Steerable Array Radars

80 IRE TRANSACTIONS ON MILITARY ELECTRONICS April

VI I. CONCLUSIONS that particular application, with a trade-off betweenA relatively complete first-order nioise theory of par- higher miinimum diode quality and lower pump fre-

ametric amplifiers is presenitly available to designiers of quenicy possible within limlits. The use of a lower pumlpsuch circuits. This theory is based oni a rather simplified frequency is almost always desirable because of ease ofmodel for the diode capacitor, and probably should be circuit design, potential bandwidth improvement, andextended in the niear future to account for voltage-var- possible use of solid-state pump sources.able series resistance of the diode, and for the effects of These conclusions, of course, have been drawn fromvarying barrier resistance. The voltage-variable series analysis based on amplifiers which are not constrainedresistance case is likely to become more important when with respect to bandwidth. In cases where bandwidthdiodes having very thin base regions become available, optimization is mandatory, it may be necessary to sacri-The existence of an optimlum pumllping frequency7 for fice diode qualitv in order to mieet an excess temperature

a given signal frequency and given diode quality cer- specification.tainly should influence the thinking of the designer ofparametric amplifiers, although perhaps not onlv in the ACKNOWLEDGMENTmost obvious manner. That is, the optimumn punmp fre- It is a pleasure to acknowledge the encouragement ofquency which provides the maximumii allowable excess H. H. Grinmm, of the General Electric Company Elec-temperature with the iminimum quality of diode should tronics Laboratory, Syracuse, N. Y., without whichbe viewed as the upper limit on pump frequencv for this paper would not have been prepared.

Steerable Array Radars*FRANK C. OGG, JR.t, SENIOR MEMBER, IRE

Summary-The general characteristics of radars using large steered by the introduction of a phase gradient acrossplanar steerable array antennas are discussed. The need for an the aperture.amplifier for each element is shown, and the tolerances and stability The best-known early example of a steerable array isrequirements for the amplifiers are discussed. Array geometry,pattern formation and gain, mutual coupling, and beam-steering the MUSA, which was built by Bell Telephone Labora-techniques are summarized. Element minimization and signal- tories before World War I I for receptioni of transat-processing techniques are analyzed. lantic radio telephone signals.1'2 A set of three inde-

I. INTRODUTCTION pendentlv steerable beanms was formed from a lineararray of rhombics, each beam being a horizontal fanl

7XA[T ECHANICAL scanning of directive antennas with about one degree vertical beamwidth.jj' A.. has been almost universally employed inexist- During World War II, steerable array radars using

ing radars. A horn-and-reflector allows only a mechanical phasing were developed. A series-fed linearlimited scanning pattern anid has a vulnerable mechani- arrav (Fig. 1) was developed for a Naval fire-controlcal structure, but has low initial cost and negligible radar.34 A possible alternate configuration is the paral-maintenance. lel-fed array (Fig. 2). A liniear slotted-waveguide arrayWeapon performance has increased rapidly in recent was designed for mounting in the leading edge of an air-

years, bringing with it increased radar requirements. craft wing, with the guide wavelength changed by mov-Among these are shock resistance, rapid volumetric ing one wall of the waveguide to scan the beam.5scanning with high angular resolution, random beam Since World War II, electrical phase shifting haspositioning for multiple target tracking, very high radi- been investigated to permit random beam positioninigated power, very large apertures and pulse-to-pulsetunability. One possible solution is the steerable array, a I H. T. Friis and C. B. Feldman, "iA multiple-unit steerablelarge fixed array of radiating elemenlts wvith the beam anltenna for short-wvae receptionl," PROC. lRE, vol. 25, pp. 841-917;

2 F. A. Polkinghorn, "AS single-sideband MLTSA receiving sv7sten4* Received by the PGM IL, janulary 23, 1961. The research herein for commercial operation on transatlantic radio telephone circ;uits,"

was supported by the UJSAF throulgh Rome Air Dev. Ctr. of the PROC. IRE, vol. 28, pp. 157-170; April, 1940}.Air Res. and Dev. Command. Preparation of the material for publi- 3H. D. Friis and Mt. D. L.ewis, "Radar antennas," Bell Sys.cation was supported through WW\RNGWY of the WYright Air Dev. Tech. J., vol. 26, pp. 219-317; April, 1947. (See especially p. 300.)Div. G. C. Southwrorth, "Principles and Applications of WVaveguidle

J Rad. Lab., The Johns Hopkins Usniversity, Baltimore, Md. Transmission,' D. V;an Nostrand, Inc., New York, N. Y.; 1950.Formerly with the Bendixs Corp., TOW-SOn, Md. Friis and l ewis, op. oit., see especially p. 315.

1961 Ogg: Steerable Array Radars 81

RADIATINGELEMENTS TRNAIER RADIATING SLOTS

PHASE-39-26 -9 +9 +29n +39- SHIFTERS DUPLER

INPUTTUNABLEl

Fig. 1-Linear array with series feeding. RECEIVER

Fig. 3-Folded-waveguide frequen-icy-scanniing linear array.RADIATING

_ELEMENTS

-39-29 -9 ~~+9 +2 PHASESHIFTERS

l | | ~~~~~~~~~TUNABLEl I ~~~~~~~~~~TRANSMITTER_

INPUT D {

Fig. 2-Liniear array with parallel feedin|g. TUNABLlRECEIVE-

anid more rapid scanniing. The slotted-waveguide array-miiay be scanned without moving the waveguide wall byvariationi of the frequency, leading to the folded-wave- PHASE SLOTTED WAVEGUIDESguide frequency-scanner (Fig. 3). Several wavelengths Fig. 4-Planar array with two-dimensional scanning uSing theof guide between slots are used to reduce the tuning "phase-frequency" principle.ranige for wide-anigle scanning to 5 to 10 per cent. Thedevelopmenit of ferrite phase-shifters permits electricalscanning of the configurations of Fig. 1 and Fig. 2.6-9 These limitations have led to consideration of arrays

