Denial of bistatic hosting by spatial–temporalwaveform design

H.D. Griffiths, M.C. Wicks, D. Weiner, R. Adve, P.A. Antonik and I. Fotinopoulos

Abstract: A set of theoretical techniques to prevent a radar from being used by a bistatic radarreceiver as a non-cooperative illuminator are analysed. This works by radiating in addition to theradar signal waveform, a ‘masking signal’ waveform which is orthogonal to the radar signalwaveform, both in the coding domain and the spatial domain. A number of different codingschemes are analysed. Two spatial coding methods are presented and analysed: the first uses a pairof interferometer elements at the extremities of the radar antenna array; the second uses a Butlermatrix to generate a set of orthogonal beams. System-level calculations are presented to show thelevel of masking of the radar signal received by a bistatic radar receiver, and the suppression of themasking signal in the host radar echo. Some ideas for further work are presented.

1 Introduction

Many countries have invested heavily in the development ofadvanced surveillance systems and technologies. Ofincreasing concern is the threat that potential adversariesmay use bistatic technologies to take advantage ofsignificant investment in advanced sensors by our owncountries [1, 2]. With relatively inexpensive receiversystems, an adversary could use the signals as bistatic‘illuminators of opportunity’. A central requirement fornon-cooperative bistatic operation is the estimation of acoherent reference signal. This estimate is used to correlatewith the received signals to extract the desired signal. Asillustrated in Fig. 1, a coherent reference is typicallyobtained by measuring a direct path signal via the sidelobesof the illuminator [3, 4]. Conventional methods to preventthe interception of the direct path signal include lowsidelobe antennas, physical isolation, and the use of spread-spectrum waveforms. These methods will becomeinadequate as surveillance sensors migrate to space.

This paper introduces and evaluates a number oftheoretical techniques to prevent a radar being used by anadversary as a bistatic illuminator of opportunity. These areall based on the idea of radiating a so-called ‘maskingsignal’ (Fig. 2) which is arranged to be orthogonal, both ina spatial sense and in a coding sense, to the radar signal, and

of a level sufficient to mask the radar signal to an adversary,and hence to deny a reference for bistatic operation [5, 6].

2 Waveform analysis and design

2.1 Ambiguity and cross-ambiguity functions

We consider a sideways-looking radar on an airborneplatform, such as would be used for synthetic aperture radar(SAR) or ground moving-target indication (GMTI) pur-poses. As shown schematically in Fig. 2, the radar transmits(and receives) a radar waveform urðtÞ at a power Pr via aradiation pattern FrðyÞ; and transmits a masking waveformumðtÞ at a power Pm via a radiation pattern FrðyÞ: Thewaveforms may be pulsed, quasi-CW or CW. We wish toquantify the degree of masking of the radar signal at anadversary’s bistatic receiver in a given direction, and thedegree of suppression of echoes (from targets or fromclutter) of the masking signal received in the channels of theradar receiver.

For a sideways-looking airborne radar and a stationarytarget, there is a direct relationship between echo Dopplershift fD and angle y such that

fD ¼ 2v

lsin y ð1Þ

where v is the platform velocity and l is the radar wavelength.Conventionally the performance of a radar waveform isquantified in terms of resolution, sidelobe structure, andambiguities, in range and Doppler domains by means of theambiguity function [7]. This plots the point target response ofthe radar as a function of delay (equivalent to range) andDoppler frequency (equivalent to velocity) by calculating theresponse of a matched filter for the waveform urðtÞ to an echoof delay t and Doppler shift fD

xðt; fDÞ ¼Z 1

�1urðtÞu�

r ðt � tÞe j2pfDt dt ð2Þ

The ambiguity function is defined as the square magnitude ofthis, jxðt; fDÞj2: For our purposes, we are interested in theresponse of the radar receiver to an echo (from a target orfrom clutter) from the masking signal. This leads to thefollowing definition of the cross-ambiguity function [8]:

IEE Proceedings online no. 20041236

doi: 10.1049/ip-rsn:20041236

H.D. Griffiths is with University College London, Department of Electronicand Electrical Engineering, Torrington Place, London WC1E 7JE, UK

M.C. Wicks, D. Weiner and P.A. Antonik are with the Sensors Directorate,Air Force Research Laboratory, 26 Electronic Parkway, Rome, NY 13441-4514, USA

