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

report series

NTIA Report TR-14-500

Spectrum Occupancy Measurements of 

the 3550–3650 Megahertz Maritime 

Radar Band near San Diego, California

Michael Cotton

Roger Dalke

U.S. DEPARTMENT OF COMMERCE

January 2014

NTIA Report TR-14-500

Spectrum Occupancy Measurements of 

the 3550–3650 Megahertz Maritime 

Radar Band near San Diego, California

Michael Cotton

Roger Dalke

iii

DISCLAIMER

Certain commercial equipment, instruments, or materials are identified in this report to

adequately describe the experimental procedure. 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 necessarily

the best available for the purpose.

ACKNOWLEDGEMENTS

This investigation required the services of a number of ITS engineers, some of whom are not 

included in the list of authors. The authors recognize Frank Sanders for his overall expertise in 

radar systems and his complete understanding of spectrum analyzer functionality especially for 

the purpose of radar detection. The authors also acknowledge Geoff Sanders for the development 

of software for instrument control, Jeffery Wepman for is his expertise in test and measurement 

equipment, and Paul McKenna for his knowledge of radiowave propagation.

v

CONTENTS

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

List of Tables ................................................................................................................................. ix

Variables and Acronyms................................................................................................................. x

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

1.1 Background........................................................................................................................... 2

1.2 Organization of this Report................................................................................................... 2

2 SPN-43 System Description ........................................................................................................ 4

3 Measurement Strategy ................................................................................................................. 5

3.1 System Description............................................................................................................... 5

3.2 Measurement Procedure ....................................................................................................... 6

3.2.1 System Calibration ...................................................................................................... 6

3.2.2 Frequency-Swept Occupancy Measurements ............................................................. 8

3.2.3 Time-Domain Signal Characterization Measurements ............................................... 9

3.3 Range of Detection ............................................................................................................. 11

4 Observed Signal Patterns........................................................................................................... 13

4.1 Calibration Data.................................................................................................................. 13

4.2 Measurement Time Resolution........................................................................................... 14

4.3 Spectrogram of Full Frequency-Swept Data Set ................................................................ 14

5 Statistical Considerations for Spectrum Occupancy Measurements ......................................... 17

5.1 Renewal Theory and the Definition of Channel Occupancy .............................................. 17

5.2 Estimation of Channel Occupancy ..................................................................................... 18

5.3 Estimation of Band Occupancy .......................................................................................... 19

6 Measurement Results................................................................................................................. 21

6.1 Band Occupancy................................................................................................................. 21

6.1.1 Daily Means .............................................................................................................. 21

6.1.2 Two-Week Statistics.................................................................................................. 22

6.2 Channel Occupancy ............................................................................................................ 24

6.2.1 Example Calculations................................................................................................ 24

6.2.2 Channel Occupancy Statistics versus Frequency ...................................................... 25

6.3 Time Intervals..................................................................................................................... 27

7 Summary.................................................................................................................................... 31

8 References.................................................................................................................................. 32

APPENDIX A: Channel Occupancy in the Context of Renewal Theory..................................... 33

A.1 Setup .................................................................................................................................. 33

A.2 Satisfying the Renewal Equation ....................................................................................... 34
vi

A.3 Asymptotic Behavior of the Renewal Process................................................................... 36

APPENDIX B: Confidence Intervals for Channel Occupancy Estimates.................................... 37

B.1 Assuming Independent Sampling in Time......................................................................... 38

B.2 Assuming Dependent Sampling in Time ........................................................................... 39

APPENDIX C: Daily Signal-Level and Band Occupancy Plots.................................................. 42
vii

LIST OF FIGURES

Figure 1. S-Band radar spectrum. ................................................................................................... 4

Figure 2. Block diagram of radar occupancy measurement system. .............................................. 5

Figure 3. Peak-to-average ratio of complex Gaussian noise versus dwell time and 

bandwidth...................................................................................................................... 7

Figure 4. Example frequency-swept occupancy measurement....................................................... 8

Figure 5. Example rotation period measurement.......................................................................... 10

Figure 6. Example pulse-interval measurement............................................................................ 10

Figure 7. Example pulse-width measurement............................................................................... 11

Figure 8. Irregular Terrain Model predictions of basic transmission loss versus range and 

distance to line-of-sight edge for different terminal heights....................................... 12

Figure 9. (Top) Calibration data acquired during San Diego measurement and (Bottom) 

maximum measured power levels compared to system dynamic range. .................... 13

Figure 10. Probability distribution of time between measurements. ............................................ 14

Figure 11. Measured signals in the 3.6 MHz band on June 8–21, 2012, near San Diego. ........... 16

Figure 12. Channel transmissions and related time intervals. ...................................................... 17

Figure 13. Probability distributions of band occupancy measured during weekdays on 

June 8–21, 2012, near San Diego................................................................................ 23

Figure 14. Probability distributions of band occupancy measured during weekends on 

June 8–21, 2012, near San Diego................................................................................ 23

Figure 15. Transition probability ( - ) versus frequency on June 8–21, 2012, 

near San Diego............................................................................................................ 26

Figure 16. Channel occupancy estimates ( - ) with 90% confidence intervals 

versus frequency on June 8–21, 2012, near San Diego. ............................................. 26

Figure 17. Channel occupancy estimates versus frequency at various threshold levels on 

June 8–21, 2012, near San Diego................................................................................ 27

Figure 18. Measured mean transmission intervals ( - ) versus frequency on 

June 8–21, 2012, near San Diego................................................................................ 28

Figure 19. Probability distributions of transmission intervals (f = 3.59 GHz, L = -83 dBm) 

measured during weekdays on June 8–21, 2012, near San Diego. Dashed lines 

are corresponding exponential distributions. .............................................................. 29

Figure 20. Probability distributions of transmission intervals (f = 3.57 GHz, 

- ) measured during weekdays on June 8–21, 2012, near San Diego. 

Dashed lines are corresponding exponential distributions.......................................... 30

Figure A-1. Renewal process X(t) and associated transmission interval random variables. ........ 33

Figure A-2. Sample function of a renewal process....................................................................... 34

Figure B-1. Illustration of confidence interval (c1, c2) for parameter p........................................ 38

Figure B-2. for N = 738 and demonstrating the difference between 

independent and dependent sampling. ........................................................................ 41

Figure C-1. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 

8, 2012......................................................................................................................... 43

Figure C-2. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 8, 2012.................................................................................. 43

Figure C-3. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 

9, 2012......................................................................................................................... 44
viii

Figure C-4. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 9, 2012.................................................................................. 44

Figure C-5. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 

10, 2012....................................................................................................................... 45

Figure C-6. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 10, 2012................................................................................ 45

Figure C-7. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 

11, 2012....................................................................................................................... 46

Figure C-8. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June11, 2012................................................................................. 46

Figure C-9. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 

12, 2012....................................................................................................................... 47

Figure C-10. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 12, 2012................................................................................ 47

Figure C-11. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on 

June 13, 2012. ............................................................................................................. 48

Figure C-12. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 13, 2012................................................................................ 48

Figure C-13. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on 

June 14, 2012. ............................................................................................................. 49

Figure C-14. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 14, 2012................................................................................ 49

Figure C-15. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on 

June 15, 2012. ............................................................................................................. 50

Figure C-16. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 15, 2012................................................................................ 50

Figure C-17. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on 

June 16, 2012. ............................................................................................................. 51

Figure C-18. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 16, 2012................................................................................ 51

Figure C-19. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on 

June 17, 2012. ............................................................................................................. 52

Figure C-20. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 17, 2012................................................................................ 52

Figure C-21. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on 

June 18, 2012. ............................................................................................................. 53

Figure C-22. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 18, 2012................................................................................ 53

Figure C-23. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on 

June 19, 2012. ............................................................................................................. 54

Figure C-24. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 19, 2012................................................................................ 54

Figure C-25. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on 

June 20, 2012. ............................................................................................................. 55

Figure C-26. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 20, 2012................................................................................ 55
ix

Figure C-27. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on 

June 21, 2012. ............................................................................................................. 56

Figure C-28. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured 

near San Diego on June 21, 2012................................................................................ 56

LIST OF TABLES

Table 1. SPN-43 design parameters [5]. ......................................................................................... 4

Table 2. Radar occupancy measurement system parameters.......................................................... 6

Table 3. Frequency-swept measurement parameters...................................................................... 8

Table 4. Time-domain measurement parameters............................................................................ 9

Table 5. Daily mean band occupancy data. .................................................................................. 22

Table 6. Band occupancy statistics for June 8–21, 2012, near San Diego. .................................. 22

Table 7. Channel occupancy statistics , c1, and c2for 90% confidence p and -83 dBm 

threshold measured in June 2012 near San Diego. ..................................................... 24

Table 8. Mean time intervals (L = -83 dBm) measured in June 2012 near San Diego................. 28
x

VARIABLES AND ACRONYMS

 Convolution operator

 Band occupancy

 Earth’s actual/effective curvature

 Pulse width

 Complimentary confidence interval

 Average rate of arrival in a Poisson counting process

 Number of successes in a Bernoulli experiment

 Microseconds (10-6seconds)

  Measured sample function of channel occupancy

 Time between samples

 Transition probabilities in the steady-state equations for a 1st order Markov chain

