1962 IRE TRANSACTIONS ON MILITARY ELECTRONICS 179

An RF Multiple Beam-Forming Technique*WILLIAM P. DELANEYt, MEMBER, IRE

Summary-An RF beam-forming matrix is described which forms and successfully tested at Lincoln Laboratory. The results"tn" simultaneous beams from an "n" element array in a passive and presented below are applicable to any size beam-formingtheoretically lossless manner. The principle of operation is explained matrix. The experimental data presented is a condensa-using some simple matrix configuration. A general expression for .the far-field pattern of any beam is derived and then used to study tion of extensive test results on a 16-element matrix.the positions of beam peaks, the position of beam nulls, the crossoverlevel between beams and the frequency sensitivity of beam positions. II. PRINCIPLE OF OPERATIONThis matrix provides a uniform illumination of the array aperture; The basic components of the beam-forming matrix arehowever, simple beam combining techniques will yield tapered il 3-db directional couplers or hybrid rings and fixed phaseluminations. An experimental 16-element beam-forming matrix

.. .

which operates at 900 Mcps is described, and results of RF and shifters. Before explaining the operation of the matrix, itantenna measurements on the matrix are presented. is necessary to adopt some conventions concerning the

phase shift through hybrids and directional couplers. TheI. INTRODUCTION conventions used are shown in Fig. 1. When the input

flFPHE PHASED ARRAY radar is often proposed as a voltages have the amplitudes and relative phase anglessolution to many present and future radar problems. shown in Fig. 1, all the input signal power will appear atAll phased array receivers combine the outputs of the indicated terminal.

the discrete antenna elements to form one or more antennabeams. This combining process can take place either in -9-O ,v v,v' IvL/-90- Iv/z Iv/0° Iv/-180- Iv!the IF portion or the RF portion of the receiver. One majordisadvantage of beam forming in the lower-frequency por-tions of the receiver is the need for amplitude and phase L|stable mixing and amplifying circuits between the antennaand the LF beam-former. This paper describes a theoreti- /2v/-90 Ov Ov 1/iv/-90 /ivZi Ov Ov s/2n:cally lossless multiple beam-forming technique which HYBRID

operates directly at the RF carrier frequency and thus can Fig. 1-Phase-shift conventions for directionalbe located directly behind the antenna elements. All the couplers and hybrid rings.beams formed by this technique have the full gain of thearray aperture. Since the beam-forming technique uses a .--- -INCIDENT WAVEFRONTS -lmatrix of passive microwave devices, it can be made very 0. -9O -90 0.

rugged, reliable, and is not susceptible to the phase and 7ANTENNASamplitude instabilities common in active RF devices.

Simultaneous RF multiple beam-forming techniques arerelatively new. Blass' has described a series-fed multiplebeam antenna which is presently used in the AHSR-1 air-

BBEAM LEFT BEAM RIGHT

port radar system. Butler and Lowe2 and Shelton andKelleher' have described the parallel-fed technique dis- Fig. 2-Simplest beam-forming matrix.cussed in this paper. Experimental results on a 4-elementmatrix4 at 3 Gc have been reported by Butler. Shortlyafterwards, an 8-element matrix' at 900 Mcps was built Now it is possible to form the simplest multibeam array

by using two antenna elements and one hybrid ring or one* Received by the PGMIL, November 30, 1961. The work reported 3-db directional coupler. Fig. 2 shows a 2-beam, 2-element

was performed at Lincoln Laboratory, Lexington, Mass., with support array using a 3-db directional coupler. A certain incidentfrom the U. S. Air Force.

t M.I.T. Lincoln Laboratory, Lexington, Mass. wavefront will excite antenna element currents that are 9001 J. Blass, "Multidirectional antenna-a new approach to stacked out of phase, and therefore all the received signal energy

beams, 1960 IRE INTERNATIONAL CONV1ENTION RECORD, Pt. 1, PP. 48-m," 1 . will come out one terminal on the directional coupler. Thus,2J. Butler and R. Lowe, "Beam forming matrix simplifies design of a "beam right" and a "beam left" are formed. If a hybrid

electronically scanned antennas," Electronic Design, vol. 9, pp. 170-173; April 12, 1961. ring had been used, the 2-element array would have a

3 J. P. Shelton and K. S. Kelleher, "Multiple beams from linear broadside beam and an endflre beam (assuming an antennaarrays," IRE TRANS. ON ANTENNAS AND PROPAGATION, vol. AP-9, pp. lmn saigcoe ooehl wvlnt)154-161; March, 1961. eeetsalgcoet n afwvlnt)

4J. Butler, "Multiple Beam Antenna," Sanders Associates, Inc., A 4-beamn matrix can be built by interlacing two 2-beamNashua, N. H., Internal Memorandum RF-3849; January 8, 1960.