R. Adve is with the University of Toronto, Dept. of Electric andCommunication Engineering, Communications Group, Rm. GB 434, 35St. George St., Toronto, Ontario M5S 3G4, Canada

I. Fotinopoulos is with Imperial College of Science, Technology andMedicine, Department of Electrical and Electronic Engineering, ExhibitionRoad, London SW7 2BT, UK

E-mail: h.griffiths@ee.ucl.ac.uk

Paper first received 5th November 2001 and in revised form 22ndNovember 2004. Originally published online 4th March 2005

IEE Proc.-Radar Sonar Navig., Vol. 152, No. 2, April 2005 81

jxr;mðt; fDÞj2 ¼Z 1

�1urðtÞu�

mðt � tÞe j2pfDt dt

��������2

ð3Þ

which is the response to a signal umðtÞ (i.e. the maskingsignal) of a filter designed to be matched to waveform urðtÞ(i.e. the radar signal).

2.2 Detection statistic of non-cooperativebistatic radar receivers

It is assumed that the non-cooperative bistatic radar receiverperforms detection by utilising an estimate of the host radartransmitted signal for correlation with the received data. Theestimate of the host radar transmitted complex envelope istypically obtained from the direct path signal observed bythe bistatic radar receiver. In general, the direct path signalis corrupted by clutter and receiver noise which in somecases can be sufficient to cause significant signal processinglosses due to poor estimates of the host radar complexenvelope. However, for our purposes it is assumed that themasking signal is mainly responsible for degradation of thecomplex envelope estimate. In this way, there is no reliancesolely on the clutter and receiver noise to prevent the non-cooperative bistatic radar receiver from ‘hosting’ off themonostatic radar. Of course, to the extent that the clutter andreceiver noise help to mask the transmitted radar waveformin the direct path, the more difficult it will be for the non-cooperative bistatic radar receiver to operate successfully.

For simplicity assume that the direct path signalbetween the monostatic and bistatic radars is used as thecoherent reference signal for the correlator in the non-cooperative bistatic radar receiver. Assume that the directpath signal intercepted by the bistatic radar receiver isdelayed by an amount tDP and Doppler shifted by a

frequency f DP: If nDPðtÞ denotes the complex envelope ofthe receiver noise in the direct path the complex envelopeof the direct path signal may be modelled as

uDPðtÞ ¼ KDPRADurðt � tDPÞe j2pf DPðt�tDPÞ

þ KDPIFMumðt � tDPÞe j2pf DPðt�tDPÞ þ nDPðtÞ ð4Þ

where KDPRAD and KDP

IFM are constants relative to themonostatic radar and masking signal powers interceptedby the bistatic radar, respectively.

The signal reflected from the target to the non-cooperativebistatic radar receiver consists of two components: one fromthe radar signal and one from the masking signal. Assumethat the total path signal received by the bistatic radarreceiver is delayed by an amount tTP and Doppler shiftedby an amount f TP: If nTPðtÞ denotes the complex envelopeof the receiver noise in the total path the complex envelope ofthe total path signal may be modelled as

uTPðtÞ ¼ KTPRADurðt � tTPÞe j2pf TPðt�tTPÞ

þ KTPIFMumðt � tTPÞe j2pf TPðt�tTPÞ þ nTPðtÞ ð5Þ

where KTPRAD and KTP

IFM are constants relative to the targetsignal power intercepted by the bistatic radar due to themonostatic radar and the masking signal antenna, respec-tively. The bistatic delay is defined as tB ¼ tTP � tDP and thebistatic Doppler shift is fB ¼ f TP � f DP: Ideally the non-cooperative bistatic receiver would like to correlateurðt � tTPÞe j2pf TPðt�tTPÞ with the total path signal uTPðtÞ:To accomplish this it would modify the direct path signal by adelay tB and a Doppler shift fB: However, these are unknownin practice and so the bistatic radar receiver would utiliseestimates of tB and fB: Let these be denoted by t̂tB ¼ tB � tand f̂fB ¼ fB � �: To detect a possible target the bistatic radarreceiver would then correlate uDPðt � t̂tBÞe j2pf̂fBðt�tDP�tBÞ withuTPðtÞ. This yields the test statistic employed for the detectionof a target. Hence the test statistic at the output of thecorrelator in the non-cooperative bistatic radar receiver is

l ¼Z 1

�1½uDPðt � t̂tBÞ�e�j2pf̂fBðt�tDP�t̂tBÞuTPðtÞ dt ð6Þ

After some manipulation

l ¼ e�j2pf TPt½k1xðt; �Þ þ k2e j2p�tZ�ð�t;��Þ

þ k3Zðt; �Þ þ k4Gðt; �Þ þ noise terms ð7Þ

where xðt; �Þ is the delay–Doppler ambiguity function ofthe host radar waveform, Zðt; �Þ is the delay–Dopplercross ambiguity function between the interferometer andthe host radar function, Gðt; �Þ is the delay–Dopplerambiguity function of the interferometer waveform, k1 ¼ðKDP

