figures 3-19 through 3-21 shows that the center of the target return 

pulse train has shifted in time. This shift in time is related to a target 

azimuth shift on the Plan Position Indicator (PPI) display. Also a 

comparison of Figure 3-18 with Figures 3-19 through 3-21 shows that the 

number of pulses above 1.0 volts (peak noise level) increases when the 

feedback integrator is used. This increase in number of pulses results in a 

decrease in angular resolution. (The property of the radar to distinguish 

between two targets.) Appendix D contains a detailed investigation of the 

trade-offs in target azimuth shift and angular resolution when an integrator 

is used. In summary, it was shown that a feedback integrator causes a target 

azimuth shift of approximately 0.90 degrees, and an angular resolution loss 

3-4 0 
8 . 

7 . 

:L 6 

L) 

""-... G . t--

_l 

;::J 4 . > 

"' .) . 

. -, 

~- . 

Figure 3-18. Simulated Normal Channel Unintegrated Target Return 

Pulse Train for a SNR = 15 dB 

,-H 

7 

1:, ~ 

I .J 

r I 

t--

_J 

C..J Lj ·:::;. 

") 

I 

,-

'-

. 

·rI 

1-

r. 

) 

T 

Figure 3-19. Simulated Normal Channel Integrated Target Re turn Pulse 

Train for the Input Limit er Set at 1.0 Volts and a 

SNR = 15 dB 

3-41 
8. 

7 . 

'L 

G. 

LJ 

'-.. r 

~. 

1--

_j 

0 4 0 

> 

3. 

r, L . 

1 0 

lj. 

0 0 

-- -,----

--1-

rI -I 

I 

I 

i 

i 

___ [ - I 

5 . 10.15.20.25o30 o35 .40 .45.50. 

S MILLI5ECONOS/CM 

Figure 3-20. Simulated Normal Channel Integrated Target Return Pulse 

Train for the Input Limiter Set at 0 .5 Volts and a 

SNR = 15 dB 

8. 

7. 

'L s, 

LJ 

'-.. f) ' 

t-

_j 

C) 4 . 

> 

...- ] . 

I") 

L1 . 

0 

o. 5.10 . 15.20 .25.30.35.40 .45.50. 

S MILL1SECBNOS/CM 

Figure 3-21. Simulated Normal Channel Integrated Target Return Pulse 

Train for t he Input Limi ter Set at 0 . 34 Volts a nd a 

SNR = 15 d B 

3- 42 
of approximately 1.2 to 1.5 degrees relative to an unintegrated target return 

pulse train. 

In congested areas when there is potential for asynchronous interference 

from other radars in the 2.1 to 2 . 9 GHz band, adjustments to the feedback 

integrator input limiter are required to suppress the asynchronous 

interference. By adjusting the integrator input limiter limit level the peak 

interference level can be suppressed to the one volt noise level at the 

integrator output. Suppression of asynchronous interference in the radar 

normal channel and the trade-offs to the desired signal are discussed in 

detail in Appendix D. The analysis showed that the suppression of 

asynchronous interference does not significantly increase the target azimuth 

shift or decrease the target angular resolution given the integrator is going 

to be used. Figure 3-22 shows a simulated normal channel radar unintegrated 

output for three interference sources (ASR-5, INR = 10 dB; ASR-8, INR = 15 

dB; and AN/FPS-90, INR = 20 dB), and a desired target signal-to-noise ratio 

of 15 dB. Figure 3-23 shows for the same interference condition the radar 

output after feedback integration for an input limit level setting of 0 . 34 

volts. The asynchronous interference has been suppressed (compare Figure 

3-21 with 3-23) by the feedback integrator. Measurements made on the 

Stapelton Airport ASR-8 radar in Denver, Colorado, showed that on-tune pulsed 

interference levels of 50 dB above the receiver noise level (approximately 

- 60 dBm) could be suppressed by the feedback integrator so that they did not 

appear on the PPI display. The measured change in target detection 

sensitivity in suppressing the asynchronous interference was 1 dB or less. 

In summary, feedback integrators can suppress asynchronous interference, in 

the normal channel, by adjusting the feedback integrator input limiter limit 

level, and the trade-offs in target azimuth shift, angular resolution, and 

target detection sensitivity appear to be minimal . 

Binary Integrator The ASR-7 and AN/GPN-12 radars are made by the same 

manufacturer, and the enhancer used in the two radars are electronically 

identical. The integrator (enhancer) used in the two radars can be 

represented by the block diagram shown in Figure 3- 24 . The binary integrator 

consists of a threshold detector or comparator, binary counter 

(adder/subcontractor circuit), a five bit shift register memory, and a 

digital-to-analog (D/A) converter. Each PRF period is divided into range 

bins of .625 sec . If a pulse of a target return pulse train exceeds the 

comparator threshold level, the enhancer stores a one level digital signal in 

the shift register memory for that range bin . If the successive pulses of 

the target return pulse train continue above the comparator threshold in the 

given range bin, the binary counter will add one level to the stored digital 

signal in the shift register memory in each PRF period until a maximum 

integrator level of 31 is reached. If in any PRF period the signal fails to 

exceed the comparator threshold, the binary counter subtracts one from the 

stored integrator state in the given range bin until a digital signal level 

of zero is reached. The subtraction provides the target return pulse train 

signal decay required after the antenna beam has passed the target, and also 

enables the suppression of asynchronous interfering signals. The voltage 

amplitude at the enhancer D/A converter output is determined by the binary 

3- 43 
8 . , 

I 

7 Desired SNR = 15 dB 

ASR-5 INR = 10 dB J 

F). ...;--

...._ 

ASR-8 INR = 15 dB 

AN/FPS-90 ~ INR -= 20 dB 

1,....,) 

'· ~) . ..-

_J 

0 4 . > 

3 ' 

"') 

(_ 

I ' 

lj 

c . L. 1 0 l ~ ..-. (1 '"' ( ...., [l I l .1 'I II ~ C ,...l ) t • 1..) • t_ t L ) c :) 1 r J ~ c U • ~ 1..) • ) • 1 • 

Figure 3-22. Simulated Normal Channel Unintegrated Radar Output 

with Interference 

8 . 

7. 

....-

"'- 6-

u 

' ~) ' 

t--

_j 

0 4 . > 

...- -:) J• 

2, 

1 . 

u 

o. 

Desired 

ASR-5 

ASR-8 

AN/FPS-90 

SNR = 15 dB 

INR = 10 dB -1 

INR = 15 dB 

INR = 20 dB 

5 . 1 0 . 1 5 .zo .zs .30 .3:) .4 0 . 4 5 .:-JCJ. 

5 MILLI5f[Q~OSICM 

Figure 3-23. Simulated Normal Channel Integrated Radar Output 

with Interf erenc e 

3-44 
UJ 

I 

J:-

1..11 

I 

ein 'l'IIHCSHOLD O,l BINARY 

CCtlPl\RATOR 

~ 

BINARY D/A .... .... COUNTER CONVERTER 

SIIIFT 

REGISTER ..-

(:11\NGE-Gl\TE) -

r 

CLOCK 

Figure 3-24. ,\SR-7 {l\N/GPN-12) Binary Integrator· Block Diagram 

eout 

.. 
counter level (0 to 31) for the particular range bin times .125 volts. 

Therefore, for a binary counter level of 31, the maximum enhancer output 

voltage would be 3.875 volts (31 x . 125). 

FAA Integrator Modification 

The FAA made modifications to the manufacturer's integrator (enhancer) 

printed circuit board due to deficiencies that were observed on the ASR-7 

video enhancer at operational field sites. Deficiencies that were observed 

were: (1) loss of weak targets due to design of the enhancer integrators, 

and (2) ~xcessive azimuth shift of the target (NAFEC Letter Report, 

FAA-MA- 76-39- LR, 1976). The major modification made by the FAA was the 

replacement of the binary counter (IC's) with a programmable read-only- memory 

(PROM) logic. The PROMs permit the bypassing of some of the intermediate 

levels (0 to 31), depending on the PROM proEramming. Figure 3-25 shows the 

FAA standard hit/miss characteristic curve which is programmed into the 

PROMs . Th~ figure shows that the enhancer state is a nonlinear function of 

the target hits above the comparator threshold level . It only takes four 

hits to get to level 8 (one volt noise level), and six hits to get to level 

31 (3 . 875 volts). This results in a strong target enhancement with only a 

few hits. The primary advantage of the PROM enhancer is that, due to its 

programmable feature, it permits a radar site flexibility in selecting a 

hit- count sequence based on the radar site environment (interference and 

clutter). Similarly, the miss- count sequence can be precisely controlled to 

minimize the target azimuth shift and loss in angular resolution. In this 

way, the video enhancer performance can be optimized to give improved 

performance in a variety of environmental conditions. 

The following discussion will center on the particular signal processing 

characteristics of the conventional integrator deployed in the ASR-7 and 

AN/GPN-12 and the modified ASR- 7 integrator to noise, desired target return 

pulse train , and asynchronous interference. Also discussed are the 

trade-offs in the desired signal transfer properties of the enhancer in 

suppr essing asynchronous interfering signals. Appendix D contains a detailed 

discussion of the binary integrator transfer properties and the trade-offs in 

suppressing asynchronous interference . 

The normal channel noise amplitude distribution at the binary integrator 

input is Raleigh distributed. It is shown in Appendix D (Equation D- 20b) 

that the probability of the binary counte~ being in state Ej due to noise 

(Pnj) can be modeled by a one-dim~~ional random walk with reflecting 

barriers where levels 0 and 31 are the reflecting barriers. Since the noise 

is continually summed in the binary integrator the number of s~s (k) in the 

random walk is infinite . It can be shown that a one-dime~~nal random walk 

with reflecting barriers model for an infinite number of steps is identical 

to a truncated single channel queue model where the probability of being in 

state Ej due to noise (Pnj) can be expressed as (Saaty, 1968): 

(3-23) 

3-4 6 
~ 

L'J 

~ 

!'< 

...:l 

0 

> 

w E-< 1 ::.:> .c-. p.. -..J E-< 

::.:> 

0 

4 

level 3 1 

3 

2 level 

/0 ::::: : ~~ 

0 --"]~0 ~ level l evel 1 

2 - '~--~ 11111111 111 1111~'------

!liT 

Figure 3- 25. 

+:----- HISS 

Hit/Hiss Ch aracteristic Curve for PAA Nodified 

ASR-7 Enhancer 
where: 

PN0 = Probability of the noise causing a 0 at the threshold 

comparator output 

p Nl = Probability of the noise causing a 1 at the threshold 

comparator output 

p = Number of states (function of counter level sequence) 

The probability distribution given by Equation 3-23 is a geometric 

distribution, and is independent of the noise amplitude distribution at the 

enhancer input . The threshold comparator threshold level is normally adjusted 

to give a peak noise level of one volt (enhancer level 8, 8 x .125) with a 

certain probability of false alarm (probability of exceeding level 8) . A 

detailed discussion of the setting of the threshold comparator threshold level 

for noise is given in Appendix D. 

The normal channel signal-plus-noise amplitude distribtuion at the binary 

integrator input is Rice distributed (see Equation 3-9, and Figure 3-10) . It 

is shown in Appendix D (Equation D-25a) that the probability of a desired 

target return pulse train of 20 pulses causing the binary integrator to be in 

state Ej can be determined by using a one-dimensional random walk with 

reflecting barriers model where levels 0 and 31 are the reflecting barriers. 

The probability of the desired target return pulse train causing the binary 

integrator to be in state Ej for a given signal-to-noise ratio is given by: 

p = Bj 

where: 

-

and: 

N , (k) 

r p ij k=l 

p N (k) 

r r pij 

j=l kzl 

j-1 

(p/q) -1 ( ) 

(p/ q)p -1 ~ 

p-1 

+ ~ I 

p r•l 

~~f)y(j) [2.Jpq cos H/p)k 

1- 2,1Pqcos rrr/p 

(r) (s) -i/2 rrri (s) (i+l)/2 x 1 -= p sin -p- - p 11 in 'lfr(i-1) 

p 

3-48 

(3-24) 

(3-24a) 

(3-24b) 
(r) (E)j /2 

y j • q, sin nrj 

p 

- ~) (j-l)/ 2sin nr(j-1) (3-24c) 

p 

0 = Number of states (function of counter level sequence) 

Q = PS0 = Probability of 0 at threshold comparator output 

p = Psl = Probability of at threshold comparator output 

N = Number of desired signal pulses in target return 

pulse train 

The values of Psj as a function 

detail in Appendix D. Also 

state Ei as a function of the 

detail In Append ix D (see TABLE 

of the signal-to-noise ratio are discussed in 

the probability of the desired signal being in 

signal-to-noise ratio is also discussed in 

D-6). 

The signal processing of the ASR-7 binary integrator was simulated to 

investigate the trade-offs to the desired signal in suppressing asynchronous 

interference . A simulated ASR-7 enhancer output for a desired target return 

pulse train of 20 pulses without noise present is shown in Figures 3- 26 and 

3-27 for the conventional ASR-7 enhancer, and the FAA modified ASR-7 enhancer, 

respectively. A comparison of Figures 3-26 and 3-27 shows that the FAA 

Modified ASR-7 enhancer provides a significant improvement in signal 

enhancement, target azimuth shift, and angular resolut)on. Figure 3- 28 shows 

the simulated radar output of the normal channel for a Signal- to-Noise- Ratio 

(SNR) of 15 dB with the binary integrator off (unintegrated) . Figure 3- 29 

shows the radar output with the enhancer on (integrated) for the same SNR . 

Appendix D contains a detailed discussion of the desired signal transfer 

properties of the binary integrator as a function of the 

signal-to- noise-ratio. 

It is shown in Appendix D that the FAA modified binary integrator causes 

a target azimuth shift of approximately .179 degrees. However, the feedback 

integrator causes a target azimuth shift of approximately 0.90 degrees. 

Therefore, the FAA modified binary integrator results in a significant 

improvement in target azimuth shift over the feedback integrator. Also the 

FAA modified integrator does not cause any loss in target angular resolution 

while the feedback integrator results in a loss in angular resolution of 1.2 

to 1.5 degeees. 

3-49 
s. 

7. I 

2:::: 

s , 

u 

.......... 

1--

5 . ~ 

_j 

0 4 . > 

.,.-; 3 . ' 

2 . 

1 . 

,,, Ill Ill ,,, CJ . 

o. 5.1 0 .15. 20 -25. 30. 35.4 0 .45.50. 

5 MILL ISECGNOS/C M 

Figure 3-26. Simulated Binary Integrator Output for Target 

Return Pulse Train (ASP-- 7, AN/GPN- 12) 

:L 

u 

.......... 

f--

_j 

0 

> 

8 . 

7 . 

6. 

5 . 

4 • 

3 . 

2. 

1 . 

0 . ,,, 

I 

' 

I I,, 

u . 5 .10. 15 .20 .25 .30 .35 .40 .45 .50 . 

5 MILLISECGNDS/CM 

Figure 3- 27. Simulated FAA Modified Binary Integrator Output f or 

Target Return Puls e Tra in (ASR-7) 

3-50 
8. 

7 . 

:L. 6. 

u 

'-... s . t-

_j 

0 4 . 

> 

~ J, 

'? L• 

1 . 

o. 

o. 

s M I L L I 5 E c 0 ~~ 0 5 I c M 

Figure 3- 28. Simulated Normal Channel Unintegrated Target 

Return Pulse Tr ain for a SNR = 15dB 

8 . 

7. 

:L 

6 . 

w 

'-... s . I 

f-

_j 

0 4 

> 

....- J , I II I 

..... 

L• 

1 ' 

. ~~I ~ ~ o. l1 II ~U I till lin ~U lJJ .!11 ni~ 

Q. S .1 Q.1 5 .20 .2S .30 .3S .40 .4 5.50. 

S MILLi5ECO~OS/CM 

Figure 3- 29. Simulated Normal Channel Integrated Target 

Return Pulse Train for a SNR = 15dB 

3-51 
The capability of the binary integrator in the ASR-7 to suppress normal 

channel asynchronous interference was also investigated using the radar 

simulation model (see Appendix E). Three interfering radar sources were 

simulated: ASR-5, ASR-8, and the AN /FPS- 90. Figures E-3 through E-5 in 

Appendix E show the respective time waveforms simulated for each of the 

radar interfering sources. Figure 3-30 shows a simulated normal channel 

radar unintegrated output for three interfere~ce sources (ASR-5, INR = 10 dB; 

ASR-8, INR = 15dB; and AN/FPS-90, INR = 20 dB), and a desired target 

signal-to-noise ratio of 15 dB. Figure 3-31 shows for the same interference 

condition the radar output after binary integration. The asynchronous 

interference has been suppressed (compare Figure 3-29 with 3-31) by the 

binary integrator. 

In summary, the FAA modified binary enhancer has the capability of 

suppressing normal channel asynchronous interference with very little 

trade-offs in target azimuth· shift, target angular resolution, and desired 

target probability of detection. Asynchronous interference can be suppressed 

by the FAA modified enhancer by either adjusting the threshold comparator 

level setting, or by programming a hit/miss state sequence that will suppress 

the interference. Thus the FAA modified ASR-7 enhancer can be adjusted to 

optimize the radar desired signal performance in a variety of environmental 

conditions. 

Normal Channel Weather Background 

Both the ASR-7 and ASR-8 have weather background circuits which can be 

selected to add a weather outline to the processor output video when the 

normal Log-FTC video is selected. The weather background video is adjustable 

in amplitude relative to the Log-FTC video to provide the operator with the 

proper contrast between ope rating video and background video. The ASR-8 has 

two display modes for the weather background. The first is merely a limited 

and adjustable display of the entire detected weather area. In this mode, 

the operator views the complete weather video pattern at a reduced 

brightness. The second mode is an adjustable brightness contour or outline 

of the storm or weather video area. In this mode the operator views the 

outline of the weather video pattern but is not distracted by the complete 

weather video pattern which can compete with aircraft returns. 

In the normal video channel, the background is generated from the 

receiver logarithmic video, which is low pass filtered to reduce the noise 

variation amplitudes. The filtering reduces the possibility of weather 

background false-alarm signals which would clutter the display, yet does not 

degrade the detection of the extended weather blocks themselves. The filter 

is designed with a time constant which matches the Log-FTC delay in the 

normal channel. The filtered weather background video is presented to 

variable threshold circuits and the threshold output signals are converted to 

a binary-coded signal. The threshold circuits are voltage comparators with 

adjustable reference voltages. The upper threshold, which is adjustable from 

10 dB above rms noise to the maximum input amplitude, is used for blanking. 

3-52 
8 . 

7 . 

:L 

6 . 

u 

.......... s . 

f-

_j 

4 ' <':) 

> 

- J , 

I") 

L • 

1 ' 

o. 

0 . 

Desired 

ASR-5 

ASR- 8 

AN/FPS-90 

SNR = 15 dB 

INR = 10 dB 

INR = 15 dB 

INR = 20 dB 

C 1 0 1 C --.0 "'"'C .....,0 ">C: A 0 A C 50 ,) • • J • L • L ,) • ..J • ..J ,) • '1 • '1 .:J • • 

5 MILLISECG~OS!CM 

Figure 3-30. Simulated Normal Channel Unintegrated 

Radar Output with Interference 

8 . I 

7 . Desired SNR = 15 dB 

ASR-5 INR = 10 dBASR-8 INR = 15 dB 

:L: 

6 . AN/FPS-90 INR = 20 dB _ 

u 

.......... 5 . 

f-

_j 

0 4 . > 

- 3 . 

2 . 

1 . 

0 . ~J"~~ ~~. U I 

ll -~~ i~~u ~J~~J uJ~J .~~~~ ~~~~~ O . lO.lS.20.25.30.35 40. 50 . 

5 MILLI5ECBND5/CM 

Figure 3-31 . Simulated Normal Channe l Integrated Radar 

Output with I nterference 

3-53 
The other two independently adjustable thresholds are for top clipping and 

bottom clipping. They are adjustable over the range from 0 to 15 dB above 

rms noise. The fourth threshold is an intermediate threshold between the 

top- clip and bottom- clip thresholds and is used when the weather video output 

is reconstructed in a multiple level form. The four possible modes of 

weather background are: 

Mode 1 - No blanking, quantize with bottom clipping 

Mode 2 - Blanking, quantize with bottom clipping 

Mode 3 - No blanking, top and bottom clipping 

Mode 4 - Blanking, top and bottom clipping 

One of the four operating modes can be selected. Input videc , before and 

after filtering, as well as representative output waveforms for these four 

modes, are shown in Figure 3-32. The normal weather background video is 

routed to the weather background/diversity combiner where it is added to the 

combined or single channel video. 

The weather background channel does not have an integrator (enhancer). 

(See Figure 3-15.) However, asynchronous pulsed interference in the weather 

background channel will be reduced by the low pass filter since the filter 

essentially averages over six to eight range bins. Also if the interference 

appears above the blanking threshold level (approximately 10 dB INR), it will 

be suppressed by the blanking circuit . Since the master channel weather 

background video is used for display on the PPI, the channel that minimizes 

interference can be chosen as the master channel . 

Processor Unit MTI Channel 

A simplified block diagram of the processor unit Moving Target Indicator 

(MTI) channel ia shown in Figure 3-33. The following types of MTI video can 

be provided at the processor unit output for display on the PPI: 

MTI Video 

Enhanced MTI Video 

MTI Log-FTC Video 

Enhanced MTI Log- FTC Video 

MTI Log- FTC with Weather Background Video 

Enhanced MTI Log- FTC with Weather Background Video 

The various MTI channel modes are obtained by switching the Log-FTC and 

enhancer selection switches on or off. 

MTI Canceller~ 

The target return signals,after phase detection are processed in the MTI 

cancellers. The MTI canceller circuits provide for cancelling fixed target 

signals (clutter), such as buildings, hills, and trees and allowing only 

moving targets, such as aircraft to be displayed on the PPI. The action of 

the MTI cancellers is that of a linear filter. In the ideal case , the 

3-54 
THRESHOLDS TOP CLIP 

{ 

BLANKING 

INPUT INTERMEDIATE 

WAVEFORN BOTTOM CLIP. 

AFTER 

FILTER 

OUTPUT MODE ------~ 

OUTPUT MODE 2 

OUTPUT t10DE 3 ---...j~ 

OUTPUT HODE 4 

WEATHER BACKGROUND INPUT 

Figure 3-32. Weather Background t-1odes. 

3-55 
VJ 

I 

V1 

"' 

RECEIVER 

INPIIASE 

MTI 

RECEIVER 

QUAD 

MTI 

' 

~ --·----------------....... __.._... ........ __. ..... , I I 

I . PROCESSOR ur~n 1111 CHf\fiNEL I I I I . ------l I 

I 

r I MTI ! I CANCELLER : 

t·tTI 

\"lEATHER 

• ~ BACKGROUND I I I I QUANTIZI:R INP IIAS~ t 

A I / D J - CANCELLER I l I I· I 

I I cormiNER/ SELECT I 

I I ANTI-LOG SWITCII 

I 

I : QUAD T' t 

I CMlCELLCR I 

L I __ I _ ___ J HTI HTI 

. LOG/FTC ENHANCER 

--- I 

t__ ______________________ _j 

Figure 3-33 . Processor Unit MTI Channel Block Diagram 

' 

-

MTI 

WEATHER 

BACKGROUND 

MTI 

VIDEO 
clutter components will appear at zero frequency and at integral multiples of 

the radar Pulse Repetition Frequency (PRF), and will be suppressed. 

Staggered PRF is generally employed by radars in the 2.7 to 2.9 GHz band 

to extend the blind speed of the radars. Analog radars typically have two or 

three staggers, while digital radars with their greater stability may have 

more than three staggers. The ASR-8 has a four-stagger system, and the ASR-7 

has a six-stagger system. The analog MTI processors do not have 

Analog-to-Digital (A/D) converters and use delay line cancellers, while 

digital MTI processors have A/D converters and use shift register cancellers. 

The digital shift register cancellers have a much higher stability and do not 

decay in time. The transfer properties of analog and digital MTI cancellers 

can be treated identically with the exception of the quantization noise due 

to A/D conversion, roundoff, and truncation inherent in digital processing. 

In general, the error due to quantization, roundoff and truncation is very 

small, and can be neglected in most cases. 

Both single channel and dual channel (inphase, I; and quadrature, Q) MTI 

processing is employed by radars in the 2.7 to 2.9 GHz band. The single 

channel MTI processors have either analog or digital cancellers, while the 

dual channel MTI processors are all digital. For dual MTI channel 

processing, it is only necessary to analyze one channel since both the I and 

Q channels are identical with the exception of the COHO signal being shifted 

90 degrees and to take into account the transfer properties of the combiner. 

Most radars in the 2.7 to 2.9 GHz band employ both single and double 

stage cancellers. Generally , the radars are operated in the double stage 

canceller mode which provides broader clutter-rejection nulls than the single 

cancellers. Some of the radars in the band also have the capability of 

introducing feedback in the double-canceller mode to improve the velocity 

response of the MTI filter, and thus have several Subclutter Visibility (SCV) 

modes of operation. The various operating modes of MTI cancellers are 

obtained by using the feed-forward coefficients (a 0, a1, a 2) and feedback 

coefficients (bl and b2) in the canceller hardware. For analytical purposes 

the single stage and double stage MTI cancellers with and without feedback 

can be represented in a canonical form as shown in Figure 3-34. TABLE 3-1 

shows the equivalent canonical coefficients for the different modes of 

operation of the MTI cancellers in the ASR-7 and ASR-8 radars. The single 

stage MTI canceller mode is CANC1, and the double stage canceller mode 

without feedback is 1 & 2 CASC. The feedback modes are SCV-25, SCV-30, 

SCV-35, and SCV-40. 

The following is a discussion of the MTI canceller transfer properties 

for the various modes for noise, desired signal, and asynchronous 

interference. A more detailed discussion of the MTI channel transfer 

properties and filter frequency response is given in Appendix C. 

Noise The noise amplitude at the MTI canceller input is Gaussian 

with zero mean. In all pulse radars, the inter pulse period ( 1/PRF) is much 

greater than 1/system bandwidth. Thus the sample of noise taken from the 

3-57 
w 

I 

Vl 

(X) 

ein ao eo 

z-1 

b] al 

z-1 

bz I a 2 

Figure 3-34. Canonical Form of Simulated ASR-7 MTI Canceller 
w 

I 

I.Jl 

\D 

~ 

MTI MODE 

CANC 1 

1&2 CASC 

SCV-25 

SCV-3 0 

SCV-35 

SCV-40 

TABLE J-1 

MTI CANCELLER 'fRANSFER PROPERTIES 

FEED-FORWARD FEEDBACK NOISE GAIN COEFFICIENTS COEFFICIENT ~ 

ao a1 a2 b1 b2 VOLTS dB 

1 -1 0 0 0 .; 2 3 

1/2 -1 1/2 0 0 11.5 1. 76 

1/2 -1 1/ 2 1 1/4 -1/ 2 10.454 - 3 . 42 

1/ 2 -1 1/2 1 - 1 / 2 10 . 6 -2.21 

1/ 2 -1 1/2 3/4 -1/2 /0 . 777 -1.09 

1/2 -1 1/ 2 1/ 2 -1/2 1.0 0 

PEAK INTER- PEAK I 

FERENCE GAIN INR 

VOLTS dB (dB) 

1.0 0 -3 

1.0 0 -1 . 76 

0.50 - 6 . 0 -2.58 

0.50 -6.0 -3.79 

0.62 5 -4 . 08 - 2 . 99 

0 . 75 -2 . 49 -2. 49 
same source at intervals of 1/PRF apart are essentially uncorrelated. Zero 

mean uncorrelated sources add rms . The noise gain of the MTI canceller is a 

function of the feed- forward and feedback coefficients, and therefore is a 

function of the MTI canceller mode . Appendix C contains an analytical 

derivation of the MTI canceller noise gains. TABLE 3-1 shows the MTI 

canceller noise gain for each of the operating modes of the ASR-7 and ASR-8 

radars. 

Since the MTI canceller sums the noise at the input to the canceller 

which has a Gaussian amplitude distribution, the canceller output noise 

amplitude distribution is also Gaussian . Therefore, the noise amplitude 

distribution at the MTI canceller input and output are Gaussian distributed 

with zero mean. 

Desired Signal For the desired signal (synchronous signal), the 

signal power transfer gain of the MTI canceller without feedback or with 

feedback when averaged over all possible Dopple~ frequencies is the same as 

the noise power transfer gain (see noise gain in TABLE 3-1). Sinc e the noise 

power density is unifor m over the MTI filter, the filter treats both noise 

and signal (on the average) alike. Thus the signal- to-noise ratio (SNR) at 

the MTI canceller output is the same as at the input to the canceller when 

averaged over all doppler frequencies. 

Interfering Signal - For an asynchronous interfering signal, the MTI 

canceller will produce sever al interfering pulses at the canceller output for 

each asynchronous inter fering pulse at the MTI canceller input. These 

interfering pulses at the MTI canceller output are synchronous with the radar 

system (i . e., fall in the same range bin in successive azimuth change 

pulses) . The amplitude and number of pulses produced by each interfering 

pulse are a function of the feed-forward coefficients (a0 , a1 , a 2 ) and the 

feedback coefficients (bland b2), and therefore are a function of the MTI 

canceller mode the radar is operating in. 

For a single stage canceller (mode CANC 1), each interfering pulse 

produces two synchronous interfer ing pulses. For a double stage canceller 

without feedback (mode 1 & 2 CASC), each interfering pulse produces three 

synchronous interfering pulses. When operating in the feedback mode, there 

are more than three pulses out for each interfering pulse. However, by the 

third or fourth pulse, the interfering signal is down below the receiver 

noise level (1 volt) depending on the feedback constants and interfering 

signal level. Appendix C Figure C- 11 and Figures C- 15 through C-20 show 

measured and simulated responses of a MTI canceller to asynchronous 

interference for the various modes of MTI canceller operation. 

The peak interfering signal transfer properties were obtained using a 

combination of analytical and simulation techniques, and are discussed in 

Appendix C. TABLE 3- 1 summarizes the peak interfering signal and peak 

Interference - to- Noise Ratio (INR) transfer properties for each of the MTI 

canceller modes after rectification. 

3- 60 
Recti n er 

The output of single channel MTI canceller circuits are fed to a 

full-wave rectifier in analog radars or a magnitude and scale algorithm in 

digital radars to convert the bipolar video at the canceller output to 

unipolar. The signal-to-noise ratio (SNR) or interference- to-noise ratio 

(INR) at the rectifier or magnitude and scale output is the same as at the 

input . The noise amplitude distribution ~t the full-wave rectifier output 

wi~l be one-sided Gaussian since the noise amplitude at the MTI canceller 

output was Gaussian. The noise amplitude PDF at the rectifier output is 

given by: 

p(v) 

where: 

2 -v2/2o2 

e 

a = rms noise level, in volts 

(3-25) 

The desired signal-plus-noise amplitude distribution PDF at the single 

channel MTI rectifier output for a double stage MTI canceller is shown in 

Figure 3- 35. It should be noted that the rectifier output signal- plus- noise 

amplitude distribution PDF shown in Figure 35 is for the radar operating in 

the staggered mode and the signal averaged over all possible doppler 

frequencies. The PDF shown in Figure 3-35 was obtained by simulation. 

Although the desired signal-plus-noise amplitude distribution PDF is not of 

the nature of a one- sided Gaussian distribution, it is shown in Appendix C 

that the desired signal- plus- noise amplitude distr~bution PDF at the single 

channel MTI rectifier output for a double stage MTI canceller can be 

approximated by a one-sided Gaussian distribution . 

Combiner 

(inphase and quadrature) MTI canceller 

The signal transfer properties of the 

identical to the single channel transfer 

output of each channel is combined in 

The output of dual channel 

circuits are fed to a combin~r. 

inphase and quadrature channels are 

properties previously discussed. The 

the following manner: 

(3-26) 

Circuit implementation to achieve Equation 3-26 in the combineP is complex. 

Often a simplified approximation to Equation 3- 26 is implemented by summing 

the larger vector amplitude with one-half the smaller vector amplitude as 

3 -61 
.ex: ... 

> 

-

0. 

w 

I 

()\ 

N 

4. r-----~~----~-------r------~------~------~------------- RMS Noise Level(o) = 0.25 Volts 

3 ·1\ I I I I I I I I 

2 • 

1. 

Noise Only 

"' S/f = 5 dB 

I . 

10 dB 

I 

S/N = 15 dB 

dB 

4. 5. 6. 7. R. 

VOLTS 

Figure 3-35 . Probability Density Functfon for Noise Only and for 

Signal-Plus-Noise at the MTI Canceller Output for a 

Single Channe l Douhl e Stage Canceller (Simulated). 
1 

I 

shown below: 

R = jrj + jQ/21 if jrj > jQj 

R = IQI + jr/21 if Jrl < jQj 

(3-27) 

The noise amplitude distribution at the combiner output of a dual MTI 

canceller is Rayleigh since the transfer properties of the combiner (Equation 

3-26) are similar to an envelope detector. The desired signal-plus-noise 

amplitude distribution PDF at the dual channel MTI combiner output for a 

double stage MTI canceller is shown in Figure 3-36. It should be noted that 

the combiner output signal-plus-noise amplitude ditribution PDF shown in 

Figure 3-36 is for the radar operating in the staggered mode and the signal 

averaged over all possible doppler frequencies. · The PDF shown in Figure 3-36 

was obtained by simulation. Although the desired signal-plus-noise amplitude 

distribution PDF is not of the nature of a Rayleigh distribution, it is shown 

in Appendix C that the desired signal-plus-noise amplitude distribution PDF 

at the dual channel MTI combiner output for a double stage MTI canceller can 

be approximated by a Rayleigh distribution. 

The fact that dual MTI cancellers have the COHO reference signal of the 

inphase and quadrature channels phase shifted by 90 ·degrees, and the method 

in which the two channels are combined, a signal-to-noise ratio (SNR) 

improvement is achieved over a single MTI channel . The SNR improvement of 

dual MTI channels over a single MTI channel was investigated by Nathanson and 

Luke ( 1972). The SNR improvement of dual channel MTI over a single channel 

MTI for a single pulse is a function of the probability of detection and 

probability of false alarm. Nathanson and Luke show the SNR improvement to 

be between 3 and 13 dB for a single pulse. However, for a desired signal 

target return pulse train of 20 pulses the SNR improvement of a dual MTI 

channel is only about 1.5 dB. For asynchronous interfering signals, the INR 

enhancement of a dual MTI channel over a single MTI channel is approximately 

1 to 2 dB at MDS. 

MTI Log-FTC 

Both the ASR-7 and ASR-8 have digital MTI log circuits. The log circuit 

converts the MTI digital video from a linear value to a base two logarithmic 

equivalent value, when Log-FTC is selected, the video is averaged over 

several range bins and subtraction takes place to eliminate weather clutter 

from the MTI video. In the ASR-8 the averaging, subtraction, and anti-log 

functions are done digitally, and in the ASR-7 the averaging, subtraction, 

and anti-log functions are done analog. The MTI Log-FTC circuit performs the 

same functions as the normal channel Log-FTC circuits, and therefore, the 

hardware can be represented by the same operations as the normal channel 

Log-FTC circuit (see Figure 3-16 ) . The signal processing properties of the 

MTI Log-FTC circuit are also identical to the normal channel, and are 

discussed in the processor unit normal channel section. 

3-63 
w 

I 

"' .c-

~ 

.. 

> 

...... 

0.. 

3. 

RMS Noise Level(a) 0.25 Volts 

Noise Only 

2. 1 f t 1 I I I I I I I 

1. II /\ \ I I I I I I I I 

10 dB 

= 15 dB 

20 dB 

0 . .,.......- >t > I "'>., I ;>, I I ,_,_ I I 

· o. 1. 2. 3. 4. s. 6. 1. a. 

VOLTS 

Figure 3-36 . Probability Density Function for Noise Only and for 

Signal-Plus-Noise at the HTI Canceller Output for a 

Dual Channel Douhle Stage Canceller (Simulated). 

.. 
In the ASR- 8 the log- anti- log circuits are also used to introduce a bias 

for each of the various MTI operating modes so that the MTI channel output 

video noise level remains constant and independent of the operating mode . 

Noise normalization is achieved by scaling the video data by some factor . In 

the MTI channel this is implemented by adding the bias to the video data . 

The video data at this point in the processing is logarithmic; therefore, 

multiplication is accomplished by adding the logarithm of the two numbers. 

Since the scaling involves both adding to and subtracting from the video 

data, the bias values are positive or negative, respectively. 

In the ASR- 7 a rms noise compensation network is used to normalize the 

noise. The rms- noise compensation network consists of a resister divider 

network . Both methods of normalizing the noise will not change the 

signal- to- noise ratio (SNR) or interference- to- noise ratio (INR) at the 

output of the noise normalization networks. 

MTI Enhancer 

The MTI channel integrator (enhancer) circuits are separate but 

electronically identical to the normal channel enhancer circuitry. 

Therefore, the MTI channel enhancer hardware and functions are identical to 

the normal channel enhancer which has been previously described in the 

processor unit normal channel. (See Figures 3- 17 and 3-24 for feedback and 

binary integrator block diagrams, respectively.) The major difference in the 

signal processing properties of the MTI channel enhancer and the normal 

channel enhancer are due to the difference in the statistical characteristics 

of the noise , desired signal, and interference signal at the input of the 

normal and MTI enhancer. The following is a summary of the MTI channel 

enhancer transfer properties for both the feedback and binary integrators 

which are discussed in detail in Appendi~ D. 

Noise The noise at the output of a single channel MTI canceller has 

a one- sided Gaussian amplitude distribution, while the noise at the output of 

a dual channel MTI canceller has a Rayleigh amplitude distribution like the 

normal channel . For the feedback integrator, the signal processing of the 

noise (attenuation, subtraction, and bottom-clipping) will result in a 

slightly different noise gain of the feedback integrator for a radar with a 

single channel MTI canceller than for a dual channel MTI canceller. However, 

this difference can be made small by adjusting the attenuation , subtraction, 

and bottom clipping circuits prior to the enhancer input. For the binary 

integrator the noise level at the integrator output for a single or dual 

channel MTI canceller can be made equal by adjusting the threshold comparator 

level at the input to the binary integrator. The adjustment of the threshold 

comparator as a function of the noise amplitude statistical characteristics 

is discussed in detail in Appendix D. 

Another factor which affects the noise gain of the MTI channel enhancens 

is that the noise is correlated from range/azimuth cell to range/azimuth cell 

due to the MTI cancellers. This correlation of the noise is discussed in 

3-65 
detail in Appendix D. The MTI channel noise correlation affect for a 

feedback integrator was simulated by Trunk (1977) , and found to be 

approximately 1 dB for a single stage MTI canceller and 1.8 dB for a double 

stage MTI canceller. Therefore, the feedback integrator signal-to-noise 

ratio enhancement (SNRE, see Equation 3-22) would be reduced by 1 dB for a 

single stage MTI canceller and 1.8 dB for a double stage MTI canceller over 

the normal channel SNRE due to MT~ noise correlation. 

Desired Signal The desired signal-plus-noise amplitude distribution 

when averaged over all possible Doppler frequencies is shown in Figure 3-35 

for a single channel MTI canceller, and Figure 3- 36 for a dual channel MTI 

canceller. The desired signal enhancement of a feedback or binary integrator 

for a single MTI channel will be significantly less than a dual MTI channel. 

This shou~d be expected when comparing the signal-plus-noise amplitude 

distribution at the MTI canceller output as a function of the signal-to-noise 

ratio (SNR) for the single and dual MTI channels . Compare Figure 3- 35 

(single MTI channel signal-plus-noise amplitude distribution) with Figure 

3- 36 (dual MTI channel signal-plus-noise distribution). 

Interference - As discussed previously in the MTI canceller signal 

processing properties of interference, and in Appendix C, each interfering 

pulse at the MTI canceller input .produces several synchronous interfering 

pulses (i.e., fall in the same range bin in successive azimuth change pulses) 

at the MTI canceller output. The oumber of interfering synchronous pulses at 

the MTI canceller output is a function of the MTI canceller operating mode. 

Because the interference at the MTI canceller output consists of several 

synchronous pulses which occur in the same range bin in successive azimuth 

change pulses, there is potential for the interference to be integrated like 

the desired signal. That i~ the peak interference-to-noise ratio (INR) at 

the MTI channel enhancer output will be greater than the peak (INR) at the 

MTI channel enhancer input . However, since the synchronous interference at 

the MTI canceller output only consists of two or three pulses that are above 

the receiver system noise level (one volt), the interference can be 

suppressed by both the feedback and binary integrators if adjusted properly. 

The capability of the feedback and binary integrators to suppress MTI 

channel asynchronous interference was investigated using a radar simulation 

model (see Appendix E). Three interfering radar sources were 

simulated: ASR-5, ASR-8, .and the AN /FPS-90 . Figures £-3 thrqugh E-5 in 

Appendix E show the respective time waveforms simulated for each of the radar 

interfering sources. Figure 3- 37 shows a simulated single channel MTI 

canceller radar unintegrated output for three interfering sources (ASR-5, 

INR ·= 10dB; ASR-8, INR = 15 dB; and AN/FPS-90, INR = 20 dB), and a 

desired target signal 7 to-noise ratio (SNR) of 20 dB. Figure 3- 38 shows a 

simulated output of a feedback integrator for the feedback integrator iQput 

limit level adjusted improperly (2.0 volts) for the same interference 

condition shown in Figure 3-37. As discussed previously the asynchronous MTI 

channel interference can be enhanced if the feedback enhancer is not adjusted 

properly. Figure 3- 39 shows a simulated output of a feedback integrator for 

the feedback integrator input limit level adjusted at . 34 volts for the same 

3-66 
8 c 

7 . 

6 - :L 

u 

........_ C, 

,_,; 

r-

_j 

0 4 . > ,.., 

J < 

0 

L 

l c 

~~. 

0 < 

Desired 

ASR-5 

ASR-8 

AN/FPS-90 

SNR = 20 dB 

INR = 10 dB 

INR = 15 dB 

INR = 20 dB 

5 MILL!SECGNOS/CM 

Figure 3-37. Simulated MTI Channel (Mode 1 & 2 CASC) Unintegrated 

Radar Output with Interference 

8. 

7 . 

:L 

6. 

u 

" s. 

t-

_j 

~ 4 " 

> 

,.---. 3 . 

2 < 

1 . 

0 . 

o. 

Desired 

ASR-5 

ASR- 8 

AN/FPS-90 

SNR = 20 dB 

INR = 10 dB 

INR = 15 dB 

INR = 20 dB 

5.10.15.20.25.30-35.40.45.50 . 

S MILLiSECO~OS/CM 

Figure 3-38 . Simulated MTI Channel (Mode 1 & 2 CASC) Radar Feedback 

Integrator Output with Interference for the Input 

Limiter Set at 2.0 Volts 

3-67 
L: 

u 

......... 

t-

_j 

0 

> 

...-. 

8 . 

7. 

6. 

5 . 

4 . 

3 . 

2. 

1 . 

o. 

Desired 

ASR-5 

ASR- 8 

AN/FPS-90 r-~r-_,---+---+--

SNR = 20 dB 

INR = 10 dB 

INR = 15 dB 

INR = 20 dB 

o. 5.10.15.20.25.30.35.40 .45 .50 . 

5 MILLISECGNOS/CM 

Figure 3-39. Simulated MTI Channel (Mode 1 & 2 CASC) Radar Feedback 

Integrator Output with Interf erence for the Input 

Limiter Set at 0. 34 Volts 

8. 

Desired SNR = 20 dB 

7. ASR-5 INR = 10 dB 

ASR-8 INR = 15 dB 

L: 

6. AN/FPS-90 INR = 20 dB 

u 

......... 5 . 

t-

_J 

0 4 . 

> 

,.......... 3 . 

2. 

1 . 

o. ~l ul u~ -~ ~l ~l~·fl ~~W~IIW llll Lu J[ ~ JJ ~~ o. 5-10 .15 .20.25.30.35.40.45 .50. 

5 MILLI5ECGN05/CM 

Figure 3-40. Simulated MTI Channel (:Hode 1 & 2 CASC) Radar Binary 

Integr a t or Output with Int er ference 

3-68 
interference condition shown in Figure 3-37. The asynchronous interference 

has been suppressed by the feedback integrator. Measurements made on the 

Stapelton Airport ASR-8 radar in Denver, Colorado, showed that on-tune 

interference levels of 50 dB above the receiver noise level (approximately 

-60 dBm) could be suppressed in the MTI channel so that they did not appear 

on the PPI display. The ASR-8 radar has a feedback integrator (enhancer) and 

dual channel (Inphase and Quadrature) MTI channel processing. Figure 3-40 

shows a simulated output of a binary integrator for the same interference 

condition shown in Figure 3-37. The asynchronous interference has also been 

suppressed by the binary integrator. 

In summary, both the feedback and binary integrators will suppress 

asynchronous interference in the MTI channel. However, if the integrators 

are not adjusted properly, the integrators will enhance the interfering 

signals due to the synchronous interfering pulse transfer properties of the 

MTI cancellers. Therefore, if the integrators are not adjusted properly, 

the interference level will be greater with the integrators on than with the 

integrators off. 

Processor Unit Aligoment/Diyersity Combiner 

Figure 3-41 shows a block diagram of the processor unit 

Ali~nment/Diversity Combiner hardware in the ASR~8. Similar operations are 

performed in the ASR-7. The FAA is modifying the ASR-7 radars for frequency 

diversity. Therefore, the operations shown in Figure 3-41 should also be 

representative of the ASR-7 when modified for frequency dirersity. The 

output of the Alignment/Diversity Combiner is sent to the Norma /MTI gating 

circuits then to the line drivers for distribution to the PPI displays. 

Mil/Normal Alignment 

The MTI and Normal Alignment circuits provide the delay required during 

STAGGER PRF operation to insure that a specific range bin in each PRF period 

occurs at the average PRF. During Non-STAGGER PRF operation, the alignment 

circuits are bypassed and the video has zero delay through the circuits. 

The circuit provides for the alignment of the MTI and Normal video as well 

as the weather background video associated with the MTI and normal channels. 

The Mil/Normal Alignment circuitry does not have any affect on the 

desired signal-to-noise ratio or interference-to-noise ratio transfer 

properties since the circuitry only realigns the video information in time. 

Output 0/A Converter 

The Digital-to-Analog (D/A) converter circuit follows the Mil/Normal 

Alignment processed to convert the realigned MTI and Normal video words to 

an analog voltage. 

3-69 
\..) 

I 

-...J 

0 

NORMAL 

VIDEO 

MTI 

VIDEO 

NORt-11\L 

WEATHER 

BACKGROUND 

MTI 

WEATHER 

BACKGROUND 

t 

NORMAL 

VIDEO 

f-iT I 

VIDEO 

~---------------~ 

PROCESSOR UNIT · 

ALI GNt1ENT /DIVERSITY 

CDr1BINER 

I .. , 

1 MTI/NORMAL OUTPUT I .. I ALIGNMENT D/ A 

I CONVERTER 

I 

I .. ... 

I 4~ . -

I 1lr 1lr ! - WEATHER ' . '! I MTI/ NORMAL BKGDN/ 

WEATHER 

I BACKGROUND 

a _.;, DIVERSI TY 

I . COMBINER 

{ . " r-

(OTHER CHANNEL) I 

,, 

I 

I (OTHER CHANNEL) I 

I 

I 

I 

I 

I 

I 

. . 

I 

'I 

I 

·r .. I 

I 

I 

I 

I 

I 

L~----- --~-----~ Figur e 3- 41. Processor _ Unit Alignn\ent/Diversity Combiner 

Block Diagr am 

NORMAL VIDEO 

MTI VIDEO 
Weather Background/Diversity Combiner 

The weather background/diversity combiner includes both MTI and normal 

combining circuits. After the MTI and Normal video is converted to an 

analog form in the output D/ A converter it is routed to both the master and 

slave channel diversity combiners. Diversity operation involves the 

simultaneous operation of both radar channels to increase the effective 

transmittal power and improve the probability of detection. To prevent 

waveguide breakdown problems, the two transmitted outputs are separated in 

time by 1. 4 ~sec. To sum the signals from the two channels corresponding t o 

the same target, this offset is realigned. A compensating delay line is, 

therefore, placed in the channel pulsed first, which is the master channel, 

thus making the two channels coincident. When two noise signals are su~ed, 

the output rms noise voltage increases by the square root of two. To 

maintain a constant output noise level from the radar, whether operating in 

diversity or single channel mode, a compeqsating attenuator is also included 

in the combiner cir cuit . When operating single channel, this attenuator is 

bypassed. After the combined or single channel video signal leaves the 

attenuator, it is applied to the output amplifier. The video output 

amplifier sums the weather background video and combined (single channel) 

video from the master channel when the weather background is enabled. Only 

the master channel weather background video is used, and it is mixed in 

after diversity combining since only one channel ~s needed to provide 

weather contour information . The output amplifier gain can be adjusted, 

however, the nominal gain is 1.4 for the combined video and 0.5 for the 

weather background video . A balance adjustment is also included in the 

summing amplifier and output amplifier. 