 Cumulative distribution function of the standard normal deviate

 Outcome of an experiment

 Set of possible outcomes of an experiment

ASR Airport Surveillance Radar

ATC Air Traffic Control

 Resolution bandwidth in context of spectrum analyzer measurements

 Noise equivalent bandwidth

 Speed of light

 Confidence limits

cdf Cumulative distribution function

 Distance to the edge of the line-of-sight region

dB Decibel; logarithmic unit used to expressed the ratio between two values

dBi Power ratio in decibels relative to isotropic radiator

dBm Power ratio in decibels of measured power referenced to one milliwatt
xi

 Domain in ̂plane that defines confidence intervals

 Base of the natural logarithm function

 { } Expected value operator

ENR Excess Noise Ratio

 Frequency

 Frequency of the maximum level of the k

th signal measured in a FS measurement

 { } Probability density function of random variables , , or 

 Noise figure

 { } Cumulative distribution function of random variables , , or 

FCC Federal Communications Commission

FS Frequency-swept (measurement)

 ̂ Joint probability density function of and ̂

 Gain (of measurement system in the context of this report)

 Gain of antenna (SPN-43 antenna in the context of this report)

 Gain of receive antenna

 Gain of transmit antenna

GHz Gigahertz (109hertz)

 Antenna height above sea level of terminal {1, 2}

iid Independent and identically distributed

ISART International Symposium on Advanced Radio Technologies

ITM Irregular Terrain Model

ITS Institute for Telecommunication Sciences

k Boltzmann’s constant or counting variable (depending on context)

 Occupancy threshold(s)

 Basic transmission or propagation loss

 Cable loss (of cable between antenna and front end of measurement system)
xii

 Loss in a LOS scenario governed by free-space propagation loss

 Loss due to polarization mismatch

LNA Low noise amplifier

LOS Line of Sight

LTE Long Term Evolution

 Mean band occupancy

 Mean transmission length

 Mean time between transmissions

 Mean inter-arrival time estimator

MHz Megahertz (106hertz)

 Number of measurements or trials

 Number of channels

 Number of renewals

NEXRAD NEXt generation RADar

NTIA National Telecommunications and Information Administration

 Probability channel is occupied, channel occupancy

 ̂ Channel occupancy estimate

 Mean system noise power or RMS-detected system noise

 Measured mean power with input signal on/off (Y-factor calibration method)

 Mean power received

 Mean power transmitted

 { } Probability operator

 { } Conditional probability operator

pdf probability density function

 Probability channel is vacant

 Maximum signal level of the k

th signal in a peak-detected FS measurement
xiii

 Peak-detected power from a frequency-swept peak-measurement

 Peak-detected system noise power

 Range

 Minimum/Maximum detectable range

RF Radiofrequency

RMS Root Mean Square

SA Spectrum Analyzer

SPN-43 Maritime air-marshaling radar that operates in the upper S-band

 Time

 Set of possible times

 Dwell time

 Temperature (Kelvin) or time interval a channel is observed

 Antenna rotation period

 Pulse interval or period

 Transmission length

 { } Variance operator

 Time between transmissions

WiMAX Worldwide Interoperability for Microwave Access

 Channel occupancy random process

 Y factor (Y-factor calibration method)

 Renewal time

SPECTRUM OCCUPANCY MEASUREMENTS OF THE 3550–3650 MEGAHERTZ 

MARITIME RADAR BAND NEAR SAN DIEGO, CALIFORNIA

Michael Cotton and Roger Dalke1

This report presents spectrum occupancy data of the 3550–3650 megahertz (MHz) 

maritime radar band measured in June 2012 near San Diego. In this band, the 

military operates SPN-43 air marshaling radar systems with well-defined signal 

characteristics. A measurement system and frequency-swept technique were 

designed specifically to detect SPN-43 emissions. Over the two-week 

measurement duration in June 2012, we observed multiple systems operating 

simultaneously in band, spectral spreading of SPN-43 emissions, and out-of-band 

pulsed emissions that spanned the entire band of interest. In this presumably highusage mostly military spectrum environment and at a low occupancy threshold 

(i.e., -83 dBm in a 1 MHz bandwidth at the output of a 2 dBi antenna), mean band 

occupancy was {36.6, 7.5}% during {weekdays, weekends}. There was a {40.0, 

59.8}% chance that the band was empty and a {18.4, 2.3}% chance that the band 

was full. During weekdays, spectrum usage was dominated by out-of-band pulsed 

transmissions that spanned the entire band at a relatively low level (approximately 

10 dB above the low threshold level). These signals were superimposed on the 

stronger SPN-43 signals. On average during weekdays, transmissions occurred

every four hours with a mean transmission length of approximately 1.5 hours. In 

contrast, weekend spectrum usage was primarily SPN-43 transmissions at 3.59 

GHz arriving every 29 hours (on average) with a mean transmission length of 

approximately 9 hours. Measured SPN-43 signal amplitudes were at times strong 

enough to overload the measurement system (exceeding the -83 dBm threshold 

level by more than 60 dB). Statistical considerations that arise when measured 

data are used to characterize spectrum occupancy are also discussed in this report. 

Covered topics include channel occupancy definition, estimation, and uncertainty. 

Key words: spectrum occupancy, maritime radar, spectrum management.

1 INTRODUCTION

The purpose of this report is to provide measured occupancy data on systems operating in the 

3550–3650 megahertz (MHz) maritime radar band (henceforth called 3.6 GHz band) in support 

of the development of well-engineered spectrum rules and decisions. 

 

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

Administration, U.S. Department of Commerce, Boulder, CO 80305.
2

1.1 Background

The 3.6 GHz band was identified as a candidate to accommodate wireless broadband systems in 

the National Telecommunications and Information Administration (NTIA) 2010 Fast Track 

Evaluation Report [1] and was a focus of the President’s Council of Advisors on Science and 

Technology (PCAST) 2012 report on realizing the full potential of government-held spectrum to 

spur economic growth [2]. Radar spectrum management and usage, in general, was also the topic 

for discussion in the 2011 International Symposium of Advanced Radio Technologies (ISART) 

[3], hosted by NTIA’s Institute for Telecommunication Sciences (ITS) with the purpose of 

developing forward-thinking rules and processes to fully exploit spectrum resources. More 

recently, the Federal Communications Commission (FCC) inquired about the possibility of new

commercial entrants using the 3.6 GHz band in ways that do not conflict with maritime military 

operations [4]. 

Incumbent SPN-43 systems in the 3.6 GHz band are U.S. Navy shipborne mobile installations

constrained geographically to U.S. littoral waters and navigable rivers. Spectrum sharing could 

be coordinated via geographic separation as described by the exclusion zones in [1]. However, 

over 55% of the U.S. population is concentrated within 50 miles of the coastline [3]. Hence, a 

spectrum sharing scheme limited to geographic separation via exclusion zones along the coast 

would exclude large markets, rendering the sharing scenario somewhat unfulfilling. Alternatively 

and in addition, temporal or dynamic coordination for systems operating inside the exclusion 

zones has been proposed [2] [3]. Given the importance and mobility of the incumbent systems, 

successful deployment of this type of dynamic coordination would require large investment to 

thoroughly evaluate the electromagnetic compatibility between the incumbent and entrant 

systems, negotiate acceptable conditions for sharing, and develop a sophisticated and secure 

sharing scheme that satisfies all stakeholders.

Before that level of investment and work can be justified, information about incumbent 

operations and usage patterns should be assessed. Toward that end, we present in this report 

spectrum measurements of the 3.6 GHz band performed over two weeks in June 2012 near San 

Diego, which is presumed to be a relatively high-usage environment given the close proximity to 

the San Diego Naval base.

1.2 Organization of this Report

In this report, we provide information and results in an increasingly rigorous fashion to develop a 

framework for measuring and modeling spectrum usage in general and (more specifically) to 

characterize how military incumbents are currently using this band near San Diego. Section 2 

provides SPN-43 system and operational parameters that are required to design an appropriate 

detection scheme optimized to detect these systems. Section 3 describes the overall measurement 

methodology, which includes system design and calibration, detection scheme and parameters, 

data acquisition procedures, and range of detection calculations. Section 4 presents observed 

signal patterns on a qualitative level for the entire two-week measurement. Data presented in this 

section include measured calibration data, maximum received signal power and system overload 

indicators, measurement time resolution, and measured signal levels versus time and frequency.
3

Next, we develop the theoretical framework to reduce the data to a meaningful set of statistics 

and estimates with quantified uncertainties. In Section 5 and supported by Appendices A and B,

we define channel occupancy in the context of renewal theory. Both channel and band 

occupancy concepts are developed according to whether or not a received signal level exceeds a 

pre-specified threshold, which allows for the problems to be modelled as a sequence of 0s and 

1s. More specifically, channel occupancy estimation reduces to counting the number of successes

in N Bernoulli trials for which many theoretical results are available. We develop estimation of 

channel occupancy from measurement of limited duration and discuss confidence in the estimate 

with consideration to dependent versus independent sampling assumptions.

