##### Document Text Contents

Page 2

ELINT

The Interception and Analysis of Radar Signals

Page 234

9.7 Interception Techniques Using the Envelope of the Received Signal 219

One Rapid Sweep Superhet Receiver covered a 2-GHz band and swept that

band in 256 steps of 8 MHz in 20 ms. Its sampling rate was 50,000 samples per

channel per second. A similar channelized receiver with 256 channels each 8 MHz

wide could provide 16 million samples per channel per second. The bandwidth of

8 MHz was selected to be wide enough to pass the pulse compression modulations

then in use. (Many current threat radar systems use bandwidths of less than

10 MHz.) A common design is to test the sample against a threshold and declare

the presence of a pulse if one sample exceeds the threshold. To provide 90%

probability of detection and a 10- 6 probability of false alarm requires a SNR of

13.2 dB. The computation of the average of the envelope over a number of samples

and then comparing the average to a threshold allows the use of a much lower

threshold to achieve the same probability of detection and false alarm. The approxi-

mate improvement in sensitivity is found from (9.4). If the waveform dwells at one

carrier frequency for 2.5 ms and the bandwidth of the channels is 8 MHz, then

BT = 20,000 and the sensitivity improvement is approximately 27 dB for the

channelized receiver. The swept receiver provides a sample every 20 ms or 125

samples in 2.5 ms. Equation (9.4) gives the improvement in sensitivity as approxi-

mately 15.5 dB for the swept receiver. There is an added benefit of the swept

receiver in eliminating interference from the pulses from ordinary radar signals.

Sampling the signal for 80 ns every 20 ms means that most pulsed signals will not

contribute much to the average over 2.5 ms. The probability of coincidence between

the sampling gate of the sweeping receiver and the pulsing of the interfering radar

is very low. Of course, this could also be seen as a drawback if one is interested

in detecting both pulsed signals and modulated CW signals.

Another way of processing the samples of the envelope is to test each sample

against a threshold and then require that a certain minimum number of samples

cross the threshold out of a given number of samples tested—often called M of N

detection or binary integration [2, 6]. Here M samples out of N must cross the

threshold (N ³ M). This process is not quite as effective as computing the average

of the samples. It has the effect of suppressing very strong signals of short duration—

which is sometimes an advantage. The computation requires use of the binary

probability distribution. The first step is to determine the probability of noise alone

crossing the threshold at least M times out of N for a given probability that a single

sample of noise crosses the threshold. The notation Pfa,1 denotes the probability that

one sample of noise alone crosses the threshold, and Pfa,N is the probability that

at least M of N samples of noise alone cross the threshold. These are related by

the binary probability distribution for N trials and for Pfa,11 the probability of

‘‘success’’ on one trial. Likewise, the probability that signal plus noise crossed the

threshold on one trial is Pd,1 and the probability that signal plus noise crosses

the threshold at least M times out of N tries is Pd,N . These are also related by the

binary probability distribution. Some examples of the results are given in Table

9.1. There is an optimum value of M for any specific case. Values of M near N/2

or 1.5N0.5 have been suggested in the literature [6, 7]. The latter is used in Table

9.1. The required SNR has a broad minimum [6], and so choosing the exact

optimum value of M is not critical.

Although there is no theoretical limit to the improvement as the value of N

increases, there are important practical considerations; namely, as the threshold

Page 235

220 LPI Radar and the Future of ELINT

Table 9.1 Examples of Integration Gain Using M of N Integration

N = 8, M = 4 N = 16, M = 6 N = 32, M = 8 N = 64, M = 12

SNR = 7.3 dB SNR = 5.4 dB SNR = 3.4 dB SNR = 1.7 dB

Gain = 5.9 dB Gain = 7.8 dB Gain = 9.8 dB Gain = 11.5 dB

M is selected as 1.5N0.5; gain compared to Pd,1 = 0.9, Pfa,1 = 10

- 6 (single pulse SNR =

13.2 dB). N determined by signal duration during its coherent processing interval for Pfa,N

= 10- 6, Pd,N = 0.9.

decreases, the value of Pfa,1 becomes larger and so does the value of Pd,1. Eventually

the threshold is so low that there is not much difference between these two values.

