A.J. Fenn

Near-Field Testing ofAdaptive Radar Systems

Large phased-array antennas with multiple displaced phase centers are applied toradar applications that require adaptive suppression of jamming and clutter. Beforethe deployment of this adaptive radar, tests must veritY how well the system detectstargets and suppresses clutter and jammer signals. This article discusses a recentlydeveloped focused near-field testing technique that is suitable for implementation inan anechoic chamber. With this technique, phased-array near-field focusing providesfar- field equivalent performance at a range distance ofone aperture diameter from theadaptive antenna under test. The technique is applied theoretically to a dual-phase­center sidelobe-canceler antenna with multiple near-field sources within the mainbeam and sidelobes. Numerical simulations indicate that near-field and far-fieldtesting can be eqUivalent.

The development of any radar system re­quires tests of the associated hardware andsoftware at various levels ofthe design. Before aradar system can be deployed, design specifica­tions mustbe verified at the subsystem develop­ment level, system prototype level, and finalsystem level. For ground-based or airborneradar systems, the final system-can be tested in

the field and modified orupgraded as necessary.For a spaceborne radar, however, where thedeployed system hardware is not accessible,comprehensive prelaunch testing and modifica­tions must be performed on the ground. Thisarticle describes a recently developed focusednear-field technique that measures the per­formance characteristics of adaptive radar sys­tems within a ground-test facility. Although thetechnique is especially suitable for space-basedradar systems [1-3], it applies to most adaptiveground-based and airborne radar systems andcommunications systems as well.

The important subsystems of an adaptiveradar system consist of an antenna, a multi­channel receiver, and a signal processor. Theradar receives desired target signals along withinterference consisting of noise, backgroundclutter, and sidelobe jamming (Fig. 1). The an­tenna collects signals that the receiver filters,downconverts, and digitizes. The digitized data

The Lincoln Laboratory Jouma1. Volwne 3. Nwnber 1 (1990)

are then processed by the signal processor,which suppresses undeSired interference sig­nals and produces desired target reports.

The radar system typically utilizes a deploy­able planar phased-array antenna structurewith a largest dimension of 10 to 50 m and anominal operating range of several thousandkilometers. Because of this long operatingrange, the antenha receives planar-shapedwavefronts from targets, clutter, and jamming.To approximate plane-wavefront conditions atmicrowave frequencies, a conventional far-fieldtest distance is on the order of 2 to 10 km. Theminimum far-field distance is determined by2rY/ A.., where D is the antenna diameter andA.. is the wavelength. For low-sidelobe antennapattern measurements, a longer far-field mini­mum test distance is often used. It is difficult ifnot impossible to place many radiating testsources on a far-field ground-test range over awide field of view, and demonstrate low side­lobes together with jammer/clutter suppres­sion. Thus an alternate ground-test configura­tion is necessary. Near-field testing, with theradar system positioned in a high-quality con­trolled-environment anechoic chamber, is adesirable method for evaluating radar systemperformance. Figure 2 shows the proposed testmethod. The antenna and test sources Uammer,

23

Fenn - Near-Field Testing ojAdaptive Radar Systems

Fig, 1-The important subsystems of an adaptive radarsystem. Noise, clutter, jamming, and desired target sig­nals are received by the antenna. These signals aredownconverted and digitized by the receiver and thenprocessed within the signal processor to provide desiredtarget information.

clutter. and target) are placed within the an­echoic chamber. and the adaptive nulling re­ceiver and signal processor are placed outsidethe anechoic chamber. The details of how thistechnique naturally develops are describedbelow.

Figure 3 depicts the various regions in frontof a test antenna. The horizontal "axis is theantenna dimension D/ltand the vertical axis isthe normalized test distance z/D. The figureindicates the far- field test region, but this regionis not considered for potential testing for the sizereasons cited above. Planar scanning with a

Clutter Jamming

Antenna

AdaptiveNulling

Receiver

SignalProcessor

Target

Noise

probe antenna at a distance of a few wave­lengths (typically 31t) from the test antenna is aconventional near-field technique for calibra­tion and far-field radiation pattern measure­ment [4.5]. This form ofplanar near-field scan­ning is a non-real-time measurement techniquein which near-field data are collected and far­field data are computed. However. an adaptivenulling test requires real-time signalwavefronts. which precludes using the planarnear-field scanning technique. The Fresnelregion [6] (or transition region between the nearfield and far field). which extends from about0.6 .JD3 / It to 2D2 / It, offers reduced-range test­ing but is still too distant for large antennas.Ranges less than 0.6.JD 3 / It define the near-fieldregion.

A compact-range reflector [7] can reduce thetest distance to two to four aperture diameters(2Dto 4D). which is within the near-field region.This technique utilizes a parabolic reflector toconvert the spherical wavefrontfrom a feed hominto a planar wavefront. A compact-range re­flector can be used for adaptive nulling testsprovided that the wavefront is sufficiently freeof multipath. The reqUired reflector diameter islarge. however (approximately 2D at L-band

.' ".: frequencies and below). and sources widely:"'~paced 'in.,the test-antenna field of view are

difficult to achieve. Thus the compact-rangereflector is also not of interest here. All of theabove techniques create plane-wave illumina­tion for the antenna, which results in impracti­cal test geometries for adaptive nulling. Todevelop a suitable testing method, the plane­wave constraint must be dropped and sphericalwaves must be considered instead.

A recently developed technique called fo­cused near-field adaptive nulling implementsconventional near-field focusing to establish aninstantaneous or real-time antenna radiationpattern that is eqUivalent to its far-field pattern[8]. This technique appears to be ideal forground-based testing. The test distance variesfrom one to two aperture diameters (D to 2D) ofthe adaptive antenna under evaluation, asshown in Fig. 3. For large antenna diametersthis test distance is located well within the near­field boundary. The incident wavefront from

24 The Lincoln Laboratory Journal. Volume 3, Number 1 (1990)

Fenn - Near-Field Testing ofAdaptive Radar Systems

Ground Test FacilityAnechoic Chamber

AdaptiveNulling

Receiver

SignalProcessor Output

Fig. 2-Focused near-field nulling concept for a ground test of an adaptive radar system. The antenna under testandradiating sources (clutter, jammer, targets) arepositioned within a high-quality anechoic chamber. Focusing thetest antenna in the near field produces conditions equivalent to the far field. By utilizing proper timing and control, asignal environment comparable to fielded-radar system co'ncjitions can be achieved. The adaptive nulling re­ceiver and signal processor operate in real time. This configuratipn provides a thorough test of the important radarsubsystems. .-. ~ " .; "

radiating sources in the near field is sphericalrather than planar. which allows the radiatingsource antennas to be simple horns or dipoles.Four principal papers describing focused near­field adaptive nulling have been published bythe author [8-11). The eqUivalence betweenconventional far-field adaptive nulling and fo­cused near-field adaptive nulling has beendemonstrated for sidelobe canceler [8) and fullyadaptive arrays [9). Near-field clutter and jam­ming for a sidelobe canceler have also beenaddressed [10). In Refs. 8 through 10. theanaly­sis assumes that the array elem~ntsand radiat­ing sources are isotropic. Reference 1Lstudiesthe effects of array polarization and mutualcoupling. and demonstrates that the equiva­lence between near-field and far-field adaptivenulling still holds for single and multiple jam­mers. The present article expands the mutual

The Lincoln Laboratory Journal. Volume 3. Number 1 (1990)

. coupling formulation to include clutter andjamming.