Twa e a s i cn bwith a transmitter and/or a receiver for each element.Two-dimensionacl electrical scanninlg can be obtainedt . .. .Very high radiated powers are possible with a inulti-by the "phase-phase" scanner, anl obvious mIlodification I* plicitv of transmitters of mioderate size. The phase-of either Fig. 1 or Fig. 2, or by the "phase-frequencyscanner

\(Fg') shifters cain be operated at low power levels. A receiverscannler (Fig. 4).Neither the "phase-phase" nor the "phase-frequency" for each element allows formation of anlunlimited num-ber of beams for reception without loss of sensitivity.

scanner fully satisfies modern requirements. Neither TIcan form multiple steerable receiving beams without Terlosses due to signal-splitting before amplification. sible, and the amplifiers provide isolation of reflectedpower.INeither can radiate very high power, since present fer- p eirite phase-shifters are limited to comparativelv low M d c a

,,I . aia array. Anl arbitrary number of receiving beams canpeak powers. The frequency scanier is not tunable, m be formied, fixed or steerable as a stack of beamns, or in-the sense that frequency at each beam position is fixed. dependentlv steerable. The transmitting array nmayIn parallel-fed arravs of both tvpes, recirculation of re- f a l a> . ' . 1 ., ~~~~floodlight a large aiigular regioin, illutiiiiiate the areaflected power often spoils the pattern, since imiultiple re- covered by a steerable stack of beams, or illuminate

flections through the phase-shifters produce cohereint separately several independetly steerable beams. Inradiatioin at- other aingles thati the beain position. Iso- Iradiatio at othe anlsta teba osto. o the last type, the transmlittinag array may radiate a se-lators or circulators OIl each phase-shifter are usually thlatyp,herlis tiigravnvrdaeas-lat srs to irculators lowiideahophase-shifterare0usual quence of closely spaced pulses with the beam moved

between pulses to illuminiate the several receivingbeams, thus obtaining a high data rate oni mainy tar-

6 F. Reggia and E. G. Spencer, "A new technique in ferrite phase- gets under simultaneous track. Both volunmetric scan-shifting for beatm scanniing of microwave anteinias," PROC. IRE, vol. . * .

-45, pp. 1510-15t7; Novemlber, 1957. mng and multiple-target tracking may be done simul-I F. E. Goodwin and H. R. Senf, "V'olumetric scanning of a radar taneously, eliminating the hanidover fromll a search

with ferrite phase shifters," PROC. IRE, vol. 47, pp. 453-454; March,1959. radar to a seDarate trackine radar.8 C. M. Johnsonl, "A ferrite phase shifter for the UHF region,"

IRE TRANS. O.N MICROWAVE THEORY AND TECHN-IQUJES, vol. MTT-7,pp. 27-31; Janutary, 1959. l' TIhe "'phase-frequenlcy" s:cannler (Fqig. 4) can he mlodlified by use

9D. D). Kinlg, C. M. Barrackc, anld C. M. Johnlsonl, "Precise control of a transmitter anld receiver onl each slotted wax'eguide. Most of theof ferrite phase shifters," IREi TRANS. ON IVIcROwAvE IFiFORXY ANI) objection1s tO this systeml are then overcomle. The array is still notJE'lcHNIQU)IES, vol. MTIT-7, p. 229-23S2; April, 1959. tulnable, and mulltiple receivinlg beams c>an be fortlued oI)ly inl the

15 Parallel-f'eeding is usulally used in large arrays withoult anllpli- "phase" dimenlsionl. The nlumlber of amlplifiers requlired is reducedPiers to avoid the losses of the series-fed type. Some mleasulred pat- from N'2 to N anld the tolerances are Correspon(Iingly tightened. Muchterns of parallel-fed arrays, with an1d withoult circullators, are given ofI the anlaly,sis given in this paper is also applicable to a "phase-bDy S. J. Rabillowitz, "Array antennas with applications to radar," frequency" array with an amplifier for each r-OW, bult the principalTrans. of the UJniversity of M


The choice of conifiguration for a specific application cis beyond the scope of this paper, which is intended to 50 80ELEYATIONbe a general survey of possibilities and limitations. _ ELEVATION

600 ELEVATIONII. GEOMETRY OF A PLANAR ARRAY goo

Unlike the horn anid reflector anteinna, an array has a SO*different pattern- at each beami position. These pattern K 700variations are rather complicated in the usual elevation- /\ \7azimuth coordinates,12 but they are greatly simplified / / k 60when a more natural coordinate system is used. l 1

-50 -40-30b-2 I 1 20o 304 50The array factor of a planar array with equal element 2 4M5 0 0

spacings is C

F(06, 02) = Z ,,, exp [2wmjd6ll + 2irnjd202], (I)1)mrt. I, 1OO EL IV % R%-Z"wavelengths and 61 = sin a -sin ao, 02= sin 13-sin O3. In 400 300 200

-0 1O , 300 40these equations, the direction cosines of the normal to AZIMUTHthe plane wave received by or radiated by the array are Fig. 5-Angular coverage of a planar arrav tilted 40 from vertical.sin a and sin 3. The beam mllaximllum is at a =ao, =fo. Beam steering is theoretically possible from -45' to +45 inthe horizontal steering angle (3 and from -40 to +400 in theThe phase distributionl onl the aperture iS factorable 1 I1 vertical steering angle a. Elevationi and azimuth contotirs arethese coordiniates, which simplifies beam steering. plotted on a rectangular grid of lines of constant a and d. TheThe conniiectioni betweeni the natural arrav coordi- zenith is at a =50, 00.

nates and elevation-azimiuth can be founid wheni the ar-ray orientation is kniowni. This conniectionl is illustrated end-fire.'3 All expressioni which is accurate at all an-in Fig. 5 for an array tilted 400 from the vertical with gles isscanniing 450 from boresight. r.The patterni variationis with scaniinig are easily beamwidtlh = arc sin sin ao + sin1]

understood in the coordiinates of Fig. 5. The relativepositions of the various beams are preserved. With a 6] (2)vertical stack of beams, the stack remains vertical in 2these coordinates. When the stack is not on the verticalprincipal plane ((,= 0), it will not generally be v,ertical where 0 is the half-power beamwidth at boresight. Thisin elevation-azimuth coordinates; in the upper corners is the array factor beamnwidth, which in small arrays orof Fig. 5 it will be almost horizontal. The same remark near end-fire may be modified by the element pattern.Of~ ~~ ~ ~ ~ ~ ~~~~~~te beam chrceitc suc asl asnbety alotmayotl.Tesmermholds for the four-beamn set of a moonopulse system, as Other beam characteristics, such as asymmetry, maywell as for the polarizationi of the radiated wavefront. be treated similarly