RADÞ�KTPRAD; k2 ¼ ðKDP

RADÞ�KTPIFM; k3 ¼ ðKDP

IFM�KTPRAD and

k4 ¼ ðKDPIFMÞ�KTP

IFM: The desired signal component of thedetection statistic is ls ¼ k1e�j2pf TPtxðt; �Þ: The remainingterms represent noise and interference. In general, thedesired signal component is corrupted by thermal noise,clutter, multipath and=or other propagation effects. How-ever, it is the intention of this effort to design the maskingsignal such that it effectively masks the direct path signalfrom the host radar. The expression for the detectionstatistic clearly shows that the objective of coherentreference denial depends on the delay–Doppler ambiguityfunctions of the host radar and masking signal waveformsand their cross-ambiguity function.

Fig. 2 Radar and masking signal radiation patterns in whichmasking signal is radiated at level such that adversary cannotobtain reference from radar signal

Fig. 1 Non-co-operative bistatic receivers require coherentreference from host illuminator

IEE Proc.-Radar Sonar Navig., Vol. 152, No. 2, April 200582

2.3 Ambiguity functions of various signals

A simulation code has been devised to calculate and plot theauto- and cross-ambiguity functions of arbitrary signals, andto include the effect of antenna radiation patterns. In thisSection we investigate the performance of various types ofwaveform; in the following Section we consider the effect oftwo different approaches to orthogonal radiation patterns.

2.3.1 Linear FM signals: An obvious candidate forthe choice of radar and masking signals is to use twocochannel chirp waveforms of opposite slope. Waveformsof this type have been used by Giuli et al. in an applicationto simultaneously measure the elements of a polarimetricscattering matrix [9]. The auto-ambiguity function of a chirpsignal has a rather high peak sidelobe level (PSL), around13.2 dB, which can be lowered in the usual way byamplitude weighting. The cross-correlation of two oppo-site-slope chirp signals was evaluated for different values oftime–bandwidth product BT. The results showed that forBT ¼ 1000 the PSL was �33 dB and for BT ¼ 200 it was�25 dB: The Doppler frequency shift was slightly smallerthan the signal bandwidth, and the isolation loss due toDoppler shift was limited even when weighting was applied.Based on those results we conclude that the use of chirpsignals for our purposes is limited because of rangedecorrelation between the compressed waveforms.

2.3.2 Pseudorandom binary sequences:Pseudorandom binary sequences (PRBSs) are another classof waveform with potentially useful properties in thiscontext. Sets of PRBS codes of given lengths have beenfound with good auto- and cross-correlation properties [10].To specify such codes we adopt the notation (n, m), where n

denotes the decimal value of the shift register tap positionsused to generate the code (the last tap is ignored because it isalways used), and m is the decimal value of the binarynumber with which the shift register is loaded at the start ofthe code. The sequences used for this purpose are cyclic. Fordifferent sequences the first sidelobe levels had differentvalues. For the sequence (115, 115) of length 255 the PSLwas �24:05 dB: For the sequence (234, 413) of length 511the PSL was found to be �27 dB: The Doppler tolerance isapproximately 1=(code length). The results showed thatalthough the peak sidelobe levels are reasonable (of order25 dB), the isolation between different codes is not so good.This problem is common in binary sequences and digitalcoding, where high isolation seems hard to achieve even iflower PSL values are accepted.