In the next section the characteristics of anincident signal wavefront are investigated as afunction ofsource distance and angle of arrival.This investigation is followed by a description ofhow focusing is used to establish appropriatequiescent conditions for near-field adaptivenulling. An applicati'op of the technique to adisplaced phase-center antenna (DPCA) ismade, and details ofthe theoretical formulationare given. Antenna modeling is accomplishedby using the method of moments, includingarray mutual-coupling effects. The theory isapplied to a linear array of dipole elements withdipole near-field sources (clutter andjamming).The results ~how that focused near-fieldadaptive nulling is a viable approach to testingfull-scale adaptive radar systems.

25

Fenn - Near-Field Testing ojAdaptive Radar Systems

where the quantity (r1

- r2)1L is the nonnalized

range difference. Equations 1 and 2 show thatthe far-field and near-field dispersions have acommon factor BLIc. If near-field nulling is

(1)

(2)

BL . eYFF = - sm l

c

and time delay as

where B is the nulling bandwidth. c is the speedof electromagnetic wave propagation. and e

iis

the angle of incidence. Note that the dispersionis maximum for endfire incidence (e. = 90°) and

l

zero for broadside incidence (e. = 0°). Next.l

consider a point source at a constant distanceZ = z. and variable angle e= e.. which produces

l l

an incident spherical wavefront. The dis-tances between the source and the two end­points are denoted r

1and r

2. The near-field

dispersion YNF is given by

.. BL h - r2 )

YNF = c L

Near-Field/Far-fteIA SoUltceWavefront Dispersion

This section explains why near-field nullingcan be equal to far-field nulling. Signalwavefront dispersion (time-bandwidth product)is an effect that limits the depth of null (orcancellation) achieved by an adaptive antenna[12. 13). The amount of wavefront dispersion Yobserved by a linear array is a function of thebandwidth. array length. source range. andangle of incidence. A simple but effective dis­persion model for spherical-wave incidenceand plane-wave incidence considers thewavefront dispersion observed across the end­points of an adaptive array. This calculationgains some initial insight into how near-fieldnulling relates to far-field nulling.

Consider a plane wave arriving from infinityand an array of length L. The far-field disper­sion for this case is denoted YFF and is com­puted according to the product of bandwid~h

1000100

~oree

"::u....

.--.:::-=--------..".- 15 = 4

~~~~~~~~ 15= 2

~~~~~~~Q-~ 15 = 1

100.1 LL....---!.l..-~J......L..I...L.I.I.l..____:~--I...u...:...JU:...L.il.l.J'_____l_WI..ll.l1 U-L..LLJ

1

QNQ)ucell(j)o(j)Q)

I­"0Q)

.!::!""iiiEoz

Antenna Dimension Of?.

Fig. 3-Summaryofantenna test regions. The hemispherical volume in frontof an antenna can be divided into a number of test regions. The three basicregions are far field, Fresnel, and near field. The near-field region (shown inred) can be further divided into compact range (a reflector-based method),focused near field (which is addressed in this article), and planar near field.The focused near-field region is located between one and two aperturediameters from the antenna under test.

26 The Lincoln Laboratory Journal. Volume 3. Number 1 (1990)

Fig. 4-Normalized wavefront dispersion as a function ofsource angle of arrival. The wavefront dispersion (time­bandwidth product), observed relative to the end points ofan antenna, is a simple but effective model for comparingthe characteristics of near-field and far-field sources.Maximum dispersion occurs when the source (either nearfield or far field) illuminates the antenna from endfire(e. = 90°). For source distances of one aperture diameterof more, the difference between the near-field and far-fielddispersion is small.

possibly eqUivalent to far-field nulling. then YFF

must be eqUivalent to YNF

• This condition isclearly satisfied when (r

1- rz)/L = sinei' Figure

4 shows a plot of the normalized dispersiony!(BL/ c) as a function of the angle of inci­dence for values of source distance from 0.25 to2 aperture lengths (Le., the normalized sourcedistance is varied from z/L = 0.25 to 2). Thisfigure shows that the near-field. dispersionapproaches the value of the far-field dispersionfor source distances greater than approxi­mately one aperture diameter. or z/L= z/D'2 1(in this article, aperture length L and aperturediameter Dare eqUivalent and interchangeable).At one diameter. the percent difference betweennear-field and far-field dispersion is less than10%. At two diameters. the percent differenceis less than 3%. Clearly. at source distancessuch that z/D '2 0.5 (one-half aperture dia­meter), the near-field dispersion is signifi­cantly different (by as much as 30%) com-

~ 1.0-JCO-- 0.8?--

c::0

0.6'wCDa-li)

0.40uCD.!:! 0.2(ijE0 0.0Z 0 30 60 90

Source Angle (Jj (deg)

Fenn - Near-Field Testing ojAdaptive Radar Systems

pared to the far-field dispersion.At source distances of one to two aperture

diameters, the incident near-field wavefrontdispersion appears to be comparable to that ofa far-field wavefront. However. before the radarsystem attempts to perform near-field adaptivenulling, the receive-antenna quiescent condi­tions must be made to appear the same as far­field quiescent conditions. This requirement isachieved by focusing the antenna under test asdescribed in the next section.