Changesinbeam shape with scanning are also The arrav is operated entirelv in the natural array co-Changes in beaim shape with scanning are alsotreated simply. The function F(61, 62) is fixed, and only ordiiiates. The fact that the resulting scan patterns andthe variation of 1 anid 62 need be considered. For ex- beam shapes may be rather unusual when viewed inample, the half-power points of the beam in the two elevation-azimuth is usually irrelevant. The radar data

coordinates a, (3are fixed values of 61and,62. If can be converted if necessary to anv desired coordinates,coordii-iates ae, 0 are fixed values Of 01 and62. IfU but it is convenient to perform beam interpolation,F(61ol,, 0) = F(-6,,, 0) = F(0, 620) = F(0 6,-0) scanning-pattern- generation, tracking, etc., in the

1 natural coordinates.=g2F(0, ), The actual position of the beam with respect to theV\/2 plane of the array is showni in Fig. 6. The beamii gen-

then the half-power points are located at sin a-sin erated by a linear array lies on a cone about the axis ofao= 61i and sin d3-sin /3,= 020, regardless of steering the array, since this cone is the locus of points with theangle. The half-power points are thus dependent only same direction cosine. In a planar array with a factora-Ol the half-power beamwidth with the beam at bore- ble phase distribution, the beam lies on the intersectionsight and do not depend 01l any other characteristic of of the two cones shown. W;hen both natural array anglesthe array. It can be shown- that the half-power beaull- are at 450, for example, the beanl lies in the plane of thewidth is given very accurately~ byT the usual cosine-fore- array. The theoretical coverage of Fig. 5 must be modi-shortenling approximlationl until the arrayx appro)achles fledl byw sulperposition of tile elemlenlt factor ulpOnl it-.

12 A detailed treatmlent of array geomletry is given1 byr XV. H1. von "3 R. XV. Bickmlore, "A note on1 the effective apertulre of electri-Aulock, "Properties of phased arrays," PROC. IRE, VOl. 48, PP. 1715- cally scanned arrays," IRE TRANS. ON ANTF.NNAS AND PROPAGATION,1727; October, 1960. v-ol. AP-6, pp. 194-196; April, 1958Q.


NORMAL TO ARRAY then Rm,ipq is the mutual radiation resistanice niornmal-ized by the self-radiation resistanice. The niormalize(d

PLANE OF ARRAY m h\ BEAM mutual radiation resistanice giveni by (5) is dependentonily oni the isolated elemiient patterni anid oni the spacing.In the case of a theoretical isotropic elemiienit, the calcula-tion is simple anid gives the result

sin 2wRRmnpq 27rR

where R2=d12(m-p)2+d22(n-q)2 iS the square of the1Fig. 6-Beain positioni with respect to the plane of the array. The separation of the two elements in wavelengths.

phase distribution on the aperture is factorable. The phase dis- The main beam gain of the array, assunming that thetribhution in the angle a produces a cone of radiated energy aboutonie axis, while the distribtutioni in d produces a cone abouLt the excitation currents are held constant, is generally de-other axis. The beam is the intersection line of the two cones. pendent on beam position, and is given byThe second intersection line (below the plane of the array) isLIsuLally suppressed by the elenment factor. A linear array produces 2onle cone, with par-t of the cone uIsually suppressed by the element ( Et

G(a(u, fia)=- P(0Eao, o) m

II]. PATTERN AND GAIN OF AN ARRAYThe exact evaluation of the gain can be carried out

If Imfl is the actual current in the m,'nth element, and either by direct integration of the pattern or by (4) andif the isolated element factor is E(CY, ,3), the radiated (5). A calculation for a unliformly illuminated planarpattern of the array is proportional to array is reported in the literature and shows that the

gain varies approximately as the change in beamwidthsF(a, A3) = E(a, d3) E I,n exp Ij2wjmdj(sin a - sin og) would indicate.14

In a linear array,+ 2irjnd2(sin3- sin fib)]. (3)

P0 Z Zm Iuexp [-2irj(m - )d:1 sin ac,]R,~p, (6))EIq.(3) assumes that the elements are far enoough apart thpso that theadjacent eleents do mnot modify the dis- wheretribution of current in the elemnent.1Thegainof the array is equal to rrted= i e(a,e )*ate*(a,d)

G(a, a)= ( ' a( ), exp [27rj(m- p)dc sin beadS, (7)which are specializations of (4) and (5). WVhenl the ele-

where Po is the total radiated power. The total radiated ments are isotropic,power may be computed by integration of the Poynting 2wd1(m -oi)vector over a sufficiently large sphere n. The result is sRr i

PO- 2rl(m-ddsina-Rp)P0=-3JssF(,t)t h*(,3)dS When the element spacinog is a half-wavelength, all

sott tdmutual radiation resistances are zero anfd the gain re-=

Z Z'm - JpQ2 exp [-2irj(m -p)d l sin ago mains constant with scan angle. A geometrical explana-

7rlt1 1'X7 ~~~~~~~tionis given by Fig. 6. The beam lies alonlg a conle and-t2ij(n -rq)dt sin /ho]Relnn (4) with isotropic elements includes the whole cone. As the

beamwidth broadens, the arc of the cone decreases.wthre Exact calculation of the gain of an array is quite

1 Fcomplicated. Inl general, the usual estimates from theRt,lnnq =- ('rElG(a, /3) e.(a. /3) exp [2rj(m - p)ddsin a beamwidth are approximately correct if the co7ical4wr J J wbeam shape of a linear array is taken into aiccounit.