Then a slight change in the noise level could drastically affect the final values of

Pd,N and Pfa,N . This is illustrated in Figure 9.5, which shows the probability of

both false alarm and detection at - 1.5-dB SNR. If the threshold is selected at 2.65

normalized units, then Pd,1 = 0.12 and Pfa,1 = 0.03. With a relatively small difference

between probability of detection and false alarm, a small change in the noise level

could cause a drastic change in the performance of the system. After the M of N

process (for M = 24, N = 256), the probability of detection and false alarm at SNR

= - 1.5 dB is shown in Figure 9.6. Now the probability of detection at the threshold

of 2.65 is 90% and the probability of false alarm is 10- 6. Detection using a single

sample would require the SNR to be 13.2 dB to give this same performance;

therefore, the M = 24, N = 256 process provides 13.2 - (- 1.5) = 14.7 dB of

processing gain. Coherent processing of 256 samples provides 24.1 dB of processing

gain; hence the loss of the M of N process is 9.6 dB relative to coherent integration.

The approximate gain expected from a noncoherent process as given by (9.2) is

Figure 9.5 Probability of detection (solid) and false alarm (dotted). SNR = - 1.5 dB. Threshold set

at 2.65 yields Pfa,1 = 0.03 and Pd,1 = 0.12.

Page 468

Recent Titles in the Artech House

Radar Library

David K. Barton, Series Editor

Advanced Techniques for Digital Receivers, Phillip E. Pace

Advances in Direction-of-Arrival Estimation, Sathish Chandran, editor

Airborne Pulsed Doppler Radar, Second Edition, Guy V. Morris and

Linda Harkness, editors

Bayesian Multiple Target Tracking, Lawrence D. Stone, Carl A. Barlow, and

Thomas L. Corwin

Beyond the Kalman Filter: Particle Filters for Tracking Applications, Branko Ristic,

Sanjeev Arulampalam, and Neil Gordon

Computer Simulation of Aerial Target Radar Scattering, Recognition, Detection,

and Tracking, Yakov D. Shirman, editor

Design and Analysis of Modern Tracking Systems, Samuel Blackman and

Robert Popoli

Detecting and Classifying Low Probability of Intercept Radar, Phillip E. Pace

Digital Techniques for Wideband Receivers, Second Edition, James Tsui

Electronic Intelligence: The Analysis of Radar Signals, Second Edition,

Richard G. Wiley

Electronic Warfare in the Information Age, D. Curtis Schleher

ELINT: The Interception and Analysis of Radar Signals, Richard G. Wiley

EW 101: A First Course in Electronic Warfare, David Adamy

EW 102: A Second Course in Electronic Warfare, David L. Adamy

Fourier Transforms in Radar and Signal Processing, David Brandwood

Fundamentals of Electronic Warfare, Sergei A. Vakin, Lev N. Shustov, and

Robert H. Dunwell

Fundamentals of Short-Range FM Radar, Igor V. Komarov and Sergey M. Smolskiy

Handbook of Computer Simulation in Radio Engineering, Communications, and

Radar, Sergey A. Leonov and Alexander I. Leonov

High-Resolution Radar, Second Edition, Donald R. Wehner

Introduction to Electronic Defense Systems, Second Edition, Filippo Neri

Introduction to Electronic Warfare, D. Curtis Schleher

Introduction to Electronic Warfare Modeling and Simulation, David L. Adamy

Introduction to RF Equipment and System Design, Pekka Eskelinen

Microwave Radar: Imaging and Advanced Concepts, Roger J. Sullivan

Page 469

Millimeter-Wave Radar Targets and Clutter, Gennadiy P. Kulemin

Modern Radar System Analysis, David K. Barton

Multitarget-Multisensor Tracking: Applications and Advances Volume III,

Yaakov Bar-Shalom and William Dale Blair, editors

Principles of High-Resolution Radar, August W. Rihaczek

Principles of Radar and Sonar Signal Processing, François Le Chevalier

Radar Cross Section, Second Edition, Eugene F. Knott et al.