Focused Near-Field Testing Concept

The near-field testing technique described inthis article assumes that the array quiescentnear-field radiation pattern has the same char­acteristics as the quiescent far-field radiationpattern. This assumption requires the forma­tion of a main beam and sidelobes in the nearfield. The dynamic range of received signalsfrom sources distributed across the radar fieldof view depends upon the antenna quiescentconditions. Phase focusing can be used to pro­duce an array near-field pattern that approxi­mately equals the far-field pattern [14].·.Figure 5 shows a continuous wave (CW)

. "cfi1.ibfati,9p. source located at a desired focalp:bint· of the' array. The array maximizes thesignal received from the calibration source byadjusting its phase shifters so that the spheri­cal wavefront phase variation is removed. Thefirst step to determine this adjustment is tochoose a reference element; this reference isusually the center element of the array. Thevoltage received at the nth array element rela­tive to the center element of the array is com­puted in this article by using the method ofmoments [15]. To maXimize the received volt­age at the array output, the phase conjugate ofthe incident wavefront must be applied at thearray elements. The resulting instantaneousarray radiation pattern seen at the source testplane z= zolooks similar to a far-field pattern[11]. In this p~ttern a main beam points at thearray focal poiht. and sidelobes exist at anglesaway from the main beam. Interferers are thenplaced on near-field sidelobes in the test (orfocal) plane. as shown in Fig. 5. Similarly.

The Lincoln Laboratory Journal. Volume 3. Number 1 (1990) 27

Fenn - Near-Field Testing ojAdaptive Radar Systems

Auxiliary Channels

Array Plane z = 0

/ Focused Array Pattern

z

AdaptiveWeights

y\

W\\\ X\\ Planar

W W ••• W Array

····Adaptive :Beamformer :

•..··(CW-Caiibratio;;Source~CiUtte(:Targeif·-----N~~:R~I~jT~~tPi~~-;::D--:::··..•.....W ~ Jammers--+-W •.•..•••.

~ I . ~•••• Focal ;- .... ~.... Point \, '+' ••••.~--------------------- ._-~---~ ---------------_._----------------------------~,,,,,,,,,,,

Focusing

. Output._-_._------------------:------~-------~~~

Fig. 5-Focused near-field adaptive nulling test concept. A CW radiating source is used as a calibration signalfor a phased-array antenna. The antenna-elementphase shifters focus the receive antenna radiation pattern inthe direction of the calibration source. This focusing creates an antenna radiation pattern that is similar to a far­field radiation pattern. Clutterand targetsources can beplacedon the main beam as desired. Similarly,jammerscan be positioned on sidelobes.

clutter sources are positioned on the near-fieldmain beam. Near-field focusing that uses onlyphase control results in some distortion of themain beam and first sidelobes. Amplitude con­trol can make the near-field pattern main beamand first sidelobes more closely resemble a far­field pattern [16]. For simplicity, this articledescribes phase focusing only. "

The minimum size of the required ground­test facility can be determined by consideringthe near-field geometry. For compatibility withconventional planar near-field scanning equip­ment, a flat test plane is assumed. Let ()maxdenote the maximum angle of interest for the

antenna radiation pattern. The reqUired near­field scan length D for pattern coverage of±()x maxis given in terms of the F/L ratio as

Dx = 2L( ~) tan ()max'

Figure 6 depicts the reqUired scan lengths for600 and 1200 field-of-view coverage with F/ Lratios ofLand 2L. To reduce the scan length (orsource deployment length) the F/Lratio must bekept as close to unity as possible. Clearly, theground-test facility must be large enough toencompass both the desired scan length D and

xthe focal length F.

28 The Lincoln Laboratory Journal. Volume 3. Number 1 (1990)

Fenn - Near-Field Testing ojAdaptive Radar Systems

Fig. 6-Examples of source deployment and scan lengtho for (a) 60 0 field of view and (b) 120 0 field of view. Thesefi§ures illustrate the importance of a close test distance.

Adaptive DPCA Radar

are not analyzed here.

The DPCA technique can be applied to air­borne or spaceborne radar systems that requireadaptive suppression of jamming and clutter(2). A DPCA array cancels stationary groundclutterfrom a moving platform by employing twoor more independent receive phase centers withwell-matched main beams. Figure 7 shows amoving target and a moving radar in a two­phase-center DPCA system. On transmit, thefull aperture ofthe array sends a burst ofpulses;on receive, two displaced portions of the aper­ture record the returned signals. Because of theplatform motion, two consecutive transmitpulses occur corresponding to the transmitphase-center positions AT and BT. The radartransmit signal illuminates both moving targetsand fixed ground terrain that, because ofthe ra­dar cross section, produces the desired signalsand clutter. Ground-based emitters also repre­sent a source of interference or jamming.

On reception, the antenna phase-center dis­placement between the two receive apertures isadjusted to compensate for the platform veloc-

.'it}i::;For two transmit pulses separated in time byone pulse-repetition interval (PRJ), the first re­ception occurs at the forward receive phase­center position, denoted A in Fig. 7. A secondreception occurs at the trailing receive phase­center position B. This bistatic radar system iseqUivalent to a monostatic radar system thatmakes two independent observations of thesignal environment at a single point in space.This common point, denoted AB, is located atthe midpoint of the line joining either points ATand A or BT and B. During a' PRJ, the targetmoves while the clutter is effectively stationary.As a result the target produces a relative phaseshift dUring this time, while the clutter has nophase shift. The clutter is assumed to be corre­lated between the two phase centers. In con­trast, widebanp noise jamming is assumed to beuncorrelated between the two phase centersdue to the one-PRJ delay imposed in the signalprocessing. When the signals received by thetwo phase centers are adaptively combined, the

FIL =2FIL = 1

".

10=OmaxI.,,

.. x

z

+;--0Ox= 2.4L

I

zA:-0

Ox= l.OLI

I

" I ",OX = 1.2L ,,. I .!

, I,A'T"*>.,,60~

'II

,,,, ..

II

Ox=3.5L........,.... 1... ..... "

.... I ".

.... ........--r---- ".... ..-.... 1200;~'"

.... ,.... • X

(b)

(a)

.....

The application ofthe focused near-field test­ing concept to a specific radar system requiresthe following important assumptions:(1) the incident near-field wavefront must be

reasonably well matched to a far-fieldwavefront;

(2) the adaptive antenna under test must befocused at the range of the test sources;

(3) the antenna characteristics, beamformercharacteristics, and receiver characteris­tics, such as channel mismatch, must beindependent of the type of wavefront (nearfield or far field); and

(4) the technique must be applicable to bothanalog and digital adaptive nullingsystems.

