NTIA Report TR-15-513

Effect of Broadband Radio Service 

Reallocation on 2900–3100 MHz Band 

Marine Radars: Background 

Robert Achatz

Paul McKenna 

Roger Dalke

Nicholas DeMinco 

Frank Sanders

John Carroll 

U.S. DEPARTMENT OF COMMERCE • National Telecommunications and Information Administration

report series
NTIA Report TR-15-513

Effect of Broadband Radio Service 

Reallocation on 2900–3100 MHz Band 

Marine Radars: Background 

Robert Achatz

Paul McKenna 

Roger Dalke

Nicholas DeMinco 

Frank Sanders

John Carroll 

U.S. DEPARTMENT OF COMMERCE

April 2015

DISCLAIMER

Certain commercial equipment and materials are identified in this report to specify adequately 

the technical aspects of the reported results. In no case does such identification imply 

recommendation or endorsement by the National Telecommunications and Information 

Administration, nor does it imply that the material or equipment identified is the best available 

for this purpose.

iii

CONTENTS

List of Figures............................................................................................................................... vii

List of Tables ...................................................................................................................................x

Acronyms....................................................................................................................................... xi

Executive Summary.......................................................................................................................xv

1 Introduction...................................................................................................................................1

1.1 Unwanted Emissions and Front-end Overload ......................................................................4

1.2 Report Series Organization....................................................................................................6

2 Interference Protection Criteria.....................................................................................................7

3 Scenario.........................................................................................................................................9

3.1 Physical Layout......................................................................................................................9

3.2 Weather Conditions .............................................................................................................10

3.3 Radar System.......................................................................................................................10

3.4 BRS System.........................................................................................................................11

3.5 Radar Target ........................................................................................................................12

3.6 Radio Wave Propagation Path Loss.....................................................................................14

4 Models.........................................................................................................................................15

4.1 Radar System.......................................................................................................................15

4.2 BRS System.........................................................................................................................16

4.3 Radar Target ........................................................................................................................16

4.4 Radio Wave Propagation .....................................................................................................18

4.5 Interference ..........................................................................................................................19

5 BRS Signal Modelling ................................................................................................................20

5.1 Measurement System Description .......................................................................................20

5.2 WiMAX Spectrum...............................................................................................................21

5.3 Signal Statistics Measurements ...........................................................................................22

5.3.1 Analysis Details..........................................................................................................23

5.3.2 2683.5 MHz................................................................................................................24

5.3.3 2550 MHz...................................................................................................................27

5.3.4 2750 MHz...................................................................................................................29

5.4 Discussion............................................................................................................................33

6 Aggregate BRS Signal Power.....................................................................................................34

6.1 Interference Power from a Single Base Station ...................................................................34

6.2 Effects of Narrow Radar Antenna Beam Width on Aggregate Power ................................34

6.3 Interference Power from a Set of Base Stations..................................................................37

6.4 Single Base Station and Aggregate Interference Power Statistics.......................................38

7 Radar SNR ..................................................................................................................................40

v
7.1 Definitions ...........................................................................................................................41

7.2 Baseline SNR.......................................................................................................................42

7.3 Variable SNR.......................................................................................................................43

7.3.1 Link Budget................................................................................................................43

7.3.2 SNR for the IEC 62388 Standard Test Cases.............................................................44

7.3.3 Excess Power Margin.................................................................................................46

8 Conclusion ..................................................................................................................................48

9 Acknowledgements.....................................................................................................................49

10 References.................................................................................................................................50

Appendix A : Analysis Parameters................................................................................................53

A.1 References...........................................................................................................................55

Appendix B : Propagation Models.................................................................................................57

B.1 Free Space Model................................................................................................................57

B.2 General Propagation Models...............................................................................................57

B.3 References...........................................................................................................................58

Appendix C : Irregular Terrain Model...........................................................................................59

C.1 References...........................................................................................................................60

Appendix D : Radar SNR ..............................................................................................................62

D.1 Definitions...........................................................................................................................62

D.2 Intermediate Expressions....................................................................................................63

D.3 Final Expressions................................................................................................................64

D.4 Other Considerations ..........................................................................................................65

D.5 References...........................................................................................................................65

vi
LIST OF FIGURES

Figure 1. Marine radar slotted array antenna (white bar) mounted on motor which spins it...........3

Figure 2. BRS base station...............................................................................................................3

Figure 3. Radio spectrum from 2500 to 3700 MHz with current allocations for air traffic control 

(ATC), weather, marine, and various Department of Defense (DOD) radar services. ....4

Figure 4. Simplified diagram of BRS base stations and radar equipment showing location of base 

station transmitter filter (TF) and radar front-end filter (FEF) which mitigate unwanted 

emissions and front-end overload, respectively. TX represents the BRS transmitter, TX 

ANT represents the transmit antenna, ANT represents the radar antenna, LNA 

represents the low-noise amplifier, IFF represents the intermediate frequency filter, and 

DET represents the threshold detector. ............................................................................5

Figure 5. Four possible reallocation scenarios illustrated with interfering and radar PSDs. The 

interfering PSD is centered around ffff. The radar PSD is centered around ffff. Radar IF 

and front-end bandwidths are shown with dashed lines. The scenarios are a) no 

interference, b) potential unwanted emission interference, c) potential front-end 

overload, and d) potential unwanted emission and front-end overload interference. ......5

Figure 6. Physical layout showing a network of BRS base stations contributing to the interfering 

signal power. The interference can cause the radar to not detect the target.....................9

Figure 7. Radar equipment components. The top diagram (a) shows the major radar system 

functional blocks, the middle diagram (b) shows components in the receiver block, and 

the bottom diagram (c) shows components in the signal processor block. FEF 

represents the front-end filter, LNA represents the low-noise amplifier, MXR 

represents the mixer, LO represents the local oscillator, and AMP represents the 

amplifier. ........................................................................................................................11

Figure 8. Block diagram of a BRS base station transmitter. MOD represents the baseband 

modulator, OFDMA represents the orthogonal frequency division multiple access 

operation, RF MOD represents the RF modulator, RF AMP represents the RF 

amplifier, TF represents the transmitter filter, and TX ANT represents the transmitter 

antenna. ..........................................................................................................................12

Figure 9. RCS and range for ten IEC 62388 standard clutter free test cases with pulse range 

limits. Short and long pulse ranges are separated by solid blue line at 5.6 km. Medium 

pulse ranges are between dashed red lines at 1.4 and 22.2 km. .....................................13

Figure 10. Radar system model. TX represents the transmitter source, TF represents the 

transmitter filter, ANT represents the antenna, RCS represents the radar cross section, 

FEF represents the front-end filter, GN represents Gaussian noise, IFF represents the IF 

filter, ED represents the envelope detector, INT represents the non-coherent integrator, 

and DET represents the threshold detector.....................................................................15

vii
Figure 11. BRS model. TX represents the base station transmitter source, TF represents the 

transmitter filter, and TX ANT represents the transmitter antenna................................16

Figure 12. RCS patterns of a large naval auxiliary ship measured at 2.8 GHz with a horizontally 

polarized antenna in 2 degree azimuth increments. Traces from the center to outside 

represent values of RCS that are exceeded by 80, 50 (median), and 20 percent of all 

RCS measured at that azimuth. Bow and stern are at 0 and 180 degrees azimuth, 

respectively. (Figure adapted from Figure 2.21(a) in Merrill L. Skolnik, Introduction to 

Radar Systems, New York: McGraw Hill Book Company, 1980, p. 45.) .....................17

Figure 13. Probability loss is less than ordinate over a 45 km range.............................................18

Figure 14. Probability loss is less than ordinate over a 20 km range.............................................19

Figure 15. Interference model. TX represents the transmitter, TF represents the transmitter filter, 

TX ANT represents the transmitter antenna, ANT represents the radar antenna, GN 

represents Gaussian noise, FEF represents the front-end filter, IFF represents the IF 

filter, ED represents the envelope detector, INT represents the integrator, and DET 

represents the threshold detector. ...................................................................................19

Figure 16. Measurement setup shown with VSA. BS represents the base station, UE represents 

the user equipment, DC represents the directional coupler, PS represents the 

preselector, and PC represents the personal computer...................................................21

Figure 17. PSD measurement. (Data Identifier: F6R2) .................................................................22

Figure 18. Signal at 2683.5 MHz showing TDD on- and off-times. .............................................25

Figure 19. APD at 2683.5 MHz. On- and off-times have not been differentiated.........................25

Figure 20. PSD at 2683.5 MHz. On- and off-times have not been differentiated. ........................26

Figure 21. APD at 2683.5 MHz of on- and off-time signals. ........................................................26

Figure 22. PSD at 2683.5 MHz of on- and off-time signals..........................................................27

Figure 23. Signal at 2550 MHz showing TDD on- and off-times. ................................................28

Figure 24.APD at 2550 MHz for on- and off-times.......................................................................28

Figure 25.PSD at 2550 MHz for on- and off-times. ......................................................................29

Figure 26. Signal at 2750 MHz showing TDD on- and off-times. ................................................30

Figure 27. APD at 2750 MHz for on- and off-times......................................................................30

Figure 28. PSD at 2750 MHz for on- and off-times. .....................................................................31

Figure 29. 2741 MHz, 1 MHz bandwidth signal derived from 2750 MHz measurement.............31

Figure 30. 2741 MHz, 1 MHz bandwidth APD derived from 2750 MHz measurement. .............32

viii
Figure 31. 2741 MHz, 1 MHz bandwidth PSD derived from 2750 MHz measurement. ..............32

Figure 32. BRS coverage area composed of tessellated hexagons. Base stations are located at 

dots at center of hexagons. Ships are located at points PP1 and PP2. ...............................35

Figure 33. Relevant hexagon parameters.......................................................................................35

Figure 34. Chord length calculation parameters. Base stations are located at points labeled bs...35

Figure 35. Interference scenario after taking into account narrow azimuthal beam width of the 

marine radar antenna. The base stations in the shaded area will provide the most 

interfering signal power. ................................................................................................37

Figure 36. Probability I is less than ordinate. Aggregate (solid lines) versus single base station 

(dashed lines)..................................................................................................................39

Figure 37. Short radar to target ranges as in (a) and (b) are analyzed with a constant SNR while 

long radar to target ranges as in (c) are analyzed with a variable SNR. ........................41

Figure 38. SNR distributions using the ITM for 10 IEC 62388 standard clutter free test cases. ..45

Figure 39. SNR distributions for 10 IEC 62388 standard clutter free test cases with excess power 

margin removed. There are 3 fewer curves visible because cases 2 and 5, 6 and 7, and 8 

and 9 have similar target parameters..............................................................................47

Figure D-1. Radar PPPP with Swerling 1 target, non-coherent integration of 6 and 14 pulses, and 

10-4 PP PP. ........................................................................................................................65

ix
LIST OF TABLES

Table 1. IEC 62388 standard clutter free test cases.......................................................................13

Table 2. Radar losses. ....................................................................................................................16

Table 3. Measurement system parameters. The measurement center frequency ffffff ff varies. 

The BRS center frequency, ffffffff, is 2683.5 MHz. ........................................................23

Table 4. Measurements’ resemblance to Gaussian noise (GN) and white Gaussian noise (WGN).33

Table 5. Baseline ideal SNR and SNR at receiver input for a 1.9 degree beam-width antenna at 

baseline performance 0.8 PP and 10 − 4 PP . PW is pulse width, PRF is pulse 

repetition frequency, BW is IF filter bandwidth, RR is rotation rate, and nnnn is the 

number of pulses integrated. ..........................................................................................42

Table 6. IEC 62388 standard clutter free test case SNR in free space channel. Shaded cells 

indicate pulse meets target range requirement. ..............................................................44

Table 7. IEC 62388 standard clutter free test case SNR quantiles using the ITM. .......................45

Table 8. IEC 62388 standard clutter free test case power margins................................................46

Table 9. Reduced mean RCS for IEC 62388 standard test cases...................................................47

Table A-1. Physical parameters. ....................................................................................................53

Table A-2. IEC 62388 standard clutter free test target physical parameters.................................53

Table A-3. IEC 62388 standard clutter free test radar parameters not related to pulse width.......53

Table A-4. IEC 62388 standard clutter free test pulse width and related parameters ...................54

Table A-5. BRS macro base station parameters for 10 MHz bandwidth signal............................54

Table A-6. BRS macro base station effective radiated power. ......................................................55

Table A-7. ITM parameters. Base station is the transmitter and radar is the receiver...................55

Table B-1. General propagation models. P2P is point-to-point mode and P2A is point-to-area 

mode. ..............................................................................................................................58

x
ACRONYMS

3GPP 3rd Generation Partnership Project

APD Amplitude probability distribution

AWGN Additive white Gaussian noise

BPF Bandpass filter

BRS Broadband radio service

BS Base station

BW Bandwidth

CFAR Constant false alarm rate

CW Continuous wave

dB Decibel

dBi Decibels relative to the gain of an isotropic antenna

dBm Decibels relative to a milliwatt

dBsm Decibels relative to a square meter

dBW Decibels relative to a watt

DOD Department of Defense

EIRP Effective isotropic radiated power

ETSI European Telecommunications Standards Institute

FDD Frequency division duplex

FDR Frequency dependent rejection

FE Front-end

FEF Front-end filter

FS Free space

GHz Gigahertz

GN Gaussian noise

Hz Hertz

IEC International Electrotechnical Committee

xi
IEEE Institute of Electrical and Electronics Engineers

IF Intermediate frequency

INR Interference to noise power ratio

IPC Interference protection criteria

ITM Irregular terrain model

ITS Institute for Telecommunication Sciences

ITU International Telecommunication Union

ITU-R ITU Radiocommunication Sector

km Kilometer

kHz kilohertz

LNA Low-noise amplifier

LNFE Low-noise front-end

LTE Long Term Evolution

MHz Megahertz

MIMO Multiple-input multiple-output

MSC Maritime Safety Committee

nmi Nautical mile

ns Nanosecond

NTIA National Telecommunications and Information Administration

OFDM Orthogonal frequency division multiplexing

OFDMA Orthogonal frequency division multiple access

OOB Out-of-band

PAM Pulse amplitude modulation

PRF Pulse repetition frequency

PRI Pulse repetition interval

PSD Power spectral density

PSK Phase shift keyed

xii
QAM Quadrature modulation

RCS Radar cross section

RF Radio frequency

RPM Revolutions per minute

SA Spectrum analyzer

SINR Signal to interference plus noise ratio

SNR Signal to noise ratio

SOLAS Safety of life at sea

STC Sensitivity time control

TDD Time division duplex

UMTS Universal Mobile Telecommunications System

UN United Nations

UN/MSC United Nations Maritime Safety Committee

USCG United States Coast Guard

VSA Vector signal analyzer

WGN White Gaussian noise

WiMAX Worldwide interoperability for microwave access

xiii

EXECUTIVE SUMMARY

Spectrum reallocation is often necessary to accommodate new services which can potentially 

increase business productivity and enhance the lives of private citizens. However, reallocating 

services to bands near those used by incumbent services—or, in some cases, to those same 

bands—can cause interference to the incumbent service.