Radar Evaluation Handbook, David K. Barton et al.

Radar Meteorology, Henri Sauvageot

Radar Reflectivity of Land and Sea, Third Edition, Maurice W. Long

Radar Resolution and Complex-Image Analysis, August W. Rihaczek and

Stephen J. Hershkowitz

Radar Signal Processing and Adaptive Systems, Ramon Nitzberg

Radar System Analysis and Modeling, David K. Barton

Radar System Performance Modeling, Second Edition, G. Richard Curry

Radar Technology Encyclopedia, David K. Barton and Sergey A. Leonov, editors

Range-Doppler Radar Imaging and Motion Compensation, Jae Sok Son et al.

Signal Detection and Estimation, Second Edition, Mourad Barkat

Space-Time Adaptive Processing for Radar, J. R. Guerci

Theory and Practice of Radar Target Identification, August W. Rihaczek and

Stephen J. Hershkowitz

Time-Frequency Transforms for Radar Imaging and Signal Analysis, Victor C. Chen

and Hao Ling

For further information on these and other Artech House titles, including previously

considered out-of-print books now available through our In-Print-Forever® (IPF®)

program, contact:

Artech House Artech House

685 Canton Street 46 Gillingham Street

Norwood, MA 02062 London SW1V 1AH UK

Phone: 781-769-9750 Phone: +44 (0)20 7596-8750

Fax: 781-769-6334 Fax: +44 (0)20 7630-0166

e-mail: [email protected] e-mail: [email protected]

Find us on the World Wide Web at: www.artechhouse.com

ELINT

The Interception and Analysis of Radar Signals

Page 234

9.7 Interception Techniques Using the Envelope of the Received Signal 219

One Rapid Sweep Superhet Receiver covered a 2-GHz band and swept that

band in 256 steps of 8 MHz in 20 ms. Its sampling rate was 50,000 samples per

channel per second. A similar channelized receiver with 256 channels each 8 MHz

wide could provide 16 million samples per channel per second. The bandwidth of

8 MHz was selected to be wide enough to pass the pulse compression modulations

then in use. (Many current threat radar systems use bandwidths of less than

10 MHz.) A common design is to test the sample against a threshold and declare

the presence of a pulse if one sample exceeds the threshold. To provide 90%

probability of detection and a 10- 6 probability of false alarm requires a SNR of

13.2 dB. The computation of the average of the envelope over a number of samples

and then comparing the average to a threshold allows the use of a much lower

threshold to achieve the same probability of detection and false alarm. The approxi-

mate improvement in sensitivity is found from (9.4). If the waveform dwells at one

carrier frequency for 2.5 ms and the bandwidth of the channels is 8 MHz, then

BT = 20,000 and the sensitivity improvement is approximately 27 dB for the

channelized receiver. The swept receiver provides a sample every 20 ms or 125

samples in 2.5 ms. Equation (9.4) gives the improvement in sensitivity as approxi-

mately 15.5 dB for the swept receiver. There is an added benefit of the swept

receiver in eliminating interference from the pulses from ordinary radar signals.

Sampling the signal for 80 ns every 20 ms means that most pulsed signals will not

contribute much to the average over 2.5 ms. The probability of coincidence between

the sampling gate of the sweeping receiver and the pulsing of the interfering radar

is very low. Of course, this could also be seen as a drawback if one is interested

in detecting both pulsed signals and modulated CW signals.