2.3.3 Costas signals: A third class of potentiallyuseful waveforms are frequency-hopped waveforms [11,12]. Frequency-hopped waveforms are conveniently rep-resented by a square binary matrix known as thepermutation matrix. An N � N matrix contains a total ofQ ¼ N2 matrix elements. Thus, when the elements arebinary, the number of different matrices possible is 2Q:However, of these only N! matrices can be obtained bypermuting the N integers contained between 0 and ðN � 1Þ:Some of these are better than others for designing the signalpattern of a radar waveform. Costas introduced a specifictype of permutation matrices, the so-called Costas arrays[13, 14] which may be used in applications such as spread-spectrum communication systems, where the objective maybe to achieve either jamming resistance, low probability ofintercept, or frequency diversity for a selectively fadingchannel. An example of a Costas array for N ¼ 7 is shownin Fig. 3, and the corresponding auto-ambiguity function inFig. 4. The equivalent auto-ambiguity function for a Costassignal for which N ¼ 30 is shown in Fig. 5. It can be seen inboth cases that the ambiguity function, although it doesnot have a smooth pedestal, approaches the shape of theideal ‘thumbtack’.

2.4 Summary

For this work the Costas signal is adopted for the host radarwaveform because it yields a thumbtack-shaped ambiguityfunction with a relatively low pedestal. For a fixed number offrequency hops within a radar pulse there are many differenthopping patterns that result in essentially the samethumbtack-shaped ambiguity function. Hence, differentfrequency-hopping patterns can be utilised to furthercomplicate the coherent reference estimation task of thenon-cooperative radar.

Fig. 3 Permutation matrix of one of 200 possible Costas arraysfor N ¼ 7

Fig. 5 Auto-ambiguity function of Costas signal for N ¼ 30Fig. 4 Auto-ambiguity function of Costas signal of Fig. 3(N ¼ 7)

IEE Proc.-Radar Sonar Navig., Vol. 152, No. 2, April 2005 83

3 Generation of radiation patterns

This Section describes two different approaches to thegeneration of radiation patterns for the masking signalwaveform. The first of these uses an interferometer; thesecond is based on a Butler matrix.

3.1 Interferometer scheme

The radar antenna is assumed to be an N-element arrayof omnidirectional elements with interelement spacing d.The masking signal is radiated via an additional twoelements, one at each end of the array (Fig. 6). The twointerferometric elements are driven separately with anindependent waveform generation, timing and controlcircuit. Ideally the interferometer antenna pattern willoverlay the sidelobes of the host radar main antenna patternwith minimal overlay of the radar main beam. Theinterferometer may or may not be on all of the time.However, as a minimum, the interferometer will be onwhile the host radar is in the transmit mode with theobjective that the interferometer signal will mask thatportion of the host radar signal emitted through the radarsidelobes. In this way a coherent reference signal is deniedto a non-cooperative bistatic receiver. To increase theeffectiveness of this masking, it is also proposed tomodulate the interferometer antenna pattern from pulse topulse such that the pattern is rotated on each pulse (Fig. 7).

3.1.1 Interferometer antenna pattern: In gen-eral, the azimuthal radiation pattern of the interferometer

array factor can be shown to have the following properties,with d ¼ l=2; y ¼ p=2; a is the azimuth angle with respectto the normal to the interferometer axis:

(i) For all integer values of N (antenna array elements),either odd or even

(a) symmetry exists about both the x- and y-axes(b) the number of major lobes is equal to ð2N þ 2Þ(c) there are no minor lobes(d) major lobes always occur at a ¼ 0� and 180�

(ii) When N is an odd integer(a) the polarity of the major lobes strictly alternate insign from one lobe to the next(b) major lobes always occur at a ¼ 90�

(iii) When N is an even integer(a) focusing entirely above or below the x-axis, thepolarity of the major lobes strictly alternate in sign fromone lobe to the next(b) the first major lobes positioned on either side of thex-axis have the same polarity(c) nulls always occur at a ¼ 90�

These properties are demonstrated by the plots in Fig. 8. Thenulls appearing at a ¼ 90� when N is an even integer areof particular interest. The derivative of the array factor iszero for a ¼ 90�: Therefore the nulls at these angles havezero slope. This is consistent with the property that the firstmajor lobes positioned on either side of the x-axis have thesame polarity. This is illustrated in Fig. 9 where a cartesianplot of FIFMðp=2; aÞ; corresponding to N ¼ 2; is presentedwith a varying from 0� to 180�: It is seen that the null ata ¼ 90�; where the polarity of FIFMðp=2; aÞ is unchangedand the slope is zero, is noticeably broader than the nulls ata ¼ 19:5� and 160:5�; where the polarity of FIFMðp=2; aÞdoes change. To avoid self-jamming of the radar andcommunication waveforms it may be desirable to steer theinterferometer pattern such that the main beam of the hostradar is centred in this broad null.

