Detection of low probability of intercept radar signals K.M. Wong, T. Davidson and S. Abelkader The scientific or technical validity of this Contract Report is entirely the responsibility of the Contractor and the contents do not necessarily have the approval or endorsement of Defence R&D Canada.

Defence R&D Canada – Ottawa Contract Report

DRDC Ottawa CR 2009-142 September 2009

Detection of low probability of intercept radar signals

K.M. Wong T. Davidson S. Abelkader McMaster University Prepared By: McMaster University 1280 Main Street West Hamilton ON L9T 2Y1 Contractor Number: W7714-061022/001SV CSA: Jim Lee, 613-998-2112 The scientific or technical validity of this Contract Report is entirely the responsibility of the Contractor and the contents do not necessarily have the approval or endorsement of Defence R&D Canada.

Defence R&D Canada – Ottawa Contract Report DRDC Ottawa CR 2009-142 September 2009

Scientific Authority

Original signed by Jim Lee

Jim Lee

Defence Scientist

Approved by

Original signed by J.F. Rivest

J.F. Rivest

SH/REW

Approved for release by

Original signed by Brian Eatock

Brian Eatock

Chairman/ DRP

© Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence, 2009

© Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale, 2009

DRDC Ottawa CR 2009-142 i

Abstract ……..

Modern radar systems employ new type of signals, which are more difficult to detect and exploit. These signals are known as Low Probability of Intercept (LPI) signals. In this project, we study the performance of the intercept receiver in the scenario of LPI signals. We propose different techniques to detect and characterize the intercepted signals. We study the application of time-frequency techniques to this problem. Namely, we apply the Wigner-Ville distribution method to construct the time-frequency spectrum of the received signal and detect the presence of a radar signal. We apply the Hough transform, as a line detector, to the Wigner-Ville spectrum to enhance the performance of signal detection and estimation. We also propose the use of a novel technique for the detection/estimation of the intercepted radar signals. This technique is based on cross-correlation properties, and is shown to enjoy very fast processing time together with very accurate detection/estimation performance. Various numerical examples are included to evaluate the performance of these proposed methods under different scenarios.

Résumé ….....

Les systèmes radar modernes utilisent un nouveau type de signaux qui est plus difficile à détecter et à exploiter. Ces signaux sont connus sous le nom de signaux à faible probabilité d’interception (LPI). Dans le présent projet, nous étudions les performances du récepteur d’interception dans le scénario des signaux LPI. Nous proposons différentes techniques pour détecter et caractériser les signaux interceptés. Nous étudions l’application de techniques temps-fréquence à ce problème. Notamment, nous appliquons la méthode de distribution de Wigner-Ville pour construire le spectre temps-fréquence du signal reçu et détecter la présence d’un signal radar. Nous appliquons la transformée de Hough, en tant que détecteur linéaire, au spectre de Wigner-Ville pour améliorer les performances de détection et d’estimation du signal. De plus, nous proposons l’utilisation d’une nouvelle technique pour la détection/estimation des signaux radar interceptés. Cette technique est basée sur les propriétés de corrélation croisée, et il est démontré qu’elle jouit d’un temps de traitement très rapide de même que de performances de détection/d’estimation de très grande précision. Divers exemples numériques sont inclus pour évaluer les performances de ces méthodes proposées dans différents scénarios.

ii DRDC Ottawa CR 2009-142

This page intentionally left blank.

DRDC Ottawa CR 2009-142 iii

Executive summary

Detection of low probability of intercept radar signals K.M. Wong; T. Davidson; S. Abdelkader; DRDC Ottawa CR 2009-142; Defence R&D Canada – Ottawa; September 2009.

Principal results: In this project, we address the problem of detection/estimation of LPI radar signals. The main points of the project are listed in the following • Two types of LPI signals are studied; the Frequency Modulated Continuous Wave (FMCW) signals and the bi-phase Barker codes signals. • Time-frequency tools are introduced to characterize the intercepted signals. Two methods are described in details 1. The cross Wigner-Ville distribution method, which is a modification of the well-known Wigner-Ville technique by using a generated reference signal together with the received signal to generate the time-frequency spectrum. 2. The Wigner-Hough method, which applies the Hough transform to the Wigner- Ville spectrum to detect the presence of LPI signals. • Cross-correlation techniques are proposed as a fast and very accurate way of detecting and characterizing the intercepted radar signal. Different methods are discussed 1. Spatially separated receivers: Here, the cross-correlation value is computed between the received signals of two (or more) spatially separated receivers. 2. Delayed signals: In this case the cross-correlation value is computed between the received signal and a delayed copy of it. 3. Square-law detection: Here, the auto-correlation value is computed for the received signal. This method is applicable only when the received signal is real. • A probabilistic approach is used to compute the thresholds values needed for Cross-correlation methods. • The threshold values corresponding to given false-alarm rates are shown to be satisfied using numerical examples. • A detailed analysis of the choice of the appropriate delay value needed for cross- correlation (delayed signals) method is provided. • The case of interference signals being present is also included. Here we assume that the intercepted signal is a mixture of the desired LPI signal and an interference signal

iv DRDC Ottawa CR 2009-142

with the same modulation scheme. • Several numerical examples are included to evaluate the detection and estimation performance of the proposed methods. Significance of results: The contributions of this work are summarized in the following • A detailed study of the application of the well-known time-frequency methods to the detection and estimation of LPI signals has been carried out. The study is supported with numerical examples providing a clear performance analysis of these methods. • A novel technique for the estimation of the important LPI parameters based on cross-correlation methods has been developed. • A detailed and clear approach for choosing values of the threshold and delays for cross-correlation techniques has been derived. The computation of these values depends on the required false-alarm rate and the sampling frequency. • Performance evaluation of all the proposed techniques for various values of the Received Signal-to-Noise-Ratio (SNR) has been carried out, where it is evident that the newly proposed techniques enjoy a superior detection and estimation performance. Future work: Based on this project, we propose the following further research directions • Improve performance of time-frequency analysis and cross-correlation methods by employing further signal processing techniques. • Incorporate both improved time-frequency and cross-correlation methods in new detection/estimation algorithms for performance improvement especially in the case of strong interference sources. • Estimate the direction-of-arrival of the intercepted signal enabling spatial processing of the signal for further enhancement of performance. • Investigate the detection and estimation of other types of LPI signals. • Examine the effect of practical system problems: clock errors and quantization errors.

DRDC Ottawa CR 2009-142 v

Sommaire .....

Detection of low probability of intercept radar signals K.M. Wong; T. Davidson; S. Abdelkader; DRDC Ottawa CR 2009-142; R & D pour la défense Canada – Ottawa; Septembre 2009.

Résultats : Dans le cadre de ce projet, nous abordons le problème de la détection/estimation des signaux radar LPI. Les faits saillants du projet sont donnés ci-dessous. • Deux types de signaux LPI sont étudiés : les signaux à ondes entretenues à modulation

de fréquence (FMCW) et les signaux à code biphase de Barker. • Des outils temps-fréquence sont introduits pour caractériser les signaux interceptés.

Deux méthodes sont décrites en détail : 1. La méthode de distribution croisée de Wigner-Ville, qui est une modification

de la technique bien connue de Wigner-Ville et consiste à utiliser un signal de référence conjointement avec le signal reçu pour générer le spectre temps-fréquence.

2. La méthode de Wigner-Hough, qui applique la transformée de Hough au spectre de Wigner-Ville pour détecter la présence de signaux LPI.

• Des techniques de corrélation croisée sont proposées à titre de moyen rapide et de très

grande précision de détecter et de caractériser le signal radar intercepté. Différentes méthodes sont analysées :

1. Récepteurs séparés dans l’espace. Ici, la valeur de corrélation croisée est calculée pour les signaux reçus de deux (ou plusieurs) récepteurs séparés dans l’espace.