+ 2irj(n - q)d2 s in ]dS (5) If a directive elemenet is used, the enlergy cannlot be ac-counted for when the maina beam is steered into a null

is proportional to the mutual radiation resistance. If of the elegent pattern. The main beam disappears or isthe elementt factor is normalized by

1Crpq exp 2rj(m p)dl sinaoiains14R. K. Thomas and M. J. King, "Gain of large scanled arrays,-P E(a,/3).*(a,/)dS 1, IRE TRANS. ON ANTENNASAN6. PIROPAGATION, VOl.Ali-8, PP. 635-

47r ~ 21r(-qd siJoR,,Q4 with isoVtbropi elne1960.udstewhl oe.A h


greatly reduced in gaiii, and the energy in the maini finite or nonuniform arrays, the taper is changed dur-beam apparently is not radiated. It has been suggested inig scanining by uinequal coupling effects on1 the variousthat this eniergy is somiiehow stored in the anitenniia struc- elemiienits.ture and reflected back to the tranismiiitters, creatinig a Ini an infinite un-iformly illumiinlated array, each ele-very large SWR at each tranismitter. Attem)pts to ob- meiit is affected by coupling in exactly the same way.serve this effect experimenitally have generally failed, IThe taper is unchaniged, and there are no pattern varia-and it is inot clear how to accounit for the energy.15 tions during scanniing except those discussed in SectionOn receptioni, the pattern is formed in a beam-formn- J1.17

ing network (Sectioni VIII) with taperiing after amplifi- The elemenit factor is modified by passive reflectionscation. If the signal comiiponienits are equal before taper- froma the other elements present in the array. The ele-ing, then they add coherenitly after taperiiig, while the menit factor used in pattern calculations is the patternuncorrelated receiver inoise comiiponients add inicoher- of ani elemenit embedded in an infinite array of similarently. Ain output signal-to-noise ratio of elements. With half-wave spacing, the effective element

/S\ (S'~ (Z a.)2 factor is usually broader thani the isolated element pat-)_8 = t__- 4 '(8) terni, which is ofteni useful inlwide-angle scanniing sys-N\ /out Vi/ Z a,,2 tems.Sis

is obtained, where a, are the taper coefficients. The gaini variationis are due to chaniges in the antenniiaIf the noise is local oscillator nioise rather thani re- im'pedanice during scanininig which prevenit matching

ceiver noise, it will be coherent rather thani incoherenit. tranismbaitters antd receivers to the anatenas except atWhen the beam is at boresight, the local oscillator noise o1e beam position. These variationxs are usually smallwill add coherently. At other beamii positions, it is re- (1 db or less in a dipole array) except near end-fire.'9'20duced by the array factor, since it will be combined The variable load presenited to the tranismitters causesafter phasing. The mnagnitude of the oscillator Inoise is a large reflected current which is often significant.increased ini proportion to the signial. An array will Stanidinig-wave ratios of about 2:1 are enicountered intherefore have a blind spot at boresight shaped like the uniformly illuminated dipole arrays scanned 450 fromreceiving beam uniless the local oscillator noise is suffi- boresight.ciently suppressed. In a finite array, the elements near the edge are af-fected differently. In a large array, edge effects are

IV. ANTENNA COUPLING EFFECTS usually niegligible. It is possible, but usually unineces-sary, to eliminate edge effects in receiving arrays withThe pattern an-d gain of an array with known cur-uni elmnsaon h dgso h prue

rents in its elements are discussed in Section III. The d In a nonuniform array an analy~sis based on an infi-currents actually present are modified by antenna n auniform array.i1 nite uniform arrav iS inaplicable. Very little is kinowicoupling effects and are therefore dependent on the cur- i V l

rents ithoteelmnsnonbabout the effects of coupling on transmitting arravsrents in the other elemeints and OIlbeam position., with power tapering. WShefi an irregular distributioiAn exact calculation of the actual currents is possible wimil.thow tapsering.eWhn anirregular distibution

in principle as a large set of coupled-network equations s t tif the mutual impedances are calculated or measured. 16 ray canl be filled in with dummy elements to equalize the

. ~~~coup)ling effects. In a transmitting arrav of this kind.In practice, however, the order of this set of linear equa- c etions is the number of elements in the arrav, and the the effects are not equalized.calculation is impractical except in small -arrays. A In Section III, the normalized mutual radiation re-large array can be regarded approximately as infinite in sistance was shown to be dependent only on the isolated

.L . r ~~~~~element pattern and on the spacingr. This result appearsextent, and the coupling effects can be obtained for an X sto contradict experience, since a varietv of elements withinfinite uniformly illumninated arrav without excessivedifficulty. This approximation can be used to obtain similar patterns are known to have very different meas-dinfrculty.Thisapproximationaboutcoupln ectsi recseii a ured couplings. These measurements are made by driv-information about coupling effects lrn receiving arrav;s

* . .r r .rs 1 r lll~~17iig oiie element with a signal source and observing thewhich are always uniformly illuminated, or in uniformtransmitting arrays.The principal coupling effects are a change in the ef- 17 J. Blass and S. J. Rabinowitz, "Mutual coupling in two-di-

fective element pattern, gain variations in scanning mensional arrays," 1957 IRE WESCON CONVENTIoN RECORD, pt. 1,due to mismatches between anten1na and amnplifier, and 18134-150. tfctri otawy bodnd ldtsulyivariations in the loads driven by the transmitters. In rather irregular when embedded in an infinite array-.19 :Near end-fire these effects are much greater. See E. A. Blasi

and R. S. Elliott, "Scanning antenna arrays of discrete elements,"IRE TRAN-S. ON ANTENNTAS AND PROPAGATION, vol. AP-7, PP. 435-

15 This problem was pointed out by S. J. Rabinowitz. .436; October. 1959.16i p. 5. Carter, "Circuit relations in radliating systems and appli- 20 p. 5%. Carter, Jr., "Mutulal impedance effects in large beamcations to anltenna problems," PRO)C. IRE, vol. 20, pp. 1004-104t; scanning arrays,"' IRE TRANS. ON ANTENNA4S AND PROPAG;ATION,June, 1932. vol. AP-8, pp. 276-285; May, 1960.