The analysis in this article accounts for as­sumptions 1, 2, and part of 3 (antenna char­acteristics). The remaining assumptions,which are not expected to limit the technique,

The Lincoln Laboratory Journal. Volume 3. Number 1 (1990) 29

Fenn - Near-Field Testing ojAdaptive Radar Systems

Clutter andMoving Target

Fig. 7-Displacedphase-center antenna (DPCA) radar system concept. Receive phase centers (or subarrays) A and Bcompensate for the radar motion by creating a phase-center displacement. To cancel stationary main-beam clutter andsidelobe jamming, and to detect the target, the radar system effectively makes two measurements of the signalenvironment at the common point AB and adaptively combines the phase centers.

and

clutter and jammer are significantly canceled. ments is frrst split into two paths that areThe corresponding target signal depends on the weighted and summed in separate power com-amount of target phase shift dUring one PRJ biners to form two independent subarray maininterval (0° phase shift produces no target signal,' -:', channels (or movable phase centers). In eachwhile 180° phase shift produces maximum tar- - element channel is a TIR module that hasget signal). The DPCA quiescent main-beam amplitude and phase control. The amplitudepattern match is a function of array geometry control provides the desired low-sidelobe arrayand scan conditions (due to array-element illumination function and phase-center dis-mutual coupling), and hardware tolerances placement. The modules utilize phase shifters(such as the quantization and random errors of that steer the main beam to a desired angle.the transmit/receive [T/R] modules). Both T/R Letmodule effects and array mutual coupling aretaken into account in the next two sections ofthis article.

Adaptive DPCA Array Formalism

Consider the DPCA array and adaptivebeamformer as shown in Fig. 8. The arraycontains N elements that form the receive mainchannel. Included within these elements is aguard band of passively terminated elementsthat provides impedance matching to the activeelements and isolation from ground-planeedges. The output from each of the array ele-

30

denote the array-element weight vectors (in­cluding quantization and random errors) ofphase centers Aand B, respectively (superscriptT means transpose). To effect phase-centerdisplacement, a portion of each subarray isturned off by applying a large value of attenu­ation for a group of antenna elements. Thisaction moves the electrical phase center to thecenter of gravity for the remaining elements.

The Lincoln Laboratory Journal. Volume 3. Number 1 (1990)

Fenn - Near-Field Testing ojAdaptiveRadar Systems

•••

N

•••Phase Center A

AAuxiliaries

VN-2VN-1

•••

Array Elements

V··· V

Auxiliaries

•••Phase Center B

AdaptiveWeights

ArrayModules

Adaptive Beamformer Output

Fig. 8-Adaptive beamformer arrangement for DPCA operation. The output from each antenna element is split into twopaths independently weighted with the array modules that contain amplitude andphase control. The outputs ofthe mainchannels andauxiliary channels are adaptively weighted to null the interference. The vertical arrow entering the adaptiveprocessor refers to the input data vector consisting ofsamples.ofp}e main and auxiliary channels. The horizontalarrowsexiting the adaptive processor refer to the adaptive weight commands. The jamming signals in phase centers A and Bare canceled at points A . and B', while the clutter is cancele.d qf the final outpUt of the adaptive beamformer.

adaptive weights (no quantization or randomerrors) are assumed. with

where * means complex conjugate and E(·)means mathematical expectation. (For nota­tional convenience. note that the superscript)in v and v in Eq. 3 has been omitted.) Since

m n

(3)

denoting the adaptive-channel weight vector.The fundamental quantities required to charac­terize the incident field for adaptive nullingpurposes are the adaptive-«;::hannel cross­correlations.

The cross-correlation RJ of the receivedmnvoltages in the mth and nth adaptive channels,due to thejth source, is given by

Thus the effective number of elements actuallyused to receive signals in phase centers A and Bare denoted by N

Aand N

B• respectively.

When a wavefront (either planar or spherical)due to the)th source (either clutter or jammer)passes across the array, the result is a set ofarray-element received voltages denoted by

Let M be the number of adaptive channelsper phase center. For a sidelobe cancelerM = 1 + N where N is the number of auxili-

a= a= "ary channels in each phase center". This adap-tive system has M degrees of freedom in eachphase center and thus a total of 2M degrees offreedom for the combined phase centers. Foreach phase center, the main- and auxiliary­channel voltages are derived from the above setof array received voltages. In this article. ideal

The Lincoln Laboratory Journal, Volume 3. Number 1 (1990) 31

Fenn - Near-Field Testing ojAdaptive Radar Systems

Wq = (1, 0, 0, ... , -1, 0, 0, ... , O)T.

where W is the quiescent weight vector (12].q

For a dual-phase-center side10be canceler, thequiescent weight vector is chosen to be

(7)

(6)

C = Pa.Pq

Substituting Eq. 6 into Eq. 7 yields

The adaptive-array cancellation ratio, de­noted C, is defmed here as the ratio of interfer­ence output power after adaption to the interfer­ence output power before adaption,

'TC = w a RWa

'T .w q RWq

Next, the covariance matrix defined by the ele­ments in Eq. 3 is Hermitian (that is, R =RoT). Bythe spectral theorem, R can be decomposed ineigenspace as

where *T means complex conjugate transpose.The interference-plus-noise-to-noise ratio.denoted INR, is computed as the ratio of theoutput power with the interferer present (de­fined in Eq. 6) to the output power with onlyreceiver noise present; that is.

*TRINR = W *T W.

W W

Thus the main-channel weights are ± 1 and theauxiliary-channel weights are zero.

The output power at the adaptive-arraysumming junction is given by

Prior to generation of an adaptive null, theadaptive-channel weight vector W is chosen tomaintain a desired quiescent radiation pattern.When undesired signals are present, the opti­mum set of weights w a to form one or moreadaptive nulls is computed by

.' ....,.

jthTransmitting

Antenna

~sourcel

where B =12 - 11 is the nulling bandwidth. Notethat Eq. 4 accounts for the spherical or planarshape of the wavefront.

Let the channel or source covariance matrixbe denoted R. If J uncorrelated broadband in­terference sources exist, then the J-source co­variance matrix is the sum of the covariancematrices for the individual sources. Thus

+v..rf!cn,]

12

Rinn = ~ f Um (1) u~ (1) dl (4)

JI

U and u represent voltages of the samem n .

waveform, but at different times, RJ is alsomn

called an autocorrelation function.In the frequency domain, assuming the

source has a band-limited white-noise powerspectral density, Eq. 3 can be expressed as thefrequency average

J

R = I R) + I (5))=1

where R. is the covariance matrix of the jthJ

source, and I is the identity matrix that repre-sents the thermal noise level of the receiver.

Fig. 9-Receive array and near-field source antennamodel. The quantityZ represents the mutual impedancebetween array elemerp,fs, while Z . represents the mutualimpedance between the nth elemJnt and the jth transmit­ting antenna.