Finally, Section 6 provides quantitative measurement results according to the theory established 

in Section 5. First, daily mean band occupancy statistics (Section 6.1.1) and plotted results 

(Appendix C) provide adequate information to develop assumptions on the stationarity in time of 

the underlying spectrum usage process. Specifically, the results call for a separation of weekday 

and weekend data, on which we follow through in the remainder of the data processing. Section 

6.1.2 provides weekday and weekday band occupancy statistics for the full two-week 

measurement duration. Section 6.2 provides channel occupancy estimates with 90% confidence 

intervals versus frequency. Finally, Section 6.3 gives mean transmission interval estimates versus 

frequency. Section 7 is an overall summary of our findings.
4

2 SPN-43 SYSTEM DESCRIPTION

It is necessary to understand the signals one aims to measure in order to design the optimal 

measurement strategy. The frequency band of interest is within the S-band radar spectrum 

(shown in Figure 1). Major systems that operate in the lower S-band from 2.7 to 2.9 GHz include 

NEXRAD, airport surveillance radar (ASR), and GPN (where G = ground, P = radar, and N = 

navigation according to the military naming convention) systems. The upper S-band, ranging 

from 2.9 to 3.65 GHz, is used for radiolocation; maritime surface search; aerial- and groundbased navigation; air traffic control (ATC); and short-range artillery search, track, and warning. 

Figure 1. S-Band radar spectrum.

The military operates SPN-43 air marshaling radar systems in a 150 MHz band from 3.5 to 3.65 

GHz. SPN-43 radar systems are mobile shipborne radar systems (primarily installed on U.S. 

Navy Aircraft Carriers), which can be located in all U.S. littoral waters and navigable rivers. 

SPN-43 transmits high-power pulses through a high-gain antenna that spins azimuthally at a 

constant rate. Table 1 summarizes SPN-43 design parameters.

Table 1. SPN-43 design parameters [5].

Transmitter

Tuning Range 3.5-3.65 GHz

Pulse Generation Method Magnetron

Pulse Interval, Tp 889 (±20) μs

Pulse Width, 0.9 (±0.15) μs

Power, PT 850 (±150) kW

Antenna

Polarization Horizontal or circular, switchable

Gain (boresight), Ga 32 dBi

Rotation Period, Ta 4 s
5

3 MEASUREMENT STRATEGY

San Diego was chosen as the measurement location because of the close proximity to the San 

Diego Naval base. Point Loma provided a good location for the measurement equipment with a 

180 degree field of view over the ocean where ships with the radar travel. The measurements 

were performed over a course of two weeks in June 2012. 

This section provides a full description of the radar occupancy measurement system and 

procedure. The system was automated and designed to run continuously unless interrupted by the 

operator. User interaction (e.g., system monitoring, start/stop) occurred via a graphical user 

interface developed specifically for this measurement. At a high level, the 150 MHz SPN-43 

band was divided into 150 one-megahertz channels. This is thought to be a reasonable unit,

approximately equal to the reciprocal pulse width of the SPN-43. The measurement system 

acquired the peak power of each channel and declared the channel occupied if the received peak 

power exceeded a pre-determined threshold. 

3.1 System Description

Figure 2 is a block diagram of the radar occupancy measurement system. Moving from left to 

right in the RF path, the antenna was a vertically (linear) polarized omnidirectional antenna with 

65 degree beamwidth and a nominal gain of at the horizon. Note the polarization 

mismatch between the SPN-43 (horizontal linear or circular) and the measurement system. This

is accounted for with a minimum polarization mismatch factor (Lpol), given by manufacturer 

specification to be Lpol = {20, 3} dB for {horizontally, circularly} polarized signals.

Figure 2. Block diagram of radar occupancy measurement system.

The antenna was connected to one input of an RF switch, which switched between the antenna 

during occupancy measurements and a noise diode with a 13.7 dB excess noise ratio (ENR) 

during calibration measurements. The received signal then moved through a 3.5–3.65 GHz bandpass filter, through a low-noise amplifier (LNA), and finally to a spectrum analyzer (SA) that 

offered frequency-swept (FS) and time-domain peak- and sample-detection measurements. The 

LNA had 33 dB gain, 5 dB noise figure, and 30 dBm 1 dBm compression point. The LNA gain 
6

improved the sensitivity of the system, which included an SA with a 22 dB noise figure. The 

high LNA 1 dB compression point ensured that the SA overloaded before the LNA. The switch, 

power to noise diode, and SA were computer controlled to minimize human error, to allow for 

automated continuous measurements, and to monitor the system (e.g., for SA overloads.)

Table 2 provides a summary of the radar occupancy measurement system parameters. Regarding 

overall system parameters, the noise figure was nominally and system gain was 

approximately G = 28 dB. As indicated in the calibration measurement description (Section 

3.2.1), these parameters are referenced to the input of the front end. Dynamic range of the system 

was from -83 dBm to -22 dBm at the antenna terminal. All power levels provided in this report 

are referenced to the receive antenna terminal.

Table 2. Radar occupancy measurement system parameters.

Antenna

Polarization Vertical

Gain, 2 dBi

Cross-Polarization Loss, 20 dB

Cable Loss, 5 dB

Front End

Noise Diode – Excess Noise Ratio, ENR 13.7 dB

Band-Pass Filter – Frequency Range 3.5 – 3.65 GHz

Band-Pass Filter – Insertion Loss 1 dB

Low-Noise Amplifier – Gain 33 dB

Low-Noise Amplifier – Noise Figure 5 dB

Low-Noise Amplifier – 1 dB compression 30 dBm

System (front end and SA)

Gain, G 28 dB

Noise Figure, 7.5 dB

3.2 Measurement Procedure

The computer-controlled measurement system was designed to cycle through a well-defined 

procedure comprised of the following tasks: (1) hourly system calibration measurements, (2) FS

occupancy measurements, and (3) time-domain signal characterization measurements.

3.2.1 System Calibration

System calibration is important for monitoring system integrity and determining minimum 

occupancy thresholds. Once per hour, and G were measured via the Y-factor method [6]. In 

this method, the RF switch set the system input to the noise diode, dc power to the noise diode

was turned off and the SA measured mean power . Next, dc power to the noise diode was 

turned on and the SA measured mean power . The mean power measurements were 

performed at the center frequency of each of the 150 one-megahertz channels using the SA root 

mean square (RMS) detector with a 1 MHz resolution bandwidth (B) and a 0.1 second averaging

time. 
7

Calibration results were calculated via

 

 

 

 

 

 

 

 (1)

where is the y-factor and Beq = 1.128B is the noise equivalent bandwidth for the 

SA utilized in this measurement [7]. and G provide the means to predict RMS- and peakdetected levels of the system noise. The mean noise power at the output of the receive antenna is

  (2)

where k is Boltzmann’s constant, T is temperature in Kelvin, and is loss in the cable that 

connects the antenna to the front end input.

The expected peak-detected system noise level is a function of dwell time (td) and B, i.e.,

 [ 

 ] (3)

where e ≈ 2.71828 is the base of the natural logarithm function (ln) [7]. Figure 3 illustrates 

 for parameters relevant to this measurement effort. As will be discussed later, td = {6 s, 5 

ms, 2 μs} for the three different peak-detected measurements performed during the automated 

measurement procedure. The peak-to-average ratios of the system noise in a 1 MHz bandwidth 

for these settings are = {12.5, 10.3, 4.9} dB.

Figure 3. Peak-to-average ratio of complex Gaussian noise versus dwell time and bandwidth.
8

3.2.2 Frequency-Swept Occupancy Measurements

The core measurement in this effort is the FS occupancy measurement with parameters provided 

in Table 3. Peak-detected data ( ) was acquired in a 1 MHz resolution bandwidth at each 

channel across the 150 MHz band. Dwell time was chosen to be to 

ensure that at least one radar antenna rotation period was captured during each channel 

measurement. Each sweep across the band took 15 minutes. Note that this peak detection scheme 

eliminates the effect of radar antenna rotation and pulse on/off from the spectrum occupancy 

calculation.

Table 3. Frequency-swept measurement parameters.

Measurement Detection Span 

(MHz)

Frequency Step

(MHz)

B

(MHz)

Dwell Time

(s)

Sweep Time

(s)

Occupancy Peak 150 1 1 6 900

Figure 4 gives an example FS measurement (blue curve). The horizontal grey band illustrates 

system noise bounded on the bottom by and on top by . In this example, there were two 

signals detected, each spanning a number of 1 MHz channels. The vertical red lines denote the 

frequency, , of the maximum level for the k

th observed signal ( ).

Figure 4. Example frequency-swept occupancy measurement.
9

The dashed green curve is the occupancy threshold which the control code sets to 

(calculated from the latest calibration measurement.) If we assume that the system noise is a 

complex Gaussian process, then the amplitude (squared) of the system noise is Rayleigh 

distributed with an amplitude probability distribution of

 { 

 } 

 

 

 

(4)

where { } is the probability operator. For the given measurement parameters, the probability of 

system noise power exceeding the threshold, i.e., { 

 

}, is on the order of 10-16

.

From this, it is reasonable to assume that the probability of peak-detected system noise 

exceeding is also negligible.

3.2.3 Time-Domain Signal Characterization Measurements

Subsequent to each FS measurement, signal characterization measurements were performed in 

the time domain at each to observe SPN-43 antenna rotation period ( ), pulse interval ( ), 

and pulse width ( ). Time-domain measurements were performed with the SA in zero-span 

mode and trigger level , i.e., 6 dB below the signal peak. This high trigger level ensured

that the time domain measurements were made when the radar antenna was pointing at the 

measurement system antenna. 