received signal at the terminals of the other element.2" Fm,, is 0 or 1 as the elemnent is failed or operatinlg, AmWith elements having essentially the same pattern as a is the fractional current error, and bmn is the phase errordipole, coupled power from 15 db to 30 db down has in radians, each for the m,nth element in the array.been observed at half-wave spacing. The discrepancy is The power array factor is P(a, d) = F(a, ,B). F*(a, A).due to the directive nature of the coupling in traveling- If all sources of error are assumed independent, thenwave antennas, such as the helix or polyrod. Some the average power array factor ismeasurements on polyrods are given by Southworth,showing that the coupling in one mode is about 30 db P(j3) [=(F)2( xpjb)2Jp(a,)greater thani in the other.22 A forward-traveling wave is

__

radiated in such an antenna while the reverse-traveling + [(F2)(1 + _A2) - (F)2(expjf)21 Z 1l (10)wave is reflected to the source. The radiated component tWIproduces the nmutual radiation resistanice giveni by (5) where Po(a, () is the designi-array factor. The distribu-anid the restultinig pattern variationi, while the reverse tiOn of amplitude error enters only as its variance A2,conmponent is responsible for the staniding-wave ratio andat the tranisimiitter. If care is takein in matching the ele-imienit to free space, the reverse component can be con- - _ Fsiderably reduced. Isolation of the transmitters from F = F2 = 1 - -,antenna impedance variations can be obtained in thismanner with strongly coupled elements. The conven- where F is the number of failures anid N is the niumbertional method for the measurement of mutual imped- of elements. The phase error appears otnly as exp jS.ance measures only the reverse component. The calculated average pattern must be reniormalized

by (1-FIN)-', since the total power in the pattern is

V. APERTURE ILLUMINATION ERRORS reduced by failures. The normalized average powerPreservation of the pattern and gain of an array de- arrav factor is then

pends on approximate matching of the multiple parallelchannels. The accuracvi with which the channels can be Fx7(a,() - (exp ja) 2] P,(a, (3)matched determines the sidelobe level and gain loss, N /iwhile the periodl of stabilitv in which matching to thedesired accturacy cani be mainitained determines the re- + [ +i 21- - ) (expj) 21quired frequenicy of realigniment. LiThe exact nature of the chaninel drifts depends oni the zEmn 2 (11)

components used and their initerconnections, but it canusually be assumed that they are independent and havethe same distributioin with mean zero in each channel. This expressioni shows that the effect of errors andCalculation of the pattern statistics under these assump- failures consists of a gain reduction in the design-arraytions has been- treated by several authors,23 based on factor with the energy removed from the main beam, re-the fundamental work of Ruze.24 distributed around the pattern as an omnidirectional

Ruze's analysis cani be extended to include ranidom "noise level."amplifier failures.225The array factor including errors and The gain loss isfailures is

F(a, B3) = E [in,zjjFmn - (1 + Amn) exp [jmn(1] - (expj )2 (12)mn

exp [J4'mu, (9) and the rms nioise level oIn the patterni iswlhere In,, and are the design currenit anid phase,

r i& ~t />Pn21 + / \--(expJ6) 2 1,,^21 E. Altshuler, "T'he m11eaSLIremeint of self alid m1Utual im11ped- t ______ _ - (13)

aniceS," IRE TIRANS. ON ANTENNAS AND PROPAGATION, vol. AP-8, F _2-pp. 526-527; September, 1960. E n

23 A bibliography is given inl R. S. Elliott, "iMechanical andelectrical tolerances in two-dimensional scanningr antenna arrays,"IRE TRANS. ON ANTTENAT-S AN-D PROPAGATION, vol1. AP'-6, PP. 114- whenl referred to the maximum amplitude of the beama.119; January, 1958. If the phase errors are distributed normally with24 J. RulZ "The effect of aperture errors on the antennla radi-ation patternl," Suppi. Nuovlo Cimento (Ital.), vol. 9, ll. 3, pp. 364- variance 62 then (exp j6)2=exp[-a21. If the channels380; 1952. aemntrdadapiir hc r u fatlr25 This analysis is based on anl unpulblished Sanlders ,Associates aemntrdadapiir hcr u fatlrMlemo. by S. J. O'Nyeil, ance be are removed, then the distribution of phase


errors should become approximately uniform, and (exp jb)2= (sin 0/o0)2. For small errors distributed uni- -2Fformly between toleranices Ao anid bo, anid for small i1um- 6bers of failures, (13) is approximatelyvD -8 -\

2/2I+ (14)

-16-o-18K

The total pattern has a modified Rayleigh distribu- 20tion regardless of the detailed distributions of error, -22and confidence levels for the distribution of sidelobe -24peaks can be conmputed when the design sidelobe level -260 20 40 60 80 00 20 40 60 I0and the error statistics are given1. 24 Although the as- PHASE TOLERANCE B. -DEGREESsumptionis of the above anialysis are somewhat ques- Fig. 7-Gain loss (one-way) as a function of phase tolerance,tionable, it is founid in practice that the peak sidelobe assuming a uniform distribution of phases between tolerancelevel of an array can usuallv be predicted within about litnits.1 db.The gaii loss is inidependenit of array size aiid ampli- 80

tude errors. Fig. 7 shows gain loss as a function of phase 160tolerance, assuming no failures. A phase tolerance of 500' , 150 - 11.0holds the gain loss to 1 db, anid a sinmilar loss is produced 40 Dby 20 per cenit failures. If low sidelobes are unimpor- L1i 0 j/

I n~~~~~~~~~~~~~~~~~120-0.0 ctant, as is often true in transmsnitting arrays, only enough 110accuracy is needed to prevenit excessive loss of gain. X0 oo0- 9.0Much tighter tolerances are required for low side- uj 90 - 8.0

lobes. Tolerances for a giveni sidelobe level are propor- 870 7ui70- 7.0'tional to V\N, where N is the number of elements in the 60 6.0

array. Fig. 8 shows the phase and amplitude tolerances 50- 5.5required for an rms sidelobe level of -50 db, which will < 4usually give a peak sidelobe level betweeni -35 and 30 3.5-40 db. - 1.5