The desired signal- to-noise ratio (SNR) improvement when operating in 

the frequency diversity mode is between 3 and 5 dB (Offi, 1969). The 

interference- to- noise ratio (INR) transfer properties of the diversity 

combiner when operating in the frequency d.iversity mode are a func tion of 

the operating frequency of the interfering radar relative t o the victim 

radar, and the interfering signal pulse width. For the case where the 

interfering signal pulse width is less than 1.4 ~sec, the interfering signal 

will not fall in the same range bin of both channels due to the 1.4 sec 

separation of the transmitted pulses of the t wo channels, and there will be 

approximately a ·3 dB loss in the INR. For the case where the interfering 

pulse is longer than 1. 4 sec (AN / FPS-6, 90; 2 sec; WSR-57, 74S; 4 . 0 sec), 

the interfering signal will fall in the same range bin of both channels, and 

there will be an increase in the INR. The maximum increase in the INR for 

this case is 3 dB which would only occur if the interference level was equal 

in both channels. When operating in the frequency diversity mode if there 

is interference above the noise level in either channel, the interference 

will appear on the PPI display. 

3- 71 
SECTION 4 

ARTS-IliA SIGNAL PROCESSING 

INTRODUCTION 

This section considers the effects of asynchronous pulse interference on 

the FAA ARTS- III Enhancement signal processing and its impact on the radar's 

probability of detection and false alarm. The Automated Radar Terminal 

System (ARTS) III processor presently employed at terminal radar control 

facilities utilizes flight plan information from Air Route Traffic Control 

Centers (ARTCC) and Air Traffic Control Beacon Interrogator (ATCBI) video. 

In addition to providing target reports on transponder aircraft, alphanumeric 

data blocks available for display are continually associated with the 

appropriate aircraft targets by a tracking program. The primary or radar 

video is not processed by the present ARTS-III system. The ARTS-III 

enhancement, referred to as the ARTS-IliA, processes the video target 

information from both the Airport Surveillance Radars (ASR) and the ATCRBS. 

The ARTS-IliA consists of a Radar Data Acquisition Subsystem (RDAS), Beacon 

Data Acquisiti on Subsystem (BOAS), and a Common Processor Subsystem (CPS). 

Primary radar inputs are processed by the RDAS to produce radar reports and 

weather map data, and the beacon inputs are processed by the BOAS to produce 

beacon reports. The CPS correlates radar and beacon reports and transmits 

target and weather reports. Interference effects on the RDAS only are 

considered in this report since it is the portion of the ARTS-IliA which 

processes the 2. 7 to 2 . 9 GHz radar signals. 

The ARTS-IliA is currently scheduled to be operationally deployed at 60 

airports throughout the United States. This is a substantial deployment 

since it involves over 25 percent of the FAA Radar equipped airports in the 

U.S. The first ARTS-IliA operational deployment is scheduled for July 1979 

at Minneapolis, Minnesota. The deployment at each of the remaining 59 

locations is scheduled at every two-month interval after this initial date. 

RADAR DATA ACQUISITION SUBSYSTEM DESCRIPTION 

The RDAS is designed to receive analog video signals from the ASR-4, 5, 

6, 7 , and ARSR-2 radar or digital signals from the ASR-8 or ARSR-3. 

Provisions are made in the RDAS design for processing analog or digital video 

input by a printed circuit board insertion. The function of the RDAS is to 

detect and report aircraft and clutter derived from the search radar. The 

RDAS, as illustrated in Figure 4-1, consists of two functional units, 

referred to as the Radar Extractor (REX) and the Radar Microcontroller (RMC). 

The RDAS/REX simultaneously accepts normal, MTI, and synchronizing signals 

from the radar receiver. 

The REX performs target detection and 

provides target reports and clutter counts 

4-1 

clutter monitor functions, and 

to the RMC. The RMC employs these 
FROM 

f RADAR N 

tJormal Video .. Target Reports 

MTI Video ~ Clutter Counts Targe t Reports ~ • Radar . ~ Radar Az1muth Micro- (Rng , Az , Qual) 

Pre-trigger Extractor Alarms ~ Controller To CPS 

(REX) ~ (RMC) 

ACPs .... N/t\1TI Selection Clutter I·lap ... Parameters ... 

ARPs ~ 

... 

Figure 4- 1 . Block Diagram of Radar Data Acquisition Subsystem 
clutter counts to determine the type video (normal or MTI) and MTI target 

detection threshold for optimum target detection performance. The video 

select and MTI threshold control signals from the RMC are fed back to the 

REX. The RDAS/RMC output provides target reports, including target range, 

azimuth, and report quality, to the Common Processing Subsystem (CPS) . A two 

level clutter map is also provided to the CPS for indication of weather 

conditions. 

A functional description of the REX and RMC follows . Only those control 

functions will be discussed that have a bearing on the interference analysis. 

Radar Extractor 

A simplified block diagram of the Radar 

Figure 4- 2. The function of each unit in 

briefly described in this subsection. 

Yideo Multiplexer Converter 

Extractor (REX) is shown in 

the signal flow path will be 

The video multiplexer converter transforms the MTI and normal video 

received from the radar into a multiplexed serial digital bit stream . The 

multiplexer converter includes analog to digital converters when the RDAS is 

interfaced with ASR- 4, 5, 6 and 7 analog video radars. When the RDAS is 

interfaced with the frequency diversity ASR- 8 radar, in which both frequency 

channels are simultaneously operated, one sample per range bin from each 

channel are received by the REX multiplexer converter. 

Rank Order Detection Process 

The ARTS-IliA employs a rank order detection process to detect target 

hits or pulse returns. The rank order detection process is performed by the 

Rank Quantizer and Hit Processor (see Figure 4-2 ) . Rank order detection is a 

binary detection concept that utilizes a nonparametrical statistical decision 

process . That is, the rank order detector has a distribution free property 

in which the probability of a 1 being generated when no target is present 

(probability of false target hit) is independent of the noise or clutter 

distribution if the samples are from an identical probability distribution 

and statistically independent. Under these conditions the rank order 

detector yields a constant false alarm rate regardless of the environmental 

clutter level. The operation of the rank order detector involves comparing 

the amplitude sample of the range or target bin of interest with the sampled 

noise and clutter levels in adjacent range bins over each Azimuth Change 

Pulse (ACP). The number of cases that the amplitude of the target sample 

exceeds adjacent range samples is defined as the rank of the target sample. 

If this rank exceeds or equals a rank threshold, a target hit (logical 1) is 

generated, otherwise a miss (logical 0 ) is generated. 

Rank Quantizer. The rank quantizer portion of the REX (see Figure 4-2) 

computes the rank of the range bin, and the hit processor unit compares thi s 

rank with a threshold to determine if a target hit has occurred. A 

4-3 
Clutter 

r1oni tor 

~ j~ 

Normal t-1TI 

~ ~, 

Norma l .. Video Rank Hit Target Output To RMC 

t1TI [Multipl e xer ~ Quantizer ~ Processing • Detection H =- .. Buffer 

Con verter 

~ 4~ 

~ 

' 

""" Thresholds 

N/'1TI Selection .l Fr 

Display Display r-

- Video - D1sp . 1 ay V1 'd eo Se l . ect1on J Rt-1 ..,. V1.deo r-. Selection .... 

om 

c 

Figure 4-2 . Block Diagram of Radar ~xtractor 
simplified block diagram of the rank quantizer portion of the rank order 

detector is shown in Figure 4-3. The digital range bin samples enter a 27 

stage shift register, in which delays between adjacent shift register stage 

taps correspond to the time resolution of the range bins. The signal 

amplitude in the range bin of interest (S14) from the center tap of the shift 

register is compared with the signal amplitude (usually noise) in the range 

bins before (S1 -S12 ) and after (S16-S27 ) the range bin of interest. Signal 

samples from range bins S13 and S15 immediately adjacent to the range bin of 

interest are not compared with the range bin of interest to prevent long 

target pulses from overlapping both target and adjacent range bins and being 

interpreted as noise samples. The comparators (Ci) associated with each 

range bin outputs a one if the signal in the bin of interest (S14) is greater 

than the compared to range bin (S1-S12 and S16-S27). The comparator outputs 

are summed to obtain a rank (0- 24) of the range bin of interest. It should 

be pointed out that the actual rank quantizer utilized in the REX is slightly 

more complicated than that indicated in Figure 4-3, because the rank 

quantizing processing is performed on a serial stream of interlaced normal 

and MTI bits. However, the logic depicted in Figure 4- 3 is identical for 

both the normal and MTI channels. 

Hit Processor. The block diagram of the hit processing logic is shown 

in Figure 4-4. The input consists of a five bit rank value from the rank 

quantizer. The rank data is processed simultaneously in two paths to produce 

target and clutter hits respectively . If the rank value in the upper path 

equals or exceeds a rank quantizer threshold (typically 23 or 24) a target 

hit is generated and a logical 1 assigned to the range bin of interest. That 

is, if the signal amplitude in the range bin of interest has exceeded the 

voltage level in all but one of the 24 adjacent reference range bins or all 

24 of the adjacent reference range bins, depending on which rank quantizer 

threshold setting is used, a target hit is generated. If the rank does not 

exceed the rank quantizer threshold, a miss is generated and a logical 0 

assigned to the range bin of interest. In the lower path (see Figure 4-4), 

if the rank exceeds or equals a rank quantizer threshold of 17, a clutter hit 

is generated and a logical 1 assigned to the range bin of interest. In other 

words, for a clutter hit to be declared the signal amplitude in the range bin 

of interest has to exceed 17 of the 24 adjacent sample range bins. This rank 

quantizer threshold testing in the upper and lower channel of the hit 

processor provides the last phase in the rank order detection process. Both 

the target and clutter hit paths include demultiplexers after the rank 

quantizer threshold comparators to separate out the normal and MTI digital 

signals. The normal or MTI target hits are selected for further target 

detection processing by a feedback control signal from the RMC . The 

selection is based on the normal clutter hit data provided by the hit 

processing logic. Basically, normal is selected in light clutter and MTI in 

heavy clutter conditions. A normal or MTI video selection is made for each 

32 azimuth change pulse (ACP) by 32 range bin (RB) zone. This represents 

approximately a 2 . 8 degree by 2 nmi zone. The normal and MTI clutter hit 

information used for the normal/MTI target hit selection is routed to the RMC 

through the clutter monitor unit and output buffer (see Figure 4-2). 

4-5 
.c-. 

I 

C1' 

ADJACENT HANGE BINS 

Sl S2 Sl2 I Sl3 

C1 

c. • { lif S14> Si 

1 o 1f s14 c s. 

1 

RANGE BIN OF 

INTEREST ADJACENT RANGE RING 

Sl4 Sl 5 SL6 

Te 24 ANK = E C. 

i=l 1 

( 0- 24) 

Figure 4-3. Block Diagram of Ra nk QuaniLzer Logic 

S26 527 {

27 ftage 

Shift 

R0.gister 

I I 

( COMPAHA'fORS 

-
From 

Rank --

.z:-. Quantizer I 

-...J 

Compare 

.-.f R ~ RQTT • 

t RQT T : 2 3, 2 4 

RQTc : 1 7 

l 

Compare 

~ R ~ RQTC .. 

N/riTI 

Demux 

N/HTI 

Demux 

MTI 

N 

f'1TI 

N 

__., 

. 

_.. 

. 

N/NTI 

Selection 

Selected 

Target 

Hits 

Clutter Hits 

Figure 4-4. Block Diagram of Ilit Processing Logic 

.. 

• 

To 

Target 

Detection 

To 

Clutter 

Monitor 
Target Detection 

The target detection stage in the REX is shown in Figure 4-2 and the 

details of the software functions in Figure 4-5. The target detection 

software logic first correlates the hit and miss data received from the hit 

processor unit with the appropriate range bins. A record of the target hits 

(1) and misses (0) in azimuth for a given range bin is initialized and 

maintained when a target hit is generated. When the consecutive misses 

(zeros) in the record equals or exceeds a miss count threshold (typically 3 

or 4), the accumulated sum of the target hits since the beginning of the 

record is examined. If the target hit count equals or exceeds the hit count 

threshold, a target is declared. For the normal radar channel the target hit 

count threshold is fixed (typically at 8 or 9) and the MTI channel is 

variable. The MTI hit target count threshold is increased from the normal 

channel threshold value up to 20 depending on the degree of pulse-to-pulse 

correlation of the clutter. When a target is declared, the hit/miss record 

is terminated. The record is also terminated under the following two 

conditions: 

(1) The miss count threshold is exceeded but the hit count threshold 

is not. 

(2) The record length (number of ACPs) reaches 30 and the consecutive 

miss count and hit count threshold are not satisfied. 

The target hit/miss record is extended beyond 30 ACPs if the hit count 

threshold is satisfied, but the miss count threshold is not. In this case, 

the hit and consecutive miss count is continued until the target detection or 

record termination criteria is met. 

Clutter Monitor Logic 

The function of the clutter monitor logic, shown in Figures 4-2 and 4-6, 

is to count ''isolated hits" over 32 range bin (RB) blocks in both the normal 

and MTI channel, and output these counts to the RMC. Isolated hits are those 

preceded and followed by a miss (010 pattern) over a 3 ACP (pulse 

transmission) sequence in azimuth at a fixed range. The "isolated hits" (010 

hit/miss pattern) are detected by the 3 stage shift register, inverters, and 11 and gate 11 logic shown in each video channel in Figure 4-6. The counters 

following the "and gate" count the number of isolated hits that occur over 

the 32 RB's. If more than 15 isolated hits occur in a 32 RB interval, a 

maximum count of 15 is outputted. 

Radar Micro Controller 

The Radar Micro Controller (RMC) is a digital data processing device 

that uses a microprogrammed control structure, involving microinstructions 

and control data stored in a read only memory (ROM). This RMC firmware 

controls the data flow between the REX and RMC and formats the RDAS output 

data. The RMC receives normal and MTI channel Isolated Hit Sum (IHS) data 

4-8 
J:-

1 

"' 

Hiss Hit 

Count Count 

Selectee\ Target Hit 

Hit Samples Range _.. 

.. . Update Record Correlation Hiss From llit .. • .. Processing Logic 

Miss Threshold , .. 

'"': 

Target Target R~por ~ 

Hit Threshold Detection ------ -- ___. 

From RMC 

Figure 4-5 Block Diagram of Target Detection 
~ 

I 

1-' 

0 

From 

Rank 

Quantizer 

Normal 

Clutter 

Hits 

t1TI 

Clutter 

Hits MTI 

-11 

Counter 

32 RC 

Reset 

32 RC 

Reset: 

ISOLATED . • I 

HITS - +1 

Counter 

Figure 4-6 Block Diagram o f Clutter Monitor Logic 

4 Bit 

Count 

4 Bit 

Counter 
from the REX clutter monitor. The normal channel IHS clutter data is used by 

the RMC to select the optimum video (normal or MTI) for tar get detection 

processing, and the MTI channel IHS clutter data to adjust the MTI target 

detection criteria (target hit count threshold) . The first paragraph below 

discusses the RMC control processing associated with the video selection, and 

the second paragraph the RMC control processing associated with the MTI 

target detection threshold control . 

The RMC receives normal channel IHS clutter data in 32 RB blocks and 

forms a clutter map of IHS's in 32 RB by 32 ACP zones. The sum of the normal 

video isolated hits for the zone on the previous antenna scan is used to 

update a clutter zone on the current antenna scan . The magnitude of the 

updated clutter count represents the level of clutter returns and is used to 

derive the video select command for the zone. The following criteria is used 

to update the zone clutter count and arrive at a video select decision . If 

the IHS for the 32 RB x 32 ACP zone on the previous antenna scan is greater 

than a variable clutter count threshold (typically 166), the clutter count 

shall be incremented by 1. If the IHS is less than or equal to this 

threshold value, the clutter count is decremented by 1. If the resulting 

clutter count exceeds 7, the MTI channel is selected. Conversely, if the 

clutter count is less than or equal to 7, the normal channel is selected. 

Basically normal video is selected in light or zero clutter zones, and MTI 

video is selected in heavy clutter zones. 

When MTI video has been selected, the RMC controls the MTI video target 

hit threshold to maintain a constant false alarm rate . Unlike noise hits, 

the amplitude of pulse-to-pulse c lutter returns are often correlated which 

results in a higher probability of false alarm. The rank order detection 

process is only partially effective in maintaining a constant false alarm 

rate for these conditions, since it only accounts for first order statistics 

(average number of independent hits) of the clutter distribution. The RMC 

uses the MTI channel clutter IHS measured by the c lutter monitor logic to 

determine the degree of pulse- to-pulse correlation. The RMC maintains a 32 

RB (2 nmi) by 32 ACP (2 . 8 degrees) sliding window of MTI cumulative IHS . The 

32 RB blocks of MTI channel IHS received from the clutter monitor logi c are 

added to the sliding window's cumulative sum , and the 32 RB block IHS 

received 32 ACPs before subtracted . The current sliding window cumul ative 

sum is u~ed to derive the MTI channel target hit count threshold. The target 

hit count threshold is linearly increased from the normal channel threshold 

value with decreasing values of sliding window IHS ' s in the manner indicated 

in Figure 4-7. This type of functional control tends to maintain a constant 

false alarm by increasing the hit count threshold for a high pulse-to- pulse 

amplitude correlated clutter or equivalently a low IHS count . 

ARIS- IIIA BOAS INTERFERENCE ANALYSIS 

The ARTS- IliA RDAS interference analysis involved determining the effect 

of radar asynchronous interference on the victim radar' s probability of false 

alarm and target detection . This involved applying a combination of 

analytical and simulation techniques. 

4-11 
0 

N 

--------+-----

O!OHS8~Hl 1NOOJ liH I1W 

4-12 

C"J 

a-

...... 

" ..c 

,-... 

v: 

....... 

=-:: 

:::> 

v: 

,._.. 

H 

= 

0 

w 

,..... 

< ,..l 

0 

U) 

,...... 

~ 

0 

~ -< 

~ 

c.:> 

z 

...... 

0 

....... 

.....J 

U) 

'"' 0 

'-' 

...... 

0 

.... '"' 

c: 

0 

u 

"0 

........ 

9 

V'. 

'll 

.c '"' " ,..... .... 

...J 

<1) 

~ 

c 

::l E 0 

u '"' Cll 

....... .... < .,.. 

;::c <li 

1/) 

....... ....... ~ <1) 

c ~ 

c 

!il 

.c c: v r:l 

...J 

V'. 

E- ::: ;:: 0 

u U) 

< :1) 

0 

~ c.c ........ c: < .... ........ c: ,..... . .... ,..... Cil I .... U) c ,..... ..... ~ Cil 

< =-:: 

,..._ 

I 

" 

<ll 

'"' ::l 

co 

..... 

~ 

,_ 
In particular, the effect of interference on the probability of a false 

target hit and target hit detection was, defined analytically for worst- case 

interference signal level conditions, and then related to probability of 

false ruarm and target detection by simulation of the processors target 

detection criteria . This method of analysis was performed for all 

combinations of ARTS- IIIA/RDAS target detection par ameters so that trade-offs 

between interference suppression and radar performance could be investigated. 

The effect of interference on the ARTS- IIIA/RDAS automatic video selection 

and MTI hit count threshold control was analyzed using statistical and 

probability theory. Those interference and target signal level conditions 

which maximized the effect of interference were assumed in the analysis . 

This worst- case approach allowed analytical techniques to be employed instead 

of the more time consuming complete ARTS- IIIA/RDAS hardware simulation. The 

rationale for this decision was that if a worst- case analysis indicated that 

asynchronous interference would not significantly affect the ARTS- IIIA/ RDAS 

performance a complete hardware simulation would not be necessary . 

The two victim radars considered were the ASR- 7 and ASR- 8 interfaced 

with the ARTS- IIIA/RDAS processor. The interfering type radars considered 

included the ASR- 7, ASR- 8, AN/CPN- 4, AN/FPS- 90 , and WSR-57. However, the 

analysis results ar e applicable to other type interfering radars in the 2.7 

to 2.9 GHz band that have the same pulse width and pulse repetition frequency 

range . 

Effect of Interference on the Probability of a Hit 

The following is a discussion of the impact of interference on the RDAS 

rank order detection process which includes the rank quantizer and hit 

processor. A general equation is presented to determine the effect of 

interference on the probability of a hit (logical 1) when noise, desired 

signal, or clutter are in the range bin of interest . The effect of 

interference on the probability of a hit when noise, desired signal, or 

clutter is present in the range bin of interest is a function of the 

probabilHy of a hit (logical 1) when noise only is present (Pn1 ), 

probability of a hit when noise and desired signal only are present (P5 1), 

and the probability of a hit when noise and clutter only are present (Pel), 

respectively. For purposes of deriving a general equation for all the above 

conditions, a general term (Pl ) will be used to represent a hit for P0 1, 

P51, and Pel · The specific equation for P0 1 , P51 , and Pel will then be 

derived in later subsections. 

Asynchronous interfering radar video pulses can affect the probability 

of a hit at the hit processor output in two ways. First, an interfering 

radar pulse falling in the rank quantizer range bin of interest increases the 

probability of a hit (logical 1) being generated. Second, an interfering 

pulse falling in the rank quantizer comparison range bins decreases the 

probability of a hit . This is because an interference pulse falling in one 

or more of the comparison range bins lowers the probability of the voltage 

level in the r ange bin of interest exceeding the comparison range bin levels. 

4- 13 
Both the above described interference mechanisms can be accounted for in a 

simple equation if it is assumed that the interfering signal-plus-noise level 

at the input to the RDAS is always greater than the target return 

signal-plus-noise level. If it is also assumed that the random arrival of 

interfering radar pulses in time can be described by a Poisson probability 

distribution, the effect of interference on the probability of a hi t 

occurring is given by: 

where 

(4-l) 

1~ Probability of a logical 1 or hit being generated with 

interference present 

P1 ~Probability of a logical 1 or hit being generated with 

no interference present 

N = Indi c ator variable which takes into account the radar 

channel connected to the ARTS-IIIA/ RDAS (N = 1 for 

Normal and N = 3 for MTI channel ) 

x1 = Time interval that interfering radar pulse overlaps 

sample time of the rank quantizer range bin of interest, 

in seconds 

x2 = Time interval that interfering radar pulse overlaps the 

sample time of the rank quantizer comparison range bins, 

in seconds 

v = interfering pulse arrival rate, in pulses per second 

The first factor in Equation 4-1 accounts for the probability of the 

interfering pulse falling in the rank quantizer range bin of interest. The 

second factor (e-NX2v) in the equation gives the probability of no 

interfering pulses falling in the comparison range bins since this is a 

necessary requirement for a logical 1 or hit to be generated. A detailed 

derivation of Equation 4-1 and justification of the assumptions is given in 

Appendix F. 

The variable N in Equation 4- 1 is set equal to 3 for the MTI channel 

because there is a high probability that one i nterfering pulse at the input 

of the double MTI canceller circuit (feed forward mode ) input will produce 

three synchronous interfering pulses at its output. This implies that the 

probability of an interfering pulse falling into a given rank quantizer range 

bin is actually equal to the probability of it falling in that range bin for 

any one of three ACPs (present and two previous ACPs). 

The values of X1, and x2 , in Equation 4-1 depends on the interfering 

radar pulse width ( T1) and victim radar range bin characteristics. In 

particular, the victim radar range bin width in time (RBw), range bin sample 

4- 14 
time (RB8 ), and range bin hold time (RBH), have to be considered. The value 

of x1 for a given range of interfering radar pulse widths is defined by: 

T. +RB 

1 s xl = o (4 -2) 

for the indicated interfering pulse width ranges. The value of x2 also 

depends on the rank quantizer threshold setting. The value X2 for a rank 

quantizer threshold {RQT) of 23 is given by: 

22( Ti - RBH) for RBH<Ti<(RBw+RBH) 

24RBw for Ti>(RBw+RBH) 

(4- 3) 

and for a RQT of 24 by: 

24RBw +2(Ti- RBH) for RBH<T i <(RBw+RBH) 

26RB for T. > (RB +RBH) w 1 w 

(4-4) 

Equations 4- 2, 4-3, and 4-4 were derived graphically by assuming the 

interfering pulses to be perfectly square shaped and of constant amplitude . 

Effect of Interference on Probability of False Alarm 

A false alarm is defined as the declaration of a target when a t arget is 

not ac tually present. For a false target to be declared, a sequence of false 

hits ( logical 1) due to noise or interference must first be generated by the 

hit processor in the same range bin in adjacent ACPs, and the target 

declaration hit and miss count threshold in the target detec tion soft ware 

equaled or exceeded. TherefJre, to analytically determine the probability of 

a false alarm, the probability of a false hit at the hit processor output for 

noise and interference must first be addressed and then be applied t o the 

target declaration hit and miss count threshold. The last portion of this 

subsection discusses the operational interpretation of the probability of 

false alarm caused by noise and interference on the ARTS-IliA . 

Probability of False Target Hit Caused by Noise 

The effects of noise (no interference present) on the probability of a 

false target hit (logical 1) at the hit processor output can be expressed as: 

= J-RQT+l 

J+l 

4- 15 

(4 - 5) 
where 

J = The number of rank quantizer comparison range bins (24) 

RQT = Possible rank quantizer threshold settings (23 or 24) 

For RQT=24, Equation 4- 5 indicates a 0.04 probability that the noise level in 

the range bin of interest will exceed the noise level in all 24 comparison 

range bins. Similarly, for RQT=23, the equation gives a 0.08 probability 

that the noise level in the range bin of interest will exceed at least 23 of 

the 24 bins. Sufficient conditions for Equation 4-5 to hold are that the 

probability distributions for all of tRe bin samples be identical and 

independent. Under these statistical conditions, the rank order detection 

technique maintains a constant probability of false target hit for varying 

levels of noise and clutter. Equation 4-5 indicates this fact by being only 

a function of hardware parameters. 

Probability of False Target Hits Caused by Interference 

In order to determine the effect of interference on the probability of 

false target hit, the probability of a false target hit due to noise only 

must also be considered since the noise is always present in the RDAS. 

Therefore, the probability of a false target hit (logical 1) at the hit 

processor output due to interference (Pil) is obtained by substituting 

Equation 4-5 (probability of target hit due to noise, P0 1) in Equation 4-1, 

whi ch after algebraic simplification gives: 

(4-6) 

For a rank quantizer threshold (RQT) of 23 Equation 4-6 becomes: 

p il (23) = { 0 . 92 [N(l-e -X~ v) -1)+1} e -NX2J V (4-7) 

and for RQT 24 

pil (24) = { 0. 96[N(l- e-Xlv)_lj+l} E:!-NX24v (4-8) 

The X1 , X23• and X24 are defined by Equations 4-2, 4-3, and 4-4, 

respectively, and evaluated for various interfering and victim radar 

combi nations in TABLE 4-1. The probability of a false target hit as a 

function of the interfering signal pulse arrival rate ( v) was computed for 

each interfering and victim radar combination , using Equations 4-7 and 4-8, 

and the X1, X23, X24 values indicated in TABLE 4-1. The results of these 

calculations are indicated in Figures 4-8 through 4-15. The graphs in 

4-16 
~ 

I 

1-' 

...... 

INTERFERWG 

RADAR TYPE 

ASR- 7 

ASR-8 

A::/CP~-4 

AN/FPS- 90 

~.'SR 57 

ASR-7 

ASR-8 

At~/CP~-4 

AN/FPS-90 

!SR. 57 

TABLE 4-1 

TIME INTERVALS ~T INTERFERI NG RADAR PULSES OVERLAP 

THE RANK QUANTIZER RANGE BI N SAMPLE TntES FOR 

VARI OUS COHBINATI ONS OF INTERFERING AND VICTIM RADARS 

I NTERFERING VICTIM x1 I N s x23 IN 11s 

PULSE \HDTH RADAR (RQT K 23 , 24) (RQT = 23) 

(Tj) lN ~s 

0 . 833 ASR- 7 0 . 989 8 . 030 

0.600 ASR-7 o. 756 2. 904 

0. 500 ASP - 7 0 . 656 o. 704 

2.000 ASR-7 2 . 156 15 . 000 

4.000 ASR-7 o.ooo 15 . 000 

0 . 833 ASR-8 0 . 999 11 . 726 

0 . 600 ASR-8 0 . 766 6 . 600 

0 . 500 ASR-8 0 . 666 4.400 

2. 000 ASR-8 0 . 000 11 . 208 

4.000 ASR-8 0 . 000 11 . 208 -- ---------- ---

NOTE: 1. VI CTIM RADAR 

RAI\t.E BIN 

CHARACTERISTICS 

ASR-7 : RBw = 0. 625 ~~ . RB5 • 0.156 ~s , RBH • 0.468 us 

ASR- 8 : RBw • 0 . 467 u~ , RB5 • 0 .166 ~s , RBH • 0 . 300 ~s 

2. RQT ~ RANK QUANliZER THRESHOLD 

x24 IN us 

(RQT c 24) 

15 . 730 

15 . 264 

15 . 064 

16 . 250 

16.250 

12 . 142 I 

11 .808 

11 . 608 

12 . 14 2 

12. 14 2 
10. 

(S) 

(S) 

-

X 9. 

tH 

~ 

AN/CPN-4 AN/FPS- 90 

j - t 

(!) e. 

0:: 

< 

tw 

(/) 

..J 1· 

<C( 

lL.. 

ASR-8 

ASR-7 

-...___ ~ 1----1----"""'- WSR- 57 

--r---_ 

lL.. 

0 

>- s. 

t-

~ H 

CQ 

<C( 

CQ s. 

0 

~ 

0... 

4. 

o. 2000. 4000. 6000. 8000. 10000. 12000. 

rNTERFERENCE RATE JN PULSES/SECOND 

Figure 4-8 . ARTS- IIIA/RDAS Probability of False Target Hit Versus 

Rate of Received Interference (ASR-7 Victim Radar, 

Normal Channel , Rank Quantizer Threshold 23) 

4-18 

.. 
B. 

{Q 

<S) . ....-

X 

tH 

:I: 

~ (!) 

~ 

<t 

tw 

(/) 

_J 

ct 

u... 

tL 

a 

>- tH 

_J 

H 

co 

< co 

a 

~ 

Q.. 

7-

6. 

s. 

4. 

3. 

2. 

o. 

~>.N t¢- _...-:--

~ ~ 

~ ~ ASR- 7 

_l 

--...._ AN/CPN-4 , ASR- 8 

I --- WSR - S 7 ,....._ 

2000. 4000. 6000. 8000. 10000.12000. 

fNTERFERENCE RATE IN PULSES/SECOND 

Figure 4-9 . ARTS-IIIA/RDAS Probability of False Target Hit Versus 

Rate of Rc~eivcd Interference (ASR- 7 Victim Radar , 

Normal Channel , Rank Quantizer Thr eshold 24) 

4-19 
X 

tH 

J: 

~ 

10. 

9. 

C..r:J 8 0:: • 

< lw 

(I) 

~ 7. 

t&... 

LL. 

0 

>- s·. lH 

_J 

H 

en 

< 

~ s. 

0:: 

0.. 

4. 

ASR-7 

o. 2000. 4000. 60()0. 800(). 10000.12000. 

rNTERFERENCE RATE JN .PULSES/SECOND 

Figure 4-10. ARTS-IIIA/RDAS Probability of False Target Hit Versus 

Rate of Received Interference (ASR- 7 Victim Radar , 

MTI Channel, Rank Quantizer Threshold 23) 

4-20 

.. 
8. 

Q 

Cs:J 

-

X 

7- tH 

:X: 

tJ 

{!) 6. Ck:: 

< ' 

tw 

(f) 

_J s. 

< u.. 

u.. 

0 

>- 4. tH 

_J 

H 

(0 

< en 3. 0 

~ 

Q., 

~ 

p..N/FPS-90 

v v----

/ 

L 

v 

ASR-7 

I 

~ ASR-8 

I - ~ ANICPI\'-4 -

~ 

~ 

~ r?

~ 

- 57 

2. 

o. 2000. 4000. 6000. 8000. 10000.12000. 

rNTERFERENCE RATE JN PULSES/SECOND 

Figure 4-11 . ARTS-IIIA/RDAS Prob~bility of False Target Hit Versus 

Rate of Received Interference (ASR-7 Victim Radar, 

HTI Channel , Rank Quant izt:r Threshold 24) 

4-21 
10. 

~ 

~ ... 

X 9. 

~ 

H 

:I: AN/CPN-4 

t;j a. 

(!) 

CY. 

< 

tw 

(f) 7-

ASR-8 

-----r------ ASR-7 

r------ FPs- ~~ 

90 I 

_J 

< u._ 

lL 

a 6. 

>-

tH 

_J 

H 

co 

<t 5. 

en 

0 

~ 

a.. 

4. 

o. 2000. 4000. 6000. 8000. 10000. lZOOO. 

rNtERFERENCE RATE JN PULSES/SECOND 

Figure 4-12. ARTS-IIIA/RDAS Probability of False Target Hit Versus 

Rate of Received Interference (ASR-8 Victim Radar, 

Normal Channel, Rank Quantizer Threshold 23) 

4-22 
a. 

~ 

~ 

-

X 7. 

tH 

:I: 

tJ 6. 

(!) 

~ 

~ 

tw 

(/) s. 

_J 

< lL ASR- 7 

lL ASR-8 

a 

4. 

>- tH 

AN/CPN 4 

AN/ FPS- 90 I 

l·J.s .L 57 

_J 

H 

co 3. cl; 

en 

a 

a:: 

a_ 

2. 

a. 2000. 4000. 6000. 8000. 10000. 12000. 

rNTERFERENCE RATE JN PULSES/SECOND 

Figure 4-13 . ARTS-IIIA/RDAS Probability of False Target Hit Versus 

Rate of Received Interfer ence (ASR- 8 Victim Radar, 

Normal Channel, Rank Quantizer Threshold 24) 

4-23 
10. 

(!~) 

~ 

-

X 9. 

tAN/CPN- 4 

H 

::I: . ~ ASR- 8 

tJ ' a. (~ 

ct; 

< tw 

en 7· . _J 

< lJ... 

lJ... 

0 6. 

>-

tH 

_. 

~ r----~ 

~ ~ 

~ N/pp .s .... 9o 

H 

co 

~ s. < co 

a 

~ 

a.. 

4. 

o. 2000. 4000. 6000. 8000. 10000. 12000. 

fNTERFERENCE RATE JN PULSES/SECOND 

Figure 4- 14. ARTS-IIIA/RDAS Probability of False Target Hit Versus 

Rate of Received Interference (ASR-8 Victim Radar, 

MTI Channel, Rank Quantizer Threshold 23) 

4-24 
8. 

(S) 

(g 

- 7. 

X 

tH 

J:. 

t 6. 

{!) 

~ 

~ 

rw s. 

(/) ASR-7 

--1 

~ 

u.. 

u... 

0 4. 

>- rH 

--1 

H 

CQ 3. ~ 

CQ 

0 

-----== 

---- AS~-8 

~ I 

1\~/CP~J 4 _ 

--.._____ ~ ~ r-----_ ANJpps -9o 

~ 

r'ls 

~ 

a.. 

2. 

o. 2000. 4000. 6000. 8000. 10000. 12000. 

rNTERFERENCE RATE IN PULSES/SECOND 

Figure 4-15. ARTS-IIIA/RDAS Probability of False Target Hit Versu s 

Rate of Received Interference (ASR-8 ~ictim Radar , 

HTI Channel, Rank Quantizer Threshold 24) 

4- 25 
F)gures 4-8 through 4- 11 are for the ART~~IIA/RDAS interfaced to the ASR-7, 

and Figures 4-12 through 4-15 the AR~$-IIIA interfaced to the ASR-8 . In 

addition, the graphs consider the ARTS- IIIA/ RDAS connected to both the normal 

and MTI channel. The family of curves on each graph represent various 

interfering radar types. However, the curves are applicable to other 

interfering radar types· in the 2 . 7- 2. 9. GHz band that have the same pulse 

widths. The interfer)ng radar pulse wid~os corresponding to the various 

radar types is g1 ven j n Appendix G. The 4. 0 \J s pulse width mode of the 

WSR- 57 · was used for calculation of the curves. The even numbered figures are 

for RQT=23 and the odd number for a RQT=24. The interference rate of zero 

value on each curve represents the probabi~1ty of a false target hit due to 

only no1se. It 1s evident from the ~~aphs that the probab111ty of false 

target hit 1s more affected for a rank quant1zer threshold sett1ng of 24 than 

23 . In addition, interference has a greater impact on the RDAS when 

connected to the MTI than the normal chanPel . This is due to the generation 

of several synchronous interfering pulse ~ by the MTI cancellers in the 

pr1mary radar (see Section 3 and Appendix C). 

The data represented by the curves in Figures 4-8 through 4-15 were 

reduced to the form shown 1n TABLES 4-2 through 4-5 to indicate the effect of 

a particular number and type of interfer)ng radars on the probability of 

false target hit. TABLES 4-2 and 4- 3 represent data for the ARTS- IIIA/ RDAS 

interfaced to an ARS-7 radar that is receiv1ng interference from one and 

three radars, respectiv~ly. Sim11arly, TABLES 4-4 and 4-5 give the 

probability of false target hit when the ARTS-IIIA/RDAS is connected to an 

ASR-8 victim radar. The interfering pulse arrival rate (v ) in TABLES 4-2 and 

4-4 are simply equal to the interfering radar average pulse repetition 

frequency (PRF), and 1n TABLES 4-3 and 4-5, 3 times tr.e interfering radar 

PRF. 

Probability of False Alarm Caused by Interference 

The decision in regard to the presence of a target is accomplished by 

the target detection software functions shown in Figure 4-5. The details of 

th1s target detection processing 1s g1ven in the RDAS desc ript1on sect1on of 

this report . Basically, a count of hits (log1cal 1's) ana c onsecutive m1sses 

(log1cal O's) are ma1ntained in az1muth for a given range bin. If the 

consecutive miss count equals or exceeds a miss count threshold and the h1t 

count equals or exceeds a hit count threshold, a target js declared. 

A computer program was wrHten to calculate the probabllity of false 

alarm as a functlon of false target hit probability The program employs 

a comb1nat1on of simulation and analytical methods. The details of this 

program are given in Appendix F, and the results of the calculat1ons are 

shown in Figure 4-16. The probabil1ty of false alarm versus probab)lity of 

false target hit for various combinations of detection parameters js shown. 

It is evident from the curves in Figure 4-16 that holding the miss c ount 

threshold constant and decreasing the h1t count threshold increases the 

probability of false alarm. This result 1s reasonable when one considers 

that a sequence of hits and misses is a set of Bernoulli trials. Since the 

4- 26 
_r,-

1 

1\J 

" 

TABLE 4- 2 

ARTS-IIIA/RDAS PROBABILITY OF FALSE Tl\RGET IIIT WilEN 

CONNECTED TO ASR-7 RADAR THAT IS R,ECEIVItlG 

INTERFERENCE FROM ONE RADAR 

VICTT~I INTERFERING PROBABILITY OF 

RADAR INTERFERING RATE v FALSE TARGET HIT 

CHANNEL RADAR PULSES/SEC (RQT=23) 

NOR.~L ASR-7 1002 0 .08026 

NORMAL ASR-8 1040 0. 0804 8 

NORHAL AN/CPN- 4 1192 0. 08065 

NOIU-tAL AN/FPS- 90 356 0. 08027 

NOJU-1AL HSR- 57 166 0 .07980 

l'ITI ASR- 7 1002 0. 08076 

MTI ASR-8 1040 0. 08143 

TI AN/CPN-4 1192 0. 08195 

Nil AN/FPS-90 356 0. 08077 

NTI \-ISR-57 166 0.07942 

----

NOTE : RQT = RANK QUANTIZER THRESHOLD 

PROBABILITY OF FALSE TARGET HIT FOR RQT 23 AND NO INTERFERENCE = 0.08 

PROBABILITY OF FALSE TARGET HIT FOR RQT 24 AND NO INTERFERENCE = 0 . 04 

PROBABILITY OF 

FALSE TARGET HIT 

(RQT=24) 

0 .04031 

0.04011 

o. 04002 

o. 04049 

0 .03989 

0 . 04087 

o. 04030 

0 . 04003 

0.04143 

0 . 03932 

I 
J>-

1 

..., 

00 

. VICTIM 

RADAR 

CHANNEL 

NORHAL 

NORMAL 

NORMAL 

NORMAL 

NQRMAL 

HTI 

MTI 

HTI 

t-1TI 

-. 

MTI 

TABLE 4-3 

ARTS- IIIA/RDAS PROBABILITY OF FALSE TARGCT HIT WHEN 

CONNECTED TO ASR- 7 RADAR THAT IS RECEIVING 

INTERFERENCE FROH THREE RADARS OF THE SAME TYPE 

INTERFERING INTERFERING PROBABILITY OF PRO'B'AB!'LITY OF 

RATE v FALSE TARGET HIT FALSE TARGET HIT RADAR PULSES/SEC (RQT=23) (RQT=24) 

ASR-7 3006 0 . 08076 0. 04087 

· ASR-8 3120 0 . 08143 0. 04030 

AN/CPN-4 3576 0.08194 0 . 04003 

AN/FPS- 90 1068 0 . 08081 0 . 04148 

WSR-57 498 0 . 07941 0.03968 

ASR-7 3006 0. 08203 0.04213 

ASR-8 3120 o. 08418 0 . 04055 

AN/CPN-4 3576 0.08582 0 . 03976 

AN/FPS-90 1068 0.08229 0.04424 

WSR-57 498 0.07824 0 . 03905 

NOTE : RQT = RANK QUANTIZER THRESHOLD 

PROBABILITY OF FALSE TARGET HIT FOR RQT 23 AND NO INTERFERENCE = 0 . 08 

PROBABILITY OF FALSE TARGET HIT FOR RQT 24 AND NO INTERFERENCE- 0.04 

i 

I 
~ 

I 

N 

<0 

VICTH1 

RADAR 

CHANNEL 

NOIU-!AL 

NOIU-tAL 

NOIU-1AL 

NORMAL 

NORMAL 

~1TI 

MTI 

HTI 

~ITI 

HTI 

TABLE 4- 4 

ARTS- IIIA/RDAS PROBABILITY OF FALSE TARGET HIT WHEN 

CotlNECTED TO ASR-8 RADAR THAT IS RECEIVING 

INTERFERENCE FROr-1 ONE RADAR 

INTERFERING INTERFERING PROBABILITY OF PROBABILITY OF 

RADAR RATE v FALSE TARGET HIT FALSE TARGET HIT 

PULSES/SEC (RQT=23) (RQT=24) 

ASR-7 1002 0.07998 0 .04046 

ASR- 8 1040 0.08018 0.04027 

AN/CPN-4 1192 0 . 08031 0 .04144 

AN/FPS-90 356 0. 07968 0 .03983 

\<ISR-57 166 0 . 07985 0. 03989 

ASR-7 1002 0 . 07990 0. 04134 

ASR-8 1040 0 . 08052 0.04076 

AN/CPN-4 1192 0. 08090 0.04056 

AN/FPS-90 356 0. 07906 0.03949 

WSR-57 166 0.07956 0.03976 

NOTE: RQT = RANK QUANTIZER THRESHOLD 

PROBABILITY OF FALSE TARGET HIT FOR RQT 23 AND NO INTERFERENCE= 0.08 

PROBABILITY OF FALSE TARGET HIT FOR RQT 24 AND NO INTERFERENCE = 0.04 

I 

I 

I 
.c1 

v.> 

0 

TABLE 4-5 

ARTS-IIIA/RDAS PROBABILITY OF FALSE TARGET HIT 

WHEN CONNECTED TO ASR- 8 RADAR TfiAT IS RECEIVING 

INTERFERENCE FROM THREE RADARS OF THE SAME TYPE 

VICTIM INTERFERtNG PROBABILITY OF PROBABILITY OF 

RADAR INTERFERING RATE v FALSE TARGET HIT 

CHANNEL RADAR PULSES/SEC (RQT=23) 

NORMAL ASR-7 3006 0 .07989 

NORMAL ASR-8 3120 0 .08052 

NORMAL AN/CPN-4 3576 0 . 08090 

NORMAL AN/FPS-90 1068 0 .07904 

NORMAL WSR-57 498 0.07956 

MTI ASR-7 3006 0. 07942 

MTI ASR-8 3120 0.08140 

MTI AN/CPN-4 3576 0.08244 

MTI AN/FPS-90 1068 0. 07718 

MTI WSR-57 498 0.07868 

NOTE: RQT = RANK QUANTIZER THRESHOLD 

PROBABILITY OF FALSE TARGET HIT FOR RQT 23 AND NO INTERFERENCE= 0.08 

PROBABILITY OF FALSE TARGET HIT FOR RQT 24 AND N0 INTERFERENCE = 0 . 04 

FALSE TARGET HIT 

(RQT=24) 

0. 04134 

0 .04076 

0.04056 

0.03948 

. 0.03976 

.. 

0.04359 

0. 04200 

0 .04136 

0.03848 

0. 03929 

I 

I 
~ ~ 

U) 

~ ~ 

~ 

0 

>'4 

H 

H 

,....:l 

H 

~ iXl 

~ p.. 

/ 

/ 

/ 

/ 

/ 

\). 

/ 

/ / / 

~ +GI / 

~/ // 

/ // cy /" / 

1o- 6 

/ ?~ // " / 

/ /£ v f'!~ · ~'? / ~G ~ , ./ 

/ f / ?(() / 

/ //v~ / 

/ //~ / 

l o- 7 

j // / 

/ // v~ ~ 

I f ~ 

~ 

G 

~ , jJ f 

/ . / 

// 

II / 

II / 

10- 8 f :/ 

L 

L 

/ 

/ 

I 

I 

I 10- 9 

0.04 0 . 05 0.06 0.07 0 . 08 0.09 0 .10 

PROBABILITY OF FALSE TARGET HIT 

Fi gur e 4-16 . ARTS-IIIA/RDAS Probability of False Alarm Versus 

Pr obability of False Target Hit for Various Hit/Hiss 

Count Threshold Parameter Combinations 

4-31 
probability of a given sequence is the product of the individual event 

probabilities, there is a higher probability that the number of noise hits in 

the sequence will satisfy a lower hit count threshold than a high one. 

It is also evident from the curves in Figure 4-16 that raising the 

consecutive miss count threshold, while maintaining a constant hit count 

threshold increases the probability of false alarm. Since there is a higher 

probability of a miss occurring than a hit, due to noise, it is more likely 

that 4 consecutive misses will occur than 3 consecutive misses and one hit. 

The probability of false target hits due to interference shown in TABLES 

4-2 through 4-5 were related to the probability of false alarm for a 

particular hit and miss count threshold by the curves in Figure 4-16. The 

resulting probability of false alarm values are shown in TABLE 4-6. The 

probability of false alarms are for the most likely ARTS- IIIA/RDAS parameter 

settings that will be used in the field: 

1. Rank Quantizer Threshold (RQT) = 23 

2. Hjt Count Threshold (HCT) = 9 

3 . Miss Count Threshold (MCT) = 3 

FAA personnel at NAFEC who have thoroughly tested the ARTS-IliA are 

recommending these detection parameter settings ~e used for optimum 

performance. In addition, this parameter combination was found in this study 

(see section on Trade-Off between Interference Suppression and ARTS-IIIA/RDAS 

Performance) to be near optimum for interference suppression. 

The probability of false alarm without interference (4.596x1cr7 ) is 

shown at the bottom of TABLE 4-6 . This number corresponds to a probability 

of false target hit (0.08) for no interference and a rank quantizer threshold 

of 23. It is evident from TABLE 4-6 that interfacing the ARTS-IIIA/RDAS to 

the ASR-7 radar usually results in a higher probability of false alarm than 

when interfaced to an ASR-8 . A higher probability of false alarm also 

results when the ARTS-IliA is connected to the MTI channel than the normal 

channel. The highest probability of false alarm for interfering and victim 

radar combinations occurred for the AN/CPN-4 and ASR-7 . This is because the 

AN/CPN- 4 radar has a higher PRF than any other interfering radar considered. 

In addition, the probability of an AN/CPN-4 radar pulse falling into a rank 

quantizer comparison range bin and preventing a hit (logical 1) from being 

generated by the hit processor is low. This is because the difference 

between the AN/CPN-4 pulse width (Ti = O.Sus) and victim radar range bin hold 

time (RBH=0.468us for ASR-7 versus 0.300us for ASR-8) is small. It can be 

seen from Equation 4-3 that a small (<i-RBH) results in a low value of x23 and therefore from Equation 4-6 a high probability of false alarm. 