Table 4 provides measurement parameters, where time interval is dwell time for peak detection 

and time between samples for sample detection. SA settings were chosen according to known 

SPN-43 design parameters to optimize detection and acquire relevant information. Rotation 

period measurement dwell time was , which guaranteed that five pulses were available 

for observation. Pulse interval measurement dwell time was to ensure adequate 

resolution. Finally, the pulse width measurement sample rate provided approximately 200 

samples per pulse width. 

Table 4. Time-domain measurement parameters.

Measurement Detection B (MHz) Time Interval (μs) Number of Samples

Rotation Period Peak 1 5000 5000

Pulse Interval Peak 1 2 5000

Pulse Width Sample 8 0.005 5000

Figures 5, 6, and 7 give example time-domain signal characterization measurements of the 

signals at 3.52 GHz and 3.545 GHz. The signal at 3.52 GHz exhibits all the characteristics of a 

SPN-43 signal, while the signal at 3.545 GHz does not exhibit SPN-43 characteristics.
10

Figure 5. Example rotation period measurement. 

Figure 6. Example pulse-interval measurement. 
11

Figure 7. Example pulse-width measurement.

3.3 Range of Detection

In this section, we estimate the maximum detectable range at the occupancy threshold as well as 

the minimum range without overloading the system. This requires predicting propagation effects 

over the spherical Earth [8], which can be done with the Irregular Terrain Model (ITM) [9].

When considering long-range propagation over a spherical Earth, there are three range regions 

characterized by three different propagation mechanisms. Closest to the terminal of interest is the 

line-of-sight (LOS) region characterized by free-space-loss propagation, i.e.,

 (

 

 

)

 

 (5)

where r is range and c is the speed of light. The distance to the edge of the LOS region ( ) is 

dependent on antennae heights ( ) above sea level. More specifically,

 √ √  (6)

where ( 

 ) is the Earth's effective curvature, m

-1

is 

the Earth's actual curvature, Ns = 301 N-units is the minimum monthly mean surface refractivity, 

and - . The region outside LOS is the diffraction region, where loss increases 

steeply with range. Finally, the troposcatter range is characterized by energy that scatters forward 

from tropospheric inhomogeneities.
12

Figure 8 shows ITM results for link geometries relevant to the San Diego spectrum occupancy 

measurement, where we approximate SPN-43 antenna height above sea level at and 

the ITS measurement antenna height on Point Loma at . The left-hand plot displays 

basic transmission loss versus range for a variety of receiver antenna heights and illustrates the 

LOS, diffraction, and troposcatter regions. The right-hand plot presents versus , where 

 for the San Diego measurement geometry.

Received power can be estimated in linear units as

 

 

 

 

 (7)

where for the current scenario. At the edge of LOS, and 

received power is predicted to be {-38, -21} dBm for {horizontal linear, circular} polarized SPN43 signals with Lpol = {20, 3} dB. Working the inverse ITM problem, the minimum propagation 

loss to avoid overload (i.e., - ) is Lmin = {125, 142} dB, which translates to

approximately rmin = {12, 72} km from Figure 8. Similarly, the maximum propagation loss that 

results in the smallest detectable signal (i.e., - is Lmax = {186, 203} dB, which 

translates to rmax = {105, 206} km. Hence, the measurement system could detect horizontal 

polarized SPN-43 systems only 27 km beyond LOS but could detect circular polarized systems 

well into the troposcatter region.

Figure 8. Irregular Terrain Model predictions of basic transmission loss versus range and 

distance to line-of-sight edge for different terminal heights.
13

4 OBSERVED SIGNAL PATTERNS

In this section, the patterns of observed signals are demonstrated on a qualitative level. 

Calibration and maximum received signal power data illustrate system parameters and condition 

versus time. Next, measurement time resolution is presented. Finally, a spectrogram of the entire 

FS data set illustrates patterns in spectrum usage over the full two-week measurement duration.

4.1 Calibration Data

Figure 9 provides calibration results during the full course of the measurement campaign. The 

vertical shaded areas denote measurement downtimes. Downtimes were needed for system 

validation, code development, and hardware changes. Note that on Monday (6/11) around noon, 

we changed the amplifier in the front end to one that could tolerate higher power levels. The new 

amplifier had higher gain and a lower noise figure, which affected the overall system gain and 

noise figure as illustrated in the top plot.

The bottom graph in Figure 9 illustrates the system dynamic range for the FS measurement, 

which is bounded by on the low end and the spectrum analyzer overload level on the high 

end. Notice that the new amplifier improved the overall sensitivity, but reduced the maximum 

power the system could tolerate. The lower plot also provides the maximum power level of all 

channels measured during each FS measurement, i.e., max( ). There were seven overload 

events over the course of two weeks.

Figure 9. (Top) Calibration data acquired during San Diego measurement and (Bottom) 

maximum measured power levels compared to system dynamic range.
14

4.2 Measurement Time Resolution

Time intervals between FS measurements ( ) were not constant nor deterministic due to (1) the 

variable number of time-domain measurements performed (corresponding to the number of 

identified in the previous FS measurement) and (2) calibration measurements that occurred on an 

hourly basis—each of which can occur between any two adjacent FS measurements. Figure 10

illustrates the complimentary cumulative distribution function (cdf) of for the full data set

(measurement downtimes not included). Notice that the probability of { } is one, 

which corresponds to the minimum time to sweep through 150 frequencies with a 6 second dwell 

time. Measurement intervals were as long as 37.3 minutes, and the mean of was 17.7 minutes.

Figure 10. Probability distribution of time between measurements.

4.3 Spectrogram of Full Frequency-Swept Data Set

Figure 11 is a presentation of measured signals for the entire two weeks in San Diego. The 

middle plot is a spectrogram, where signal level is mapped to color and plotted versus time and 

frequency. All received signals below -83 dBm are white.

Two signals were continuously present over the entire measurement duration at 3.53 GHz and 

3.54 GHz. Figure 11(a) identifies an example of these signals in an FS measurement when no 

other signals were present. In the time-frequency plot, these signals show up as two thick blue 

horizontal lines spanning the entire time dimension. In the FCC spectrum license database, these 

signals correspond to a license to test WiMAX equipment for export markets in the frequency 

range from 3.4 to 3.6 GHz. 
15

In terms of SPN-43 observations, we observed signals with SPN-43 characteristics at 3.52 and 

3.55 GHz (see Figure 11(b) and (c)). Notice the frequency concurrence of these signals with the 

WiMAX signals. Figure 11(d) shows an SPN-43 signal at 3.59 GHz with a high signal-to-noise 

ratio. At ISART 2011 [3], we discussed how radar systems commonly operate at power levels 

outside of the amplifier’s linear range, which causes spectral spreading. Notice in this example 

that spectral spreading caused the SPN-43 signal to exceed occupancy threshold L for all 150

one-megahertz channels from 3.50 to 3.65 GHz. This is also a measurement where the spectrum 

analyzer was overloaded, as indicated by the red axis. Figure 11(e) illustrates multiple SPN-43 

systems operating simultaneously at 3.52, 3.60, and (presumably) 3.61 GHz. Multiple 

simultaneous SPN-43 signals were common in the last days of the measurements.

Finally, significant out-of-band signals2 were observed. Figure 11(f) is a measurement taken 

three hours after the measurement shown in Figure 11(e). One can observe that the three SPN-43 

signals were still present, but there was an additional emission that raised the noise floor across 

the entire band by about 15 dB. These were out-of-band pulsed signals that turned on and off 

intermittently over the course of the two weeks. Sometimes, there were high power levels at the 

lower band edge; other times it was flat across the entire 150 MHz. These out-of-band signals 

caused many of the vertical blue lines in the time-frequency plot.

 

2 The system’s in-band emissions were below 3.5 GHz; out-of-band emissions occurred above 3.5 GHz.
16

Figure 11. Measured signals in the 3.6 MHz band on June 8–21, 2012, near San Diego.
17

5 STATISTICAL CONSIDERATIONS FOR SPECTRUM OCCUPANCY 

MEASUREMENTS

Section 3 provided a measurement and detection strategy specific to the SPN-43 signal 

characteristics. In this section, we discuss the general definition of channel occupancy as well as 

means for estimating channel occupancy to a desired level of uncertainty. Further, we consider 

the aggregate of multiple channels and discuss band occupancy as a metric.

5.1 Renewal Theory and the Definition of Channel Occupancy

Assuming that the received signal power is a random process (which we identify, along with 

random variables, with bold font), the usual procedure is to define a related two-state random 

process as follows

 {

 

 (8)

and define channel occupancy as 

 { } (9)

(see Figure 12 for a depiction of received signal power versus time.) This definition seems 

satisfactory, i.e., occupancy is equal to the probability that the signal power will exceed a 

specified level. However, there is a difficulty if is some unspecified function of time. In 

that case, defining a reasonable methodology for measuring occupancy, i.e., estimating , is 

perhaps not tractable. Hence, we need to make some assumptions about .

Figure 12. Channel transmissions and related time intervals.