2M

R = 1: Akeke~Tk=l

where Ak

, k = I, 2, .... 2M are the eigenvalues

32 The Lincoln Laboratory Journal. Volume 3. Number 1 (1990)

ofR, and ek

, k = 1,2, .... 2M are the associatedeigenvectors of R (17). The multiple-sourcecovariance matrix eigenvalues (AI' ,1,2' .••• A2M)

are a convenient quantitative measure of theutilization ofthe degrees offreedom of the adap­tive array. Because the identity matrix was add­ed to the covariance matrix. the minimum am­plitude that an eigenvalue can have is 0 dB. (thereceiver noise level). The number ofeigenvaluesabove the receiver noise level directly indicateshow many degrees of freedom are used to sup­press the undesired signals [13. 18).

Array Antenna/Source Modeling

This section applies the method of moments.already mentioned on p. 25, to compute thearray-element received voltages (given in Eq. 3)due to near-field or far-field sources. The far­field formulation in this article is similar to theformulation considered by I.J. Gupta and A.A.Ksienski (19). Assume that each element isterminated in a known load impedance ZL(Fig. 9). Let v . represent the open-circuit

nJvoltage in the nth array element due to thejth source. The jth source can denote eitherthe CW calibrator-a movable source probe forsampling the near-field radiation pattern-orone of the jammer or clutter sources. Next. let Zbe the open-circuit mutual-impedance matrixfor the N-element array. The array elementsare assumed to be dipoles over an infiniteground plane. The array received-voltagematrix, denoted v~ec. due to thejth source. can

Jbe expressed as

(20). In Eq. 8 the nth element ofv. is computed.J

for near-field sources, by the relation

where i. is the terminal current for thejth sourceJ

and Z . is the open-circuit mutual impedancenJ

between the jth source and the nth array ele-ment. For thin-wire array antenna elements,the moment-method expansion and testing

The Lincoln Laboratory JournaL Volume 3. Number 1 (1990)

Fenn - Near-Field Testing ojAdaptilJe Radar Systems

functions are assumed to be sinusoidal. Theabove open-circuit mutual impedances arecomputed on the basis of modified subroutinesfrom a well-known moment-method com­puter code (21). In the modified subroutines.double-precision computations are necessaryto evaluate Z .for thejth interferer. For far-field

nJsources. V

nJis evaluated by assuming plane-

wave incidence. The main-charmel output iscomputed by using WA'Tv ilj for receive phasecenter A-and W;TVBJ for receive phase center B.where vAJ and v BJ are the received voltages ofphase centerA and B, respectively. duetothejthsource.

As mentioned earlier, each phase center ofthe array is initially calibrated (phase focused)by a CW radiating dipole. To accomplish thiscalibration numerically. after computation ofthe CW received voltage the receive-array weightvector WA (or WB) has its phase commands setequal to the conjugate of the correspondingreceived phases. Receive-antenna radiationpatterns are obtained by scarming (moving) adipole with half-length l in either the far- field ornear-field region and computing the antennaresponse. Far-field receive patterns are com­puted by using a 8-polarized dipole source atir'finity to generate plane-wave illumination ofthe array. The open-circuit voltage is then setequal to the amplitude and phase ofthe incidentfar-field wavefront. For a far-field source. theincident wavefront amplitude is a constant andthe phase varies linearly from element to ele­ment. The coordinates (x. y. z) specifY a near­field point in front of the test antenna. Principalplane near-field radiation pattern cuts (versusangle) are obtained by computing the nearfield on the line (x;. O. z) with the relation8(x) = tan,l(x/z). The near-field source is anx-polarized dipole with half-length l. LetvxNF(e) denote the voltage received by the arraydue to the x-directed near-field dipole. and letpie) denote the 8 component of the dipoleprobe pattern. Then the probe-compensated ar­ray near-field received pattern is expressed as

(9)

33

Fenn - Near-Field Testing ojAdaptive Radar Systems

PhaseCenter

A

PhaseCenter

B

J = JammerIC = Clutter Digitally Controlled SourcesT = Target

Fig. 1Q-Near-field source positioning for a displacedphase-center antenna. Two sets of sources, "A Hand UB, "are used one set ata time to illuminate the test antenna.

(10)

the impedance matrix Z is computed at K fre­quencies and the system of equations given byEq. 8 is solved at each frequency. The interfer­ence covariance matrix elements are computedby numerically integrating Eq. 4 according toSimpson's rule. For multiple sources, the co­variance matrix is evaluated by using Eq. 5.Adaptive-array radiation patterns are com­puted by superimposing the quiescent radiationpattern with the weighted sum of auxiliary­channel received voltages.

where the value

(8) = cos(f3l sin 8) - cos(f3l) .Po cos 8

The propagation constant f3 is 2n/A.The array received-voltage matrix for thejth

source (denoted v:ec) is computed at K frequen­cies across the nulling bandwidth. To obtain thereceived voltages

DPCA Near-FieldSource Distribution

Figure 10 shows the position of near-field- .-"

sources for two-phase-center DPCA operation;'~"

Two sets of sources exist, one set for phase'centerA and one set for phase center B. Multipieclutter sources are distributed across the mainbeam of both phase centers. The figure alsoshows a desired target signal embedded withinthe clutter signals. Jammer signals are as­sumed to radiate from antennas located withinthe sidelobe region. As mentioned before. theclutter is correlated between phase centers Aand B. As an example, denote the first cluttersource in phase center A as CAl (8

1) and the first

clutter source in phase center B as Cal (81),

Clearly. in theory CAl (81) equals Cal (81), Similarequalities exist for the remaining cluttersources. To achieve this correI'ation in an experi­mental configuration requires digitally con­trolled arbitrary-waveform generators. Thesesignal generators can also create the jammersand desired target signals. The two sets ofsources must be operated dUring different time

intervals separated by the radar PRJ delay.Thus, for example, a measurement ofthe phasecenter A signals is performed with only the MAWgroup of sources radiating. The next measure­ment (o~e PRJ later) is for the phase center Bsignals with only the MB" group of sources radi­ating. This switching is implemented by usingtiming and control, as suggested earlier inFig. 2.

The near-field source antennas do not inter­act through mutual coupling in such a way thatthe adaptive nulling performance is modified.For example, with one source radiating, thesurrounding source antennas represent pos­sible multipath" The near-field sources areknown to couple. but this coupled interferencedoes not influence the adaptive weights, pro­vided that the coupled signal is reradiated andreceived at below the receiver noise level. Themultipath contribution between two antennas(one radiating and the other passively termi­nated in~ a load) is accurately computed asfollows. Let II be the terminal current generatedon the active source antenna. Similarly, let 1

2denote the parasitic current generated on the

34 The Lincoln Laboratory Journal. Volume 3. Number 1 (1990)

Fenn - Near-Field Testing ojAdaptive Radar SystemsTT<ansm;n;ng Source D;pole

Dipole Array

TerminatedElements

TerminatedElements

I m (Receive Current)

---..-+- -+- -0- -0- ••• -0- ••• -0-... -0- -0- -+- -+-

1 23m n 146 147 148

777777777777777777777777777777777777Infinite Ground Plane

1.....·1--------------0-----------·..1

Fig. 11-Geometry for dipole receive array and dipole source antenna. The transmitting source antenna re~·

resents clutter, jammer, the target, and noise.