Spectrum reallocation can cause interference in radar systems in a number of ways. A system 

reallocated to a nearby band can introduce unwanted signals into the radar detection bandwidth. 

Also, a system reallocated to a nearby band can overload the radar receiver front-end and cause 

gain compression, increased noise power, and intermodulation in the radar detection bandwidth. 

The U.S. Coast Guard (USCG) asked the National Telecommunications and Information 

Administration Institute for Telecommunication Sciences (NTIA/ITS) to investigate effects of 

reallocation on the 2900–3100 MHz band marine radar service by determining interference 

protection criteria (IPC) and analyzing strategies for mitigating the interference.

Here we investigate the effects of reallocation to accommodate the broadband radio services 

(BRS) on the 2900–3100 MHz band marine radar service. The BRS is the next generation of 

personal communications services which will provide wideband Internet communications to 

mobile users. Results of our investigations have been assembled into three reports subtitled 

“Background,” “Unwanted Emissions,” and “Front-end Overload.”

This report provides background information needed to analyze effects of BRS reallocation on 

2900–3100 MHz band marine radars. Key topics covered are interference protection criteria 

(IPC), interference scenario, and the various system and propagation models.

Comprehensive IPC include performance levels, powers, and reliabilities for baseline 

(interference-free) and allowable degraded conditions. Reliability in this context is determined 

solely by radio wave propagation path loss variability caused by terrain and atmospheric 

conditions and is independent of electrical or mechanical malfunction.

The interference scenario consists of a maritime radar target such as a boat or buoy between a 

network of base stations and a ship with a maritime radar. Magnetron radar and radar target 

models are derived from the IEC 62388 standard for shipborne radars. BRS system models are 

derived from WiMAX and LTE standards. Radio wave propagation is modelled with the ITS 

Irregular Terrain Model (ITM) because of its ability to model path loss variability.

A BRS base station signal was measured and statistically characterized. The signal statistics were 

found to be nearly Gaussian in the necessary bandwidth and Gaussian in the spurious domain. 

Statistics in the necessary bandwidth are considered nearly Gaussian because of a slight drop in 

peak signal levels. The roll-off or out-of-band (OOB) regions between the necessary bandwidth 

and spurious regions were not measured due to measurement system dynamic range 

considerations. Pending future measurements, we are assuming OOB emissions are Gaussian as 

well. Consequently, it is reasonable to model the BRS signal as Gaussian noise. This finding 

greatly simplifies analysis of interference in marine radars from base station unwanted 

emissions.

xv
Statistical characterization was done on measurements in a wide bandwidth. However, since the 

statistics are Gaussian they should also be Gaussian when the BRS signal is filtered to a narrower 

bandwidth and when any number of BRS signals are added to represent the signal from an 

aggregate of base stations. 

A method for computing aggregate interference power distributions using the radio wave 

propagation model and Monte Carlo analysis was developed. These distributions are essential for 

analyzing radar link reliability. Because of the radar antenna’s narrow azimuthal beam width, 

maximum aggregate interference power was found to come from base stations along a line 

formed by the most closely repetitively-spaced base stations. The aggregate interference power 

was found to be as much as 6 dB greater than the power from a single base station. Hence it is 

important that interference analysis be done with an aggregate of base stations.

Although interference path loss variability is usually included in interference analysis, desired 

path loss variability often is not. In the maritime radar case the desired path is the radar to target 

path. In devising a method for including radar to target path loss variability into our analysis we 

found excess signal to noise ratio (SNR) in the radar to target link budgets used for industry 

acceptance tests. Although this excess SNR could potentially mitigate interference, we found that 

it is needed to accommodate reductions in target mean radar cross section (RCS) due to changes 

in target aspect, shape, and construction materials. Consequently we recommend removing the 

excess SNR by reducing mean RCS prior to interference analysis.

xvi
EFFECT OF BROADBAND RADIO SERVICE REALLOCATION ON 2900–3100 MHZ 

BAND MARINE RADARS: BACKGROUND

Robert Achatz, Paul McKenna, Roger Dalke, Nicholas DeMinco, Frank Sanders, John Carroll1

Spectrum reallocations may place broadband radio services (BRS) near spectrum 

used by 2900–3100 MHz band marine radars. Interference effects from these 

reallocations include unwanted emissions in the radar detection bandwidth and 

front-end overload. This report provides background information for subsequent 

reports that analyze these effects. Interference protection criteria (IPC) are 

identified, an interference scenario is described, and models for the radar system, 

BRS system, radar target, and radio wave propagation are presented. The BRS 

signal is shown to be reasonably emulated by Gaussian noise. A method for 

determining the aggregate power distribution using a realistic propagation model 

and Monte Carlo analysis is described. The aggregate power from the base 

stations was found to be as much as 6 dB more than power from a single base 

station. Finally a method for incorporating a variable SNR, caused by variable 

radar to target path loss, into interference analysis is shown.

Keywords: aggregate power, broadband radio service, front-end overload, interference, 

interference protection criteria, marine radar, radar, radio spectrum engineering, 

radio wave propagation, signal characterization, unwanted emissions

1 INTRODUCTION

Spectrum reallocation is often necessary to accommodate new services which can potentially 

increase business productivity and enhance the lives of private citizens. However, reallocating 

services to bands near those used by incumbent services—or, in some cases, to those same 

bands—can cause interference to the incumbent service.

Spectrum reallocation can cause interference in radar systems in a number of ways [1], [2], [3], 

[4]. For example, a system moved to a nearby band can introduce unwanted emissions into the 

radar detection bandwidth. Also, emissions from a system reallocated to a nearby band can 

overload the radar receiver front-end (receiver circuits operating at the carrier frequency) and 

cause gain compression, increased noise power, and intermodulation in the radar detection 

bandwidth.

The U.S. Coast Guard (USCG) asked the National Telecommunications and Information 

Administration Institute for Telecommunication Sciences (NTIA/ITS) to investigate effects of 

1

The authors are with the Institute for Telecommunication Sciences, National Telecommunications and Information 

Administration, U.S. Department of Commerce, Boulder, CO 80305.

 
spectrum reallocation on the 2900–3100 MHz band marine radar service by determining

interference protection criteria (IPC) and analyzing strategies for mitigating the interference.

Results of these investigations are expected to be useful to regulatory and standards bodies which 

are responsible for developing IPC including the NTIA [5]; the International Telecommunication 

Union (ITU) [6]; the International Electrotechnical Commission (IEC) [7], which is currently 

devising IPC tests on behalf of the United Nations Maritime Safety Committee (UN/MSC) [8];

and the Institute of Electrical and Electronics Engineers (IEEE) [9].

In this series of reports we analyze the effects of reallocation to accommodate broadband radio 

services (BRS) on the 2900–3100 MHz band marine radar service. The BRS is the next 

generation of personal communications services which will provide wideband Internet 

communications to mobile users. Spectrum regulators are currently investigating various 

reallocation strategies to accommodate BRS growth.

Marine radars are used by ships to avoid collisions with objects while traveling in oceans, seas, 

lakes, and rivers. An example of a marine radar antenna mounted on a ship is shown in Figure 1. 

Detection of objects, referred to as targets, is often difficult. Even on calm seas, the target can 

have significant radar cross section (RCS) variation and corresponding reductions in signal 

power. The target can also be obscured by signal reflections or clutter from waves and 

precipitation.

These 2900–3100 MHz band radars are often referred to as S-band marine radars. Similar radars 

that operate in the 9200–9500 MHz band are often referred to as X-band marine radars. The 

primary advantage of S-band radar signals is that they have less precipitation attenuation than Xband radar signals. This allows S-band radars to detect smaller objects at longer distances in 

adverse weather conditions. Large ships subject to international safety of life at sea (SOLAS) 

regulations generally operate with radars in both bands.

BRS providers promise to deliver fast, reliable Internet service to users wherever they are. An 

example of a BRS base station is shown in Figure 2. Potential unwanted emissions and front-end 

overload problems in S-band marine radars from BRS base stations were brought to the attention 

of the International Telecommunication Union in November 2009 by the United Kingdom [10]. 

Significant amounts of spectrum are needed for widespread BRS use. BRS systems are already 

operating in the 2500–2690 MHz band. The 3500–3650 MHz band has been evaluated for 

reallocation [11]. Other reallocations in the 2700–3700 band, currently allocated to a number of 

radar services as shown in Figure 3, could also affect 2900–3100 MHz band marine radars.

BRS and radar system characteristics are derived from those used by internationally recognized 

groups. The BRS system is modeled after systems devised by the European Technical Standards 

Institute (ETSI) Universal Mobile Telecommunications System (UMTS) committee/3rd

Generation Partnership Project (3GPP) [12], ITU [13], and the WiMAX Forum [14]. The radar 

system is modeled after a system devised by the IEC 62388 standard shipborne radar committee

[7] for industry acceptance testing.

2
Figure 1. Marine radar slotted array antenna (white bar) mounted on motor which spins it.

Figure 2. BRS base station.

3
Figure 3. Radio spectrum from 2500 to 3700 MHz with current allocations for air traffic control 

(ATC), weather, marine, and various Department of Defense (DOD) radar services.

1.1 Unwanted Emissions and Front-end Overload

Figure 4 is a general diagram of the interference scenario. On the left is a network of base 

stations emitting signals in the direction of the marine radar. The marine radar receives these 

signals along with its own signal returning from the target. Key components in analyzing the 

interference include the base station transmitter filter, the radar receiver front-end filter and lownoise amplifier, and the radar signal processor detection filter often referred to as the 

intermediate frequency (IF) filter.

Figure 5 illustrates four possible outcomes of spectrum reallocation with regard to unwanted 

emissions and front-end overload. A generic interfering signal power spectral density (PSD), 

centered at ffii, is depicted by the shaded area. The unwanted emissions are represented as the 

sloped section of the PSD. The radar receiver front-end and signal processor IF bandwidths are 

depicted with dashed lines. The radar received signal PSD, centered at ffrr, is shown for reference 

purposes.

In Figure 5(a) the radar receiver is free of interference because the interfering PSD does not 

introduce unwanted emissions into the radar detection IF bandwidth and the radar front-end 

bandwidth excludes most of the interfering signal power. In Figure 5(b) the radar receiver has 

potential interference from unwanted emissions in the radar detection IF bandwidth. In Figure 

5(c) the radar receiver has potential interference from the interfering signal in the radar front-end 

bandwidth. Finally, Figure 5(d) has both interference potentials.

There are a number of ways the interference can be mitigated. Both unwanted emissions and 

front-end overload can be mitigated by decreasing transmitted power, increasing the distance 

separation between the base stations and the radar locations, and increasing the frequency 

separation between the base station and radar center frequencies. Interference from the unwanted 

emissions can be controlled with the base station transmitter filter. Front-end overload can be 

prevented with the radar front-end filter.

4
Figure 4. Simplified diagram of BRS base stations and radar equipment showing location of base 

station transmitter filter (TF) and radar front-end filter (FEF) which mitigate unwanted emissions 

and front-end overload, respectively. TX represents the BRS transmitter, TX ANT represents the 

transmit antenna, ANT represents the radar antenna, LNA represents the low-noise amplifier, 

IFF represents the intermediate frequency filter, and DET represents the threshold detector.

Figure 5. Four possible reallocation scenarios illustrated with interfering and radar PSDs. The 

interfering PSD is centered around ffii. The radar PSD is centered around ffrr. Radar IF and frontend bandwidths are shown with dashed lines. The scenarios are a) no interference, b) potential 

unwanted emission interference, c) potential front-end overload, and d) potential unwanted 

emission and front-end overload interference.

5
1.2 Report Series Organization

Results of our investigations have been assembled into three reports subtitled Background, 

Unwanted Emissions, and Front-end Overload. This Background report identifies IPC, defines

the scenario where interference will be evaluated, and distills the scenario into models for 

analysis. In addition, three fundamental modeling issues are examined. First, BRS signal 

statistics are tested to see if the BRS signal can be emulated with a more analytically tractable 

Gaussian noise process. Second, aggregate power from all base stations in the network is

calculated to determine if it is necessary to use the aggregate power as an interference source.

Third, we develop a method for incorporating variable radar SNR caused by dynamic

atmospheric conditions into our analysis so that we can include scenarios with long radar to 

target ranges.

The Unwanted Emissions report determines relevant IPC and the distance and frequency 

separations needed to mitigate interference. Distance separation is analyzed with constant and 

variable SNRs corresponding to short and long radar to target ranges, respectively. Results are 

compared to determine worst case conditions. Frequency separation is analyzed using frequency 

dependent rejection (FDR) which takes the transmitted PSD and the radar receiver IF filters 

frequency responses into account. We also show how interference can be mitigated by the 

combination of distance and frequency separation.

The Front-end Overload report determines relevant IPC, front-end filter attenuation, and 

separation distances needed to prevent overload. IPC are determined from probability of 

detection measurements with a custom test fixture. Results are compared to commonly used 

overload metrics such as receiver front-end gain compression which are easier to execute than 

probability of detection measurements.

6
2 INTERFERENCE PROTECTION CRITERIA

Marine radars are used to avoid collisions with other objects in the water such as boats or 

underwater objects marked by buoys. Radar receiver noise and signal reflections or clutter from 

the sea or precipitation can obscure these objects and thereby contribute to collisions. Engineers 

design radar systems so that the probability of a collision is reasonably low without placing 

undue burden on the cost of the radar. Interfering signals can also obscure objects. IPC are 

needed to keep the probability of collision low while not placing onerous burdens on other 

systems using the radio spectrum.

IPC are based on measurable performance parameters. Radar manufacturers quantify 

performance with four principal parameters, i.e., RCS, range, probability of detection (PPdd), and 

probability of false alarm (PPffff). As an example [7], a 2900–3100 MHz band marine radar must 

be able to detect a small boat with a 1.4 m2 RCS at a range of 5.6 km (3.0 nmi) with a 0.8 PPdd and 

10-4 PPffff.