2. Signaux retardés. Dans ce cas, la valeur de corrélation croisée est calculée entre le signal reçu et sa reproduction retardée.

3. Détection quadratique. Ici, la valeur d’autocorrélation est calculée pour le signal reçu. Cette méthode n’est applicable que lorsque le signal reçu est un signal réel.

• Une approche probabiliste est utilisée pour calculer les valeurs de seuil nécessaires

aux méthodes de corrélation croisée. • Il est démontré à l’aide d’exemples numériques que les valeurs de seuil correspondant

à des taux de fausses alarmes donnés sont atteintes. • Une analyse détaillée du choix de la valeur de retard appropriée pour la méthode de

corrélation croisée (signaux retardés) est présentée.

vi DRDC Ottawa CR 2009-142

• Le cas de la présence de signaux brouilleurs est également abordé. Ici, nous

présumons que le signal intercepté est un mélange du signal LPI voulu et d’un signal brouilleur ayant le même type de modulation.

• Plusieurs exemples numériques sont inclus pour évaluer les performances de

détection et d’estimation des méthodes proposées. Portée : Les contributions de ce travail sont résumées ci-dessous. • Une étude détaillée de l’application des méthodes temps-fréquence bien connues à la

détection et à l’estimation de signaux LPI a été effectuée. L’étude est étayée par des exemples numériques donnant lieu à une analyse claire des performances de ces méthodes.

• Une nouvelle technique pour l’estimation des paramètres LPI importants basée sur

des méthodes de corrélation croisée a été élaborée. • Une approche détaillée et claire pour le choix des valeurs du seuil et des retards pour

les techniques de corrélation croisée a été dérivée. Le calcul de ces valeurs est fonction du taux de fausses alarmes et du taux d’échantillonnage.

• L’évaluation des performances de toutes les techniques proposées pour diverses

valeurs du rapport signal/bruit (S/B) reçu a été effectuée, et il est évident que les techniques nouvellement proposées jouissent de performances de détection et d’estimation supérieures.

Recherches futures : Compte tenu de ce projet, nous proposons les directions suivantes pour les recherches futures : • Améliorer les performances des méthodes d’analyse temps-fréquence et de

corrélation croisée en utilisant d’autres techniques de traitement des signaux. • Intégrer des méthodes améliorées temps-fréquence et des méthodes améliorées de

corrélation croisée à de nouveaux algorithmes de détection/estimation en vue d’améliorer les performances, notamment dans le cas des sources de brouillage fortes.

• Estimer l’angle d’incidence du signal intercepté pour permettre le traitement spatial

du signal afin d’améliorer encore les performances. • Étudier la détection et l’estimation d’autres types de signaux LPI.

• Examiner l’effet des problèmes système pratiques (erreurs d’horloge et erreurs de quantification).

Table of contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Resume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i

Executive summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Sommaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Table of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

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

2 LPI Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

3 Algorithms for the Detection of LPI Signals . . . . . . . . . . . . . . . . . . . . 3

3.1 Cross Wigner-Ville Distribution . . . . . . . . . . . . . . . . . . . . . . . 4

3.2 Wigner-Hough Transform . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.3 Cross-Correlation Techniques . . . . . . . . . . . . . . . . . . . . . . . . 10

3.4 Square-Law Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Performance Evaluation of the Proposed Detection Methods . . . . . . . . . . . 18

5 Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

6 Detection in the Presence of Interference Sources . . . . . . . . . . . . . . . . . 29

7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

List of figures

Figure 1: Time-Frequency distribution, test signal, SNR -3 dB . . . . . . . . . . . 2

Figure 2: First iteration, cross Wigner-Ville, SNR -10 dB . . . . . . . . . . . . . . 6

Figure 3: Last iteration, cross Wigner-Ville, SNR -10 dB . . . . . . . . . . . . . . 7

Figure 4: Wigner-Hough algorithm, line representation . . . . . . . . . . . . . . . 8

Figure 5: Wigner-Hough spectrum, SNR -10 dB . . . . . . . . . . . . . . . . . . 9

Figure 6: Histogram: spatial cross-correlation of the noise . . . . . . . . . . . . . 11

Figure 7: CDF: spatial cross-correlation of the noise . . . . . . . . . . . . . . . . 12

Figure 8: Histogram: time-delayed cross-correlation of the noise . . . . . . . . . 13

Figure 9: CDF: time-delayed cross-correlation of the noise . . . . . . . . . . . . . 14

Figure 10: Histogram: mean value of the noise squared . . . . . . . . . . . . . . . 16

Figure 11: CDF: mean value of the noise squared . . . . . . . . . . . . . . . . . . 17

Figure 12: Wigner-Hough spectrum, SNR -10 dB . . . . . . . . . . . . . . . . . . 25

Figure 13: Wigner-Hough spectrum, SNR 10 dB . . . . . . . . . . . . . . . . . . . 26

Figure 14: Wigner-Hough spectrum, signal plus interference . . . . . . . . . . . . 30

Figure 15: Wigner-Hough spectrum, strong interference signal . . . . . . . . . . . 31

List of tables

Table 1: Barker codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Table 2: Detection rate, FMCW signals, 100 simulation runs, 1024 samples . . . . 18

Table 3: Detection rate, FMCW signals, 1000 simulation runs, 2048 samples . . . 19

Table 4: Detection rate, Barker codes, 100 simulation runs, 2048 samples . . . . . 19

Table 5: False alarm rate, 1000 simulation runs, 512 samples . . . . . . . . . . . 20

Table 6: False alarm rate, 1000 simulation runs, 2048 samples . . . . . . . . . . . 20

Table 7: Cross Wigner-Ville, FMCW signals, 100 simulation runs . . . . . . . . . 24

Table 8: Wigner-Hough, FMCW signals, 100 simulation runs . . . . . . . . . . . 24

Table 9: Cross-correlation, FMCW signals, 100 simulation runs . . . . . . . . . . 27

Table 10: Time-frequency methods, Barker codes, 100 simulation runs . . . . . . . 28

Table 11: Cross-correlation, Barker codes, 100 simulation runs . . . . . . . . . . . 28

Table 12: Wigner-Hough, 100 Simulation Runs, SNR -10 dB, INR -5 dB . . . . . . 30

This page is intentionally left blank

x DRDC Ottawa CR 2009-142

1 Introduction

Conventional radar systems are known to transmit short-duration pulses with high-peakpower. The design of these radars was based solely on better detection of targets in clut-ter. Later, it became more important to consider the threats of intercepting and detectingthe radar signal. In the modern battlefield, radars are facing more and more serious threatsfrom Electronic Counter Measures (ECM) and Anti-Radiation Missiles (ARM). Therefore,an important feature of a modern radar system is the ability “to see and not to be seen” [7].This has motivated research in the direction of developing new radars that transmit signalwaveforms which are difficult to intercept. The goal is to keep the radar capabilities ofdetecting targets while minimizing the probability of being detected by ECM of enemies.To achieve this goal, the radar employs in its transmissions what is known as Low Proba-bility of Intercept (LPI) signals [3], [10], [12]. These signals are designed to be difficult tointercept by means of using wider frequency bandwidth (wideband), frequency hopping,using a frequency-modulated continuous-wave signal, and using only the minimum powerrequired for the task. The most common design of LPI signals is pulse compression, whichreduces the peak transmitted power while maintaining the range and resolution of the radar.The Electronic Support Measures (ESM) receiver must operate when both the high powershort-duration (conventional) signals as well as low power long-duration (LPI) signals arepresent. This requires special methods for detection and characterization of the receivedsignal at the intercept receiver. Moreover, the implementation of these methods should besuitable for real time processing.