3.1.2 Steering the interferometer: It was firstassumed that the interferometer elements are placed on alinear grid about the main radar elements and theinterferometer pair steered by inserting an appropriateFig. 6 Configuration of system using interferometer

Fig. 7 Pulse-to-pulse phase modulation of sidelobes denies coherent reference to non-cooperative receivers

IEE Proc.-Radar Sonar Navig., Vol. 152, No. 2, April 200584

phase shift into each channel. It was noticed that severedistortion occurred in the array factor radiation pattern whenthe interferometer was steered and that although there was anull at a ¼ 0�; this was not a broad null. It was concludedtherefore that it is not possible to steer a broad null to a ¼ 0�

when the interferometer is placed on a linear grid about themain radar elements.

On the other hand, a broad null was obtained at a ¼ 0�;when the interferometer was placed on the y-axis while thelinear array of the main radar remained along the x-axis. Asbefore, the two dipole antennas of the interferometer pairwere directed in the z-direction. However, the elementswere now placed on the y-axis. Because the interferometerelements no longer straddle the main radar elements on thex-axis, it is convenient to measure the interferometerspacing in units of half wavelength. Therefore theinterferometer spacing was defined to be

dIFM ¼ ks

l2

ð8Þ

where ks is an integer. Polar plots of the azimuthal radiationpattern of the interferometer array factor, where the

elements are on the y-axis, are presented in Fig. 10 fory ¼ p=2 and ks ¼ 3; 5; and 7. Note that these values of ks

correspond to dIFM ¼ 3l=2; 5l=2 and 7l=2; respectively.As expected, because ks is an odd integer for each of theplots, a broad null is seen to exist at a ¼ 0� in each case.Therefore, assuming that the main radar antenna elementsare positioned on the x-axis while the interferometerelements are placed along the y-axis, broad nulls occurbroadside to the main radar antenna in both the horizontaland vertical planes whenever ks is an odd integerguaranteeing the orthogonality property between radar andmasking signal. Since the interferometer excitation is likelyto be considerably smaller than the radar excitation,placement of the broad null of the interferometer at thecentre of the main beam of the radar is likely to be aneffective technique for preventing the interferometer signalfrom interfering with the desired radar target returns.

3.2 Butler matrix scheme

Consider, as in the previous Section, an N-element linearantenna array. Suppose initially that the array is fed by aButler matrix [15] (Fig. 11). A Butler matrix may beconsidered to be a hardware realisation of the Cooley–Tukey fast Fourier transform algorithm [16]. This generatesa set of spatially orthogonal antenna beams, each of the form

jEj ¼ 1

N

sinðNc=2Þsinðc=2Þ ð9Þ

with

c ¼ kd

lsinðy� dmÞ ð10Þ

where d is the element spacing, l is the wavelength, k ¼2p=l; y is the azimuth angle and dm is the angle of themaximum of the mth beam. For an N-element array

Fig. 8 Azimuthal radiation pattern of interferometer array plotted for d ¼ l0=2; y0 ¼ p=2

a dIFM ¼ 3l0=2b dIFM ¼ 2l0

c dIFM ¼ 5l0=2d dIFM ¼ 3l0

e dIFM ¼ 7l0=2f dIFM ¼ 4l0

Fig. 9 Cartesian plot of FIFM(p=2; a) corresponding to N ¼ 2;with a varying from 0� to 180�

IEE Proc.-Radar Sonar Navig., Vol. 152, No. 2, April 2005 85

dm ¼ ð2m � 1ÞpN

ð11Þ

so the normalised far-field pattern of the mth beam is

Em ¼ 1

N

sin Npdl2 sin y� ð2m�1Þp

N

� �h i

sin pdl2 sin y� ð2m�1Þp

N

� �h i ð12Þ

The orthogonality of this set of beams is maintained over abroad bandwidth, dictated by the hardware of the Butlermatrix but typically an octave or more. For this to be so, thebeamwidths and directions of the beams must changewith frequency. The beams have a first sidelobe level of�13:2 dB; which is rather high for radar purposes; thesidelobe level can be lowered by an amplitude taper acrossthe array in the usual way, but this destroys the orthogonalitycondition. The set of beams may be steered electronically bya set of phase shifters at the antenna elements.

Suppose that one of the central beams is used for theradar, both for transmitting and receiving. One or more ofthe remaining beams is used to radiate the masking signal orsignals, at an appropriate relative power level.