Failure or remioval for repair of a large fraction of the 0Q 8 16 24 32 40 48 56 64 72 80amplifiers has almost no effect on the pattern. Fig. 9 ARRAY GAIN ABOVE ELEMENT GAIN - dbshows the fraction of elements which mav be inopera- Fig. 8--Phase and amplitude tolerances required for -50-db rmstive while a - 30-db rms sidelobe level is maintained. sidelobe level in arrays of various sizes.The required channel stability is a function of the

number of channels and of the amount of mainteniance l0which is possible. If an array radar with 10,000 trans-miiitters and 10,000 receivers is to be maintained by a 0.9crew which can remove, repair, and realign a hundredamplifiers a day, then an average stability of about six 0.8 /months is necessary. .7o

Channel matching and relative stability are compli- >cated by the requirement for tunability of the radar. ' 0.6|Since individual tuning of each amplifier is impossible,

0.5-all RF components are broad band over the desired tun-ing range. Change of radiated frequency is then ac- 0.4complished by oscillator tuning. Matching of anitenniia zelemenits, duplexers and RF amplifiers over a large fre- ) 03 |quency band is considerably mlore difficult than malctch- /inlg at a single frequency. 0.2_/From the equations given, the consequences of failure/

to maintain the correct aperture illumination can be 0.l1computed. lI'vethods of maintaining the aperture illumi- 0l ,/tnation over a long period of timle fall intto two classes: 0 l0 20 30 40 50closed-loop stabilization and design of extremely stable ARYGI BV LMN AN-dconventional amplifiers. Inlterest in verx--loxv sidelobes Fig. 9 Fraction of elemlents removable in a random manlner without

-... ~~~exceeding aul rms sidelobe level of -30 db, in arrays of varioushas led to investigationls of phase-stabilization tech- sizes.


niques.261-0 Stabilizers able to correct a half-cycle phase beamii is redistributed around the patterni as a ranidomerror in a few microsecon-ds are available and could be omunidirectionial componient. In a full aperture nearlyused on each cormponent subject to drift. Phase sta- all of the radiated energy goes into the maini beam,bilizationi simplifies channel matching, sinice the chain- while in a thini distributioin imlost of the energy appearsniels are automiiatically matched in phase (although not in the sidelobe regioni. If 90 per cenit of the elements inin amiplitude) over their banidwidth. It reduces the pat- the aperture are removed, the maini-beamii gain is de-terni distortionis due to elemenit coupliing, since it is the creased by 10 db an-d about 90 per cenit of the radiatedactual current in the antennia element which is equal- energy is wasted in the sidelobe regioni rather thanized in phase with the reference phase. The aperture applied to target illuminationi.distribution will therefore be correct in phase at all These characteristics are n1ot dependenit oni thetimes, although the amplitude distribution may be dis- random character of the distributioti. Any removal pro-torted. cedure which preserves beamwidth and elemenit spacingOn the other hand, a conisiderable complication of the will lead to main-beam gain reduction anid to anl increase

anmplifier is necessary. Phase stabilization in itself is in the fractioni of integrated gain in the sidelobe region.not sufficient to preserve low sidelobes; phase stabiliza- In extreme cases, such as elimninationi of alternate rowstion to one degree is useless unless amplitude variations or columns, the energy removed from-n the imiaini beamcan be held to about 0.1 db. The phase variations in appears as a single large grating lobe. The average side-the actual current will be large and rapid, even though lobe level of a thin distribution is determined by thethe amplifier itself is stable, due to frequency changes amount of etnergy removed from the main beamii, whichand element coupling changes with beam steering. A is depenident on the fraction of elements removed. Thestabilizer nmust therefore operate on each pulse sep- difference between elimination schemes is in the unii-arately and correct the phase within a small fraction of formitv of the sidelobes. An ideal thin- distributionia pulse length. would have regular sidelobes with equal amplitudes

For these reasons, a stable conventional anmplifier is and the required average level. No synthesis m-lethodsa more satisfactory solution when feasible; however, for such distributions are knlown.the feasibility of such amplifiers is beyond the scope of Thin distributions are therefore not applicable tothe present paper and is dependent on the array char- tranismitting arrays. If it is necessary to use a smalleracteristics. number of transmitters, the only efficient solutioii is to

use a smaller transmitting aperture and to obtaini angu-VI. ELEMENT MINIMIZATION lar resolution- with multiple simultaneous receivinig

beaims. In receiving arravs, thin distributionis cail beMinimization of the number of amplifiers required to b I rachieve a giveni gain and/or anigular resolutioii is of used to maximize angular resolution for given gaini. TIher * * * - ~~~~~~required gain determnlles the number of receiversinterest for practical and economic reasons. Fig. 9 sug- needed aintese reiving elementsecanfthenebeeargests that randoom removal of elements leads to a pat-ter *with fewer elements and the same resolution as a ranged in a thin distribution over a larger aperture. Tlhelimit on the size of the aperture (or the thinness of thesolid aperture distribution. In a sufficienltly large array,v

.. . . '' ~~~distribution) is the acceptable sidelobe level."ta useful degree of directivitv can be obtained with avery thinl (listributioll of elements over the aperture. A substantial reductioni in the number of amplifiersThe sidelobe level in the resulting array is random and can be obtained by removing the tapering. A uniformthe peak si(lelobe level will usually be about 10 to 15 db array of unit elemenits (equal amplitude anid Ino relativeabove the rms level given by (13). No gratinlg lobes will phase) is the most economical way to design both re-appear. ceiving and transmitting arrays. The only serious objec-

Consideration of random element removal shows the tion to uniform arrays is a high sidelobe level near thefundamental limitations of thin aperture distributionis. miaini beam.TIhe gaiin is decreased in proportion to the number of In a tranismiiitting array, power tapering is im11practi-elements remlloved. The gainl remnovedl fromll the main1 cal for other reasonls. It is extremiiely clifficult to imcatch

amplifiers with a differenit numiiber of stages over aband of frequencies. T\'aximum total power is generated

"i "hase Stabilization Techniques for Electrically Scaned Ar- by full power on each transmitter, and m-an4ufacturingrays," Res. Lab. of Electronics, Mass. 11nst. Tech., Camlbridge, l'ech. anld mlainltenance are simplified by idenltical tran1smlit-Rept. on Contract INo. AF 30(602)-1862; Junle, 1959.