All probability of false alarms for the WSR-57 (<i=4.0 us mode) in TABLE 

4-6 are less than for no interference. This is because the WSR- 57 wide pulse 

width cannot overlap the rank quantizer range bin of interest without 

4-32 
.s::-

1 

w 

w 

TABLE 4-6 

ARTS-IIIA/RDAS PROBABILITY OF FALSE ALARN FOP. TYPICAL DETEC~ION 

PARAMETERS AND VARIOUS COt1BINATIONS OF INTERFERING AND VICTI~l RADARS 

NUMBER 

VICTIM VICTIM INTERFERING ASR-7 

RADAR RADAR RADARS OF Tf•0 . 831JS CHANNEL SAl-lE TYPE 

PRF•l002 

ASR-7 NORMAL 1 4.914 x Io-7 

ASR-7 NO~IAL 3 5.524 x 107.7 

ASR-7 HTI 1 5.524 X ]0-7 

ASR-7 MTI 3 1 . o75 x 10-1 

ASR-8 NORMAL 1 4.589 X 10-7 

ASR-8 NORMAL 3 4.562 X 10-7 

ASR-8 ~!TI J 4.565 X 10-7 

ASR-8 MTI 3 4.417 X 10-7 

NOTE : 1. ARTS-IIIA/RDAS TYPICAL TARGET DETECTION PA~~ETERS 

RANK QUANTIZER THREBSOLD s 23 

HIT COUNT THRESHOLD x 9 

HISS COUNT THRESHOLD • 3 

ASR-8 

--Tf=Q.601JS 

PRF•l040 

5.182 x Io-7 

6.342 X 10-7 

5.182 X 10-7 

9.699 x 10-7 

4.816 X 10-7 

5.231 X 10-7 

5.231 X 10 -7 

6.305 X 10 -7 

2 . PROBABILITY OF FALSE ALARM WITHOUT INTERFERENCE • 4.596 x 10-7 

INTERFERING RADAR TYPE 

AN/CPN-4 AN/CPN-4 

ti•0.51JS t 1•2.01JS 

PRFcll92 PRF=356 

5.390 x 1o-7 4.926xlo-7 

6.965 X 10-7 -7 5.585 X 10 

6 . 977 X 10-7 5.536 X 10 -7 

11.702 X 10-7 1.392 x 10-7 

4 . 975 X 10-7 4.497 X 10-7 

5.695 X 10- 7 4. 299 X 10-7 

-7 5. 695 X 10 4.305 X 10-7 

7.575 X 10-7 3 . 723 X 10-7 

WSR-57 

---

J Ti~4.QIJS 

PRfs166 

4.534 x 1o-7 J 

4 .41) X 10-7 

4.417 X 10-7 I 

4.051 x 1o-7 

4.550 X 10-7 

4 . 460 X 10-7 

4 . 460 X 10-7 

4.187 X 10-7 
overlapping many comparison range bins. Consequently, there is a very low 

probability of the range bin of interest having a higher interference signal 

level than the comparison range bins, which precludes generation of a hit . 

Interoretation of Interference Effects on False Alarms 

The probability of false alarms shown in TABLE 4-6 can be related to the 

approximate number of false alarms (false target detection indication on the 

PPI) per antenna rotation by: 

PRFxT FA = PFA x M x K 

where 

PFA = Probability of false alarm 

(4-9) 

M = Number of range bins in victim radars radial coverage 

( 1200 for ASR-7 and 1607 for ASR-8) 

PRF = Victim Radar Pulse Repetition Frequency (1002 for ASR-7 

and 1040 for ASR-8), in pulses per second 

T = Victim Radar Antenna Rotation Time (5 seconds assumed 

for ASR-7 and ASR-8) 

K = The average number of azimuth change pulses (ACPs) since 

initial hit for a probability of false alarm to occur 

The average number of ACPs (K) for a false alarm to occur was determined 

from the program used to compute the probability of false alarm as a function 

of the probability of a false target hit. The resulting values of K for 

possible hit and miss count thresholds are given in TABLE 4-7. The 

probability of false alarms listed in TABLE 4-6 are for a hit and miss count 

threshold of 9 and 3, respectively. Therefore K=17 was used in Equation 4- 9 

to relate TABLE 4-6 false alarm probabilities to false alarms per antenna 

rotation. Evaluating Equation 4- 9 for the false alarm probability without 

interference (4.596x1o-7 ) and the maximum false alarm probability listed in 

TABLE 7-6 for interference ( 11. 702x1o-7) for an ASR-7 victim radar indicates 

that the number of false alarms per antenna rotation can increase from 0 .1625 

to 0.41383. This corresponds to an approximate increase from 2 to 5 false 

alarms every 12 antenna rotations, or 1 additional false alarm every 4 

antenna rotations. It should be pointed out that this result reflects 

extreme worst-case interference conditions. That is, three radars 

simultaneously and continually interfering over the entire antenna rotation 

period, and a worst-case interfering radar and victim radar channel 

combination. 

NTIA noted in its 1975 Los Angeles area radar interference measurements 

(Hinkle, 1976) that FAA radars did not receive interference from more than 

4-34 
TABLE 4-7 

AVER.r'\G:C NUHI3:CR OF AZH1UTH CIIA~GE 

PULSE SINCE INITIAL HIT FOR A FALSE 

ALARM TO OCCUR 

HIT COUNT MISS COUNT AVERAGE NO . 

THRESHOLD THRESHOLD OF ACPS FOR PFA 

(HCT) (MCT) TO OCCUR (K) 

8 3 15 

8 4 18 

9 3 17 

9 4 21 

4-35 
one radar at a given time. In addition, interference coupling in all 

measurement cases were caused by antenna mainbeam-to- mainbeam or antenna 

mainbeam-to-backlobe coupling and resulted in interference occurring only 

over small sectors of the PPI. The maximum false alarm probability listed in 

TABLE 4-6 for one interfering radar and the ARTS-IliA connected to the MTI 

channel is 6.977x1o-7. 

From Equation 4-9, this corresponds to an increase in false alarms pe~ 

antenna rotation from 0 . 1625 to 0.2463, or one additional false alarm every 

12 antenna rotations. If interference is received over less than 50 percent 

of the antenna rotation, due to a single radar or combination of radars 

interfering one at a time, only one additional false alarm would occur every 

24 antenna rotations. It is therefore concluded that present radar 

interference conditions in congested terminal areas of the U.S . would not 

significantly affect the ASR-7 or ASR-8 probability of false alarm when these 

radars are interfaced to the ARTS-IIIA/RDAS. 

The hit count threshold of 9 used in the false alarm analysis 

corresponds to only the lowest hit count threshold value that the MTI channel 

can have at any given time . As discussed in a previous section and described 

in Figure 4-7, the MTI channel hit count threshold is increased from 8 to a 

maximum of 20 depending on the degree of clutter correlation. The 

probability of false alarm versus probability of false target hit curves in 

Figure 4-16 have nearly the same slope regardless of the hit count threshold. 

Therefore, it is reasonable to assume that an increase in the MTI target hit 

count threshold would not result in interference having any greater impact 

than indicated in TABLE 4-6. 

Effect of Interference on Probability of Target oetection 

The following discusses the impact of interference on the RDAS 

probability of target detection. The probability of target detection is 

defined as the probability of declaring a target when the target is actually 

present. For a target to be declared, a sequence of hits (logical 1) due to 

target return pulses must be generated by the hit processor in the same range 

bin for adjacent ACPs, and the target declaration hit and miss count 

threshold in the target detection software satisfied. Therefore, to 

analytically determine the probability of target detection, the probability 

of a target hit at the hit processor output for the target and interference 

signal are first determined, and then related to probability of target 

detection through simulation of the target detection criteria. The last 

portion of this subsection discusses the interpretation of the results. 

Probability of Target Hit Caused by a Target 

The probability of a logical 1 occurring at the Hit Processor output 

when a target is present is defined as the probability of a target hit and 

derived in Appendix F to be: 

4-36 
- +oof ! (J) K J-K Psl(J,RQT)- ~ K [F(v)] (1-F(v)] d[G(v)] 

-"" K=RQT 

(4-ll)) 

where 

v :: Voltage level , in volts 

J :: Number of rank quanti zer comparison range bins (24) 

RQT :: Rank quantizer threshold (23 or 24) 

F(v) :: Statistical cumulative distribution for noise 

G(v) :: Statistical cumulative distribution for signal - plus- noise 

The probability of target hit (PTH), unlike the probability of false target 

hit, is dependent not only on the distribution of noise but also the signal -

plus- noise distribution. Equation 4-1 0 gives the probability of the target 

range bin (range bin of interest with target in it) having a voltage level 

greater than at least RQT of the surrounding J comparison range bin noise 

samples. These noise range bins are assumed to each have the same cumulative 

distribution F(v). The particular distributions for F(v) and G{v) depends on 

the rad~r channel (normal or M7I) connected to the ARTS-IIIA/RDAS . 

Normal Channel . The noise distribution at the radar normal channel 

output (before integrator) is Rayleigh distributed (Skolnik , 1962) and given 

by: 

F(v) 

2 

-v / 2 1-e (4-1 1) 

Where v is a sample of the voltage amplitude . The cumulative distribution 

for signal-plus-noise at the radar normal channel output is given by the Rice 

distribution (Skolnik, 1962): 

G(v) 

v 

= J 

0 

t e I (t/z · SNR) dt 

0 

t :: Dummy variable of integration 

SNR :: Signal - to- noise voltage ratio 

10 = Modified Bessel function of the first kind and of zero order 

Substituting F(v) and G(v) into Equation 4-10 gives: 

-f-ooJ 

p sl (J' RQT) = J l: ( J) (1-e ° K=RQT K 

2 v 

'l K .. ) (e 

2 

v 

2 J-K 

) 

4-37 

2 

v +?. • Sl\TR 

2 

v e I (vi2·SNR) dv 

0 

(4-13) 
For a rank quantizer threshold (RQT=23) and range bin sample number (J=24 ) , 

Equation 4- 13 becomes: 

2 2 

-f 23 - f 

P 51 (24, 23) '"' 24 j (1- e ) (e )v e .,/ 

2 

v -- 24 

+ j Cl-e 2 ) 0 

2 

v +2·SNR 

2 

v e 

2 

v +2·SNR 

2 

I (vh · SNR) dv 0 

I (v.h · SNR) dv 

0 

EvaluaUon of Equation 4- 13 for a rank quantizer thr eshold of 24 

2 2 v 24 v +2 · SUl co -2 2 I•

51 (24,24) = /(1-e ) v e I (vi2·SNR) dv 

0 0 

(4-14) 

gives: 

\4- 15) 

The two above integral equations were evaluated for various signal - to- noise 

ratios (SNRs) using a Fortran numerical integration routine. The resulting 

curves are shown plotted on probability paper in Figure 4- 17. The 

probability of target hit curves for RQT=23 is higher than for RQT =24 because 

there is a higher probability of the signal - plus- noise level in the target 

range bin exceeding 23 range bin noise samples than 24 . Since the 

distribution of noise and signal - plus- noise out of the ASR- 7 and ASR- 8 radar 

normal channel are identical, the curves in Figure 4- 17 apply to an 

ARTS- IIIA/RDAS connected to either an ASR- 7 or ASR-8 radar ~ormal channel . 

MTI Channel. The ASR- 7 has a single channel MTI canceller, and the 

ASR- 8 has a dual (Inphase and Quadrature) MTI canceller. The probability of 

a target hit with the ARTS-IIIA/RDAS connected to these circuits was computed 

by the following form of Equation 4-10 . 

P (J ,RQT) = 51 f (4-16) 

where d[G(v)]/dv is the signal-plus-noise amplitude distribution PDF. 

The noise only amplitude distribution PDF at the output of the ASR- 7 MTI 

channel is a one-s~ded Gaussian and described by Equation C- 40. Therefore, 

the noise only cumulative distribution js given by: 

2 v ::> 2 

F(v) = -- J ev-/2o dv 

127To 0 

2ERF(v) 

4- 38 
. 9999 

. 9990 

. 9950 

. 9900 

. 98 

. 95 

. 90 

f-< 

H . 80 ::t: 

f-< 

w . 70 l.? 

0.:: 

< 

f-< . 60 L:... 

c . 50 

:>" 

f-< . 40 H 

.....:l 

~ . 30 

< co 

0 

c:: . 20 

p.. 

. 10 

II 

17 

II 

v; 

7 v 

II 

II 7 

~ o; 

V/ 

/ / 

// 

// 

.,--/ v/ 

~ v 

. 05 

. 02 

. 01 

. 005 

. 002 

. 001 r I I ' , , l \ I T -r I I 

-3 0 5 10 15 

SJGNAL-TO·-t:OJSE RATIO IN dB 

Figure 4-17 . Probability of Target Hit Versus Signal-to-Noise Ratio for the 

ARTS-IIIA/RDAS Connected to the ASR- 7 or ASR-8 Radar Normal 

Channel (Rank Quantizer Threshold 23 and 24) 

4-39 

I 

20 
where ERF(v) is the mathematical error function. The signal - plus-noise 

amplitude distribution PDF was determined from actual ASR-7 radar MTI channel 

simulations and is shown in Figure C- 21. The probability of a target hit 

occurring was computed by substituting Equation 4- 17 for F(v) in Equation 

4-16, and the density distribution data obtained from simulations for 

d[G(v))/dv in Equation 4- 16 . Equation ~-16 was then evaluated for various 

signal -to-noise ratios (SNR ' s) using Fortran error function and numerical 

integration routines. The resulting probability of target hit versus 

signal-to- noise ratios are shown plotted on probability paper in Figure 4-18. 

The noise only amplitude distribution PDF 

output is Rayleigh distributed and given by Equation 

noise only cumulative distribution is given by: 

- v

2 /2cr2 

F(v)= 1 - e 

at the ASR- 8 MTI Channel 

D-1 5. Therefore, the 

(4- 18) 

As in the case of the ASR-7 MTI channel, the ASR-8 MTl channel was simulated 

to determine its output signal - plus- noise amplitude distribution PDF. The 

resulting density function, shown in Figure C- 23 , was substituted for 

d[G(v)]/dv in Equation 4- 16. Similarly, Equation 4-1 8 was substituted for 

F(v) in Equation 4- 16. Equation 4-16 was then evaluated for various 

signal - to- noise ratios (SNR ' s) by a numerical integration routine. The 

resulting probability of target hit versus signal-to- noi3e ratios are shown 

plotted in Figure 4- 19. The RMS noise voltage level (o) was set at 0 .25 

volts for the calculation , since this corresponds to the one volt peak noise 

level usually set at the radar receiver output . 

Interference Effect on Target Hit 

A 0.7 probability of target hit was chosen for a zero interference 

reference base in the analysis. It will be shown later in this section that 

this probability of target hit results in a worst-case interference effect on 

probability of target detection. It is evident from Figures 4-1 7, 4- 18 , and 

4- 19 that a 0 . 7 probability of target hit and RQT=23 corresponds to a 

signal -to: noise ratio of approximately 6 dB for the ARTS- Ill/RDAS connected 

to the normal channel, 12 dB for the ASR-7 MTI channel, and 7 dB for the 

ASR-8 MTI channel . The effect of interference on the probability of false 

target hit can be determined from Equation 4-1. As discussed earlier, for 

worst-case interfer ing signal level assumptions Equation 4-1 defines the 

effect of interference on a hit (logical 1) caused by either noise or 

signal - plus- noise . Substituting 0.7 for Pr in Equation 4- 1 and evaluating it 

for various interfering pulse arrival rates (v) , gives the curves shown in 

Figures 4-20 through 4- 27. The graphs in Figures 4- 20 through 4-23 are for 

4-40 
.. 

.9999 ~------T------------T------------~-----------r-----------, 

9990 +-------+------------+------------+-----------~-----------1 

9950 ~------+-----------~------------+------------+----------~ 

9900 ~------~------------~------------~------------~----------~ 

. 98 

. 95 

. 90 

f-1' 

~ . 80 

f-1 t5. 70 

~ f-1 • 60 ~ 

0 .50 

>-' 

~ . 40 

.....:l 

~----~----------+-~- ~ ~~~~----------~--------~ 

H 

~ . 30 ~ 

0 

~ . 20 

. 10 

.05 

. 02 

. 01 

. 005 

. 002 

. 001 I 

-3 0 

/V 

I f I I • I I I I I I I I 

5 10 15 

SIGNAL- TO-NOISE RATIO IN dB 

Figure 4-18 . Probability of Target Hit Versus Signal- to-Noise Ratio for the 

ARTS- IIIA/RDAS Connected to the ASR- 7 Radar HTI Channel 

(Rank Quantizer Threshold 23 and 24) 

4- 41 

20 
.9999 

. 9990 

. 9950 

. 9900 

. 98 

. 95 ~ 

E-' 

r-1 

::X:: 

Col 

t::J 

t:> 

0:: 

~ 

8 

~ 

0 

>-< 

8 

H 

....:I 

H 

r:!1 

~ 

r:!1 

0 

0:: 

0.. 

.90 

. 80 

. 70 

. 60 

. 50 

.40 

. 30 

L_ . 20 

. 10 v . 05 

. 02 

.01 

. 005 

. 002 

. 001 

- 3 0 

~ v 

~ ~ ., 

~ 

L./ 

L ~L 

/L v 

// . 

/ 

I o I I ' ' ' . ' ' ' ' 5 10 15 

I~TO-OO SE RATI O IN dB 

Figure 4- 19. Probability of Target Hit Versus Signal- to- Noise Ratio for the 

ARTS-IIIA/RDAS Connected to the ASR- 8 Radar !~I Channel (Rank 

Quantizer Threshold 23 and 24) 

4- 42 

20 
70. 

(g 

(g 65. 

-

X 

tH 

~so. 

tJ 

C!) 

0:: 

4( 

...... ss. 

LL 

0 

~ ...J so. -

~ m 

0 

cr 

a. 45. 

40. 

o. 

.., 

AN/CPN- 4 

ASR- 8 

2000. 4000. 6000. 8000. 10000. 12000. 

INTERFERENCE RATE tN PULSES/SECOND 

Figure 4-20. ARTS-IIIA/RDAS Probability of Target Hit Versus Rat e 

of Received Interference (ASR- 7 Victim Radar , Normal 

Channel, Rank Quantizer Threshold 23) 

4-43 
0 

0 

... 

70. 

ss. 

40. 

o. 2000. 4000. 6000. 8000. 10000. 12000. 

rNT£RFERENCE RATE IN PULSES/SECOND 

Figure .4-21 . ARTS-IIIA/RDAS Probability of Target Hit Versus Rate 

of Received Interference (ASR-7 Victim Radar, Normal 

Channel, Rank Quantizer Threshold 24) 

4-44 
0 

0 

-

70. 

65. 

X 60. 

t:: 

:I: 

ti 

~ ss. 

~ 

LL. 

0 

~so. 

d 

~ m 

0 45. 

0:: 

a. 

40. 

o. 2000. 4000. 600(). 8000. 10000. 12000. 

rNTERFERENCE RATE IN PULSES/SECOND 

Figure 4-22. ARTS-IIIA/RDAS Probability of Target Hit Versus Rate 

of Received Interference (ASR-7 Victim Radar, 

MTI Channel, Rank Quantizer Threshold 23) 

4-45 
0 

0 

..-

70. 

65. 

X 60. 

t:: 

:1: 

ti 

~ ss. 

~ 

L&. 

0 

~so. 

d 

~ aJ 

0 45. 

0: 

a. 

40. 

o. 2000. 4000. 6000. 

fNTERFERENCE RATE IN PULSES/SECOND 

Figure 4- 23. ARTS-IIIA/RDAS Probability of Tar get Hit Versus 

Rate of Received Interference (ASR- 7 Victim Radar, 

MTI Channel, Rank Quantizer Threshold 24) 

4-46 

o. 
70. 

(g 

(g 65. 

-

X 

1-

H 

:I: 60. 

t 

(!) 

0:: 

~ 

1- ss. 

LL. 

0 

...J 

~ so. 

~ m 

0 

cr 

a. 45. 

40. 

o. 

""" ~ .I r--- AN/CP'N- 4 - ~ "'-

r-----~ 4sJ?_1 

~I-go 

~ 

. . 

-

2000. 4000. 6000. 8000. 10000. 12000. 

rNTERFERENCE RATE rN PULSES/SECOND 

Figure 4-24. ARTS-IIIA/RDAS Probability of Target Hit Versus 

Rate of Received Interference (ASR-8 Victim Radar, 

Normal Channel, Rank Quantizer Threshold 23) 

4-47 
70. ~ 

~ 

0 

0 

-

65. 

X 60. 

t:: 

:I: 

40. 

o. 

~ llo.. 

A.sR-J ~ A.SJ? -a A.N/pp • A.f.l/cp 8-9o 'N-4 , "'sR -sl ~ 

~ 

2000. 4000. 6000. 8000. 10000. 12000. 

rNTERFERENCE RATE IN PU~S/SECOND 

Figure 4- 25. ARTS-IIIA/RDAS Probability of Target Hit Versus Rate 

of Received Interference (ASR-8 Victim Radar, Normal 

Channel, Rank Quantizer Threshold 24) 

4-48 
0 

0 

-

70. 

65. 

X 60. 

c 

:I: 

~ 

~ ss. 

~ 

u.. 

0 

~so. 

d 

~ aJ 

a 45. 

0! 

a. 

40. 

o. 2000. 4000. 6000. 8000. 10000. 12000. 

rNTERFERENCE RATE JN PULSES/SECOND 

Figure 4-2 6. ARTS-IIIA/RDAS Pr obability of Target Hit Versus 

Rate of Received Interference (ASR-8 Victim Radar, 

MTI Channel , Rank Quantizer Threshold 23) 

4-49 
0 

0 

.... 

70. 

65. 

X 60. 

t:: 

:I: 

ti 

~ ss. ~ 

1.&.. 

0 

~so. 

d 

~ m 

0 45. 

0:: 

a. 

,o. 

o. 2000. 4-00D. 6000. 8000. 10000. 12000. 

INTERFERENCE RATE JN PULSES/SECOND 

Figure 4- 27. ARTS-IIIA/RDAS Probability of Target Hit Versus 

Rate of Received Interference (ASR-8 Victim Radar, 

MTI Channel, Rank Quantizer Threshold 24) 

4-50 
the ARTS-IIIA/RDAS interfaced to the ASR- 7, and Figures 4- 24 through 4-27 

interfaced to the ASR-8. The graphs also account for the radar channel 

(normal or MTI) that is connected to the ARTS-IIIA/RDAS. The family of 

curves on each graph represent various interfering radar types. The even 

numbered graphs are for RQT=23 and the odd number graphs for RQT:24. The v =O 

value on each curve gives the probability of a target hit (0.7) without 

interference present. The same factors (interfering radar pulse width and 

PRF, and victim radar range bin characteristics) which affected the degree of 

interference impact on the probability of false target hit also applies to 

the probability of target hit. However, tqe probability of target hit 

decreased with interference, while in most cases the probability of a false 

target h~t increased. This is because the probability of target hit (P1 in 

Equation 4-1) is much greater than the probability of an interference pulse 

falling in the range bin of interest (1-e-Xl~ in Equation 4-1). Under these 

conditions, Equation 4-1 can be approximated by: 

P.l J.. 

P -NX2v 

le (4-19) 

It is evident from this expression that the probability of hit can only 

decreas~ with increasing v~lu~s of v. 

The data representing the curves in Figures 4-20 through 4-27 were 

reduced to the form shown in TABLES 4-8 through 4-11 to indicate the effect 

of a particular number and type of interfering radars on the probability of 

target hit . TABLES 4-8 and 4-9 represent data for an ARTS-IIIA/RDAS 

interfaced to an ASR-7 radar that ~s rece1v1ng interference from one and 

three radars, respectively. Similarly, TABLES 4-10 and 4-11 gives the 

probability of target hit when the ARTS-IIIA/RDAS is interfaced to an ASR-8 

radar that is receiving interference. The interfering pulse arrival rate ( v) 

in TABLES 4-8 and 4-10 are simply equal to the average PRF of the interfering 

radar. In TABLES 4-9 and 4-11, v is equal to three times the PRF of the 

interfering radar. The probab1lity of target hit values listed in TABLES 4-8 

through 4-11 indicate that connecting the ARTS-IIIA/RDAS to the MTI channel 

results in a lower probability of target hit than when connected to the 

normal channel. This is because N in Equation 4-19 is 3 for MTI and only 1 

for normal channel . In other words, the probability of an interference pulse 

falling in a rank quantizer comparison range bin and precluding generation of 

a hit (logical 1) is greater for the MTI channel. 

Interference Effect on Target Detection 

The decision to declare a target is accomplished by the target detection 

software fupctions shown in Figure 4-5~ The details of this target detection 

processing is given in the RDAS Subsystem Description section of this report. 

A computer program was written to determine the probability of target 

detection as a function of probability of target hit. The program involves 

4- 51 
~ 

I 

Vl 

N 

VICTIH 

RADAR 

CHANNEL 

NORMAL 

NORMAL 

NORMAL 

NOR.t-1.AL 

NORHAL 

MTI 

MTI 

MTI 

~1TI 

MTI 

TABLE 4-8 

ARTS-IIIA/!1Dl\S PROBABILITY OF Tl\RGI:T HIT NHEN 

CONNECTED TO ASR-7 RADAR TIIAT IS RECEIVING 

INTERFERENCE FOID4 ONE RADAR 

INTERFERlNG PROBABILITY OF 

INTERFERING RATE v TARGET IIIT 

RADAR PULSES/SEC (RQT = 23) 

ASR-7 1002 0. 69lt7 

ASR-8 10lt0 0 . .6981 

AN/CPN-lt 1192 0.6996 

. 

AN/FPS-90 356 0. 6965 

WSR-57 166 0. 6983 

ASR-7 1002 0.68lt2 

. ASR- 8 lOltO ·0 .69ltlt 

AN/CPN-lt 1192 .o .6989 

AN/FPS-90 356 0.6897 

. 

WSR-57 166 0 .69lt9 

NOTE: RQT = RANK QUANTlZER THRESHOLD 

PROBABILITY OF TARGET HIT WITHOUT INTERFERENCE= 0.7 

PROBABILITY OF 

TARGET lilT 

(RQT = 2ft) 

0 . 6893 

o. 6892 

0 . 6878 

0. 6962 

0.6981 ' 

' 

0.6686 1 

0. 6681 

o. 66ltl 

0 .. 6888 

0 . .69lt5 
.1:-

1 

\.11 

w 

VICTIM 

RADAR 

CHANNEL 

~ 

NORMAL 

NORHAL 

NOR!-1AL 

NORHAL 

NORl-IAL 

HTI 

NTI 

NTI 

HTI 

HTI 

TABLE 4-9 

ARTS - -::IIA/RDAS PROBABILITY OF TARGET HIT WHEN 

CONNECTED TO ASR- 7 RADAR THAT IS RECEIVING 

INTERFERENCE FROM THREE RADARS OF TilE SAME TYPE 

INTERFERING INTERFERING PROBABILITY OF 

RADAR RATE v TARGET HIT 

PULSES/SEC (RQT = 23) 

ASR- 7 3006 0. 6842 

ASR-8 3120 0 . 6944 

AN/CPN-4 3576 0 .6989 

AN/FPS-90 1068 0 . 6895 

WSR-57 498 0. 6948 

ASR-7 3006 0.6536 

ASR-8 3120 0. 6832 

AN/CPN-4 3576 0 0 6968 

AN/FPS-90 1068 0 . 6692 

WSR-57 498 0. 6847 

NOTE: RQT = RANK QUANTIZER THRESHOLD 

PROBABILITY OF TARGET HIT WITHOUT INTERFERENCE= 0.7 

PROBABILITY OF 

TARGET HIT 

(RQT = 24) 

0.6686 

0. 6681 

0 .6639 

0.6886 

0.6944 

0.6097 I 

I 

l 

I 

I 

0.6087 

0.5975 

0. 6665 

0.6834 
::-

1 

V1 

::-

. VICTIM 

RADAR 

CHANNEL 

NORJ-1AL 

NO£U-1AL 

NO£U-1AL 

NO£U-1AL 

.. 

NORMAL 

MTI 

MTI 

MTi. 

HTl 

tiT! 

TABLE 4- 10 

ARTS - IIIA/RDAS PROBABILITY OF TARGET HIT ffi!EN 

CONNECTED TO ASR-8 RADAR TIIAT I S RECEIVING 

INTERFERENCE FROM ONE RADAR 

INTERFERING lNTERF ERI NG PROBABILITY OF 

RATE v TARGET HIT RADAR PULSES/SEC (RQT = 23) 

ASR-7 1002 0.6921 

ASR-8 1040 0.6954 

AN/CPN- 4 1192 0. 6965 

AN/FPS-90 356 0 . 6972 

WSR-57 166 0 . 6987 i 

.. 

ASR-7 1002 0. 67 67 

. . ASR-8 1040 . 0 . 6864 

AN/CPN-4 1192 o. 6898 

AN/FPS-90 356 0 . 6918 

WSR-57 166 0 . 6961 

NOTE: RQT = RANK QUANTTZER THRESHOLD 

PROBABILITY OF TARGET HlT WITHOUT INTERFERENCE = 0. 7 

PROB/l.BILITY OF 

TARGET HIT 

(RQT = 24) 

0. 6918 

0.6916 

0 . 6906 

0 . 6970 

0. 6985 I 

0.6758 

.. 

0. 6753 

0. 6723 

0. 6911 

0.6958 
~ 

I 

lJ1 

\J1 

VICTIM 

RADAR 

CHANNEL 

NO~IAL 

NORMAL 

NORMAL 

NORHAL 

NORMAL 

HTI 

HTI 

HTI 

MTI 

~!TI 

TABLE 4-11 

ARTS-IIIA/RDAS '"PROBABILITY OF TARGET HIT WHEN 

CONNECTED TO ASR-8 RADAR THAT IS RECEIVING 

INTERFERENCE FROM THREE RADARS OF THE SAME TYPE 

INTERFERING INTERFERING PROBABILITY OF 

RATE v TARGET HIT RADAR PULS-ES/SEC (RQT = 23) 

ASR-7 3006 0. 67 67 

ASR- 8 3120 0.6870 

AN/CPN-4 3576 0.6898 

AN/FPS-90 1068 0 . 6917 

WSR-57 498 0. 6961 

ASR-7 3006 0.6323 

ASR-8 3120 0.6601 

AN/CPN-4 3576 0. 6698 

AN/FPS-90 1068 0. 6753 

WSR-57 498 0.6885 

NOTE: RQT = RANK QUANTIZER THRESHOLD 

PROBABILITY OF TARGET HIT WITHOUT INTERFERENCE= 0.7 

PROBABILITY OF 

TARGET HIT 

(RQT = 24) 

0. 67 58 

0.6753 

0. 6722 

0.6910 

0.6958 I 

0.6300 

0.6287 

0.6200 

0.6733 

0. 687 5 
Monte-Carlo simulating a series of target nctts and misses and comparing this 

binary sequence to the target detection criteria. The details of this 

program are given in Appendix F, and the results of the calculations plotted 

on probability paper in Figures 4-28 and 4- 29. The probability of target 

detection versus probability of target hit curves in Figure 4-28 are for a 

rank quantizer threshold of 23 and those in Figure 4-29 for a rank quantizer 

threshold 24. The family of curves on each graph represent combinations of 

hit and miss count threshold detection parameters. From the graphs, it is 

evident that for a given hit and miss count threshold, a rank quantizer 

threshold setting of 23 results in a slightly higher probability of target 

detection tnan 24. This is because a rank quantizer threshold setting of 23 

results in a greater probability of hit due to noise alone (probability of 

false target hit), which in effect increases the probability of the hit count 

satisfying the target detection criteria (hit count threshold). That is, the 

noise hits in azimuth for a given range b~n can cause an initial non-zero hit 

count befqr.e radar return pulses from the target are received. The 

probability of this occurring is greater for a rank quantizer threshold 

setting of 23 than 24. 

The curves in Figures 4-28 and 4-29 were used to relate the interference 

effect on probability of target hit to probability of target detection. This 

procedure was followed to relate the probability of target hits in TABLES 4-8 

through 4-11 for various interfering conditions to the probability of target 

detection values shown in TABLE 4-12. The values are for the most likely 

ARTS-IIIA/RDAS detection parameters that will be used in the field (hit count 

threshold of 9, miss count threshold. of 3 , and rank quantizer threshold 

setting 23). The probability of c;ietection without nt~rference (0.8892') is 

shown at the bottom of TABLE 4-12. It is evident from TABLE 4-12 that 

interfacing the ARTS-IIIA/RDAS to the ASR-8 results in, except for the 

AN/FPS-90 and WSR-57 interfering radar types, a lower probability of target 

detection than when interfaced to an ASR-7. A lower probability of detection 

also results when the ARTS-IiiA is connected to a single MTI channel than to 

a normal or dual MTI channel. The lowest probability of detections occurred 

for the interferer and victim radar combinations involving the ASR-7 and 

ASR-8, because this combination resulted in the greatest decrease in 

probability of target hit due to interference . The impact of interference on 

the probability of target hit detection was defined for rank quantizer 

threshold 23 by Equations 4-3 and · 4-19. For the case iin which ·the 

interfering pulse width is less than the sum of the victim radar range bin 

width and hold time, radars with the largest duty cycles (T1 x PRF) have thegreatest interference effect on ARTS-IIIA/RDAS performance. For the case in 

which the interfering radar pulse width is greater than the sum of the victim 

radar range bin width and hold time, the impact of interference is 

independent of the interfering r~dar pulse width and increases only wi th 

interfering radar PRF. 

Interpretation of Interference Effects on Target Detection 

It is evident from TABLE 4-12 that the 

probability of target detection (0.7581) 

4-56 

difference 

ahd that 

between 

for no 

the lowest 

interference 
z 

0 

H 

H 

. 99Y9 

.9990 

.9950 

.9900 

• 98 

.95 

. 90 

~ . 80 

H 

w 

Q. 70 

~ 

~ .60 

H . 50 ~ 

0 . 40 

~ 

~ . 30 H 

~ 

~ . 20 

0 

p::; 

P-1 

. 10 

. 05 

.02 

. 01 

. 005 

. 002 

. 001 

I 

/; 

7; / ~ V/ 

//1 v 

r111 

V/ 

//; o/ 

0 v 

I 

77 177 

V// v 

/; ~I V71 [7 

.0 ?7 

~I 7 

~ ~/ y 

7// 1/ 

I r// 1 

71 VI ~ v 

V/ 

[7 

0. 1 0. 2 0 . 3 0 . 4 0 . 5 0.6 0. 7 0 . 8 0 . 9 1.0 

PROBABILITY OF TARGET HIT 

Figure 4-2 8. ARTS-IIIA/RDAS Probability of Target Detection Versus Pr obability 

of Target Hit for Rank Quantizer Threshol d 23 and Various Hit/Miss 

Count Threshold Parameters Combinations (Probability Scale) 

4-57 
z 

0 

H 

H 

u 

~ 

H 

~ 

0 

H 

~ 

(.,!) 

~ H 

r.... 

. 999 

. 999 

. 995 

. 990 

. 98 

. 95 

. 90 

. 80 

. 70 

. 60 

.so 

9 

(). 

0. 

(). 

z 

~ 

~ 

Cb L 

/ ') 

9 ;'// 

L ~ ~ I 

/ 

/; VL 

//1 v 

L ~L LL 'l 

V

~ L 

II" 

0' L// / ~ H 

,....l 

H 

p::j 

~ 

0 

~ p., 

. 40 

. 30 

. 20 

.10 

. 05 

. 02 

. 01 

. 005 

. 002 

. 001 

/ /L/ 

LL ~ 

~ v 

/ 

//, V/ 

~ v 

L_ 

L/ V/ ~ v 

VLL VL 

0 . 1 0. 2 0 . 3 0 . 4 0.5 0.6 0 . 7 0. 8 0. 9 1.0 

PROBABILITY OF TARGET HIT 

Figure 4- 2 9. ARTS-IIIA/RDAS Probability of Target Detection Versus Probability 

of Target Hit for Rank Quantizer Threshol d 24 and Various Hit/Miss 

Count Thr eshold Parameter Combinations (Probability Scale) 

4- 58 

· 

._ l 

r 

I 
.t:--

1 

~" \0 

VICTIM 

TABLE 4-12 

ARTS- IIIA/RDAS PROBABILITY OF TARGET DETECTION FOR TYPICAL 

DEtECTION PARAMETERS AND VARIOUS COMBINATIONS OF 

INTERFERINa AND VICTIM RADARS 

NIJMllER I NTERFERING RADAR TYPE 

VICTIM RADAR INTERFERING ASR-7 ASR-8 AN/CPN-4 AN/FPS-90 

RADAR CHANNEL RADARS OF ~ 0.83 IJ8 

SAME TYPE PRF • 1002 

ASR-7 NORMAL 1 0 .8789 

ASR-7 NORMAL 3 0 .8586 

ASR-7 MTI 1 0.8586 

ASR-7 MTI 3 0. 7994 

ASR- 8 NORMAL 1 0.8739 

ASR-8 NORMAL 3 0.8441 

ASR-8 MTI 1 0.8441 

ASR-8 MTI 3 0. 7 581 

NOTE: 1. ARTS IIIA/RDAS TYPICAL TARGET DECTECTION PARAMETERS 

RANK QUANTIZER TIIRESliOLD • 23 

HIT COUNT TH.RESHOLO • 9 

MISS COUNT THRESHOLD • 3 

li • 0.60 IJS 

PRF • 1040 

0.8855 

0.8784 

0.8784 

0.8567 

0 .8803 

0 .8640 

0 .8628 

0.8119 

2. PROBAB ILITY OF TARGET DETECTION WITHOUT INTERFERENCE • 0.8892 

li • 0.5 IJS li • 2.0 IJS 

PRF • 1192 PRF • 356 

0 .8884 0.8824 

0 .8871 0.8 689 

0.8871 0.8693 

0.8830 0 .8296 

0.8824 0.8838 

0.8695 0.8731 

0.8695 0 .8733 

0.8307 0.8414 

WSR-57 ' ~4.0 IJS I PRF • 166 

I 

0.8859 

0 .8791 

0 .8793 

. 

0.8596 

0 .8867 

0.8816 

0.8816 

0.8669 
(0 . 8892) is 0.13. This reduction in probability of target detection is for 

the MTI channel of the victim radar receiving continual and simultaneous 

interference from three radars. A 0 . 13 reduction in target detection 

probability implies that if 350 targets per antenna rotations are detected 

without interference, only about 305 would be detected with interference . 

This degree of target detection degradation due to interference would be 

unacceptable. However, it should be pointed out that this number represents 

extremely worst-case interference conditions which do not currently exist in 

congested U.S. terminal areas. Recent measurements by NTIA (Hinkle, 1976) in 

the Los Angeles and San Francisco area indicated that for those FAA radars 

which received interference, interference was usually received from one radar 

at a time over only small sectors of the PPI. The lowest probability of 

target detection listed in TABLE 4-12 for one interfering radar is 0 . 8441, 

and represents a 0.045 decrease due to interference . This implies that if 

350 targets are detected without interference, only 334 targets would be 

detected with interference. If it is assumed that interference is received 

over only 50 percent of the antenna rotation and that aircraft targets are 

uniformly distributed in azimuth, the number of targets detected per antenna 

rotation would be decreased by interference from 350 to 342 . This is 

equivalent to a 0 . 02 decrease in the probability of a target being detected 

in one antenna rotation. The decrease corresponds to one radar interfering 

over 50 percent of the antenna rotation, or multiple interfering radars which 

do not interfere simultaneously but in combination, interfere over 50 

percent of the antenna rotation. 

The above estimated reduction in detection probability (0.02) due to 

present interference levels in congested terminal areas, and in general those 

detection probabilities listed in TABLE 4-12, are pessimistic. In addition 

to worst-case interference signal level assumptions, the 0 . 7 target hit 

probability chosen for a zero interference reference base results in a 

worst-case interference impact on target detection probability . This can be 

seen from the linear plot of target detection probability versus target hit 

probability shown in Figure 4-30. The slope of the (9/3) curve (used in the 

analysis) in the 0.7 target hit probability region is very steep. 

Consequently, a decrease in probability of target hit from 0.7 due to 

interference results in a significant decrease in probability of target 

detection. For interference reference target hit probabilities greater than 

0.1 the slope of the curve approaches zero. Therefore, interference has 

considerably less impact on target detection probability for these target hit 

probability ranges. 

It is evident from Figures 4-17, 4-18, and 4-19 that a 0.7 probability 

of target hit and rank quantizer threshold of 23 chosen for the analysis 

corresponds to a signal - to- noise ratio of approximately 6 dB, 12 dB, and 7 dB 

for the ARTS-IIIA/RDAS connected to the ASR-7 or ASR-8 normal channel, ASR-7 

MTI channel, and ASR-8 MTI channel, respectively. The 12 dB signal-to-noise 

ratio for the single MTI channel is fairly typical; however, the 6 dB and 1 

dB signal-to-noise ratio for the normal and dual MTI channel is considerably 

less than typical. For this reason, the interference effects on target 

detection indicated in TABLE 4-12 are more pessimistic for the normal and 

4- 60 
1.0 

0.8 

HCT=8,MCT=4 

I 

z 9,4 

0 I 

H 8,3 E-< 

u I 

w 9,3 E-< 

I-Ll 0.6 

0 

E-< 

w 

t.:> 

ex: 

< E-< 

!:>.. 

0 0 . 4 

~ H 

..J 

H 

:::0 

< :::0 

0 

~ 

p.. 0.2 

0 

0 0. 2 0.4 0 . 6 0.8 1.0 

PROBABILITY OF TARGET HIT 

Figure 4-30 . ARTS-IIIA/RDAS Probability of Target Detection Versus 

Probability of Target Hit for Rank Quantizer Threshold 23 

and Various Hit/Miss Count Threshold Parameter Combinations 

(Linear Scale) 

4-61 
dual MTI channel than the single MTI channel . 

The hit count threshold of 9 used in the tar get detection analysis 

corresponds to only the lowest hit count threshold value that the MTI channel 

can have at any given time . As discussed in a previous section and described 

in Figure 4- 7, the MTI channel hit count threshold is automatically increased 

from 9 to a maximum of 20 depending on the degree of clutter correlation. 

From comparison of the target detection probability curves in Figure 4- 30, it 

is evident that the slope of the curves for hit count thresholds greater than 

9, in the 0.7 target hit probability region, would be approximately the same 

as for the (9, 3) hit/miss count threshold curve . Since the (9, 3) curve and 

a 0 . 7 target hit probability (zero interference reference base) was used to 

determine the interference impact on detection probability, the analysis 

results should at least typify ASR- 7 MTI channel performance for a 12 dB 

signal - to- noise ratio, and 1 dB signal - to- noise ratio for the ASR-8 MTI 

channel, in the lower portion of the automatically varied hit count threshold 

range of 9 to 20. 

Trade-Off Between Interference Suopression and ARTS- IIIA/RDAS Performance 

This subsection addresses the trade- offs between interference 

suppression and radar performance for various ARTS- IIIA/ RDAS detection 

parameter settings. The interference case chosen for the trade-off analysis 

included three continually interfering radars and the ARTS- IIIA/RDAS 

connected to the victim radar MTI channel . This combination was chosen for 

the trade- off analysis because it results in the greatest impact of 

interference on tar get detection probability . 

TABLES 4- 13 through 4-16 indi c ates the effect of interference on the 

probability of detection and false alarm for various interfering radar types 

and ARTS-IIIA/RDAS detection parameter combinations . In particular, TABLES 

4-13 and 4- 14 indicate the affect of interference on false alarm and TABLES 

4-15 and 4-16 the i nterference effect on target detection. The first column 

of the table gives the ARTS- IIIA/RDAS rank quantizer , hit count, and miss 

count threshold combinations. The probability of. false alarm or target 

detection for no interference and a particular combination of detection 

parameters is given in the last column of the tables. From the tables and 

detection theory, it is evident that increasing probability of target 

detection also increases probability of false alarm . An optimum set of 

detection par ameters involve maximizing the probability of detection while 

maintaining an acceptable false alarm rate (probability of false alarm). FAA 

considers probability of false alarms that exceed approximately 10-6 to be 

unacceptable . Therefore, the false alarm probability (1.164 x 10-5) listed 

in TABLES 4-13 and 4- 14 for no interference and the (23, 8, 4) rank/hit/miss 

detection threshold parameter combination would likely be unacceptable. 

Rank Quantizer Threshold Trade-Off 

It is evident from TABLES 4-13 and 4-14 that, with the exception of the 

4- 62 
.c1 

0' 

w 

TABLE 4 - 13 

ARTS- IIIA/RDAS PROBABlLlTY OF FALSE ALAR~! WHEN CONNECTED 

TO ASR- 7 RADAR (HTI CHANNEL) THAT IS RECEIVING INTERFERENCE 

FRml THREE RADARS OF TilE SMIE TYPE 

ARTS- IliA IK ERFERI~G ~~DAR TYPE 

P AR.lu'1I:Ti:RS 

ASR- 7 ASR- 8 

PIJ = 0 . 83 us PW = 0 . 60 us 

RQ1 HCT T PRF = 1002 PRF = 1040 

23 8 3 3.176 )( 10- 6 3 . 893 X 10- 6 

23 8 4 1. 505 X 1Q - 5 1. 8(,9 X 10- 5 

23 9 3 7. 075 X 10- 7 9. 699 X 10- 7 

23 9 4 4 . 085 X 10- 6 4 . 956 X 10- 6 

24 8 3 2. 129 x 10- 8 1. 152 X 10- 8 

2 ,, 8 4 10 . 839 X J0- 8 7 . 997 x 1o- 8 

24 9 3 2 . 688 X 10-9 1. 621 X 10- 9 

24 9 ,, 2 . 323 X 10 - 8 1. 384 X lQ - 8 

tlOTE: RQT = RANK QUANTIZER THRES HOLD 

llCT = HIT COUt-;T TIIKESHOI.D 

}iCT = MI 55 COUNT THRESHOLD 

·. 

A~/CPN 4 

PH = 0 . 5 us 

PRF = ll92 

'' .440 x 1o-6 

2 .145 X 10- 5 

11.702 X 10- 7 

5 . 622 X ]Q- 6 

1 .o1s x 1o-B 

CJ.766 x J o- 8 

1 . 238 X 10- 9 

1. 04 3 X 10 - 8 

AN/FPS-90 WSR-57 

P\4 = 2 . 0 us P'.J = 4 . 0 us 

PRF = 356 PP.F = 166 

3 . 263 X 10 - 6 2 . 195 >: 10-6 

1.550 X 1Q - 5 2 . 408 X 10- 5 

7.392 X 10-7 4 . 051 X 10-7 

4 . 190 X 10 - 6 2.881 X 10- 6 

3 . 168 X 10-B 0 . 909 x lo- 8 

14 . 633 x 10-s 6 . 050 x 1o-B 

4 . 112 X 10-9 1 . 203 X 10-9 

1.577 X ]Q - 8 1. 003 X lQ- B 

PROBABILITY OF 

FALSE ALAR.:·! 