In this project, we propose different techniques for the interception receiver to deal withLPI radar signals. We introduce different methods for the detection of these signals andexamine their performance at low SNR values. We also propose ways to estimate themodulation parameters of the intercepted signals. We study the case when interferencesources are present at the same time and frequency range as the desired radar signal, andtest the performance of our methods in this scenario.

In the next section we describe in great details the structure and different characteristicsof LPI signals. Following that we introduce our methods for detection and estimation andevaluate the performance of these methods with various numerical examples.

2 LPI Signals

There are two types of signals commonly used for LPI radar transmissions; the FrequencyModulated Continuous Wave (FMCW) and the bi-phase compound Barker code signals[8]. The FMCW signal, sometimes called a chirp, is characterized by a constant amplitudeand a frequency modulation that is linearly changing with time

s(t) = e j2π(αt+ β2 t2) (1)

1

The instantaneous frequency fi(t) of this signal is

fi(t) =dφ(t)

dt= α+βt (2)

where φ(t)�= (αt + β

2 t2). At the receiver, the LPI signal is accompanied by a noise signaln(t), which is assumed to be a circular complex Gaussian process with zero mean and unitvariance. Hence, the received LPI signal y(t) is given by

y(t) = s(t)+n(t) (3)

As an example, we generate a FMCW signal with a unit amplitude and a linear frequencymodulation that varies from 0 to 25MHz in an interval of approximately 10µs. Figure1 shows the time-frequency analysis using the Wigner-Ville distribution of the receivedsignal assuming an SNR value of -3 dB.1

WV, lin. scale, imagesc, Threshold=5%

Time [µs]

Fre

quen

cy [M

Hz]

2 4 6 8 100

5

10

15

20

25

100

200

300

400

500

600

700

800

Figure 1: Time-Frequency distribution, test signal, SNR -3 dB

Another pulse compression technique is achieved by phase coding. The type most com-monly used is the bi-phase modulation, where the phase of the carrier signal is changed by

1In this work, we fix the noise power to 1, and change the signal power to realize different SNR values.The signal is generated with a certain magnitude A such that it satisfies the required signal power P = A 2.

2

0◦ or 180◦ according to a certain technique. The technique used to determine the phase ofthe signal is known as Barker codes, which have the advantages of achieving the smallestpossible sidelobe levels of the autocorrelation functions as compared to the mainlobe value[5], [13]. A Barker code is a sequence aj of N values of +1 and −1, such that

|N−v∑j=1

a ja j+v| ≤ 1 for all 1 ≤ v < N and j = 1, · · · ,N (4)

A list of known Barker codes up to reversal of digits and negation is displayed in Table 1.

The longest available Barker code is of length 13 [4]. To achieve longer codes we maycompound various combinations of Barker codes.

Length CodesB2 2 +1 -1 OR (+1 +1)B3 3 +1 +1 -1B4 4 +1 -1 +1 +1 OR (+1 -1 -1 -1)B5 5 +1 +1 +1 -1 +1B7 7 +1 +1 +1 -1 -1 +1 -1B11 11 +1 +1 +1 -1 -1 -1 +1 -1 -1 +1 -1B13 13 +1 +1 +1 +1 +1 -1 -1 +1 +1 -1 +1 -1 +1

Table 1: Barker codes

For example a code of length 65 can be generated by combining two Barker codes of length13 and 5. The compound code B13×5 is related to the outer code B5 and the inner code B13

as followsB13×5 = B5 ⊗B13 (5)

where ⊗ represents the Kronecker product defined as

A⊗B =

⎡⎢⎣

a11B · · · a1nB...

. . ....

am1B · · · amnB

⎤⎥⎦ (6)

where A and B are two matrices of size m×n and p×q, respectively.

In this project, we test the performance of our proposed methods using radar signals ofboth the FMCW and bi-phase Barker codes types.

3 Algorithms for the Detection of LPI Signals

In this section, we introduce some techniques that are suitable for the detection of LPI radarsignals. These techniques can be classified into two categories; time-frequency methods

3

and cross-correlation methods. Time-frequency tools are particularly useful for the case ofFMCW signals, where we can exploit the time-frequency properties of the signal to detectits presence even in the case of very low SNR values. Cross-correlation methods have twomain advantages; they enjoy fast processing which increases only linearly with increasingthe sampling points, and they can be realized using simple hardware implementations.Cross-correlation methods are based on generating a copy of the LPI signal either by theuse of another receiver channel or by artificially introducing a calculated delay on thereceived signal. Then, the cross-correlation process is performed on the received signaland the generated copy to detect the presence of the signal. Both the time-frequency andcross-correlation techniques are discussed in greater detail in the following subsections.

3.1 Cross Wigner-Ville Distribution

The Wigner-Ville distribution is a well known technique to study the time-frequency char-acteristics of a signal, and this technique can be adopted as a detection method of FMCWsignals. The Wigner-Ville distribution is defined as

W (t, f ) =∫ ∞

−∞y(t + τ)y∗(t− τ)e− j4π f τdτ (7)

However, the performance of the conventional Wigner-Ville distribution is degraded at lowSNR values [6], [9]. Therefore, we suggest an alternative approach based on the idea thatunderlies the Wigner-Ville technique. In our approach, we use an iterative algorithm tocompute the cross Wigner-Ville distribution and estimate the instantaneous frequency. Thealgorithm is described as follows:

1. Obtain an initial estimate of the instantaneous frequency of the received signal usingthe peaks of the Short Time Fourier Transform (STFT) or the conventional Wigner-Ville distribution.

2. Form a unit amplitude, frequency modulated reference signal yr(t)

yr(t) = e j2π∫ t−∞ f̂i(t)dt (8)

where f̂i(t) is the initial instantaneous frequency estimate.

3. Compute the cross Wigner-Ville distribution WX(t, f ) between the received signaland the reference signal

WX(t, f ) =∫ ∞

−∞y(t + τ)y∗r (t − τ)e− j4π f τdτ (9)

4. Estimate the instantaneous frequency from the cross Wigner-Ville distribution.

4

5. Stop the iterations if the relative error in the estimated instantaneous frequency pa-rameters, α̂ and β̂ is less than 5% of the previous estimates. Otherwise, go to step2.

The method is declared successful in detecting the presence of a signal if it converges inless than 20 iterations.

A detailed convergence analysis of this method is available in [11], where it is proven thatthe method will converge for asymptotically long signals. It is worth mentioning that eachiteration of the algorithm computes the Wigner-Ville distribution which is implemented us-ing Fast Fourier Transform (FFT), and hence the computational complexity of this methodis of order n logn where 2n is the number of sampling points.

As an example, we test the performance of this method using a FMCW signal generatedusing the following parameters: the instantaneous frequency changes from 20 MHz to20.5117 MHz in an observation interval of 2048 samples with sampling frequency f s = 200MHz. This means that α = 20MHz and β = 50MHz/ms. The SNR used to simulate thereceived signal is −10 dB. In Figures 2 and 3, we show the time-frequency distribution ofthe received signal for the first and last iteration of this algorithm, respectively. We can seethe enhancement of the spectrum obtained using our technique (the number of iterationsused in this example is 5).