Another way of processing the samples of the envelope is to test each sample

against a threshold and then require that a certain minimum number of samples

cross the threshold out of a given number of samples tested—often called M of N

detection or binary integration [2, 6]. Here M samples out of N must cross the

threshold (N ³ M). This process is not quite as effective as computing the average

of the samples. It has the effect of suppressing very strong signals of short duration—

which is sometimes an advantage. The computation requires use of the binary

probability distribution. The first step is to determine the probability of noise alone

crossing the threshold at least M times out of N for a given probability that a single

sample of noise crosses the threshold. The notation Pfa,1 denotes the probability that

one sample of noise alone crosses the threshold, and Pfa,N is the probability that

at least M of N samples of noise alone cross the threshold. These are related by

the binary probability distribution for N trials and for Pfa,11 the probability of

‘‘success’’ on one trial. Likewise, the probability that signal plus noise crossed the

threshold on one trial is Pd,1 and the probability that signal plus noise crosses

the threshold at least M times out of N tries is Pd,N . These are also related by the

binary probability distribution. Some examples of the results are given in Table

9.1. There is an optimum value of M for any specific case. Values of M near N/2

or 1.5N0.5 have been suggested in the literature [6, 7]. The latter is used in Table

9.1. The required SNR has a broad minimum [6], and so choosing the exact

optimum value of M is not critical.

Although there is no theoretical limit to the improvement as the value of N

increases, there are important practical considerations; namely, as the threshold

Page 235

220 LPI Radar and the Future of ELINT

Table 9.1 Examples of Integration Gain Using M of N Integration

N = 8, M = 4 N = 16, M = 6 N = 32, M = 8 N = 64, M = 12

SNR = 7.3 dB SNR = 5.4 dB SNR = 3.4 dB SNR = 1.7 dB

Gain = 5.9 dB Gain = 7.8 dB Gain = 9.8 dB Gain = 11.5 dB

M is selected as 1.5N0.5; gain compared to Pd,1 = 0.9, Pfa,1 = 10

- 6 (single pulse SNR =

13.2 dB). N determined by signal duration during its coherent processing interval for Pfa,N

= 10- 6, Pd,N = 0.9.

decreases, the value of Pfa,1 becomes larger and so does the value of Pd,1. Eventually

the threshold is so low that there is not much difference between these two values.

Then a slight change in the noise level could drastically affect the final values of

Pd,N and Pfa,N . This is illustrated in Figure 9.5, which shows the probability of

both false alarm and detection at - 1.5-dB SNR. If the threshold is selected at 2.65

normalized units, then Pd,1 = 0.12 and Pfa,1 = 0.03. With a relatively small difference

between probability of detection and false alarm, a small change in the noise level

could cause a drastic change in the performance of the system. After the M of N

process (for M = 24, N = 256), the probability of detection and false alarm at SNR

= - 1.5 dB is shown in Figure 9.6. Now the probability of detection at the threshold

of 2.65 is 90% and the probability of false alarm is 10- 6. Detection using a single

sample would require the SNR to be 13.2 dB to give this same performance;

therefore, the M = 24, N = 256 process provides 13.2 - (- 1.5) = 14.7 dB of

processing gain. Coherent processing of 256 samples provides 24.1 dB of processing

gain; hence the loss of the M of N process is 9.6 dB relative to coherent integration.

The approximate gain expected from a noncoherent process as given by (9.2) is

Figure 9.5 Probability of detection (solid) and false alarm (dotted). SNR = - 1.5 dB. Threshold set

at 2.65 yields Pfa,1 = 0.03 and Pd,1 = 0.12.