WITHOt;T 

INTERFERENCE 

2 . 500 X 10- S 

1. 11)4 X 10- 5 

4 . 596 X 10- 7 

3 . 262 X 10 - 6 

1.081 X lQ- 8 

7 . QQ8 X 10- 8 

1.250 X lQ - 9 

1. 057 X 10- 8 
.f:-

1 

C1' 

.f:-

~ABLE 4-14 

\RTS-IIIA/RDAS PROBABILITY OF FALSE ALARH WHEN CONNECTED 

TO ASR-8 RADAR (HTI CHANNEL) THAT IS RECEIVING INTERFERENCE 

FROM THREE RADARS OF THE SAME TYPE 

ARTS-IliA 

PARA;IETERS 

ASR- 7 

--pw-;; 0 . 83 \JS 

RQT llCT MCT PRF = 1002 

23 8 3 2 . 400 x w-6 

23 8 4 1.116 X 10 -5 

23 9 3 4 . 417 x lo-7 

23 9 4 3.1}6 X 10- 6 

24 8 3 2 . 848 x 10-a 

24 8 4 lJ. 464 X 10-8 

24 9 3 3 . 673 X 10 -9 

24 9 4 3.190 x 10-8 

NOTE: R~T = RANK QUI\tiTIZER THRESHOLD 

HCT = HIT COUNT THRESHOLD 

MCT = 1-IISS COU~T THRESHOLD 

INTERFERING RADAR TYPE 

ASR-8 AN/CPN-4 AN/FPS-90 WSR-57 

P\o: = 0 . 60 \JS PI~ = 0 . 5 \JS PW = 2.0 \JS PW = 4.0 \JS 

PRF ~ 1040 PRF ., 1192 PRF = 356 PRF = 166 

2 . 966 X 10-6 3. 313 x 1o-6 2 . 011 X 10-6 2. 211 x 1o-6 

1. 400 X 10-5 1.575 X 10 -5 0.931 X 10-5 1.0'i5 x 10-5 

6 . 305 x lo-7 7.575 x Io- 7 3.723xlo-7 4 .187 X 10-7 

4. 364 X lQ-6 5.183 X 10-6 2 . 652 :< 10 -6 ? . 976 x 1o-6 

2 . 065 X ~-8 1 . 175 X 10-8 0 . 872 X 10-S o . 887 x Io-8 

10 . 606 )( 10-8 \J .454 X 10-8 5 . 997 X 10-8 6 . 292 X 10-8 

2.600 X 10-9 2 . 168 X 10-9 1. 174 X 10-9 1. 215 X 10-9 

2 . 245 x 1o-8 1. 8fi5 x Io-8 0.938 X 10-8 1 . 001 X 10-8 

PROBABILITY OF 

FALSE ALARH 

\HTilOUT 

INTERFERE:-;CE 

2 . 500 Y. 10- 6 

1.1()4 X 10- 5 

4 . 596 x lo- 7 

1 .2_6_2 X 10-6 

' 

1. 081 X 10-8 l 

7.008 X 10-8 

1.250 X 10- 9 

1.057 X 10-8 I 
.PI 

0' 

\Jl 

TABLE 4-15 

ARTS-'IIIA/ RDAS PROBABILITY OF TARGET DETECTION WHEN CONNECTED 

TO ASR-7 RADAR U1TI CHANNEL) THAT IS RECEIVING INTERFERENCE 

FROH THREE RADARS 

ARTS-IliA 

PA!'.A.'!ETERS 

HCT I NCT 

IISR-7 

Ph! = 0.83 \.!5 

RQT PRF = 1002 

21 8 3 0 .8559 

23 8 4 0 . 9352 

23 9 3 0 . 7994 

2) 9 4 0 . 9068 

24 8 3 0 . 7786 

24 8 4 0 .8924 

24 9 3 0 . 7026 

24 9 4 0 .8513 

~;on: : RQT = RA:~K QUA~ITIZER THRESHOLD 

IICT = HIT COUn 1flR?.SHOLD 

:iCT = :-ass COU:"T THRESHOLD 

INTERFERI~G RADAR TYPE 

IISR-8 A'N/CP'f.-1• AN/FPS-90 \o.'SR- 57 

P\o.' = 0 . 60 us 1'\v = o. 5 us Pt-r = 2.0 us P\·1 = 4 . 0 )J S 

PRF = lOt.O PRF = ll'?2 rr:.r = 356 PPF = 166 

0. 9028 0. 9242 0 .8806 0 . 9051 

0.9619 0 . 974 1 0 . 9492 0 . 9632 

0 .8567 0.8830 0 .829? 0 .8596 

0 . 9418 0 . 9579 0.9253 0 . 9436 

o. 7770 0 . 7568 0 .8688 0 . 8955 

0 .8915 0.8788 0.9426 0.9576 

0 . 7006 0 . 67?2 0 .8160 0 .8497 

0 .8506 0 . 3338 0. 9176 0 . 9373 

L- - - - -- -

PROBABILITY OF 

DETECTION 

WITH OCT 

IN7SRFC:R::NCC: 

0.9293 

0 . 9770 

0.8892 

0 . 9617 

9~19 

0. 9723 

0.8829 

0.9567 
.c--

1 

(]\ 

(]\ 

TABLE 4- 16 

ARTS-IIIA/RDAS PROBABILITY .OF TARGET DETECTlON \vHEN CONNECTED 

TO ASR-8 RADAR (MTI CHANNEL) THAT IS RECEIVING INTERFERENCE 

FROM THREE RADARS OF THE SAME TYPE 

ARTS-IliA 

PARtL:ETERS 

ASR...:7 ASR-8 

P\~ = 0.83 JJS PW = 0. 60 JJS 

ROT HCT MCT PRF = 1007 PRF = 1040 

23 8 3 0 . 8223 0 . 8663 

23 8 4 0.9160 0 . 9411 

23 9 3 0 . 7581 0 . 8120 

23 9 4 0 . 8816 0.9145 

24 8 3 0.8109 0 . 8088 

24 8 4 0.9104 0. 9092 

24 9 3 0 . 7431 0.7405 

24 9 4 0.8750 0.8735 

NOTE: RQT = RANY QUANTIZER THRCSHOLD 

IICT = lilT COUi;T TIII' ESHOLD 

MCT = :HSS COU~T THRESHOLD 

INTERFERING RADAR TYPE 

AN/CPN-4 A..'II/FPS- 90 WSR-57 

P\.J = 0 . 5 )JS P\.J - 2. 0 )JS P\.J =4 .0 1.15 

PRr = 1192 PRF = 355 PRF = 166 

0.8816 0.890) 0. 9111 

0 . 9498 0.9547 0.9666 

0 . 8307 0.8414 0.8669 

0. 9620 0.9325 0.9481 

0 . 7Q50 0 . 8796 0.9021 

0.9015 ·o. 9487 0 . 9612 

0 . 7232 0.8296 0.8579 

0.8()33 0.9255 0.9421 

PROBABILITY OF 

DETECTIO~ 

WITP.OUT I 

INTERFERE~CE 

0.9293 

0 . 9770 

0.8892 

0 .9617 

0.9219 

0 . 9723 

0 .8829 

0. 9567 
(23, 8, 4) detection parameters combinatjon, either a rank quantizer 

threshold setting of 23 or 24 would yield an acceptable false alarm 

probability. Even for heavy interfering conditions, the probability of false 

alarm is not increased up to an unacceptable level for these two parameter 

settings. 

The probability of target detection values listed in the right column of 

TABLES 4-15 and 4-16 for no interference jndicates that for a given hit and 

miss count threshold, and target hit probability, that detection performance 

is slightly greater for a rank quantizer threshold 23 than 24 . However, the 

probability of detecting a target without interference is actually larger for 

a rank quantizer threshold setting of 23 than indicated. It is evident from 

Figures 4- 17, 4- 18, and 4- 19 that approximately 1 to 2 dB greater 

signal-to-noise ratio is required for a rank quantizer threshold of 24 than 

23 to achieve a given probability of target hit. This implies that for a 

given signal - to- noise ratio, a rank quantizer threshold setting of ~3 results 

in a higher probability of target detection. Therefore, a rank quantizer 

threshold setting of 23 is optimum for radar detection performance without 

interference. 

It is evident from TABLES 4-15 and 4-16 that a rank quantizer threshold 

setting of 23 is also more desirable than 24 for interference suppression . 

For a given interfering radar and hit/miss threshold combination, the 

decrease in probability of detection caused by interference is significantly 

less for a rank quantizer threshold setting of 23 than 24 . This is because 

there is a lower probability of interfering pulses falling in two rank 

quantizer comparison range bins than one. As discussed previously, a rank 

quantizer threshold setting of 24 implies that the signal level in the target 

range oin of interest has to exceed all 24 comparison ran~e bin signal levels 

before a target hit (logical 1) is generated. However, the signal level in 

the target range bin of interest for rank quantizer threshold setting 23 only 

has to exceed 23 of the 24 comparison range bins for a target hit to be 

generated. 

It is evident from this logic and the results of the analysis that rank 

quantizer thresholds lower than 23 would further reduce the impact of 

interference on target detection probability. However, lowering the rank 

quantizer threshold below 23 would begin to adversely affect the rank order 

detection processor ' s capability to maintain a constant false alarm rate 

(probability of false alarm) in varying levels of clutter . 

Hit and Miss Count Threshold Trade- Off 

It was shown in the previous section that a rank quantizer threshold 

setting of 23 is superior to 24 for ARTS-IliA performance, with or without 

interference. This section considers the hit and miss count threshold 

detection parameter combinations associated with this rank quantizer 

threshold which yields optimum ARTS-IliA performance. As previously 

discussed, the (23, 8, 4) rank/hit/miss detection threshold parameter 

l -67 
combination yields an unacceptably high false alarm probability. Therefore, 

only the (23, 8, 3) , (23, 9, 3), and (23 , 9, 4) parameter combinations will 

be considered . 

It is evident from TABLES 4-13 and 4-14 that for a rank quantizer 

threshold of 23, the probability of false alarm increased the most for the 

(9, 3) hit/miss count threshold combination and the least for the (8, 3) 

combination. The probability of false alarm increase for the (9 , 4) 

combination was between that for the (8, 3) and (9, 3) combination . 

However , the increase in false alarm probability is not significant enough to 

warrant recommendation of a particular hit/miss count threshold combination . 

From TABLES 4-15 and 4-1 6, it is evident that the probability of target 

detection decreased the most for the (9, 3) hit/miss count threshold 

parameter combination and the least for the (9, 4) combination. For example, 

the probability of detection for an ASR-7 radar interfering with an ASR-8 and 

(9, 3) hit/miss count threshold combination decreased from 0.8892 to 0 . 7581 

(14.7 percent decrease) . On the other hand, for a (9 , 4) hit/miss count 

threshold parameter combination, the probability of detection decreased from 

0 . 9617 to 0 . 8816 (8 . 3 percent decrease). The target detection probability 

decreased for the (8, 3) hit/miss count threshold parameter combination from 

0 . 9293 to 0.8223 represents a 11.5 percent decrease. 

The reason that the (23, 9, 4) rank/hit/miss detection threshold 

parameter combination results in the probability of detection being less 

affected by interference than other parameter combinations can be seen from 

Figure 4-30. The graph indicates a linear scale plot of target detection 

probability versus target hit probability for various hit/miss count 

threshold parameter combinations. The tangential slope of the (9 , 4) curve 

for a 0 . 7 target hit probability (value used as zero interference reference) 

is less than that for the (8, 3) and (9, 3) hit/miss parameter curves. This 

implies that a smaller reduction in probability of detection occurs on the 

(9, 4) curves, for a given reduction jn probability of target hit due to 

interference, than for the (8 , 3) and (9 , 3) curves. In general the 

tangential slope of the (9, 4) curve is less than the (8, 3) and (9 , 3) ~urve 

for target hit probabilities g~eater than 0.5 . From Figures 4-17, 4-18, and 

4-19, a 0.5 probability of target hit corresponds to a 4 dB signal-to-noise 

ratio for the ARTS-IIIA/RDAS connected to the normal (ASR- 7 or ASR-8) and 

ASR-8 MTI channel, and 7.5 dB when connected to the ASR- 7 MTI channel . Since 

typical signal-to- noise ratios are greater than these values, the (9 ,4 ) 

hit/miss count parameter combination will result in suppression of 

interference most of the time . 

The previous analysis indicated that the (9 , 4) hit/miss count threshold 

parameter combination yields a maximum probability of target detection with 

and without interference while yielding an acceptable probability of false 

alarm. It should be pointed out that the analysis was based on the MTI 

channel with uncorrelated noise and clutter. As discussed previously, the 

MTI hit count threshold is automatically varied from 9 to 20 depending on the 

degree of pulse-to- pulse clutter correlation . However, comparison of the 

4-68 
curves in Figure 4- 30 for a given miss count threshold indicate that the 

interference s uppression benefits of the (9 , 4) hit/miss count thr eshol d 

parameter combination should at least be realized over the lower hit count 

thr eshold values in the 9 to 20 range . If the tangential slope of the curve 

that represents the initial hit count threshold is low, the tangential slope 

of the curves which r epresent higher hit count thresholds will also be low. 

FAA ' s NAFEC (National Aviation Faci l ity Experimental Center) 

an evaluation of the ARTS- IIIA/RDAS performance at the end of 1978. 

their measurements, they are recommending (23, 9, 3) rank/hit/miss 

threshold RDAS parameter settings for operational ARTS- IliA's in the 

Second Order Interference Effects 

completed 

Based on 

detection 

field . 

This section addresses the possible interference effects on the 

ARTS- IIIA/RDAS channel (normal or MTI) video select and MTI channel tar get 

hit count threshold controls. As discussed previously , the ARTS-IIIA/ RDAS 

automatically selects normal radar channel video in zero or light clutter 

conditions, and MTI radar video in heavy clutter conditions. In addition, 

the MTI hit count threshold is adjusted to maintain a constant false alarm 

rate in pulse- to- pulse correlated clutter. The RDAS estimates the level of 

clutter by counting the normal channel isolated hits and the clutter 

correlation by counting the MTI channel isolated hits. An isolated clutter 

hit is defined as a clutter hit (logical 1) preceded and followed by a miss 

(logical 0) on adjacent ACP ' s. 

Interference Effect on Clutter Hit Probability 

A rank quantizer threshold of 17 is employed in the rtDAS hit processing 

logic (see Figur e 4- 4) for generation of a clutter hit. This implies that 

the clutter level in the rank quantizer cell of interest must equal or exceed 

17 or more of the 24 comparison range bins before a clutter hit is generated . 

Substituti ng 17 fo r RQT in Equation 4- 5 gives a c l utter hit pr obability of 

0 . 32 . Equation 4- 6 can be used to determine the effect of i~terferenc e on 

clutter hit probability by substituting 17 for RQT: 

(4-20) 

The variable x23 in Equation 4-6 was changed to X17 in Equation 4- 20 to 

i ndicate that the equation is for a rank quantizer threshold of 17 . The 

variable x17 in Equation 4- 20 is given by : 

for T.<6 RB 

1 v 

for Ti>6 RE w 

(4-21 ' 

4-69 
where 

Ti = Interfering radar pulse width, i~ ~s 

=Vi ctim radar range bin hold time (0 .468 ~s for ASR-7 

and 0 . 300 s for ASR-8) 

= Victim radar range bin width (0.625 s for ASR-7 and 

0.467 s for the ASR-8) 

It is evident from Equation 4-21 that X17 is zero for an ASR-7 victim radar 

if the interfering radar pulse width is less than 3 . 75 ~s . Similarly, X17 is 

zero for the ASR-8 as a victim radar if the interfering radar pulse width is 

less than 2.8 . The only radar considered in the analysis that has a pulse 

width greater than these two values is the WSR-57 (4 . 0 s pulse width mode). 

Therefore, all interfering radars considered in the analysis have a zero X1 7 

value except the WSR-57. From Equation 4-21, the value of X17 for the WSR-57 

interfering with the ASR-7 is 7 . 064 x 10-6 and for the ASR-8, 7.40 x 10-6. 

The variable X1 in Equation 4-20 is independent of rank quantizer threshold 

and is given by Equation 4-2. The value of x1 for various interfering and 

victim radar combinations is shown in TABLE 4-1. Equation 4- 20 with 

appropriate values of x1 and x17 substituted was used to compute the effect 

of interference on clutter hit probability for various interfering and victim 

radar combinations . The results of these calculations are shown in TABLE 

4-17. The probability of clutter hit for normal and MTI channel are shown 

for three continually interfering radars of the same type. Therefore, a v 

value equal to three times the interfering radar PRF was used in Equation 

4-20 for the calculations. A value of 3 for N was used in Equation 4-20 to 

compute MTI channel clutter hit probability and a value of 1 for normal 

channel clutter hit probability. 

Interference Effect on Video Selection Control 

The RDAS radar micro controller maintains a count of the normal channel 

isolated clutter hits in each 32 Range Bins (RB) by 32 Azimuth Change Pulse 

(ACP) zone, and compares this sum with a clutter map threshold (typically 

166). If the Isolated Hit Sum (IHS) for the zone exceeds the map threshold , 

the clutter count parameter is incremented by 1. If the IHS for the zone is 

less than the clutter map threshold, . the clutter count parameter is 

decremented by 1. Normal channel is selected if the clutter count parame ter 

is less than or equal to 7; otherwise the MTI channel is selected . 

The probability of a normal channel isolated clutter hit (010 hit/ miss 

sequence) occurring is given by : 

(4 - 22) 

4-70 
~ 

I 

-...J 

I-' 

VICTIM 

RADAR 

ASR-7 

ASR-7 

ASR-7 

ASR-7 

ASR-7 

ASR-8 

ASR-8 

ASR-8 

ASR- 8 

ASR-8 

TABLE 4-17 

ARTS-IIIA/RDAS PROBABILITY OF CLUTTER HIT WHEN CONNECTED 

TO VICTIM RADAR THAT IS RECEIVING INTERFERENCE FROM 

THREE RADARS OF THE SAME TYPE 

INTERFERING PROBABILITY OF PROBABILITY OF 

INTERFERING PULSE ARRIVAL CLUTTER HIT Pel CLUTTER HIT P c1 

RADAR RATE (PULSES/SEC) (NORMAL CHANNEL) (MTI CHANNEL) 

. ASR-7 3006 0 . 32192 0.32575 

ASR-8 3120 0 . 32160 0. 32481 

AN/CPN-4 3576 0 . 32159 0.32478 

AN/FPS-90 1068 0 . 32156 0.32469 

WSR-57 498 0.31888 0 . 31664 

ASR-7 3006 0.32204 0.32612 

ASR-8 3120 0. 32162 0.32487 

AN/CPN-4 3576 0. 32162 0.32485 

AN/FPS-90 1068 0.32000 0.32000 

WSR-57 498 0. 31882 0.31648 ------ -

NOTE: PROBABILITY OF CLUTTER HIT WITHOUT INTERFERENCE= 0.32000 

I 

I 

I 

! 

' 

I 

I 

! 
where P11 is the probability of a clutter hit caused by interference and 

defined by Equation 4-20. Each of the 1024 range-azimuth bins in the 32 RB 

by 32 ACP clutter zone has an isolated clutter hit probability given by 

Equation 4-22. The isolated hit sum for the zone is the sum of 1024 (322 ) 

binary random variables and therefore has a binomial distribution given by: 

(4-23} 

where K is the sum of isolated hits in the clutter zone. 

Equation 4-22 for PN(ICH) in Equation 4-23 gives: 

Substituting 

(

1024) PN(IHS=K) = K 

1024-K 

[P il (1-P il)] [1-P il (1-P 11)] (4-24) 

The probability of the zone IHS equaling or exc~eding the clutter map 

threshold (166) and causing th& clutter count parameter to be incremented by 

1 is therefore given by: 

The probability of the zone IHS being less than the clutter map 

and causing the clutter count parameter to be decremented by 1 is: 

PDOWN 

= 1~5 (1024) [P ( 1-P ) ] K [1-P ( 1 _p. ) ] 1024-K ~ K i1 i1 il 11 K=O 

(4-25) 

threshold, 

(4-26) 

Since the number of samples (1024) is large, 1024 x [1-Pn (1 -P11 )]»5, 

the binomial distribution can be closely approximated by a normal 

distribution with a standardized variable given by: 

z (4- 27) 

4-72 
The symbol IHS is the mean isolated clutter hit sum for the binomial 

distr ibution and is given by : 

2 

1024 [P il (1- P il) ] (4 - 28) 

The crN in Equation 4- 27 is the standard deviation of the normal distribution 

and given by: 

2 2 

1024 [P il (1- P il) ) [1-P il (1-P il) ] (4-29) 

The approximation of Equations 4- 25 and 4- 26 by the normal distribution with 

standardized variable Z is: 

e (4 - 30) 

PDOWN = 

- z<=-;2 " 

e dZ = (4 - 31) 

where z1 =(166-IHSN)/O N, z2 =(1024-IHSN)/ON, and Z3 =(165-IHSN~_/ON.. The 

ERF symbol in Equations 4-30 and 4-31 represent s the mathemati cal error 

function associated with the normal distribution and can readily be evaluated 

from probability tables (Ng , 1977). 

The maximum (0 . 32204) and m1n1mum (0 . 31882) clutter hit probability for 

interference and clutter hit probability for no interference (0 . 3200) listed 

in TABLE 4-17 were relat ed to the probability of clutter parameter change by 

Equations 4- 30 through 4-31 . The results of these calculations are shown in 

TABLE 4-1 8 . The first t wo columns of the table describes the probability o~ 

clutter hits extracted from TABLE 4-17 . The last four columns, from left to 

right, indicate the results of evaluating Equations 4-28, 4-29, 4-30, and 

4-31 . From the last two columns, it is evident that the difference in the 

4-73 
.c1 

-...) 

.t:-

TA3LE 4- 13 

CLUTTER HIT 

CP.ARACTERISTICS 

NO 

IHERFERE~CE 

~IAXniUN DUE 

TO INTERFI:RE:"'CE 

MI::UIU~t DUE 

TO I~TERFCRENCE 

TABLE 4-3 

CLL'TTER HIT 

CHARACTERISTICS 

t\0 

INTERF ERENCE 

~:AXI:-IUI DUE 

TO ISTE!!FERENCE 

m:nxt..x DUE 

TO TXTERFERENCE 

TABLE 4-18 

ARTS- IIIA/RDAS PROBABILITY OF CLUTTER PARAMETER DECREMENT AND INCREMENT 

DUE TO INTERFERENCE EFFECT ON NOllilAL CHANNEL CLUTTER HITS 

PROBABILITY 01' MEAl\ ISOLATED STD. DEV. OF PROBABILITY OF 

NORMAL CHAXNEL CLUTTER HIT ISOLATED CLUTTER CLUTTER PARk~ETER 

CLCTTER HIT (Pil) 5L'M (rr.S"~;) HIT Sill1 (o N) DECREME~T (PDO~) 

0 . 32000 151 . 51923 11.36218 0. 3830 

0 . 32204 151.56879 11 . 36372 0 . 3810 

0. 31882 151.48488 11 . 36112 0 . 3815 

TABLE 4- 19 

ARTS- I IIA/RDAS PROBABILITY OF MTI HIT COUNT THRESHOLD ANI> SLIDING 

WINDOW ISOLATED HIT SUM CHANGE DUE TO INTERFERENCE 

PROBABILITY OF MEA~: ISOLATED STD . DEV . OF PROBATILITY OF 

HTI CHA~NEL CLUTTER I!IT ISOLATED CLUTTER HIT COUNT THRESH. 

CLUTTER HIT (Pil) SU~I (THSM) HIT SUN (OM) CHANGE BY 1 OR HORE 

0.32000 95.97231 9 . 36958 

0.32517 97 . 05650 9.37322 < 10-18 

o. 31648 95.90109 9.36650 < 1o-18 

PROBABILITY OF 

CLUTTER PAR/01ETER 

INCRE1·1ENT (Pep) 

0.6170 

0.6190 

0 . 6185 

PROBABILITY OF 

I ISOLATED HIT Silll 

CHAI\GE BY l OR HORE 

I 

I 

0.01351 

0.01243 
orobability of a clutter parameter being changed (incremented or decremented) 

due to interference is no greater than 0.002 . This implies that 500 

antenna rotations would occur before a clutter parameter is changed in a 

particular clutter zone due to interference. It is therefore concluded that 

continuous interference from three radars would not have a significant 

degradation effect on automatic video selection control. 

Int~rference Effect on MTI Channel Hit Count Threshold Control 

The RDAS radar micro controller maintains a count of radar MTl channel 

isolated clutter hits in a sliding 32 RB by 32 ACP window . The MTI channel 

target hit count threshold is adjusted every ACP based on the current 

isolated hit count sum of the sliding window. The adjusted value of the MTI 

hit count threshold as a function of the sliding window isolated clutter hit 

sum is shown in Figure 4-7 . Basically, the MTI hit count threshold is 

increased for high pulse- to- pulse correlation which is characterized by low 

isolated clutter hit sums. 

The probability of a MTI channel isolated clutter hit (010 hit / miss 

sequence) occurring for correlated clutter can be derived using Discrete Time 

Markov Chain probability theory (Barnes, 1975) . The resulting equation is 

given by: 

2 2 

P il (1-P il) (1- r) 

where Pi1 is the probability of a single clutter hit caused by interference , 

and def1ned by Equation 4-20. The symbol r in Equation 4- 32 depicts the 

pulse- to- pulse correlation of the clutter. There is a probability of an 

isolated clutter hit occurring in each of the 1024 range- azimuth bins in the 

32 RB by 32 ACP sliding window. The refore, the isolated clutter hit sum for 

the sliding window is the sum of 1024 binary random variables, and is defined 

by the binomial distribution: 

(

1024) PM(IHS=K) = K [P (ICH)] K[l-P (ICH)] 1024-K 

M M 

where K is the sum of the isolated hits in the sliding window. 

Equation 4- 32 for PM(ICH) in Equation 4- 33 gives 

(4-33) 

Substituting 

( 1024) 2 2 K 2 2 1024-K PM(1HS=K) = K (p il (1-P il) (1-r) ] (1-P il (1-P il) (1-r) ] (4-34 ) 

4- 7 5 
The mean isolated hit sum for the binomial distribution is: 

2 2 1024 [P il (1-P il) (1-r) ] 

and standard deviation: 

Since the number of trials (1024) is large, 

1024 x [ 1-P il ( 1-P il )2 ( 1-r )2] »5, the 

approximated by a normal distribution. 

(4-35) 

(4-36) 

1024 x Pu(1 - Pu )

2 ( 1-r)

2»5, and 

binomia~ d1stribution can be 

The normal distribution approximation to the binomial distribution can 

be employed to determine the probability of interference increasing the IHS 

by a sufficient amount to result in a MTI hit count threshold change . If 

IHSi and IHS0 represent sample sliding window isolated hit sums with and 

w1thout interference, respectively, the distribution of their difference can 

be closely approximated by a normal distributi on. This is possible because 

the IHSi and IHS0 samples are normally distributed and their population 

standard deviations are known exactly (computed from Equation 4- 36) . The 

standard variable for the normal distribution which describes the IHS sample 

dHference is given by (Nat rell a, 196 3): 

z 

where 

IHSi 

IHS 

0 

IHSMi 

IH~0 

(IHS .-IHS )-(IHSM . - ·IHSM ) l. 0 1 0 

= 

= 

= 

= 

1 ( 2 + 2 ) 1/2 

N °Mi 0Mo 

the sample isolated 

the sample isolated 

the actual isola ted 

from Equation 4-35 

the actual isolated 

computed by Equation 

hit sum with 

hit sum mean 

hit sum mean 

hit sum 

4- 35 

4- 7 6 

(4 - 37) 

interference 

without interference 

with interference computed 

mean without interference 
aMi = the actual isolated hit sum standard deviation with 

interference computed by Equation 4-36 

crMo = the actual isolated hit sum standard deviation without 

interference computed by Equation 4- 36 

N = the number of samples (1024 in thj s 

The probability of the difference, between the 

without interference, exceeding a particular 

integral: 

analysis) 

isolated 

value Z 

hit 

is 

sum 

given 

with 

by 

2 

-z /z 

e dZ (4-38) 

where 

6 IHS =difference between isolated hit sums in sliding window 

(IHS.- IHS) with and without interference ~ 0 

ERF(Z) = mathematical error function that can be readily evaluated 

from probability tables 

z1 = value of standard normal variable (Z) from evaluation of 

Equation 4- 37 

and 

the 

Similarly, the probability of the difference IHS) being less than a 

par ticular value z 2 is given by: 

= --

1 Zz -z2f2 f e dZ = 0. 5+ERF(Z2) (4-39) 

The maximum (0.32617) and minimum (0.31648) clutter hit probability for 

interference and clutter hit probability for no interference (listed in TABLE 

4- 17 for the MTI channel) were related to the mean and standard deviation of 

the isolated clutter hit sum by Equations 4- 35 and 4- 36. The results of 

thes e calculations are indicated in the third and fourth columns of TABLE 

4- 19. A clutter correlation coefficient (r) of 0 .2 was assumed for the 

calculation because this value gives a typical isolated hit sum of 96.97 (see 

Figure 4- 7). The probability of worst- case interference increasing the 

4-77 
isolated hit sum enough to cause a hit count threshold decrease was computed 

from Equations 4-37 and 4-38, and t he result is indicated in TABLE 4- 19 

(second row, fifth column) . The isolated hit sum mean and standard deviation 

list ed in the third and fourth columns of TABLE 4- 19 were used in this 

calculation. In par ticular , the mean and standard deviation associated with 

no interfer ence and maxi mum clutter hit probabilities due to interference, 

were used to calculate z1 in Equation 4- 37 . This combination resulted in the 

greatest (worst- case) probability of interference decreasing the MTI hit 

count threshold. 

The probability of worst-case interference decreasing the isolated hit 

sum enough to cause a hit count threshold increase was computed from 

Equations 4- 37 and 4- 39 , and the result is indicated in the bottom of the 

fifth column of TABLE 4-19. The isolated hit sum statistical parameters 

(mean and standar d deviation listed in columns three and four of TABLE 4- 19) 

that correspond to no interference , and mini mum clutter hit probabilities due 

to inter ference, were used to calculate Z in Equation 4- 37. This 

combination of values resulted in the greatest (worst- case) pr obability of 

interference increasing the MTI hit count thereshold. 

An isolated hit 

the above calculations 

threshold change of 1 . 

threshold changes by 

10.66. However, it 

inter ference is closer 

than 10 . 66 . For this 

analysis. 

sum difference (IHSi- IHS0 ) 

(Equation 4- 37) to r epresent 

It is evident from Figure 

value of 5.333 was used in 

a MTI channel hit count 

4- 7 that the MTI hit count 

for each sliding window isolated hit sum change of 

is likely that the hit 

to the point required for 

reason, a median value 

sum sample value without 

a hit count threshold change 

of 5. 333 was chosen for the 

The probability of interference causing the sliding window isolated hit 

sum to change by 1 was also computed from Equations 4-35 , 4-36, 4- 37, 4- 38 , and 4-39 by setting (IHSi- IHS0 ) in Equation 4- 37 to 1. The results of these 

calculations are indicated in the last column of TABLE 4-19. It is evident 

from the above probability calculations and TABLE 4-19 that continual 

interfer ence from three radars will not have a significant degradation effect 

on RDAS automatic MTI hit count threshold control . The probability of 

interference causing the MTI hit count threshold to change by 1 or more is 

less then 10-18 . In addition, the probability of interference causing the 

sliding window isolated hit sum count to change by only 1 or more is less 

than 0.01243. 

4- 78 
APPENDIX A 

MIXER TRANSFER PROPERTIES 

INTRODUCTION 

The RF to IF conversion of received signals in radars is accomplished 

by the radar mixer which mixes the stable local oscillator (STALO) output 

signal with the amplified RF received signal. Figure A-1 shows a simplified 

block diagram of a radar mixer. The following is a discussion of tne Noise, 

Signal-to-Noise (SNR), and Interference-to-Noise (INR) transfer properties 

of a typical radar mixer. 

MIXER TRANSFER PROPERTIES 

The radar STALO signal time waveform, v5 (t), can be expressed as: 

(A-1 ) 

where: 

R0 = Receiver tuned IF frequency, in radians per second 

~ = Phase of STALO signal s 

Assuming linear transfer properties for a radar mixer, the noise and 

signal can be treated separ~tely. 

Noise 

To calculate ~i and , the noise 

the mixer, the bandpass noise model is 

signal, "mi(t), is given by: 

power at the input and output of 

used, and the mixer input noise 

(A- 2) 

Where nm1 (t) is the RF bandpass noise at the input of the mixer, and the 

mixer input noise power (mean square of "mi(t) is given by: 

(A- 3) 

A-1 
:J> 

I 

rv 

F.F INPUT IF SIGNAL 

vmi(t) =A p(t)cos[(w0 +6w)t+¢ v mo (t) 

STALO SIGNAL 

V5 (t) =cos( (~ +e )t+¢ ] 

F igure A-1. Radar Mixer Block Diagram 
Generally, the STALO signal power level is greater than 0 dBm. 

Therefore, the mixer noise figure (conversion loss) is very small and can be 

neglected. Also, the STALO signal is usually filtered and the noise 

suppressed, thus permitting the STALO signal noise level to be neglected. 

If nmi(t) is applied at the input of the mixer (whi ch multiplies the 

incoming noise signal, Omi(t) by vs(t), then (t), the output noise of the 

mixer, is given by: 

n (t) rna nJ t) cos w0 t·cos [(w0 

+ 80 ) t + ~s ] 

+ ns(t) sin w0 t • cos [(w0 + 80 ) t + ~s ] 

nc(t) [cos[(2w0 + 80 ) t + ] +cos [80 t + ~s11 

2 

+ ns(t) [sin[(2w0 + 80 ) t + ] - sin[80 t + s]] 

2 

(A-4a) 

(A-4b) 

The terms cos [( 2w )t+~s] and sin [(2 +S t+~s ] represents the spectra 

of nc(t) and n5 (t), respectively, shifted at (2wo + S0 ) and are filtered 

out by the IF filter at the mixer output. Hence, nroo(t) is given by: 

nc(t) cos (80 t + ~s) - ns( t) sin (8 0 t + ) 

2 2 (A-5) 

The mixer output noise power (mean square of nro0 (t) can be related to the 

mixer input noise power, Equation A- 3, and the mixer noise power transfer 

properties expressed as: 

(A-6a) 

(A- 6b) 

Desired/Interfering Signal 

The desired and interfering signal voltage waveform at the mixer input, 

vmi(t), can be expressed as: 

Ap(t) cos [(w0 + 6w)t + ] (A-7) 

A- 3 
where: 

A = Signal voltage amplitude 

p(t) = Signal amplitude modulation, value between 0 and 1 

= Receiver tuned RF frequency, in r adians per second 

6w = Frequency separation between interfering signal carrier 

frequency and receiver tuned frequency ( 6w = 0 for 

desired signal), in radians per second 

= Phase of signal 

Since we are only concerned with 

interfering signal, p(t) equals 1, and 

mixer (the mean square of vmi(t) is: 

the peak power of the desired or 

the signal power at the input to the 

A :t 

2 (A- H) 

The signal voltage time waveform at the mixer output , vm0 (t), can be 

found by performing the operation shown in Figure A-1 and is g i ven by: 

2 

cos [(w0 + flw )t + $]· cos [(w0 + 80 )t + <sJ 

[cos [(2w0 + 6w + 80 ) t + ~ + ] 

+cos {(80 - 6w)t + cps - ¢ ]] 

(A- 9a ) 

(A- 9b) 

(A- 9c) 

The first term of Equation A-9c is filtered out by the lF filter, resul t i ng 

in a signal with a frequency ( 80 - 6w) where 6w = 0 for the de sired si g nal, 

and a mixer output power (the mean square of vmo (t) o f: 

p 2 

8 (A-l Oa) 

(A-l Ob) 

A- 4 
Therefore, the signal peak power is reduced 6 dB by the mixer. 

SNR Transfer Properties 

Using Equations A-6b and A-lOb, the mixer signal- to- noise (SNR) 

transfer properties of the mixer are given by: 

SNR 

mo 

(A-ll) 

Therefore, the SNR at the mixer output is equal to the SNR at the mixer 

input . Equation A- 11 is also applicable to the interference-to-noise (lNR) 

transfer properties of the mixer. 

IMAGE RESPONSE 

For the case when the interfering signal frequency separation, ~w , is 

equal to 2 80 , the interfering signal frequency at the mixer output will 

equal the IF tuned frequency. However, in most radars in the 2.7 to 2.9 GHz 

band, the preselector filter attenuates the interfering signal image 

response by approximately 50 to 60 dB. 

A-5 
APPENDIX B 

IF FILTER TRANSFER PROPERTIES 

INTRODUCTION 

The interfering signal peak power level and time waveform at the radar 

receiver IF output is a function of the interfering signal emission spectrum, 

victim receiver IF selectivity characteristics, and the frequency separation 

between the interfering and victim radars. This appendix discusses the 

techniques and models used to compute the victim radar receiver IF selectivity 

characteristics, Frequency- Dependent- Rejection (FDR), interfering sigryal IF 

output time waveform, receiver equivalent noise level, and IF filter 

interference-to-noise ratio (INR) transfer properties. 

IF SELECTIVITY 

Since a victim radar receiver's IF selectivity characteristic is the 

principal means by which the receiver discriminates against undesired signals, 

the receiver's IF selectivity characteristic is required to determine a 

receiver's Frequency- Dependent-Rejection (FOR) of an undesired signal and IF 

output undesired signal time waveform. 

Receiver spurious responses must also be considered wh en determining the 

FOR of a victim radar to an undesired signal . Spurious responses occur when 

the undesired signal is at a frequency such that it mixes with the local 

oscillator to produce an output at the receiver IF frequency. Since most 

radars have relatively clean local oscillator signals or employ balanced 

mixers, only image responses were investigated. The local oscillator 

frequency of most radars are tuned to 30 MHz above the receiver RF tuned 

frequencies in order to obtain an IF frequency of 30 MHz. An RF undesired 

signal that is 30 MHz above the local oscillator frequency (60 MHz above RF 

receiver center tuned frequency) will also be down-converted to the 30 MHz IF 

frequency. Modern radars normally employ an image-rejection mixer or a notch 

filter at the radar input to suppress image responses. The image response of 

the AN /CPN-4 and AN/MPN-13 radars are generally only 15 dB down from their 

center- tuned response, the ASR-4 through ASR-8 have an image response greater 

than 50 dB down. Reduced FOR due to receiver image response was not 

incorporated in the FOR model, but was considered in an independent FDR 

calculation. 

The selectivity of a receiver is the composite selectivity of all the 

tuned circuitry in the receiver prior to detection; however, in a 

superheterodyne receiver, the selectivity is determined by the IF stages 

because the preceding mixer and RF circuits are relatively broader band. This 

is because the required filter characteristics are more physically realizable 

and less expensive to build at the lower IF frequency. 

~1 
IF Selectivity Modeling 

The radars in the 2.7 to 2.9 GHz band generally employ a combination of 

synchronously-tuned, staggered- tuned doublet, and stagger-tuned triplet 

stages of IF amplification . Figure B-1 shows a few stages of the ASR-8 normal 

channel IF amplifier. Neglecting the bias resistors, since they are usually 

larger than the source resistor, and also the coupling and bypass capacitors, 

the equivalent "Y '' parameter circuit for one ASR-8 normal channel IF amplifier 

stage is shown in Figure B-2. 

The gain of the equivalent cir cuit shown in Figure B-2 is: 

A 

v2 = Yfe (B-l) 

v1 Yoe+G+G' 

Where: Yoe goe + jScoe 

Letting: c = 

.. The equivalent impedance of the parallel combination of capacitor 

(-j/SC) and inductor (R+jSL) can be expressed as: 

L 

(1 J-. R ) 

Z' c SL = (B-2) 

R [1 + j SL 

R ( l- ~)] 

Letting: So = l/I'Lc (B-3) 

0 s F - Fo - 1 (B-4) 

80 Fo 

Q = 

S0L 1 (B- 5) 

R 80CR 

Nhere: Receiver tuned IF frequency, in radians per second 

B-2 

• 
L6 

+!SV 

TPt: 

-= r 

T I 

I 

~c~~ 30 MHZ \L c. 

t:tl 

IF ---0-j 

I 

w ~C23 

Figure B-1. 

L7 

R4G 

TPS 

c:q 

---'-- C2 7 

R44 R45 R52 

8

R-l7 

20 

u ~ 

R40 

L4 

j_ 

TC25 

LO 

R54 

R4 9 

RS3 

TP6 

C29'" 

~30MHZ ' RSS 

010 j_ - I I IF 

C30 

RSO T > R58 

C3 1 

H~ 

~ RS 1 -::-

R59 

1 o-- -1s vee 

j_ 

T 

ASR-8 Normal IF Bandpass Filter Schematic 
~ 

I 

:;:-. 

_ rl - I 2 

+ 

vl Yfcvl 

cl 

.i?igure B-2 . "Y" Parameter Equivalent Circuit for On e IF 

Amplifier Stage Shown in Figure B- 1. 

L 

G 

n. 

... .. 
Using Equations B- 3 through B- 5, Equation B-2 becomes: 

RQ2 ( 1 - j~ ~0 ) Z ' (B-6a) 

1 + jQ ( :0 - :~) 

RQ2 [ (1 + 0) - j (1/Q) 

(1 + 0) + jQo(2 + o> J (B- 6b) 

At resonance 8 Bo , and o = 0, then 

Z ' RQ2 (1 - j~ ) Q 

(B-7) 

Since the Q for the circuit used is usually high, Q > 10, then with good 

approximation 

Z' RQ2 

Therefore, the gain at resonance combining Equations B-1 and B-8 is: 

ARES 

Yfe 

9oe + G + 

BoLQg + BoLQG + l 

oe 

Equation B-9b may be written as: 

Where Qe, the effective "Q" of the amplifier, is: 

Q 

Wh ere : B5 = The amplifier stage 3 dB bandwidth, in Hz 

B-5 

(B-8) 

(B-9a) 

(B-9b) 

(B-10) 

(B-lla) 

(B-llb) 
The impedance, Z', o£ the single- tuned 

frequency, 8, where 8 ~ 80 and 6 is small is: 

Z' 

1 + j20Q 

Therefore, the off- tuned gain is: 

A -Yfe 

9oe + G + 1 + j 20Q 

RLQ2 

-Yte8oLQe 

1 + j20Q 

amplifier at some 

!hus the gain ratio can be obtained from Equations B-10 and B- 13a as: 

A 

ARES 

A(F) 1 

1 + j200 

off- tuned 

(B- 12) 

(B-13) 

(B-13a) 

(B-14) 

For ''m" cascaded synchronous single- tuned stages, the gain ratio becomes: 

A(F) 1 (B-15) 

[1 + j26Q]m 

The gain ratio for a single- tune stage using an electron tube is identical to 

Equation B-14, and is derived by Seeley (1958) . 

The IF bandwidth of "m" cascaded synchronous- tuned stages is given by: 

Bs J 21/m - 1 (B-16) 

Wh ere: BIF = Receiver IF 3 dB bandwidth, in Hz 

Substituting Equations B-4 and B-11a into Equation B-14, the amplitude 

characteristic in dB form of a single- tuned stage is: 

Where: 

X 

2 ~ - 20 1og10 (1 + x l 

2 (F-F0 ) 

Bs 

(B-17) 

(B- 18) 

B- 6 

' ' 
The IF selectivity characteristics, AdB(F) for "m" cascaded synchronous 

single- tuned stages is given by: 

= 2 m/2 -20 log10 <1 + x l (B-19) 

For "m" cascaded amplifiers consisting of "n" staggered-tuned stages, the IF 

filter amplitude characteristics are given by Seeley (1958). 

2n m/ 2 -20 log10 (1 + x ) 

RECEIVER FR£QUENCY-DEPENDENT-REJECTION CHARACTERISTICS 

(B-20) 

A necessary component in predicting radar to radar interference is the 

victim radar receiver's Frequency Dependent Rejection (FOR) characteristic to 

cochannel and adjacent ch~nnel undesired signals. The victim receiver's IF 

selectivity characteristic and undesired signal emission spectrum 

characteristic determine the victim receiver's rejection (peak power loss) of 

the undesired signal which is dependent on the frequency separation (~~ 

between the victim receiver RF tuned frequency (Wo), and the undesired signal 

RF carrier frequency. The following is a discussion of the technique and 

model used to determine a radar receiver's FOR of an undesired signal. 

FOR is the sum of attenuation of the undesl~ed signal due to 

Off- Frequency Rejection (OFR) and the On-Tune Rejection (OTR) in dB. 

FDR(dB) = OFR(dB) + OTR(dB) 

Off-Frequency Rejection (OFR) is definPd by Fleck (1967) as: 

OFR 

Where: 

I P(F) 

A(F + 6F) 

I P(F) 

A(F) 

dF 

dF 

P(F) = Transmitter relative power density 

A(F) . - Relative receiver selectivity 

6F = Frequency separation between interfering signal 

carrier frequency and receiver tuned frequency, in Hz 

(B-21) 

(B-22) 

Absolute transmitter power and receiver sensitivity does not enter into the 

calculation because FOR depends only on the shape of the victim receiver IF 

B-7 
selectivity and undesired signal emission spectrum. 

Since the undesired signal emission spectrum 

selectivity curves are usually given in dB units, a more 

Equation B-22 in dB is: 

and victim receiver 

practical form of 

[Pda(F) - Ada(F +ill')] /10 

OFR 

Where: 

f 

i 

10 log 10 

' -· [ PdB (F) - AdB (F)) 

-10 log ( 10 

) 

= Emission spectrum, in dB 

= Receiver IF selectivity curve, from 

Equations B-17 through B- 20, in dB. 

dF (B-23) 

/ 10 

dF 

Approximations to Equation B-23 can be obtained using the following equations 

(Newhouse): 

Case I, TBIF > l and llF any value 

OFR 20 log TBIF + (F&) 

Case II, TBIF > 1 and /::,p 2__!+ 8 IF -- ITT 2 

OFR 0 dB 

Case III, TB 

IF > 1 and 6F > _!+ 

8 IF 

ITT 2 

OFR 20 log TBIF 

Where: 

T = Interfering signal pulsewidth, in seconds 

F = 6F Interfering signal emission spectrum level 

relative to fundamental frequency, in dB. 

(B-24) 

(B-25) 

(B-26) 

The victim receiver On- Tuned Rejection (OTR) factor is derived by Wh i te 

B-8 
(1972). In summar y, the OTR factor can be obtained by considering the Laplace 

transforms of a single pulse of amplitude "A" and width T: 

~ rsiNGL El 

c/.... LPULSE J 

AT 

( 

s i n 7T F T) e _ j 7T F T 

TTFT 

(B-27) 

Where the Laplace transform parameter, s, has been replaced by j27TF. The 

phase given by the exponential factor indicates that when the receiver 

bandwidth Brp is less than the emission bandwidth BT = 1/ T, the phase 

variation over the receiver bandwidth is small. This means that the voltage 

must be summed first and then squared instead of summing the square of the 

voltages as many documents imply. For a relatively constant emission spectrum 

over the IF pass band, the received peak power is therefore proportional to 

the ratio of the receiver to transmitter bandwidths and the OTR factor in dB 

is given by: 

OTR = (B- 28) 

0 

Where: 

BIF = Receiver IF 3 dB bandwidth, in Hz 

BT = Emission 3 dB bandwidth, in Hz 

IE Q!.!If!.!T TIME WA:iEEQBt1 

The following analysis considers the tranformation of pulsed signals 

through an effective linear IF filter. In general, the IF amplifier output 

for a pulsed input signal can be expressed as the sum of a steady state term 

and a transient term . The transient term represents a distortion term and 

includes the amplitude and phase modulation produced in the IF amplifier. The 

transient term arises because the system response is unable to build up and 

decay as fast as the input si gnal. 

It is necessary to have an IF filter model to predict these transi ent and 

steady state terms. One method of modeling the IF filter function is in terms 

of cascaded tuned amplifiers. Both single- tuned and stagger-tuned amplifiers 

are used in radar receivers. For this analysis, eight cascaded single-tuned 

amplifier stages were used to model the radar receiver IF filter 

characteristics. The transfer function for eight cascaded synchronous tuned 

amplifiers is given by Equation B-15 as: 

A(F) 1 

[1 + j2oQ] 8 (B- 29) 

B- 9 
If the IF filter· has an· impulse rP.sponse a(t), the IF filter output 

response to an input signal, x(~), is given by the convolution integral: 

h(t) = / 00

00 

x(T)a(t-T)dT (B- 3 0) 

Since convolution in the time domain is equivalent to multiplication in the 

frequency domain, it will be more convenient to use the frequency domain 

expressions. If the input signal, x(~), has a Fourier transform, X(F ) , and 

the transfer function of the IF filter is A(F), then the output spectrum is 

given by: 

H(F) X(F)A(F) (B-31) 

The interfering signal spectrum for a periodic trarezoidal pulse is given 

by Meyers (1971). 

X(F) 1 sin [TrTFx(l +d)] sin (TfTdFx) (B-32) 

Where: 

T = Radar pulse period, 1/PRF 

T = Interfering signal pulse width, in seconds 

d = Rise time IT = Fall time/ T 

Fx = F - 6.F 

0 

The interfering signal output spectrum H(F), after being band limited by 

the IF filter, is the product of the filter transfer function and the pulse 

spectrum. The inverse Fourier Transform of H(F) will be the IF filter output 

time waveform h(t)'. For modeling ~urposes, the carrier frequency can, without 

loss of generality, be assigned the value of the center frequency, 80 , of the 

IF filter. The interfering signal at the IF output can then be expressed as: 

v (t) = .:BP(t ' )cos[B t + <P + cj>(t ' )] Ifu o o 

Where: 

B = Interfering signal voltage amplitude 

p(t') = Interfering signal amplitude modulation 

after IF filtering, value between 0 and 

<P 0 = Interfering signal carrier phase angle 

t' : t - t 0 where t 0 is the delay time of the IF 

B-10 

(B- 33) 

.. 
filter 

(t') = Interfering signal phase modulation after 

IF filtering 

Typical IF filter bandwidths of radars in the 2.7 to 2.9 GHz band are 1.2 MHz 

to 5.0 MHz. The following is a discussion of the IF output time waveform as a 

function of the interfering signal pulsewidth, T, and off-tuning(~). The 

simulated output time waveforms were obtained using the RWS Model, Meyers 

(1971) . 

When the pulse bandwidth is much greater than the bandwidth of the IF 

filter, TBrp{<1, the spectrum of the pulse within the IF passband for the 

on- tune, F = 0, case is approximately flat and has even symmetry about the 

carrier f r equency . The Fourier transform of the resulting spectrum will 

approximate the impulse respons e of the network with some ringing on the 

trailing edge . The output time waveform will be much longer than the input 

pulse time waveform with the peak amplitude of the output pulse reduced 

approximately by the ratio of the pulse bandwidth to the filter bandwidth . 

Since the bandwidth of the pulse is much greater than the IF bandwidth, the 

shape of the spectrum within the IF passband as the pulse is off- tuned will be 

approximately the same except near the nulls of the input spectrum. 