The obvious thing to do is to obtain a realization (i.e., a high fidelity or ideal measurement) of 

 . From this, we can obtain a series of on-times ( ) and off-times ( ). Note that and are 

random variables. In principle, the distributions of these random variables can be accurately 

estimated from our ideal measurement. We will assume that and are independent and their 
18

statistics are the same during other similar time periods (e.g., daytime on a weekday). From this 

measurement, it would seem obvious that occupancy is equal to the fraction of time that the 

measurement exceeds the specified level. But how does this relate to our original definition of 

occupancy? For the answer, we look to the theory of renewal processes.

A two-state random process, such as the one described above, with independent on and off times 

is a renewal process. For such a process, satisfies the renewal equation [10]

 { } ∫ 

 

 

 (10)

where is the cdf of the recurrence time .

Furthermore, there are limit theorems that show that as time goes on, tends to a constant,

and in our particular case

 

 

 

 { }

 { }

(11)

(see Appendix A for the development of this theorem from first principles). This is good news, 

because it tells us that our original definition of occupancy tends to the estimate that we would 

obtain from an ideal measurement. Perhaps more importantly, it tells us that we do not need to 

accurately measure the statistics of and , which would significantly tax our resources. All we 

need to do is estimate { } from measurement samples. In fact, if the samples are 

independent, we have a Bernoulli process that can be used to estimate to the desired level of 

uncertainty (see Section B.1). Similarly, if the samples are dependent, a Markov process can 

used to estimate to the desired level of uncertainty (see Section B.2).

5.2 Estimation of Channel Occupancy

In general, to estimate channel occupancy, we make observations of random process 

over time interval and calculate the time average

 ̂ 

 

 

∑ 

 

 

 

 

 

 (12)

where are the observations and is the number of successes. Uncertainty of the estimate is 

established with the expression

 { ̂ ̂ } (13)

which states that the actual channel occupancy lies within confidence interval 

 with 

probability . Appendix B develops expressions for and from first principles under 

independent and dependent sampling assumptions.
19

As indicated by the measurement results in the following section, our sampling interval is less 

than a typical SPN-43 transmission length; hence, dependent sampling is a better assumption. 

Confidence limits for dependent sampling are given as

 

 ̂ 

 ̂ 

 

 

 

 √(

 

 

)

 

 

 ̂ ̂

 

 

 

 

 

 (14)

where ̂ ̂. The variable ̂ ̂ ⁄ was introduced in the derivation to 

simplify the math. It is dependent on the estimate of transition probability , which can be 

achieved from data via

 ̂

 

 

 

∑ 

 

 

 (15)

Finally, is the parameter that adjusts the confidence limits according to the desired confidence 

level. It is calculated for a specified via 

 , where 

 

√ 

∫ 

 

 ⁄ 

 

is the cdf 

of the standard normal deviate. Solutions to this integral equation are accessible via look up table 

or the complementary error function, i.e., 

 

 

 

 

√ 

 .

5.3 Estimation of Band Occupancy

A useful metric in the context of FS spectrum occupancy measurements is band occupancy, 

which is intuitively defined at any given time as the fraction of frequencies (or channels) with a 

detected signal level that exceeds a predetermined threshold. Then measured band occupancy at 

a given time is given by

 

 

 

∑ 

 

 

 (16)

where is the channel observation, is the time index, k is the channel index, and Nc is the 

number of channels sampled. Further, we acquire N measurements over time duration T when 

spectrum usage in the band is assumed to be stationary and acquire the mean band occupancy as

 

 

 

∑ 

 

 

 

 

 

∑ ̂ 

 

 

 (17)

where ̂ is the channel occupancy estimate for channel k given in (12).

Given that military spectrum usage is based on coordinated frequency assignments, it is not 

expected that the discrete random process would be stationary in frequency. More 
20

specifically, we expect higher mean channel occupancy at assignment center frequencies and 

lower usage at frequencies between assignments that are kept relatively quiet in order to avoid 

interference between frequency-adjacent systems. A further complication is that individual 

channels are not independent due to the fact that the observed signals occupy a number of 

adjacent channels (defined by our measurement scheme to be 1 MHz). Consequently, since we 

are accumulating Bernoulli trials from different populations (i.e., from different channels), we do 

not pursue an uncertainty analysis on the mean band occupancy statistic.
21

6 MEASUREMENT RESULTS

In this section, band and channel occupancy statistics are provided according to the theoretical 

framework established previously. Frequency range is limited to 3.55–3.65 GHz, which 

corresponds to the frequency band specified in the NTIA Fast Track Report [1]. Note that this 

removes contributions of the WiMAX signals (3.53 and 3.54 GHz) from the occupancy results.

6.1 Band Occupancy

For band occupancy results, threshold levels { } dBm are applied 

to the entire data set. This is in contrast to those used during measurements, where was 

set according to the latest calibration measurement. At the largest measured system noise level,

 - , the probability of system noise exceeding the lowest threshold, - , 

is calculated from (4) to be on the order of 10-10, which we consider to be negligible.

6.1.1 Daily Means

Band occupancy results provide a coarse view of the data and allow for assumptions to be 

developed about stationarity in time. Table 5 provides daily mean band occupancy numbers with 

the number of FS measurements performed on that day. For subsequent discussions, we assume 

 is not stationary in general (as observed in Table 5 by the significant differences in weekday 

versus weekend band occupancy). We do assume, however, that is stationary in time on a 

daily basis if the time duration is limited to weekdays only or weekend days only. This provides 

some justification for separated weekday and weekend occupancy statistics, which we carry 

through in the remainder of this report. Given that the full measurement duration is only two 

weeks, we combine all weekday data together and all weekend data together. If the measurement 

duration were longer or even continuous, however, we would likely provide weekly statistics for 

weekday and weekend data.

Appendix B accompanies this data and provides plots of daily band occupancy results and signal 

levels. Band occupancy data are plotted versus time along with hourly means. Signal levels are 

in the time versus frequency spectrogram format. Also, maximum, mean, median, and minimum 

(M4) signal level statistics over a 24 hour period versus frequency are shown. M4 statistics are 

good for visualizing signal patterns versus frequency over a specified period of time.
22

Table 5. Daily mean band occupancy data.

Date N

 (%)

 

Fri 06/08 45 37 35 32 27 21

Sat 06/09 86 2 1 1 1 1

Sun 06/10 63 1 1 0 0 0

Mon 06/11 49 38 35 31 21 9

Tue 06/12 83 31 21 12 9 6

Wed 06/13 84 44 34 25 17 11

Thu 06/14 82 19 12 5 3 2

Fri 06/15 85 32 24 12 6 4

Sat 06/16 82 5 3 2 1 1

Sun 06/17 75 22 16 12 8 4

Mon 06/18 78 56 42 28 18 12

Tue 06/19 77 46 36 25 13 5

Wed 06/20 78 37 30 21 13 6

Thu 06/21 77 28 23 18 12 6

6.1.2 Two-Week Statistics

Under the assumption that weekday spectrum usage is one stationary random process and 

weekend spectrum usage is another stationary random process, we accumulate weekday and 

weekend realizations of band occupancy over the full two week measurement duration and plot 

the complementary cdfs (see Figures 13 and 14). At the left hand side of the plots, observe that 

the curves do not go to one. In the case of the weekday - threshold (blue curve), 

 { } , which means that there is a 0.40 probability that the band is empty, i.e., 

 { } ,. Similarly, one can deduce from the right side of the blue curve that the 

band is completely occupied with probability { } . Table 6 provides a 

summary of two-week band occupancy statistics.

Table 6. Band occupancy statistics for June 8–21, 2012, near San Diego.

Category N

 

(dBm)

 

(%)

 { }

(%)

 { }

(%)

Weekday 738

-71 7.5 64.8 0.7

-74 13.0 60.0 1.6

-77 19.7 50.8 4.5

-80 28.5 45.7 9.8

-83 36.6 40.0 18.4

Weekend 306

-71 1.6 69.6 0.0

-74 2.5 67.7 0.0

-77 3.9 66.3 0.7

-80 5.3 63.4 1.6

-83 7.5 59.8 2.3
23

Figure 13. Probability distributions of band occupancy measured during weekdays on June 8–21, 

2012, near San Diego.

Figure 14. Probability distributions of band occupancy measured during weekends on June 8–21, 

2012, near San Diego.
24

6.2 Channel Occupancy

Channel occupancy results allow for observation of spectrum usage versus frequency. We 

narrow the scope in this subsection to statistics for the - threshold. 

6.2.1 Example Calculations

Before presenting data for each measured channel across the band, we give example calculations 

for individual cases to make data interpretation more straightforward. Table 7 presents measured 

channel occupancy statistics for six channels spaced evenly across the band. In the discussion 

that follows, we focus on the 3.59 GHz and 3.57 GHz channels.

Table 7. Channel occupancy statistics , c1, and c2for 90% confidence p and -83 dBm threshold 

measured in June 2012 near San Diego.