The Lincoln Laboratory Journal. Volume 3. Number 1 (1990)

Near-Field/Far-Field Simul~tions

passive antenna. From circuit theory the ratio ofthe parasitic current to active current is given by

This section analyzes a specific adaptiveDPCA array and demonstrates the eqUivalencebetween near-field clutter andjammer suppres­sion and far-field clutter and jammer suppres­sion. Consider a corporate-fed phased-array16-m antenna that consists of a single row of

receive dipole elements. The array, which has atotal of N = 148 elements with two elements ateach end used as passive terminations, has 144active receive antenna elements. The antennaelements are one-half-wavelength-long electri­cally thin dipoles that are center fed and spacedone-quarter wavelength above an infiniteground plane (Fig. 11). The center frequency is

·,'ch'osen to be 1.3 GHz (L-band) and the interele­~ent'spaCing' is 10.922 cm, or 0.473 wave-

, lengths. Thus the active portion of the arrayspans 15.61 m. The output from each activereceive antenna element is divided into twopaths to form two independent phase centers.The T/R modules are chosen to have 5 bits ofamplitude and phase control with rms errors of0.3 dB and 3.0°. The load impedance ZL isassumed to be 50 Q resistive at each array ele­ment.

The near-field test distance' z is chosen tobe 15.61 m, which corresponds to one activereceive aperture diameter. Seven auxiliarychannels. randomly selected from the elementoutputs of one ofthe phase centers, form a mul­tiple-sidelobe canceler configuration. This ran­dom pattern repeats in the second phase center.Since the value ofN is 7 in each phase center,

awethe total number ofdegrees offreedom is 16. Thechannel covariance matrix is dimensioned16 x 16 and has 16 eigenvalues. The receiver

35

(11)1121 IZ 211TIJ = IZ22 + ZL I

where Z21 is the open-circuit mutual impedancebetween the two antennas, Z22 is the self-imped­ance of the passive antenna, and ZL is the loadimpedance of the passive antenna. Clearly, asmall value of mutual impedance is desired.Equation 11 will be used later to verify that themutual coupling between source antennas issufficiently small for a particular near-fieldsource configuration. An important point to bestressed here is that mutual coupling betweensource antennas in a particular near-field testconfiguration needs to be carefully evaluated.However, with proper source antenna design.and judicious placement of anechoic materialbetween source antennas, mutual couplingshould not be a problem.

FenD - Near-Field Testing ojAdaptive Radar Systems

60-30 0 30

Probe Angle 9 (deg)

-80 L..-__..L-__......l...__--I.__---J

-60

Or----~--,.---__,_-----,

synthesize a -40-dB uniform-sidelobe-levelChebyshev radiation pattern (in the absence ofT/R module errors) with a scan angle Osequal to-300

• Assume that the phase centers are fullysplit apart. so that the effective number ofreceive elements per phase center (N

Aand N

B) is

one-half of 144, or 72. This number gives aphase-center separation of 7.86 m. Figure 12shows the subarray amplitude illuminationfunction for phase centers A and B. The ex­pected random amplitude error of the T/R

"OffState"-

10

1+-----16m----..

-10

0.15

OJ

~ 0.10C.~ 0.05

o

-5 0 5

Element Position x (m)

Fig. 12-SimulatedOPCA illumination functions for the 16­m linear test array. The phase-center displacement t:. iscreated by turning off the left half of the array for phasecenter A and the right half of the array for phase center B.

bandwidth (also called the nullingbandwidthl is1 MHz. The auxiliary channels are attenuatedby 20 dB to have a signal output power compa­rable to the main channels. In a practical radar.auxiliary-channel attenuation will be imple­mented to keep the dynamic range of signalswithin the limits of the adaptive nullingreceiver.

Let the array illumination be chosen to

0.20 r---.-.:..----r---'-~--_,

O.---.-....,.....--r----..,~--r--__r_-___,

! !ArrayB A

Range = D..........~ .

~ ~'·9: ·9:'" .,., .,

-- Phase Center A

-- Phase Center B

Fig. 14-Near-field radiation patterns at one-aperture-di­ameter test distance for phase centers A and B, as afunction ofobservation angle. The patterns are computedfrom Eqs. 9 and 10 by using the simulated near-field datain Fig. 13.

. '-. ~ ..::., - ...

105o-80 L...-_..l-_--l..._---l._--I.__..l-_...J

-20 -15 -10 -5

CD"-;; -20

".~C.E -40~

.~iii -60a;a:

Probe Position x (m)

Fig. 13-Simulatednear-fieldprobe scan at one-aperture­diameter test distance for the OPCA 16-m linear testarray.The source frequency is 1.3 GHz and the receive-arrayscan angle is -30°.

-- Phase Center A

-- Phase Center B

CW Probe Scan•••••••• , ••••••••x

FIO= 1

~rrayB A

modules makes the illumination functionsslightly different from one another. Notice howeach illumination function is equal to zero over7.86 m. This illumination shifts the apparentphase center by 3.93 m to the left of the antennacenter for.phase center B and 3.93 m to the rightof the antenna center for phase center A

To phase-focus the DPCA array in the nearfield to the distance z = 15.61 m and angles° = -300 (with respect to each phase center).sa CW radiating dipole source is positionedat x = -12.95 m for phase center B and at

36 The Lincoln Laboratory Jownal. Volume 3. Nwnber I (l990)

Fenn - Near-Field Testing ofAdaptive Radar Systems

O.-------r---.......---r-----,Figure 13 shows the resulting near-field re­ceived amplitude distribution for both phasecenters. Notice that the peak amplitudes occurat the desired locations. The main beams arefully separated so that one phase center has apeak when the other phase center has a side­lobe. While the test distance is specified as oneaperture diameter for the full length ofthe array.the test distance effectively appears to be twosubarray. diameters for the displaced phasecenters. Figure 14 shows the near-field datareplotted as a function of angle with respect toeach phasecenter. The near-field main beams ofphase centers A and B are clearly well matchedas desired in a DPCA system. Because ofphase­center displacement. the near-field patternscover different angular sectors. Figure 15 showsthe corresponding far-field radiation patterns ofphase centers A and B. A good main-beammatch is also apparent in this figure.