3.2 Wigner-Hough Transform

A modification to the Wigner-Ville distribution method to enhance its detection capabilitiesis the application of Hough transform to the Wigner-Ville distribution [1]. The resultingtransform, known as Wigner-Hough transform, is given by

WH(α,β) =∫

T

{∫ ∞

−∞y(t + τ)y∗(t− τ)e− j4π(α+βt)τdτ

}dt (10)

where α + βt represents the instantaneous frequency with β being the sweep rate. Theintegration is computed for every possible value of α and β. The implementation of thisestimator is illustrated in Figure 4, and is described as follows. For every point (t, f ) weintegrate the Wigner-Ville distribution with respect to t for all possible values of α andβ. In Figure 4, we display a single instance of the algorithm for a certain value of αand β, which represents a certain line ( f = α + βt) in the time-frequency plane and weintegrate the Wigner-Ville distribution along this line. For faster implementation, we usepolar representation (ρ,θ), where ρ is the magnitude of the normal to the line measuredfrom the origin point (0,0) and θ is the angle of the normal to the line measured from thetime axis. This transformation from (α,β) to (ρ,θ) is crucial because we have an infiniterange of value of (α,β) over which we need to compute the Wigner-Hough transform. Inpolar coordinates, however, we have a finite range of values of ρ ∈ [0,ρmax] and θ ∈ [0,2π],

5

WV, lin. scale, imagesc, Threshold=5%

Time [µs]

Fre

quen

cy [M

Hz]

2 4 6 8 100

5

10

15

20

25

100

200

300

400

500

600

700

800

900

1000

Figure 2: First iteration, cross Wigner-Ville, SNR -10 dB

where ρmax =√

(m2 +n2) is determined by the size of the Wigner-Ville spectrum (m is thenumber time points and n is the number of frequency points used to construct the Wigner-Ville distribution).

After computing the Wigner-Hough transform in polar representations, we estimate the co-ordinates (ρp,θp) of the peak point, and transform this value to (αp,βp) using the relations

α = ρ/sinθβ = −cotθ (11)

The Wigner-Hough transform enjoys the advantage of emphasizing the peak values used todetect and estimate the signal frequency parameters. It both detects the presence of a signaland estimates its important parameters (the nominal carrier frequency, and the sweep rate).The Wigner-Hough estimator can be shown to be asymptotically efficient, which meansthat it reaches the Cramer-Rao bound (the lower bound for unbiased estimators) as theobservation interval tends to infinity. Also, the Wigner-Hough method has a better SNRthreshold as compared to the conventional Wigner-Ville distribution.2 Furthermore, this

2The SNR threshold is the SNR value below which the method fails to detect the presence of a signal.

6

Cross Wigner−Ville, last iteration, −10 dB

Time [µs]

Fre

quen

cy [M

Hz]

2 4 6 8 100

10

20

30

40

50

60

70

80

90

100

200

400

600

800

1000

1200

1400

1600

1800

2000

Figure 3: Last iteration, cross Wigner-Ville, SNR -10 dB

threshold is related to the observation time and hence can be enhanced by increasing theobservation window [2].

The drawback of this method is the long processing time needed to compute the Houghtransform. Furthermore, the processing time increases significantly with increasing numberof sampling points, which makes it impractical in some scenarios to enhance the detectionperformance by increasing the number of samples.

As an example of the operation of the Wigner-Hough method, we use a test FMCW signalwith the same parameters as specified in the previous subsection. To reduce the processingtime, we decreased the number of samples to 1024 (in the previous subsection, we used2048 samples). In Figure 5, we show the Wigner-Hough spectrum of our received testsignal, where we can see the strong peak indicating the presence of a radar signal.

7

Frequency

Time

Normal to the line

A line with a certain values for

A

B

C

ED

α

(α,β)

ρ

ψ

ψ

θ

(t, f )

Figure 4: Wigner-Hough algorithm, line representation

8

Figure 5: Wigner-Hough spectrum, SNR -10 dB

9

3.3 Cross-Correlation Techniques

In this class of algorithms, we make use of the possibility of employing two (or more)spatially separated receivers at the Electronic Support Measures (ESM) site. The mainidea behind this technique is described as follows. Let yi(t) represent the output of the ithreceiver, we have

y1(t) = s(t)+n1(t)y2(t) = s(t− τ)+n2(t)

(12)

where s(t) is the LPI signal, which can be a FMCW or a Barker code signal, τ is the timedelay for the signal to propagate from one receiver to the next, while the noise terms (n1(t)and n2(t)) are assumed independent. Hence, the cross-correlation between the two outputswill cancel-out the noise component while constructing the signal autocorrelation function.

Using this algorithm, an LPI radar signal is detected if the output of the cross-correlationmodule exceeds a fixed threshold.

The value of the threshold is set in a probabilistic approach using previous observations ofthe noise waveform. We construct a histogram (Figure 6) of the recorded absolute values ofthe cross-correlation between the noise waveforms obtained from the two receivers. Fromthis histogram, we can build an empirical Cumulative Density Function (CDF) as illustratedin Figure 7.

The threshold is chosen using the CDF such that we satisfy a certain false-alarm rate. Inour example, we choose a threshold of 0.077 to satisfy a false-alarm rate of 5%.

If employing more than one receiver at the ESM side is not physically possible, we proposea single receiver alternative for the aforementioned technique.

In this case, the cross-correlation function is computed between the output of the receivery(t) and its delayed version y(t − τ). Here, τ represents the time delay, which can bearbitrary set to ensure that the noise terms have no correlation while preserving signalcorrelation.

The basic idea in this technique is the fact that the noise is temporally as well as spatiallyuncorrelated, and hence the cross-correlation between y(t) and y(t − τ) will cancel-out thenoise component and build the signal autocorrelation function.

In principle, this algorithm enables the intercept receiver to have a built-in matched filter.While a general matched-filter receiver correlates the received signal plus noise with alocally generated signal, this algorithm correlates signal plus noise with a delayed versionof the signal plus an independent noise input. In this way, the intercept receiver can detectthe LPI signal even at very low SNR values.

Similar to the case of employing more receivers, we need to choose a threshold for detec-tion. We use previous observations to compute the absolute cross-correlation value between

10

0 0.02 0.04 0.06 0.08 0.1 0.120

50

100

150

200

250mean noise spatial

Cross−correlation value E |n1* (t) n

2(t)|

Figure 6: Histogram: spatial cross-correlation of the noise

the noise signal and its delayed version. These values are then used to build a histogramand consequently the CDF, as illustrated in Figures 8 and 9, respectively. Using the CDFplot, we can choose the threshold value that corresponds to a certain false-alarm rate. Inour example, we choose a threshold value of 0.08 to satisfy a false-alarm rate of less than5%.

11

0 0.02 0.04 0.06 0.08 0.1 0.120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

F(x

)

Empirical CDF Noise cross (spatial)

Figure 7: CDF: spatial cross-correlation of the noise

12

0 0.02 0.04 0.06 0.08 0.1 0.120

20

40

60

80

100

120

140

160

180

200mean noise delayed

Cross−correlation value E |n*(t) n(t+τ)|

Figure 8: Histogram: time-delayed cross-correlation of the noise

13

0 0.02 0.04 0.06 0.08 0.1 0.120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

F(x

)

Empirical CDF Noise cross (delayed)

Figure 9: CDF: time-delayed cross-correlation of the noise

14

3.4 Square-Law Detection

In some scenarios, we may use auto-correlation techniques (square-law detection meth-ods) for the detection of LPI radar signals. In particular, if we have the scenario that thetransmitted signal is purely real

s(t) = sin

(2π(αt +β

t2

2))

(13)

we may end up with a situation where we receive a real signal embedded in complexnoise. In this case, the square-law detection method may be applied taking advantage of thecircularly Gaussian complex property of the noise. This property means that the varianceof the real part of the noise is the same as the variance of the imaginary part resulting in

E{n2(t)} = E{(nR + jnI)2}= E{n2

R +2 jnRnI −n2I } = 0

(14)

where E denotes the expectation operator, and nR and nI are the real and imaginary parts ofthe noise, respectively. On the other hand, we have that

E{s2(t)} = p (15)

where p is the signal power. Hence, the LPI can be detected if the output of the square-lawdetection module exceeds a certain threshold.