We have chosen to quantify performance with PPdd at a specific PPffff while controlling RCS and 

range with signal to noise ratio (SNR) so the method can be implemented in the laboratory via 

conducted measurements. With this approach there are six IPC:

• Baseline performance level:

The desired probability of detection, PPdd,bb, and probability of false alarm, PPffff,bb, in the 

absence of the interfering signal.

• Baseline signal and noise power:

Signal and noise power required to meet baseline performance level.

• Baseline reliability:

The probability, PP �PPdd > PPdd,bb�, that PPdd will exceed PPdd,bb at a specified percentage of 

locations and times. This reliability depends on propagation path loss variability caused by 

terrain and atmospheric conditions and is independent of electrical or mechanical 

malfunction.

• Allowable degraded performance level:

The probability of detection, PPdd, , and probability of false alarm, PPffff, , corresponding to the 

degraded performance allowable in the presence of the interfering signal. To minimize 

variables, PPffff, is assumed to be the same as PPffff,bb. The corresponding allowable degraded 

performance percentage is a relative measure of degradation.

allowable degraded performance percentage = �

PPdd,bb− PPdd,aa

PPdd,bb

� ∙ 100 % (1)

• Allowable interference power level:

The interference power that degrades radar performance from baseline to allowable 

degraded. The power is dependent on the interfering signal characteristics. As an example the 

7
allowable degraded power level of a Gaussian distributed interfering signal is expected to 

differ from that of a continuous-wave (CW) interfering signal.

• Allowable reliability:

The probability, PP �PPdd > PPdd, �, that PPdd will exceed PPdd, at a specified percentage of 

locations and times. This reliability depends on propagation path loss variability caused by 

terrain and atmospheric conditions and is independent of electrical or mechanical 

malfunction.

8
3 SCENARIO

3.1 Physical Layout

The physical layout of the radar, target, and base stations are shown in Figure 6. The radar is 

mounted on a ship and the target the radar is to detect is between the ship and the closest base 

station. Other base stations are located behind and to the side of the closest base station. The 

potential for interference in this scenario is enhanced in two ways. First, BRS base station 

antenna heights can be tall enough to transmit signals over considerable line-of-sight distances. 

Second, the radar can receive signals from more than one or an aggregate of base stations.

Figure 6. Physical layout showing a network of BRS base stations contributing to the interfering 

signal power. The interference can cause the radar to not detect the target.

9
3.2 Weather Conditions

Marine radars operate in all weather conditions. Signals reflected from the waves, rain, and snow 

present in adverse conditions create clutter that obscures signals returned from the target. The 

IEC 62388 standard has tests with [15] and without clutter [16]. Rain clutter tests are identical to 

tests without rain clutter except that range requirements are reduced. Sea clutter tests are 

performed with an additional short range test that reduces probability of detection requirements 

as wave height increases.

3.3 Radar System

The radar system is assumed to be a conventional magnetron radar modeled after the radar used 

in the IEC 62388 standard [17], [18]. The block diagram of the radar in Figure 7(a) shows that it 

is comprised of a rotating antenna, rotary joint, transmission line, circulator, transmitter, receiver, 

signal processor, data processor, and display.

The radar antenna is horizontally polarized. It has a narrow azimuthal beam width, necessary for 

discriminating against targets that are close in bearing. It also has a wide elevation beam width 

so that the radar can detect near and far targets and accommodate ship rocking.

Installation is assumed to be down-mast, i.e., the antenna and rotary joint are installed in a 

radome at a high, unobstructed location such as the top of a mast and the electronics are installed 

at a lower location such as the bottom of the mast. A transmission line carries signals between 

the antenna and the circulator. The circulator directs signals from the transmitter to the antenna 

and from the antenna to the receiver while isolating the receiver from the strong transmitted 

signals.

The radar signal is created by modulating the output of a magnetron oscillator with a train of 

periodic rectangular pulses. Typically short, medium, and long pulse widths are available. Pulse 

widths and corresponding pulse repetition frequencies used depend on a number of factors 

including target range, target resolution, and clutter conditions.

The purpose of the receiver is to convert the received signal to the intermediate frequency (IF).

As shown in Figure 7(b), the receiver contains the limiter, front-end filter (FEF), low-noise frontend (LNFE), filter, and amplifier. The LNFE has a low-noise amplifier (LNA) and frequency 

down-conversion mixer. The circulator is not ideal and passes a portion of the transmitted 

signal’s power to the receiver. The limiter prevents the LNFE from being damaged by the 

transmitted signal. The FEF protects the LNFE from overload. The LNFE amplifies the received 

signal and multiplies it by the local oscillator continuous wave (CW) signal which shifts it to the 

IF. The filter and amplifier after the LNFE represent initial stages of IF filtering and 

amplification.

The signal processor extracts target range from the IF signal. Details of the signal processor 

block are shown in Figure 7(c). It consists of a detection or final IF filter which we refer to more 

generally as the IF filter, envelope detector, non-coherent integrator, and threshold detector. The

signal processor filters and then integrates the pulses to increase SNR. In magnetron radars, the 

IF filter is not always matched to the transmitted pulse shape. For a rectangular pulse this means 

10
that the IF filter equivalent noise bandwidth is not always the reciprocal of the transmitted pulse 

width.

Detection is accomplished by comparing the integrated pulse envelope to a threshold determined 

by the PPffff and the constant false alarm rate (CFAR) function. The data processor uses range data 

provided by the signal processor for tasks such as target tracking.

Figure 7. Radar equipment components. The top diagram (a) shows the major radar system 

functional blocks, the middle diagram (b) shows components in the receiver block, and the 

bottom diagram (c) shows components in the signal processor block. FEF represents the frontend filter, LNA represents the low-noise amplifier, MXR represents the mixer, LO represents the 

local oscillator, and AMP represents the amplifier.

3.4 BRS System

The BRS system is modeled after those described in the ETSI UMTS [12], 3GPP, ITU [13], and 

WiMAX Forum [14] standards. The base stations within the system work cooperatively as a 

cellular network. In this work we are only concerned about the BRS base station transmitter 

whose simplified block diagram is shown in Figure 8.

In the block diagram, the baseband modulator block converts bits to either phase shift keyed 

(PSK) or quadrature amplitude modulated (QAM) symbols [19]. The orthogonal frequency 

division multiple access (OFDMA) block serializes the modulated symbols, performs an inverse 

11
Fourier transform operation, adds a cyclic prefix, and applies a window that shapes the spectrum. 

OFDMA is a multi-user implementation of orthogonal frequency division multiplexing 

(OFDM).The RF modulator and amplifier blocks convert the signal to a higher frequency and 

power, respectively, for transmission. The transmitter filter block reduces unwanted emissions 

prior to transmission out of the antenna.

The base station antennas are typically mounted on a tower or building high above ground level. 

The base station antenna azimuth beam width divides the coverage areas into wedge shaped 

sectors. The elevation beam width is narrow and can be tilted down to decrease interference in 

other base stations. The signal is transmitted with 45 ̊ slant-angle cross polarization. Multiple 

antennas within each sector are used to transmit independent data streams for multiple-input 

multiple-output (MIMO) signal processing to enhance performance. 

The frequency allocation or channel that accommodates the signal is defined by its center 

frequency and bandwidth; the bandwidth ranges from 1.25 to 20 MHz. BRS channels are reused 

by multiple base station sectors to boost spectrum efficiency The same BRS channel can be 

reused by all base stations and sectors. Under some circumstances, all channels can be used by 

the same sector [20].

The signal’s temporal characteristics are dependent, amongst other factors, on how the system 

duplexes received and transmitted signals. If it uses time division duplexing (TDD), the channel 

is alternately used by the base station and the mobile. If it uses frequency division duplexing

(FDD), the channel is exclusively used by the base station.

Figure 8. Block diagram of a BRS base station transmitter. MOD represents the baseband 

modulator, OFDMA represents the orthogonal frequency division multiple access operation, RF 

MOD represents the RF modulator, RF AMP represents the RF amplifier, TF represents the 

transmitter filter, and TX ANT represents the transmitter antenna.

3.5 Radar Target

We use the targets in the IEC 62388 standard clutter free tests [16],[21]when it is necessary to 

know all the target’s characteristics such as range, height above water, and RCS. The set of 

targets is diverse in that it includes distributed targets such as shorelines, complex targets such as 

ships and boats, and point targets such as channel markers and buoys.

A summary of target parameters is provided in Table 1. The incongruity between the descriptive 

shoreline height and the height used in calculations is assumed to be due to terrain irregularity.

Figure 9 displays the targets with respect to their RCS and range. Range limits for each pulse 

12
width based on manufacturer literature are also shown. The short pulse is limited to ranges up to 

5.6 km (3 nmi) and the long pulse from 5.6 to 44.4 km (3 to 24 nmi). The medium pulse range 

from 1.4 to 22.2 km (0.75 to 12 nmi) overlaps short and long pulse ranges.

Table 1. IEC 62388 standard clutter free test cases.

Case Target

Height 

(m)

Range RCS 

(m2 nmi km )

1 60m high shoreline 50.0 20.0 37.0 50000.0

2 6 m high shoreline 5.0 8.0 14.8 5000.0

3 3 m high shoreline 2.5 6.0 11.1 2500.0

4 SOLAS ship > 5000gt 10.0 11.0 20.4 30000.0

5 SOLAS ship > 500gt 5.0 8.0 14.8 1000.0

6 Small boat with reflector 4.0 3.7 6.8 0.5

7 Buoy with reflector 3.5 3.6 6.7 1.0

8 Buoy 3.5 3.0 5.6 0.5

9 Small 10 m long boat 2.0 3.0 5.6 1.4

10 Channel marker 1.0 1.0 1.9 0.1

Figure 9. RCS and range for ten IEC 62388 standard clutter free test cases with pulse range 

limits. Short and long pulse ranges are separated by solid blue line at 5.6 km. Medium pulse 

ranges are between dashed red lines at 1.4 and 22.2 km.

13
3.6 Radio Wave Propagation Path Loss

Generally speaking, propagation path loss varies with location and time. Path loss varies over 

location because of differences in terrain and over time because of changes in atmospheric 

conditions such as rain, fog, or snow. However, in the maritime environment, terrain irregularity

is minimal. Consequently, most variability is due to atmospheric conditions which change from 

hour to hour.

Path loss variability increases with path length. Short paths have lower and more constant path 

loss. Signals transmitted across short paths have higher powers and less power variability. 

Longer paths have higher and more variable path loss. Signals transmitted across long paths have 

lower powers and more variability.

In some cases atmospheric conditions can trap radio waves in atmospheric layers which create 

propagation ducts. Propagation ducts can decrease propagation path loss considerably as 

compared to free space. In the U.S., propagation ducts occur less than 10% of the time. The 

higher percentages occur in the south where there is significant variation from season to season

[22].

14
4 MODELS

In this section we describe the various models used for interference analysis. Specific model 

parameter values are provided in Appendix A.

4.1 Radar System

The radar system model and its associated parameters are shown in Figure 10. The radar transmit

power is tttt. The impulse response of the radar transmitter filter is htt(tt). The radar signal is 

modeled as a continuous wave modulated by a periodic, rectangular pulse. The pulse width, 

pulse repetition interval (PRI), and pulse repetition frequency (PRF) are ττ, TT, and ffpp, 

respectively.

The transmitter and receiver share the same antenna whose gain is gg. The propagation path loss

from the radar to the target and from the target to the radar is llpp. Consequently the total path loss 

is llpp

2. The target RCS is σσ.

The Gaussian noise block represents the composite receiver noise factor, ffrr . The receiver frontend gain and impulse responses are ggffffand hffff(tt), respectively. The IF gain and impulse 

response are ggii and hii (tt), respectively.

Figure 10. Radar system model. TX represents the transmitter source, TF represents the 

transmitter filter, ANT represents the antenna, RCS represents the radar cross section, FEF 

represents the front-end filter, GN represents Gaussian noise, IFF represents the IF filter, ED 

represents the envelope detector, INT represents the non-coherent integrator, and DET represents 

the threshold detector.

A number of losses, shown in Table 2, are common in these types of radars. The radome, which 

protects the antenna from weather, attenuates the radio wave during transmission and reception. 

The rotary joint, transmission line, and circulator introduce circuit losses. Integration beam shape 

loss is caused by the rotating antenna modulating pulse amplitude within the pulse integration 

period.

Finally, there are a number of losses associated with signal processing such as the IF filter not 

being matched to the transmitted pulse shape, the digitizer missing the highest signal, and the 

CFAR function misestimating the detection threshold.

15
Table 2. Radar losses.

Loss Parameter Equation Notes

Transmitter circuit llcc Circulator, transmission line, and rotary joint

Receiver circuit llcc Rotary joint, transmission line, and circulator

Radome ll Transmission and reception

Integration beam shape ll Transmission and reception

Signal processing ll

System ll llcc llcc ll ll ll

Radar signal processors integrate pulses to enhance SNR. The number of pulses integrated within 

the time the rotating antenna beam is pointed at the target is determined from 

nnpp = θθffpp

6ωωrr

(2)

where θθ is the antenna 3 dB azimuth beam width in degrees, ffpp is the PRF in Hz, and ωωrr is the 

antenna rotation rate in revolutions per minute (RPM), assuming the antenna rotates completely 

around.

4.2 BRS System

The BRS system model, shown in Figure 11, is composed of the base station transmitter, circuit 

loss, transmitter filter, and antenna blocks. The transmitter contains the modulator, OFDMA 

block, RF modulator, and RF amplifier described previously. The transmitter filter decreases the 

unwanted emissions power. The power at the output of the transmitter source is ̂

tttt, the circuit 

loss from the transmitter block to the antenna is ll

̂

cc , and the transmit antenna gain is gg�tt.

Figure 11. BRS model. TX represents the base station transmitter source, TF represents the 

transmitter filter, and TX ANT represents the transmitter antenna.

4.3 Radar Target

Radar targets are characterized by their RCS. In our analysis we assume that scattering off the 

target causes RCS fluctuations about a mean and the mean is dependent on target aspect angle, 

shape, and material. Aspect angle is the angle between the target longitudinal axis and the radar 

beam axis. The fluctuations are characterized by the exponential distribution probability density 

function

16
(σσ) = 1

σσ aa

ee �− σσ

σσ aa

� (3)

where σσ is the radar cross section and σσ aa is the average or mean radar cross section. The 

exponential distribution is identical to that used in the Swerling 1 RCS model [23]. As in the 

Swerling 1 RCS model, fluctuations are assumed to be constant during the pulse integration 

period.