5J. L. Allen, et al., "Phased Array Radar Studies, 1 July 1959 to matrices arid then providing a second level of directional1 July 1960," M.I.T. Lincoln Lab., Lexington, Mass., Tech. Rept. No7 couplers or hybrid rings to combine the outputs into beams.228;rAugu,Mst,1960.ASTIA Do. No7. 297,HyeLiry,M. It is necessary to insert fixed phase shifters between the

180 IRE TRANSACTIONS ON MILITARY ELECTRONICS April

upper and lower levels of couplers to form the output beam. _Nc,DENTWAvEFRoNr _- ____Fig. 3(a) shows a 4-element, 4-beam array using direc- _ - __tional couplers. The amplitudes and phases of an incident ///"beam 1 Left" signal are shown at various points in thematrix. Fig. 3(b) shows the amplitudes and phases of an

DIRI;CTIONALincident "beam 2 Left" signal. The "shaded" directional COUPLER .vl ovcouplers are the ones used to form the particular beam. FIXED -4-Thus, it can be seen that the beam-forming matrix behaves SHIFTERlike a multiple corporate feed structure which routes asignal originating at a particular point in space to a par- 0. l 0' 2V/-I8O,ticular output port of the matrix. Since the matrix is sym- BEAMI LEFmetrical about a vertical line through the center, the 1Right and 2 Right beams can be found by using the ap- (a)proach of Fig. 3.A 16-element matrix can be thought of as four inter-

laced 4-element matrices. Two extra levels of phase shifters OEH .,AvEF_2L \~and combining elements (directional couplers or hybridrings) are required to form the beams. Fig. 4 shows the IVL@ ____ Iv/-270 Iv/-05diagram of the 16-element matrix used to obtain the ex- i 2

perimental measurements presented in this paper.This beam-forming technique can be used in two-dimen-

sional (planar) arrays by first combining the columns of 2,, Lantenna elements in matrices and then combining the out-

AA

puts of the column matrices in a group of row matrices.At this point, it is worthwhile to list and briefly discuss

some of the fundamental characteristics of the RF beam- oV 2v/-135 Ov Ov

forming matrix. Some of these topics are discussed at BEAM RIGHT BEAM 2 LEFT BEAM 2 RIGHT BEAM LEFTgreater length later. (b)

Number of Beams: The number of beams formed is Fig. 3-(a) Amplitude and phases of a "beam 1 Left" signal in a 4-element matrix. (b) Amplitude and phases of a "beam 2 Left" signal

equal to the number of antenna elements used. The in a 4-element matrix.

ANTENNAS

2 3 4 5 6 7 8 9 10 12 i3 14 15 16

1-76.75'l 0' 0'o -11.25' -3375' 0' 0@ |-O -56.25' -5625' 0' 5*° 3375* -*15.2- °0' 0'7-78.5*

I L BR 5L 4R *3L 6R 7L 2R 2L 7R 6L 3R 4L 5R 8L R

BEAM TERMINALS

Fig. 4-A 16-element beam-forming matrix.

1962 Delaney: RF Multiple Beam-Forming Technique 181

number of antenna elements in the array must be equal to antenna element number 1 also connects to antennato a power of 2, namely 2, 4, 8, 16, 32, etc. element number 9. Similarly, elements 2 and 10 are fed byNumber of Directional Couplers or Hybrids: The num- a common directional coupler. The first beam from broad-

ber of combining devices required can be shown to equal side is formed when an incident wavefront excites currentsN/2 log2 N where N==number of elements in the array. in elements 1 and 9 (and thus elements 2 and 10, 3 and 11Number of Fixed Phase Shifters: The number of phase etc.) with a phase difference of 900. Similarly the second

shifters required is N/2 (log2N- 1). beam from broadside is formed when this phase differenceOperating Frequency: The operating frequency is is 2700, and in general the Kth7 beam is formed when the

limited only by the practicality of building and inter- phase difference between elements 1 and 9 is (2K- l)r/2connecting fixed phase shifters and directional couplers radians. Therefore, for a 16-element array, the element toor hybrids. (Hybrid transformers can be used in VLF element phase shift for the kth beam is (2K-1)ir/16matrices.) radians.