The threshold is chosen in the same probabilistic manner, where we record the values ofthe mean of the squared noise samples. The histogram and CDF are constructed (Figures10 and 11, respectively) and we choose the threshold value from the CDF plot to satisfythe desired false-alarm rate.

In our example, we choose a threshold value of 0.11 to satisfy a 5% false-alarm rate.

It is worth mentioning that this method can be realized using hardware implementationsas follows. First, the received signal y(t) is boosted using a Low-Noise Amplifier (LNA),then it is processed by a square-law circuit element. The expectation operation in Eqs.(14) and (15) is approximated by integration over time, and the output of the integrator(which is proportional to the signal power after boosting) is passed to a comparator. Asignal is detected when the output of the integrator is greater than a pre-set threshold,which is chosen to satisfy a fixed false-alarm rate. This method is simple and effectiveand its performance can be tested easily. However, a drawback of this algorithm is the factthat signal parameters (instantaneous frequency and sweep rate for example) have to beestimated separately by other methods.

15

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180

50

100

150

200

250mean noise squared

Cross−correlation value E |n2(t)|

Figure 10: Histogram: mean value of the noise squared

16

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

F(x

)

Empirical CDF Noise squared

Figure 11: CDF: mean value of the noise squared

17

4 Performance Evaluation of the ProposedDetection Methods

In this section, we examine the performance of the proposed detection methods under var-ious scenarios. The signals used to test the performance are the FMCW and Barker codessignals described in previous sections. Various numerical examples are included in thissection to evaluate the detection performance under different scenarios.

Example 1In this example we use a FMCW signal with modulation parameters: α = 20MHz andβ = 500MHz/ms. The sampling frequency is 200MHz, and the number of samples usedis 1024. We vary the SNR value from −10 dB to 10 dB and use 100 independent simula-tion runs to compute the detection rate of the different proposed methods. The results aredisplayed in Table 2, where we can see the excellent detection performance of all of thesuggested methods.

Method −10 dB −5 dB 0 dB 5 dB 10 dBCross Wigner-Ville 100% 100% 100% 100% 100%Wigner-Hough 100% 100% 100% 100% 100%Cross-delayed 99% 99% 100% 100% 100%Cross-spaced 99% 100% 100% 100% 100%Square-law 99% 100% 100% 100% 100%

Table 2: Detection rate, FMCW signals, 100 simulation runs, 1024 samples

It is worth mentioning that the cross-correlation techniques and the square-law method(when applicable) have relatively low complexity in detecting the LPI signal. While thetime-frequency techniques (cross Wigner-Ville and Wigner-Hough) have much higher com-plexity, they enjoy the capability of characterizing the intercepted signal by estimating themodulation parameters α and β as we will discuss in the next section.

Example 2We use the same FMCW signal, but we reduce the SNR values to start from −20 dB, whilethe number of samples is increased to 2048. The results are averaged over 1000 simulation

18

runs and are listed in Table 3.

Method −20 dB −15 dB −10 dBCross Wigner-Ville 0% 10% 100%Wigner-Hough 10% 30% 100%Cross-delayed 99.8% 99.9% 100%Cross-spaced 99.9% 99.9% 100%Square-law 64.1% 84.1% 99.9%

Table 3: Detection rate, FMCW signals, 1000 simulation runs, 2048 samples

From this example, we conclude that the performance of the time-frequency methods (crossWigner-Ville and Wigner-Hough) deteriorates at very low SNR values. Although it is the-oretically possible to enhance the performance of the Wigner-Hough method by increas-ing the number of samples, the processing time needed becomes prohibitively high whenthe number of samples exceeds 2048. On the other hand, the performance of the cross-correlation methods does not change much with reducing the SNR values. Moreover, theprocessing time needed increases only linearly with increasing number of samples andhence better detection rates can be achieved by simply increasing the sampling points. Thisobservation makes the use of cross-correlation techniques more favorable for fast detectionof FMCW signals at low SNR values.

Example 3In this example we change the test signal, and we use bi-phase Barker code signals gener-ated as a compound code B13×5 as described in previous sections. The pulse width is setto 6.5µs, the pulse repetition interval is 100µs, the carrier frequency is 25 MHz, and thesampling frequency is 170 MHz. The SNR varies from −20 dB to 0 dB, and we use 2048sampling points. All results are averaged over 100 simulation runs and are displayed inTable 4.

Method −20 dB −15 dB −10 dB −5 dB 0 dBCross Wigner-Ville 0% 9% 100% 100% 100%Wigner-Hough 8% 23% 100 % 100% 100%Cross-delayed 100% 100% 100% 100% 100%Cross-spaced 100% 100% 100% 100% 100%Square-law 100% 100% 100% 100% 100%

Table 4: Detection rate, Barker codes, 100 simulation runs, 2048 samples

To evaluate the false-alarm rate of our suggested methods, we use a noise-only signal gen-erated as a complex Gaussian process with zero-mean and unit-variance. We used 1000independent simulations runs and recorded the times where a radar signal is erroneously

19

declared present. The threshold values used are those obtained in the previous section,which have been estimated based on our previous noise observations using 512 samplingpoints.3 The results are listed in Table 5.

Method False-Alarm RateCross-delayed 5.1%Cross-spaced 3.5%Square-law 0.8%

Table 5: False alarm rate, 1000 simulation runs, 512 samples

We can reduce the false-alarm rate further by increasing the sampling points (recall that thisdoes not increase much the processing time of the cross-correlation methods). By increas-ing the sampling points, we average the cross-correlation value of the noise waveform overmany samples and hence the result approaches the true expected value of zero (the noisesignal is assumed to be uncorrelated). The results for 2048 sampling points are displayedin Table 6.

Method False-Alarm RateCross-delayed 0.1%Cross-spaced 0%Square-law 0%

Table 6: False alarm rate, 1000 simulation runs, 2048 samples

It is worth mentioning that the time-frequency techniques (cross Wigner-Ville and Wigner-Hough) have zero false-alarm rate because having a unique peak in the time-frequencydistribution is only possible when there is a true signal.

5 Parameter Estimation

Another aspect of the project is signal characterization by estimating the important mod-ulation parameters of the intercepted radar signal. In this section, we examine the perfor-mance of the cross Wigner-Ville and the Wigner-Hough methods as time-frequency toolsto estimate the frequency modulation parameters α and β. We also propose the use ofcross-correlation techniques for parameter estimation as well. The estimation accuracy ofthe different methods is evaluated using various numerical examples.

3Note that in our simulations, we always fix the noise power to unity and realize different SNR values bysimply changing the radar signal power.

20

Time-Frequency Techniques

The parameters values can be estimated from the cross Wigner-Ville method by means ofdata fitting to a linear model. From the Wigner-Ville distribution, we find the frequencyposition of the maximum point of the spectrum at each time slot. These points are recorded,and then fitted to a linear model to estimate the modulation parameters α and β.

The Wigner-Hough method utilizes a different approach to estimate the signal modulationparameters. For every possible value of α and β, the Wigner-Hough transform integratesthe Wigner-Ville distribution with respect to time, and record the value of the integration.The maximum value occurs at the true value of α and β. This approach is better imple-mented using the polar representation of the line equation, and at the end we transformback to compute the values of α and β as explained in previous sections.