Therefore, as the pulse spectrum is off- tuned the IF output time waveform will 

remain approximately the s ame as the on-tune case with the inband power 

determining the peak level of the output pulse. In the vicinity of the null 

point the spectrum will no longer be flat and it will approach odd symmetry 

when centered about the null point. The Fourier transform of an unsymmetrical 

spectrum will produce both amplitude and phase modulation as shown in Equation 

B- 33 . Simulated IF output time waveforms for an IF bandwidth of 1.2 MHz and a 

5 ~ pulse (TB1p<<l) for ~F = 0, 5 . 0 MHz and 20.0 MHz off-tune are shown in 

Figures B- 3, B- 4 and B- 5. The input pulse of width T and unity amplitude is 

assumed to be symmetrical about time t = 0 . This is true for all pulses 

discussed in this section . 

When the pulse bandwidth is approximately equal to the IF bandwidth 

TB F~l , the spectrum of the pulse within the IF passband for the on- tune, AF = 

0, case will be symmetrical and even . The sidelobes will be attenuated by the 

filter function causing a more rapid fall- off of the pulse spectrum. The 

Fourier transform of the resulting spectrum will approximate the impulse 

response, with the amount of energy within the passband again determining the 

peak level of the output pulse. As the pulse i s off- tuned the pulse spectrum 

out of the IF filter will be uns ymmetrical, thereby producing both amplitude 

and phase modulation as shown in Equation B- 33. The Fourier transform of the 

output pulse spectrum produces time waveforms that appear to contain a 

separate response for the leading and t r ailing edge of the IF input pulse. As 

the off- tuning i s increased the double response becomes more pronounced due to 

the attenuation of the steady state portion of the pulse by the filter 

characteristics. Simulated IF output time waveforms for an IF bandwidth of 

2 . 7 MHz and a .83 s pulse for (TB F~l) for F = 0, 5.0 MHz and 20.0 MHz are 

shown in Figures B- 6, B- 7, and B- 8, respectively. 

B-11 
I I 

BIF = 1.2 MHZ 

1: = • 5 lJSec 

crr = crf = .025 llSec -

~F = 0 

1.0 

. 8 

tJ:1 

I ~ 

1-' Cl 

N :::::> 

8 

H • 6 H 

P-t 

~ 

~ 

U) 

H • 4 :::::> 

P-t 

I \ 

I \ 

I \ . 2 1\ v 

0 / ~ ~ 

-1.0 -0.5 0 0.5 1.0 1.5 2 . 0 2 . 5 3.0 3.5 4.0 

Time in llSec 

Figure B-3. Simulated IF Output Time Waveform Envelope 

.,. •• Jill- - ~ r~· =' • ...... .:.. 
I I 

BIF = 1. 2 MHz 

l = . 5 lJSec 

or = of = .025 llSec 

f:J.F = 5.0 MHz 

1.0 

0 • 8 

...-l 

tD 

I >< . ....... 

L;.. ~ . Cl 

:::> 

8 . 6 

H 

H 

0.. 

~ 

~ 

U) • 4 

H 

:::> 

0.. 

• 2 

~ 

' ( \ 

J 

v ~ 

J \_ " ... .. " 

........ '"'--.. r-- . 0 

-1.0 -0.5 0 0 . 5 1.0 1 . 5 2 . 0 2 . 5 3 . 0 3.5 4 . 0 

Time in llSec 

Figure B-4. Simulated IF Output Time Waveform Envelope 
I I 

BIF = 1.2 MHz 

1.2 

T :::; • 5 )..lsec 

Or= Of = .025 )..lsec -

!J.P = 20.0 MHz 

1.0 

0 

0 

r-l 

>< 

r.:l • 8 tJj Q I ::> 1-' E:-4 ~ H 

H 

~ 

~ . 6 

r.:l 

U) 

H 

::> 

~ 

• 4 

7 [\ 

I \ 

7 \ 

7 

I 1\ 

I \ 

) \ v-~ 

~ 

. 2 

0 

-1.0 -0.5 0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 

Time in lJsec 

Figure B-5. Simulated IF Output Time Waveform Envelope 

.. 7 . .-... - , 
tJj ~ 

I 0 

t:-' ::::> 

l.n E-4 

H 

H 

p. 

~ 

~ 

U) 

H 

::::> 

p. 

1.2 

1.0 

• 8 

• 6 

,4 

• 2 

0 

-1.0 

I l 

BrF = 2. 7 MHz 

, = .83 J,Jsec 

ar = of • .025 J,Jsec -

~ = 0 . . -

0 ~ 

I \ 

I \ 

I ' 

\ I 

) \ ' 

-.5 0 • 5 1.0 

~ 1.5 2.0 2.5 3.0 3.5 4.0 

Time in J,Jsec 

Figure B- 6. .Simulated IF Output Time Waveform Envelope 
I I 

BrF =~ 2.7 M.Hz 

1.2 T = .83 psec 

Cr = Cf ~ .025 ~~ec -

AF = 5.0 MHZ 

-

1.0 

0 

r-1 

>< 

~ • B 0 

~ A 

\ 1\ 

I 

t» ::> 

I 8 

t.-! H 

0\ ...:1 

~ • 6 ~ 

U) 

...:1 

::> 

p.. 

• 4 

\ 

'--

./ 

fJ ~ r----... 

• 2 

0 

-1.0 -.5 0 • 5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 

Time in lJSec 

Figure B-7. Simulated IF Output Time Waveform Envelope 
0 

0 

r-i 

til X 

I ~ ....... Cl ..._, :.:> 

E-l 

H 

.....:! 

Pol 

~ 

~ 

(/) 

.....:! 

::::> 

Pol 

1. 8 

1.6 

1.4 

1.2 

1.0 

• 8 

• 6 

• 4 

. 2 

0 

- 1.0 

I I I 

A 

BIF = 2. 7 .MHz 

n T = .83 )Jsec 

CJr = Of = • 025 l1Sec -

!J.F = 20.0 .MHz 

I f\ ......___.. i'\/ V\ ) ~ 

-. 5 0 • 5 1. 0 1. 5 2 . 0 2 . 5 3 . 0 3 . 5 4. 0 

Time i n )Jsec 

Figure B- 8. Simu lated IF Output Time Wave form Envelope 
When the pulse bandwidth is much narrower than the IF filter bandwidth, 

TB >>1, and 6F less than one half the IF bandwidth, the input time 

ch~~acteristics are produced at the filter output along with some ringing or 

overshoot on the leading and trailing edges. As the pulse is further 

off-tuned, the pulse spectrum out of the filter will be unsymmetrical, thereby 

producing amplitude and phase modulation. The steady state portion of the 

output pulse will again be attenuated by the off-tuned characteristics of the 

filter and, therefore, the shape and magnitude of the output pulses will be 

determined by the power and shape of the spectrum within the filter passband. 

Simulated IF out time waveform for an IF bandwidth of 5.0 MHz and a .83 s 

pulse (TB>>l) for 6F = 0, 5.0 MHz and 20.0 MHz are shown in Figures B-9, B-10, 

and B-11, respectively. Photographs of measured IF output time waveforms on 

an ASR-8 (Figures B-12 through B-14) are shown for identical parameter 

conditions as the simulated waveforms shown in Figures B-9 through B-11, 

respectively. 

Figure B-15 is a plot of phase angle as a function of time at the output 

of a 5 .0 MHz bandwidth IF filter for a .83 s pulse off-tuned 5.0 MHz. The 

plot shows the phase modulation produced by an off- tuned pulse during the 

leading edge, steady state and trailing edge of the pulse. The 5.0 MHz beat 

tone phase modulation during the steady state portion of the pulse is equal to 

the 5.0 MHz off-tuning of the pulse. The effect of this phase modulation 

produced by off-tuned pulsed interference on the MTI channel phase detector is 

discussed in Appendix C. 

In summary, the transformation of pulsed signals through a radar linear 

IF filter has been discussed in terms of TBrF categories and off-tuning. An 

understandihg of the transfer properties of radar IF filters is required since 

the IF output time waveform determines the waveform at the normal channel 

detector output, and the phase modulation produced by the IF filter determines 

the MTI channel phase detector output waveform. 

IF OUTPUT NOISE LEVEL 

The receiver equivalent noise level at the radar input is essentially 

determined by the radar receiver RF stages since the noise contribution due to 

the IF stages is small because of the high gain of the IF and previous 

receiver stages. Since the radar receiver can be modeled as a linear receiver 

with 0 dB gain up to the receiver IF output, which allows the signal and noise 

to be treated separately, the noise level at the radar IF output can be 

treated as being equal to the receiver RF input equivalent noise level Nr. 

Thus, the receiver equivalent noise level at the receiver input is given by: 

(B-34) 

Where: 

NI = Receiver noise (referenced to RF input) 

T0 = Reference Temperature = 290ok 

B-18 
1.4 

I I I 

1.2 

BIF = 5 . 0 MHz I 

! 

· T = .83 lJSec - ?r = af = .025 lJ Sec 

~F = 0 

l. O I ~ 

rx:l 

0 

::> 

E-4 

H . 8 H 

I \ 

A< 

to 

I ~ ....... 

\1:) rx:l 

(/) 

H • 6 

::> 

A< 

. 4 

. 2 

o_l. o - . 5 

-

0 • 5 

~ l.O 1 . 5 2.0 2.5 3.0 3.5 4 . 0 

Time in lJ Sec 

Figure B-9. Simulated IF Output Time Waveform Envelope 
0 

.--1 

X 

~ 

Cl 

:::::> 

8 

H 

H 

~ 

~ -

~ 

U) 

H 

:::::> 

~ 

2 .8 I I I I 

8 rF = 5.0 MHZ 2.6 - T = .83 }.I sec 

ar = Of = .025 }.!Sec 

AF = 5.0 MHz - 2.4 

2.2 

2.0 1\ 

1.8 

1.6 

1.4 

1.2 

1.0 

. 8 

. 6 

. 4 

./""'-... 

v \ 

. 2 \ 

\ 

0 J f'-., 

-1.0 -.5 0 . 5 1. 0 1.5 2.0 2 . 5 3.0 3 . 5 4 . 0 

Time in vsec 

Figure B-10. Simulated IF Output T~e Waveform Envelope 

B-20 
3.2 

3.0 

2.8 

2.6 

2.4 

2.2 

2.0 

1.8 

0 

...-t 1.6 

...-t 

>< 

r.:l 1.4 

0 

0 

8 

H 

H 1.2 Po. 

~ 

r.:l 

U) 1.0 

H 

0 

Po. 

. 8 

. 6 

.4 

• 2 

0 

I I I 1 

8 IF = 5.0 MHz -

.. = .83 J.lSec 

CJr = C1f = .025 ).lSeC 

6.F = 20.0 MHZ -

~ 

) l~ ~ 

-1.0 -.5 0 . 5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 

Time in ).lsec 

Figure B-11. Simulated IF Output Time Waveform Envelope 

B-21 
B-22 

Figure B-12. Measured IF 

Output Time Waveform 

BIF = 5.0 MHz 

T = . 83 lJSec 

D.F = 0 

Figure B-13. Measured IF 

Output Time Waveform 

8 IF = 5 . 0 MHz 

T = .8 3 lJSec 

D.F = 5.0 MHz 

Figure B-14 . Measured IF 

Output Time Waveform 

BIF = 5. 0 MHz 

T = .83 llSec 

D.F = 20.0 MHZ 
1 80 

1 20 

60 ~ 

....:l 

~ 

tx:t ~ I 

"' [J.l 

l.oJ (/) 0 

,ex; 

::r: 

A.. 

-60 

-120 

- 180 

BrF= 5. 0 MHz I T = .83 }.lSec ~ or= of= .025 }.lsec 

6F = 5. 0 MHZ 

-.6 -.4 -.2 0 .2 . 4 . 6 . 8 1.0 1.2 

Time in usee 

Figure H-15 . Simulated IF Output Phase Modulation for an 

off-tuned Pulse Signal 
k = 

F = 

= 

Boltzmann's constant = 1. 38 x 10 - 23 Watt- sec 

Ok 

Receiver noise figure = 4 dB 

Receiver IF 3 dB bandwidth, in Hz 

Expressing Equation B- 34 in dBm 

NidBm ::- - 174 dBm + 10 log BIF + F (B- 35) 

The interference- to- noise ratio at the receiver RF input can be expressed as: 

INRI = 

Where: 

II dBn = Interfer ing signal peak power level a_t the receiver 

input, in dBm 

IF FILTER INR TRANSFER PROPERTIES 

(B- 36) 

Since the IF filter has the narrowest bandwidth and sharpest selectivity 

characteristics in the radar receiver front end, the filtering prior to the 

receiver IF filter can be neglected for analytical simplicity, and the 

interference to noise ratio at the IF filters input (INRIFi} can be treated as 

being equal to the receiver input interference to noise ratio. Thus: 

INRIFi = INR1 (&-37) 

= Ir - Nr d&n d&n tB-37a) 

The receiver IF output interference to noise ratio, INRIFo• is determined by 

the receiver FDR, and can be expressed as: 

INRIFo = INRr - FDR (B-38) 

Where the FDR factor is given by Equation B- 21. 

B-24 
APPENDIX C 

MTI CHANNEL TRANSFER PROPERTIES 

INTRODUCTION 

Radars in the 2.7 to 2.9 GHz band generally employ coherent Moving 

Target Indicator (MTI) phase detector. Coherent MTI radars make use of the 

phase fluctuations in the target return signal to recognize the doppler 

component produced by a moving target. In these systems, the amplitude 

fluctuations are removed by the phase detector. A 30 MHz signal coherent 

with the transmitted pulse signal is mixed with the 30 MHz target IF output 

response to produce a signal proportional to the phase difference between the 

target return and the coherent reference signal. The video signal out of the 

phase detector is then low pass filtered and fed to the cancellers which 

suppress stationary targets since their phase difference is the same from 

pulse-to-pulse. 

Both single channel and dual channel (inphase and quadrature ) MTI 

processing is employed by radars in the 2.7 to 2.9 GHz band. The single 

channel MTI processors are either analog or digital types. The analog MTI 

processors do not have A-D converters and use delay line cancellers, while 

digital MTI processors have A-D converters and use shift register cancellers. 

The digital shift register cancellers have a much higher stability and do not 

decay in time. Figure C-1 shows a block diagram of a typical single channel 

digital MTI processor. Figure C-2 shows the block diagram of a dual channel, 

inphase (I) and quadrature (Q), digital MTI processor. 

This appendix discusses the noise, desired signal, and interfering 

signal transfer properties of the MTI phase detector, low pass filter, and 

cancellers. The transfer properties of analog and digital MTI cancellers can 

be treated identically with the exception of the quantization noise due to A-D 

conversion, roundoff, and truncation inherent in digital processing. For 

dual MTI channel processing, it is only necessary to analyze one channel 

since both the I and Q channels are identical with the exception of the COHO 

signal being shifted 90 degrees and to take into account the transfer 

properties of the combiner. The signal processing properties of the IF 

linear-limiting amplifier are discussed in Section 3 and Appendix B. 

PHASE DETECTOR TRANSFER PROPERTIES 

Figure C-3 shows a simplified block diagram of a coherent MTI radar 

phase detector. The analysis of the signal transfer properties of the MTI 

phase detector is very similar to the radar mixer (Appendix A). Assuming 

linear transfer properties for the phase detector, the noise and signal can 

be treated separately. 

To calculate the noise power at the input and output of the phase 

C-1 
(") 

I 

N 

IF LINEAR ~ PHASE t- LOW 

LIMITING DETECTOR PASS 

.IIJ.fPLIFIER FILTER 

COHO 

REFERENCE 

SIGNAL 

Figure C-1. Digital MTI Channel Block Diagram 

t-- A-D f---4 CANCELLER 

CONVERTER 
() 

I 

w 

c 

LINEAR - LIMITING 

AJ.IPLIFIER 

Figure C-2 . 

PHASE LOW 

DETECTOR PASS A-D CANCELLER 

FILTER CONVERTER 

COHO 

REFERENCE 

SIGNAL CO!~BINER 1-

90° 

PHNiE . SHIFTER · 

LOW 

4 PHASE PASS A-D CANCELLER DETECTOR FILTER CONVERTER 

' --

Inphase and Quadrature Digital MTI Channel Block Diagra m 
(") 

I 

~ 

PHASE DETECTOR INPUT PHASE DETECTOR OUTPUT 

vpdi(t) = Bp(t')cos[ t+ (t')] vpdo(t) 

COHO SIGNAL 

v (t) = cos[ S t+ ~ ] c 0 c 

Figure C-3. Radar Coherent MTI Phase betector 
detector (Npdo and Npdi), the bandpass noise model is used, and the input 

noise signal, npdi(t), is given by: 

cos Bt + ns(t) sin ~t • 

(C-1) 

Where npdi(t) is the IF bandpass noise at the input of the MTI phase 

detector, and the noise power of Npdi(t) is given by: 

(C-2) 

Generally, the COHO signal power level is greater than 0 dBm. 

Therefore, the COHO noise figure (conversion loss) is very small and can be 

neglected . Also, the COHO signal is usually filtered and the noise 

suppressed, thus permitting the COHO signal noise level to be neglected . If 

npdi(t) is applied at the input of the phase detector (which multiplies the 

incoming noise signal, npdi(t), by vc(t), then npdo(t) , the output noise of 

the MTI phase detector is given by: 

nc(t) cos ~t.cos (~t ~c) 

+ ns(t) sin 6t

0 . cos Cet 0 +~c) 

nc(t) [cos (2~t ~c) +cos (¢c)] 

2 

~in (2Bt + ¢c) - sin (¢c)] 0 

(C-3a) 

(C-3b) 

The terms cos (2St~c) and sin Q 

ns(t), respectively, shifted at 

video filter at the phase detector 

(28~~c) represent the spectra of nc(t) and 

(2~t) and are filtered out by the low pass 

output. Hence, npdo(t) is given by: 

npdo(t) nc(t) 

2 

cos ($c) - ns(t) sin (~c) 

2 

c-s 

(C-4) 
and the MTI phase detector output noise power is: 

2 npd.o (t) (C-Sa) 

(C-Sb) 

Since the phase detector is sensitive to both the amplitude and phase of 

the detector input, the noise amplitude distribution at the phase detector 

output is Gaussian since the phase detector input noise amplitude 

distribution is Gaussian. 

Desired/Interfering Signal 

It is shown in Appendix B that the desired and interfering signal IF 

output time waveform (Vrp0 (t), Equation B-33), MTI phase detector input time 

waveform, can be expressed as: 

v pd i ( t) Bp(t') cos t + $ 0 + <P(t')] (C-6) 

Since we are only concerned with the peak power of the signal, p(t') equals 

1, and phase detector input signal peak power (the mean square of vpdi(t)) 

is: 

2 v p di (t) (C-7) 

The radar COHO signal can be defined as: 

vc(t) cos [B0 t + <Pe l (C-8) 

Where: 

0 = Receiver tuned IF frequency, in radians per second 

cflc = Phase of COHO signal, in radians 

The signal voltage time waveform at the phase detector output can be 

found by performing the operation shown in Figure C- 3, and is given by: 

C-6 
vpdo(t) ( C- 9a) 

= Bp(t') cos [30 t + ¢> 0 + ¢>(t ' )] .cos [80 t + d>c] 

= Bp(t') [cos[280 t + ¢> 0 + ¢>C t') +<Pel 

2 

+cos [ cf>(t ') + 4> 0 - <l>cll 

< c - 9b > 

( c - 9c) 

The first term of Equation C-9c is filtered out by the low pass video filter 

at the phase detector output, resulting in a signal at the phase detector 

output of: 

Bp(t') cos [~(t') + ~cl 

2 

and a signal output peak power (the mean square of vpdo(t)) of: 

2 [vpdo (t)) 

(C-10) 

(C-lla) 

(C-llb) 

The term ~(t') in Equation C-5 is the phase modulation produced by the 

radar IF filter transfer properties when the pulsed interfering signal is 

off- tuned. ~(t') consists of a steady state term which is a function of the 

frequency separation (6F) between the interfering signal and victim radar 

tuned frequency, and a transient term. A detailed discussion of this phase 

modulation on the interfering signal is given in Appendix B (see Figure 

B-15). A further discussion of the steady state and transient phase 

modulation properties of off- tuned pulsed interference will follow in the MTI 

video low pass filter transfer properties. 

In the case where the signal is on-tune, 6F=O, the term ~(t') equals 

zero for the steady state portion of the pulse. For this case the signal at 

the phase detector output is given by: 

C-7 
Vpdo(t) Bp(t') cos 0 ~c) 

2 

and the signal phase detector output peak power is given by: 

(C-12) 

(C-13) 

The term cl is the phase difference between the signal and the reference 

COHO signal. Therefore, the signal voltage waveform at the phase detector 

output will vary between ± B/ 2. The signal at the phase detector input can 

be assumed to have a uniform phase difference distribution between 0 to 360 

degrees with the reference COHO signal. Thus, if the signal power at the 

phase detector output is averaged over all phase angles, the si gnal power is 

given by: 

(C-14a ) 

(C-14b) 

Using Equations C-5b, C-11b, and C-14b, the MTI phase detector SNR and 

INR transfer properties are given by: 

SNRpdi (C-15 ) 

Signal-Plus-Noise Distribution 

The noise probability density function at the phase detector output is 

Gaussian. This is due to the fact that the phase detector is amplitude as 

well as phase sensitive . The noise amplitude Probability Density Function 

(PDF ) at the input to the phase detector is Gaussian distributed, and the 

noise phase PDF is uniform distributed. Therefore, the noise amplitude PDF 

at the phase detector output is Gaussian. If one considers a fixed amplitude 

( non-fluctuating) desired or interfering signal at the phase detector input, 

the signal-plus-noise at the phase detector output is given by: 

vpdo ( t) N ( t) + A cos ~ (C- 16) 

C-8 
where: 

N(t) = Noise amplitude which is Gaussian distributed, in volts 

A = Desired or interfering signal amplitude, in volts 

~ = Phase difference between received signal and COHO which 

is uniform distributed 

Papoulis (1965) derives the probability density function for Equation C-16 

which can be expressed as: 

where: 

p(v,A) 1 [ e 

-(v-Acosp) 2 

2<12 

o = rms noise level, in volts 

(C-17) d~ 

Equation C-17 can not be written in closed form . The MTI channel phase 

detector output was simulated to investigate trade-offs in suppressing 

asynchronous interfering signals. The simulation of the radar MTI channel is 

discussed in Appendix E. Figure C-4 shows the PDF given by Equation C- 17 as 

a function of the signal-to-noise ratio. The PDF was obtained by simulation. 

M[I LOW PASS FILTER TRANSFER PROPERTIES 

The low-pass filter in the MTI channel is used to reduce the MTI channel 

video noise level. The low- pass filter bandwidth (Blpf) is approximately 

equal to 1/T where T is the desired signal pulse width. The MTI channel IF 

bandwidth is always much greater than 1/T (generally 5.0 MHz) to produce a 

constant phase characteristic across the desired pulse . Therefore, a 

narrower low-pass filter bandwidth will improve the video signal-to-noise 

ratio. The MTI channel low pass filters are usually several stages. The lowpass filter frequency response can be expressed as: 

ALp(F) 

where: 

n = 

y 

1 

[l + j (-F-)y]n 

FL 

Low pass filter 3 dB cutoff frequency, in Hz 

Number of low pass filter stages 

C-9 

(C-18) 
.:X: 

' 

:> 

~ 

(") 

I 0., 

1-' 

0 

3. l I I I 

RMS Noise Level (o) = 0 . 25 Volts 

2. 

Noise Only 

! / 

l. 

S/N = 5 dB 

{[ ~ I 

S/N = 10 dB 

~ ~lSdB S/N~2 dB 

~ I 

0. 

-5 . 

V' 

-4 . -3 . 

/ // 7 

-2 . - 1. 

'" '-' <:--< I 

0. l. 2 . 3 . 4. 5 . 

VOLTS 

Figure C-4 . Probability Density Funct1on for Noise Only 

and for Signal-Plus- Noise at the MT! Phase 

Detector Output. 
~ 

The noise t r ansfer pr operties of the MTI low pass filter can be 

expressed as: 

Nlpo Nlpi + 10 log 

Blpf 

BrF ( C-19) 

For a radar with a 5.0 MHz IF bandwidth and a 1.2 MHz low pass filter 

bandwidth, the noise power at the low pass filter output is given by: 

Nlpi - 6 . 2 dB (C-20) 

Therefore, the low pass filter reduces the MTI channel noise level by 6 . 2 dB . 

Desired/Interfering Signal 

The desired and interfering signal low pass filter output time response, 

V1 0 (th can be obtained by multiplying in the f r equency domain the low pass 

fil~er frequency response with the· phase detector output signal frequency 

spectrum, Vpdo(F) , and taking the Fourier transform. That is: 

,../ -1 

_;f [Vpdo(F) .ALp(F)] (C-21) 

Measurements made on an ASR- 8 showed that as an interfering signal is 

off-tuned (6F), the signal level followed the low pass filter selectivity due 

to the sinusoidal modulation during the steady state portion of the pulse . 

However, for 6F greater than 3 MHz, the off- tuned interfering signal response 

started to follow the interfering signal RF frequency spectrum, and the low 

pass filter interfering signal output response was caused by the phase 

modulation that occurs during the transient part (rabbit ear response 

occurring at the leading and trailing edge of the IF filter output response, 

see Figures B-10, B-11, B-13, and B-14) of the interfering signal time 

waveform. Figure C- 5 shows a photograph of.the phase detector output time 

waveform of a 60 ~s pulse signal off-tuned'200 KHz . The measurement was made 

on an ASR-8 radar . The pulse width was set at 60 ~s to demonstrate the 200 

KHz sinusoidal modulation during the steady state portion of the pulse which 

is caused by the phase modulation produced by the IF filter transfer 

C-11 
C-12 

Figure C-5, Measured MTI 

Low Pass Filter Output 

Time Waveform 

T = 60 ll SeC 

6F = 200 kHz 

Figure C-6, Measured MTI 

Low Pass Filter Output 

Time Waveform 

T = .83 lJSec 

6F = 5. 0 MHZ 

Figure C-7, Measured MTI 

Low Pass· Filter Output 

Time Wav eform 

T = ,83 ll SeC 

6F = 5. 0 MHZ •I 
properties, and is equal to the off-tuned frequency . Figure C-6 shows a 

photograph of an ASR- 8 low pass filter output of a .83 s pulse off- tuned 5.0 

MHz. Since the low pass filter interfering signal output response for 

off- tuned interference is due to the phase modulation which occurs during the 

transient portion of the IF filter response, the low pass filter output 

interfering signal time response changes from pulse- to- pulse. However, the 

average pulse amplitude appears to follow the interfering signal RF spectrum 

envelope. Figure C- 7 shows a photograph of the low pass filter output for 

the same interfering signal parameters as in Figure C- 6 . However, the phase 

modulation during the transient portion of the interfering signal did not 

cause a low pass filter output response. 

MTI CANCELLER TRANSFER PROPERTIES 

The target return ~'gnals after phase detection are processed in the MTI 

cancellers. The MTI canceller circuits provide for cancelling fixed target 

signals (clutter) , such as buildings, hills, and trees and allowing only 

moving targets, such as aircraft to be displayed on the PPI. The action of 

the MTI cancellers is that of a linear filter. In the ideal case, the 

clutter components will appear at zero frequency and at integral multiples of 

the radar Pulse Repetition Frequency (PRF), and will be suppressed . 

Most radars in the 2.7 to 2.9 GHz band employ both single and double 

cancellers. Generally , the radars are operated in the double canceller mode 

which provides broader clutter-rejection nulls than the single cancellers. 

Some of the radars in the band also have the capability of introducing 

feedback in the double- canceller mode to improve the velocity response of the 

MTl filter. 

Both analog and digital filtering is used by the radars in the 2.7 to 

2.9 MHz band. Radars using analog filters (delay lines) have the capability 

of continuously variable feedback control, while the digital filter (shift 

registers) radars generalJy have several modes of fixed feedback . 

Staggered PRF is also generally employed by radars in the 2 . 7 to 2 . 9 GHz 

band to extend the blind speed of the radars. Analog radars typically have 

two or three staggers, while digital radars with their greater stability may 

have more than three staggers. The ASR- 8 has a four- stagger system, and the 

ASR- 7 has a six-stagger system. A radar operating in the staggered mode 

affects the range bins in which the interfering pulses may occur. However, 

the peak interfering signal transfer properties through the MTI canceller are 

not affected when operating in the staggered mode . Therefore, the staggered 

PRF modes of the radars can be neglected for analytical simplicity in 

determining the interfering signal peak power transfer properties of MTI 

cancellers. 

Single Stage Canceller Transfer Properties 

Figure C- 8 shows a block 

(first- order nonrecursive filter). 

diagram of a 

The canonical 

C-13 

single 

form 

stage canceller 

o f the single stage 
1 l~ ____ ----~~---~~ E+~---••o . Figure C- 8 . Firs t - Or der Nonrecursive Filter 

Figure C-9. Canonical Form of First- Order Nonrecursive 

Filter 

C- 1 4 
canceller is shown in Figure C-9. The Z- Transfer function of the first-order 

nonrecursive filter is given by : 

H(Z) 

where: 

= 

T = 

= 

n = 

1- z-1 

Unit delay (t - T) 

Radar pulse period, in seconds 

Binomial weighting factors, ( -1) i (~) 

Filter order, 1 

(C-22) 

The frequency response magnitude of the first- order nonrecursive filter 

transfer function is determined by letting z-l=e-jwdT, and is given by: 

(C-2Ja) 

(C-23b) 

where: 

= Doppler frequency of return signal, in radians per second 

Figure C-10 shows the frequency response characteristics for a first- order 

nonrecursive filter. The improvement factor (I) is 21.3 dB. The improvement 

factors are defined as the signal-to- clutter ratio at the output of the MTI 

system compared with that at the input, where the signal is understood as 

that averaged uniformly over all radial velocities, that is: 

I 10 log 

Equation C- 22 can be expressed in canonical 

n-order difference equation relating the input signal, 

signal, e 0 , by : 

C-15 

(C-24) 

form (Figure C-9) as a 

ein , to the output 
(l) 

Ul 

c: 

0 

P.. 

Ul 

(l) 

~ 

14 4 H ITS PER 

BEAMWIOTH 

08 Q9 1.0 

Figure C- 10. Frequency Response for a Single Stage MTI 

Canceller 

Figure C- 11 

T = . 83 usee 

PRF1 = 800 

Measured Single Stage MTI Canceller 

Output Time Waveform 

C-16 
where: 

n 

E 

i=O 

i=O,l, ... n 

ai = Binomial weighting factors, (-l)i (~) 

< c- 2 s) 

Therefore, the impulse response of a first-order nonrecursive filter to a 

single pulse is given by: 

(C-26) 

Noise 

The rms noise transfer properties of a single stage MTI canceller is: 

nMTilo = )ao2nMTili2 + ai2nMTili2 

[2nMTI 

li 

(C-27a) 

(C-27b) 

Thus, the noise power transfer function of a single stage MTI canceller is: 

NMTI + ~ dB (C- 28) 

li 

Desired Signal 

For a desired signal (synchronous signal), the signal power transfer 

gain for a single stage MTI canceller when averaged over all possible doppler 

frequencies is 3 dB (Nathanson , 1969). Since the noise power density is 

uniform over the MTI filter, the filter treats both noise and signal (on the 

average) alike. Thus, there is also a 3 dB power transfer gain in both noise 

and desired signal in a first-order MTI filter. Hence, the signal-to-noise 

ratio (SNR) at the MTI canceller output is the same as at the input to the 

MTI canceller. 

C-17 
Interfering Signal 

For an asynchronous interfering signal 1 the number of interfering pulses is 

increased by a factor of two for a single stage MTI canceller, resulting in 

an increase in the interfering signal average power. The asynchronous 

interfering signal bipolar output is converted back to unipolar resulting in 

two positive output pulses for each asynchronous input pulse. Figure C-11 

shows an aysnchronous interfering signal output measured on an ASR-8 

operating in the CANC 1 mode. Equation C- 26 indicates that the interfering 

signal peak power transfer properties of a single stage MTI canceller is 

given by: 

I MTilo (C-29) 

Using Equations C-28 and C- 29, the INR transfer properties of a single stage 

MTI canceller for asynchronous interference are given by: 

INRMTI lo - 3 dB 

Double Stage Canceller Transfer Properties 

(C-30) 

Figure C-12 shows a block diagram of a double stage MTI canceller with 

feedback (second-order recursive filter). The canonical form of the double 

stage canceller with feedback is shown in Figure C-13. Different modes of 

MTI canceller operation are obtained by varying the feedback coefficients 

(bland b2) . By changing the feedback coefficients, the doppler frequency 

response of the MTI filter is shaped to permit improvement in the subclutter 

visibility (SCV). TABLE C-1 shows the canonical feed-forward coefficients 

(ao, a1, a2) and feedback coefficients (bland b2) for the different modes of 

operation of the double stage cancellers in the ASR-7 and ASR-8. The 

Z-Transfer function of the second-order recursive filter is given by : 

H(Z) 

where: 

e 

0 a + a z-l + a z-2 

0 1 2 

z-l = Unit delay, (t- T) 

C-18 

(C-31) 
Figure C-12. Second-Order ~TI Filter with Feedback for 

Velocity Shaping 

Figure C-13. Canonical Form of Second-Order Recursive 

Filter 

C-19 
(') 

I 

N 

0 

'-

MTI MODE 

CANC 1 

1&2 CASC 

SCV- 25 

SCV-30 

SCV- 35 

SCV-40 

TABLE C-1 

MTI CANCELLER TRANSFER PROPERTIES 

FEED-FORWARD FEEDBACK NOISE GAIN COEFFICIENTS COEFFICIENT~ 

ao a1 a2 b1 b2 VOLTS dB 

1 -1 0 0 0 I 2 3 

1/2 - 1 1/2 0 0 /1.5 1. 76 

1/2 -1 1/2 1 1/4 -1/2 10 . 454 -3 . 42 

1/2 -1 1/2 1 -1/2 10 .6 - 2 . 21 

1/2 - 1 1/2 3/4 -1/2 /0 . 777 -1. 09 

1/2 -1 1/2 1/2 -1/2 1.0 0 

PEAK INTER- PEAK 

FERENCE GAIN INR 

VOLTS dB (dB) 

1.0 0 -3 

1.0 0 - 1.76 

0 . 50 - 6 . 0 -2 . 58 

0 . 50 - 6 .0 -3 . 79 

I 

0.625 -4. 08 -2 . 99 

I 

0 . 75 -2.49 - 2 .49 

J 
T = Radar pulse period, in seconds 

ai = Binomial weighting factors, (-1) i ( ~) n = filter order, 2 

bi = Canonic feedback factors 

The binomial weighting factors .are 1, -2, and 1 for a second order filter. 

However, on some of the new digital radars binomial weighting factors 

(feed-forward coefficients) of 1/2, -1, and 1/2 are used to reduce word size. 

Equation C-21 can be rewritten using the non-canonic feedback coefficient 

(Kl and K2): 

e 

H(Z) 0 

ein (C-32) 

The frequency response magnitude of the second-order recursive filter 

transfer function is determined by letting z-1 = e-jwdT and is given by: . . 

2 ( l + ( K l + K 2 ) + K 1 ) -·2 ( l + K 1 ) ( K 1 + K 2 ) c o s W d T + 2 K 1 co s 2 W d T 

(C-33) 

where: 

wd = Doppler frequency of return signal, in radians per second 

K1 and K2 = Feedback constants 

Figure C-14 shows the frequency response characteristics and improvement 

factor for several feedback constants for a second-order recursive filter. 

For the non-feedback MTI canceller mode ( 1 and 2 CASC, hl and b2 = 0 ) 

the MTI filter has no poles, and Equation C-31 reduces to: 

H(Z) (C- 34) 

Therefore, the MTI canceller output response becomes: 

(C-35) 

C-21 
0 

~ 

't:l 

--' 

Q) 

Ul 

~ 

0 

~ 

If} 14.4 HITS PER 

Q) BEAMWIDTH 

~ -50 

0 0.1 0.2 0 .3 0 .4 0 .5 0.6 0 .7 0.8 0 .9 LO 

Figure C-1~ . 

Wd/Radar PRF 

Frequency Response for a Double Stage 

Canceller with Feedback 

C-22 
Noise 

The rms noise transfer properties of a double stage MTI canceller for 

the non-feedback mode ( b1 and b2 = 0) is given by : 

n MTI 20 

Jl:SnMTI 2 i; 

,.;-;;--, nMTI2i i 

for 

f o r 

a· ~ ~, 

ai 1, 

{ c - :; ~·a ) 

- 1 , and ~ (C - 3 6b ) 

- 2, and 1 (C-36c) 

Thus, the noise power transfer function of a double stage MTI canceller is: 

' -1, and ~ (C - 37a) 

N + 7 . 8 dB; for a. MTI 2 i ~ l, - 2 , and 1 (C - 3 7b ) 

For the MTI canceller feedback modes of operation the 

properties are determined using a recursive algoritnm . 

transfer properties for the different feedback modes 

simulation (see Appendix E), and are shown in TABLE C-1. 

rms noise transfer 

The noise power 

were obtained by 

The noise amplitude distribution at the canceller output is Gaussian 

distributed with a zero mean . Since the MTI cancelJer sums the noise at the 

input to the canceller whir.h has a Gaussian amplitude distribution, the 

output noise amplitude distribution is also Gaussian. 

Desired Signal 

For des1red signal (synchronous signal ) , the signal power transfer gain 

for a double stage MTI canceller without feedback or wi th feedback when 

averaged over all possible doppler frequencies is the same as the noise power 

transfer gain (see noise gain in TABLE C- 1) . Since the noise power density 

is uniform over the MTI filter , the filter treats both noise and signal (on 

the average) alike . Thus the signal-to-noise ratio (SNR ) at the MTI 

canceller output is the same as at tne 1nput to tne canceller wnen averagea 

over all possible doppler frequencies. 

t--23 
Interf ering Signal 

For an asynchronous inter fering signal , a double stage MTI canceller 

will produce several interfering signal pulses at the canceller output for 

each interfering pulse at the MTI canceller input. These interfering pulses 

at the MTI canceller output are synchronous with the radar system (i.e., f~ll 

in the same range bin in successive azimuth change pulses) . The amplitude of 

these pulses pr oduced by a single interfering pulse are a function of the 

feed - forward coefficients (a 0 , a1, a 2 ) and the feedback coefficients 

(bl and b2) . 

For the non - feedback MTI canceller mode ( 1 and 2 CASC, h1 and h2 = 0), 

the response of a double stage MTI canceller to a single interfering pulse is 

given in Equation C- 35. The r efore , ea~h interfering pulse produces three 

synchronous interfering pulses. Equation C-35 indicates that the interfering 

signal peak power transfer properties of a double stage MTI canceller due to 

the binomial weighting factor s (feed- forward coefficients) is given by: 

for a. = ~. - 1, and ~ l. (C: - 38a.) 

I MTI 20 + 6 dB; for a. 

l. 

1 , - 2, and 1 (C - 3 8b ) 

Figure C- 15 shows a photograph of a MTI canceller output measured on an ASR- 8 

operating in the 1 and 2 CASC mode . The center pulse in Figur e C-1 5 is twice 

the amplitude of the first and thir d pulses due to the binomial weighting 

factors of 1/2, - 1, and 1/2 . Figure C- 16 shows a simulated MTI canceller 

output for the 1 and 2 CASC mode , and a four volt interfering pulse . The two 

additional pulses generated by the MTI canceller ane synchronous with the 

radar PRF . 

Using Equations C- 37 and C- 38 , the INR 

stage MTI canceller in non - feedback mode for 

and 1 are given by: 

- 1.8 dB 

transfer properties of a double 

a i = 1 /2 , - 1 , and 1 /2 or 1 , - 2, 

(C- 39) 

The double stage MTI canceller output response after rectification to an 

interfering pulse for various feedback modes of operation were simulated and 

a r e shown in Figures C- 17 through C- 20. The simulated responses are for a 

four volt inter fering signal at the MTI canceller input. The figures show 

that when operating in the feedback mode , there are mor e than three pulses 

out for each interfering pulse . However, by the third or fourth pulse, the 

interfer ing signal is down below noise level (1 volt) depending on the 

feedback constants and inter fering signal level . The interfering signal peak 

C-24 

• 
Figure C- 15 . Measur ed Double Stage MTI Canceller Response 

to an Int erfer ing Pulse (1&2 CASC Mode) 

8-

7 & 

6 & 

~ 

u 5 & 

"" ~ 4. 

0 

> 3 . 

2 . 

1 • 

o. 

o. 5 . 10 -15 .20. 25 .30.35.40.45 .50. 

5 MILLISECONDS/ CM 

Figure C-16 . Simulated Double Stage MTI Canceller Response 

to an Interfering Pulse (1&2 CASC Mode) 

C-25 
8. 

7. 

6. 

~ 

u 5. 

"-.. 

~ 4. 

0 

> 3. 

2. 

1 . 

o. L I II• 

0. 5. 10-15.20 .. zs .. 30-35 .40 .45 .so. 

5 MILUSECONDS/CM 

Figure C- 17. Simulated Double Stage MTI Canceller Response 

to an Interfering Pulse (SCV- 25 Mode) 

8. 

7. 

6. 

~ 

u 5. 

'-.,. 

~ 4. 

0 

> 3. 

2. 

1 . 

o. II I I 

o. 5. 10.15 .zo .zs .3o .35 .4o . 45 .sa. 

5 MILLISECONDS/CM 

Figure C- 18. Simulated Double Stage MTI Cance~.ler Response 

to an Interfering Pulse (SCV-30 Mode) 

C-26 

I 

. I 
8 -

7 .. 

6 .. 

2 us .. 

""" ~ 4 .. 0 

> 3 .. 

2 .. 

1 . 

0 .. II I I 

o. 5-10.15.20.25.30 .. 35.40.45.50. 

5 MILLISECONDS/CM 

Figure C-19 . Simulated Double Stage MTI Canceller Response 

to an Interfering Pulse (SCV-35 Mode) 

8-

7 . 

6 . 

2 

u 5 . 

""" ~ 4. 

0 

> 3. 

2 . 

1 . 

0. 

I 

I I 

o. 5.10 .. 15-20.25.30.35.40-45.50. 

5 MILLISECONDS/CM 

Figure C- 20 . Simulated Double Stage MTI Canceller Response 

to an Interfering Pulse (SCV-40 Mode) 

C-27 
power transfer properties for each of the MTI canceller modes are shown in 

TABLE C- 1 along with the INR transfer properties of the various MTl canceller 

feedback modes. 

RECTIFIER 

The output of the MTI canceller circuits are fed to a full-wave 

rectifier in analog radars or an absolute value algorithm in digital radars 

to convert the bipolar video at the canceller output to unipolar. The 

rectifier output signal- to- noise ratio (SNR) is the same as at the rectifier 

input. The noise amplitude distribution at the full- wave rectifier output 

will be one- sided Gaussian since the noise amplitude at the MTI canceller 

output was Gaussian. The noise amplitude PDF at the rectifier output is 

given by: 

p(v) 2 0 < v < 00 

(C-40) 

where: 

o = rms noise level , in volts 

The desired signal- plus- noise amplitude distribution PDF at the single 

channel MTI rectifier output for a double stage MTI canceller is shown in 

Figure C-21. It should be noted that the rectifier output signal- plus- noise 

amplitude distribution PO~ shown in figure C- 21 is for the radar operating in 

the staggered mode and the signal averaged over all possible doppler 

frequencies . The PDF shown in Figure C- 21 was obtained by simulation. 

Although the signal-plus- noise amplitude distribution PDF at the rectifier 

output is not of the nature of a one- sided Gaussian distribution, it can be 

approximated by: 

p(v,A) 2 0 < v < + (X) (C-41) 

where: 

o = rms noise level, in volts 

A = Desired signal amplitude, in volts 

Figure C- 22 shows a plot of Equation C- 41 for comparison with the 

C-28 
(") 

I 

N 

\0 

~ 

,.:( 

' :> 

........ 

0. 

4 . r-------~------~-------r------~------~~------~------~-------

RMS Noise Level(o) = 0.25 Vol t s 

3. 

I __.JI' Noise Only 

I 

2 . 

N 

1 . ~~~-------+------~------+-----~~-----T-------r------1 

15 dB 

~ 

I S/N =, 20 dB 

0 .0. 1. 2 . 1. 4. 5. 6 . 7 . 

VOLTS 

Figure C- 21 . Probability Density Function for Noise Only and for 

Signal-Plus-Noise at the MTI Canceller Output for a 

Single Channel Double Stage Cancell e r (Simulated) . 

R. 
~ 

..:!; .. 

::> 

-

0. () 

I 

w 

0 

4 . .-----~------~----~------,------,------~----~~-----

.~ 

1r 

2 . 

1\, 

1. 

() . 

() . 

RMS Noise Level(o) = 0 . 25 Volts 

I 

Noise Only 

I . . 

= 5 dB 

= 10 dB 

I 

S/N = 15 dB 

20 dB 

1. 2 . 3 . 4. 5. 6 . 7 . 

VOLTS 

Figure C-22 . Probability Density Function of One-Sided 

Gaussian Distribution (Equation C- 41) . 

8 . 

. 
simulated single channel MTI rectifier output signal-plus-noise amplitude 

distribution PDF shown in Figure C-21. 

DUAL Mil CHANNEL TRANSFER PROPERTIES 

Figure C- 2 shows a block diagram of a dual channel (inphase and 

quadrature) MTI radar. The signal transfer properties of the inphase and 

quadrature channels are identical to the single channel transfer properties 

previously discussed. The output of each channel is combined in the 

following manner: 

( C-4 2) 

Circuit implementation to achieve Equation C-42· in the combiner is complex. 

Often a simplified approximation to Equation C-42 is implemented by summing 

the larger vector amplitude with one-half the smaller vector amplitude as 

shown below: 

R = Jrl + IQ/21 if lrl > Jql 

R c Jql + II/21 if III < lql 

(C-43) 

The noise amplitude distribution at the output of a dual Mil canceller 

is Rayleigh since the transfer properties of the combiner (Equation C-42) are 

similar to an envelope detector. The desired signal-plus-noise amplitude 

distribution PDF at the dual channel MTI combiner output for a double stage 

MTI canceller is shown in Figure C- 23. It should be noted that the combiner 

output signal-plus-noise amplitude distribution PDF shown in Figure C- 23 is 

for the radar operating in the staggered mode and the signal averaged over 

all possible doppler frequencies. The PDF shown in Figure C- 23 was obtained 

by simulation. Although the signal-plus-noise amplitude distribution PDF at 

the combiner output is not of the nature of a Rayleigh distribution, it can 

be approximated by: 

v p(v,A)= -- -­

(o2+A2/2 

where: 

2 2 2 

-v /2(0 +A /2) e 

o = rms noise level, in volts 

0 < v < + 00 (C-44) 

C-31 
() 

I 

w 

N 

-

~ 

' :> 

~ 

0. 

3 . 

RMS Noise Level(cr) 0 . 25 Volts 

Noise Only 

2. 1 f 1 t I I I I I I I 

l. tt 1\ \1 I I I I I I I 

10 dB 

15 dB 

20 dB 

Q. ew;; y > I:>, I ;>, I I ........... I I 

0. 1. 2. 3. 4. 5 . 6. 7. 8. 

VOLTS 

Figure C-/.3. Probability Density Function for Noise Only and for 

Signal-Plus-Noise at the MTI Canceller Output for a 

Dual Channel Double Stage Canceller (Simulated). 
A = Desired signal amplitude, in volts 

Figure C- 24 shows a plot of Equation 

simulated dual channel MTI combiner output 

distribution PDF shown in Figure C- 23 . 

C-44 for comparison with the 

signal- plus- noise amplitude 

The fact that dual MTI cancellers have the COHO reference signal of the 

inphase and quadrature channels phase shifted by 90 degrees , and the method 

in which the t wo channels are combined , a signal- to- noise rati o (SNR ) 

improvement is achieved over a single MTI channel . The SNR improvement of 

dual MTI channels over a single MTI channel was investigated (Nathanson and 

Luke , 1972), and is shown in TABLE C- 2. The table shows the SNR improvement 

for a single pulse (unintegrated pulse train) as a function of probability of 

false alarm (Pr) and probability of detection (Pd) . For an asynchronous 

interfer ing signal , the INR enhancement of a dual MTI channel over a single 

MTI channel is appr oxi matel y 1 to 2 dB at MOS . 

C-33 
r. 

I 

w 

.c-

.:!: 

> 

~ 

p, 

3· .------.-------r------r------.r------r------~----~------~ 

RMS Noise Level( o) 0 . 25 Volts 

~Joise Only 

2 · I I \ I I I I I I I I 

5 dB 

1. II f ' \ I I I I I I I I 

0 . 

10 dB 

= 15 dB 

= 2() dR 

~ '\..I~ -----1 :t I I I 

0 . 1. 2 . 3 . 4 . 5 . 6. 7 . 8 . 