Figure 16 compares near-field and far-fieldradiation patterns. Figures 16(a) and 16(b) showthe radiation patterns for phase centers B andA, respectively. The near-field main beam agreeswith the far-field main beam down to -20 dB.Amplitude calibration can compensate for adefocusing ofthe near-field main beamand first

._~g:telobes. as mentioned earlier. Although thenear-field sidelobes do not match the far-field

60

Range = 00......~'~~...-.0: -.0:., .,I, I,

b bArrayB A

-30 0 30Probe Angle () (deg)

-80 L..-__.....L.. I....-__-'-__--J

-60

-- Phase Center A

-- Phase Center B

CD:£. -20Gl"0

E0..-40E«Gl>~-60Qia:

Fig. 15-Simulated far-field radiation pattern for the OPCA16-m linear array. The focal distance and observationdistance are both set to infinity.

x = -5.09 m for phase center A. To focus thesubarrays. the conjugate of the moment­method-calculated element phases is applied tothe receive modules. The CW source is scannedacross 26.29 m and the array output is com­puted at uniformly spaced probe positions.

Far Field (F10 = 00 )

Near Field (FlO = 1)

O,....---~r;----.-----.-------,

CD~ -20OJ"0

.-Ea.E -40<:OJ>.~

(jj -60a:

(a)-80 L- .L.- L- L-__---'

-60 -30 0 30 60 -60

Probe Angle e (deg)

(b)

-30 0 30

Probe Angle e (deg)

60

Fig. 16-Comparison of simulated near-field and far-field OPCA radiation patterns (before adaptive nulling) previouslyshown in Figs. 14and 15, respectively. The (a) phase centerB radiationpatterns and (b) phase centerA radiationpatternsestablish the quiescent conditions for the adaptive antenna.

The Lincoln Laboratory Journal. Volume 3. Number 1 (1990j 37

Fenn - Near-Field Testing ojAdaptive Radar Systems

sidelobes on a point-by-point basis. the averagesidelobe levels are equal.

When proper quiescent conditions are estab­lished. seven clutter sources are uniformly dis­tribu ted across the main beam ofboth near-fieldand far-field patterns. For this dual-phase­center example. seven clutter sources exist perphase center. In each phase center. all squrcesare assumed to have equal power and allsources are uncorrelated. Note that equal­power sources are chosen for convenience. Thesources are distributed in angle over a 50 sectorcentered at the beam peak. and they cover themain beam down to -20 dB. The total power thatthese sources produce in one phase centerequals 40 dB relative to receiver noise. Anincrease in the number of clutter sources be­yond seven does not significantly influence theadaptive nulling results that follow. Finally. letone jammer be positioned at () = -;-200 to pro­duce an output power for the combined phasecenters of 50 dB above noise.

As mentioned earlier. mutual couplingamong near-field signal sources can be animportant consideration. In the current ex­ample. since the sidelobe jammer power is largethe coupling between the radiating jammerantenna and a clutter antenna is the most

important case to consider. The sidelobe level atthe jammer position is approximately -35 dBdown from the main-beam peak. The main­beam level at the nearest clutter antenna posi­tion is -20 dB. Thus a parasitically generatedjammer signal at the clutter antenna is effec­tively increased by 15 dB at the test antennabecause of the pattern directivity increase.Without the contribution of mutual coupling.the parasitic jammer power in the main beamwould be 65 dB above noise. The parasiticjammer current at the clutter antenna iscomputed by using Eq. 11. The self-imped­ance of a one-half-wavelength clutter dipoleis ~2 = 73 + j42 Q. The separation betweenthe jammer and the nearest clutter anten­na is approximately lOA.. For this spacing. themutual impedance is computed to beZ21 =-0.03748 - jO.000618 n. Substitutingthese values and the load impedance (ZL= 50 Q)into Eq. 11 yields

11211111 = 0.000289.

In decibels. the parasitic jammer current isdown by -71 dB. The parasitic jammer signal isthen the difference between 65 dB and 71 dB.

: ~or -6 dB below receiver noise. According to. '-

Far Field (F /0 = 00 )

Near Field (F /0 = 1)

Or-----.......----,.----r------.

60

Moving Target(Phase Shift = 180°)

-30 0 30

Probe Angle (J (deg)

(b)

Cancellation

49.3 dB Far Field48.0 dB Near Field

(a)-80 L-- -'----L__-J-_~_-J... ......I

-60 -30 0 30 60 -60

Probe Angle e (deg)

Clutter

ro -+- ...-~ -20QJ"0

.Ea.E -40~QJ>~Qi -60a:

Fig. 17-Adapted radiation patterns for the combinedphase centers of the OPCA 16-m lineararray for the (a) stationarytarget and (b) moving target. The near-field simulation is ata test distance of one aperture diameter and the far-fieldsimulation is ata testdistance ofinfinity. Seven white-noisecluttersources are distributeduniformlyacrossthe main beam,and one white-noise jammer is in a sidelobe. The nulling bandwidth is 1 MHz.

38 The Lincoln Laboratory Journal. Volwne 3. Nwnber 1 (1990)

theoretical simulations. this power level doesnot affect the computation of the adaptiveweights.

For the signal environment. the covariancematrix was computed and the adapted weightswere derived and then applied to cancel theinterference. Figure 17 shows the near-field andfar-field adapted radiation patterns. In Fig.17(a). both the clutter and jammer are clearlysuppressed by the pattern nulls. and the pat­terns are very similar. The total cancellation ofjamming and clutter power is 48.0 dB in thenear field and 49.3 dB in the far field. As theamount ofcancellation is large. this small differ­ence (1.3 dB) is insignificant. The radiationpatterns in Fig. 17(a) show a stationary targetwhose signal is effectively canceled because ofzero phase shift in one PRI. In contrast. areceived signal from a moving target that pro­duces a 1800 phase shift in one PRI sees theantenna radiation pattern shown in Fig. 17(b).where full antenna gain is available in the main­beam direction. Finally. Figure 18 shows a plotof the covariance matrix eigenvalues. A total ofeight eigenvalues above receiver noise indicatesthat eight degrees offreedom are consumed. Thenear-field and far-field eigenvalues are in goodagreement over a large dynamic range. By tak­ing all ofthe above results into consideration. wecan now state that. for all practical purposes.near-field nulling is eqUivalent to far-fieldnulling.