Page 468

Recent Titles in the Artech House

Radar Library

David K. Barton, Series Editor

Advanced Techniques for Digital Receivers, Phillip E. Pace

Advances in Direction-of-Arrival Estimation, Sathish Chandran, editor

Airborne Pulsed Doppler Radar, Second Edition, Guy V. Morris and

Linda Harkness, editors

Bayesian Multiple Target Tracking, Lawrence D. Stone, Carl A. Barlow, and

Thomas L. Corwin

Beyond the Kalman Filter: Particle Filters for Tracking Applications, Branko Ristic,

Sanjeev Arulampalam, and Neil Gordon

Computer Simulation of Aerial Target Radar Scattering, Recognition, Detection,

and Tracking, Yakov D. Shirman, editor

Design and Analysis of Modern Tracking Systems, Samuel Blackman and

Robert Popoli

Detecting and Classifying Low Probability of Intercept Radar, Phillip E. Pace

Digital Techniques for Wideband Receivers, Second Edition, James Tsui

Electronic Intelligence: The Analysis of Radar Signals, Second Edition,

Richard G. Wiley

Electronic Warfare in the Information Age, D. Curtis Schleher

ELINT: The Interception and Analysis of Radar Signals, Richard G. Wiley

EW 101: A First Course in Electronic Warfare, David Adamy

EW 102: A Second Course in Electronic Warfare, David L. Adamy

Fourier Transforms in Radar and Signal Processing, David Brandwood

Fundamentals of Electronic Warfare, Sergei A. Vakin, Lev N. Shustov, and

Robert H. Dunwell

Fundamentals of Short-Range FM Radar, Igor V. Komarov and Sergey M. Smolskiy

Handbook of Computer Simulation in Radio Engineering, Communications, and

Radar, Sergey A. Leonov and Alexander I. Leonov

High-Resolution Radar, Second Edition, Donald R. Wehner

Introduction to Electronic Defense Systems, Second Edition, Filippo Neri

Introduction to Electronic Warfare, D. Curtis Schleher

Introduction to Electronic Warfare Modeling and Simulation, David L. Adamy

Introduction to RF Equipment and System Design, Pekka Eskelinen

Microwave Radar: Imaging and Advanced Concepts, Roger J. Sullivan

Page 469

Millimeter-Wave Radar Targets and Clutter, Gennadiy P. Kulemin

Modern Radar System Analysis, David K. Barton

Multitarget-Multisensor Tracking: Applications and Advances Volume III,

Yaakov Bar-Shalom and William Dale Blair, editors

Principles of High-Resolution Radar, August W. Rihaczek

Principles of Radar and Sonar Signal Processing, François Le Chevalier

Radar Cross Section, Second Edition, Eugene F. Knott et al.

Radar Evaluation Handbook, David K. Barton et al.

Radar Meteorology, Henri Sauvageot

Radar Reflectivity of Land and Sea, Third Edition, Maurice W. Long

Radar Resolution and Complex-Image Analysis, August W. Rihaczek and

Stephen J. Hershkowitz

Radar Signal Processing and Adaptive Systems, Ramon Nitzberg

Radar System Analysis and Modeling, David K. Barton

Radar System Performance Modeling, Second Edition, G. Richard Curry

Radar Technology Encyclopedia, David K. Barton and Sergey A. Leonov, editors

Range-Doppler Radar Imaging and Motion Compensation, Jae Sok Son et al.

Signal Detection and Estimation, Second Edition, Mourad Barkat

Space-Time Adaptive Processing for Radar, J. R. Guerci

Theory and Practice of Radar Target Identification, August W. Rihaczek and

Stephen J. Hershkowitz

Time-Frequency Transforms for Radar Imaging and Signal Analysis, Victor C. Chen

and Hao Ling

For further information on these and other Artech House titles, including previously

considered out-of-print books now available through our In-Print-Forever® (IPF®)

program, contact:

Artech House Artech House

685 Canton Street 46 Gillingham Street

Norwood, MA 02062 London SW1V 1AH UK

Phone: 781-769-9750 Phone: +44 (0)20 7596-8750

Fax: 781-769-6334 Fax: +44 (0)20 7630-0166

e-mail: [email protected] e-mail: [email protected]

Find us on the World Wide Web at: www.artechhouse.com