Category N f (GHz) ̂

 (%) ̂(%) (%) (%)

Weekday 738

3.55 53 81.5 39.0 33.1 47.0

3.57 56 79.8 38.4 32.7 45.9

3.59 44 86.3 43.6 37.0 52.9

3.61 69 72.2 33.7 28.9 40.0

3.63 52 79.7 34.8 29.2 42.5

3.65 53 77.9 32.7 27.2 40.0

Weekend 306

3.55 9 77.3 15.0 9.4 26.4

3.57 10 47.4 6.2 3.6 11.1

3.59 3 96.4 27.5 21.5 68.4

3.61 5 58.3 3.9 1.8 9.2

3.63 5 64.3 4.6 2.1 10.9

3.65 4 73.3 4.9 2.2 13.0

First, consider the channel at 3.59 GHz over the full two week measurement duration. This 

channel (shaded in red in Table 7) is of interest because it had relatively high channel occupancy

due to SPN-43 transmissions. The weekday data is comprised of N = 738 trials of which 

 exceeded L = -83 dBm for a channel occupancy estimate of ̂ %. The

probability of the channel being occupied given it was occupied on the previous measurement 

was relatively high, i.e., ̂

 , which justifies using the dependent sampling model for 

calculating confidence intervals for ̂. For 90% confidence level, and . 

Substitution into (14) gives confidence limits and .

Weekend data for the same frequency were comprised of N = 306 measurements and 

successes for a channel occupancy estimate of ̂ . There were only renewals 

and the highest dependence between samples, e.g., ̂

 , which indicates that the 

transmission stayed on for a relatively long time. The relatively small probability of success, 

high transition probability (correlation between samples), and small N resulted in increased 

confidence limits and .

Next, we consider the 3.57 GHz channel, which is of interest because it is 20 MHz away from 

the nearest SPN-43 center frequency that we observed; hence, occupancy appears to be strongly 
25

influenced by spectral spreading and out-of-band contributions. Consider the weekday data 

where successes, for a channel occupancy estimate of ̂ . There were fewer 

correlated samples as indicated by a reduced transition probability, i.e., ̂

 , which 

resulted in smaller confidence intervals with limits and .

The 3.57 GHz weekend data provide a large number of renewals, i.e., , when 

considering the low channel occupancy estimate, ̂ . The measured transition probability 

is indicative of independent sampling, i.e., ̂

 , and a relatively small confidence 

intervals with limits and .

6.2.2 Channel Occupancy Statistics versus Frequency

Figures 15 and 16 illustrate ̂

 and ̂ versus frequency. Figure 17 illustrates ̂versus 

frequency for = {-83, -80, -77, -74, -71} dBm. For each of these figures, calculations were 

performed separately for data acquired during weekdays (shown in top plots) and weekends 

(shown in bottom plots).

Weekday channel occupancy statistics were relatively flat across the band; this is because the 

out-of-band signals contributed significantly across the band during weekdays. During the 10 

weekdays when measurements occurred, there were 5–7 renewals per day (on average) which 

resulted in mean renewal times ranging from 3 to 5 hours. Channel occupancy across the band 

was in the range ̂ . As the occupancy threshold increases (i.e., increases from -

83 dBm to -71 dBm in Figure 17), channel occupancy decreases somewhat uniformly across the 

band.

In contrast, weekend channel occupancy statistics were more frequency dependent; this is 

because out-of-band signals did not have significant contributions during the weekends. 

Channels near 3.59 GHz and 3.55 GHz, where SPN-43 signals were observed, showed elevated 

levels of ̂

 and ̂. Note that dependent sampling is a questionable assumption for channels that 

are quiet during the weekend, as indicated by channels with ̂

 .
26

Figure 15. Transition probability ( - ) versus frequency on June 8–21, 2012, near San 

Diego.

Figure 16. Channel occupancy estimates ( - ) with 90% confidence intervals versus 

frequency on June 8–21, 2012, near San Diego.
27

Figure 17. Channel occupancy estimates versus frequency at various threshold levels on June 8–

21, 2012, near San Diego.

6.3 Time Intervals

As discussed in Section 5.1 measuring time intervals is a challenging task where accuracy is 

related to the time resolution of the measurement. Consider the 15 minute minimum time 

resolution of the measurement strategy described in this report, which would cause difficulties

when measuring relatively short transmission lengths. If the mean transmission length were one 

minute, for example, there could easily be 5 transmissions lost in between samples. In a less 

severe scenario, if the mean transmission length were one hour, then measured values would be 

the expected value (one hour) plus or minus 15 minutes.

With these caveats, we also estimated time intervals , , and to obtain qualitative 

information on the temporal characteristics of the channel. This information can be valuable in 

scenarios where coordinated or opportunistic spectrum sharing is considered for improving 

spectrum utilization. 

Estimates of the expected values for , , and are calculated as

 { } 

 

 

∑{ }

 

 

 (18)

where is the number of renewals and { } are realizations of { }.
28

Table 8 provides measured mean time intervals for the limited set of channels discussed in 

Section 6.2.1 and Figure 18 illustrates the measured time intervals for all channels. Note that the 

weekend 3.59 GHz channel had a mean transmission lengths ( ) of 8.9 hours due to SPN-43 

transmissions (largely in the absence of out-of-band signals). The other channels which were 

primarily influenced by out-of-band emissions during the weekdays had mean transmission 

lengths of 1–2 hours. 

Table 8. Mean time intervals (L = -83 dBm) measured in June 2012 near San Diego.

Category N f (GHz) (hours) (hours) (hours)

Weekday 738

3.55 53 4.1 1.6 2.5

3.57 56 3.9 1.5 2.4

3.59 44 4.9 2.2 2.7

3.61 69 3.1 1.0 2.1

3.63 52 4.2 1.4 2.7

3.65 53 4.1 1.3 2.7

Weekend 306

3.55 9 9.8 1.5 8.3

3.57 10 8.8 0.6 8.1

3.59 3 29.3 8.9 20.4

3.61 5 17.6 0.7 16.8

3.63 5 17.6 0.8 16.7

3.65 4 22.0 1.2 20.8

Figure 18. Measured mean transmission intervals ( - ) versus frequency on June 8–

21, 2012, near San Diego.
29

Figures 19 and 20 present measured complementary cdfs of , , and for the weekday 

3.59 GHz and 3.57 GHz channels, respectively. There were not enough renewal events measured 

during weekends to warrant distribution plots. For comparison, exponential distribution curves 

with rate parameters equal to the appropriate reciprocal mean transmission interval are also 

shown. Mathematically, the exponential complementary cdf is given by { } .

Figure 19. Probability distributions of transmission intervals (f = 3.59 GHz, L = -83 dBm)

measured during weekdays on June 8–21, 2012, near San Diego. Dashed lines are 

corresponding exponential distributions.
30

Figure 20. Probability distributions of transmission intervals (f = 3.57 GHz, - )

measured during weekdays on June 8–21, 2012, near San Diego. Dashed lines are 

corresponding exponential distributions.
31

7 SUMMARY

A measurement technique optimized to detect SPN-43 maritime radar signals was described.

Further, statistical considerations that arise when measured data are used to characterize 

spectrum occupancy were discussed. Specifically, a theoretical framework modeling spectrum 

usage as a renewal process and measuring channel occupancy to a specified level of confidence

were established.

The measurement technique was implemented and deployed to measure spectrum occupancy in 

the 3.6 MHz band for two weeks in June 2012 near San Diego. In this presumably high-usage 

mostly military spectrum environment and at a low occupancy threshold (i.e., -83 dBm in a 1 

MHz bandwidth), mean band occupancy was {36.6, 7.5}% during {weekdays, weekends}. There 

was a {40.0, 59.8}% chance that the band was empty and a {18.4, 2.3}% chance that the band 

was full. During weekdays, spectrum usage was dominated by out-of-band pulsed transmissions 

superimposed on the stronger SPN-43 signals that spanned the entire band at a relatively low 

level (approximately 10 dB above the low threshold level). On average during weekdays, 

transmissions arrived every four hours with a mean transmission length of approximately 1.5 

hours. In contrast, weekend spectrum usage was primarily SPN-43 transmissions with 

amplitudes strong enough to overload the measurement system (sometimes exceeding the low 

threshold level by more than 60 dB). On average during weekends, transmissions (at 3.59 GHz) 

arrived every 29 hours with a mean transmission length of approximately 9 hours.
32

8 REFERENCES

[1] National Telecommunications and Information Administration, “An Assessment of the 

Near-Term Viability of Accommodating Wireless Broadband Systems in the 1675–1710 

MHz, 1755–1780 MHz, 3500–3650 MHz, and 4200–4220 MHz, 4380–4400 MHz Bands,“ 

NTIA Report, Oct. 2010.

[2] President’s Council of Advisors on Science and Technology, “Realizing the Full Potential 

of Government-Held Spectrum to Spur Economic Growth,” OSTP/PCAST Report to the 

President, Mar. 2012.

[3] M. Cotton, M. Maior, F. Sanders, E. Nelson, D. Sicker, “ISART 2011 Proceedings –

Developing Forward Thinking Rules and Processes to fully Exploit Spectrum Resources: 

An Evaluation of Radar Spectrum Usage and Management,” NTIA Special Publication SP12-485, Mar. 2012. 

[4] Federal Communications Commission, “Amendment of the Commission’s Rules with 

Regard to Commercial Operations in the 3550–3650 MHz Band,” FCC 12-148, Dec. 2012.

[5] Department of Defense, “Military Standardization Handbook,” MIL-HDBK-162B, Dec. 

1973.

[6] Agilent, “Noise Figure Measurements Accuracy – The Y-Factor Method,” Application 

Note 57-2, May 2010.

[7] Agilent, “Spectrum and Signal Analyzer Measurements and Noise,” Application Note, 

May 2012.