Bandwidth: The basic components (phase shifters and Generalizing this result to an "n" element array,directional couplers) can be built with bandwidths (2K - 1)irgreater than 30 per cent; however, there are certain K==(3)problems involved in operating phased arrays over nbandwidths of this size. Combining this result with (1) and (2), the normalized far-

Insertion Loss: The beam-forming technique is field amplitude of the Kth beam from broadside istheoretically lossless and in practice matrices can bebuilt with low values of insertion loss. s -rd 2K 1 rAntenna Array Illumination: The matrix provides a 1 ssnnn--ns/

uniform illumination of the array elements. However, EK = - _ (4)simple beam combining techniques can yield (cosine)n n sird n- -illuminations. LX n 12]

The "antenna" characteristics of this matrix such as where:beam shape, beam position, beam crossover, etc. are dis- |EKI =normalized (peak = 1) magnitude of far-field fieldcussed in Section III. intensity

III. THEORETICAL PERFORMANCE IN AN n=number of elements in the arrayANTENNA SYSTEM d= element to element spacing

AS= wavelengthThe normalized magnitude of the field intensity in the K=beam number

far field of a linear array of n isotropic sources is given6 by: a= angle from the array normal.

sin- If a beam-forming matrix were built using hybrid rings as

1 2 combining devices instead of directional couplers, the far-E = (1) field amplitude of the Pth5 beam can be shown to be

sin-2 . Fird . Pir]

sin n -sisn -P1where |Ep'- 1 L n

n .frd. Pir]2ird (2) sin -sin a-

d=element spacing Hereafter this paper will consider only matrices using 3-dbX = wavelength directional couplers. Similar results can be obtained for

a=angle from the array normal hybrid ring matrices by using (5).Eq. (4) is now used to examine various antenna properties=-element to element phase shift.ofteba-rmnmtix

Of the beam-forming matrix.The element to element phase shift, b, can be found byreferring to the schematic diagram of the particular matrix K is defined as the beam number. Values of K are limited to positiveunder consideration. Using a 16-element array as an ex- nonzero integers. When these values of K are used, the equations which

and~~~~~~thrfrreern.otemarxshmtco follow apply only to beams to the right of the array normal. However,ample, an hrfr eern otemtl ceal fsince the matrix forms b)eams wshich are located symmetrically about theFig. 4, it is seen that the directional coupler which connects array normal, this restriction does not hinder the usefulness of the results.

The mathematical simplicity more than compensates for the slight lossin generality.

8 Positive values of P yield beams to right of broadside. Negative6 J. D. Kraus, "Antennas," McGraw-Hill Book Co., Inc., New York, values of P yield beams to left of broadside. P=O yields the broadside

N. Y., p. 78; 1950. beam.

182 IRE TRANSACTIONS ON MILITARY ELECTRONICS April

Positions of Beam Peaks Beam CrossoversThe peaks of various beams occur at values of the angle The angular position at which two beams cross over can

ca which make the numerator and denominator of (4) equal be found9 from (4) by equating the amplitudes of the Kthzero. Designating these angles as "ap" and the adjacent (K+l)th beams. Defining "a," as the

1I angular position of the crossover,sin ap (nq + K--) (6) KI,nd 2 a, = sin-1 (10)

where q = any integer.The beam crossover level E| is found by substituting (10)

A value of q = 0 yields the position of the main beam. into (4):Nonzero values of q give the positions of grating lobes.