Cross-Correlation Methods

Although the use of cross-correlation methods is not common for direct estimation of sig-nal parameters, we have been motivated by the superior detection rate of these techniquesto test the application of these methods to parameter estimation. The idea is that the com-puted cross-correlation value between the received signal and the generated delayed copyis proportional to the signal parameters as follows. Let y1(t) be the intercepted LPI signal,and generate a delayed version of the received signal y2(t) = y1(t − τ), where τ is the in-troduced artificial delay. For a chirp signal, τ is chosen not so small that noise componentsmay not cancel out and not so large that signal correlation is not attenuated. A reason-able value for τ that is used in our simulation is 13 samples. In the case of Barker codes,however, a careful choice of τ is critical and will be discussed in detail at the end of thissection.

The cross-correlation C between y1(t) and y∗2(t) will cancel out the noise component (noiseis assumed to be temporally white) and we are left with a term that is function on thesignal parameters. In the following, we explain in more details the steps of the estimationalgorithm for the cases of FMCW and bi-phase Barker coded signals.

In the case of FMCW signals, we have

y1(t) = e j2π(αt+βt2/2) +n(t) (16)

The receiver will delay this signal with τ samples to generate

y2(t) = y1(t− τ) = e j2π(α(t−τ)+β(t−τ)2/2) +n(t− τ) (17)

We replace the expectation operator with the time average, and we compute the cross-correlation value to be

21

C =∑N−1

t=0 y1(t)y∗2(t)=

∑N−1t=0 e j2π(ατ−βτ2/2+βτt) (18)

where the noise terms are cancelled since we assume that the noise signal is uncorrelated.Equation (18) can be simplified to

C = e j2π(ατ−βτ2/2) 1− e j2πβNτ

1− e j2πβτ (19)

which is function of the desired parameters α and β. We first estimate β by equating themagnitude value of both sides of equation (19) to get

|C| =∣∣∣∣∣1− e j2πβNτ

1− e j2πβτ

∣∣∣∣∣ (20)

For a measured value of |C| at a certain τ, we calculate β as estimate from equation (20).This estimate of β is substituted into equation (19) to estimate the value of α.

In the case of bi-phase signals, we have that the received signal is given by

y1(t) = BL×M(t)e j2π fct +n(t) (21)

where fc is the carrier frequency, and BL×M is a compound Barker code with BL and BM asthe inner and outer codes, respectively. The delayed version of the signal is given by

y2(t) = y1(t− τ) = BL×M(t− τ)e j2π fc(t−τ) +n(t − τ) (22)

Hence, the cross-correlation between y1(t) and y∗2(t) is given by

C =∑N−1

t=0 y1(t)y∗2(t)C =

∑N−1t=0 BL×M(t)e j2π( fct)BL×M(t− τ)e− j2π( fc(t−τ)) (23)

This is equivalent to

C = e j2π fcτ ∑N−1t=0 BL×M(t)BL×M(t − τ)

= re j2π fcτ (24)

where r =∑N−1

t=0 BL×M(t)BL×M(t − τ) is a real number. We can eliminate r by dividingequation (24) by the absolute value of C

C̃�=

C|C| = e j2π fcτ (25)

22

and we can estimate the carrier frequency fc from the angle of C̃. However, we mayhave different values of fc due to the ambiguity inherent in e j2π fcτ where adding integermultiples of 2π to the exponent does not change the value of the expression. Therefore,we may have the case when different estimates of the carrier frequency are obtained usingthe cross-correlation method. We propose that, in this case, we test the output at each ofthe candidate frequencies and detect the presence of a signal component using the cross-correlation methods as a detection tool. Note that these methods are very fast and thistechnique does not impose a significant computational load on the processor.

Here, we describe our approach to choose τ such that we eliminate the aforementioned am-biguity. First, we note that τ has to be short enough that we do not lose signal correlation.4

We consider equation (25), which is used for estimating the carrier frequency for Barkercoded signals using cross-correlation methods

C̃ = e j2π fcτ

We compute ∠C̃, which lies in the range of [0,2π] and equate it to 2π fcτ. No error occursif 2π fcτ is in the same range [0,2π]. Hence, our criterion is to choose τ such that 2π fcτ ∈[0,2π]. Replacing τ by nts where n is the number of delay samples and ts is the samplingtime, we get

0 < 2π fcnts ≤ 2π (26)

This is equivalent to

0 < fcnfs≤ 1 (27)

We have the condition on the number of delay samples n

0 < n ≤ fsfc

(28)

We know that fc ∈ [0,0.5 fs], hence we have

0 < n ≤ 2 (29)

In other words, a delay of 1 or 2 samples will guarantee that the true carrier frequencycan be estimated from the basic value of ∠C̃ (without adding multiple integers of 2π), andwe have eliminated the ambiguity effect. Note that this choice also guarantees that thesignal cross-correlation is not significantly reduced by the Barker codes autocorrelationproperties.

In the following we provide numerical evaluation of the estimation performance of bothtime-frequency and cross-correlation methods using different examples.

4Barker codes are chosen because they have very low sidelobes in the autocorrelation function. Any largedelay will significantly reduce the correlation value. For example, the ratio of the second sidelobe peak (adelay of 1 sample) to the mainlobe peak is approximately 1

the code length .

23

Example 1In this example, we test the performance of time-frequency methods using a FMCW signalwith modulation parameters: α = 20MHz and β = 50MHz/ms. The sampling frequencyis 200MHz. We vary the SNR value from −10 dB to 10 dB. We use 2048 samples forcross Wigner-Ville and 1024 samples for Wigner-Hough. We run the algorithm 100 timesand record the relative error in the estimate of α and β. The results obtained for the crossWigner-Ville and Wigner-Hough methods are listed in Table 7 and Table 8, respectively.As we can see from Table 7, the cross Wigner-Ville method gives relatively poor estimatesat very low SNR values, but its performance is significantly improved with increasing theSNR value.

Relative Error -10 dB -5 dB 0 dB 5 dB 10 dBα 0.1449 0.0888 0.0633 0.0212 0.0147β 0.4296 0.2615 0.1125 0.0473 0.0245

Table 7: Cross Wigner-Ville, FMCW signals, 100 simulation runs

The relative error in the estimates (Table 8) for the Wigner-Hough method is the same (upto the fourth decimal place) within the range of SNR values tested (-10 dB to 10 dB).

Relative Error -10 dB to 10 dBα 0.0194β 0.0461

Table 8: Wigner-Hough, FMCW signals, 100 simulation runs

This peculiar behavior is examined in Figures 12 and 13, where we plot the Wigner-Houghspectrum for SNR values of -10 dB, and 10 dB, respectively. We can see from the figuresthat the position of the peak (which is used to estimate α and β) is the same in both figures.This behavior is expected as the Wigner-Hough method is known to enjoy a low SNRthreshold. The method searches for lines of maximum values in the Wigner-Ville time-frequency spectrum. Since the noise time-frequency distribution is scattered, it does notaffect location the line of maximum value in the time-frequency plane. Therefore, thebasic component of error is due to quantization errors in the search for these lines in thetime-frequency plane.

It is worth mentioning that using a 1.9 GHz Pentium processor and 1 GB RAM, the crossWigner-Ville method takes approximately 4 S to estimate the signal parameters, while theWigner-Hough method takes about 45 S to do the same job (the number of samples is 512).

24

Figure 12: Wigner-Hough spectrum, SNR -10 dB

25

Figure 13: Wigner-Hough spectrum, SNR 10 dB

26

Example 2In this example, we examine the performance of cross-correlation methods using the sameFMCW test signal. Because of the excellent detection performance of cross-correlationmethods, we start from a very low SNR value (-30 dB) and record the relative errors inestimating α and β. The results are averaged over 100 simulation runs and we have used10000 samples, which is possible since the computational complexity of this method in-creases only linearly with the sampling size. The delayed copy of the signal is obtainedby delaying the intercepted signal by τ = 13 samples. In Table 9, we display the obtainedresults.