This model is inspired by ship RCS measurements [24] performed at 2.8 GHz with a horizontally 

polarized antenna in 2 degree azimuth increments. The RCS exceeded by 80, 50 (median), and 

20 percent of all RCS measured at each azimuth are shown in Figure 12. Differences between the 

20th and 80th percentiles are independent of aspect. However, the 50 percentile or median varies

significantly. For example the median RCS is as high as 65 dBsm near 270 degrees aspect and as

low as 40 dBsm near 0 degrees for a total 25 dB variation. Another study [25] found ship median

RCS to vary on the order of 15 dB as the aspect changed from bow to broadside. Assuming the 

RCS is exponentially distributed, the median is approximately ln 2, 0.69, or -1.6 dB of the mean.

Figure 12. RCS patterns of a large naval auxiliary ship measured at 2.8 GHz with a horizontally 

polarized antenna in 2 degree azimuth increments. Traces from the center to outside represent 

values of RCS that are exceeded by 80, 50 (median), and 20 percent of all RCS measured at that 

azimuth. Bow and stern are at 0 and 180 degrees azimuth, respectively. (Figure adapted from 

Figure 2.21(a) in Merrill L. Skolnik, Introduction to Radar Systems, New York: McGraw Hill 

Book Company, 1980, p. 45.)

17
4.4 Radio Wave Propagation

The radar link, BRS link, and interference link between the two systems have radio wave 

propagation path loss which can vary with location and time. Characteristics of a number of 

propagation path loss models are discussed in Appendix B. The ITS Irregular Terrain Model 

(ITM) is used because our work needs both signal fading and enhancement statistics. Details 

regarding how ITM generates these statistics are provided in Appendix C. 

Figures 13 and 14 show ITM hourly path loss statistics for the interfering signal path when the

BRS antenna height is 30 meters, the ship radar height is 15 meters, and there is no precipitation. 

The results do not go below the model’s 1 km minimum distance.

Path loss variability is evident from the spread of probabilities at a distance. The figures show

that there is little path loss variability below 5 km. Path loss variability increases above 5 km and 

increases even more above 29 km, well before the 38 km smooth earth radio horizon where 

diffraction effects dominate.

The same scenario was evaluated for propagation over land. Because of the relatively low 

antenna heights compared to the separation distance and corresponding low grazing angle, overland results were essentially the same as over-sea. Consequently, results over sea can be 

extended to mixed land sea paths where a portion of the path is over land.

Figure 13. Probability loss is less than ordinate over a 45 km range.

18
Figure 14. Probability loss is less than ordinate over a 20 km range.

4.5 Interference

The overall interference model is a combination of the radar, BRS, target, and radio wave 

propagation models as shown in Figure 15. The summation of multiple BRS signals represents

the aggregate effect where the radar receives power from more than one base station. The 

significance of this effect is discussed in Section 6 .Two new parameters are introduced in this 

diagram. They are the propagation loss from the base station to the radar, ll

̃

pp, and the antenna 

polarization loss between the base station and radar antennas, llpppppp.

Figure 15. Interference model. TX represents the transmitter, TF represents the transmitter filter, 

TX ANT represents the transmitter antenna, ANT represents the radar antenna, GN represents 

Gaussian noise, FEF represents the front-end filter, IFF represents the IF filter, ED represents the 

envelope detector, INT represents the integrator, and DET represents the threshold detector.

19
5 BRS SIGNAL MODELLING

In interference analysis, it is often convenient to replace the actual signal with one that is more 

analytically tractable [26], [27]. In this case we would like to replace the signal transmitted from 

a BRS base station with Gaussian noise. This section shows measurements and statistical 

analysis that support this replacement.

The BRS base station signal we investigated conformed to the WiMAX OFDMA, time division 

duplexed (TDD) standard [28]. Since we are able to analytically separate on- and off-times we 

are assuming results for on-times would apply to frequency division duplexed (FDD) signals.

The signal was transmitted at a 2683.5 MHz center frequency and had an approximate 9.3 MHz 

equivalent noise bandwidth. The TDD on-time and period are 3 and 5 ms, respectively, which 

results in a 60% duty cycle. A single WiMAX OFDMA symbol with guard time is 

approximately 103 μs. In one 3 ms on-time there are approximately 29 OFDMA symbols. 

5.1 Measurement System Description

The measurements were performed in a laboratory with the setup shown in Figure 16. The base 

station (BS) was connected to the user equipment (UE) by a cable. An attenuator in the cable 

replicated radio wave propagation path loss. The measurement system was connected to the 

cable with a directional coupler located between the path loss attenuator and the UE. The 

measurement system consisted of a custom preselector unit,

2 instrument, and computer. The 

instrument is either a spectrum analyzer (SA) or vector signal analyzer (VSA). The custom 

preselector unit had a variable attenuator, preselector filter, and low-noise amplifier (LNA).

The WiMAX spectrum was measured with the spectrum analyzer (SA). The WiMAX time 

series, used to analyze the signal statistics of smaller portions of the WiMAX spectrum, was 

measured with the vector signal analyzer (VSA). For the purposes of this section, the SA powers 

are reported as the power at the input to the preselector and the VSA powers are reported as the 

power at the input to the VSA.

The preselector filter had a 30 MHz bandwidth and approximately 8 dB loss at 3 GHz. The LNA 

had 25 dB gain and an approximately 4.5 dB noise figure at 3 GHz. SA and VSA noise figures 

were approximately 21 dB at 3 GHz. Measurement system noise figure was 15.2 dB at 3 GHz 

with the preselector.

2 3rd generation Radio Spectrum Measurement System (RSMS) preselector unit.

20

 
Figure 16. Measurement setup shown with VSA. BS represents the base station, UE represents 

the user equipment, DC represents the directional coupler, PS represents the preselector, and PC 

represents the personal computer.

5.2 WiMAX Spectrum

The WiMAX spectrum was measured with the stepped frequency measurement algorithm which 

maximizes measurement dynamic range by allowing the user to vary preselector attenuation as 

the measurement system center frequency is stepped across a range of frequencies. At 

frequencies where strong signals are present, attenuation is added. Conversely, at frequencies 

where weak signals are present, attenuation is reduced.

The average power of a signal with noise characteristics is best measured with an RMS voltage 

or average power detector. Since a spectrum analyzer with average power detection was 

unavailable, average power detection was approximated by envelope detection followed by

10 Hz video bandwidth filtering, 0.5 second per step integration time, sample detection, and 

addition of a 2.5 dB noise correction factor to the measured power.

Figure 17 shows the noise corrected PSD measurement in terms of power at the preselector 

input. The measurement was performed with a 1 MHz frequency step and 100 kHz resolution 

bandwidth. The center frequency and bandwidth are estimated to be 2683.5 MHz and 9.3 MHz, 

respectively. A horizontal line at -108.8 dBm demarks the average measurement system noise 

power, often referred to as the noise floor.

The signal is occupying a 10 MHz BRS channel adjacent to the lower edge of the 2700–2900 

radar band and has unwanted emissions above and below the BRS channel. The unwanted 

emissions below the BRS channel fall to approximately -90 dBm by 2640 MHz then level off 

until 2450 MHz where they reach the measurement system noise floor. Unwanted emissions 

above the BRS channel fall to the noise floor by 2760 MHz.

Unwanted emissions are precisely defined by the ITU-R [29], which recognizes three transmitted 

signal power spectral density (PSD) domains referred to as necessary bandwidth, out-of-band 

(OOB), and spurious. Collectively, OOB and spurious emissions are referred to as unwanted 

emissions. The necessary bandwidth contains most of the modulated signal power, the spurious 

region contains unwanted signals incidental to transmission, and the OOB region between them 

contains both modulated and incidental signals.

21
In general the OOB domain begins at the edge of the necessary bandwidth and ends at ± 2.5 

times the necessary bandwidth from the transmitter center frequency. The spurious domain 

follows the OOB domain. The boundaries of these domains can be adjusted to meet various 

spectrum management objectives. For example the ETSI UMTS standard [12] has different 

power limits for spurious emissions in the BRS band and spurious emissions outside of the BRS

band.

Using ITU-R definitions, the necessary bandwidth is 10 MHz and within 2678.5 to 2688.5 MHz, 

the out-of-band emissions extend from 2658.5 to 2678.5 MHz and 2688.5 to 2708.5 MHz. The 

spurious emissions extend below 2658.5 MHz and above 2708.5 MHz.

Figure 17. PSD measurement. (Data Identifier: F6R2)

5.3 Signal Statistics Measurements

Signal statistics measurements were made at 2550, 2683.5, and 2750 MHz with the VSA. The 

2683.5 MHz measurement is made at the BRS signal center frequency and represents the signal 

in the necessary bandwidth. The 2550 MHz measurement is made where unwanted emissions are 

not attenuated by a transmitter filter. It is representative of spurious emissions inside the BRS 

band. The 2750 MHz measurement is made where unwanted emissions are attenuated by the 

transmitter filter. It is representative of filtered spurious emissions outside the BRS band.

The measurement in the necessary bandwidth was taken without the preselector. The remaining 

spurious measurements used the preselector to reject the strongest portion of the signal in the 

necessary bandwidth and thereby increase measurement dynamic range.

22
The VSA converts the real passband signal at a center frequency to a complex baseband (i.e. 

inphase and quadrature) signal centered at 0 Hz. The measurements were made in an 18 MHz 

VSA two-sided bandwidth. The signal was sampled at 23.041 MHz with a time increment of 

43.4 ns.

VSA input range varied with the center frequency as shown in Table 3. The VSA begins 

compressing a CW signal at approximately 8 dB above the input range [30]. Caution should be 

used when commenting on measurements with samples that are more than 8 dB above the input 

range.

Table 3. Measurement system parameters. The measurement center frequency ffmm mm varies. The 

BRS center frequency, ffbb , is 2683.5 MHz.

ffmmmmmmmm

(MHz)

ffmmmmmmmm − ffbbbb

(MHz)

VSA input 

range (dBm)

Preselector 

attenuation (dB) Description

2550.0 -133.5 -30 0 Spurious domain inside BRS band

2683.5 0 0 NA Necessary bandwidth

2750.0 66.5 -45 0 Spurious domain outside BRS band

5.3.1 Analysis Details

Statistical analysis consisted of calculating the signals amplitude probability distribution (APD) 

and power spectral density (PSD). The APDs were plotted on Rayleigh graphs where the 

Rayleigh distributed amplitude of complex baseband Gaussian noise appears as a straight, 

negatively sloped line with mean power at approximately the 37th percentile. The PSD of white 

Gaussian noise (WGN) is flat; colored Gaussian noise may be any shape but flat. Measurement 

system noise is represented by the dashed red line on these graphs.

The periodicity of TDD causes the signal statistics to be cyclostationary. We addressed this issue 

by separating the signal into distinct on- and off-time signals which we analyzed as though they 

were stationary. It is important to note that incidental unwanted emissions and measurement 

system noise are present at all times. The on- and off-time signals were obtained by multiplying 

the data by a gating function specified by an on-time, period, and delay and removing residual 

zeros.

Processing used 4,194,304 or 222 samples which were separated into 2,516,582 on-time samples

and 1,677,721 off-time samples. The samples spanned 182 ms or 36.4 TDD periods. For APD 

processing the samples were decimated by 3 to assure sample independence yielding 

approximately 838,860 on-time samples and 559,240 off-time samples. For PSD processing 

524,288 un-decimated on- and off-time samples organized into 512 blocks of 1024 samples were 

used. The corresponding block period was 44.4 μμs which produced a 22,500 Hz frequency 

resolution.

23
5.3.2 2683.5 MHz

The 2683.5 MHz signal represents the signal in the necessary bandwidth. Figure 18 shows a 

sequence of TDD frames with prominent on- and off-times. The on-time has a dip in amplitude 

that begins and ends at approximately 100 and 300 μμs, respectively. This feature is caused by 

lower power preamble and control information OFDMA symbols. Data OFDMA symbols fill the 

rest of the on-time.

Figures 19 and 20 are the APD and PSD of the whole signal over a number of TDD periods. The 

APD, broken into two segments, shows the differences in amplitudes between the on- and offtimes. The break between the two occurs at the percent corresponding to the duty cycle. 

Although illustrative, this APD is not useful for determining whether the signals are Gaussian 

since it does not address the signal’s statistical cyclostationarity. The PSD is flat and the 

bandwidth corresponds to the signal’s.

Figures 21 and 22 are the APD and PSD of the signal after they have been separated into distinct 

on- and off- time signals. The gating function on-time, period, and delay parameters were 3000, 

5000, and 2704 μμs, respectively.

The on-time APD resembles GN with the exception of the flattening below 1 percent. This 

flattening could be due to OFDMA peak suppression. However since it occurs where VSA 

overload begins we cannot be entirely certain. The on-time PSD resembles WGN across the 

necessary bandwidth. The on-time power, 2.3 dBm, is greater than the whole signal’s power, -0.2 

dBm, by approximately the reciprocal of the duty cycle.

The off-time statistics are elevated above measurement system noise indicating that the off-time 

signal is due to incidental emissions from the transmitter and not the measurement system. The 

off-time APD resembles that of GN and the off-time PSD resembles that of WGN. 

With the exception of the possible overload in the small on-time APD percentages, these 

statistics show that the on- and off-times can be reasonably emulated with WGN.

24
Figure 18. Signal at 2683.5 MHz showing TDD on- and off-times.

Figure 19. APD at 2683.5 MHz. On- and off-times have not been differentiated.

25
Figure 20. PSD at 2683.5 MHz. On- and off-times have not been differentiated.

Figure 21. APD at 2683.5 MHz of on- and off-time signals.

26
Figure 22. PSD at 2683.5 MHz of on- and off-time signals.

5.3.3 2550 MHz

The signal at 2550 MHz represents unwanted spurious emissions inside the BRS band. Figure 23

shows that the signal has well defined on- and off-times. Preamble and control OFDMA symbols 

are not evident at the beginning of the on-time. The gating function on-time, period, and delay 

parameters were 3018, 5000, and 2495 μμs, respectively.

The on-time APD in Figure 24 resembles that of Gaussian noise and the on-time PSD in Figure 

25 resembles that of WGN. The off-time APD also resembles Gaussian noise and the PSD 

resembles that of WGN. Both off-time statistics are approximately one dB above receiver noise 

indicating that the incidental emissions from the transmitter are approximately 6 dB below 

receiver noise.

The APD and PSD analysis indicates that on- and off-time emissions can be emulated by WGN.

27
Figure 23. Signal at 2550 MHz showing TDD on- and off-times.

Figure 24.APD at 2550 MHz for on- and off-times.