1E1Positions of Beam Nulls c

Pattern nulls occur at those zeros of the numerator of sin )(4) which are not accompanied by zeros in the denomina-tor. Designating angles of pattern nulls as ao, For values of n> 10

x / ~~~~~~~~~~~~~~~~~~~~2sinao= (m+K--K- (7) E 2 (12)

nd\ 2/7

where m = 1, 2, 3, etc. but m X qn Thus the crossover level is independent of beam position,element spacing and wavelength and for larger arrays

where q = any integer. (n> 10) it is effectively constant at 2/r. Since the peak of

Relative Positions of Peaks and Nulls any beamn has an amplitude of unity due to the normaliza-RElative P ns7)pointoftPeakandtNulstingcharacteristicstion of (4), this crossover level is approximately -4 dbEqs. (6) and (7) point out two interesting characteristics (-3.92 db).

of beams formed by this technique:1) All the nulls of all the beams occur at certain common Beam Movement with Changes in Frequency

angles. As the operating frequency is changed the position of the2) The peak of any beam occurs at one of these same peak of any matrix beam changes due to the factor of X

common angles. in (6). The amount of beam movement is also a function ofcharacteristics of the matrix beams are sum- beam position as evidenced by the beam number, K, in

Thrizes in Fig. 5 which shows three typical beams. (6). This fact will complicate any compensation schemedesignied to allow operation over wide instantaneous band-

BEAM tIBEA9 2 BEAM 3 widths. The change10 in beam position with frequency isI/f g~~~~~~ivenby

dX., |\v dap = tan ap - (13)

For beams near endfire where acp approaches 900, thedifferential equation (13) can be solved to give:

Sector Coverage -A 2V2/_X * (14)The angular sector 6, covered by the multiple beams from ap X

the matrix, can be found from (6). "6" is the angle between As an example consider the effect of a 10 per cent frequencythe peaks of the extreme right and extreme left beams change. The near-in beam positions will be shifted by(K=n/2 for these beams). about 10 per cent; whereas a beam close to endfire will

have its position shifted by 28 per cent.62 [n[(- - )] (8) IV. TAPERED APERTURE I.LUhINATIONS

The b)eam-*forming matrix provides a uniform illumina-For large arrayswhere n>~~~1 tion of the andtenna array. While this illumination provides6~~2sn1 \) the narrowest beamwidth and the greatest directivity, it

9The solution of interest occurs when ,6= -{K+i where ^6 is definedThus for a large array the sector coverage is determinled in (1).

10 Assume the phase shifters and the couplers in the matrix are in-only by the element spacing and the wavelength, sensitive to changes in frequency.

1962 Delaney: RF Multiple Beam-Forming Technique 183

has a relatively high first sidelobe level (-13 db). Lower the uniform illumination beam. The crossover point be-sidelobes can be achieved at the expense of beamwidth tween the adjacent cosine beams is down 2.1 db from theand directivity by combining the output beams of the peak.matrix. Allen" has shown that it is possible to achieve There are some limitations on forming adjacent tapered-arbitrary aperture illuminations using weighted addition illumination beams as shown in Fig. 6. Allen'3 has shownof selected beams. The discussion below considers the that the beam shape and beam spacing obtainable from asimple addition of two adjacent beams. lossless simultaneous beam-forming matrix are not com-The addition (after phase correction) 12 of two adjacent pletely arbitrary. The results of this analysis indicate that

beams will result in a cosine illumination of the aperture. if the beam-forming process is to be lossless the crossoverThis fact is readily demonstrated by adding the illumina- level of adjacent tapered illumination beams cannot betions of the Kth and the (K-+ 1)th beams. In the interest of higher than the crossover level of the uniform illumina-mathematical simplicity the array is considered as a line tion beams. Thus, the cosine illumination beams of Fig. 6source for this derivation. cannnot be realized simultaneously in a lossless manner.

IK = Ej(2K-1)# This fact is easily recognized if one tries to build a beamK combiner to simultaneously form the beams of Fig. 6.

IK+1 = Ej(2K+±1) Signal energy from the center uniform illumination beammust be split to form the two cosine beams. Therefore,where when a signal arrives on the peak of the left cosine beam,

IK = illumination of Kth beam some of the signal energy is coupled to the right cosine

7r x beam and thus is lost in the beam combining process.3=- Cosine illumination beams which are formed simultane-

2 l ouly and losslessly are located further apart than the beamsI = array length of Fig. 6. The crossover levels of such beams are 9.5 db

x = length variable along the array. down from their peaks.An approach similar to the one used to develop (15) will

'K + 'K+r1 = eJ(IK i)2 ± E2(IK+i): show that three uniform illumination beams can be com-= Ei2K#[E-' + E+Hi] bined to form a cosine-squared illumination of the array.