V0LTS 

Pigure C-24. Probabilitv Density Function of Rayleigh 

Oistrihution (E~uation C-44). 
() 

I 

w 

V1 

~ ' 

0. 5 

0 . 8 

0 .9 

0.95 

TABLE C-2 

SIGNAL-TO-NOIS~ IMPROVEMENT (IN DECIBELS) RELATIVE TO 

DETECTION OF I2 + Q2 (FLUCTUATING SIGNAL) , SINGLE PULSE 

lrl Only or lol Only 

10- l l0- 2 10- 3 10- 4 lo- 6 10-8 

. 3 . 29 3.81 4.05 4.19 4.35 4 . 45 

6 . 45 7 . 17 7.48 7 . 66 7 . 86 7 .97 

9 . 12 9 . 92 10.26 10.45 10.66 10.78 

11. 95 12.79 1 3 . 1 4 13.34 13 . 56 13 . 68 

10-10 

4.51 

8.04 

10.85 

13.7 6 

I 
APPENDIX D 

INTEGRATOR TRANSFER PROPERTIES 

INTRODUCTION 

The process of summing the echo pulses from a target is called 

integration . This appendix discusses the transfer properties of integrators 

(enhance rs) used by radars in the 2.7 to 2.9 GHz band. The discussion 

includes the integrator transfer properties of noise , desired signal, and 

asynchronous interfering signals. It should be noted that this appendix does 

not discuss the cathode ray tube display integration, or the integration 

properties of the eye and brain of the radar operator, but is limited to the 

discussion of electronic device integrators only . 

Integrators are generally used in the primary radars for two reasons: 

1. To enhance weak desired targets for PPI display. 

2. To suppress asynchronous pulsed interference. 

The principle of the radar video integrator is that radar signal returns from 

a point target consist of a series of pulses generated as the radar antenna 

beam scans past the target, all of which fall in the same range bin in 

successive periods (synchr onous with the system) . It is this series of 

synchronous pulses from a target which permits integration of target returns 

to enhance the weak signals. The number of pulse returns (N) from a target 

depends upon the radar antenna beamwidth (BW), the rate J f antenna r otation 

(RPM), the radar pulse repetition rate (PRF) and the target characteristics. 

The equation for the number of pulses from a point target is given by 

(Skolnik, 1962 ) : 

N PRF BW (D-1) 

6 

Where: 

PRF = Radar pulse repetition frequency, in PPS 

BW = Antenna 3 dB beamwidth, in degrees 

RPM = Antenna scan rate, in rpm 

A range value of N for radars in the 2.7 to 2 . 9 GHz band is 12 to 20 . The 

integrator will suppress asynchronous interference since the interfering 

pulses will not be separated in time by the radar period, and thus will not 

occur in the same range bin in successive periods (asynchronous with the 

system). Therefore, the asynchronous interference will not add- up, and can 

be suppressed . 

D- 1 
All rada rs in the 2.7 to 2 . 9 GHz band empl oy post detection or 

noncoherent integr ators. The types of post detection integrator employed in 

radars in the 2.7 to 2.9 GHz band can be categorized either as a feedback 

integrator or a binary integrator. Radars employing feedback integrators may 

be of analog (delay line) or digital (shift register) type. Only digital 

binary integrators are used. 

The following is a discussion of the transfer properties of the feedback 

and binary integrators. The noise, desired signal and asynchronous 

interfering signal transfer properties are discussed along with the tradeoffs 

of the desired signal transfer properties in suppressing asynchronous 

interference . The transfer pr operties were investigated by measurements, 

analytically and by simulating the noise, desired signal, interfering 

signals, and the feedback and binary integrator hardware . Appendix E 

contains a detailed discussion of the methods used to simulate the noise, 

desired signal, interfering signal, and the actual radar hardware simulated. 

fEEDBACK INTEGRATOR 

Figure D- 1 shows a block diagram of a typical feedback integrator. The 

radar period delay (1/PRF) for digital radars is achieved by clocking a shift 

register, and the actual integrator hardware is essentially represented in 

rigure D- 1. Analog radars in the 2 . 7 to 2 . 9 GHz h3nd generally use quartz 

delay lines, thus accomplishing the delay ousti~ally to reduce the size of 

the delay line. However, the inherent loss of quarLz delay lines requires 

use of additional hardware, such as, modulators, attenuators, amplifiers, 

detectors, and balancing circuits (AGC) to achieve integration . If the 

analog integrator balancing circuitry is aligned properly, the transfer 

properties of an analog integrator can, for analytical si~plicity , be modeled 

by the operations shown in Figure D- 1. Digital integrators will also 

introduce some r oundoff or truncation error. However, the error due to 

roundoff and truncation is generally very small and can be neglected in most 

cases. 

The feedback integrator depicted in Figure D- 1 consists of an input 

limiter, an adder, and a feedback loop with an output limiter and a delay 

equal to the time between transmitter pulses (1/PRF). The following is a 

discussion of the transfer properties of these feedback integrator elements 

to noise , desired signal and asynchronous interference . 

Input Limiter Transfer Properties 

The integrator input limiter serves as a video clipping circuit to 

provide constant level input pulses to the feedback integrator, and is a 

necessary integrator circuit element to suppress asynchronous interference . 

The input limiter limit level is always adjustable, and controls the transfer 

properties of the feedback integr ator. The effect of the limiter limit level 

setting on the desired signal, interfering signal, and noise transfer 

properties of the integrator are discussed in detail in latter sections of 

this appendix . The desired signal- to- noise (SNR ) transfer properties of the 

D-2 
0 

I 

w 

Cin INPUT +I \ OUTPUT eout 

LIMITER \ I LIMITER 

+.......,,......, 

DELAY .___ K - T0 = l/PRF 

Figure D-1 . Feedback Integralor Block Diagram 
limiter are given by: 

SNR0 

Where: 

SNRi ;for SNRi < LNR 

LNR ; for SNRi > LNR 

(D-2) 

= Limiter output peak signal- to-rms noise ratio, in dB 

SNR i 

LNR 

= Limiter input peak signal-to-rms noise ratio , in dB 

= Limiter limit- to-rms noise ratio, in dB 

The interference-to- noise (INR) transfer 

can also be expressed by Equation D- 2 . Also 

transfer properties of the output limiter. 

limit level is set at 4.0 volts. 

Feedback Integrator Loop Transfer Properties 

properties of the input limiter 

Equation D- 2 represents the 

Generally the output limiter 

The feedback integrator loop consists of an adder, an output limiter, a 

feedback loop with a delay equal to the time between transmitter pulses 

(1/PRF) and a loop gain of K. The overall gain, K, of the feedback loop is 

less than unity to prevent instability . 

The signal transfer properties of the integrator feedback loop to noise, 

desired signal, and asynchronous interference will be treated separately. 

This is possible since the integrator feedback loop is a linear device . 

First consider noise. 

Noise 

The noise voltage amplitude distribution at the feedback intPgrator 

input is either Rayleigh distributed (normal channel or inphase and 

quadrature MTI channel) or a one-sided Gaussian distributed (single channel 

MTI). Both the Rayleigh and one-sided Gaussian distributions have a non-zero 

mean. To minimize the noise gain through the feedback integrator, prior to 

the feedback integrator circuitry shown in Figure D- 1, the radar recei vers 

generally have an attenuator, subtracter and bottom clippe r. The noise 

transfer properties of a non-zero mean distribution can be expressed as: 

2j 2 { M 

K llnri+\j ~ o (D - 3) 

D-4 
Where: 

onii = The input noise amplitude distribution rms level, in volts 

~nri = The input noise amplitude distribution mean level , in volts 

K = Integrator feedback factor . 

The sum series in the above equation are a geometric series, and the equation 

can be rewritten as: 

nli __ 1 __ a2 ( ) 

1 K2 

+ ( D-1<>) 

The affect of the attenuator, subtracter, and bottom clipper is to r educe the 

mean level of the noise amplitude distribution . Alignment procedures o f this 

circuitry generally result in the rms noise level being much greater than the 

mean noise level. In this case , the second term of Equation D- 4a can be 

neglected for analytical simplicity, and the noise treated as an uncorrelated 

zero mean amplitude distribution . Making this assumption , Equation D- 4a 

becomes: 

(D -4b) 

Therefore, the noise power transfer function of a feedback i ntegrator loop 

f or the radar normal channe l is: 

= (D-5) 

In digital radars such as the ASR-8, the analog- to-digital (A/D) 

converter causes quantization errors due to truncation . The truncation at 

low signal levels (less than one volt) has an effect of causing a non-linear 

feedback constant , K. For low signal levels the feedback signal can vary 

between K and approximately 1/2 . This has an overall affect of reducing the 

feedback integrator noise gain given by Equation D-4b. 

Since the feedback integrator sums or convolves the noise distribution 

at the input of the feedback loop with itself continuously, the central limit 

theorem applies which states that the noise distribution at the integrator 

feedback loop output will be Gaussian distributed even though the input noise 

distribution was Rayleigh (normal or dual MTI channel) . 

D-5 
The noise out of the MTI channel is correlated from range/ azimuth cell 

to range/ azimuth cell. Figure D-2 shows how the noise becomes correlated by 

the transfer properties of a second-order MTI filter. The figure shows the 

input noise samples (N 1 through N 5) for a specific instant in time (T1 

through T9. The noise level at the canceller output as a function of time 

(T1 through T5 ) is also shown. The figure shows that at time T5 , the noise 

output consists of noise samples N3 , N4 , and N

5

• At timeT 4, the noise 

output consists of noise samples N2 , N :y and N 4. Since noise samples N 3 and 

N4 contribute to the noise level at time T4 and T5, the noise at the MTI 

canceller output is correlated. The increase in no1se amplitude caused by 

the integration of the correlated MTI channel noise, is a function of the MTI 

canceller Type (single stage canceller, double stage canceller, etc. ) . The 

MTI channel noise level increase was simulated by Trunk, 1977, and found to 

be approximately 1 dB for a single stage canceller and 1.8 dB for a double 

stage canceller. Therefore, the feedback integrator noise transfer 

properties for the MTI channel can be obtained using Equation D-5 and adding 

1 dB for a single stage MTI canceller and 1.8 dB for a double stage MTI 

canceller. 

Desired Signal 

The desired signal phases at the input of the feedback loop i ntegrator 

are coherent and add directly since the feedback loop delay is equal to the 

desired signal pulse period. For the feedback loop shown in Figure D-1, the 

general output response (YN) at the Nth input pulse (XN) is given by: 

= (D- 6) 

Equation D-6 is a first order constant coefficient linear difference equation 

with a solution 

(

1-I<N ) 

1-K 

(D- 7) 

Recognizing the transfer f~ncti n in Equation D-7 as the geometric 

progression for a series, Equation D-7 become s: 

[ 1 +K+K2+ •. . + KN- l] • XN 

N 

l.: 

i=l 

K(i- 1) • X 

N 

D- 6 

(D- 8a) 

( D- 8 b) 
::J 

I 

'-.) 

= 

ein ao eo 

(nl) Tl 

(nl) Tl 

(n2 - 2nl)T2 

(n2)T2 DELAY (n 3- 2n2i n1l T., T =1/PRF (n3)T3 D (n4 - 2n3+n2)T (n4)T4 al (ns- 2n 4+n3)T (n5) T 

5 

DELAY 

TD=l/PRF 

a2 

Figure D- 2 . Canonical Form of Second - Order MTI Canceller Filter Showing 

Noise Correlation at MTI Channel Output 

J 

4 

5 
Thus, for N equal amplitude voltage input pulses (Sri), the Nth pulse 

amplitude at the integrator output (S 1 0) can be expressed as : 

("' 

~Io 

N 

= Sii E 

i=l 

(D- 9) 

The series exprrssed in Equation D-8a can be intuitively obtained using 

Figure D-1 (feedback loop), and recursively applying a series of N equal 

voltage amplitude pulses to the input . 

The signal-to- noise ratio enhancement (SNRE) factor for the integrator 

feedback loop for the normal channel can be obtained from Equations D-4b and 

D-7, and is given by : 

= - N 

20 log10 I ~=~ ) ... 

(IJ- 10) 

It should be noted that Equation D- 10 is only a first order 

approximation of the actual signal- to- noise ratio enhancement of a feedback 

integrator since it assumes a zero mean noise amplitude distribution, and a 

constant desired signal level. For the MTI channel the signal- to- noise ratio 

enhancement given by Equation D- 10 should be reduced by 1.0 dB for a single 

stage canceller and 1. 8 dB for a double stage MTI canceller due to the 

correlation of noise by the MTI cancellers. 

Equation D- 10 can be used to approximate the optimum feedback factor K 

for the radar design by max~m~zing the signal-to-noise ratio enhancement 

(SNRE). TABLE D-1 shows the SNRE as a function of the integrator feedback 

factor (K) for a range of number of pulses integrated (N) between 12 and 20 , 

which is a typical range of N for radionavigation radars in the 2.7 to 2 . 9 

GHz band . The asterisks in each column of the table indicate the maximum 

SNRE and optimum integrator feedback factor (K) for that particular value of 

N. For the range of number of pulses integrated (N) between 12 and 20, the 

optimum feedback factor (K) ranges from .90 to .94. The table also shows 

that if an integrator feedback factor of . 92 is used for radars with a range 

of N between 12 and 20, the loss in actual SNRE and maximum SN~ is less than 

.1 dB. Therefore , the design of the integrator feedback factor (K) for a 

range of number of pulses integrated is not that critical. 

Actually, the optimum value of K is difficult to obtain due to 

fluctuations in target returns (scintillation) and antenna pattern amplitude 

modulation, and thus requires a complicated Monte Carlo model to determine. 

Skolnik (1970) gives an empirical value of K as: 

K 1 -

1 . 56 

N (D-ll) 

D-8 
TABLE D-1 

FEEDBACK INTEGRATOR PEAK SIGNAL-TO- NOISE ENHANCEMENT 

FOR NORMAL CHANNEL ** 

Feedback Peak Signal-to- Noise Enhancement (SNRE) 

Factor N=12 N=l4 K N-16 N=18 N=20 

.70 7.41 7.47 7.50 7.52 7 . 53 

. 71 7 . 56 7.63 7.67 7.69 7 . 70 

.72 7 .7 1 7.80 7.84 7.86 7. 87 

.73 7 . 87 7.96 8 . 01 8.04 8.05 

.74 8.02 8 .13 8.19 8 . 22 8.23 

.75 8.17 8.29 8.36 8.40 8.42 

.76 8 . 32 8 . 46 8.54 8.59 8.62 

. 77 8 . 48 8 . 64 8.73 8.78 8.82 

. 78 8 . 63 8.81 8 . 92 8.98 9.02 

. 79 8 . 78 8.98 9.10 9.18 9.23 

. 80 8 . 92 9.15 9 . 29 9 . 38 9.44 

. 81 9.07 9.32 9.49 9 . 59 9.66 

.82 9.21 9.49 9 . 68 9 . 80 9.88 

.83 9.34 9.66 9.87 10 . 01 10 . 11 

.84 9 . 46 9.82 10 . 06 10.22 10.34 

.85 9.58 9.97 10.24 10.43 10 . 57 

.86 9.68 10.11 10 . 42 10.64 10.80 

.87 9 . 77 10.25 10.59 10.84 11.03 

.88 9 . 84 10.36 10.75 11.03 11.25 

.89 9.89 10.46 10.89 11.21 11.46 

.90 9 . 90* 10.53 11.01 11.37 11.66 

. 91 9.89 10.57* 11.10 11.51 11.84 

.92 9 . 82 10.56 11. 15* 11.61 11.99 

.93 9 . 69 10.50 11.14 11. 66* 12.09 

.94 9 . 48 10.36 11.06 11.64 12.12* 

. 95 9.16 10.10 10.87 11.51 12.05 

. 96 8 . 66 9.68 10.52 11.23 11.83 

. 97 7 . 89 8.98 9 . 90 10 . 68 11.36 

.98 6 . 62 7 . 79 8. 78 9.64 10.39 

.99 4 . 10 5 . 35 6. 43 7.36 8.19 

*Maximum signal-to-noise ratio enhancement 

**For MTI channel signal-to -noise ratio enhancement reduce the 

values in the table by 1.0 dB for a single stage canceler 

and 1.8 dB for a double stage canceler. 

D-9 
For N = 20, the value forK from Equation D-11 is .92, which is close to the 

value of K obtained using Equation D-10 (see TABLE D-1). 

Studies (Trunk, 1970) have been made which take into account pulse 

amplitude variations due to the antenna beam shape. Trunk concluded that the 

SNRE could be reduced by as much as 1.6 dB due to the antenna beam shape 

pulse amplitude variations. The actual reduction in SNRE due to the radar 

antenna pattern is between 0 and 1.6 dB, and is also a function of the 

integrator input limiter limit level setting. 

In congested areas where there is potential for asynchronous 

interference, adjustments to the integrator input limit level setting are 

required to suppress the asynchronous interference. However, adjustments of 

the limiter level setting affect the desired signal pulse train processing 

characteristics of the feedback integrator. Desired signal pulse train 

characteristics which are effected include: target azimuth shift, angular 

resolution and probability of detection . The following is a discussion of 

the desired signal transfer properties of a feedback integrator loop as a 

function of the input signal-to-noise ratio (SNR) and input limiter level 

setting. 

Figures D-3 through D- 6 show a simulated radar performance of a feedback 

enhancer for the normal channel as a function of the signal-to-noise ratio 

(SNR). The enhancer input limiter limit level (VL) was set at 2.0 volts, and 

the feedback factor (K) was set at 0.9~. The desired target return pulse 

train consists of 20 pulses. Each figure shows the simulated radar output 

with the enhancer off (unintegrated) and enhancer on (integrated). Figures 

D-3 (SNR = 3 dB) and ~ (SNR = 5 dB)show that with the enhancer off the 

desired signal is down in the noise. However, when the enhancer is on the 

signal is pulled out of the noise by the feedback enhancer. Figures D-7 

through D- 10 show the affect on the desired signal of adjusting the input 

limiter limit level (VL> of the feedback enhancer. The SNR for Figures D-7 

through D-10 was 15 dB. For comparison with the simulated integrator model 

(Figures D-7 through D-10), Figures D-11 through D-13 show actual measured 

ASR-8 normal channel integrated output for input limiter switch settings of 

15, 9, and 7, respectively. The receiver input desired signal level was set 

at 8~ dBm. 

Where: 

The target azimuth shift (w5 ) due to integration can be calculated by: 

Shift of the center pulse position of an integrated 

video pulse train relative to an unintegrated 

pulse train (Figure D-6a). 

D-10 

(D-12) 
!:: 

u 

.......... 

I-

_j 

0 

> 

,....... 

8 . 

7. 

6 . 

s . 

4 . 

3 . 

2 . 

1 ' 

o. 

o. 5 -10 .15 -20 -25 -30 .35.40 .45.50. 

5 MILLISECGNOS / CM 

Figure D- 3a . Simulated Normal Channel Unintegrated Target 

Return Pulse Train for a SNR = 3dB 

L: 

u 

.......... 

I-

_j 

0 

> 

........... 

s . 

7 . 

6 . 

5 . 

4 . 

3" • 

2 . 

1 • 

0 . 

o. 5-10.15-20.25.30.35.40.45-50. 

5 MILLISECGNOS / CM 

Figure D- 3b. Simulated Normal Channel Integrated Target Re t urn 

Pulse Train for a SNR = 3dB (VL = 2. 0) 

D-11 
8 . 

7 .• 

::L 

6. 

u 

-......... s. 

I-

_j 

0 4 . 

> 

......... 3 . 

f') L , 

1 ' 

o. 

o. 

Figure D-4a. 

8 . 

7 . 

::L 

6 . 

u 

-......... 5 . I-

_j 

0 4 . > 

..---. 3 . 

2 . 

1 . 

0 . 

o. 

S . lO . lS .20 .2S .30 .3S. 40 .4 S .50 . 

S MIL L. I S E C 0 N 0 SI C M 

Simul a t ed Normal Channel Unintegr a t ed Tar get 

Retur n Pulse Train for a SNR = 5dB 

S . lO . lS .20 .2S .30 .3S .40 .4S .50 . 

S MILLISECONOS/CM 

~igure D- 4b. Simulated Norma l Cha nnel Integrated Tar ge t Return 

Pulse Tr a in for a SNR = SdB (VL = 2.0) 

D-1 2 
8 . 

7. 

L 

6. 

u 

"- 5 . 1-

_J 

0 4 . 

> 

........ 3 . 

2. 

1 . 

0 < 

o. 

Figure D- 5a. 

8. 

7. 

L 

6 . 

u 

"- 5 . 1-

_j 

0 4 . 

> 

........ 3 . 

2. 

1 . 

o. 

0 . 

5 . 10 .15 .20 .25 .30. 35 .4 0 .45 .50 . 

5 MILLISECBNOS/CM 

Simulated Normal Channel Un integrated Target 

Return Pulse Trai n f or a SNR = lOdB 

5 . 10 .15 .20 -25 .30 .35 .40 .45 .50 . 

5 MILLISECBNOS/CM 

Fi gure D- Sb. Simulated Normal Channel Integrat ed Target Retur n 

Pulse Train for a SNR = lOdB (VL = 2.0) 

D-13 
L: 

LJ 

r-" 

_j 

~ 

;> 

~ 

8. 

7 . 

6. 

s. 

4. 

3. 

2. 

1 . 

o. 

0 . 5.10.]5.20.25.30.35-40-45.50. 

5 MILLISECBNDS/CM 

Figure D-6a. Simulated Normal Channel Unintegrated Target 

Return Pulse Train for a SNR = lSdB 

8 ·~~--~--~~--~--~--~~--~~ 

7 ·~-+--~--+-~---+--~--+-~---+~ 

6 ~-+--~--+-~---+--~--+-~---+~ 

s.~-+--4--4--~--+--4--~--+--+--~ 

4 ·~-rt~~~~~+-~---+--~--4---+-~ 

3.~+H+H+H~~~~M--+--4---~-+~ 

2 ~+H~H+H++H~H+H++HH+H+~---+--~--~ 

1 ·~~~H++H+H4+~H+~~~~H++H~~~ 

u. 

o. 5 .]0.15.20 .25.30.35 .40.45 .50 . 

5 MILLISECBNOS /CM 

Figure D- 6b. Simulated Normal Channel Integrated Target Return 

Pulse Train for a SNR = lSdB (VL = 2.0) 

D-14 
8. 

7 . 

::L 6-

u 

'-. 5. 

1-

_j 

~ 4 . 

> 

.......... 3 . 

2. 

1 . 

o. 

o. 

Figure D-7 . 

8 . 

7 . 

::L 

6 . 

u 

'-. s. 

1-

_j 

~ 4 . 

> 

.......... 3 . 

2 . 

1 . 

Q, 

0 . 

... 

Figure D-8. 

5.10.15.20.25.30.35.~0.~5.50. 

5 MILLIGECBNOS/CM 

Simulated Normal Channel Integrated Target Return 

Pulse Train for a SNR = 15 (VL = 1.0) 

5.10.15.20.25.30.35.40.AS.50. 

5 MILLISECBNDS/CM 

Simulated Normal Channel Integrated Target Return 

Train for a SNR = 15 (VL = 0.7) 

D-15 
L 

u 

........... 

t-

_j 

0 

> 

~ 

\'"'~ 0· 

7 . 

G. 

5 . 

4 . 

3 c 

') 

L.< 

1 . 

o. 

o. s . to.Js.zo.25 .30 .35. 40.45 .5o . 

5 MILLISECBNOS/CM 

Figure D-9. Simulated Normal Channel Integrated Target Return 

Pulse Train for a S~~ = 15 (VL = 0.5) 

L 

u 

........... 

t-

_j 

0 

> 

...---. 

8 . 

7 . 

6 . 

5 . 

4 . 

3 . 

2. 

1 . 

0 . 

0 . 5.10 .15 -20-25 .30.35.40 -45 .50 . 

5 MILLISECBNDS/CM 

Figure D-10 . Simulat ed Norma l Channel Integrated Target Return 

Pulse Trai n fo r a SNR = 1 5 (VL = 0. 34 ) 

D-16 
D- 17 

Figure D-11. Measured 

ASR-8 Normal Channel 

Integrated Output 

Limit Adjust = 15 

S z-84 dBm 

Figure D-12. Measured 

ASR-8 Normal Channel 

Integrated Output 

Limit Adjust = 

s 

9 

-84 dBm 

Figure D-13. Measured 

ASR-8 Normal Channel 

Integrated Output 

Limit Adjust 7 

S = -84 dBm 
$ 5 = Degrees of antenna rotation per pulse 

6 ·RPM 

p~ 

For an ASR-8 with an antenna RPM of 12.5 and PRF equal to 1000, $ s equals 

0.075 degrees per pulse. TABLE D-2 shows the target azimuth shift (Equation 

D-12) due to target integration for various SNRs and feedback integrator 

input limiter limit level settings. The table shows a target azimuth shift 

due to integration of approximately .900 degrees relative to an unintegrated 

target return pulse train. Also shown in TABLE D-2 is the fact that the 

target azimuth shift due to integration is essentially independent of the 

integrator input limit level setting. Therefore, hard limiting in the 

integrator input limiter to suppress asynchronous interference does not cause 

a significant increase in target azimuth shift. However, the feedback 

integrator causes a target azimuth shift of .900 degree3 over an unintegrated 

target return pulse train. 

The property of the radar to distinguish between targets is called 

resolution. A comparison of Figure D-6a (unintegrated target return pulse 

train) with Figures D-6b through D-10 (integrated target return pulse train) 

shows a decrease in target angular resolution when the feedback enhancer is 

used. The decrease .. in target resolution is determined by: 

~RES = 

Where: 

p = Difference in number of pulse~ above the noise 

level at the integrator input and output . 

(D-13) 

Figures D-6b through D-10 show a decrease in target angular resolution due to 

use of the feedback integrator of 1.2 to 1.5 degrees. For aircraft at a 

range of 60 nautical miles, this would result in a decrease in angular 

resolution of 1.5 nautical miles. 

In order to determine the effect of the integrator input limit level 

settings on the probability of target detection, the integrator output pulse 

train distribution must be best fitted to a Chi-square distribution by 

determining the degrees of freedom of the Chi-square distribution which best 

fit the integrator output pulse train. The probability of target detection 

was determined for the integrator input limit level set at 2 . 0 volts (Figure 

D-6b), and for the integrator input limit level set at 0.34 volts (Figure 

D-10). The mean peak signal-to-noise ratio for the pulse train shown in 

Figure D-6b was 20.35 dB, and the pulse train distribution best fitted a 

Chi-square distribution with four degrees of freedom. The mean peak 

signal-to-noise ratio for the pulse train shown in Figure D-10 was 18.48 dB, 

and the pulse train distribution best fitted a Chi-square distribution with 

D-18 

.. 
t:l 

I 

...... 

\.0 

Figure 

Reference 

Figure D-Jb 

Figure D-4b 

Fjgure D-Sb 

Figure ;)-6b 

Figure D-7 

Figure D-8 

Figure D-9 

Figure D-10 

TABLE D- 2 

TARGET AZIMUTH SHIFT CAUSED BY FEEDBACK INTEGRATION 

Signal- Input Center Pulse Target 

to-Noise Limiter Position Azimuth 

Ratio Limit Relative to Shift 

(JB) (Vol ts) Unintegra ted (Degrees) 

Pulse (ilCp) 

3 2.0 8 0 . 600 

5 2 . 0 10 o. 750 

10 2 . 0 12 0 . 900 

15 2 . 0 l3 0.975 

15 1.00 l3 0 . 975 

15 0. 7 13 0 . 975 

15 .so 12 0 . 900 

15 .34 12 0 . 900 
two degrees of freedom. For a Swerling Case III target and probability of 

false alarm of 10-6, the probability of target detection for the integrator 

output pulse trains shown in Figures D-6b and D-1 0 was determined using 

probability of detection curves given by Meyer and Mayher (1973) and making 

appropriate adjustments for the different degrees of freedom. The 

probability of target detection was determined to be .9998 and .9995 for the 

integrator output pulse trains shown in Figures D- 6b and D-10 , respectively. 

The high probability of detection for the two target return pulse trains 

shown in Figures D- 6b and D- 10 is due to the high mean signal-to-noise ratio 

of the pulse trains, and the number of pulses at the integrator output 

(approximately 35 pulses above 1.25 volts). Therefore, the probability of 

target detection does not change significantly by varying the integrator 

input limit level from 2.0 volts to . 34 volts. 

Also, measurements were made on the ASR-8 radar using observers to 

determine the PPI Minimum Discernible Signal ( HDS) level as a function of 

integrator input limit level settings. The measurements showed the desired 

target PPI MDS level was independent of the integrator (enhancer) limit level 

adjust switch settings greater than five. This was due to the fact that the 

integrated (enhanced) target PPI MDS level was -1 04 dBm (peak signal-to- noise 

approximately 5 . 0 dB) which produced a SNR approximately equal to the 

integrator input limit level setting five . With the integrator limit level 

adjust switch set at five, the integrator suppressed non-synchronous 

interference for both the normal and MTI channel. Therefore, the PPI MDS 

measurements made on the ASR-8 indicate that asynchronous interference can be 

suppressed by the feedback integrator without a significant change in the 

radar PPI MDS level. 

Interference 

The following is a discussion of the feedbacV. integrator signal 

processing properties to asynchronous normal and MTI channel interference . 

To analyze the signal processing properties of a feedback integrator, a 

careful investigation of the Pulse Repetition Frequency (PRF) relationship of 

the interfering and desired signal must be made. If the interfering signal 

PRF is different from the desired signal, the recirculated interference 

pulses will not arrive back at the input to the integrator coincidentally 

with the next pulse in the interfering train, and integration of successive 

pulses will not occur. However, for certain PRF's, partial integration can 

occur. 

If the relationship in the following equation holds, partial integration 

will occur: 

(D-14 ) 

Where: 

D-20 
PRFINT = PRF of the interfering radar 

PRFosR = Design PRF of the receiver 

r and s are integers 

The integer, r, indicates minimum number 

circulate through the integrator before 

interference pulse. 

of times an interfering pulse must 

it will coincide with another 

Generally, a more thorough investigation than the application of 

Equation D- 14 is required to determine if partial integration will occur. 

This is due to the fact that all aeronautical radionavigation radars in the 

2.7 to 2.9 GHz band operate in a staggered PRF mode to suppress blind speeds 

in the radar MTI channel. For radars operating in the stagger mode, both the 

interfering and desired signal stagger pulse train must be investigated. 

Aeronautical radionavigation radars in the 2.1 to 2.9 GHz band have two , 

three, four, and six stagger modes. Figures D- 14 and D-15 show the six 

stagger modes of the ASR- 7 (AN/GPN-12) and the four stagger modes of the 

ASR- 8 (AN/GPN- 20), respectively. An examination of these figures indicates 

that partial integration of an interfering signal is very unlikely. Also, 

most aeronautical radiolocations radars in the 2 . 7 to 2.9 GHz band have 

several PRF modes which ar e not integral multiples of each other. Therefore, 

it is very unlikely that partial integration of an interfering signal will 

occur between aeronautical radionavigation radars in the 2.7 to 2 . 9 GHz band. 

The height finding radar s in the 2 . 7 to 2.9 GHz band have a PRF of 250 to 

400, and could potentially cause partial integration interference . 

Figures D-16 thr ough D-18 show the simulated response of a feedback 

integrator to a single interfering pulse for normal channel asynchronous 

interference. The first interfering pulse at the integrator output is 

slightly greater than the integrator input limit level setting (VL) due to 

the addition of noise, and each recirculated pulse has an amplitude of K 

times the preceding pulse. Figure D-18 shows that an input limit level 

setting of 0.34 volts will suppr ess asynchronous normal channel interference. 

For comparison purposes, Figures D-19 through D-21 show a measured ASR-8 

normal channel feedback integrator (enhancer) output signal response to 

asynchronous interference for integrator input limiter switch settings of 63, 

15, and 7, respectively. Figure D-21 shows that for an integrator input 

limiter switch setting of 7, asynchronous normal channel interference will be 

suppressed to a one volt peak noise level, and will not be visible on the PPI 

display. 

Figure D- 22 shows a simulated normal channel radar unintegrated output 

for three interference sources (ASR-5, INR = 10 dB; ASR- 8, INR = 15 dB; and 

AN / FPS, INR = 20 dB) , and a desired target signal-to-noise ratio of 15 dB . 

Figure D- 23 shows for the same interference condition the radar output after 

feedback integr ation for an input limit level setting of 0 . 34 volts. The 

asynchronous inter ference has been suppressed (compare Figure D- 23 with D-10 ) 

by the feedback integrator. 

D- 21 
0 

I 

I\) 

N 

_j au J Ul l e •l l IOU 1 U> 1 UO> 1 

Figure D-14. ASR-7 Six Stagger Sequence 

630. 200 .. ,. 117 7. 4 0 0 ·l· 8 76 .400+-96 1.333 ---f..e30.200+-- 11 7 7.400 .. ,. 876.400 

------~------ ------~L------~'---------~------~---------------A------

Figure D-15. ASR-8 Four Stagger Sequence 
:L 

u 

........... 

1-

_.J 

~ 

> 

......... 

8 . 

7. 

6. 

5 . 

4 . 

3 . 

2 . 

1 . 

o. 

0 ·. 5 -1 0 . 15.20 .25 .30.35 .4 0 .4 5 .50 . -

5 MILLISECBNDS/CM 

Figure D-16. Simulated Feedback Integrator Output for Asynchronous 

Normal Channel Interference (VL = 2 .0, INR = 30 dB) 

'L 

u 

........... 

1-

_.J 

~ 

> 

...--< 

8 . 

7. 

6' . 

5 . 

4 . 

3 . 

2. 

1 . 

0 . 

o. 5.10 .15.20.25.30 .35 .40.45 .50 . 

5 MILLISECBNDS / CM 

Figure D- 17. Simulated Feedback Integrator Output for Asynchronous 

Normal Channel Interference (VL = 1.0, INR = 30 dB) 

D-23 
8. 

7. 

L: 

6. 

u 

.......... 5 . 1--

__J 

~ 4. 

> 

.....-. 3 . 

2 . 

1 . 

o. 

o. 

Figure D-18. 

5.10.15.20 .25.30 .35 .4 0 .45.50. 

5 MILLISECBNOS/CM 

Simulated Feedback Integrator Output for Asynchronous 

Normal Channei Interference (VL = 0.34, INR a 30 dB) 

D-24 
D- 25 

Figure D-19. Measured ASR-8 

Integrator Output for 

Asynchronous Normal Channel 

Interference 

Limit Adj us t 63 

I = -80 dBm 

Figure D-20. Measured ASR-8 

Integrator Output for 

Asynchronous Normal Channel 

Interference 

Limit Adjust 

I 

15 

-80 dBm 

Figure ~21. Measured ASR-8 

Integrator Output for 

Asynchronous Normal Channel 

Interference 

Limit Adjust = 

I 

7 

-80 dim 
s. 

7. 

:L 

6. 

u 

""- 5. 

I-

__j 

0 '4 -. > 

..---. 3 . 

2. 

1 . 

o. 

0 . 

Desired 

ASR- 5 

ASR-8 

AN/FPS-90 

SNR = 15 dB 

INR = 10 db 

INR = 15 dB 

INR = 20 dB 

5.10.15.20.25.30.35.40 .4 5.50 . 

5 MILLISECBNOS/CM 

Figure D-22. Simulated Normal Channel Unintegrated 

Radar Output with Interference 

7. 

:L 

6. 

u 

""- 5 . I-

__j 

-0 4 . 

> 

........ 3 . 

2. 

1 . 

o. 

o. 

Desired 

ASR-5 

ASR-8 

AN/FPS-90 

SNR = 15 dB 

INR = 10 dB 

INR = 15 dB 

INR = 20 dB 

5.10.15.20.25.30 .35 .40.45.50. 

5 MILLISECBNOS/CM 

Figure D-23 . Simulated Normal Channel Integrated Radar 

Output with Interference 

D-26 
Figures D- 24 through D- 26 show the simulated response of a feedback 

integrator to a single interfering pulse for MTI channel asynchronous 

interference. The MTI channel is simulated for a double stage canceller 

without feedback (1 and 2 CASC mode). As mentioned in Appendix C, for 

asynchronous interference a double stage MTI canceller will cause three 

synchronous pulses at the MTI canceller output for each asynchronous 

interfering pulse. Thus, asynchronous MTI channel interference will be 

enhanced by the feedback integr ator unless the integrator input limit level 

is properly adjusted. This MTI channel asynchronous integration effect is 

shown in Figures D- 24 through D- 26 . These figures show a three pulse 

integration, and then a pulse train decay of K times the previous pulse. For 

a radar operating in a single stage MTI canceller mode, only two pulses would 

be integrated. If the radar is operating in a MTI mode where canceller 

feedback is used for velocity response shaping, several pulses will be 

integrated for each asynchronous interfering pulse . Figure D- 26 shows that 

for asynchronous interference _in a double stage MTI canceller channel, a 

feedback integrator input limit level (VL) setting of . 34 volts will suppress 

the asynchronous i~terference level at the integrator output to 1. 0 volts. 

In order to suppress the interference to the 1.0 volt level, additional 

subtraction (0 . 5 volts for the MTI channel as compared to 0 . 3 volts for the 

normal channel) was required at the integrator input. This additional 

subtraction reduces the noise level below the standard one volt level . A 

discussion of the additional circuitry prior to the feedback integrator is 

given in Appendix E. ;J C• 

Figures D- 27 through D-29 show for comparison with the simulated 

integrator model (Figures D- 24 through D-26) measured ASR-8 MTI channel 

integr ator (enhancer) output signal response to asynchronous interferenece 

for integrator input limit switch settings of 63, 15, and 5, respectively. 

Figures D-27 and D-28 show the enhancement of the asynchronous interference 

by the integrator due to the three pulse synchronous response of the MTI 

double canceller circuitry . Figure D- 29 shows that for an integrator 

(enhancer) limiter switch setting of 5, asynchronous MTI channel interference 

will be suppressed to the one volt peak noise level, and thus will not be 

visible on the PPI display . It should also be noted that the MTI channel 

required a limiter switch setting of 5 to suppress the asynchronous 

interference as compared to a limiter switch setting of 7 to suppress normal 

channel asynchronous interference . This is to be expected because of the 

synchronous pulse output response of the MTI channel to asynchronous 

interference. Also a comparison of Figure D-19 with Figure D-27 shows that 

the feedback integrator will enhance the MTI channel interference if the 

feedback integrator is not adjusted properly. 

Figure D-30 shows a simulated single channel MTI canceller radar 

unintegrated output for three interfering sourc es (ASR-5,INR = 10 dB; ASR-8, 

INR = 15 dB; and AN/FPS-90, INR = 20 dB), and a desired target 

signal-to- noise ratio (SNR) of 20 dB. As discussed previously the 

asynchronous MTI channel interference can be enhanced if the feedback 

enhancer is not adjusted properly. Figure D- 31 shows a simulated output o f a 

D- 27 
:L 

u 

-......... 

1-

_j 

~ 

> 

8 · 

7 . 

6. 

5 . 

4. 

3 

2 

. 

. 

1 

0 

. 

. I I ill 1.1 .. l.I .IJI II IU lljj.l. I I.!. I. I. lu 

o. 5 .1 0 .15 .20 .25- 30.35.40.45.50 . 

5 MI LL ISECBNOS / CM 

Figure D-24. Simul ated Feedback Integrator Output for Asynchronous 

MTI Channe l In terf erence (VL = 2.0, INR • 30 dB) 

8 . 

7 . 

:L 

6. 

u 

-......... 5 . 1-

__J 

0 4 . 

> 

........... 3 . 

2 . 

1 . 

o. J lilt 11 111..1..1.. l.LIJJ. JJI.J.J !J.J.Lh lto lolo 

o. 5 .10 . 15.20 .25 .30 .35 .4 0 .45 .50 . 

5 MILLISECBNOS/C M 

Figure D- 25. Simula t ed Feedback I ntegr ator Output fo r Asynchronous 

MTI Channel Interference (VL = 1 . 0, INR = 30 dB) 

D-28 
8 . 

7. 

L: 

6. 

u 

........... 5 . 

I-

_J 

0 4 . > 

.......... 3 . 

2. 

1 • 

o. uJJI I .I.IJ .I .Utltl 1111 ~ lldl ~l.il.illlhu I "'u" . l. Jddo 

o. 5.10.15.20 .25.30.35.40.45.50. 

S MILLISECBNOS/CM 

Figure D- 26 . Simulated Feedback Integr ator Output for Asynchronous 

MTI Channel Interference (VL= 0.34, INR 30.0 dB) 

D-29 
D-30 

Figure D-27. Measured ASR-8 

Integrator Output for 

Asynchronous MTI Channel 

Interference 

Limit Adjust 

I 

63 

-80 dBm 

Figure D-28. Measured ASR-8 

Integrator Output for 

Asynchronous MTI Channel 

Interference 

Limit Adjust 

I 

15 

- 80 dBm 

Figure D-29. Measured ASR-8 

Integrator Output for 

Asynchronous MTI Channel 

Interference 

Limit Adjust 

I 

5 

-80 dBm 
s. 

7. 

:L 

6. 

u 

........... s . 

f-

_j 

~ 4 . 

> 

...--' 3 . 

2. 

1 . 

o. 

0 . 

Desired 

ASR-5 

ASR-8 

AN/FPS-90 

SNR = 20 dB 

INR = 10 dB 

INR = 15 dB 

INR = 20 dB 

5.]0.15.20.25.30.35.40.45.50 . 

5 MILLISECBNOS/CM 

Figure D-30. Simulated MTI Channel (mode 1 & 2 CASC) 

Unintegrated Radar Output with Interference 

:L 

u 

........... 

f-

_j 

~ 

> 

s . 

7 . 

6 . 

5 . 

4 . 

3. 

2. 

1 . 

o. 

Desired 

ASR-5 

ASR-8 

AN/FPS-90 

I 

-~-~~- u 

SNR = 20 dB 

INR = 10 dB 

INR = 15 dB 

INR = 20 dB 

~ ~ '~~~~ ~tnltJ J o. 5.10.15.20.25.30.35 .40.45.50. 

5 MILLISECBNDS/CM 

Figure D- 31. Simulated MTI Channel (mode 1 & 2 CASC) 

Integrated Radar Output with Interference 

D-31 
feedback integrator for the feedback integrator input limit level adjusted at 

.34 volts for the same interference condition shown in Figure D- 30 . The 

asynchronous interference has been suppressed by the feedback integrator. 

In summary, the simulation of the feedback integrator has shown that 

asynchronous interference can be suppressed by a feedback integrator if 

adjusted properly. Measurements made on the Stapleton Airport ASR-8 radar in 

Denver, Colorado, also showed that on-tune interference levels of 50 dB above 

the receiver noise level (approximately - 60 dBm) could be suppressed in both 

the normal and MTI channels so that they did not appear on the PPI display. 

The ASR-8 radar has a feedback integrator (enhancer) and dual channel 

(Inphase and Quadrature) MTI channel processing. The measured change in 

target detection sensitivity in suppressing the asynchronous interference was 

found to be 1 dB or less. Also given that the feedback integrator is going 

to be used, the trade-offs in target azimuth shift, angular resolution and 

target detection sensitivity to suppress asynchronous interference are 

minimal. 

BINARY INTEGRATOR 

The ASR-7 and AN/GPN-12 radars are made by the same manufacturer, and 

the enhancer used in the two radars are electronically identical. The 

integrator (enhancer) used in the two radars can be represented by the block 

diagram shown in Figure D-32. The binary integrator consists of a threshold 

detector or comparator, binary counter (adder/subcontractor circuit), a five 

bit shift register memory, and a digital-to-analog (D/A) converter. Each PRF 

period is divided into range bins of .625 ~s . If a pulse of a target return 

pulse train exceeds the comparator threshold level, the enhancer stores a one 

level digital signal in the shift register memory for that range bin . If the 

successive pulses of the target return pulse train continue above the 

comparator threshold in the given range bin, the binary counter will add one 

level to the stored digital signal in the shift register memory in each PRF 

period until a maximum integrator level of 31 is reached. If in any PRF 

period the signal fails to exceed the comparator threshold, the binary 

counter subtracts one from the stored integrator state in the given range bin 

until a digital signal level of zero is reached. The subtraction provides 

the target return pulse train signal decay required after the antenna beam 

has passed the target, and also enables the suppression of asynchronous 

interfering signals. The voltage amplitude at the enhancer D/A converter 

output is determined by the binary counter level (0 to 31) for the particular 

range bin times .125 volts. Therefore, for a binary counter level of 31, the 

maximum enhancer output voltage would be 3.875 volts (31 x . 125) . 

FAA Integrator Modification 

The following is a discussion on the modification the FAA made to the 

ASR-7 integrator (enhancer) to improve the desired signal probability of 

detection, target azimuth shift, and angular resolution loss caused by the 

conventional integrator used in the ASR-7 radar. 

D- 32 

I . 
t:; 

I 

w 

w 

" 

ein THRESHOLD 0 , 1 BINARY ... 

COMPARATOR 

• 

BINARY D/A _ .. 

... -... COUN'I'ER CONVERTER 

SHifT ... REGISTER ~ 

(RANGE- GATE) 

CLOCK 

Figure D-32 ASR-7 (AN/GP~-12) Binary Integrator·B1ock Diagram 

eout 

-... 
The FAA made 

printed circuit 

video enhancer at 

were: (1) loss of 

(2) excessive 

FAA-MA-76-39-LR, 

modifications to the manufacturer's integrator (enhancer) 

board due to deficiencies that were observed on the ASR-7 

operational field sites. Deficiencies that were observed 

weak targets due to design of the enhancer integrator, and 

azimuth shift of the target (NAFEC Letter Report, 

197 6). 

Figure D-33 shows a block diagram of the FAA modified video enhancer. 

The major modification made by the FAA is the replacement of the binary 

counter (IC's) with a programmable read-only- memory (PROM) logic. The PROMS 

permit the bypassing of some of the intermediate levels (Ej = 0 to 31), 

depending on the PROM programming. Figure D-34 shows the FAA standard 

hit/miss characteristic curve which is programmed into the PROMS. The figure 

shows that the enhancer state is a nonlinear function of the target hits 

above the comparator threshold level. It only takes four hits to get to 

level 8 (one volt noise level), and six hits to get to level 31 (3.875 

volts). This results in a strong target enhancement with only a few hits. 

The primary advantage of the PROM enhancer is that, due to its programmable 

feature, it permits a radar site flexibility in selecting a hit-count 

sequence based on the radar sites environment (interference and clutter). 

Similarly, the miss-count sequence can be precisely controlled to minimize 

target azimuth shift and maximize angular resolution . In this way, the video 

enhancer performance can be optimized to give improved performance in a 

variety of environmental conditions. 

The following discussion will center on the particular signal processing 

characteristics of the conventional integrator deployed in the ASR-7 and 

AN/GPN-12 and the modified ASR-7 integrator to noise, desired target return 

pulse train, and asynchronous interference . 

Noise 

The noise amplitude distribution at the normal or dual MTI channel 

integrator (enhancer) input is Rayleigh distributed, and the noise amplitude 

distribution at a single MTI channel integrator input is one-sided Gaussian 

distributed. The noise amplitude distributions at the normal or dual MTI 

channel output can be expressed as: 

p(v) = 0 < v < + co (D-15) 

where the rms noise level is cr • The noise amplitude distribution at the 

output of a single channel MTI canceller after rectification can be expressed 

as: 

e 0 < v < + co (D-16) P ( v) = 

2 

D- 34 
VIDEO ENHANCER ASSEMBLY 

r--

r;::: PROM 22 

_U cor~P ARATOR 

t>]~J y 

D/A r- ,.. 

~ p. ~== ~ I ..___ .. PROM Zl \I DRIVER ~' y f-<J 

e in 

-- eo 

CLOCK 

~ 

- SHIFT .___ ~ REGISTER I ......._ 

.l 

I 

- Figure D-33 FAA Modified ASR-7 Enhancer Block Diagram 

D-35 
4 

3 

~ 

~ 

..:X: 

E-i 

H 

0 2 

> t:l 

E-i I 

l..: :::> 0" 0.. 

E-i 11 :::> 

0 

level 31 

d 

I 

level 8 

level 4 

II IT l MI SS 

T 

Figure D- 3 4 . Hit ~1iss Characteristic Curve for FAA Modified 

ASR-7 Enhancer 
where the rms noise level is a. 

The probability of noise causing the threshold comparator to put out a 

binary one in a range bin, PNl• can be found for the normal and MTI c hannels 

by integrating Equations D-1 5 and D- 16 from the threshold voltage level, T, 

to plus infinity . Figure D-35 shows the probability of noise causing a 

binary one, PNl• at the threshold comparator output as a function of the 

threshold comparacor threshold-~o-rms noise ratio in dB for the normal and 

MTI channels. 