28
Figure 25.PSD at 2550 MHz for on- and off-times.

5.3.4 2750 MHz

The signal at 2750 MHz represents unwanted spurious emissions outside the BRS band. The 

emissions are at a lower power level after being attenuated by the transmitter filter. Figure 26

shows on- and off-times that are differentiated by an approximately 4 dB change in amplitude. 

There is no evidence of specific preamble or control word OFDMA symbols. The gating 

function on-time, period, and delay parameters were 3000, 5000, and 5135 μμs, respectively.

The on-time APD in Figure 27 resembles that of Gaussian noise but the on-time PSD in Figure 

28 has a definite slope from low to high frequencies, i.e. it is colored rather than white. The offtime APD resembles that of Gaussian noise and the off-time PSD resembles that of WGN.

The 2750 MHz measurement was reduced to a 1 MHz bandwidth signal centered at 2741 MHz 

or -9 MHz on the PSD graph to increase SNR. Results are consistent with the 2750 MHz 

measurement.

These analyses indicate that the on-time emissions can be emulated with colored GN and the offtime with WGN.

29
Figure 26. Signal at 2750 MHz showing TDD on- and off-times.

Figure 27. APD at 2750 MHz for on- and off-times.

30
Figure 28. PSD at 2750 MHz for on- and off-times.

Figure 29. 2741 MHz, 1 MHz bandwidth signal derived from 2750 MHz measurement.

31
Figure 30. 2741 MHz, 1 MHz bandwidth APD derived from 2750 MHz measurement.

Figure 31. 2741 MHz, 1 MHz bandwidth PSD derived from 2750 MHz measurement.

32
5.4 Discussion

The results of our analysis are summarized in Table 4. The analysis showed that the 2683.5 MHz 

signal in the necessary bandwidth was approximately or nearly Gaussian. It is nearly Gaussian 

because on-time signal levels occurring less than 1% of the time were slightly compressed 

compared to GN. This could be due to OFDMA peak suppression but also may be due to VSA

overload. 

The analysis also showed that the 2550 MHz unfiltered spurious emissions below the BRS 

channel can be modeled as WGN during both on- and off-times. Finally, the analysis showed 

that the 2750 MHz filtered spurious emissions above the BRS channel have WGN characteristics 

during the off-time and colored GN characteristics during the on-time. 

The roll-off or OOB regions between necessary bandwidth and the spurious regions were not 

measured due to measurement system dynamic range considerations. Pending future 

measurements, we will assume OOB emissions are Gaussian as well.

It is important to note that the noise outside of the necessary bandwidth can be colored and 

therefore correlated over time. The correlation decreases the number of independent samples but 

does not prevent us from using GN theoretical results in our analysis of BRS interference effects.

Correlation is quantified by correlation time, which we assume to be short compared to the 

magnetron radar pulse repetition interval. Therefore correlation will not affect the integrated 

radar pulse statistics.

The analysis was done in a wide measurement bandwidth. However, since the statistics are 

Gaussian they will be Gaussian in smaller bandwidths as well. Consequently we can conclude 

that unwanted emissions from the BRS base station signals can also be modeled as GN processes

for bandwidths smaller than our measurement bandwidth. 

Finally, BRS base stations operate in a network and a victim receiver is likely to see emissions 

from an aggregate or number of base stations at once. Since the emissions from a single base 

station are Gaussian and the sum of any number of Gaussian random variables is still Gaussian it 

follows that the emissions from any number of base stations in an aggregate will also be 

Gaussian.

Table 4. Measurements’ resemblance to Gaussian noise (GN) and white Gaussian noise (WGN).

ffmmmmmmmm

(MHz)

On-time Off-time

GN WGN GN WGN ITU Domain

2683.5 Nearly Yes Yes Yes Necessary bandwidth

2550.0 Yes Yes Yes Yes Spurious 

2750.0 Yes No Yes Yes Spurious 

33
6 AGGREGATE BRS SIGNAL POWER

In this section we are interested in determining how much greater the aggregate BRS signal 

power from all base stations in the network is than the power from a single BRS base station. If it 

is significantly more, interference analysis needs to be done with the aggregate BRS signal and 

its statistics.

6.1 Interference Power from a Single Base Station

The general interference link power budget for a single base station is

ssss ( ) = ̂

tt gg�ttgg

�llddllbb llppppppllcc ll

̃

pp( ) (4)

where is the distance from the radar to the base station, ̂

tt is the signal power at the transmit 

antenna, gg�tt is the gain of the base station antenna in the direction of the radar, gg is the gain of the 

radar antenna in the direction of the base station, lldd is the radome loss, llbb is the beam shape 

loss, llpppppp is the polarization loss between the base station and radar antennas, llcc is the radar 

receiver circuit loss, and ll

̃

pp is the path loss from the base station to the radar. Note that ll

̃

pp = �ll

̃

ff

where � is the excess path loss and ll

̃

ff is free space path loss. In general, the interference power 

is a random variable due propagation path loss variability.

6.2 Effects of Narrow Radar Antenna Beam Width on Aggregate Power

We begin by assuming that the base stations coverage areas can be represented by tessellated 

hexagons as shown in Figure 32, where the dots in the hexagons represent base station locations. 

We also assume that the maximum aggregate power received by a narrow radar antenna beam

width will come from base stations along a line of repetitively-spaced base stations.

There are only two such lines that connect repetitively-spaced base stations. The lines, labeled l1

and l2, connect base stations across the hexagonal sides and vertices, respectively, and terminate 

at ship locations labeled P1 and P2 , respectively. The ships are located distance d1 from the base 

station at point B.

Using the hexagon parameters in Figure 33 it can be shown that the repetitively-spaced base 

station distances are AB=√3tt for line l1 and EB=3tt for line l2. Consequently the base stations 

along line l1 are more closely spaced and a ship at point P1 will receive more aggregate power 

than a ship at point P2.

34
Figure 32. BRS coverage area composed of tessellated hexagons. Base stations are located at 

dots at center of hexagons. Ships are located at points PP1 and PP2.

Figure 33. Relevant hexagon parameters.

Figure 34. Chord length calculation parameters. Base stations are located at points labeled bs.

35
Next we calculate at what distance the radar antenna main beam will receive signals from base 

stations distances CD/2 and AD/2 from lines l1 and l2, respectively. We want to ensure the 

aggregate power can be adequately represented without including base stations near but not on 

the line. As shown in Figure 34, the two base stations define the chord, yy, subtended by an angle 

corresponding to the antenna beam width, θθ. The length of the chord is

yy = 2 sin�θθ

2� �, (5)

the length of the radius is 

= yy

2 sin�θθ

2� � (6)

and the distance of interest is 

= � 2 − �

yy

2� �

2

. (7)

The chord AD for line l2 is equal to √3tt and is the same as the distance between base stations 

which we assume to be 3.0 km. The chord CD for line l1 is 3tt or 5.2 km. Finally, assuming the 

antenna beam width, θθ, is 1.9 degrees then is 156.7 km for line l1 and 90.4 km for line l2. 

Calculations have shown little change in aggregate power past 10 base station distances or 30

km. Consequently, our aggregate model does not need to include base stations near the lines.

In summary, because of the radar antenna’s narrow azimuthal beam width, maximum aggregate 

interference is from base stations along the line formed by the most closely repetitively-spaced

base stations as shown in Figure 35.

36
Figure 35. Interference scenario after taking into account narrow azimuthal beam width of the 

marine radar antenna. The base stations in the shaded area will provide the most interfering 

signal power.

6.3 Interference Power from a Set of Base Stations

The aggregate BRS signal power from base stations along the line formed by the most closely 

repetitively-spaced base stations is 

( 1) = � ssss ( )

NN

=1

= � ̂

tt gg�ttgg

�llddllbb llppppppllcc ll

̃

pp( )

NN

=1

(8)

where NN is the number of base stations and nn is the base station index. The aggregate separation 

distance, 1, is defined as the distance from the radar to the closest base station along the line. 

The distance from the closest base station to the nnth base station along the line is 

37
= 1 + (nn − 1) bb , nn > 1 (9)

where bb is the distance between adjacent base stations.

Because of propagation path loss variability, the aggregate power is a random variable with a 

statistical distribution. The aggregate power distribution is different than the power distribution 

of any one base station. Although the aggregate distribution mean is equal to the sum of the base 

station distribution means, this is not necessarily true for any other quantile. To find other 

quantiles the aggregate distribution must be determined.

The aggregate distribution can be computed using the ITM and Monte Carlo techniques. 

Specifically, the excess path loss means and pseudo-standard deviations of the individual 

interfering stations at distances { 1, ... NN} are obtained from the ITM, and these are used along 

with the link budget to generate a random set of interfering powers, � ssss ( 1), ... iissssssssssss( NN)�, 

which are added together to get ( 1). We then repeat this process MM times, order the results, and 

pair them with corresponding probabilities �1,

MM−1

MM , ⋯ 1MM�.

If the smallest interference power is paired with the smallest probability, 1�MM, we have the 

cumulative distribution function

FF( ) = PP {ii < }. (10)

Similarly, if the smallest is paired with probability 1 we have the complementary cumulative 

distribution function

GG( ) = PP {ii ≥ } = 1 − FF( ). (11)

The number of Monte Carlo trials determines how confident we can be in our results. This is 

particularly important at the lowest probabilities where there are fewer samples. We found that 

106 trials is a reasonable number in predicting quantiles with probabilities as low as 1%. We also 

tested our random number generator for normality for sample sizes up to 107, with very 

satisfactory results. Consequently we are confident that we can predict quantiles with 

probabilities as low as 1% with 10 base stations in the aggregate.

6.4 Single Base Station and Aggregate Interference Power Statistics

Figure 36 shows various interference power quantiles from distributions across a range of 

distances from an aggregate of 10 base stations spaced 3 km apart. Parameters for the 

calculations are taken from Appendix A. As expected, power variation increases with distance. 

The figure also shows the difference between received interference power from an aggregate of 

10 base stations and the interference power from a single base station. The difference is greatest 

between 5 and 30 km. At 15 km the difference is approximately 6 dB. Consequently, it is 

important to use the aggregate signal for interference analysis.

38
Figure 36. Probability I is less than ordinate. Aggregate (solid lines) versus single base station 

(dashed lines).

39
7 RADAR SNR

One of the key IPC is the baseline SNR. The baseline SNR determines radar performance 

without interference and influences the amount of interference power needed to degrade 

performance to the allowable level. Previous interference analyses have set SNR to a constant 

baseline level [3]. This approach, which we will refer to as constant SNR analysis, is applicable 

to short radar to target ranges where there is little or no path loss variability. However, at longer 

distances, atmospheric conditions introduce path loss variability and corresponding SNR 

variability. In this section we show how baseline SNR is determined and how a variable SNR 

can be included in interference analysis.

Situations that highlight where constant and variable SNR analyses are applicable are shown in 

Figure 37. Figures 37(a) and 37(b) illustrate situations where the radar to target path is short and 

constant SNR analysis is appropriate. Figure 37(c) illustrates a situation where the radar to target 

path is long and variable SNR analysis is appropriate. While constant SNR analysis is not 

accurate for long radar to target ranges, variable SNR analysis is accurate for all radar to target 

ranges. The main advantage of using a constant SNR is that it does not require radar to target 

link budget analysis.

40
Figure 37. Short radar to target ranges as in (a) and (b) are analyzed with a constant SNR while 

long radar to target ranges as in (c) are analyzed with a variable SNR.

7.1 Definitions

Signal and noise powers are evaluated at the receiver input. The signal power is 

= 1

TT � 2(tt)

TT

2�

−TT

2�

(12)

where TT is the pulse period. The power is the average power while the pulse is on but may also 

be referred to as the peak power over the pulse repetition interval.

The receiver noise power is

41
nn = E ��� nn(ττ)hii (tt − ττ)

∞

−∞

�

2

� (13)

where E{∙} is the expectation operator. When the noise power spectral density is constant,

nn = kkTT0ffrr ii (14)

where kk is Boltzman’s constant, TT0 is the ambient temperature in degrees K, ffrr is the receiver 

noise factor, and ii is the IF filter equivalent noise bandwidth.

The signal to noise ratio is

ww = /nn (15)

Finally capital letters SS, NN, and WW correspond to , nn, and ww in dB and script letters SS, NN, and 

WW correspond to SS, NN, and WW random variables.

7.2 Baseline SNR

Baseline SNR is the SNR needed to provide the 0.8 PPdd and 10−4 PPffff baseline performance level. 

It can be computed in a number of ways. The way we computed the ideal SNR and the SNR at 

the receiver input, which includes signal processing loss, is described in Appendix D. 

With no integration, the ideal baseline SNR is 10.98 and 16.05 dB for non-fluctuating Swerling 0 

and fluctuating Swerling 1 target RCSs, respectively. The corresponding SNR at the receiver 

input with 1.8 dB signal processing loss are 12.78 and 17.85, respectively.

Table 5 shows baseline SNR with integration for the various pulse widths and antenna rotation 

rates in the IEC 62388 standard. Short and medium baseline SNR are the same because their 

pulse repetition frequencies and bandwidths are identical.

Table 5. Baseline ideal SNR and SNR at receiver input for a 1.9 degree beam-width antenna at 

baseline performance 0.8 PPdd and 10−4 PPffff. PW is pulse width, PRF is pulse repetition frequency, 

BW is IF filter bandwidth, RR is rotation rate, and nnpp is the number of pulses integrated.

Pulse

PW 

(ns)

PRF 

(Hz)

BW 

(MHz)

RR 

(rpm) nnpp

Ideal SNR (dB) SNR at receiver input (dB)

Swerling 0 Swerling 1 Swerling 0 Swerling 1

Short 50 1800 20 20 29 0.29 5.62 2.09 7.42

Short 50 1800 20 40 14 2.31 7.58 4.11 9.38

Medium 250 1800 20 20 29 0.29 5.62 2.09 7.42

Medium 250 1800 20 40 14 2.31 7.58 4.11 9.38

Long 800 785 3 20 12 2.75 8.01 4.55 9.81

Long 800 785 3 40 6 4.83 10.03 6.63 11.83

42
7.3 Variable SNR

This section describes a variable SNR analysis method. The method is demonstrated with the set 

of targets described in the IEC 62388 standard clutter free test [16], [21] and SNR distributions 

determined by the ITM propagation model.

We start by creating a link budget expression for the radar’s received power and use it to 

compute the received power for the targets in the IEC 62388 standard clutter free test. It will be 

shown that the SNR for all targets in the clutter free test is in excess of that needed for baseline 

performance. We assume that the excess power margin is needed to compensate for reduced 

RCS due to different target aspects, shapes, and construction materials and remove it prior to 

interference tests by decreasing the RCS.