= (2 cos 3)Ei2K#. (15) Also, by a proper choice of how these beams are combinedit is possible to achieve cosine-squared-on-a-pedestal

Thus the amplitude of the new illumination is a cosine illuminations.function, and the phase distribution of the new illumina- Section V presents experimental data taken on a multipletion points a beam halfway between the K and the K+1 beam-forming system. Antenna patterns for uniform,component beams. Fig. 6 shows the addition of uniform cosine and cosine-squared illuminations are included.illumination beams to form cosine illumination beams.A 1/V/2 factor is introduced in the addition process to keep V. EXPERIMENTAL RESULTS ON A 16-ELEMENTthe power in a cosine illumination beam the same as the BEAM-FORMING MATRIXpower in a uniform illumination beam so that the gain ofthe beams can be compared. Fig. 6 shows that the cosine the shematic diagramofthis matrixin gbeam has 0.92 db less gain than the uniform illumination No attempt was made to achieve an especially compactbeam and a null-to-null beamwidth 1.5 times greater than package in this experimental model. The use of strip

transmission line permitted the fabrication of several di-1.0---;_------IR -R -3R rectional couplers and phase shifters on the same board.

2/7, The boards were then interconnected using coaxial fittings./ / \ / \ \ The directional couplers14 and phase shifters'5 used in the- - t . - /matrix are of the coupled strip type. Both these com-

"7\.", -ponents have bandwidths greater than 30 per cent. Thesewideband components were used to more fully explore the

1/,/-2-0.7071+2Re < ) ( SR_ __possibilities of this beam-forming technique. The measure-ments reported here were made at 900 Mcps.

Fig. 6-Formation of cosine illumination beams. 13 J. L. Allen, "A theoretical limitation on the formation of losslessmultiple beams," IRE TRANS. ON ANTENNAS AND PROPAGATION, vol.AP-9, pp. 350-353; July, 1961.

"Allen, et al., op. cit., pp. 221-223. 14 J. K. Shimizu, "A Strip Line 3 db Directional Coupler," Stanford12 Fixed phase shifters must be inserted in the beams to guarantee in- Rtes. Inst., Stanford, Calif., SRI Project 1592, Sci. Rept. No. 1 (AF19

phase addition of the signal energy. For an example of a phase correction 604-1571); June, 1957.calculation see W. P. Delaney, "An RF Multiple Beam Forming 11 B. M. Shiffman, "A new class of broad-band microwave 90-degreeTechnique," Lincoln Lab., Lexington, Mass., Group Rept. No. 41G-0012; phase shifters," IRE ON MICROWAVE THEORY AND TECHNIQUES, vol.Sec. 4.1; 1961. (ASTIA No. 262 017). MTT-6, pp. 232-238; April, 1958.

184 IRE TRANSACTIONS ON MILITARY ELECTRONICS April

Antenna Measurements'~The beam-forming matrix was tested in a 16-element

linear array of parallel dipoles spaced 0.58X apart. Fig. 8shows the major lobes of all sixteen beams. The angular

, sector covered by all the beams is 1070 which agrees closely' with the value of 1080 predicted by (9). The beam peaks

occur very close to the positions predicted by (6). TheE worst case is a 1.20 error in beam 7 Right. The envelope of

the beam peaks follows the antenna element pattern veryE closely as would be expected from the principle of pattern

multiplication.Figs. 9-13 show typical antenna patterns of individual

matrix beams. The sidelobe performance of the near-inbeams (1 Right, 2 Left, 3 Right) is quite good with firstsidelobes of - 13 db. The antenna element spacing of0.58X used in this test allows grating lobes to form forbeams further than 450 off broadside. The start of this

Fig. 7--The 16-element matrix. grating lobe structure is evident in beam 7 Right (Fig. 13).It was shown earlier that a cosine illumination of the

aperture could be achieved by adding two adjacent beams.RF Measurements at 900 Mcps Fig. 14 shows a cosine illumination beam obtained by add-