SNR Relative Error in α Relative Error in β-30 dB 0.3660 0.3652-25 dB 0.3740 0.1396-20 dB 0.1040 0.0368-15 dB < 10−4 0.0081-10 dB < 10−4 0.0028-5 dB < 10−4 0.00200 dB < 10−4 0.00205 dB < 10−4 0.002010 dB < 10−4 0.0020

Table 9: Cross-correlation, FMCW signals, 100 simulation runs

Cross-correlation methods are very fast which is a big advantage that makes them morefavorable in detection and estimation of radar signals. Using the same hardware as de-scribed in the previous example, cross-correlation methods need about 30 mS to estimatethe parameters of the intercepted signals.

Example 3In this example, we examine the performance of time-frequency methods using the bi-phase Barker coded signal described in Example 3 of Section 4. The results are averagedover 100 simulation runs, and the number of samples used is 2048 for the cross Wigner-Ville method and 1024 for the Wigner-Hough transform. The relative errors in estimatingthe carrier frequency are displayed in Table 10.5

5Estimating the Barker code itself can be implemented in a subsequent module after estimating the car-rier frequency. The baseband signal is obtained by filtering the received signal using our estimated carrierfrequency. This baseband signal can then be classified into one of the known Barker codes.

27

SNR Cross Wigner-Ville Wigner-Hough-20 dB Failed Failed-15 dB Failed Failed-10 dB 0.6791 0.1732-5 dB 0.5865 0.14670 dB 0.3998 0.02635 dB 0.3549 0.0155

10 dB 0.3527 0.0137

Table 10: Time-frequency methods, Barker codes, 100 simulation runs

Example 4In this example, we examine the performance of cross-correlation methods using the Barkercoded signal described in Example 3. Although there is an inherent ambiguity in the esti-mation of fc, we have overcome this problem by a careful choice of the delay τ = 2 samplesas discussed in the previous section. The relative errors in estimating the carrier frequencyfc as the SNR changes from −30 dB to 10 dB are displayed in Table 11.

SNR Relative Error in fc-30 dB 0.4472-25 dB 0.4667-20 dB 0.4236-15 dB 0.4146-10 dB 0.3699-5 dB 0.20330 dB 0.06215 dB 0.021510 dB 0.0102

Table 11: Cross-correlation, Barker codes, 100 simulation runs

From these examples, we observe the excellent performance of cross-correlation methods,which is not affected by reducing the SNR value. This feature and the low computationalload of cross-correlation methods make them more favorable than time-frequency methodsin dealing with LPI signals. However, a serious drawback of cross-correlation methods isthat the estimation algorithm depends on the modulation scheme of the intercepted signal.In other words, FMCW signals and bi-phase Barker codes signals have different estimationsteps, and in the absence of knowledge of the modulation scheme of the intercepted signalwe may not be able to directly apply cross-correlation methods for parameter estimations.On the other hand, time-frequency methods display the time-frequency properties of thesignal, where we can easily identify the modulation scheme to be either linear frequency

28

modulation (FMCW signal) or constant frequency modulation (Barker codes). This obser-vation may motivate a direction for future investigation, where we combine the advantagesof both time-frequency and cross-correlation methods. We may first apply time-frequencymethods (less accurate estimation) to just identify the modulation scheme, and then ap-ply the cross-correlation estimation algorithm (excellent estimation performance) that issuitable for this specific modulation scheme.

6 Detection in the Presence of InterferenceSources

In this section, we study the case of detecting the desired LPI signal in the presence of aninterference source. We assume the most difficult scenario where the interference signalhas the same modulation scheme as the desired LPI signal. In particular, we assume aFMCW interference signal with modulation parameters αi and βi different from those ofthe desired signal (αs and βs).

The method that is most suitable for this scenario is the Wigner-Hough method. It detectsthe presence of all signals as peaks in the spectrum while suppressing any cross termsbetween the two signals. However, as we mentioned earlier, the performance of this methoddeteriorates at very low SNR values unless we increase the number of samples which isnot practical since it significantly increases the required processing time. Although cross-correlation techniques are very fast and can be made more accurate with linearly increasingcomputational load by simply increasing the sampling point, their direct application tothis scenario is complicated due to the increased number of unknown parameters (signalparameters, interference parameters, and cross terms). Therefore, we choose the Wigner-Hough method as the most appropriate estimation technique for this particular scenario.6

Example 1In our first example, we use the same FMCW signal as described in the previous section.We simulate the desired LPI signal to have an SNR value of -10 dB, while the interfer-ence source has an Interference-to-Noise-Ratio (INR) of -5 dB. The interference signal issimulated to be a FMCW signal with αi = 40 MHz and βi = 12GHz/ms. The numberof samples used is 1024. The Wigner-Hough spectrum is displayed in Figure 14, wherewe can see the two different peaks indicating the successful separation of the desired andinterference signals.

The relative errors in estimating αs and βs are computed for 100 simulation runs and are

6Note that as a direction for future work, we will examine the use of a hybrid method combining bothcross-correlation methods and the Wigner-Hough transform for better estimation of the desired LPI signalparameters in the presence of strong interference sources.

29

Figure 14: Wigner-Hough spectrum, signal plus interference

listed in Table 12.

Relative Error in αs 0.0222Relative Error in βs 0.0279

Table 12: Wigner-Hough, 100 Simulation Runs, SNR -10 dB, INR -5 dB

Example 2In this example, we examine the performance of the Wigner-Hough method when the in-terference signal is more powerful. We use the same signal and interference parameters asdescribed in Example 1 but change the INR value to 10 dB. The Wigner-Hough spectrumfor this case is displayed in Figure 15, where we can see that the method fails to iden-tify the desired weak LPI signal. This observation motivates the implementation of othertechniques to deal with this scenario and is a point for future investigation.

30

Figure 15: Wigner-Hough spectrum, strong interference signal

7 Summary and Conclusions

In this project, we studied the problem of detection and characterization of LPI radar sig-nals by the intercept receivers. Different techniques have been proposed for this task. Inparticular, we studied the application of time-frequency tools such as the cross Wigner-Ville distribution and the Wigner-Hough transform to this scenario. We pointed out thatthe Wigner-Hough method outperforms the cross Wigner-Ville method at low SNR val-ues at the expense of increased processing times. We have also observed that the per-formance of the Wigner-Hough method can be enhanced by increasing the number ofsampling points used. However, the computational complexity in this case will be pro-hibitively high an practical implementations are not possible with currently available tech-nology. We also studied the use of cross-correlation methods for the detection task. Wesuggest two alternatives; the first one is to employ two spatially separated receivers andcompute the cross-correlation between their outputs, and the second one is to use a singlereceiver and generate a delayed copy of the received signal to compute the cross-correlationvalue. Cross-correlation methods require a threshold value, and if the strength of the cross-correlation exceeds this value the method will declare the presence of a radar signal. Weused a probabilistic approach to compute this threshold based on previous observations.

31

A histogram of the cross-correlation value of noise-only observations is constructed and aCDF is computed. From the CDF plot, we can determine the threshold value to satisfy agiven false-alarm rate. We pointed out that cross-correlation methods enjoy fast process-ing time, which increases only linearly with number of samples. Hence, we can furtherincrease the accuracy of these methods by increasing the number of samples used withoutsacrificing the advantage of real time processing. Furthermore, hardware realizations ofthese methods can be easily implemented.

The detection performance of both time-frequency and cross-correlation techniques hasbeen evaluated using different numerical examples. We concluded that the use of cross-correlation methods is more favorable in terms of accuracy and processing times as com-pared to time-frequency methods.