Furthermore, if the radar signal and masking signals wereto be generated at the beam ports of the Butler matrix bydirect digital synthesis, which could include the effect ofphase shifts to steer the beams electronically, then since thesignals radiated from each element are simply weightedcombinations of the beam port signals, the element signalsmay be calculated and generated directly without any needfor the Butler matrix hardware.

4 Results

To assess whether the level of masking is sufficient to maskthe radar signal to an adversary, and hence to deny areference for bistatic operation, a radar signal to maskingsignal ratio for the case of an adversary listening from aparticular angle y is defined:

LðyÞ ¼ level of masking signal

level of radar signalð13Þ

This can be evaluated either at a particular value of y; or asan average over the sidelobe region. The value of L at y ¼ 0(i.e. at the centre of the host radar main lobe) will obviouslytake negligible values first because of the broad null of themasking signal at this angle and secondly because of theorthogonal coding of the signals. An adversary could onlyrecover the radar signal if listening from that specificdirection.

The further the angle of the adversary from boresightðy ¼ 0Þ; the worse the recovery. This is because we can varythe radar to masking signal ratio by varying the power of thetransmitted masking signal in order to cause considerabledisruption of the reception of the radar signal while ofcourse maintaining consistent radar operation.

We wish to quantify the degree of masking of the radarsignal at a receiver in a given direction, and the degree ofsuppression of echoes (from targets or from clutter) of themasking signal received in the channels of the radarreceiver. To achieve this we formulated a radar-to-maskingsignal ratio and a radar signal echo to masking signal echoratio explained in the following Sections.

4.1 Radar signal to masking signal ratio

Following (13) in the previous Section the radar signal tomasking signal as a function of angle will be

LðyÞ ¼ PrFrðyÞPmFmðyÞ

ð14Þ

This ratio depends on the geometry of the antennas used andtheir radiation patterns. In the following Section weinvestigate how this ratio is expressed for the interferometerand Butler matrix cases.

4.1.1 Interferometer: The main radar array factoris given by

Frðy; aÞ ¼1

lpd sin y sin a

sin pdl sin y sin a

� � ð15Þ

Fig. 10 Azimuthal radiation pattern of interferometer array factor, where elements are on the y-axis, for y0 ¼ p=2

a dIFM ¼ 3l0=2b dIFM ¼ 5l0=2c dIFM ¼ 7l0=2

Fig. 11 Configuration of system using Butler matrix in which thebeam ports provide set of orthogonal beams

One beam is used for the radar, and the masking signal radiated, at asuitable power level, from the others

IEE Proc.-Radar Sonar Navig., Vol. 152, No. 2, April 200586

The masking signal array factor when the interferometerscheme is used is given by

Fmðy; aÞ ¼ cos pdIFM

lsin y cos a

ð16Þ

So the radar signal to masking signal ratio when aninterferometer is used would be

LðyÞIFM ¼ PrFrðyÞPmFmðyÞ

¼ Pr

Pm

pd sin y sin a

l sin pdl sin y sin a

� �cos p dIFM

l sin y cos a� �

ð17Þ

4.1.2 Butler matrix: As in the previous Section, themain radar array factor is given by

Frðy; aÞ ¼1

lpd sin y sin a

sin pdl sin y sin a

� �The masking signal array factor for the Butler matrixscheme is given by

Fmðy; aÞ ¼1

lpd sinðy� dÞ sin a

sin pdl sinðy� dÞ sin a

� � ð18Þ

The radar signal to masking signal ratio for the Butlermatrix scheme is therefore

LðyÞBM ¼ Pr

Pm

�sin y sin pd

l sinðy� dÞ sin a� �

sinðy� dÞ sin pdl sin y sin a

� � ð19Þ

It is evident that in a given direction y; the ratio FmðyÞ=FrðyÞwill be constant. Therefore the power levels Pm; Pr are theonly parameters that need to be adjusted to achieve a desireddegree of masking.

4.2 Suppression of masking signal in radarreceiver

The suppression of the masking signal in the radar receiverwill include the echoes received from the target andclutter. The masking signal levels will be further suppressedbecause the filter at the receiver is matched to the radarsignal.