This beam-forming matrix is a matched device at all in- ing beams 4 Right and 5 Right in a hybrid ring. The firstput and output ports. The maximum VSWR at any port sidelobe in this beam is about 22 db down which is close tois 1.27. the theoretical value of -23.2 db for a cosine illuminationAny beam terminal is isolated from any other beam on a 16-element array. The hybrid ring also provides the

terminal due to the inherent isolation of the directional difference of the two adjacent beams (corresponding to a

couplers. The average isolation at 900 Mcps is 28 db with a sine illumination). The difference pattern, Fig. 15, has a

lowest value of 15 db. The antenna terminals of the matrix sharp null at the same position as the peak of the sum beamare isolated from each other in the same manner. The aver- and thus, it may be useful for amplitude comparison mono-age isolation is 30 db with a lowest value of 20 db. pulse applications.The insertion loss of the matrix is 0.74 db. Practically Fig. 16 shows the antenna pattern of a cosine-squared-

all of this insertion loss is due to the strip transmission on-a-pedestal illumination. Weighted addition of beams 1line which has a loss of 0.18 db per foot at 900 Mcps. The Left, 2 Left and 3 Left yielded a 24 per cent pedestaluse of new strip-line materials and more compact packag- (theoretical highest sidelobe= -27 db). The first sidelobesing should allow a significant reduction in this insertion measure -27 db but amplitude and phase errors in theloss. component beams and in the beam combiner cause a fewThe matrix provides a uniform amplitude illumination other sidelobes to exceed this level. The peak of the beam

of the array. However, slight variations in the coupling occurs at the peak of the 2 Left beam as expected.ratios of the directional couplers cause amplitude errors VI. CONCLUSIONin the illumination. The worst rms amplitude error is 0.41db and the average rms error for all beams is 0.30 db. In conclusion, it is worthwhile to reiterate the ad-RMS phase errors in the array illumination average 4.80 vantages of this beam-forming technique and also point out

for all beams with a worst case of 12.90. p

~~~~~~~~~~~~00 4

Fig. 8-Major lobes of at sixteen beams (vertial scale=40 db, Fig. 9-BeamI Right...erticats ...........h.rizonta

horizontal scale=20 per_smallest division). scale=20 per smallest..ivision).

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1962 Delaney: RF Multiple Beam-Forming Technique 185

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186 IRE TRANSACTIONS ON MILITARY ELECTRONICS April

Considered from an antenna standpoint, the major ad- monopulse would have to be replaced by amplitude com-vantage of this technique is the realization of simultaneous parison monopulse.multiple beams, all of which have the full gain of the aper- The matrix is limited in power-handling capabilityture. Rather than having to steer a single beam using, for (from a transmitting standpoint) by the high power char-example, RF phase shifters, one has only to observe the acteristics of the transmission line used. For large matricesoutputs of the matrix in a selective or simultaneous man- it is discouraging to think of using coaxial line or waveguidener. In view of the continuing advances in microwave and thus the power limit is set by the strip transmissionswitching diodes, it seems reasonable to reduce the number line. Also, since the matrix behaves like a power divider,of receivers required by time sharing a particular receiver the bottom directional couplers and phase shifters willto several matrix beams using diode routing switches. have to handle much higher powers than the upper ones.

Since the matrix is theoretically lossless (and in prac- For lossless simultaneous beam forming the aperturetice has a low insertion loss) it can, in many applications, be illuminations are limited to a uniform illumination whichlocated directly behind the antenna elements with a re- has relatively high first sidelobes or tapered illuminationssultant saving in phase and gain stable HF circuits. The which have far-field patterns with undesirably low cross-microwave elements used in the matrix are passive and over levels.nonvariable; thus the matrix can be made rugged and Several of these problem areas such as matrix fabrica-reliable using strip transmission line techniques. tion and packaging, angle tracking with fixed beams andThe matrix itself can be made broad-band, but the high-power operation of strip transmission line are pres-

frequency limitations of phased arrays (as opposed to ently under study.time-delayed arrays) are still present.A major drawback of this beam-forming technique, when

large arrays are considered, is the complexity of the matrixarrangement. For example, a 64-element matrix requires The author wishes to acknowledge the contributions of192 directional couplers and 160 fixed phase shifters. Thus Dr. Judd Blass, J. Butler and P. Shelton to multiple beam-some ingenuous fabrication and packaging techniques are forming techniques. The 16-element matrix described inrequired if low matrix insertion loss is to be maintained. this paper was built by Sanders Associates.A possible drawback of this technique from an antenna The author is especially indebted to J. Allen, J. Resnick

standpoint is that the simultaneous beams are fixed in and J. Sklar of Lincoln Laboratory for their helpful discus-space. An angle tracking technique such as null tracking sions on beam forming.