Fenn - Near-FY.eld Testing ofAdaptiveRadar Systems

Conclusion

A theory for analyzing sources radiating inthe near field of an adaptive radar system isdeveloped. Conventional phase focusing of anarray is used to create antenna far-field patternconditions in the near-field region. Cluttersources are distributed across the main beam ofthe focused antenna pattern. and jammers arepositioned within the sidelobes. The method ofmoments is used to analyze a displaced phase­center antenna linear array with near-field andfar-field clutter and jamming. Focused near­field adaptive nulling is shown to be eqUivalentto conventional far-field adaptive nulling. Thenear-field range distance can be one aperturediameter. which opens the possibility for indooranechoic chamber testing. Thus a radar systemdesigned for far-field conditions can potentiallybe evaluated by using near-field sources. Thistechnique is particularly attractive for space­based radar systems for which prelaunchground testing is desirable. With this method.integrated testing of a phased-array antenna.receiver. and adaptive signal processor can beperformed. Array calibration. antenna radia­tion patterns. adaptive cancellation. and tar­g~t detection can be verified. Experimental

. \i.etification ,of this technique is currentlyunder investigation.

Acknowledgements

Far Field (F 10 = 00 )

80

60CD~Q) 40u.~

20i3..E~

0

-201

ReceiverNoiseLevel

16

Initial development of the near-field testingtechnique was encouraged by V. Vitto and H.Kottler. and their support is appreciated. Tech­nical discussions with G.N. Tsandoulas. R.W.Miller. J.R. Johnson. H.M. Aumann. F.G. Will­werth. E.J. Kelly. D.H. Temme. and S.C. Pohligwere valuable in the development of this work.The software support of S.E. French is alsoappreciated.

ReferencesIndex

Fig. 18-Covariance matrix eigenvalues for near-field andfar-field source distributions. Eigenvalues 1 to 8 are abovethe receiver noise level and represent the consumption ofeight degrees of freedom.

The Uncoln Laboratory Journal. Volume 3. Number 1 (1990)

1. L.J. Cantafio ... ed., Space-Based Radar Handbook (Ar­tech House. Dedham, MA, 1989).

2. E.J. Kelly and C.N. Tsandoulas, ~A Displaced PhaseCenter Antenna Concept for Space Based RadarApplications: IEEE 16th Ann. Electron. and Aero­space Con] and Expo.• Washington. DC. 19-21 Sept.

39

Fenn - Near-Field Testing ojAdaptive Radar Systems

1983. p.141.3. G.N. Tsandoulas. "Space-Based Radar." Science 237.

257 (1987).4. AD. Yaghjian. "An Overview of Near-Field Antenna

Measurements." IEEETrans. Antennas Propag.AP-34.30 (1986).

5. AJ. Fenn. F.G. Willwerth. and H.M. Aumann. "Dis­placed Phase Center Antenna Near Field Measure­ments for Space-Based Radar Applications: PhasedArrays 1985 Symp. Proc.• BedJord. MA. 15-18 Oct.1985. p. 303. RADC-TR-85-171,ADA-169316.

6. C.H. Walter, Traveling Wave Antennas (Dover, NewYork. 1970). p. 38.

7. RC. Johnson. H.A Ecker. and RA Moore, "CompactRange Techniques and Measurements." IEEE nuns.Antennas Propag. AP-17, 568 (1969).

8. AJ. Fenn. "Theory and Analysis ofNear-Field AdaptiveNulling." 1986 IEEE AP-S Symp. Digest. VoL 2 (IEEE.New York. 1986). p. 579.

9. AJ. Fenn. "Evaluation of Adaptive Phased Array An­tenna Far-Field Nulling Performance in the Near-FieldRegion," IEEE Trans. Antennas Propag. AP-38. 173(1990)

10. AJ. Fenn. "Theoretical Near-Field Clutter and Interfer­ence Cancellation for an Adaptive Phased ArrayAntenna." 1987 IEEE AP-S Symp. Digest. VoL I (IEEE.New York. 1987). p. 46.

11. A.J. Fenn. "Moment Method Analysis of Near-FieldAdaptive Nulling." lEE 6th Inti. Con] on Antennas andPropagation. ICAP 89. Coventry. UK. 4-7 Apr. 1989. p.295.

12. RA Monzingo and T.W. Miller. Introduction toAdaptiveArrays (Wiley, New York. 1980). p. 253.

ALAN J. FENN is a staffmember in the Space RadarTechnology group. wherehis research is in the devel­opment of near-field testingtechniques for adaptive ra­

dar systems. He has a B.S. degree from the University ofIllinois at Chicago, and M.S. and Ph.D. degrees from OhioState University, all in electrical engineering. Before comingto Lincoln Laboratory in 1981, Alan worked for MartinMarietta Aerospace Corporation in Denver, Colo. He iscurrently an associate editor in the area of adaptive arraysfor the IEEE Transactions on Antennas and PropagatiorL

40

13. J.T. Mayhan, "Some Techniques for Evaluating theBandwidth Characteristics of Adaptive NullingSystems," IEEE Trans. An1l?nnas Propag. AP-27, 363(1979).

14. W.E. Scharfman and G. August. "Pattern Measure­ments of Phased-Arrayed Antennas by Focusing intothe Near Zone." Phased Array Antennas (Proc. oj the1970 Phased Array Antenna Symp.J. eds. AA Olinerand C.H. Knittel (Artech House. Dedham. MA. 1972).p.344.

15. W.L. Stutzman and G.A. Thiele. Antenna Theory andDesign (Wiley, New York., 1981). p. 306.

16. H.M.AumannandF.G. Willwerth, "Synthesis ofPhasedArrayFar-FieldPatterns byFocusingin the Near-Field."Proc. oj the 1989 IEEE NaiL Radar Con] Dallas. TX.29-30Mar. 1989. p. 101.

17. G. Strang. Linear Algebra and. Its Applications (Aca­demic Press, New¥ork, 1976). p. 213.

18. AJ. Fenn. "Maxim.izing Jammer Effectiveness forEvaluating the Performance ofAdaptive Nulling ArrayAntennas: IEEETrans. Antennas Propag. AP-33, 1131(1985).

19. I.J. GuptaandA.A. Ksienski. "EtTectofMutual Couplingon the Performance of Adaptive Arrays." IEEE Trans.Antennas Propag. AP-31. 785 (1983).

20. AJ. Fenn. "Moment Method Analysis of Near-FieldAdaptive Nulling: Technical Report842. Lincoln Labo­ratory (7 Apr. 1989). AD-A208-228.

21. J.H. Richmond. "Radiationand ScatteringbyThin-WireStructures in a Homogeneous Conducting Medium(Computer Program Description)," IEEE Trans. Anten­nas Propag.AP-22. 365 (Mar. 1974).

The Lincoln Laboratory Journal, Vo[wne 3. Number 1 (1990)