27 .r. R. Cummings, "A D)ifferential Phase Stabilization System, ' ters.M.S. thesis, I)ept. of Elec. Engrg., Mass. Inst. Tech., Camlbridge; da itiuin fuiteeet-r h piuMay, 1957.' Ida stbtoso nteeetarth pmul28XV P. I)elaney, "A Phase Stabilization Technique for Pulsed design for both transmitting and receiving arrays. SinlceUHF Power Amplifiers,' M.S. thesis, Dept. of Elec. Engrg., Mas>s.Int Tech. Cabide Jue 1959.^^R no syInthesis methods are known, some examples were

29 K. XV'. Exworthy, "Two Systems for Accurate MicrowavePhase Control," M.S. thesis, DMept. of Elec. Engrg., Mass. Inst.Tech., Camhridge; April, 1959.

30 F. XV1. Markow, "Serv-o phase conltrol shapes


Fig. 10 -Circular arrayv of in it elements with 1.5 beanmividth aiid fall gain. Eleiieiit spacing approxi mately mne-halIf wavelenigt h withblack spaces illtiitiniiated, white spaces oiiitte(.

construlcte(d enipirically.32 Ain ordinary alilplitti(le (is- of utnit elemienits over the aperture, and the exact posi-tribtition (ustially Gaussian or Tceheyclleff) was se- tions are founid l)y experinientation.lected with the (lesire(l apertuire, beamwidths ani( si(le- Hg. 10 shows a circular array whicih forims a 1.5lobes. It was then normalized to ialike the sUIml of its beanim \with ftill gain from 3260 elemienits in an 80X(8(0taper coefficients equtal to the nuilmiber of Unlit elenients aperture. Fig. 11 show\s a circular array wllichl formisdlesiredi in the tlistributioii. For transilmittinig arrays, a similar beanm with about one fifth of full gaini fronithe nutimiber of Unlit clemilemits was approximately equal 758 elemenits in a 78X78 aperture. Fig. 12 showsto the gaini above the elemienlt gain indicated by the a rectangular array which forms a shaped fan-beam.beamwidths. For receivinig arrays, the number of unit In all three cases, the main beams are identical withelements was a givenI fraction of this gain. Fractions those of the original amiplittide tal)ers. IThe pealk side-from 20 per cent to 100 per cent were selected. The nor- lobe levels are about -20 to -22 (lb. In the thin dlis-malized amiplittide taper then gives the average density tribution (Fig. 11), the sidelobes remain high throughotit

the pattern, as in all thinl distributions, but the patternsof the full-gaini apertures have only a few sidelobes

12 These distributions were constracted by J. 1-1. Best. A Inore above -30 (db). Thlese empirical tlistribtitiolns are fardetailed disctission of them will be presented at the next PGItll,Natl. Conventioni, Washington, D. C., June 26-28, 1961. from optim1um11, but are appreciably better thani uiii-

Fi.1 Crlla rayo llteemlt wt .5 ellwdh le ol-ifho fllgal.Eltlll peil ppoilltl; n-al areeltritbalspcsIlllllae,sht p(solitd

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FF 4o c-oo X tc coloelllllWllllllll0lllo | lo | lollollolI II I I I I I II I ILT zFF- c tc c zF4 Illilllllllllllllllllllllllololllllollolllllllllllllllllll~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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db

.2idb Idb~~~~-Nd

d' *LPRINCIPAL 9EAMS*_

0 GRATING LOBES

Fig. 13-Beaml steering usinlg a 2 X2 subarray. The element factor of the sulbarray is superimposed as a contoulr plot. The points A, B, C, D,E, indic>ate variouls pOSitiOnlS of the mlainl arrcay beaml anld its gratinlg lobes.

form apertures. The thin distribution has irregular the permissible beam offset would be smaller. The sub-sidelobes, but is an improvemenlt over a uniforml aper- array technique is therefore nlot applicable when multi-ture with ranldoml elemenlt eliminationl. The alperture pie beams are required unlless the offset is very small. Aarea for the distributions of Figs. 10 and 11 is about stack of beams could be formed in elevationl if each rowhalf againl as large as the aperture required for a com- wvere a linIear subarray and if anl amlplifier were used iIIparable uniform distribution, adding to structure costs. each row before summation of the row sums.Another method of reducing the naumber of amplifiers

is by the division of the array7 into subarrayrs with anl RF VzI I. BEAM-STEERAING lECHNIQUTESphase-shifter onl each elemenlt anld anl amplifier on each In an arrcay without amlplifiers, bearm steering issubarray. The subarray forms anl "elemenlt" which is nlecessarily performned with RF phase-shifters. \Vith anm-uch more directive than the original elemenlt and must amplifier presenlt Onl each elemnelt, a set of properlyitself be steered for wide-anlgle scanninlg. The group of phased signlals may be genlerated at anly convenient fre-elements with RE phasing form a "steerable elemnelt"' quenlcy anld then heterody-ned to the desired frequency.xvhich is steered with the beam of the array. Since lower-frequency circuitry is simpler and more