The echo of the masking signal is proportional to PmFm:Similarly the echo of the radar signal is proportional to PrFr:These signals are received by the radar antenna pattern whichwe will consider to be the same as the transmit radar pattern.The following two expressions can thus be written:

Sm ¼ PmFmðyTARÞFrðyRECÞ ð20Þ

Sr ¼ PrFrðyTARÞFrðyRECÞ ð21Þ

These are applied to the matched filter for the radarsignal. The degree of suppression of the masking signal istherefore

RðyÞ ¼ PmFmðyTARÞFrðyRECÞR1�1 umðt � tÞu�

r ðtÞe j2pfDt dt

PrFrðyTARÞFrðyRECÞR1�1 urðt � tÞu�

r ðtÞe j2pfDt dt

ð22Þ

where FmðyTARÞ is the Doppler shifted echo of the maskingsignal from the target; FrðyTARÞ is the Doppler shifted echo of

the radar signal from the target; FrðyRECÞ is the radar signal atreception;

Z 1

�1umðt � tÞu�

r ðtÞe j2pfDt dt

is the response to the masking signal of the filter matched tothe radar signal (cross-ambiguity function); and

Z 1

�1urðt � tÞu�

r ðtÞe j2pfDt dt

is the response to the radar signal of the filter matched to theradar signal (auto-ambiguity function).

As a result it can be seen that the radar signal echo tomasking signal echo ratio depends on the relative trans-mitted levels of the radar signal and masking signal, as wellas the responses of the radar and masking signals at a givenDoppler shift to the filter matched to the radar signal at zeroDoppler. All of this also depends on the position of thetarget, so it is not controllable by the radar designer.However, the power levels Pm and Pr of the radar andmasking signals are controllable and can be set to achievethe desired results.

As examples, Figs. 12 and 13 show the degree ofsuppression of the masking signal in the radar receiver,calculated according to (22), for the cases of theinterferometer scheme and the Butler matrix scheme,

Fig. 12 Degree of suppression of masking signal in radarreceiver ( for Costas signal of Figs. 3 and 4 and Pr=Pm ¼ 20 dB),interferometer case

Fig. 13 Degree of suppression of masking signal in radarreceiver (for Costas signal of Figs. 3 and 4 and Pr=Pm ¼ 20 dB),Butler matrix case

Side-on view shows shape of null at y ¼ 0; both because of low level ofjamming signal radiated around that direction and because codeorthogonality is good close to zero Doppler

IEE Proc.-Radar Sonar Navig., Vol. 152, No. 2, April 2005 87

respectively. For both plots the ratio of masking signal toradar signal Pr=Pm has been chosen to be 20 dB, which givesan acceptable degree of masking in the sidelobe region.In both Figures it can be seen that close to zero Doppler therejection of the masking signal in the radar receiver is almosttotal, both because of the level of the jamming signal radiatedaround that direction and because the code orthogonality isgood close to zero Doppler. Away from this direction therejection degrades, to a minimum value of about 30 dB ineach case, corresponding to an average value of about 35 dB.

5 Conclusions

5.1 Summary

We have introduced and analysed a set of theoreticaltechniques to prevent a radar being used by a bistaticreceiver as a non-cooperative illuminator by radiating inaddition to the radar signal waveform a ‘masking signal’waveform. This is designed to be orthogonal to the radarsignal waveform, both in the coding domain and the spatialdomain. A number of waveform coding techniques havebeen analysed, and of those considered, Costas codes appearto offer best performance and flexibility. Two spatial codingtechniques have been devised and analysed; one based on aninterferometer, and one based on a Butler matrix.Expressions as a function of the system parameters havebeen derived for the degree of suppression of the radarsignal by the masking signal, and for the suppression of themasking signal in the host radar echo. Evaluation andplotting of these expressions have demonstrated that it ispossible to obtain adequate masking of the radar signal,while at the same time achieving suppression of echoesfrom the masking signal of the order of 30 or 40 dB. In thisrespect the performance of the interferometer and Butlermatrix schemes are comparable.

5.2 Further work

Both interferometer and Butler matrix schemes appear togive acceptable results, and both are worthy of furtherinvestigation. The Costas codes used in the examplespresented in Figs. 12 and 13 are of length 7, and improvedperformance could probably be obtained by using longerCostas codes, or orthogonal codes of other kinds. For theButler matrix scheme it would be interesting to examine thetradeoff between sidelobe level and beam orthogonality.Also, in the treatment so far it has been assumed that theradar signal radiation patterns are identical on transmit andon receive. It would be interesting to explore the use of non-identical antenna patterns, and indeed it may be anticipatedthat the use of STAP-type methods to adaptively suppressclutter returns from the masking signal would give goodresults. Finally, the hardware implications of using directdigital synthesis, for example in the requirement for poweramplifiers with very low intermodulation, should be lookedat critically.