The probability of the receiver noise causing the binary counter in the 

integrator to reach state Ej can be modeled by a one-dimentional 

random walk with reflecting barriers where levels 0 and 31 are the reflecting 

barriers. That is, the first and last rows of the Markov chain transition 

matrix are defined by (PNO• PNl• 0 , ... ) and (0, . . . .. . . .. , O, PNO' PN 1 ). 

Since the noise is continually summed in the binary integrator the numoer of 

steps (k) in the random walk is infinite. It can be shown that a 

one-dimentional random walk with reflecting barriers model for an inf ini t e 

number of steps is identical to a truncated single channel queue. The 

arrival rate, A, and the departure rate, , of the queuing system is given 

by: 

PN1 A = 

t.T (D-1 7 ) 

~ = 

1-PN1 = PNO 

t.T (D-18) 

LIT 

Where: 

= Probability of the noise causing a 0 at threshold comparator output 

= Probability of the noise causing a 1 at thr eshold comparator output 

LIT = Period of the radar range bin 

= False alarm time 

The probability that the binary counter is in state, Ej , at epoch t + t.T c an 

be expressed as (Suaty, 1968): 

P.(t+tl T) J = Pj ( t-. ) [1 - ;\.!:I T - Ll T] 

+ PJ·- 1 (t) ;\.tiT+ p. (t) Ll T J+l 

( D-19 ) 

It can be shown that the probability of the binary counter being in 

state, Ej (from the difference equation solution) due t o noise Pnj• can 

expr essed as: 

D- 37 

an~r 

be 
1 0 

-

-

-

1 

: 

-

-

-

-

-

2 

-

-

-

-

-

= 

-

-

-

-

-

-

= 

-

-

: 

-

-

-

-

-

: 

: 

-

-

-

-

-

-R ~ "' Rayleigh Noise 

(Normal Channel or 

Dual MTI Channel) 

One-Sided 

Noise (Single Gaussian MTI ~ Channel) I 

\ 

\ 

\ . 

\ 

o.o -5 . 0 0 5.0 10.0 15.0 

THRESH OLD -TO-NOISE (IN dB) 

Figure D- 35. Probability of Noise Causing a Binary 1 at the 

Threshold Conparator Output 

D-38 

20 . 0 
p = Lim p. (t) (D- 20a) nj J 

t -+ 00 

( 1./J:! ) j -1 

j-1 

(PN/PNO) 

p p (D- 20b) 

(1./].l)j - 1 j -1 E E (PNl / PNO) 

j =l j =l 

Where : 

P ::. Number of states (function of counter level sequence) 

The values for ~1 as a function of the threshold-te-rms noise ratio are 

obtained from Figur e D-35 for the various channels, and PNo ::. 1- PNl· It 

should also be noted that the integrator output noise amplitude dist ributi on 

is independent of the noise amplitude distribution at the input to t he 

integrator. Since the integrator output noise distribution is independent o f 

the noise amplitude distribution at the input of the integrator, an 

analytical expression for the integrator noise gain can not be expressed . 

However, the integr ator output rms noise level can be expressed as: 

j P 

E [ 0 . 12 5 (j -1) P nj ] 2 

j =l 

(D- 21) 

The rms noise level at the integr ator output is a func t ion of the 

threshold comparator threshold level setting. Normally the thresho ld 

compar ator threshold level is adjusted to produce a peak noise level a t the 

integr ator outputs of one volt. Therefore, the binary counter level should 

not exceed counter level 8 (8 x .125 = 1.0 volts) with a probability of .00 0 1 

for a pr obability of false alarm of 10-4. That is: 

c 

E 

j 1 

where: 

p . > .999 9 

OJ -

c = State corre sponding t o coun t er level 8 

( D- 2 2 ) 

TABLE D-3 shows the pr obability of the binary counter reaching each state due 

to noise, Pnj• and the cumulative probability of Pn j f or comparator thresho ld 

settings with a probability of binary one, PNl' of 10'- 2 , 10- l , and . 2625. 

D-39 
t:;j 

I 

... 

0 

State 

F.j 

1 

2 

) 

4 

5 

(, 

7 

8 

9 

10 

11 

12 

I J 

14 

l5 

lb 

17 

18 

19 

2tl 

2l 

22 

23 

24 

25 

26 

27 

28 

29 

]I) 

)l 

32 

CountPr 

l.evel 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

TABLE D-3 

PROBABILITY OF NOISE CAUSING THE INTEGRATOR TO BE IN STATE Ej 

PNl • 10- 2 ~'Nt • to-1 PNt• .2625 

Pnj ll'n.l ~'nj l:Pnj Pnj I:PnJ 

. 989898990+000 .989898990+000 .888888891+000 .888888891+000 .644067805+000 .644067805+000 

.999897957-002 .999897970+000 .987654306-001 .987654321+0110 . 229244467-t000 .873312273+000 .100999792-01D .999998969+000 . Hl97 39365-001 .998628258-tD00 .815954864-001 .9549077 59+000 .102019991-005 .999999990+000 .121932626-002 .999847584+000 . 290424606-001 .983950220+000 .103D50495-007 .1A0000000+001 .135480693-003 • 999983065H~00 .103371467-D01 . 9942873fi6+000 

.104 0914 08-009 . Hl0000000+001 . 150534101-004 • 999998118+0110 .367932332- 002 .997966690+eeo . 105142835-011 .10130110000+001 .167260109-005 .999999791+000 . 130950963-002 • 999276279Hl00 . 106204882-013 . 1000CWOOOi-110 l .185044562-01\6 .999999977+000 . 4661251 10-003 • 999742405HIOO 

.107277657-1115 .10001111000Hl01 . 206493955-007 .999999997-1000 . 1659089)]-003 999900313~000 .108361269-017 .100000000-+001 • 229437723-008 .100000000 001 . 590523308-004 .999967366+000 .109455826-019 . 100000000Hl01 .254930799-009 .100000000-+001 . 210186257-004 .999981.1384-+000 .1105614 39-021 .1000ll0000+001 . 283256438-010 .100000000Hl01 . 740120557-005 . 99999~866-+ IHJO . 111678219-023 • 1000CHI1100+ 001 . 314729370-011 . 1 00000000+001 . 266280192-01}5 .999990528-1000 I .11 2806261-025 .1 00000000 1-0tH .349699294-012 • 1 00000000+001 .947776931-006 . 999999476-+000 

I .113945737-027 .100000000+001 .388554765-01 3 . 100000000+001 .337344323-006 .99999981 44000 . 115096702-029 .100000000+001 .431727509-014 . 100000000+001 .120071705-006 • 999999934Hl00 I 

.116259294-031 .1000001100+001 . 479697223-015 .100000000+001 . 427373856-007 . 999999976+000 

.117433629-033 .100000000-1001 .532996905-016 . 100000Cl00Hl01 .152116115-007 . 999999992-+000 

.118619826-035 .100000000+001 • 592218773-017 .100000000H~01 .541430225-008 . 999999997+000 

.119818004-037 .100000000+001 .658020847-018 . 100000000+001 .192712448- 008 . 999999999+000 

.12lfl28205-039 . 10!HHl0000+001 . 731134 262-019 .100000000+001 .685925647-009 100000000~001 

.122250792-041 • H10000000+001 .812371388-020 . 100000000+001 .244143021-009 .100000000+001 

.123485647-043 .100000000+001 .902634859-021 .100000000HJ01 .868983613-010 100000000+~01 

.124732975-045 .100000000+001 . Hl0292760-021 .100000000Hl01 .309299244-010 • Hl0000000+001 

.125992903-047 .1000(}01100+001 .111436398-022 .100000000-+001 .110089559-010 .100000000+001 

.127265557-049 .100000000+001 .123818218-023 • Hl0000000+001 .391844183-011 .100000000+001 

.12855Hl66-051 .1000(}0000+001 .137575796-024 .100M0001H001 .139469960-011 .100000000+001 

.129849560-053 . HHlOA0000+001 .152061993-025 . 100000000+001 .496418490-012 . HH1000000 Hl01 .131161170-055 .100000000+001 .169846655-026 .100000000+001 .176691323-012 .1000000004601 

.132486028-057 • J 00001'001l+OIH .188718503-1127 .1000110000-tfl01 . 628901303-IH3 • 100(}00000 Hl01 .133824269-059 .100000000+001 .209687221-028 .100000000+001 . 223846221-013 .100000000+001 

.135176028-061 .1000000013+(}01 . 232985797-029 .10000~11001001 .7967 40767-014 . 100000000+001 

I 
The table shows that for a probability of a binary one due to noise of .2625, 

Equation D- 22 is satisfied. That is, the peak noise level will be 

approximately one volt if the threshold comparator is set for PNl = .2625 . 

Therefore, using figure D- 35, the threshold comparator threshold-te- rms noise 

(TIN) rati o should be set at 1.5 dB for the MTl channel and 4. 2~ dB for the 

normal channel. 

TABLE D-4 shows the probability of the binary counter reaching each 

state due to noise , Pnj, and the gumulative probability of Pn j for the FAA 

modified integrator and PNl of 10-2 , 10-1 , and .1 35 . The table shows that a 

threshold comparator setting of PNl = .135 will limit the peak noise level to 

approximately one volt . That is, Equation D-22 is satisfied for a PNl of 

.135. Again, using Figure D- 35 , the threshold comparator TIN ratio should be 

set for the FAA modified integrator at 3.2 dB for the MTI channel and 6 . 0 db 

for the normal channel . 

TABLE D-5 shows the probability of the binary counter reaching each 

state due to noise, Pnj, and the cumulative probability of Pnj for a computer 

simulation of the enhancer hardware (see Appendix E) . The simulated run was 

for a threshold comparator setting of FNl = .2625 (same as in TABLE D- 3) . 

Only one thousand noise samples were taken. Therefore, the probability of 

being in each state, Pnj, will only be accurate for Pnj > . 005. TABLE D- 5 

compares favorably with TABLE D-3, thus validating Equation D-20b. 

Desired Signal 

For a nonfluctuating target (Marcum's Case 0), the probability of the 

desired signal exceeding the threshold comparator level (P51 probability for 

a binary one in a range bin) for the normal channel has a Rice 195~) PDP 

(also known as the Modified Rayleigh and Q- function). 

- (v2+A2) 

where: 

; · - -· -,.,-·-- 2cr ·-

:~- 10 (~) dv 

(D- 23) 

= Modified Bessel function of the first kind of order zero 

A = Peak signal-amplitude, in volts 

a = rms noise level, in volts 

T = Threshold comparator threshold level, in volts 

The integrand of Equation D- 23 is the signal-plus-noise amplitude 

distribution at the threshold comparator input for the normal or dual MTI 

channel (see Figure 3- 10) . Figure D- 36 shows the probability of the desired 

signal- plus-noise exceeding the threshold comparator level (Psl, probability 

D-41 
State 

Ej 

1 

2 

3 

4 

5 

6 

7 

State 

E. 

J 

1 

2 

3 

4 

5 

6 

7 

State 

E· J 

1 

2 

j 

4 

5 

6 

7 

TABLE D-4 

PROBABILITY OF NOISE CAUSING THE MODIFIED 

FAA INTEGRATOR TO BE IN STATE Ej 

PNl = lo-2 

Counter 

Level 

pnj LPnj 

0 . 989898990+000 . 989898990+000 

1 .999897957- 002 . 999897970+000 

2 . 100999792- 003 . 999998969+000 

4 . 102019991- 005 . 999999990+000 

8 . 103050495-007 . 100000000+001 

16 . 104091408- 009 . 100000000+001 

31 .105142835-011 . 100000000+001 

PNl = 10-1 

Counter 

Level 

Pnj EPnj 

. 

0 . 888889077+000 . 888889077+000 

1 .987654512-001 . 987654528+000 

2 .109739388-001 . 998628467+000 

4 . 121932652-002 . 999847793+000 

8 . 135480722-003 . 999983274+000 

16 . 150534132-004 . 999998327+000 

31 . ]67260144-005 . 100000000+00] 

Counter PNl = .135 

Level 

pnj EPnj 

0 . 843932543+000 . 843932543+000 

1 . 131712012+000 . 975644555+000 

2 . 205562096-001 . 996200765+000 

4 . 320819449-002 . 999408959+000 

8 . 500700862-003 . 999909660+000 

16 .781440635-004 .999987804+000 

31 .]21958940-004 .100000000+00] 

D-42 
State 

E· J 

l 

2 

3 

4 

5 

6 

7 

~ 

9 

ltl 

ll 

12 

13 

14 

15 

16 

17 

18 

19 

(J 

21 

22 

23 

24 

25 

26 

27 

28 

29 

30 

31 

32 

TABLE D-5 

PROBABILITY OF NO I SE CAUSING THE 

INTEGRATOR TO BE IN STATE Ej (SHIULATED) 

Co unt e r 

PN1 = . 2625 

Lev e l Pnj EPn_; 

0 6321~3689+000 . 6321036tjY+01111 

1 . 2352941 18+000 . 867397807+00V' 

2 .867397807-001 . 954137587+00;. 

3 . 329012961- (i}fl . 987038883+000 

4 . 109670987- 001 . 998005982+081.1 r 

~ 

.199401795-002 . 100000000+00) 

E· . 000000000 . 100000000+001 

7 . 000000000 . 100000000+002. 

e .0000000010 .100000000+001 

9 . 000000000 . 100000000+001 

10 0000000~0 . 100000000+001 

ll . 000000000 . 100000000+001 

12 . 000000000 . 100000000+001 

13 . 000000000 . 100000000+001 

14 . 00000000QJ . 100000000+001 

15 . 000000000 . 100000000+001 

16 . 000000000 . 100000000+001 

17 . 000000000 . 100000000+001 

18 . 000000000 . 100000000+001 

19 .000000000 . 100000000+00: 

20 . 000000000 . 100000000+001 

21 . 000000000 . Hl0000000+001 

22 0CIJ0~000010 . Hl0000000+001 

23 . 000000000 . 100000000+001 

24 . 000000000 . 100000000+001 

25 . 000000000 . 100000000+001 

26 . 000000000 .100000000+001 

27 . 000000000 . 100000000+001 

28 . PI00000000 . 100000000+001 

29 . 000000000 . 100000000+0(1. 

30 . 000000000 .100000000+001 

31 . 000000000 .100000000+001 

D-4 3 
-rl 

ll) 

0.. 

.-i 

~ 

0 

~ 

E-< 

H 

1-4 

'-! 

c::l 

.:4 

tQ 

0 

c.:; 

0.. 

. 9999 

. 9990 1117 I I 

.9950 I vI I/ . 9900 

. 98 

. 95 

. 90 

. 80 

. 70 

. 60 

. 50 

. 40 

. 30 

. 20 

. 10 

.05 

. 02 

. 01 

. 005 

II L I / 

II I I I 

II 1/ I I 

/I I I I 

/ v/ I I I 

1,01,() 7 / I I 7 ~~--:. · / / I I I - :-

,s / I I I ~ 1/ I I 

-f- ~y / I / 

v · / I v 

~~~1,/ I I 7 V I 

v 

"" £L :y t / 

'\- // '/ ~~ ~"v / ~/ 

I I . I 

. 002 

. 001 - 3 . 0 0 5 1 0 1 5 

SI GNAL- TO-NOISE RATIO (IN dB) 

Figure D-36. Probability of 1 at the Threshold Comparator 

Output as a Function of the Signal- to-Noise 

Ratio at the threshold Comparator Input for 

the ~ormal Channel . 

D-44 

20 
of a binary one in a range bin). The probability of exceeding the threshold 

comparator level, Ps1, is shown as a function of the signal-to-noise ratio 

(SNR) and probability of the noise causing the threshold comparator to put 

out a binary one in a range bin, PNl· The curves were obtained by simulating 

the signal-plus-noise distribution at the normal channel output. The 

simulation is discussed in Appendix E. 

For a nonfluctuating target (Marcum 's Case 0), the probability of the 

desired signal exceeding the threshold comparator level (Psl• probability of 

a binary one in a range bin) for a single channel MTI canceller when averaged 

over all doppler frequencies can be approximated by (See Equation C-41): 

Ps1 =/ oo 2 e 

_ 12n(a2+A2!2) 

-v2 

dv 

(D-24) 

The 1ntegrand of Equation D-24 is the signal-plus-noise distribution at the 

threshold comparator input for a single channel MTI canceller (see Figure 

3-35) . Figure D- 37 shows the probability of the desired signal-plus-noise 

exceeding the threshold comparator level (Ps11 probability of a binary one in 

a range bin). The probability of exceeding the threshold comparator level, 

Ps11 is shown as a function of the signal-to-noise ratio (SNR) and 

probability of the noise causing a binary one in a range bin, ~l. The 

curves were obtained by simulating the signal-plus-noise distribution at the 

single channel MTI canceller output. The simulation is discussed in Appendix 

E. 

A comparison of Figures D-36 and D-37 shows that for signal-to-noise 

ratios (SNR's) greater than zero dB the probability of the signal-plus-noise 

exceeding the threshold comparator level (Psl 1 probability of a binary one in 

a range bin) is greater for the normal channel than for the single MTI 

channel. This would be expected when comparing the signal- plus-noise 

amplitude distributions at the integrator threshold comparator input. (See 

Figure 3-10 for the normal channel and Figure 3-35 for the single MTI 

channel) . 

The probability of a desired target return pulse train of 20 pulses 

causing the binary integrator to be be in state ~ can be determined by using 

a one-dimensional random walk with reflecting barriers model where levels 0 

and 31 are the reflecting barriers. That is, the first and last rows of the 

Markov chain transition matrix are defined by (Pso• Psl• 0 .... ) and 

(0, · · · 0, Pso• Ps1 ) . The term Pso is defined as the probability of the 

desired signal not exceeding the threshold comparator level <Pso, probability 

of a binary zero in a range bin) 1 and Ps1 is defined as the probability of 

the desired signal exceeding the threshold comparator level (%1 1 probability 

of a binary one in a range bin). The actual probability of the desired pulse 

train causing the binary integrator to be in state E j for a given 

signal-to-noise ratio is given by: 

D-45 
. 9 9 99 

. 9990 

.9950 

. 9900 

. 9 8 

. 95 

rl 

U) 

p.. • 90 ......... 

...... 

----=== ~ ...,..... 1'4 . 80 

0 

.70 

:>l 

E-t 

_____. ~ ~-- H . 60 -

~ _____. ~ ~~ H 

H . 50 ~6~-~ o:l 

.::X: . 4 0 cQ 

0 

p:; . 30 

p.. 

. 20 

. 10 

. 05 

.02 

. 01 

. 005 

.002 

~ ~ / ,.~ 

-~ ¥'" . / // -~~ v 

-1-?~1. -- / // 

~ / v / 7 ... / // v 

"/"'>-\) 

~~~ . 1// 

v / / 

_..b. / --~ / 

"/"'>-\)/ 9),\) / 

-~ 2_ ~~Y 

.001 v / I I I I I I I I I I I I I I I I I I 

-3 . 0 0 5 10 15 

SIGNAL-TO-NOISE RATIO (in dB) 

Figure D-37 . Probability of 1 at the Threshold Comparator 

Output as a Function of the Signal-to - Noise 

Ratio at the Threshold Comparator Input for 

a Single Channel MTI Canceller 

D-46 

20 
wh ere: 

and 

Psj = 

N (k) 

r p ij k=l 

p N 

r r 

j=l k=l 

(plq) -1 

(pi q)p -1 

( k) 

p ij 

j-1 

(~) p-1 

+ £.2 1: 

p r=l 

~(f )y(j) [2/ici" cos urlp] k 

1 - 2/PCI cos nr lp 

( r) (.9.) -i I 2 . n r i (S ) ( i + 1) I 2 

x i = p sl.n - P-- p sin 

1Tr (i-1) 

p 

nrj 

p 

-(E) (j-l)l2sin 

q I 

nr(j- 1) 

p 

(D- 25a) 

(D- 25b) 

(D- 25c) 

(D-32d) 

p = Number of states (function of counter level sequence) 

q Pso = Probability of 0 at threshold comparator output 

p = Ps 1 = Probability of at threshold comparator output 

N = Number of desired signal pulses in target return 

pulse train 

The values for P51 as a function of signal-to-noise ratio are obtained from 

Figure D-36 for the normal channel and Figure D-37 fo r the single 

MTI channel, and P50 = 1- P81. The term P{~J is defined as the 

probability of a trans1tion from state Ei to stat~ Ej in exactly k steps. In 

other words,Pi~ ) is the conditional probability of entering state Ej at 

the kth step given the initial state is Ei · Equation D-25b was obtained from 

Feller ( 1968). 

TABLE D-6 shows the probability of the FAA modified integrator being in 

state E j for a desired target return pulse train of 20 pulses, given that the 

initial state, Ei , was state 1 . The table shows the probability of the 

D-47 
TABLE D-6 

PROBABILITY OF DESIRED SIGNAL TARGET RETURN PULSE TRAIN OF 20 

PULSES CAUSING THE FAA MODIFIED INTEGRATOR TO BE IN STATE Ej 

Psl = . 600 State Counter 

Ej Level Psj EP sj 

1 0 • 147409993+000 • 147409993..000 

2 1 . 177353622+000 • 3247 6361 ~.000 

3 2 . 156627014+000 • 481390628+000 

4 4 . 136325570+000 .61771 61 98+000 

5 8 . 1220561 0 3+000 .739772301..000 

6 16 . 11~57942..000 • 858630243..000 

7 31 . 141369757 +000 • 100000000..001 

State Counter PS1 = .800 

Ej Level p . EP sj SJ 

1 0 . 333096427- 001 .333096427-001 

2 1 • 833176873-001 • 116627330..000 

3 2 • 83666 3318- 001 . 200293662..000 

4 4 . 859261801-001 • 286219842..000 

5 8 • 984266549-001 • 384646497..000 

6 16 . 160277434+000 . 544923930..000 

7 31 .455076070+000 • 100000000..001 

PSl = .995 Sta te Counter 

Ej Level 

p sj IPsj 

1 0 .505040409-003 • 505040409--0113 

2 1 .505040408-001 • 510090813-e~n 

3 2 .505040413-001 . 101513123+ee0 

4 4 .505041066-001 .152017229+i00 

5 8 .505190671-0i1 .202536296+1J00 

6 16 .537338534-001 .256270150+900 

7 31 .743729850+0riJS .100000000+illll 

D-48 
desired signal being in state Ej as a function of the probability of the 

desired signal exceeding the threshold comparator level (Psl) of .6, .8, and 

.995. The initial state, Ei, of 1 was chosen since for a probability of the 

noise exceeding the threshold comparator level (PNl) of .135 the integrator 

is in state 1 with a probability of .8439 (see TABLE D-4). 

The signal processing of the ASR-7 binary integrator was simulated to 

investigate the tradeoffs to the desired signal in suppressing asynchronous 

interference. Both the normal and single HTI channel signal processing was 

simulated. A detailed discussion of the simulation model is given in 

Appendix E. A simulated ASR-7 enhancer output for a desired target return 

pulse train of 20 pulses without noise present is shown in Figures D- 38 and 

D-39 for the conventional ASR-7 enhancer and the FAA modified ASR-7 enhancer 

respectively. A comparison of Figures D-38 and D-39 shows that the FAA 

Modified ASR-7 enhancer provides a significant improvement in signal 

enhancement, target azimuth shift, and angular resolution . 

Figures D-40 through D-43 show simulated radar performance of the FAA 

modified enhancer for the normal channel as a function of the signal-to-noise 

ratio (SNR). The desired target return pulse train con sists of 20 pulses. 

Each figure shows the simulated radar output with the enhancer off 

(unintegrated ) and enhancer on (integrated). Figure D-40, SNR = 3 dB; and 

Figure D-41, SNR = 5 dB; show that with the enhancer off the desired signal 

is down in the noise . . However, when the enhancer is on the signal is pulled 

out of the noise by the binary enhancer. This should be expected since the 

probability of the desired signal exceeding the threshold comparator level, 

s~ is greater than the probability of the noise exceeding the threshold 

comparator level, PNl = .135, for SNR's of 3 and 5 dB (see Figure D-36). 

Figures D-44 through D-46 show simulated radar performance of the FAA 

modified enhancer for the single MTI channel (mode 1 and 2 CASC) as a 

function of the signal-to-noise ratio (SNR ) with the enhancer off 

(unintegrated) and on (integrated). A comparison of Figures D-40 with D-44 

and D-42 with D-45 (same SNR for normal and MTI channels) shows that the 

signal enhancement is greater for the normal channel than for the MTI 

channel. This should be expected since the probability of the desired signal 

exceeding the threshold comparator level, Psl• is greater for the normal 

channel than for the single MTI channel for a given SNR. (Compare Figures 

D-36 and D-37.) 

The target azimuth shift due to integration is given by Equation D-1 2. 

Using Figure D-39 and Equation D-12, the FAA modified binary enhancer causes 

a target azimuth shift of approximately .179 degrees. The feedback 

integrator caused a target azimuth shift of approximately .900 degrees. 

Therefore, the FAA modified binary enhancer results in a significant 

improvement in target azimuth shift over the feedback integrator. 

The property of the radar to distinguish between targets is called 

resolution. Using Figure D-39 and Equation D-13, the use of the FAA modified 

binary enhancer does not cause any loss in target angular resolution. It was 

D-49 
::L 

u 

.......... 

1-

__J 

0 

> 

s. 

7. 

6 : 

5 . 

4 . 

3 . 

2 . 

1 . 

0 . il l 

I 

Ill I II !11 

o. 5.10 . 15.20 .25.30 .35.40 .4 5.50. 

S MILLISEC~NOS/CM 

Figur e D- 38 . Simulated Binar y Integrator Output for Target 

Return Pulse Train (ASR- 7 , AN/GPN- 12) 

::L 

u 

.......... 

1-

__J 

0 

> 

....-' 

8 . 

7 . 

6. 

5 . 

4 . 

3 . 

2 . 

1 . 

0 . '" 

,,1 

u . 5.10.15.20.25.30.35.40.45.50. 

5 MILLISEC~NOS/CM 

Figure D-39. Simulated FAA Modified Binary Integrator Output for 

Target Return Pulse Train (ASR-7) 

D-50 

I 

:· 
L: 

u 

.......... 

1-

_j 

~ 

> 

........ 

8 . 

7 . 

6 c 

5 . 

4 . 

3 . 

2 . 

1 • 

0 c 

0 . 5 . 10 .15.20.25.30.35.40.45.50. 

5 MILLISECBNDS/CM 

Figure D-40a. Simulated Normal Channel Unintegrated Target. 

Return Pulse Train for ·a SNR = 3dB 

s. 

7. 

L: 

6. 

u 

.......... s . 1-

_j 

~ 4 " 

> 

3. 

0 

L • 

1 L 

o. ~J~~~ ,~ , W l~~~~,J~i .~~jJ. ~~~ I~ II J~ II 

o. s.Jo.ls.zo.zs.Jo.35.40.4s.so. 

5 MILLISECBNDS/CM 

Figure D-40b . Simulated Normal Channel Integrated Target 

Return Pulse Train for a SNR = 3dB 
2: 

u 

.......... 

1-

_j 

0 

> 

......... 

s. 

7 . 

6 . 

5 . 

4 . 

3 . 

2 . 

1 . 

o. 

0 . 5.10 . 15 .20.25 .30 .35 .40.45 .50. 

5 MILLISECBNDS/CM 

Figure D-4la . Simulated Normal Channel Unintegrated Target 

Return Pulse Train for a SNR = 5dB 

8 . 

7 . 

L 

s. 

u 

.......... s . 

1-

_j 

0 4, 

> 

......... 3 . 

2 . 

1 . 

Q. ~~ w~ u ~~JJ uJ~~ ~·~JJ uJliJ II Ill II JJ~11 

o. 5.10.15.20.25.30 .35.40 .4 5 .50 . 

5 MILLI SECBNOS/CM 

Figure D-4lb. Simulated Normal Channel Integrated Target 

Return Pulse Train for a SNR = SdB 

D-52 
:L 

u 

.......... 

I-

.....J 

~ 

> 

.....-. 

8 .. 

7. 

6. 

5 . 

4 . 

3 . 

2. 

1 . 

o. 

o. 5.1'0.15 .20.25.30.35.40.45.50. 

5 MILLISECBNDS/CM 

Figur e D-42a. Simulated Normal Channel Unintegrated Target 

Return Pulse Train for a SNR = lOdB 

8. 

7. 

:L 

6. 

u 

.......... 5 . I-

.....J 

~ 4 . > 

...... 3 . 

2. 

1 . 

0 c 

~Juj~ ~ II II ll ~ .1~11 .,.Ju ~~~JJ IJIJliL ~. ~uJ~JI 

o. 5.10.15.20.25.30.35.40.45.50. 

5 MILLISECGNDS / CM 

Figur e D-42b . Si mulated Normal Channel Integrated Target 

Return Pulse Train for a SNR = lOdB 

D-53 
L: 

u 

.......... 

I-

_J 

~ 

> 

...-J 

8. 

7. 

6. 

5 . • 

4 < 

3 . 

2. 

o. 5.10.15.20.25.30.35.40.45.50 . 

5 MILLISECGNOS/CM 

Figure D-43a. Simulated Normal Channel Unintegrated Target 

Return Pulse Train for a SNR = 15dB 

8. 

7. 

L: 

6. 

u 

.......... 5 . 

I-

_J 

~ 4. 

> 

.......... 3 . 

n 

L • 

1 ' 

o. ~~~ u~. u ~~tuu ~~utrnJ11n~uu~J~~G~J~~ 

o. 5.)0.15.20.25.30.35.40.45.50. 

5 MILLISECGNOS/CM 

Figure D-43b . Simulated Normal Channel Integrated Target 

Return Pulse Train for a SNR = 15dB 

D-54 
L: 

u 

.......... 

I-

_J 

(!) 

> 

........ 

8 . 

7 . 

6. 

s . 

4 . 

3 . 

2. 

1 . 

o. 

o. 5.10.15.20.25 .30 .35.40 .45.50 . 

5 MILLISECBNOS/CM 

Fig~re D-44a. Simulated MTI Channel (Mode 1 & 2 CASC) Unintegrated 

Target Return Pulse Train for a SNR = 3dB 

8. 

7. 

L: 

6. 

u 

" 5 . I-

_J 

0 4 . 

> 

~ 3. 

2. 

1 . 

o. ~luul .~~;J .Llil .lu ~lL ~ ... 1 W~ll~ l .w. lll JJ~~~ .Hi lJ 

o. 5 . }0 . 15.20 .25-30 .35 .4 0 .45.50. 

5 MILLISECBNOS/CM 

Figure D-44b. Simulated MTI Channel (Mode 1 & 2 CASC) Integrated 

Target Return Pulse Train for a SNR = 3dB 

D-55 
L 

u 

........... 

f-

_j 

~ 

> 

,.._, 

8 . 

7. 

6. 

5 . 

4. 

3 . 

2. 

1 . 

o. 

o. 5 .] 0.15 .20 .25 .30 .35 .40 .45.50 . 

5 MILLISECBNDS/CM 

Figure D-45a . Simulated MTI Channel (Mode 1 & 2 CASC) Unintegrated 

Target Return Pulse Train for a SNR = lOdB - , 

8 . 

7 . 

:L ·s . 

u 

........... s . f-

_j 

~ .4. 

> 

...---' 3 . 

2. 

1 . 

o. Junl I HIIIJII ll~~Lit ll ~~~JJIJl~ J~U o. 5 . 10 . 15 .20 .25 .30 .35.40.45 .50. 

5 MILLISECBNDS/CM 

Figur e D-45b. Simulated MTI Channel (Mode 1 & 2 CASC) Integrated 

Target Return Pulse Train for a SNR = lOdB 

D-56 
L: 

u 

......... 

I-

_j 

~ 

> 

....... 

8 . 

7. 

6. 

5 . 

4-

3 . 

2. 

1 . 

(1. 

o. 5.]0.15.20 .25 .30 .35. 40 -45.50 . 

5 MIL LISECBNOS/CM 

Figure D- 46a . Simulated MTI Channel (Mode 1 & 2 CASC) Unintegrated 

Target Re t ur n Pulse Train for a SNR = 20dB 

L: 

u 

......... 

I-

_j 

0 

> 

,......... 

s . 

7. 

6. 

s . 

4 . 

3. 

f') 

'- . 

1 ' 

n III IIIIJ y Ill ~ 11 uw~.l li ~ . JJ P '.,.II" Ht~ o. 5 . 10.]5 .20.25.30 .35 .40 . 45 .50 . 

5 MILLISECBNOS/CM 

Figure D-46b . Simulated MTI Channel (Mode 1 & 2 CASC) Integrated 

Target Return Pulse Train for a SNR = 20dB 

D-57 
previously shown that the feedback integrator caused between 1.2 and 1.5 

degrees loss in angular resolution . 

Interference 

The capability of the 

asynchronous interference was 

binary integrator in the ASR- 7 to suppress 

model (see Appendix E). 

also investigated using the radar simulation 

Three interfering radar sources were 

AN/FPS- 90 . Figures E- 3 through E-5 in 

waveforms simulated for each of the radar 

simulated: ASR- 5, ASR- 8, and the 

Appendix E show the respective time 

interfering sources. 

For the normal radar channel, the probability of the interference, Pij• 

appearing above the one volt peak noise level (enhancer state 8) can be 

ex pressed as: 

where: 

Pns = 

Pn = 

\) = 

T : 

RBS = 

Probability of the noise causing the enhancer 

to be in l evel 8 

Probability of the interference exceeding the 

threshold comparator level setting 

Interfering pulse arrival rate, in pulses per second 

Interfering signal pulse width, in seconds 

Radar quantizer range bin sample time, in seconds 

(D-26) 

The probability of the nois e causing the enhancer t o be in level 8 is a 

function of the enhancer threshold comparator level setting, and the hit/ miss 

sequence programmed in the enhancer. For the FAA modified enhancer and a 

probability of the noise exceeding the threshold comparator level PN ~ of 

.135, the probability of the noise causing the enhancer to be in level 8 is 

.0005 (see TABLE 0-4) . For an ASR-8 interfering source ( ) = 1040, 

T = 0 . 6 lJ sec, RB5 = . 166 1J sec), the probability of the interference 

causing the enhancer to exceed level 8 (one volt level) is 3.98 x 10-7 

assuming PI 1 = 1 . The value of PI 1 is a function of the 

interference- to- noise ratio at the enhancer input and can be obtained using 

Figure D-36 . Figure D-47a shows a simulated normal channel radar 

unintegrated output for three interference sources (ASR-5, INR = 10 dB; 

ASR- 8, INR = 15 dB; and AN/FPS-90, INR = 20 dB), and a desired target 

signal-to-noise ratio of 15 dB. Figure 0- 47b shows for the same interference 

condition the radar output after integration. The asynchronous interference 

has been suppressed (compare Figure 0-43b with 0-47b). 

D-58 
B. 

7. 

::L 

6 ·. 

u 

.......... s . 

I-

_j 

0 4 . 

> 

......... 3 . 

0 

L • 

1 . 

0 ' 

o. 

Desir ed 

ASR- 5 

ASR- 8 

AN/FPS- 90 

SNR = 15 dB 

INR = 10 dB 

INR ,;. 15 d.B 

INR = 20 dB 

5 .1 0 .l5.Z0.25.J0 .3S.40 .4 5.50 . 

5 MILLISECBNOS/CM 

Fi gur e D-47a . ~ulated No.rmal Channel Uni ntegr ated 

Radar Output wi th Interference 

:L: 

u 

.......... 

I-

_j 

D 

> 

....-

8 . 1 

De~ ired 1 SNR = 15 dB 

7 . ASR-5 INR = 10 dB 

ASR- 8 INR = 15 dB6. AN/FPS-90 INR = 20 dB 

5 . 

4. 

3 . 

2. 

1 . 

o. ~ u~.~ II 1~u LWJU lJ~Jf I 11J111 ~~ ~~~~ ~Ub o. 5.]0 .]5 .20.25 .30 .35 .40.4 5 .50. 

5 MILLISECBNOS/CM 

Figur e D-47b. Simulated Normal Channel Integrated Radar 

Output with Interference 

D-5 9 
For the MTI channel, the analytical expression for the probability of 

the interference, Pi j• appearing above the one volt noise level (enhancer 

level 8) becomes complex. This is due to the fact that the MTI canceller 

transfer properties to asynchronous interference results in several 

synchronous interfering pulses at the MTI canceller output. (See Figures 

C-16 through C-20.) To assess the probability of the interference causing the 

enhancer to exceed l evel 8, all the combination of ways of exceeding level 8 

must be considered along with the varying INR of the synchronous interfering 

pulses at the canceller output. Because of this, the best way of analyzing 

the capability of the enhancer to suppress asynchronous interference in the 

radar MTI channel is by simulation. Figure D-48a shows a simulated MTI 

channel radar unintegrated output for three interfering sources (ASR-5, 

INR = 10 dB; ASR-8, INR = 15 dB; and AN / FPS-90, INR = 20 dB), and a 

desired target signal-to-noise ratio (SNR) of 20 dB. Figure D-48b shows for 

the same interference condition the radar output after integration. The 

asynchronous interference has been suppressed (compare Figures D-46b with 

Figure D-48b). 

In summary, the FAA modified binary enhancer has the capability of 

suppressing asynchronous interference with very little trade-offs in target 

azimuth shift, target angular resolution and desired target probability of 

detection. Asynchronous interference can be suppressed by the FAA modified 

enhancer by either adjusting the threshold comparator level setting, or by 

programming a hit/miss state sequence that will suppress the i nterference. 

Thus the FAA modified ASR-7 enhancer can be adjusted to optimize the radar 

desired signal performance in a variety of environmental conditions. 

D- 60 
'L 

u 

........... 

1-

_j 

0 

> 

~~--~~--~--~-.--.--.--~~-. Desired SNR = 20 dB 

7 ASR-5 INR = 10 dB ·~~---+--~--+-

ASR-8 INR = 15 dB 

AN/FPS-90 INR = 20 dB 6·~-+--+--4--~--r--+--~-;--~~ 

5.~~--+--+--+--4--~~r--r--r-~ 

4 ·~-+~~~~-+--~--+-~---r--~~ 

3---~~~+H+r~-+--+-~~,_~H-~ 

2.~~~H+~~~H-+-~~~-++-~~~ 

1 . 

. 

o. 5.10 . 15.20.25.30 .35 .40 .45 .50. 

5 MILLISECGNDS/CM 

Figur e D- 48a. Simulated MTI Channel (mode 1 & 2 CASC) 

Unintegrat ed Radar Output with Interference 

a. 

Desired SNR = 20 dB 

7. ASR-5 INR = 10 dB 

ASR-8 INR = 15 dBL: 

6 c 

AN/FPS-90 INR = 20 dB 

(_) 

........... 5 . 1-

_j 

0 4 . 

> 

......... 3 . 

2 . 

1 . 

0 . ~~ ~ u. u I I ~ JIJtJ .J~ lJ 

o. 5.10.15.20.25.30.35 .40 .45.50 . 

5 MILLISECGNDS/CM 

Figure D-48b. Simulated MTI Channel (mode 1 & 2 CASC) 

Integrated Radar Output with Interference 

D-6 1 
APPENDIX E 

RADAR SIMULATION 

INTRODUCTION 

This appendix discusses the techniques used to simulate the primary 

radar performance so that trade-off investigations could be made as a 

function of radar signal processing characteristics in the presence of a 

parametric range of noise, desired signal, and asynchronous interfering 

signal conditions. The primary radar simulated was the ASR-7. Only the 

normal and Moving Target Indicator (MTI) channels of the radar were 

simulated. The portion of the ASR- 7 radar simulated was the processor unit 

(i.e., normal channel envelope detector output and MTI channel phase detector 

output to the radar output). 

In addition, for study of the properties of the feedback enhancer, the 

simulation provides the capability to use a feedback enhancer in place of the 

ASR-7 binary enhancer. It should be noted however, that the ASR- 7 does not 

have a feedback enhancer. 

PROCESSOR UNIT DESCRIPTION 

A detailed description of the primary radar processor unit is given in 

Section 3. Figure E-1 shows a block diagram of the ASR-7 processor unit 

hardware which was simulated. The portion of the processor unit normal 

channel simulated was the normal channel enhancer functional switch, enhancer 

and alignment hardware. The portion of the processor unit MTI channel 

simulated was the MTI cancellers, enhancer functional switch, enhancer, and 

alignment hardware. The simulation model has the capability of displaying 

the processor unit output ir. the unenhanced and enhanced modes of both the 

normal and MTI channels on either an oscilloscope or Plan Position Indicator 

(PPI) display. 

In order to reduce the simulation model computer run time and for 

analytical simplicity, the conventional analog-to-digital (A/D) and digitalto-analog (D/A) converters at the processor unit input and output 

respectively were not simulated. However, the received signal amplitudes 

were simulated in time by dividing the radar receive period after each 

transmitted pulse into 1200 range bins .625 microseconds long corresponding 

to the actual A/D and D/A converter hardware of the ASR-7. Since the 

quantization noise caused by A/D converters is small compared to the inherent 

receiver noise, not simulating the A/D and D/A converters will not result in 

unrealistic simulation of the ASR-7 processor unit. 

The clock timing for the range bins and 

are shown in Figure E-2 . The ASR-7 system 

E-1 

desired signal characteristics 

clock timing and desired signal 
t'Il 

I 

N 

NORMAL 

CHANNEL 

ENVELOP I: 

DETECTOR 

OUTPUT 

MTI 

CHANNEL 

PHASE 

DETECTOR 

OUTPUT 

;;;-c;;~ ---------

UNIT 

I ENHANCER I FUNCTIONAL 

SWITCH I ON/OFF 

I 

• I 

I ' I 

I MTI;'NORNAL 

ENHANCER rI 

I . "' 

I 

I 

I ENHANCER 

I -

HTI FUNCTIONAL : 

CANCELLERS St'liTCH ' I r 

ON/OFF 

I 

NORMAL ...... CHANNEL r 

ALIGNMENT 

j 

SYSTEl-1 

CLOCK 

MTI __. CHANNEL 

ALIGNMENT 

I 

I 

I 

INOillilAL 

I CHANNEL 

IOUTPUT 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

IHTI 

I CHANNEL I OUTPUT 

L--------------------~ 

Figure E-1 . Block Diagram of Simulated ASR- 7 Processor Unit 

.. 

--.. 
trl 

I 

w 

' 

PW = 0 . 833 ~sec 

PPF = l0U2 Averaqe (6-Pulse Stagger) 

RF TRIG I ~~~c I 953 I 853 I 1053 I 833 I 1403 I 893 I 

Fiqure E-2 . Clock Timing and Desired Signal Characteristics for ASR-7 Radar 
characteristics were simulated for the radar operating in the six-stagger 

mode which has an average Pulse-Repetition-Frequency (PRF) of 1002 

Pulses-Per-Second (PPS). The clock timing also controls the video realignment 

(destaggering to an average PRF of 1002) at the processor output for Plan 

Position Indicator (PPI) display . Using the nominal ASR-7 characteristics, 

the degrees of antenna scan per pulse (~ ) is given by: 

where: 

6 ' RPM 

PRF 

6 ·12 

1002 

0.0718562874°/pulse 

RPM= Antenna scan rate, in rpm (12 for ASR-7) 

(E- 1) 

PRF = Radar pulse repetition frequency, in PPS (1002 for ASR-7 ) 

The number of Azimuth Change Pulses (ACP) per antenna scan for the ASR-7 is: 

ACP 5010 (E- 2) 

Therefore, in summary the simulation of the ASR-7 processor unit was 

done by : 

a. Dividing the receive period after each pulse into 1200 

range bins .625 microseconds long, 

b. each range bin is approximately 0.0718 degrees wide, 

and 

c. there are 5010 azimuth change pulses (ACPs) per antenna 

scan. 

DESIRED SIGNAL 

Figure E-2 shows the pulse width and PRF stagger sequence of the ASR-7 

desired signal. The radar simulation model has the capability of simulating 

a single desired target at any specified range and bearing. The received 

desired signal pulse train (number of pulses from a target (N)) consists of 

20 pulses determined by: 

p~ BW 

N 

6 RPM 

where: 

(1002)(1 . 5) 

(6) (12) ~ 20 

E-4 

(E-3) 
PRF = Radar pulse repetition frequency, in PPS (1002 for 

ASR-7) 

BW = Ant.enna 3 dB beamwidth, in degrees (1.5 degrees for 

ASR- 7) 

RPM = Antenna scan rate, in rpm (12 for ASR-7) 

The range bin in which the target is located (TRB) was calculated by: 

TRB TR 

RTT · RBT 

where: 

TRB = Target range bin location, between 1 and 1200 

TR = Target range, in nautical miles 

RTT = Round-trip time, equals .081 nautical miles per 

microsecond 

RBT = Range bin time, equals .625 microseconds per range bin 

(E- 4) 

The target location (bearing) in Azimuth Change Pulses (ACP) was calculated 

by: 

TACP TB·PRF 

6.RPM 

where: 

TACP = Target azimuth change pulse, between 1 and 5010 

TB = Target bearing, in degrees 

PRF = Radar pulse repetition frequency, in PPS (1002 for 

ASR-7) 

RPM = Antenna scan rate , in rpm (12 for ASR-7) 

(E-5 ) 

The desired signal voltage amplitude in each range bin as a function of the 

desired signal signal-to-noise ratio (S/N) is discussed later in the normal 

and MTI channel simulation sections. 

E-5 
INTERFERING SIGNALS 

Three types of interfering radar signals were simulated: ASR-5, ASR-8, 

and AN/FPS- 90. The radar simulation model has the capability of having any 

combination of the three interfering sources present. Figures E-3 through 

E- 5 show the signal timing characteristics of the ASR-5, ASR-8, and AN/FPS- 90 

interfering radars used in the simulation model. The interfering signal 

voltage amplitude in each range bin as a function of the 

interference-to-noise ratio (I/N) is discussed later in the normal and MTI 

channel simulation sections. 

NOISE 

In range bins where there was no desired signal or interfering signal 

the radar inherent noise level was simulated. The simulation of the noise 

amplitude in each range bin is discussed in the normal and MTI channel 

simulation sections. 

NORMAL CHANNEL SIMULATION 

The following is a discussion of the techniques used to simulate the 

noise, desired signal, and interfering signal levels in the normal channel, 

and the processor unit hardware in the normal channel. 

Noise Distribution 

The voltage amplitude distribution of the noise at the normal channel 

envelope detector output is Rayleigh distributed. The Rayleigh distributed 

voltage amplitude characteristics of the noise were simulated by letting 

ol-2 ln u' (E-6) 

where : 

o = RMS noise level at detector input, in volts 

U = Random number uniformly distributed between 0 and 1. 0 

For each range bin 

amplitude using Equation 

between 0 and 1.0 for U. 

in which 

E-6 was 

noise only 

simulated 

is 

by 

present, a noise voltage 

randomly selecting values 

Signal-Plus- Noise Distribution 

The signal-plus-noise voltage amplitude 

detector output has a Rice distribution 

function) . The amplitude characteristics 

E-6 

distribution at the envelope 

(also called the Marcum "Q" 

of the signal-plus-noise for the 
M 

I 

..... 

PW = 0 . 833 j.Jsec 

PRF = 1170 Average (2-Pulse Stagger) 

1 ~ : ~c 1 7 4 8 1 9 6 2 1 7 4 8 1 9 6 2 1 7 4 8 1 9 6 2 1 7 4 8 1 

RF TRIG --~-- ~~~----~--------~------~--------~------~------~-------L---

Figure E- 3 . ASR-5 Interfering Signal Characteristics 

PW = 0.6 j.JSec 

PRF = 1040 Average (4-Pulse Stagger) 

RF TRIG I ~!~~ I 876 I 961 I 830 I 1177 I 876 I 961 I 

PW 

PRF 

Figure E-4. ASR- 8 Interfering Signal Characteristics 

= 2 . 0 j.Jsec 

= 370 Pulses 

RF TRIG 1 j.J2702 sec I 2702 I 

Figure E-5 . AN/FPS-90 Interfering Signal Characteristics 
desired and interfering signals were simulated by: 

(E-7 ) 

where: 

X ::: R cos (2nV)+ A 

y = R sin (2nV) 

R = ol-2 ln u' 

0 = RMS noise level at envelope detector input, in volts 

A = Peak-signal level at envelope detector input, in volts 

u and v = Random numbers between 0 and 1 . 0 

For the case where rtArt equals zero (no signal present), Equation E-7 is 

equivalent to Equation E- 6. Equation E- 7 was used to simulate the 

signal- plus- noise voltage amplitude for both the desired pulse train and 

interfering signal. The timing of the desired and undesired signals were 

programmed using List Processing Techniques. ~or each range bin in which a 

desired or interfering pulse is present, a signal-plus-noise voltage 

amplitude using Equation E-7 was simulated by randomly selecting values 

between 0 and 1.0 for U and V. Figure E-6 shows the simulat ed 

signal-plus-noise voltage amplitude distribution as a function of the 

signal-to- noise ratio (SIN) in dB generated using Equation E-7. The RMS 

noise voltage level (o ) was set at .25 volts. This corresponds to a one vol t 

peak noise level generally set at the radar receiver output. 