[8] M.P.M. Hall, “Effects of the Troposphere on Radio Communication,” IEEE 

Electromagnetic Wave Series, 1979.

[9] G.A. Hufford, A.G. Longley, W.A. Kissick, “A Guide to the Use of the ITS Irregular 

Terrain Model in the Area Prediction Mode,” NTIA Report 82-100, Apr. 1982.

[10] W. Feller, An Introduction to Probability and Its Applications, Vol. 1, New York, New 

York: John Wiley & Sons, Inc., 1968, p. 184.

[11] R. Dalke, “Statistical Considerations for Noise and Interference Measurements,” NTIA 

Technical Report TR-09-458, Nov. 2008.

[12] H. Cramer, Mathematical Methods of Statistics, Princeton, NJ, Princeton University Press, 

1946, pp. 507 - 524

[13] A.D. Spaulding, G.H. Hagn, “On the Definition and Estimation of Spectrum Occupancy,” 

IEEE Transactions on Electromagnetic Compatibility, Vol. EMC-19, No. 3, Aug. 1977.

[14] J.G. Kemeny, J.L. Snell, Finite Markov Chains, D. Van Nostrand Company, Inc., 

Princeton, 1960.
33

APPENDIX A: CHANNEL OCCUPANCY IN THE CONTEXT OF RENEWAL THEORY

Following Feller [10], we develop the concept of channel occupancy in the context of renewal 

theory. We first set up the problem and establish nomenclature. Next, we demonstrate that the 

quantity of interest satisfies the renewal equation. Finally, we solve the resulting renewal 

equation in the limit as time goes to infinity. Interested readers are referred to [10] for further 

explanation and details on the subject. Regarding nomenclature in this appendix: bold fonts 

denote random variables and processes and unspecified limits on integrals and summations imply 

limits of 0 to .

A.1 Setup

As illustrated in Figure A-1, we let be a binary two-stage renewal process. The defining 

property of a renewal process is that it starts over independently of the past at each renewal. 

Two-stage refers to the two events, i.e., { } and { }, that must occur in each 

renewal period. Let equal the sojourn time for { }, and equal the sojourn time for 

{ }. We assume and are independent random variables with probability density 

functions (pdfs) and and cumulative distribution functions (cdfs) and , respectively.

Figure A-1. Renewal process X(t) and associated transmission interval random variables.

Then is the recurrence time with pdf

 

 [ ] ∫ (A-1)

and cdf

 

 [ ] ∫  (A-2)

Note that 

  . Also, notice the subtle difference in the convolution operators

 , where (A-2) could be written with [ ] [ ] . Convolutions (in 

both senses) are associative and linear. In general, the convolution between a distribution and 

continuous function is not commutative, i.e., the order of the terms is important. The 

convolution between distributions, however, is commutative as is the * convolution in general.
34

To be more explicit with each individual recurrence event as illustrated in Figure A-2, are 

independent identically distributed (iid) random variables. The epoch of the m

th recurrence is 

 with cdf

 

 

 (A-3)

where we use 

 

as a shorthand notation for convolutions of [10].

Figure A-2. Sample function of a renewal process.

A fundamental measure in renewal theory is the expected number of renewals, in the 

interval ], which we obtain by counting renewal events. More specifically, ∑ 

where the random variable if and only if { } and equals zero otherwise. Taking 

the expected value yields

 { } {∑ 

 

} ∑ { }

 

 ∑[ { } { }]

 

 ∑  

 

 ∑ 

 

 

 

 

(A-4)

A.2 Satisfying the Renewal Equation

In Section 5.1 , we defined channel occupancy as { }. We will now show that 

 satisfies a renewal equation of the form

 ∫ 

 

 

 

 [ ] (A-5)

where is a continuous bounded function for .

We can write the unconditional probability of the event { } in terms of the sum over the 

events { } (i.e., the first renewal occurs at time ) as follows
35

 ∫ { } (A-6)

Given that the first renewal event occurs at time , the process starts anew at , hence

 { } { } (A-7)

For times , the event { } occurs if and only if is within the on-time (i.e., { }), 

hence { } { }. Substitution into (A-6) gives

 ∫ { } 

 

 

 ∫ 

 

 

 

 { } { } ∫ 

 

 

 

 

(A-8)

The first integral evaluates as shown because if (as dictated by the range of integration), 

then the integrand is equivalent to { } { }, which can be 

pulled out of the integral because there is no dependence on . The remaining integral evaluates 

to ∫ 

 { }

 

 

. Bayes theorem, { } { } { } { } { }, 

allows us to further simplify with

 { } { } { } { } { } (A-9)

since the event { } occurs whenever { }, i.e., { } . This yeilds

 { } ∫ 

 

 

 

 { } [ ] (A-10)

To obtain this last expression with the convolution, the limits of integration were replaced by 0 

to because it is understood that vanishes on the negative half axis, i.e., for 

 . Equation (A-10) shows that satisfies the renewal equation.

To obtain a solution to the renewal equation, we set 

 { } and convolve (A-10) 

with , i.e.,

 (A-11)

Recalling that 

 

  , the last term in equation (A-11) reduces to

 

  

 

 

 { } 

(A-12)

where { } because we assume that the first arrival is at . Substitution and 

solving for leads to the following solution
36

 [ 

] ∫ 

 

 

 (A-13)

A.3 Asymptotic Behavior of the Renewal Process

In the context of channel occupancy, it suffices to understand the behavior of after the 

process has been operating for a long time. Hence, in the limit as , we have

 

 

 

 

∫ 

 

 

 (A-14)

where the integrand and integral limits result from the change of variable . Recall that 

 is a complementary cdf, which is small as goes to infinity. To evaluate the 

differential, the renewal theorem states

 

 

 { }

 

 

 

 { }

 (A-15)

which can be written on the interval ] as { } [10]. 

Hence, the differential in the limit can be interpreted as

 

 

 { }

 (A-16)

Substitution into (A-14) and integration by parts, i.e., ∫ 

  

 

 

 ∫ 

 

with

 and , gives

 

 

 

 

 { }

∫[ ] 

 

 { }

∫ 

 

 { }

 { }

 (A-17)

hence, tends to a constant, { } { }, for large .
37

APPENDIX B: CONFIDENCE INTERVALS FOR CHANNEL OCCUPANCY ESTIMATES

To estimate channel occupancy, consider the discrete random variable

 (  ) {

 

 

(B-1)

In this expression, random process is a finite function which, for every , is a

measurable function of . Parameter set represents time variation and is the set of 

possible outcomes of an experiment [11]. Note that random variables and process are identified 

with bold font.

Probability is the unknown fixed3statistic that we aim to estimate via measurement. Toward 

that end, we make N observations over time interval T and estimate p as the time average

 ̂ 

 

 

∑ 

 

 

 

 

 

 (B-2)

where ̂denotes an estimate. Estimate ̂ is a random variable because it is a function on the 

probability space consisting of events . It is properly described by its pdf ̂ ,which 

can be interpreted as a distribution (that integrates to unity) on the vertical at in the ̂

plane illustrated in Figure B-1 [12].

Suppose there are two functions and such that 

 { ̂ } ∫ ̂ ̂

 

 

 (B-3)

which defines the interval (for fixed p) that contains estimate ̂with probability . Domain 

 is the region situated between and that defines this interval for all possible 

values of p. Equivalently, can be derived from distributions in the horizontal dimension as 

 { ̂ ̂ } { ̂ } (B-4)

which establishes accuracy of estimate ̂ with confidence interval 

 with probability .

 

3

Inherent to p being fixed is the assumption that the discrete random process  is stationary. A stationary 

random process is invariant under translation in a parameter of interest, e.g., time. We limit our concern here to 

wide-sense or weakly stationary processes that have constant mean and variance under translation. It is possible to 

adequately characterize a random process using measurements over time scales during which the process is 

approximately stationary. In general, however, spectrum usage processes are non-stationary in time due to the 

human element. Diurnal variations, for example, result from daytime versus nighttime dependencies. There are also 

weekly variations associated with the typical workweek structure. If it is believed that a statistic changes during the 

acquisition of data, the data should be separated into subsets and tested for differences, i.e., the statistics are treated 

as random variables.
38

Figure B-1. Illustration of confidence interval (c1, c2) for parameter p.

Confidence limits are obtained by taking the inverse of and , i.e., 

 

 ̂ 

 

 ̂  ̂ 

 

 ̂ (B-5)

We need to make some simplifying assumptions about ̂ in order to obtain expressions for 

 and . Recall from (12) that the basis for estimate ̂is counting the number of 

successes in N Bernoulli trials, i.e., . In the following subsections, we 

develop how basic assumptions on independent versus dependent Bernoulli trials can lead to 

expressions for confidence intervals.

B.1 Assuming Independent Sampling in Time

For a sequence of N independent Bernoulli trials, the number of successes (with probability p) 

and failures (with probability ) is governed by the binomial distribution, i.e.,

 { } (

 

 

) 

  

 (B-6)

with { } and { } . 

For (i.e. large N) and 

 

 

 (i.e., counts reasonably close to the 

mean) [10], the central limit theorem approximates the pdf of as a normal distribution, i.e.,

 { 

 

√ 

 } 

 

√ 

∫ 

 

 

 

 

 

  (B-7)
39

where 

 

√ 

∫ 

 

 ⁄ 

 

is the cdf of the standard normal deviate.