7.3.1 Link Budget

For free space, i.e. propagation in an empty vacuum, the radar’s received power is

= ttttgg

4ππ rr

2 ∙ σσ aa

4ππ rr

2 ∙ (16)

where tttt is the peak transmitted power, gg is the radar antenna gain relative to an isotropic 

antenna, σσ aa is the target average or mean RCS in square meters, rr is the distance from the 

radar to the target in meters, and is the effective antenna aperture in square meters. The 4ππ 2

terms in the denominator indicate that the transmitted signal and the signal reflected off the 

target spread isotropically.

But it can be shown that the aperture of an antenna is related to the gain of an antenna relative to 

an isotropic radiator by

= ggλλ2

4ππ

(17)

where λλ is the wavelength, so

= ttttgg

4ππ rr

2 ∙ σσ aa

4ππ rr

2 ∙

ggλλ2

4ππ

(18)

and

= ttttgg2σσ aaλλ2

(4ππ)3 rr

4 (19)

To emulate practical terrestrial propagation conditions we introduce the excess path loss factor, 

which is dependent on rr . The factor is assumed to be completely correlated between the 

outbound path from the radar to the target and the inbound path from the target to the radar. 

Consequently it is squared in the link budget equation

43
= ttttgg2σσ aaλλ2

(4ππ)3 rr

4 2 (20)

Finally adding in the radar losses to refer power to the receiver input

= ttttgg2σσ aaλλ2

(4ππ)3 rr

4 2llddllbb llcc llcc

(21)

Since is evaluated at the receiver input, receiver signal losses, ll , are not included.

7.3.2 SNR for the IEC 62388 Standard Test Cases

Table 6 shows the SNR for the free space channel where the excess path loss, , is 1. To limit the 

scope of the problem we only use pulse widths that satisfy range limits shown in Figure 9 and 

provide the highest SNR. 

Figure 38 shows the SNR distributions, PP {WW > WW} using ITM where is random. Cases 1–9 

use the long pulse and case 10 uses the short pulse. Table 7 summarizes various quantiles. Case 

10 has the shortest range and an approximately constant SNR while case 1 has the longest range

and the most variability. Clearly variability increases with radar to target range.

Table 6. IEC 62388 standard clutter free test case SNR in free space channel. Shaded cells 

indicate pulse meets target range requirement.

Case Target

Height 

(m)

Range RCS 

(m2)

FS SNR (dB)

Pulse width

nmi km Short Med Long

1 60m high shoreline 50.0 20.0 37.0 50000.0 27.9 27.9 36.1

2 6 m high shoreline 5.0 8.0 14.8 5000.0 33.8 33.8 42.0

3 3 m high shoreline 2.5 6.0 11.1 2500.0 35.8 35.8 44.0

4 SOLAS ship > 5000gt 10.0 11.0 20.4 30000.0 36.1 36.1 44.3

5 SOLAS ship > 500gt 5.0 8.0 14.8 1000.0 26.8 26.8 35.1

6 Small boat with reflector 4.0 3.7 6.8 0.5 7.2 7.2 15.4

7 Buoy with reflector 3.5 3.6 6.7 1.0 10.7 10.7 18.9

8 Buoy 3.5 3.0 5.6 0.5 10.8 10.8 19.1

9 Small 10 m boat 2.0 3.0 5.6 1.4 15.3 15.3 23.6

10 Channel marker 1.0 1.0 1.9 0.1 22.9 22.9 31.2

44
Figure 38. SNR distributions using the ITM for 10 IEC 62388 standard clutter free test cases.

Table 7. IEC 62388 standard clutter free test case SNR quantiles using the ITM. 

Case Description

Height 

(m)

Range RCS

m2 Pulse

FS

SNR

(dB)

ITM SNR (dB)

PP {WW > WW}

nmi km 0.50 0.80 0.90 0.95 0.99

1 60m high 

shoreline

50.0 20.0 37.0 50000.0 Long 36.1 36.5 33.1 31.3 29.8 27.1

2 6 m high 

shoreline

5.0 8.0 14.8 5000.0 Long 42.0 28.0 27.1 26.6 26.2 25.5

3 3 m high 

shoreline

2.5 6.0 11.1 2500.0 Long 44.0 25.8 25.2 25.0 24.7 24.3

4 SOLAS ship > 

5000gt

10.0 11.0 20.4 30000.0 Long 44.3 32.6 31.0 30.2 29.5 28.2

5 SOLAS ship > 

500gt

5.0 8.0 14.8 1000.0 Long 35.1 21.0 20.1 19.6 19.2 18.5

6 Small boat with 

reflector

4.0 3.7 6.8 0.5 Long 15.4 15.6 15.5 15.4 15.3 15.2

7 Buoy with 

reflector

3.5 3.6 6.7 1.0 Long 18.9 18.2 18.0 17.9 17.8 17.7

8 Buoy 3.5 3.0 5.6 0.5 Long 19.1 19.0 18.9 18.8 18.8 18.7

9 Small 10 m 

boat

2.0 3.0 5.6 1.4 Long 23.6 16.5 16.4 16.4 16.3 16.2

10 Channel marker 1.0 1.0 1.9 0.1 Short 22.9 22.0 22.0 22.0 22.0 22.0

45
7.3.3 Excess Power Margin 

We define the excess power margin as the ratio of the SNR exceeded 99% of the time to the 

baseline SNR

= ww99

wwbb � (22)

where ww99 is the SNR exceeded 99% of the time and wwbb is the baseline SNR. Note that the SNR 

exceeded 99% of the time is limited by fading and not ducting enhancement.

Assuming the mean RCS varies with target aspect, shape, and construction materials we remove 

the excess power margin by reducing the mean RCS by

σσ� aa = σσ aa� (23)

The radar link budget with the excess power margin removed is now

= ttttgg2σσ aaλλ2

(4ππ)3 rr

4 2llddllbb llcc llcc

(24)

Table 8 shows the free space and ITM 99% SNR power margins for the IEC 62388 standard 

clutter free test cases. The table shows maximum FS margin of 32.5 dB for case 4 i.e. the

SOLAS ship > 5000 gt. This corresponds to the standard which states the RCS may be reduced 

as much as 30 dB because of target aspect, shape, or constructions materials and justifies 

removal of the excess SNR by reducing the RCS prior to interference analysis. The

corresponding ITM 99% margin is only 16.4 dB. The smaller margin is caused by the ITM 99% 

SNR being less than the FS SNR.

Figure 39 shows the SNR distributions with the excess power margin removed so that the 

baseline SNR is exceeded 99% of the time. Finally, Table 9 shows the reduced RCSs. The RCS 

for case 4 was reduced 16.4 dB to 691.3 square meters from 30000. This reduction is 

commensurate with the measured RCS discussed in Section 4.3 .

Table 8. IEC 62388 standard clutter free test case power margins.

Case Description

Height

(m)

Range

Baseline 

SNR

(dB)

FS 

SNR

(dB)

FS 

Margin

(dB)

ITM 99% 

SNR

(dB)

ITM 99% 

Margin

nmi km (dB)

1 60 m high shoreline 50.0 20.0 37.0 11.83 36.1 24.27 27.1 15.2

2 6 m high shoreline 5.0 8.0 14.8 11.83 42.0 30.17 25.5 13.6

3 3 m high shoreline 2.5 6.0 11.1 11.83 44.0 32.17 24.3 12.5

4 SOLAS ship > 5000gt 10.0 11.0 20.4 11.83 44.3 32.5 28.2 16.4

5 SOLAS ship > 500gt 5.0 8.0 14.8 11.83 35.1 23.3 18.5 6.7

6 Small boat with 

reflector

4.0 3.7 6.8 11.83 15.4 3.6 15.2 3.3

7 Buoy with reflector 3.5 3.6 6.7 11.83 18.9 7.1 17.7 5.9

46
Case Description

Height

(m) Range

Baseline 

SNR

FS 

SNR

FS 

Margin

ITM 99% 

SNR

ITM 99% 

Margin

8 Buoy 3.5 3.0 5.6 11.83 19.1 7.3 18.7 6.8

9 Small 10 m boat 2.0 3.0 5.6 11.83 23.6 11.8 16.2 4.4

10 Channel marker 1.0 1.0 1.9 9.38 22.9 13.5 22.0 12.6

Figure 39. SNR distributions for 10 IEC 62388 standard clutter free test cases with excess power 

margin removed. There are 3 fewer curves visible because cases 2 and 5, 6 and 7, and 8 and 9 

have similar target parameters.

Table 9. Reduced mean RCS for IEC 62388 standard test cases. 

Case Description 99%Margin (dB)

σσ aa σσ� aa

m2 dBsm m2 dBsm

1 60 m high shoreline 15.2 50000 46.98 1492.7 31.7

2 6 m high shoreline 13.6 5000 36.98 216.2 23.3

3 3 m high shoreline 12.5 2500 33.97 142.0 21.5

4 SOLAS ship > 5000gt 16.4 30000 44.77 691.3 28.4

5 SOLAS ship > 500gt 6.7 1000 30.00 216.2 23.3

6 Small boat with reflector 3.3 0.5 -3.01 0.232 -6.4

7 Buoy with reflector 5.9 1.0 0.00 0.258 -5.9

8 Buoy 6.8 0.5 -3.01 0.103 -9.9

9 Small 10 m boat 4.4 1.4 1.46 0.512 -2.9

10 Channel marker 12.6 0.1 -10.0 0.006 -22.6

47
8 CONCLUSION

This report provides background information needed to analyze effects of BRS reallocation on 

2900–3100 MHz band marine radars. Key topics covered are interference protection criteria 

(IPC), interference scenario, and the various system and propagation models.

Comprehensive IPC include performance levels, powers, and reliabilities for baseline 

(interference-free) and allowable degraded conditions. Reliability in this context is determined 

solely by radio wave propagation path loss variability caused by terrain and atmospheric 

conditions and is independent of electrical or mechanical malfunction.

The interference scenario consists of a maritime radar target such as a boat or buoy between a 

network of base stations and a ship with a maritime radar. Magnetron radar and radar target 

models are derived from the IEC 62388 standard for shipborne radars. BRS system models are 

derived from WiMAX and LTE standards. Radio wave propagation is modelled with the ITS 

Irregular Terrain Model (ITM) because of its ability to model path loss variability.

A BRS base station signal was measured and statistically characterized. The signal statistics were 

found to be nearly Gaussian in the necessary bandwidth and Gaussian in the spurious domain. 

Statistics in the necessary bandwidth are considered nearly Gaussian because of a slight drop in 

peak signal levels. The roll-off or OOB regions between the necessary bandwidth and spurious 

regions were not measured due to measurement system dynamic range considerations. Pending 

future measurements, we are assuming OOB emissions are Gaussian as well. Consequently, it is 

reasonable to model the BRS signal as Gaussian noise. This finding greatly simplifies analysis of 

interference in marine radars from base station unwanted emissions.

Statistical characterization was done on measurements in a wide bandwidth. However, since the 

statistics are Gaussian they should also be Gaussian when the BRS signal is filtered to a narrower 

bandwidth and when any number of BRS signals are added to represent the signal from an 

aggregate of base stations. 

A method for computing aggregate interference power distributions using the radio wave 

propagation model and Monte Carlo analysis was developed. These distributions are essential for 

analyzing radar link reliability. Because of the radar antenna’s narrow azimuthal beam width, 

maximum aggregate interference power was found to come from base stations along a line 

formed by the most closely repetitively-spaced base stations. The aggregate interference power 

was found to be as much as 6 dB greater than the power from a single base station. Hence it is 

important that interference analysis be done with an aggregate of base stations.

Although interference path loss variability is usually included in interference analysis, desired 

path loss variability often is not. In the maritime radar case the desired path is the radar to target 

path. In devising a method for including radar to target path loss variability into our analysis we 

found excess SNR in the radar to target link budgets used for industry acceptance tests. Although 

this excess SNR could potentially mitigate interference, we found that it is needed to 

accommodate reductions in target mean RCS due to changes in target aspect, shape, and 

construction materials. Consequently we recommend removing the excess SNR by reducing 

mean RCS prior to interference analysis.

48
9 ACKNOWLEDGEMENTS

This work was sponsored by the U.S. Coast Guard Spectrum Management Telecommunications 

Policy Division, U.S. Coast Guard CG-652, 2100 2nd St. SW Stop 7101, Washington DC 20593-

7101. The authors would like to acknowledge Fred Mistichelli (former Division Chief), Joseph 

Hersey (former Division Chief), and Daniel Freedman (former Spectrum Engineer) for their 

sponsorship.

The authors would also like to acknowledge David Turnage, Research and Development 

Manager, Kelvin Hughes Ltd.; Lawrence Cohen, Electronics Engineer, U.S. Naval Research 

Laboratory; Jon Higham, Program Coordinator, United Kingdom Office of Communication 

(OFCOM); David G. Money, consultant to the OFCOM; Richard Rees, Spectrum Policy and 

Technical Standards Manager, United Kingdom Maritime and Coastal Agency; and David 

Blevins, Senior Staff Engineer, Northrup Grumman Marine Systems, for sharing their insights 

into this issue.

Finally, the authors would like to acknowledge Geoffrey Sanders, of the Institute for 

Telecommunication Sciences, for his contributions towards measuring WiMAX signal 

characteristics and Al Romero, Visual Information Specialist, of the National Oceanic and 

Atmospheric Administration (NOAA), for creating the illustrative figures.

49
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Release 11, Oct. 2012.

[13] International Telecommunication Union Joint Task Group 4-5-6-7, Appendix 1 

“Characteristics of terrestrial IMT-Advanced systems for frequency sharing/interference 

analyses” in Attachment 1, “Protection criteria, system characteristics, related materials on 

modelling considerations and sharing studies already performed or underway in ITU-R 

related to the terrestrial services” in Annex 2 “Compilation of material maintained by the 

Joint Task Group 4-5-6-7 working groups” of Report on the Fourth meeting of the Joint 

Task Group 4-5-6-7, Document 4-5-6-7/393-E, October 30, 2013.

[14] WiMAX Forum, “Mobile WiMAX – Part 1: A Technical Overview and Performance 

Evaluation,” WiMAX Forum white paper, August 2006.

[15] International Electrotechnical Commission, Assessment of target detection in clutter in

“Maritime navigation and radiocommunication equipment and systems – Shipborne radar –

Performance requirements, methods of testing and required test results,” IEC 62388, 

Edition 1.0, 2007-12, Section 5.9.3, p. 40.