Normal Channel Enhancer 

The ASR-7 enhancer hardware which was simulated is shown in Figure E-7. 

The enhancer is oasically a digital circuit with an adjustaole threshold 

detector as a simple A/0 converter . The enhancer circuit consists of the 

threshold detector, the digital adder/subtracter circuits, a full range shift 

register storage, and a 0/A converter. If an echo signal exceeding the set 

threshold level exists in any given range bin, the enhancer stores a one 

level digital signal in its shift register memory. If the signal continues 

above the threshold in the given range bin, the enhancer will increase the 

level stored in each PRF period until a maximum amplitude of 31 is reached. 

If in any PRF period the signal fails to exceed the threshold level, the 

enhancer subtracts from the stored level in that particular range bin . The 

clock timing for the shift register was simulated for the ASR-7 six-stagger 

mode (see ~igure E-2). 

A detailed discussion of the signal processing properties of the ASR-7 

enhancer is given in Appendix D. 

E-8 
10 

.:t: ~ 

> 

-

0.. 

ttl 

I 

\0 

3. ~--------~r---------~-----------r----------,---------~ 

Rv1S tbise Level(a) = 0.25 Volts 

Noise Only 

.~--~------~~--------~-----------;------------~--------~ 

S/N = 20 dB 

/ 

l. 

Q. r < > 1.,.<>. ":.I ',,.,£1 I., I 

0 . l. 2 . 3 . 4. 

VOLTS 

Figur e E-6. Probability Density Function for Noise Only 

and for Signal-Plus-Noise at the Normal 

Channel Envelope Detector Output. 

5 . 
t'>1 

I 

1-' 

0 

ein THRESHOLD 0 , 1 BINARY .. COMPARATOR 

• 

BINARY D/ A eout 

.. -.. COUNTER CONVERTER 

SHI FT ... REGISTER 

(RANGE- GATE) 

CLOCK 

Figure E- 7 . ASR-7 (AN/GPN-12) Binary Integrator· B1ock Diagram 
Normal Channel Alignment 

The normal channel alignment circuits provide the delay required during 

STAGGER PRF operation to insure that a specific range bin in each PRF receive 

period occurs at the average PRF of 1002 . The STAGGER PRF operation and 

clock timing which was simulated is shown in Figure E- 2. The stagger video 

occurs with the PRF periods of 893 microseconds, 953 microseconds, 853 

microseconds, 1053 microseconds, 833 microseconds, and 1403 microseconds. To 

align these with the average period of 998 microseconds,olock timing from the 

RF trigger is used to control the alignment circuit delay selection. 

MTI CHANNEL SIMULATION 

The following is a discussion of the techniques used to simulate the 

noise, desired signal, and interfering signal in the MTI channel, and the 

processor unit hardware in the MTI channel. 

Noise Distribution 

The voltage amplitude distribution of the noise at the phase detector 

output is Gaussian distributed. The Gaussian distributed voltage amplitude 

characteristics of the noise were simulated by letting: 

npdo(t) R cos 2nV (E-8) 

where: 

R = ol- 2 ln u' 

o = RMS noise level at phase de t ec t or i nput, in vol t s 

U and V =Random numbers uniformly distributed between 0 and 1. 0 

For each range bin in 

amplitude using Equation E-8 

between 0 and 1.0 for U and V. 

which noise 

was simulated 

only is present, a noise voltage 

by randomly selecting values 

Signal-Plus- Noise Distribution 

The signal- plus-noise voltage amplitude 

detector output was simulated by: 

R Cos 2nV + A cos 2nW 

E-ll 

distribution at the phase 

(E- 9) 
where: 

A Peak-signal level at phase detector input, in volts 

V and W =Random numbers uniformly distributed between 0 and 1.0 

For the case where "A" equals zero (no signal present), Equati on E-9 is 

equivalent to Equation E- 8. Equation E- 9 was used to simulate the 

signal-plus-noise voltage amplitude for both the desired pulse train and 

interfering signal . The timing of the desired and undesired signals were 

programmed using List Processing Techniques. For each range bin in which a 

desired or interfering pulse is present, a signal-plus-noise voltage 

amplitude using Equation E-9 was simulated by randomly selecting values 

between 0 and 1.0 for U, V, and W. Figure E- 8 shows the simulated 

signal-plus-noise voltage amplitude distribution as a function of the 

signal-to-noise ratio (S/N) in dB generated using Equation E-9. The rms 

noise voltage level was set at . 25 volts. 

MTI Cancellers 

The MTI .double stage canceller hardware in the ASR- 7 radar was 

simulated . It was necessary to simulate the ASR-7 MTI canceller hardware in 

order to investigate the performance of the ASR- 7 enhancer in the presence of 

asynchronous interference since the impulse response of a double stage MTI 

canceller with feedback will produce several synchronous pulses. A detailed 

discussion of the signal transfer properties of a double stage MTI canceller 

to asynchronous interference is discussed in Appendix C. The following is a 

discussion of the simulation of the ASR-7 double stage MTI canceller. 

The ASR-7 digital canceller consists of two identical delay line type 

cancellers in cascade, with switch selectable feedback . Figure E-9 shows the 

canonical form of the ASR-7 MTI canceller which was simulated. The figure 

shows the transfer function coefficients which represent the ASR-7 hardware . 

The feedforward coefficients (ai) are a 0 = 1/ 2, a1= -1, and a2= 1/ 2. The 

feedback coefficients (bi) for the various canceller modes are: 

CANC 2 bl 0 i b2 = 0 

25 dB SCV : bl = 1~; b2 _., 

30 dB SCV: b l 1 b2 = - 0, 

35 dB SCV.: bl 3 

-1; b2 -0, 

4 0 dB SCV: b l ~ b2 _., 

A digital word from each range bin is fed into the canceller. If this range 

bin contains only clutter, the canceller output will be virtually zero . If 

it contains a moving target the difference amplitude will represent a sample 

taken from the doppler cycle. The storage element in each canceller consists 

of eight parallel shift register chains 1200 range bins long. The digital 

words are clocked in parallel down the 1200 shift- register bins at a 1.6 MHz 

rate. The timing for the delays in the MTI canceller were simulated for the 

ASR-7 six-stagger mode shown in Figure E-2. List Processing Techniques were 

E-12 
tT' 

I 

;,...) 

.. 

< ~ 

> 

~~ 

0. 

.. ~~-----· ··!·

3 . 

RHS Noise Level (o) = 0. 25 Volts 

\ 

2 . 

Noise Only 

/ 

1. 

0 . 

-5 . -4 . -3 . -2 . -1. 0. 1. 2 . 3 . 

VOLTS 

Figure E-8 . Probability Density Functlon for Noise Only 

and for Signal-Plus -Noise at the MTI Phase 

Detector Oulput . 

20 dB 

4 . 5 . 
M 

I 

t-' 

.p. 

!ill a 0 =1/2 

z - 1 

bl=l/2,3/4,1,1-1 al=-1 

z-1 

b2=- l/2 a 2=1/2 

Figure E-9 . Canon ical Form of Simulated ASR-7 MTI Cancelle r 
used in programming the timing of the ASR-7 six- stagger sequence. 

Appendix C contains a detailed discussion of the signal processing 

properties of the MTI cancellers. 

MTI Channel Enhancer 

The MTI channel enhancer circuitry is identical to the normal channel 

enhancer. The simulation of the enhancer was discussed in the normal channel 

simulation section. 

MTI Channel Alignment 

The MTI channel alignment circuitry is identical to the normal channel 

alignment circuitry. The simulation of the alignment circuitry was discussed 

in the normal channel simulation section. 

FEEDBACK ENHANCER 

As mentioned at the beginning of this appendix, a feedback enhancer 

capability was added to the simulation. Figure E- 10 shows the feedback 

enhancer model used in the simulation . The first three blocks: the 

attenuator, subtracter and bottom clipper are ,strictly speaking, not part of 

the ASR-8 enhancer circuit board (which it attempts to model). However, 

these functions are effectively found in other circuits, and it was found 

necessary to include them to achieve realistic results. Appendix D has a 

detailed discussion of the feedback integrator. 

OUTPUT DISPLAY 

Two radar output displays were simulated: the radar output oscilloscope 

display, and the radar output PPI display. The radar simulation model has 

the capability of displaying both the normal and MTI channels in the 

unenhanced and enhanced modes. Appendix D contains oscilloscope display 

outputs as a function of a parametric range of noise, desired signal, and 

asynchronous interfering conditions. Also, the trade-offs of the desired 

signal properties in utilizing an enhancer to suppress interfering signals 

are discussed in Appendix D. Figure E-1 1 is 45 degrees of a simulated PPI 

display of interference . 

E-15 
r:1 

I 

t-' 

a-

--~~~ ATTENUATOR I •I SUBTRACTOR 

Gin INPUT 

Lir1ITER 

+ 

+ 

L 

I30TTOt1 

CLIPPCR 

OUTPUT 

LHIITER 

K ~ DELAY ~ To = 1/PRF 

Figure C- 10 . Feedback Integrator Block Diagram 

eout 
270 

g 

0 

90 

180 

QC.DG !2.!5 24.30 36.~5 48.SC 60.15 

RANGE IN NAUTICAL MILES 

Figure E-ll . Simulated PPI Display of Interference 

E-17 
APPENDIX F 

INTRODUCTION 

This Appendix includes derivations of the equations, and a description 

of the computer programs used to analyze the impact of radar pulse 

interference on ARTS-IIIA/RDAS performance. The first section derives the 

equation used to evaluate the effect of interference on target and false 

target hit probabilites. The derivation of equations used to compute clutter 

hit, target hit, and noise hit probability are also included in the first 

section. The second section describes computer programs that were written to 

compute the probability of false alarm and target detection . 

DERIVATION OF EQUATIONS 

Effect of Interference on Hit Probability 

The following is a derivation of the equation that gives the probability 

of a hit (logical 1) at the rank order detection process (includes the rank 

quantizer and hit processor shown in Figure 4-4) output when interference is 

present. The derived equation is a general equation that can be used to 

determine the effect of interference on the probability of a hit (logical 1) 

when noise, desired signal or clutter are in the range bin of interest. The 

effect of interference on the probability of a hit when noise, desired 

signal, or clutter is present in the range bin of interest is a function of 

the probability of a hit (logical 1) when noise onl y is present (Pnl), 

probability of a hit when noise and desired signal only are present (P5 1), 

and the probability of a hit when noise and clutter only are present (Pel) , 

respectively. For purposes of deriving a general equation for all of the 

above conditions, a general term (P1 ) will be used to represent a hit for 

Pnl• Psl • and Pel · The equations for Pnl• P51 , and Pel will then be derived 

later. The derivations are described for a rank quantizer threshold 24 to 

m1n1m1ze verbiage. However, the results are applicable to any rank quantizer 

threshold. 

The rank order detecti~n processing technique employed in the Radar Data 

Acquisition Subsystem (RDAS) involves comparing the voltage level in the 

range bin of interest with that in 24 other adjacent range bins. A logical 1 

or hit is generated if the voltage level in the range bin of interest exceeds 

a particular number (rank quantizer threshold ) of the adjacent comparison 

range bins. If it is assumed that no interfering pulses fall in the 

comparison range bins and, the level of the interfering pulses is al ways 

greater than the voltage level in the comparison range bins, a hit will be 

generated every time an int erference pulse falls in the range bin of 

interest . Let A represent the event in which one or more interfering pulses 

fall in the range bin of interest. A hit can also be generated without the 

presence of interference if the v~ltage level due to signal-plus-noise, noise 

only, or clutter exceeds the voltage level in the comparison range bins. Let 

B represent the event in whi ch a hit is generated when no interference is 

F-1 
present. The probability of a hit being generated with interference or 

without interference is given by (Davenport, 1958): 

P(A U B) P(A) + P(B) - P(A n B) (F-1) 

where A U B represents the event in which A or B occurs and A n B represents 

the event in which both A and B occur. Since events A and B are independent 

of each other, Equation F- 1 can be written in the form: 

P(A U B) = P(A) + P(B) - P(A)P(B) (F-2) 

The generatlon of a hit (logical 1) ·can be inhibited if a strong 

interfering pulse falls in one or more of the rank quantizer comparison range 

bins, because the voltage level in the range bin of interest will then not 

exceed all the comparison range bin voltage levels. The following 

derivations assume that all the interfering pulses are the same level, and as 

previously stated, greater than the noise, clutter, or target voltage level . 

These assumptions imply that an interfering pulse falling in the rank 

quantizer range bin of interest will not generate a hit if one or more of the 

interfering pulses simultaneously fall into the rank quantizer comparison 

range bins. Let C represent the event of an interfering pulse falling into 

one or more of the comparison range bins, and P(C) the probability of that 

event occurring. A hit can only occur if event A or B occurs and no 

interfering pulses fall in the comparison range bins. Since Equation F- 2 

gives the probability of A or B occurring and 1- P(C) the probability of an 

interfering pulse not falling in the comparison range bins, the probability 

of a hit occurring with interference present is given by: 

P il = [P(A) + P(B) - P(A)P(B)] [1-P(C)] (F-3) 

The product of Equation F- 2 and [1-P(C)] is used in Equation F-3 because 

event C can be considered independent of events A and B. This is possible 

because the interfering pulses arrive randomly in time and the no 

interference voltage level is assumed to be insignificant compared with the 

level of the interfering pulses. 

Equation F-3 defines the probability of a hit due to asynchronous 

interference for the ARTS-IIIA/RDAS connected to the victim radar normal 

channel. This equation will be expanded for the case in which the 

ARTS- IIIA/RDAS is connected to the radar MTI channel. Approximately three 

synchronous interfering pulses are generated by the MTI canceller circuits 

for each asynchronous interference pulse at its input. This affects the 

probability of interfering pulses falling in a given rank quantizer range 

bin. An interfering pulse falling in the rank quantizer range bin of 

F-2 
interest could be due to an asynchronous interfering pulse at the input of 

the MTI falling in the range bin of interest on the present ACP (event Al), 

previous ACP (event A2 ), or two ACPs before (event A3). Therefore, the 

probability of an interfering pulse falling in the rank quantizer range bin 

of interest is given by: 

P (A1 UA2UA3)=P (A1)+P (A2 )+P (~) - P (Al fl A2) -P (A1ILt>,.3) -P (A:fA3) 

+P (A1 n.A2

M 3 ) 

(F-4 ) 

Since the probability of an asynchronous interfering pulse falling in a 

particular range bin is the same for all ACPs, and independent of each other, 

Equation F-4 can be written in the form: 

(F-5) 

Equation F- 5 can be closely approximated by 3P(A) since P(A) <1o- 4 and the 

product terms are small compared to 3P(A) . 

Based on the assumptions in this analysis, it is requi red that no 

interfering pulses fall in the rank quantizer comparison range bins for a hit 

to be generated. In order for this to occur with the ARTS-IIIA/RDAS 

connected to the MTI channel, it is necessary that interfering pulses do not 

fall in these range bins at the MTI circuit input for three consecuti ve ACPs. 

It was previously shown that 1-P(C) is the probability of an interfering 

pulse not falling in the comparison range bins, where P(C) is the probability 

of interfering pulses falling in the comparison range bins. Therefore, the 

probability of interfering pulses not falling in the comparison range bin for 

three consecutive ACPs is [1 - P(C)]3 . Substituting [1-P(C)]3 for [1-P(C)] and 

3P(A) for P(A) in Equation F-3 gives: 

P i1 = [3P(A) + P(B) - 3P(A)P(B)) [1-P(C) )

3 (F-6) 

Equations F-3 and F-6 can be represented by one general equation 

Pil = [N P(A) + P(B) - N P(A) P(B)] [1-P(C)]N (F-7) 

where N is set equal to for the ARTS-IIIA/RDAS connected to the radar 

normal channel and set equal to 3 if connected to the MTI channel . 

The random arrival of asynchronous interfering pulses in time 

described by a Poisson probability distribution (Davenport, 

F-3 

can be 

19 58) . 

. ' 
Therefore, the probability of an interfering pulse overlapping the sample 

time of the range bin of interest is given by: 

I' (A) 

where: 

\) 

= Time interval that aninterfering radar pulse can 

overlap the sample time of the rank quantizer 

range bin of interest, seconds 

= Interfering pulse arrival rate, pulses/ second 

(F- 8) 

The probability of an interfering pulse overlapping the sample time of one or 

more comparison range bins is giverr by: 

P(C) 

where: 

Time interval that an interfering radar pulse can 

overlap one or more of the rank quantizer 

0omparison range bins sample times, seconds 

(F-9) 

Substituting Equations F-8 and F-9 into Equation F-7 and letting the 

probability of a hit without interferenc e, P(B), equal P1 gives: 

( F-10) 

Algebraic simplification of this equation gives the basic equatio~ that was 

used in the analysis: 

(F-11) 

Some justification for the assumption that the interfering pulses are 

greater than the target return pulses at the ASR-7 radar MTI circuit output 

needs to be presented, since the amplitude of a given interfering pulse out 

of the ASR-7 MTI circuit can be zero depending on its phase angle relative to 

the COHO reference signa1 . For example, the MTI phase detection in the ASR-7 

radar will give a zero output voltage if the difference in phase between the 

interfering pulse and the coherent osc illator signal is 90 degrees (see 

Appendix C). The simulation of interfering radar effects on the ASR-7 radar 
-· 

(see Appendix E) involved obtaining pulse amplitude statistics at the MTI 

circuit output. A modified cumulative distribution of these statistics are 

shown in Figure F- 1 for various signal-to- noise ratios (SNR's). The vertical 

axis gives the percentage of time that the horizontal axis signal-plus-noise 

voltage level is exceeded. The curves are applicable to either randomly 

arriving constant amplitude interfering or target return pulses since the 

simulations assumed no phase correlation between pulses. The curves in 

Figure F-1 indicate that if the interfering pulse levels are much greater 

than the target return pulses at the input of the MTI circuits, there is a 

high probability that this condition will also exist at the MTI circuit 

outputs (ARTS-IIIA/RDAS input). For example, assume that the 

interference-to-noise ratio (INR:20 dB) is 10 dB greater than the 

signal-to- noise ratio (SNR=10 dB). For this case, Figure F-1 indicates the 

interference-plus-noise level would exceed 1.5 volts at the MTI output 60 

percent of the time while the signal-plus- noise level would exceed this level 

only 2 percent of the time . This example indLcates that it is reasonable to 

make the worst - case assumption that the interfering pulses are greater than 

the target return pulses at the ARTS-IIIA/RDAS input when connected to the 

ASR- 7 MTI channel. This worst - case assumption is even more reasonable for 

the ASR- 8 radar dual channel MTI since it employs quadrature phase detectors. 

A single non-zero amplitude pulse at the dual channel MTI input, regardless 

of its phase, will not be zero amplitude at its output . 

Probability of Fal s e Target Hit 

This subsection derives the equation for probability of a false target 

hit due to noise without the presence of interference. A false target hit is 

defined as the generation of a target hit (logical 1) when no target is 

present . A hit is generated for these conditions if the noise level in the 

rank quantizer range bin of interest is greater than RQT of the J comparison 

range bins. Thi s rank order detection process results in a constant false 

target hit probability if the rank quantizer range bin sample outputs v1 , v

2 , 

. •• , Vj, Vj"1""1 are independent and identically distributed. These 

statistical conditions are assumed for the following derivations. Let F 

define the cumulative distribution, 

F(v) 

samples. 

quanti zer 

quantizer 

quantizer 

= P (V<v) , where V represents rank quantizer comparison range bin 

In J independent noise samples ~ , i=1, .... J, from the J rank 

comparison range bins, the probability that exactly RQT (rank 

thres hold) will be less than the J+1 sample (sample from rank 

range bin of interest) is given by: 

( R~T) (F(v) ]RQT [1-F(v) ]J-RQT (F-12) 

The value of v in 

range bin of interest. 

this equation represents the noise voltage level in the 

The binomial coefficient in Equation F-12 takes into 

F-5 
A 

r.Ll 

A 

r.Ll 

r.Ll 

u 

>< r.Ll 

H 

~ r.Ll 

H 

r.Ll 

tTj 0 

<I! I E-t 0\ H 

0 

> 

~ H 

E-t 

rx.. 

0 

r.Ll 

0 

<I! 

E-t 

z 

r.Ll 

u 

p:; 

r.Ll 

A. 

100 

80 

6o 

40 

20 

0 

0 1 2 3 4 5 

Signal Plus Noise Voltage Level 

Figure F-1 . Modified Cumulative Distribution of Signal- Plus- Noise at 

ASR-7 Radar MTI Channel Output for Various Signal- toNoise Voltage Ratios 

6 
J 

account the different combinations of RQT out of J things. The probability 

that the sample in the rank quantizer range bin of interest is greater than 

RQT of J comparison range bins is given by: 

J 

E ( J) [F(v) ]K [1-F(v) ]J-K (F-13) 

K=RQT 

The value v can be considered sample values drawn from the rank quantizer 

range bin of interest. If it is assumed that this sample space has a 

cumulative distribution F(v), taking the expected value of the Equation F-13 

gives the probability CP0 1) that a sample from the rank quantizer range bin 

of interest will exceed RQT of the rank quantizer comparison range bin sample 

levels: 

1 

P

01 

f E ( J) [F(v)]K[l-F(v)]J-Kd[F(v)] 

o K=RQT K 

~ Jl ( KJ ) ~ [F(v)]K[l-F(v)]J-Kd[F(v)] K=RQT o 

(F-14) 

This equation gives the probability of a false target hit occurring due to 

only noise. A general term in Equation F-14 is: 

/ ( i) [F(v) ]K[1-F(v) ]J-Kd [F(v)] (F-15) 

0 

Substituting the dummy variable u for F(v) and evaluation of F-15 by repeated 

integration by parts gives: 

1 

J+1 

Substituting Equation F- 16 for each term in Equation F-14 gives: 

J 

E 

K=RQT 

1 

J+l 

J+l-RQT 

J+1 

F-7 

(F-16) 

(F-17) 
This equation indicates that the probability of a false target hit due to 

noise is independent of the noise distribution F(v) and only a function of 

hardware parameters. It should, however, be reiterated that the equation is 

only valid when range bin noise samples are independent and identi call y 

distributed. The equation would only give approximate false hit values for 

correlated clutter. 

Probabill.l.Y. __ o_f __ T_a,rget Hit 

This subsection derives the equation for probability of target hit 

without interference present. A target hit is defined as the generation of a 

target hit (logi cal 1) when a target is present. The derivation considers 

the target signal present in the rank quantizer range bin of interest and no 

target signal present in the rank quantizer comparison range bins. Assume 

that the samples from the comparison range bins are independent and 

identically distributed with a cumulative distribution function 

F(v) = P (V<v). The probability of the target signal-plus- no1se level in the 

range bin of interest being greater than the level in RQT of the J comparison 

range bins is therefore given by: 

J 

E ( ~) [F(v)]K[l-F(v)]J-K 

K=RQT 

(F- 18) 

The value v in this equation represents the signal-plus-noise voltage level 

in the range bin of interest. Assume that the target-plus-noise-signal level 

v in the rank quantizer range bin of interest has a cumulative distribution 

function G(v) = Ps+n(V<v). The signal-plus-noise level v can be considered 

as sample values from probability space with cumulative distribution function 

G(v). If it is assumed that these samples (target return pulses) are from an 

identical target distribution and independent, the expected values of 

Equation F-18 can be taken to obtain the probability of a hit occuring when 

the target is present: 

ps1(J,RQT) 

1 

J 

0 

J 

E ( ~) [F(v) )K [1-F(v) )J-Kd [G(v)) 

K=RQT 

(F-19) 

After substituting the appropriate cumulative distribution for signal-plusnoise G(v) and noise F(v), Equation F-19 was used in the analysis to compute 

the target hit probability. It should be pointed out that the assumption of 

pulse-to-pulse independence in deriving Equation F-19 implies that the 

equation will only give estimated values when the target return pulse are 

correlated in amplitude. 

F-8 
CQHPUTER PROGRAM DESCRIPTIONS 

Probability of False Alarm Program 

This subsection describes a computer program written for the analysis to 

compute probability of false alarm. The previous sections derived equations 

for computing the probability of false target hits with and without 

interference. These false target hits were related to the probability of 

false alarm from curves generated by the false alarm probability program. 

The target detection stage of the (see Figure 4- 2) ARTS-IIIA/RDAS 

maintains a record of the target hits and misses in azimuth for a given range 

bin. When the consecutive misses in the record equals or exceeds a miss 

count threshold (3 or 4), the accumulated sum of the target hits in the 

record is compared with a hit count threshold. If the hit count equals or 

exceeds the hit count threshold, a target is declared. The record of hits 

and misses is initialized when the first hit occurs and continues for 30 

ACPs. The record is extended beyond the 30th ACP if the hit count threshold 

at this ACP is satisfied, but the miss count threshold is not. 

Because the record azimuth window can vary in length, a mathematical 

expression describing the hit processing becomes intractable. A 

straightforward method of calculating the false alarm probability is to 

employ a Monte Carlo simul~~ion. However, the false alarm probabilities have 

approximate values of 10 and would require more than one million 

repetitions in the simulation to evaluate. Consequently, the computation 

time on even modern computers would bec oraa excessive. For this reason , and 

to avoid questions of statistical confidence, a deterministic approach was 

taken to compute the probability of false alarm. A computer program was 

written which employs a combination of simulation and analytical methods. 

The technique basically involves identifying all possible combinations of hit 

and miss sequences which satisfy the target declaration criteria and 

computing the probability of each occurring. The type of calculations 

performed by the computer program can be described mathematically by: 

PFA = 

30 

E 

where: 

L= 

(HCT+MCT) 

PFA = Probability of false alarm 

P1 = Probability of false target hit occurring 

HCi = Hit count (sum of hits) for i th hit/miss ~equence 

combination and record length L 

F- 9 

(F-20) 
and 

MC 1 = Miss count (sum of misses) for i t h hit/miss 

sequence combination and record length L 

HCT = Hit count threshold required to be satisfied 

target declaration 

MCT = Miss count threshold required to be satisfied 

target declaration 

L.= Record length or window width in ACPs 

. f (1) = { ~ target declaration criteria sati~fied 

target declaration criteria not satisfied 

for 

for 

(F-21) 

The "i " in the above equation signifies a particular hit/miss sequence 

combination. A computer subroutine algorithm sets f(i) equal to 1 if the 

particular hit/miss sequence combination satisfies the target declaration 

criteria and zero otherwise. The upper index of the inner summation 

indicates that 21 hit / miss sequence combinations were examined for a given 

record length (azimuth window) to determine if the target declaration 

criteria had been met. The probability of each sequence occurring, whi ch 

satisfies the target declaration criteria, was computed and summed. The 

outer summation is taken . to add the fal~e alarm probabilities for all 

possible record lengths up to the system maximum (without extension) of 30 

ACPs. The lower limit of the summation (HCT + MCT) gives the minimum record 

length (azimuth window) in which the target declaration criteria can be 

satisfied. It should be ·POinted out that Equation F-20 implies that the 

probability of a noise hit occurring on a given ACP is independent of it 

occurring on any other ACP. Therefore, the results of the simulation are not 

applicable to correlated clutter. 

The actual implementation of Equation F-20 in the computer program took 

a ~lightly different form to eave computer time: 

24 

PFA "" I: 

L= 

(HCT+MCT) 

(F-22) 

This form of the equation reduced the number of binary (hit/ mi~s ) sequences 

that had to be generated and tested for compliance with the target 

declaration criteria. It takes advantage of the fact that every binary 

sequence that satisfies the target declaration criteria begins with a hit and 

ends with a hit plus MCT consecutive misses. For example, with a MCT of 3 

the binary sequence takes the form (1 ..•.... 1000). Therefore only the hit 

F-10 
(1) and miss (0) combinations between the first and last need to be 

considered. To further save computer time, the program was written to 

generate false alarm versus record length curves for record lengths up to 24 

ACPs. These curves were then used to extrapolate the probability of false 

alarm for record lengths up to 30 ACPs. The error in tne final extrapolated 

probability of false alarm value due to extrapolation is estimated to oe less 

than 2 percent. This error is small oecause the contrioution to tne fa~se 

alarm probability calculation was relatively small for record lengths greater 

than 2ll. 

As previously stated, the record of nits and misses are extended oy tne 

RDAS beyond 30 ACPs if on the 30th ACP the hit count thresnold has been 

satisfied, but the miss count threshold has not. The contribution of record 

lengths greater than 30 ACPs to the system probability of false alarm was 

computed and found to be insignificant. 

The sequence of program operations to compute the probability of false 

alarm is outlined below: 

(1) For a given record length (azimuth window), generate all possible 

hit/miss sequence combinations. 

(2) Test each hit/miss sequence combination to determine wnich 

satisfy the target declaration criteria . 

(3) For each identified hit/miss sequence combination that satisfies 

the target declaration criteria compute the probability of it 

occurring using the known probabilities of lndi~idual nits or 

misses occurring. 

( lj) Add the probabilities 

combinations occurring 

criteria. 

computed for 

that satisfy 

each 

the 

hit/miss 

target 

sequence 

declaration 

(5) Perform the above operations for each recora length (azimutn 

window) up to 24 ACPs. 

(6) Generate a curve of false alarm probaoility versus recora :engtn. 

Probability of Target Detection Program 

This subsection descrioes a compute r program that was written :o comp· .. ne 

probability of target detection. The program generated curves that were used 

in the analysis to relate probability of target h:t to probability of target 

detection. 

Basically, the computer program uses the l'ionte Carlo technique to 

simulate target hit and miss sequences and then counts the num~er of nit / miss 

sequence cases which satisfy tne target declaration criteria . Tne pe~centage 

of hit/miss sequence cases that satisfy tne target dete~tion c~iter:a was 

F-~1 
computed to obtain the predicted tar get detection probability . A total of 30 

ACPs wer e considered in each simulated sequence of hits and misses. The 

first five and last five ACPs of the s equence considered only the presence of 

noise in the range bin while the middle 20 ACPs in the sequence considered 

the target to be present. It was assumed in the simulation that the target 

was present for 20 ACPs because this is the typical number of return pulses 

received by an ASR-7 or ASR-8 radar from an aircraft target. This is evident 

from evaluation of Equation 3- 21 for typical ASR- 7 and ASR- 8 radar parameter 

combinations . Noise only ACPs, before and after the target, were included in 

the simulation because noise in these range bins affect the probability of 

the target being detected. In particular, the noise in the range bins (ACPs) 

before the target increases the probability of the hit count threshold being 

satisfied, and noise in the range bin following the end of the target 

decrease the probability of the miss count threshold being satisfied. A 

number of test simulations were conducted to determine how many range bins 

should be included before and after the target range bins. The test 

simulations indicated that including five noise only range bins before and 

after the target range bins provides a good trade-off between computer time 

and predicted detection probability accuracy. It is estimated that including 

only five range bins before and after the target range bins, instead of an 

infinite number , introduces less than 1 percent error in the predicted target 

detection probability. 

The Monte Carlo simulation of the hit/miss sequence is described 

mathematically by the function: 

f.(U) 

J ~ for 

for 

wher e : 

j = The particular ACP index number which can range from 1 

to 30 , 

U =Random number uniformly distributed between 0 and 1 . 0 

P1= The probabillity of a hit (logical 1) occurring. 

(F-23) 

The value of P1 in Equation F- 22 depends on the particular ACP and if noise 

only or signal - plus- noise is considered present in the range bin 

corresponding to a particular ACP. The value of P1 for the first five and 

last five ACPs (j = 1- 5 and 26- 30) in each simulated hit/miss sequence 

corresponds to the probability of a target hit occurring due to only noise 

and was computed from Equation 4- 5 . A noise hit probability of 0 . 08 was used 

for a rank quantizer threshold setting of 23, and a noise hit probability of 

0 . 04 for a rank quantizer threshold of 24. The value of P1 in Equation F- 23 

F-12 

. . 
for the middle 20 ACPs (j = 6-25) in each simulated hit/miss sequence 

represents the probability of a hit occurring due to the presence of an 

aircraft target. The simulation considered the probability of a hit 

occurring on a given ACP to be independent of the probability of it occurring 

on any other ACP. In other words, the simulation does not consider the 

possibility of pulse-to- pulse correlation of the target or clutter return 

pulses . In addition, the computed detection probabilities are for one 

antenna rotation and do not include the improved detection characteristics 

that can result from antenna scan- to-scan target tracking. 

As stated previously, the program was used to generate target detection 

probability versus target hit probability curves (see Figures 4-27, 4-28 and 

4- 29) . Each curve corresponds to a particular combination of detection 

parameter settings (rank quantizer threshold, hit count threshold, and miss 

count threshold). Each point on the curve was determined from ten thousand 

repeated hit/miss sequence simulations. Other points on the curves were 

obtained by performing these simulations with different target hit 

probability P1 values substituted in Equation F-23. However, the value of P1 

in Equation F- 23 for noise only ACPs was held constant for all points on a 

given curve . 

It should be pointed out that the simulations did not include the effect 

of interference on the noise hit probabilities corresponding to the range 

bins not occupied by the target. This drastically reduced the number of 

curves and computer time required for the target detection calculations. 

Neglecting the interference effects on noise hit probabilities did not 

significantly affect the computed detection probability values. This fact is 

evident from the detection probability curves in Figures 4-27 and 4-28 . The 

curves in Figure 4-27 are f or a rank quantizer threshold of 23 or 

equivalently (see Equation 4-5) a noise hit probability of 0. 04, and the 

curves in Figure 4- 28 for a noise hit probability of 0 .08 . Comparison of 

corresponding curves in Figures 4-27 and 4- 28 for the same hit and miss count 

thresholds indicates a 0. 04 change in noise hit probability does not change 

the predicted detection probability by more than 0.02 . It was shown in the 

false alarm portion of ~he analysis (see TABLES 4-3 and 4-5) that c ontinual 

interference from three radars does not change the noise hit probability by 

more than 0 . 006. This indicates that the effect of interference on noise hit 

probability is small enough to be neglected in the detection probability 

calculation . 

F-13 
j 

APPENDIX G 

SYSTEM CHARACTERISTICS 

INTRODUCTION 

This appendix contains a conpendium of system characteristics of radars in 

the 2.7 to 2 . 9 GHz band. 

G-1 
TABLE G-1 

ASR-5 SYSTEM CHARACTERISTICS* 

ANTENNA CHARACTERISTICS 

A. Type: 

B. Gain: 

c. Beamwidth: 

elevation: 5 degrees 

azimuth: 1. 5 degrees 

D. Polarization: 

E. Antenna Rotation Rate: 

TRANSMITTER CHARACTERISTICS 

A. Output Tube: 

B. Frequency : 

C. Peak Power: 

D. Pulsewidth: 

E. PRF: 

RECEIVER CHARACTERISTICS 

A. System Noise Figure: 

B. Receiver Bandwidth: 

Normal IF: 

MTI IF: 

Normal Video: 

MTI Video: 

2. 7 MHz 

5. 0 MHz 

2.0 MHz 

2.0 MHz 

C. Minimum Discernible Signal 

(MDS): 

Normal Receiver : - 109 dBm 

MTI Receiver: -107 dBm 

D. Scope Range (NM): 

Shaped beam, cosecant squared in elevation 

from half power point to +30 degrees 

34 dB 

Linear, vertical, or circular; 

remotely selectable 

13 or 15 RPM 

Magnetron (5586, DX276 or QK1643) 

Tunable 2.7 to 2.9 GHz 

400 - 500 kW 

.833 microsecond 

Selectable 900 to 1200 PPS (2-pulse 

stagger on or off) 

4 dB maximum 

60 nautical miles 

*Also applicable to ASR- 4, ASR-6, and AN/FPN-47 

G-2 
) 

TABLE G-2 

ASR- 7 SYSTEM CHARACTERISTICS' 

ANTENNA CHARACTERISTICS 

A. Type: 

B. Gain: 

c. Beamwidth: 

elevation: 5 degrees 

azimuth: 1. 5 degrees 

D. Polarization: 

E. Antenna Rotation Rate: 

TRANSMITTER CHARACTERISTICS 

A. Output Tube: 

B. Frequency: 

C. Peak Power: 

D. Pulsewidth: 

E. PRF: 

RECEIVER CHARACTERISTICS 

A. System Noise Figure: 

B. Receiver Bandwidth : 

Normal IF : 

MTI IF: 

2. 7 MHz 

5 . 0 MHz 

C. Minimum Discernible Signal 

(MDS): 

Shaped beam, cosecant squared in elevation 

from upper half power point to +30 degrees 

34 dB 

Linear, vertical, or circular; remotely 

selectable 

15 RPM 

Magnetron (DX276 , 8798) 

2.7 to 2 . 9 GHz 

425 kW 

0.833 microsecond 

6-pulse stagger with 1002 PPS average, 

or fixed (selectable from 713 - 1200 

PPS) 

4.75 dB 

Normal Receiver: - 108 dBm 

Log Receiver: - 106 dBm 

MTI Receiver: - 106 dBm 

Log MTI Receiver : - 104 dBm 

D. Scope Range (NM): 60 nautical miles 

*Also applicable to AN /G PN-1 2 

G- 3 
TABLE G-3 

ASR-8 SYSTEM CHARACTERISTICS 

ANTENNA CHARACTERISTICS 

A. Type: 

B. Gain: 

C. Beamwidth: 

elevation: 

azimuth: 

4.8 degrees 

1.35 degrees 

D. Polarization: 

E. Antenna Rotation Rate: 

TRANSMITTER CHARACTERISTICS 

A. Output Tube: 

B. Frequency: 

C. Peak Power: 

D. Pulsewidth: 

E. PRF: 

RECEIVER CHARACTERISTICS 

A. System Noise Figure: 

B. Receiver Bandwidth: 

Normal IF: 

MTI IF: 

Log IF: 

MTI Video: 

1. 2 MHz 

5.0 MHz 

1. 2 MHz 

585 kHz 

C. Minimum Discernible Signal 

(MDS): 

Normal Receiver: -110 dBm 

Log Receiver: -109 dBm 

MTI Receiver: -108 dBm 

D. Scope Range (NM): 

Shaped Beam, cosecant squared in 

elevation from half power point to +30 

degrees 

33.5 dB Normal Beam 

32.5 dB Passive Beam 

Linear verticle or circular, remotely 

selectable 

12.5 RPM 

Klystron (VA-87E) 

Tunable 2.7 to 2.9 Hz 

1.4 MW 

0.6 microsecond 

4- pulse stagger with 1040 average, or 

fixed (selectable from 700 - 1200 PPS) 

4.0 dB maximum 

60 nautical miles 

G-4 
TABLE G-4 

WSR- 57 SYSTEM CHARACTERISTICS 

ANTENNA CHARACTERISTICS 

A. Type: 

B. Gain: 

C. Beamwidth: 

D. Polarization: 

E. Antenna Rotation Rate: 

TRANSMITTER CHARACTERISTICS 

A. Output Tube: 

B. Frequency : 

C. Peak Power: 

D. Pulsewidth: 

E. PRF: 

RECEIYER CHARACTERISTICS 

A. System Noise Figure: 

B. Receiver IF Bandwidth: 

C. Minimum Discernible Signal 

(MDS): 

- 100 dBm (short pulse) 

-1 08 dBm (long pulse) 

D. Scope Range (NM): 

Parabolic disk (12 ft. diameter) 

38 dB 

2.2 degrees 

Linear, horizontal 

0 to 5'RPM - 5 to +45 degrees elevation 

Magnetron {QK729- 733) 

Tunable 2.7 to 2.9 GHz 

500 kW 

0.5 microsecond (short pulse) 

4.0 microseconds (long pulse) 

658 PPS (short pulse) 

164 PPS (long pulse ) 

4.0 dB 

4.5 MHz for short pulse and 0.75 

MHz for long pulse 

250 nautical miles 

G-5 
TABLE G-5 

WSR-7~S SYSTEM CHARACTERISTICS 

ANTENNA CHARACTERISTICS 

A. Type: 

B. Gain: 

c. Beamwidth: 

D. Polarization: 

E. Antenna Rotation Rate: 

TRANSMITTER CHARACTERISTICS 

A. Output Tube: 

B. Frequency: 

C. Peak Power: 

D. Pulsewidth; 

E. PRF: 

RECEIVER CHARACTERISTICS 

A. System Noise Figure: 

B. Receiver IF Bandwidth: 

C. Minimum Discernible Signal 

(MDS): 

D. Scope Range (NM): 

Parabolic Disk (12 ft. diameter) 

38 dB 

2.2 degrees maximum 

Linear, horizontal 

0 to 5 RPM 

-5 to +45 degrees elevation 

Coaxial Magnetron 

2 . 7 to 2.9 GHz 

565 kW 

1 microsecond (short pulse) 

4 microseconds (long pulse) 

545 PPS on short pulse 

164 PPS on long pulse 

Not less than 1.5 MBz for short pulse 

and .375 MHz for long pulse 

50, 125, and 250 nautical miles 

G-6 

I 
) 

TABLE G- 6 

AN/FPS- 6 SYSTEM PARAMETERS* 

ANTENNA CHARACTERISTICS 

A. Type : 

B. Gain: 

C. Beamwidth: 

vertical : 0 . 85 degree 

horizontal: 3.2 degrees 

D. Polarization: 

E. Antenna Rotation Rate: 

TRANSMITTER CHARACTERISTICS 

A. Output Tube: 

B. Frequency : 

C. Peak Power: 

D. Pulsewidth: 

E. PRF: 

RECEIVER CHARACTERISTICS 

A. System Noise Figure: 

B. Receiver Bandwidth: 

C. Minimum Discernible Signal 

(MDS): 

Normal: -106 dBm 

D. Scope Range (NM): 

*Also applicable to AN/FPS-90 

Shaped beam, fan beam in azimuth 

39 dB 

7.5 RPM, 20-30 CPM 

Magnetron (QK327A) or Coaxial Magnetron 

(VSM-1143) 

Tunable 2 . 7 to 2.9 GHHz 

5.0 MW 

2.0 microseconds 

250 to 400 PPS 

8 . 0 dB 

800 kHz 

200 nautical miles 

G-7 
TABLE G- 7 

AN/GPN-20 SYSTEM CHARACTERISTICS 

ANTENNA CHARACTERISTICS 

A. Type: 

B. Gain : 

c. Beamwidth: 

elevation: 4 . 8 degrees 

azimuth: 1. 35 degrees 

D. Polarization: 

E. Antenna Rotation Rate : 

TRANSMITTER CHARACTERISTICS 

A. Output Tube: 

B. Frequency: 

C. Peak Power: 

D. Pulsewidth: 

E. PRF: 

RECEIVER CHARACTERISTICS 

A. System Noise Figure: 

B. Receiver Bandwidth: 

Normal IF : 

MTI IF: 

Log IF: 

MTI Video: 

1. 2 MHz 

5 . 0 MHz 

1. 2 MHz 

585 kHz 

C. Minimum Discernible Signal 

(MDS): 

Normal Receiver: - 110 dBm 

Log Receiver: -1 09 dBm 

MTI Receiver: - 108 dBm 

D. Scope Range (NM): 

Shaped beam, cosecant squared in elevation 

from half power point to +30 degrees 

33.5 dB Normal beam 

32.5 dB Passive beam 

Vertical or circular (LH) 

12 or 15 RPM 

Magnetron (8798), diplex filtered 

Tunable 2.7 to 2 . 9 GHz 

500 kW 

0 . 833 microsecond 

Staggered with 1040 average (selectable 

from 849 - 1204 PPS) 

4 dB 

60 nautical miles 

G-8 
TABLE G- 8 

AN/CPN-4 SYSTEM CHARACTERISTICS 

ANTENNA CHARACTERISTICS 

A. Type : 

B. Gain: 

c. Beamwidth: 

elevation: 3.6 degrees 

azimuth: 2.2 degrees 

D. Polarization: 

E. Antenna Rotation Rate: 

TRANSMITTER CHARACTERISTICS 

A. Output Tube: 

B. Frequency: 

C. Peak Power: 

D. Pulsewidth: 

E. PRF: 

RECEIVER CliARACTERISTICS 

A. System Noise Figure: 

B. Receiver Bandwidth: 

Normal IF: 2.25 MHz 

MTI IF: 4.5 MHz 

C. Minimum Discernible Signal 

(MDS): 

Normal: -106 dBm 

MTI: -104 dBm 

D. Scope Range (NM): 

Shaped beam, cosecant squared in elevation 

from half power point to +30 degrees 

31 dB 

Horizontal or circular, remotely selectable 

20 ± 2 RPM 

Magnetron (5586) 

Tunable 2780 to 2820 MHz 

600 kW 

0.5 microsecond 

1500 PPS 

4.0 dB 

30 nautical miles 

G-9 
TABLE G- 9 

AN/MPN- 13 SYSTEM CHARACTERISTICS* 

ANTENNA CHARACTERISTICS 

A. Type: 

B. Gain: 

c. Bearnwidth: 

elevation: 3. 6 degrees 

azimuth: ' 2. 2 degrees 

D. Polarization : 

E. Antenna Rotation Rate: 

TRANSMITTER CHARACTERISTICS 

A. Output Tube : 

B. Frequency: 

C. Peak Power : 

D. Pulsewidth: 

E. PRF : 

RECEIVER CHARACTERISTICS 

A. System Noise Figure: 

B. Receiver Bandwidth : 

Normal : 

MTI: 

2.25 MHz 

4. 5 MHz 

C. Minimum Discernible Signal 

(MDS) : 

Normal: - 106 dBm 

MTI: - 104 dB, 

D. Scope Range (NM): 

Shaped beam, cosecant squared in elevation 

from half power point to +30 degrees 

32 dB 

Horizontal or circular, remotely selectable 

15 RPM 

Magnatron (8798) 

Tunable 2780 to 2820 MHz 

750 kW 

0 . 7 microsecond 

1100 PPS (3-pulse stagger on or off) 

4. 0 dB 

30 nautical miles 

*Also applicable to AN/MPN- 14 and AN/ MPN-15 

G-10 

•' 
) 

TABLE G-10 

AN-TPN-24 SYSTEM CHARACTERISTICS 

ANTENNA CHARACTERISTICS 

A. Type: 

B. Gain: 

c. Beamwidth: 

elevation: 6 degrees 

azimuth: 1.55 degrees 

D. Polarization: 

E. Antenna Rotation Rate: 

TRANSMITTER CHARACTERISTICS 

A. Output Tube: 

B. Frequency: 

C. Peak Power: 

D. Pulsewidth: 

E. PRF: 

RECEIYER CHARACTERISTICS 

A. System Noise Figure: 

B. Receiver Bandwidth: 

Normal: 1.0 MHz 

C. Minimum Discernible Signal 

(MDS) : 

Normal: -112 dBm for 

6 dB S/N 

D. Scope Range (NM): 

Shaped beam, cosecant squared in elevation 

from half power point to +30 degrees 

33 .6 dB 

Vertical or circular 

15 RPM 

Magnetron (8798), diplex filtered 

Tunable 2.7 to 2.9 GHz 

450 kW 

1 . 0 microseconds 

12 staggered (1050Hz average) 

2.5 dB 

60 nautical miles 

G-11 
APPENDIX H 

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~ , McGraw-Hill Book Co . 

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Maiuzzo, Michael A. (July, 1972) , 

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"Analysis 

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in the 2700 to 2900 MHz 

Meyer, Daniel P. and Herbert A. Mayer (1973), Radar Targek Dekeckion. 

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H-1 
Nathanson, ~red E. (1969), Radar Design Principles , McGraw-Hill Book Co. 

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A . ( 19 65 ) , J..PJ..r.l.!o.!:!bsa..!.lb~i~l.,.i-~<t..:r..Y ..... __ .AJR..s~a.AJnolold~o:HOm..___~v..liia'.!.r-"i~au.b'""l~e'""s'""._ .... a...,nL!>Id.___,sott..:.o'-"c..,h..,.a..,sutui..x.c 

McGraw-Hill Book Co. 

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Skolnik, M. I. (1970), Radar Handbook , McGraw- Hill Book Co . 

Summary Minutes ~irst OTP ~eeting on 2700-2900 MHz Spectrum Resource and 

Al location Provision, 27 October 1972. 

Summary Minutes Second OTP Meeting on 2700- 2900 MHz Spectrum Resource and 

Allocation Provision , 13 December 1972. 

Trunk, G. V. (July, 1970), "Detection Results for Scanning Radars Employing 

Feedback Integration", I£EE Transactions on Aerospace and Electronic 

Systems , Volume AES-6 No. 4 . 

Trunk, G. V. ~July, 1972), "Comparison of the Collapsing Losses in Linear and 

Square- Law Detectors", Proc. IEEE. Volume 60, No. 6, pp. 743- 744 . 

Trunk, G. V. (April, 1977) "MTI Noise Integration Loss" NRL Report 8132. 

Offi, Domenick J. (December, 1969), "Test and £valuate Dual Diversity for 

Airport Surveillance Radars (ASR)", Report No. NA-69-50 (RD- 69 - 56). 

White, D. R. J ., (1972) , "Electromagnetic Interference Handbook," Vol. 5. 

H-2 

I 

.. 

t 

. 

' I