The ideas presented are just one example of the idea of‘waveform diversity’, in which waveform coding techniques

are used with multiple transmit and receive beams, probablyin conjunction with adaptive processing in spatial andtemporal domains. Central to the analysis of such schemesis the cross-ambiguity function, weighted by the appropriatetransmit and receive radiation patterns It should be possibleto generalise the formulation to other types of system, tosituations where the transmit and receive antenna patterns aredifferent, and to broadband signals.

It may also be interesting to investigate whether it ispossible to design the spatial denial signal to carry usefulinformation, such as air-to-ground telemetry or navigationsignals, as well as the bistatic masking function. Thisimposes an additional constraint, but it may be possible alsoto design the radar waveform signal adaptively in real time,so as to maintain the coding orthogonality.

6 Acknowledgments

This work has been supported by the US Air Force Office ofScientific Research (Dr. John Sjogren) and by AFRL/SNRT(Gerard Genello). The authors express their thanks toDr. Richard Schneible and Kenneth Stiefvater, of SteifvaterConsultants, for invaluable discussions.

7 References

1 Willis, N.J.: ‘Bistatic radar’ (Artech House, Boston, 1991)2 Dunsmore, M.R.B.: ‘Bistatic radars’, in Galati, G. (Ed.): ‘Advanced

radar techniques and systems’ (Peter Peregrinus, Stevenage, 1993),Chap. 11

3 Griffiths, H.D., and Carter, S.M.: ‘Provision of moving target indicationin an independent bistatic radar receiver’, Radio Electron. Eng., 1984,54, (7/8), pp. 336–342

4 Thomas, D., Jr.: ‘Synchronization of non-cooperative bistatic radarreceivers’. PhD dissertation, Syracuse University, NY, 1999

5 Wicks, M.C., Bolen, S.M., and Brown, R.D.: ‘Waveform diversity forspatial–temporal denial of radar and communications systems’. USpatent 6,204,797, 20 March 2001

6 Ertan, S., Wicks, M.C., Antonik, P., Adve, R., Weiner, D., Griffiths,H.D., and Fotinopoulos, I.: ‘Bistatic denial by spatial waveformdiversity’. Proc. IEE Conf. Radar 2002, Edinburgh, UK, 15–17 Oct.2002, IEE Conf. Publ. 490, pp. 17–21

7 Woodward, P.M.: ‘Probability and information theory, with appli-cations to radar’ (Pergamon Press, London, 1953; republished byArtech House, Dedham MA, 1980)

8 Rihaczek, A.W.: ‘Principles of high resolution radar’ (McGraw-Hill,New York, 1969; republished by Artech House, Norwood, MA, 1996)

9 Giuli, D., Fossi, M., and Facheris, L.: ‘Radar target scattering matrixmeasurement through orthogonal signals’, IEE Proc. F, Radar SignalProcess., 1993, 140, (4), pp. 233–242

10 Griffiths, H.D., and Normant, E.: ‘Adaptive SAR beamformingnetwork’. European Space Agency Contract Report, Contract6553/89/NL/IW, 1990, ESA Technical and Publications Branch,ESTEC, Noordwijk

11 Levanon, N.: ‘Radar principles’ (Wiley, New York, USA, 1988)12 Nathanson, F.E.: ‘Radar design principles’ (McGraw-Hill, New York,

1991, 2nd edn.)13 Golomb, S.W., and Taylor, H.: ‘Construction and properties of Costas

arrays’, Proc. IEEE, 1984, 72, (9), pp. 1143–116314 Costas, J.P.: ‘A study of a class of detection waveforms having nearly

ideal range-Doppler ambiguity properties’, Proc. IEEE, 1984, 72,pp. 996–1009

15 Butler, J.L.: ‘Digital, matrix and intermediate-frequency scanning’, inHansen, R.C. (Ed.): ‘Microwave scanning antennas’, Vol. 3 (PeninsulaPublishing, 1985)

16 Cooley, J.W., and Tukey, J.W.: ‘An algorithm for the machinecalculation of a complex Fourier series’, Math. Comput., 1965, 19,pp. 297–301

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