[16] International Electrotechnical Commission, Table 2 - Range of first detection in minimal 

clutter in “Maritime navigation and radiocommunication equipment and systems –

Shipborne radar – Performance requirements, methods of testing and required test results,” 

IEC 62388, Edition 1.0, 2007-12, Section 5.9.2, p. 38.

[17] International Electrotechnical Commission, Table D.6 – Additional radar system 

parameters in “Maritime navigation and radiocommunication equipment and systems –

Shipborne radar – Performance requirements, methods of testing and required test results,” 

IEC 62388, Edition 1.0, 2007-12, Appendix D, pp. 154.

[18] International Electrotechnical Commission, Table D.8 - S-band radar parameters in 

“Maritime navigation and radiocommunication equipment and systems – Shipborne radar –

Performance requirements, methods of testing and required test results,” IEC 62388, 

Edition 1.0, 2007-12, Appendix D, pp. 156.

[19] A. Toskala and T. Lunttila, “OFDMA Basics,” Chapter 4.3 of LTE for UMTS – Evolution 

to LTE-Advanced, H. Holma and A. Toskala, Eds., Second Edition, New York: Wiley, 

2011, pp. 70-76.

[20] D. Astely, E. Dahlman, A. Furuskar, Y. Jading, M. Lindstrom, and S. Parkvall, “LTE: The 

evolution of mobile broadband,” IEEE Communication Magazine, April 2009, pp. 44–51.

[21] International Electrotechnical Commission, Table D.7 – Target size, height, and RCS 

values in “Maritime navigation and radiocommunication equipment and systems –

Shipborne radar – Performance requirements, methods of testing and required test results,” 

IEC 62388, Edition 1.0, Section 5.9.2, 2007-12, p 155.

51
[22] P.L. Rice, A.G. Longley, K.A. Norton, and A.P. Barsis, “Transmission loss predictions for 

tropospheric communication circuits,” National Bureau of Standards Technical Note 

101,Vol. 1, pp.10-14 to 10-18, Revised January 1, 1967, http://www.its.bldrdoc.gov/

publications/2726.aspx. 

[23] P. Swerling, “Probability of detection for fluctuating targets,” IRE Transactions on 

Information Theory, vol. 6, no. 2, April 1960, pp. 269–308.

[24] E.F. Knott, J. Shaeffer, Michael Tuley, Radar Cross Section, Second Edition, SciTech 

Publishing, 2004, Raleigh, N.C., pp. 258-260.

[25] P.D.L. Williams, H.D. Cramp, and K. Curtis, “Experimental study of the radar cross 

section of maritime targets,” Electronic Circuits and Systems, July 1978, pp. 121–135.

[26] M. Cotton, R. Achatz, J. Wepman, and B. Bedford, “Interference potential of 

ultrawideband signals, Part 1: Procedures to characterize ultrawideband emissions and 

measure interference susceptibility of C-band satellite digital television receivers,” NTIA 

Report TR-05-419, February 2005, http://www.its.bldrdoc.gov/publications/2449.aspx. 

[27] M. Cotton, R. Achatz, J. Wepman, and P. Runkle, “Interference potential of ultrawideband 

signals, Part 2: Measurements of gated Gaussian noise interference to C-band satellite 

digital television receivers,” NTIA Report TR-05-429, August 2005, 

http://www.its.bldrdoc.gov/publications/2459.aspx. 

[28] Frank H. Sanders, Robert L. Sole, John E. Carroll, Glenn S. Secrest, T. Lynn Allmon,

“Analysis and Resolution of RF Interference to Radars Operating in the Band 2700-2900 

MHz from Broadband Communication Transmitters,” NTIA Technical Report TR-13-490,

October 2012, http://www.its.bldrdoc.gov/publications/2684.aspx. 

[29] ITU-R, “Unwanted emissions in the spurious domain,” Recommendation ITU-R SM.329-

10, February 2003.

[30] M. Cotton, R. Achatz, J. Wepman, and B. Bedford, “Dynamic range of the vector network 

analyzer”, Appendix E in “Interference Potential of Ultrawideband Signals, Part 1: 

Procedures to characterize ultrawideband emissions and measure interference susceptibility 

of C-band satellite digital television receivers,” NTIA Report TR-5-419, February 2005, 

http://www.its.bldrdoc.gov/publications/2449.aspx.

52
APPENDIX A: ANALYSIS PARAMETERS

Analysis parameters are provided in the following tables. Radar and target parameters are taken 

from the IEC standard [A-1], [A-2], [A-3], [A-4]. BRS base station parameters are derived from 

the ITU [A-5] and WiMAX forum [A-6]. The radio wave propagation ITM parameters are 

defined in [A-7].

Table A-1. Physical parameters.

Parameter Value Note

Climate Maritime temperate

Terrain Sea/Coastal

Precipitation No IEC 62388 standard clutter free test

Radar sea clutter No IEC 62388 standard clutter free test

Radar precipitation clutter No IEC 62388 standard clutter free test

Radar target fluctuation Swerling 1 IEC 62388 standard clutter free test

Table A-2. IEC 62388 standard clutter free test target physical parameters

Case Target

Height 

(m)

Range RCS

(m2 (nmi) (km) )

1 60 m high shoreline 50.0 20.0 37.0 50000.0

2 6 m high shoreline 5.0 8.0 14.8 5000.0

3 3 m high shoreline 2.5 6.0 11.1 2500.0

4 SOLAS ship > 5000gt 10.0 11.0 20.4 30000.0

5 SOLAS ship > 500gt 5.0 8.0 14.8 1000.0

6 Small boat with reflector 4.0 3.7 6.8 0.5

7 Buoy with reflector 3.5 3.6 6.7 1.0

8 Buoy 3.5 3.0 5.6 0.5

9 Small 10 m boat 2.0 3.0 5.6 1.4

10 Channel marker 1.0 1.0 1.9 0.1

Table A-3. IEC 62388 standard clutter free test radar parameters not related to pulse width.

Parameter Value Note

Center frequency 3050 MHz

Source power 30 kW

Integration Non-coherent

Antenna azimuth beam width 1.9 degrees

Antenna rotation rate 40 revolutions/minute

Antenna polarization Horizontal

Antenna gain 27.0 dB

Antenna height 15 m

Receiver noise figure 5.0 dB Referred to limiter input

53
Parameter Value Note

Antenna radome loss 1.0 dB Transmit and receive

Receiver circuit loss 2.7 dB

Transmitter circuit loss 2.7 dB

Signal processing loss 1.8 dB

Integration beam shape loss 1.6 dB Transmit and receive

Table A-4. IEC 62388 standard clutter free test pulse width and related parameters

Descriptor Width (ns)

Pulse repetition 

frequency (Hz)

Receiver bandwidth 

(MHz)

Short 50 1800 20 

Medium 250 1800 20

Long 800 785 3

Table A-5. BRS macro base station parameters for 10 MHz bandwidth signal.

Parameter Units Report

WiMax 

Forum

ITU WP-5D

Rural Suburban Urban Note

Cell radius km 1.5 1.4 > 2 0.4-2.5 0.2-0.8

Antenna height m 30 32 30 25 20

Sectorization sectors 3 3 3 3 3

Down-tilt degrees 3.5 3 3 6 10

Frequency reuse 1 NA 1 1 1

Horizontal beam width degrees 65 70 65 65 65

Vertical beam width degrees 12.0 14.0 7.5 12.0 12.0 1

Antenna polarization Slant 

linear

NA Slant linear Slant linear Slant linear 2

Feeder loss dB 3 3 3 3 3 3

Maximum base station 

output power

W 40 40 40 40 40 3,4

Maximum antenna gain dBi 16 15 18 16 16

Note 1: Calculated from equations in Recommendation ITU-R F.1336 [A-8].

Note 2: ±45 degree slant also referred to as cross linear polarization

Note 3: WiMAX Forum specifications did not include feeder loss. Maximum base station output power was 

increased by an assumed 3 dB feeder loss to compensate.

Note 4: Maximum power amplifier output.

54
Table A-6. BRS macro base station effective radiated power.

Parameter Units Report

WiMax 

Forum

ITU WP-5D

Rural Suburban Urban Note

Maximum base station 

output power

dBmW 46 46 46 46 46

Feeder loss dB 3 3 3 3 3

Maximum antenna gain dBi 16 15 18 16 16

Downtilt loss dB 1 0.5 2 3 8 1

Effective antenna gain dBi 15 14.5 16 13 8 2

Effective radiated power dBmW 58 57.5 59 56 51

Note 1: Calculated from mechanical tilt and peak gain equations in Recommendation ITU-R F.1336 [A-8].

Note 2: Effective antenna gain is maximum antenna gain minus downtilt loss.

Table A-7. ITM parameters. Base station is the transmitter and radar is the receiver.

Parameter Value Note

Frequency (MHz) 3050

Radio climate surface refractivity (Ns) 325 1

Ground conductivity (S/M) 0.005 (land), 5.0 (sea)

Ground dielectric constant 15.0 (land), 81.0 (sea)

Delta h (meters) 0 Terrain irregularity, 2

Effective earth radius factor 1.4

Polarization Vertical

Transmitter site criteria Random 3

Receiver site criteria Random 3

Radio climate North America marine temperate

Note 1: Average of continental temperate (301) and marine temperate (350).

Note 2: Forces location variability to 0 leaving only time variability.

Note 3: Random used so effective height is the same as actual height above sea level.

A.1 References

[A-1] International Electrotechnical Commission, Table D.6 – Additional radar system 

parameters in “Maritime navigation and radiocommunication equipment and systems –

Shipborne radar – Performance requirements, methods of testing and required test 

results,” IEC 62388, Edition 1.0, 2007-12, Appendix D, pp. 154.

[A-2] International Electrotechnical Commission, Table D.8 - S-band radar parameters in 

“Maritime navigation and radiocommunication equipment and systems – Shipborne radar 

55
– Performance requirements, methods of testing and required test results,” IEC 62388, 

Edition 1.0, 2007-12, Appendix D, pp. 156.

[A-3] International Electrotechnical Commission, Table 2 - Range of first detection in minimal 

clutter in “Maritime navigation and radiocommunication equipment and systems –

Shipborne radar – Performance requirements, methods of testing and required test 

results,” IEC 62388, Edition 1.0, 2007-12, Section 5.9.2, p. 38.

[A-4] International Electrotechnical Commission, Table D.7 – Target size, height, and RCS 

values in “Maritime navigation and radiocommunication equipment and systems –

Shipborne radar – Performance requirements, methods of testing and required test 

results,” IEC 62388, Edition 1.0, Section 5.9.2, 2007-12, p 155.

[A-5] International Telecommunication Union Joint Task Group 4-5-6-7, Appendix 1

“Characteristics of terrestrial IMT-Advanced systems for frequency sharing/interference 

analyses” in Attachment 1, “Protection criteria, system characteristics, related materials 

on modelling considerations and sharing studies already performed or underway in ITUR related to the terrestrial services” in Annex 2 “Compilation of material maintained by 

the Joint Task Group 4-5-6-7 working groups” of Report on the Fourth meeting of the 

Joint Task Group 4-5-6-7, Document 4-5-6-7/393-E, October 30, 2013.

[A-6] WiMAX Forum, Table 7: Mobile WiMAX System Parameters and Table 10: DL Link 

Budget for Mobile WiMAX in “Mobile WiMAX – Part 1: A Technical Overview and 

Performance Evaluation,” WiMAX Forum white paper, August 2006, pp. 31-33.

[A-7] G.A. Hufford, A.G. Longley, and W.A. Kissick, “A Guide to the Use of the ITS Irregular 

Terrain Model in the Area Prediction Mode,” NTIA Report 82-100, April 1982, 

http://www.its.bldrdoc.gov/publications/2091.aspx. 

[A-8] International Telecommunication Union, Reference radiation patterns of omnidirectional, 

sectoral and other antennas in point-to-multipoint systems for use in sharing studies in the 

frequency range from 1 GHz to about 70 GHz, Recommendation ITU-R F.1336-3, March 

2012.

56
APPENDIX B: PROPAGATION MODELS

B.1 Free Space Model

The free space (FS) model assumes the radio wave is transmitted into an empty vacuum.

Practically, we use it when the radio wave is not expected to interact with the atmosphere or 

objects such as the earth.

With the FS model the propagation path loss is

llff = �

4ππ

λλ �

2

(B-1)

and the corresponding distance is

= λλ�llff

4ππ

(B-2)

where λλ is the wavelength in the same units as .

B.2 General Propagation Models

There are a number of general propagation models used for practical terrestrial propagation paths 

with irregular terrain and atmospheric effects. These models characterize path loss as 

llpp = llff (B-3)

where is the excess path loss due to line of sight, diffraction, and scattering losses, or in dB

LLpp( dd) = LLff + AA . (B-4)

The excess path loss covers both signal fading and signal enhancement and is modeled as a 

random variable whose statistics vary with location and time. The location variability is due to 

terrain and the time variability is due to atmospheric effects. In the maritime case, location 

variability is insignificant but time variability is important. 

Table B-1 lists some commonly used general propagation models including Recommendation 

ITU-R P.1812 [B-1], ITU-R P.1546 [B-2], and ITU-R P.452 [B-3] models, used by the ITU-R, 

and the ITS Irregular Terrain Model (ITM) [B-4], [B-5], [B-6], [B-7] used by the ITS. The 

models are valid over the listed frequency range. All account for smooth earth diffraction and so 

are valid at distances beyond the radio horizon. Unless otherwise noted, the models include 

tropospheric scatter, surface ducting, and elevated ducting.

Among the many differences in these models, the features that were most important to us were 

the mode of operation, i.e. point-to-point or point-to-area, and excess attenuation. Our analysis 

57
requires point to area mode with both fading and enhancement. ITS-ITM was the only 

propagation model that satisfied these requirements.

Table B-1. General propagation models. P2P is point-to-point mode and P2A is point-to-area 

mode.

Model Frequency range P2P P2A Fading Enhancement Note

ITU-R P.1812 30 MHz-3 GHz Yes No No Yes No gaseous absorption

ITU-R P.452 700 MHz-50 GHz Yes No No Yes

ITS-ITM 20 MHz-20 GHz Yes Yes Yes Yes

ITU-R P.1546 30 MHz-3 GHz No Yes No Yes

B.3 References

[B-1] International Telecommunication Union, “A path-specific propagation prediction method 

for point-to-area terrestrial services in the VHF and UHF bands,” Recommendation ITUR P.1812-2, February 2012.