Estimation of signal parameters has also been studied. It has been shown that time-frequency methods can be applied to both FMCW and bi-phase signals to estimate themodulation parameters. On the other hand, cross-correlation methods can efficiently esti-mate the modulation parameters of FMCW signals but they may suffer from an ambiguityproblem in estimating these parameters for bi-phase signals. We have developed a criterionfor the choice of the number of delay samples that eliminates this ambiguity problem andguarantees good estimation performance. The estimation performance of both methods hasbeen evaluated using different numerical examples.

Finally, we studied the problem of estimating the modulation parameters of the desiredLPI signals when a stronger interference signal is present. We pointed out that the Wigner-Hough method is the only method that is directly applicable to this scenario. We examinedthe performance of this method and highlighted its limited resolution capabilities at highINR values.

32

References

[1] S. Barbarossa and A. Zanalda, “A combined Wigner-Ville and Hough transform forcross-terms suppression and optimal detection and parameter estimation,”ICASSP’92, vol. 5, CA, Mar. 1992, pp. 173-176.

[2] S. Barbarossa, “Analysis of multicomponent LFM signals by a combinedWigner-Hough transform,” IEEE Trans. Signal Processing, vol. 43, no. 6, pp.1511-1515, Jun. 1995.

[3] E. J. Carlson, “Low probability of intercept (LPI) techniques and implementationsfor radar systems,” IEEE National Radar Conference, MI, Apr. 1988, pp. 56-60.

[4] M. N. Cohen, “Principles of modern radar,”, J. L. Eaves and E. K. Reedy (Eds.), VanNostrand Reinhold, New York, 1987.

[5] M. N. Cohen, J. M. Baden and P. E. Cohen, “Biphase codes with minimum peaksidelobes,” IEEE National Radar Conference, TX, Mar. 1989, pp. 62-66

[6] C. De Luigi and E. Moreau, “Wigner-Ville and polynomial Wigner-Ville transformsin the estimation of nonlinear FM signal parameters,” ICASSP’02, vol. 2, FL, May2002, pp. 1433-1436.

[7] K. L. Fuller, “To see and not be seen,” IEE Proc. F Radar, Sonar, and NavigationSignal Processing, vol. 137, no. 1, pp. 1-10, Feb. 1990.

[8] J. E. Gonzalez, J. M. Pardo, A. Asensio, and M. Burgos, “Digital signal generationfor LFM-LPI radars,” Electronic Letters, vol. 39, no. 5, pp. 464-465, Mar. 2003.

[9] C. Guanghua, M. Shiwei, Q. Tinghao, W. Jian, and C. Jialin, “The Wigner-VilleDistribution and the Cross Wigner-Ville Distribution of Noisy Signals,” The 8thInternational Conference on Signal Processing, vol. 1, China, Nov. 2006, pp. 16-20.

[10] L. I. Ruffe and G. F. Stott, “LPI considerations for surveillance radars,” IEEEInternational Radar Conference, Brighton, United Kingdom, Oct. 1992, pp.200-202.

[11] B. Boashash and P. O’Shea, “Use of the cross Wigner-Ville distribution forestimation of instantaneous frequency,” IEEE Trans. Signal Processing, vol. 41, no.3, pp. 1439-1445, Mar. 1993.

[12] G. Schrick and R. G. Wiley, “Interception of LPI radar signals,” IEEE InternationalRadar Conference, VA, May 1990, pp. 108-111.

[13] K. R. Veerabhadra Rao and V. R. Umapathi, “Biphase Sequence Generation withLow Sidelobe Autocorrelation Function,” IEEE Trans. Aerospace and ElectronicSystems, vol. AES-22, no., pp. 128-133, Mar. 1986.

33

34 DRDC Ottawa CR 2009-142

This page intentionally left blank.

DOCUMENT CONTROL DATA (Security classification of title, body of abstract and indexing annotation must be entered when the overall document is classified)

1. ORIGINATOR (The name and address of the organization preparing the document. Organizations for whom the document was prepared, e.g. Centre sponsoring a contractor's report, or tasking agency, are entered in section 8.) McMaster University 1280 Main Street West Hamilton ON L9T 2Y1

2. SECURITY CLASSIFICATION (Overall security classification of the document including special warning terms if applicable.)

UNCLASSIFIED

3. TITLE (The complete document title as indicated on the title page. Its classification should be indicated by the appropriate abbreviation (S, C or U) in parentheses after the title.) Detection of low probability of intercept radar signals

4. AUTHORS (last name, followed by initials – ranks, titles, etc. not to be used) Wong, K.M.; Davidson, T.; Abdelkader, S.

5. DATE OF PUBLICATION (Month and year of publication of document.) September 2009

6a. NO. OF PAGES (Total containing information, including Annexes, Appendices, etc.)

48

6b. NO. OF REFS (Total cited in document.)

13 7. DESCRIPTIVE NOTES (The category of the document, e.g. technical report, technical note or memorandum. If appropriate, enter the type of report,

e.g. interim, progress, summary, annual or final. Give the inclusive dates when a specific reporting period is covered.) Contract Report

8. SPONSORING ACTIVITY (The name of the department project office or laboratory sponsoring the research and development – include address.) Defence R&D Canada – Ottawa 3701 Carling Avenue Ottawa, Ontario K1A 0Z4

9a. PROJECT OR GRANT NO. (If appropriate, the applicable research and development project or grant number under which the document was written. Please specify whether project or grant.)

9b. CONTRACT NO. (If appropriate, the applicable number under which the document was written.)

W7714-061022/001SV

10a. ORIGINATOR'S DOCUMENT NUMBER (The official document number by which the document is identified by the originating activity. This number must be unique to this document.)

10b. OTHER DOCUMENT NO(s). (Any other numbers which may be assigned this document either by the originator or by the sponsor.) DRDC Ottawa CR 2009-142

11. DOCUMENT AVAILABILITY (Any limitations on further dissemination of the document, other than those imposed by security classification.)

Unlimited

12. DOCUMENT ANNOUNCEMENT (Any limitation to the bibliographic announcement of this document. This will normally correspond to the Document Availability (11). However, where further distribution (beyond the audience specified in (11) is possible, a wider announcement audience may be selected.)) Unlimited

13. ABSTRACT (A brief and factual summary of the document. It may also appear elsewhere in the body of the document itself. It is highly desirable that the abstract of classified documents be unclassified. Each paragraph of the abstract shall begin with an indication of the security classification of the information in the paragraph (unless the document itself is unclassified) represented as (S), (C), (R), or (U). It is not necessary to include here abstracts in both official languages unless the text is bilingual.)

Modern radar systems employ new type of signals, which are more difficult to detect and exploit. These signals are known as Low Probability of Intercept (LPI) signals. In this project, we study the performance of the intercept receiver in the scenario of LPI signals. We propose different techniques to detect and characterize the intercepted signals. We study the application of time-frequency techniques to this problem. Namely, we apply the Wigner-Ville distribution method to construct the time-frequency spectrum of the received signal and detect the presence of a radar signal. We apply the Hough transform, as a line detector, to the Wigner-Ville spectrum to enhance the performance of signal detection and estimation. We also propose the use of a novel technique for the detection/estimation of the intercepted radar signals. This technique is based on cross-correlation properties, and is shown to enjoy very fast processing time together with very accurate detection/estimation performance. Various numerical examples are included to evaluate the performance of these proposed methods under different scenarios.

14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Technically meaningful terms or short phrases that characterize a document and could be helpful in cataloguing the document. They should be selected so that no security classification is required. Identifiers, such as equipment model designation, trade name, military project code name, geographic location may also be included. If possible keywords should be selected from a published thesaurus, e.g. Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus identified. If it is not possible to select indexing terms which are Unclassified, the classification of each should be indicated as with the title.) Low Probability of Intercept (LPI) signals, Wigner-Ville distribution, cross-correlation