We divide both numerator and denominator of the random variable inside the probability 

measure by N to provide the normalized distribution of ̂ and write the resulting expression in 

the form of (B-4), i.e., 

 { √

 

 

 ̂ √

 

 

} 

 (B-8)

We took the liberty of setting (as is customary), which can be calculated for a 

specified via 

 . Solutions to this integral equation are accessible via look up table or 

the complementary error function, i.e., 

 

 

 

 

√ 

 .

The resulting expressions 

 √ define as an ellipse in the ̂ plane. 

To take the inverse per (B-5), we write the single equivalent expression

 ̂ √

 

 

 (B-9)

square, and solve the resulting quadratic equation for p. The solution gives the confidence limits 

for independent sampling, i.e., 

 

 ̂ 

 ̂ 

 

 

 

 √(

 

 

)

 

 

 ̂ ̂

 

 

 

 

 

 (B-10)

B.2 Assuming Dependent Sampling in Time

In some cases, when the sample interval is designed to be less than the mean transmission length, 

the probability of a 1 on the j

th trial depends on what happened on the (j-1)th trial. In this 

scenario, a more practical simplification is to assume that the measured sequence is reasonably 

characterized by a first-order Markov chain [13]. The steady-state equations for a first-order 

Markov chain in matrix form are [ ] [ ] ̅ (where the overbar denotes a matrix) or 

written out as

 { } 

 { } 

 (B-11)

where the transition probabilities are defined as

 { } (B-12)
40

and { } indicates a conditional probability. For a two-state process, the identity 

applies. Expressions for the transition probabilities are found by solving these four equations and 

six unknowns in terms of p, q, and , yielding

 ̅ [

 

 

] [

 

 

] (B-13)

Note that , or alternatively , is a condition for the Markov process to 

exist. Otherwise, if , then , which results in a transition probability 

(either or depending on ) that exceeds unity. 

The Central Limit Theorem for Markov Chains [14] states that, for large N, the pdf of tends 

toward a normal distribution with { } and limiting variance

 

 

 

(B-14)

where

 

 

 

 (B-15)

Consequently, the pdf of tends toward a normal distribution, i.e.,

 { 

 

√ 

 } 

 

 

∫ 

 

 

 

 

 (B-16)

As was done in the in the previous subsection for independent samples, this expression can be 

written in the form of (B-4), i.e.,

 { √

 

 

 ̂ √

 

 

} 

 (B-17)

where 

 √ define . To take the inverse, we write the equivalent 

expression

 ̂ √

 

 

 (B-18)

square, and solve the resulting quadratic equation for p. The solution gives the confidence limits 

for dependent sampling as

 

 ̂ 

 ̂ 

 

 

 

 √(

 

 

)

 

 

 ̂ ̂

 

 

 

 

 

 (B-19)
41

Figure B-2 illustrates for and N = 738 (corresponding to the number of weekday 

measurements acquired during the June 2012 San Diego measurement effort presented in the 

main body of this report). This plot demonstrates the dependence on p and as well as the 

difference between independent and dependent sampling. Note that the confidence interval 

increases as increases, which corresponds to an increase in the correlation between samples.

Also observe the constraint at the right side of the plot.

Figure B-2. for N = 738 and demonstrating the difference between independent and 

dependent sampling.
42

APPENDIX C: DAILY SIGNAL-LEVEL AND BAND OCCUPANCY PLOTS

This appendix provides daily signal level and band occupancy statistics calculated for the 3.55–

3.65 GHz band measured near San Diego, CA, in June 2012.

Odd numbered plots provide daily maximum, median, minimum, and mean (M4) signal level 

statistics versus frequency. M4 statistics are calculated using all frequency-swept measurements 

over a 24 hour period. Means are computed in linear units and converted to dBm. The horizontal 

grey band is bounded by mean and peak system noise, i.e., and 

 , calculated from 

the last calibration measurement of each day. Note that minimum, median, and mean statistics 

are missing from the Monday June 11 plots. This is because the system noise level changed in 

the middle of that day rendering these statistics invalid. The change in system noise was due to a 

change in the front-end hardware as discussed in Section 4.1.

Even numbered plots provide time versus frequency spectrogram plots and band occupancy 

versus time plots. For the spectrograms (upper plots), signal levels are mapped to color and 

plotted versus time and frequency. The lowest value displayed in the spectrogram color bar is the 

minimum threshold level - . Vertical grey areas denote measurement down times.

Band occupancy (given in the lower plots) is also calculated at this threshold. A channel is 

considered occupied when the received power is above the threshold. At a particular

measurement time, the number of occupied channels, , is divided by the total number of 

channels, Nc = 100, to obtain band occupancy. Band occupancy is shown as blue x’s in the lower 

plots. The red curve is an hourly mean and the daily mean is given in the plot title. The number 

of measurements performed on a given day, N, is also shown in the title.
43

Figure C-1. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 8, 

2012.

Figure C-2. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near San 

Diego on June 8, 2012.
44

Figure C-3. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 9, 

2012.

Figure C-4. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near San 

Diego on June 9, 2012.
45

Figure C-5. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 10, 

2012.

Figure C-6. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near San 

Diego on June 10, 2012.
46

Figure C-7. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 11, 

2012.

Figure C-8. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near San 

Diego on June11, 2012.
47

Figure C-9. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 12, 

2012.

Figure C-10. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 12, 2012.
48

Figure C-11. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 13, 

2012.

Figure C-12. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 13, 2012.
49

Figure C-13. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 14, 

2012.

Figure C-14. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 14, 2012.
50

Figure C-15. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 15, 

2012.

Figure C-16. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 15, 2012.
51

Figure C-17. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 16, 

2012.

Figure C-18. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 16, 2012.
52

Figure C-19. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 17, 

2012.

Figure C-20. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 17, 2012.
53

Figure C-21. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 18, 

2012.

Figure C-22. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 18, 2012.
54

Figure C-23. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 19, 

2012.

Figure C-24. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 19, 2012.
55

Figure C-25. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 20, 

2012.

Figure C-26. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 20, 2012.
56

Figure C-27. M4 statistics of 3550–3650 MHz spectrum measured near San Diego on June 21, 

2012.

Figure C-28. Spectrogram and band occupancy for 3550–3650 MHz spectrum measured near 

San Diego on June 21, 2012.
FORM NTIA-29 U.S. DEPARTMENT OF COMMERCE 

(4-80) NAT’L. TELECOMMUNICATIONS AND INFORMATION ADMINISTRATION

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION NO.

TR-14-500

2. Government Accession No. 3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

Spectrum Occupancy Measurements of the 3550–3650 Megahertz Maritime Radar Band near 

San Diego, California

5. Publication Date

January 2014

6. Performing Organization Code

ITS.T

7. AUTHOR(S)

Michael Cotton and Roger Dalke

9. Project/Task/Work Unit No.

8. PERFORMING ORGANIZATION NAME AND ADDRESS 3105012-300

Institute for Telecommunication Sciences

National Telecommunications & Information Administration

U.S. Department of Commerce

325 Broadway

Boulder, CO 80305

10. Contract/Grant No.

11. Sponsoring Organization Name and Address

National Telecommunications & Information Administration

Herbert C. Hoover Building

14th & Constitution Ave., NW

Washington, DC 20230

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.)

This report presents spectrum occupancy data of the 3550–3650 megahertz (MHz) maritime radar band measured in June 2012 near 

San Diego. In this band, the military operates SPN-43 air marshaling radar systems with well-defined signal characteristics. A 

measurement system and frequency-swept technique were designed specifically to detect SPN-43 emissions. Over the two-week 

measurement duration in June 2012, we observed multiple systems operating simultaneously in band, spectral spreading of SPN-43 

emissions, and out-of-band pulsed emissions that spanned the entire band of interest. In this presumably high-usage mostly military 

spectrum environment and at a low occupancy threshold (i.e., -83 dBm in a 1 MHz bandwidth at the output of a 2 dBi antenna), mean 

band occupancy was {36.6, 7.5}% during {weekdays, weekends}. There was a {40.0, 59.8}% chance that the band was empty and a 

{18.4, 2.3}% chance that the band was full. During weekdays, spectrum usage was dominated by out-of-band pulsed transmissions 

that spanned the entire band at a relatively low level (approximately 10 dB above the low threshold level). These signals were 

superimposed on the stronger SPN-43 signals. On average during weekdays, transmissions occurred every four hours with a mean 

transmission length of approximately 1.5 hours. In contrast, weekend spectrum usage was primarily SPN-43 transmissions at 3.59 

GHz arriving every 29 hours (on average) with a mean transmission length of approximately 9 hours. Measured SPN-43 signal 

amplitudes were at times strong enough to overload the measurement system (exceeding the -83 dBm threshold level by more than 60 

dB). Statistical considerations that arise when measured data are used to characterize spectrum occupancy are also discussed in this 

report. Covered topics include channel occupancy definition, estimation, and uncertainty.

16. Key Words (Alphabetical order, separated by semicolons)

spectrum occupancy, maritime radar, spectrum management

17. AVAILABILITY STATEMENT

UNLIMITED.

FOR OFFICIAL DISTRIBUTION.

18. Security Class. (This report)

Unclassified

20. Number of pages

75

 

19. Security Class. (This page)

Unclassified

21. Price:

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