[B-2] International Telecommunication Union, “Method for point-to-area predictions for 

terrestrial services in the frequency range 30 MHz to 3000 MHz,” Recommendation ITUR P.1546-4, October 2009.

[B-3] International Telecommunication Union, “Prediction procedure for the evaluation of 

interference between stations on the surface of the Earth at frequencies above about 0.1 

GHz,” Recommendation ITU-R P.452-14, October 2009.

[B-4] P.L. Rice, A.G. Longley, K.A. Norton, and A.P. Barsis,”Transmission loss predictions 

for tropospheric communication circuits,” NBS Technical Note 101, Vol. I, Jan. 1, 1967, 

http://www.its.bldrdoc.gov/publications/2726.aspx.

[B-5] P.L. Rice, A.G. Longley, K.A. Norton, and A.P. Barsis,”Transmission loss predictions 

for tropospheric communication circuits,” NBS Technical Note 101, Vol. II, Jan. 1, 1967, 

http://www.its.bldrdoc.gov/publications/2727.aspx.

[B-6] A.G. Longley and P.L. Rice, “Prediction of tropospheric radio transmission loss over 

irregular terrain,” ESSA Tech. Report ERL 79-ITS 67, July 1968, 

http://www.its.bldrdoc.gov/publications/2784.aspx.

[B-7] G.A. Hufford, A.G. Longley, and W.A. Kissick, “A Guide to the use of the ITS irregular 

terrain model in the area prediction mode,” NTIA Report 82-100, April 1982, 

http://www.its.bldrdoc.gov/publications/2091.aspx.

58
APPENDIX C: IRREGULAR TERRAIN MODEL

The Irregular Terrain Model (ITM) radio wave propagation model [C-1]–[C-4] characterizes 

path loss, llpp, as a random variable. The randomness is due to changes in time, location, and 

situation.

3 Mathematically the path loss is

llpp = llff (C-1)

where llff is free space loss and is the excess path-loss or attenuation random variable. Written 

in decibels we have

LLpp( dd) = LLff + AA . (C-2)

The random variable AA is defined as

AA = �

AA′ AA′ > 0

AA′ � 29 − AA′

29 − 10AA′

� oo h (C-3)

where

AA′ = AArr − VVmm − YYTT − YYLL − YYSS. (C-4)

AArr is the reference attenuation that characterizes line of sight, diffraction, and scatter loss, 

VVmm is a climatic adjustment to the reference attenuation, and YYTT, YYLL, and YYSS are time, location, 

and situation variability deviates. All factors are dependent on distance and climate.

The attenuation for a specific fraction of times, locations, and situations is written as 

AA(qqTT, qqLL, qqSS). In the maritime temperate climate, variability in either location or situation is 

minimal so we are left with only time variability which we abbreviate AA(qqTT) and is computed 

from 

AA′ = μμ − YYTT (C-5)

where μμ = AArr − VVmm .

The time variability deviate, YYTT, is zero mean and log normally distributed

ff(YYTT) = 1

√2ππσσ ee �

−YYTT

2

2σσ2 �. (C-6)

3 Situation refers to considerations not accounted for by other model parameters such as receiver design, antenna 

mounting, and operator experience.

59

 
In terms of the standard normal deviate, zzTT, we have

YYTT(qqTT) = σσTTzzTT (C-7)

where

qqTT = PP {ZZTT ≥ zzTT} = QQ(zzTT) (C-8)

and

QQ( ) = PP {XX ≥ } = 1

√2ππ

� −tt2

2� ∞

. (C-9)

In practice, YYTT is only approximately normal since the mechanisms that give rise to signal fading 

where qqTT ≤ 0.5 and zzTT ≤ 0 are different from the mechanisms that give rise to signal 

enhancements where qqTT > 0.5 and zzTT > 0. Enhancement is also complicated by ducting 

phenomena that occur qqDD of the time when zzTT > zzDD.

In order to maintain the ease of computation that the standard normal deviate affords, the 

distribution is divided into three normally distributed segments corresponding to fading, 

enhancement, and ducting phenomena. Each segment has its own pseudo-standard deviation. The 

ducting segment has two terms.

The expression for YYTT is

YYTT = �

σσTT−zzTT, zzTT ≤ 0 (ff ff )

σσTT+zzTT, 0 < zzTT ≤ zzDD ( h )

σσTT+zzDD + σσTT (zzTT − zzDD), zzTT > zzDD ( dd )

(C-10)

where σσTT−, σσTT+, and σσTT are the fading, enhancement, and ducting pseudo-standard deviations.

The pseudo-standard deviations have the ordering σσTT− < σσTT+ < σσTT . In other words fading 

causes the least variation in signal level and ducting the most.

To generate a random AA at distance for Monte Carlo analysis, the parameters μμ, σσTT−, σσTT+,

σσTT , and zzDD are obtained from the propagation model and the deviate zzTT is obtained from a 

Gaussian random number generator. In the temperate maritime case qqDD is 0.9 and zzDD is 1.28. The 

deviate, zzTT, is tested to determine whether it is in the fading, enhancement, or ducting regions

and the appropriate expression is then used to determine YYTT.

C.1 References 

[C-1] P.L. Rice, A.G. Longley, K.A. Norton, and A.P. Barsis,”Transmission loss predictions 

for tropospheric communication circuits,” NBS Technical Note 101, Vol. I, Jan. 1, 1967.

http://www.its.bldrdoc.gov/publications/2726.aspx

60
[C-2] P.L. Rice, A.G. Longley, K.A. Norton, and A.P. Barsis,”Transmission loss predictions 

for tropospheric communication circuits,” NBS Technical Note 101, Vol. II, Jan. 1, 1967, 

http://www.its.bldrdoc.gov/publications/2727.aspx.

[C-3] A.G. Longley and P.L. Rice, “Prediction of tropospheric radio transmission loss over 

irregular terrain,” ESSA Tech. Report ERL 79-ITS 67, July 1968.

[C-4] G.A. Hufford, A.G. Longley, and W.A. Kissick, “A Guide to the use of the ITS irregular 

terrain model in the area prediction mode,” NTIA Report 82-100, April 1982, 

http://www.its.bldrdoc.gov/publications/2091.aspx.

61
APPENDIX D: RADAR SNR

Radar performance is quantified by probability of detection, PPdd, and probability of false alarm, 

PPffff. The signal to noise ratio (SNR) required to achieve a performance level is largely 

determined by the type of integration, i.e., coherent or non-coherent, number of pulses

integrated, nnpp, and radar cross section (RCS) fluctuation.

This Appendix describes a method for computing the average SNR for non-coherent integration 

and Swerling1 RCS fluctuation. The method begins with estimating the SNR needed to envelope 

detect a non-fluctuating target without integration. We then adjust the SNR with estimates of 

integration gain and fluctuation loss [D-1].

Regarding SNR nomenclature, the SNR for a steady Swerling 0 target before integration is 

referred to as γγ0�nnpp� and after integration is γγ0(1). Similarly, the average SNR for a fluctuating 

or Swerling 1 target before integration is γγ1�nnpp� and after integration is γγ1(1). Our goal is to 

compute γγ1�nnpp�.

For clarity the method is explained in three sections: definitions, intermediate expressions, and 

final expressions.

D.1 Definitions

We begin with definitions for integration improvement gain, integration loss, and fluctuating loss

[D-2]. Integration improvement gain is the gain realized by pulse integration when detecting a 

steady Swerling 0 target. 

ggii (nnpp) ≝ γγ0(1)

�γγ0(nnpp)

. (D-1)

The corresponding integration loss is defined as

llii (nnpp) ≝ nnpp

�ggii (nnpp) (D-2)

For coherent integration, improvement gain is nnpp and therefore lossless.

Fluctuation loss is the loss in detecting a fluctuating target relative to a steady target when the 

average RCS of the fluctuating target is equivalent to the RCS of the steady target. Without 

integration it is

llff(1) ≝ γγ1(1)

γγ0(1) � (D-3)

and with integration it is

62
llff(nnpp) ≝ γγ1(nnpp)

γγ0(nnpp) � . (D-4)

D.2 Intermediate Expressions

We have at our disposal expressions for γγ0(1), γγ1(1), ggii �nnpp�, and llff�nnpp� which can be used in 

conjunction with the definitions above to solve for γγ1(nnpp). The SNR needed to envelope detect a 

non-fluctuating target without integration, γγ0(1), can be estimated with the empirically derived 

expression [D-3]

γγ0(1) = AA + 0.12AA + 1.7 (D-5)

where AA = ln�0.62⁄PPffff� and = ln[PPdd⁄(1 − PPdd)]. This expression is accurate to within 0.2 

dB for PPffff between 10-3 and 10-7

, and PPdd between 0.1 and 0.9.

The average SNR, γγ1(1), can be determined from the exact solution for a Swerling 1 target 

without integration by [D-2]

PPdd =

ln�PPff �

�1+ γγ1(1)� . (D-6)

Rearranging terms

γγ1(1) = ln� PPff �

ln( PPdd) − 1. (D-7)

The integration improvement gain, ggii �nnpp�, for non-coherent integration and a Swerling 0 

target can be estimated with the empirically derived approximation [D-4]

GGii �nnpp� = 6.79[1 + 0.253PPdd] �1 +

log10 �1

PPffff � �

46.6 � log10�nnpp� �1

− 0.14 log10�nnpp� + 0.0183�log10�nnpp��

2

� ( dd)

(D-8)

where GGii �nnpp� = 10 log10 ggii (nnpp). This approximation is accurate to within 0.8 dB for PPffff = 

10-2, 10-4, 10-6, 10-8, and 10-10 for all values of PPdd = 0.5, 0.7, 0.9, 0.99, and 0.999 and nnpp = 1, 3, 

10, 30, and 100.

And finally, the fluctuation loss with integration relative to the fluctuation loss without 

integration for the Swerling 1 targets is [D-2]

llff�nnpp� = llff(1)(1+αα) (D-9)

63
or

llff�nnpp� = �

γγ1(1)

γγ0(1) � �

(1+αα)

(D-10)

where αα = 0.035 log10(nnpp).

D.3 Final Expressions

We will now show how the definitions and intermediate expressions can be used to solve for the 

SNR before integration, γγ1(nnpp). Beginning with (D-4) 

γγ1�nnpp� = γγ0(nnpp)llff(nnpp) (D-11)

then 

γγ1�nnpp� = γγ0(1)llff(nnpp)

ggii (nnpp) (D-12)

or

γγ1�nnpp� = γγ0(1)llii (nnpp)llff(nnpp)

nnpp

(D-13)

Performance for the radar in this report, calculated with this method, is shown in Figure D-1. The 

figure shows that the average SNR for PPdd = 0.8 and PPffff = 10-4 is 10.0 and 7.6 dB for 6 and 14 

non-coherently integrated pulses, respectively.

64
Figure D-1. Radar PPdd with Swerling 1 target, non-coherent integration of 6 and 14 pulses, and

10-4 PPffff.

D.4 Other Considerations

The SNR, γγ1�nnpp�, is the SNR required at the input to the receiver without signal processing 

losses. With signal processing losses, ll , the SNR required at the input to the receiver is 

ww = γγ1�nnpp�ll (D-14)

or

ww = γγ0(1)llii (nnpp)llff(nnpp)ll

nnpp

(D-15)

Possible sources of processing loss include one or more of the following: the IF filter not being 

matched to the transmitted pulse shape, the digitizer missing the highest signal, or the constant 

false alarm rate function misestimating the detection threshold.

D.5 References

[D-1] D.K. Barton, “Simple procedures for radar detection calculations,” IEEE Trans. On 

Aerospace and Electronic Systems, Vol. AES-5, No. 5, Sept. 1969, pp. 837-846.

[D-2] D.K. Barton, “Theory of Target Detection” in Radar System Analysis and Modeling, 

Artech House, Boston, MA, 2005.

65
[D-3] M.L. Skolnik, “The radar equation,” Chapter 2 in Introduction to Radar Systems, Third 

Edition, McGraw Hill, New York, N.Y., 2001.

[D-4] P.Z. Peebles, Radar Principles, John Wiley Inc., New York, N.Y., 1998, pp. 401-402.

66
NTIA FORM 29 U.S. DEPARTMENT OF COMMERCE 

(4-80) NATIONAL TELECOMMUNICATIONS AND INFORMATION ADMINISTRATION

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION NO.

TR-15-513

2. Government Accession No. 3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

Effect of Broadband Radio Service Reallocation on 2900–3100 MHz band Marine 

Radars: Background

5. Publication Date

April 2015

6. Performing Organization Code

NTIA/ITS.T

7. AUTHOR(S)

Robert Achatz, Paul McKenna, Roger Dalke, Nicholas DeMinco, Frank Sanders, John 

Carroll

9. Project/Task/Work Unit No.

3105011-300

8. PERFORMING ORGANIZATION NAME AND ADDRESS

Institute for Telecommunication Sciences

National Telecommunications & Information Administration

U.S. Department of Commerce

325 Broadway

Boulder, CO 80305

10. Contract/Grant Number.

11. Sponsoring Organization Name and Address

U.S. Coast Guard Spectrum Management Telecommunications Policy Division

U.S. Coast Guard CG-652,

2100 2nd St. SW Stop 7101

Washington, DC 20593-7101

12. Type of Report and Period Covered

14. SUPPLEMENTARY NOTES

15. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or 

literature survey, mention it here.)

Spectrum reallocations may place broadband radio services (BRS) near spectrum used by 2900–3100 MHz band marine 

radars. Interference effects from these reallocations include unwanted emissions in the radar detection bandwidth and frontend overload. This report provides background information for subsequent reports that analyze these effects. Interference 

protection criteria (IPC) are identified, an interference scenario is described, and models for the radar system, BRS system,

radar target, and radio wave propagation are presented. The BRS signal is shown to be reasonably emulated by Gaussian 

noise. A method for determining the aggregate power distribution using a realistic propagation model and Monte Carlo 

analysis is described. The aggregate power from the base stations was found to be as much as 6 dB more than power from a 

single base station. Finally a method for incorporating a variable SNR, caused by variable radar to target path loss, into 

interference analysis is shown.

16. Key Words (Alphabetical order, separated by semicolons)

aggregate power, broadband radio service, front-end overload, interference, interference protection criteria, marine radar, 

radar, radio spectrum engineering, radio wave propagation, signal characterization, unwanted emissions

17. AVAILABILITY STATEMENT

UNLIMITED.

FOR OFFICIAL DISTRIBUTION.

18. Security Class. (This report)

Unclassified

20. Number of pages

87

19. Security Class. (This page)

Unclassified

21. Price:

N/A
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