In translmittinlg arrays which forml a single beaml, this stable than microwave comlponenlts, anl IF beam-steer-technique is applicable, but is limlited by- the power- ing systeml is appreciably simpler thanl a set of RFhandling capability of the RE phase-shifter. Inl receiv- phase-shifters.inlg arrays, a mlultiplicity of receiving beamls is usually Since a linear phase gradienlt across the aperture isformed by a beam-z-formnilg netwxork after the amlplifiers, to be generated, a tapped delay line driven by- a vani-The effects of displacing the receiving beaml from the alble frequenlcy oscillator suggests itself. The outputdirection in which the subarray is steered are shownl inl frequency7 at the taps on the line will vary with beamlFig. 13. WJhen the alrraly beaml- is a:t "A,"^ the gratinlg pOSitiOnl, since the beam- is steered by chanaginlg the fre-lobes fall inlto the nulls of the subarray patternl anld are quency inl the linle. To elimnilate the resultinlg variationsuppressed. W\henl the beam is displaced slightly froml inl the radiated frequency a dual mlixing schemle is used,the center of the subarraly pattern, the gratinlg lobe iml- as shownl in Fig. 14. This tapped dlelay linle produces amediately appears. At "B," the displacemlent froml the linear phase gradient at a fixed frequency, since phasecenter of the subarray pattern is a smlall fraction of the is preserved inl a mlixer and the frequency variation issubarray beamwidth, but the gratinlg lobe is suppressed eliminlated. There are a nlumber of possible variationsonly 10 db. The smallest possible subarray (2 X2) has of the system- of Fig. 14.been used in this calculation. WVith larger subarrays, Two such beam-steerinlgsystems are required for two-


FIXED f fo + fc VIII. BEAM-FORMING NETWORKSFREQUENCY D1 LA DEA LOSCILLATOR sZ . . The formation of a monopulse or stacked-beam con-

figuration of receiving beams requires that the ele-VARI 4SLE f menitary signals, after amiiplificationi anid conversion toOSCILLATOR C LX'i' L{i' L,;z IF, be divided and theni comiibinied with the proper

phase-shifts to fornm beamns offset from boresight. InfoL t L20 foL3# this manner, an IF beam-forming network can be used

Fig. 14-I F beam-steering system with duial mixing and fixed to form a set of beams which can be steered as a group.3ouitpuLt frequency. In a planar array, the rows are usually summed first

and then the row sums are combined as a column. If AIdimensional beam positioning. The steering signal for beams are formed in each row-combiniing network andthe m,nth element is derived by nmixing together the N beams are formed in the column-combiniing network,output of the mth tap of the horizontal-steerinig system then a set of MXN beams which are fixed with respectand the nth tap of the vertical-steering system. The to each other are formed. For conveniience, only a lin-

e r are c w the s o ear array is considered here.twouiputhfrequencia a which isthe sum oft A beam squinted at an angle 6 from boresight is cre-two input frequencies and a phase which iS the sum OfI tdb omn h uth tw ip tphss ated by forming the sumthe two input phases.The tolerances on the tap outputs are very tight. I, exp [2rjnd sin 6]. (15)

Each tap controls the phase of an entire row or column nof the array and its phase must be held to a few degreeseven in a very large array. The equations of Section V The simplest type of network uses a parallel RC com-are applicable if the tapped delay line is considered to bination to provide the phase-shift; that is the sumbe a linear array with a number of elements equal to ZL R1-1+icCj (16)the number of rows or columns in the array. These ntolerances are more easily met at lower frequencies, but s formed withthe delay line becomes longer and its size and weightincrease. R^-i = + cos (27rnd sinG0)The IF beam-steering system imposes a lower bound woC. = sin (2irnd sin 6)

on range resolution which may be important in someapplications.ii When a very short pulse is received from where wo is the IF used in the network. The appropriatea target not at boresight, the signal will enter the ampli- sign is obtained by inversion in a double-ended ampli-fiers on one side of the array before reaching those on fier. A part of a simplified form of an RC network isthe other side. The pulse will be delayed equally in shown in Fig. 15.each chaniiel and, at the output of the beam-forming This network provides the desired output when thenetwork, will have a ramp-like leading edge and trailing signal is a sine wave at the design frequency coo, but notedge of lei-ngth D sinl 6lc, where D is the aperture di- in the presence of an unpredictable Doppler shift or aameter, c is the speed of light, anid 0 is the anigle off bore- broad-band signal.sight. If the pulse-length is less thani this quanitity, The network corresponding to (16) can be separatedwhich is the tranisit time across the aperture, the pulse into two networks, a resistive network I [cos 27rndwill niever reach full amplitude. In milost arrays, the sin 0] and a reactive network j ZIn sin [27rnd sin 0].transit time is a small fraction of a miiicrosecond anid the Only the reactive network distorts the pattern. The pat-effect is not significanit. If very high ranige resolution terns due to these two nietworks considered separatelyis wanted, then beanm steering maust be done with time- are shown in Fig. 16. The cosine-amplitude taper pro-delays rather than phase-shifts in order to compensate duces beamiis at 0 andcl -0 with the same polarity, whilethe delay across the aperture. Ferrite phase-shifters the sine taper produces the same two beamas with oppo-will approximately resemble time-delays, and so a se- site polarity. Wheni the two networks produce the sameries-fed ferrite-phased array may be made to have range output, the two spurious beams at -0 cancel, while theresolution less than the transit time.34 two beams at 0 add.

IF beam-steering systems also produce a beam shift The Doppler shift of a sinle wave of frequency co pro-with a chanlge of radiated frequency. This effect must be duces a network output oftaken into account in setting the variable-frequency /-oscillator which controls the beamn position. I= Io + j E (( 0) xQn, (t17)

33 L. R. Dausinl, K. E. Niebuhr, anld N. J. Nilsson, "TIhe effectsof wide-band signals on radar antenna design, " 1959 IRE WNESCONCONVENTION RECORD, pt. 1, pp. 40--48. 135 am-forming networks of this type were originated and de-

34 C. M. Johnson, "Bandwidth of ferrite phase shifters for phased veloped by Sanders Assoc., Inc. Section VIII is based on some un-array and direction-finding use,' PROC. IRE, vJol. 47, P. 1665, published Sanders Assoc. memcoranda and on an ulnpublished BendixSeptember, 1959. report by J. C. Nolen.


+ The wavefornm which appears in the main beam is=IIi~- f(t) -jj2wof'(t), and that which appears in the spurious

+ beanm is j'/2wof'(t). The waveform-i after passage throughI2 3 the beamii-forminig nietwork thus has a distortioni which

SUMMING depeinds oni the pulse shape. This distortion is chieflv+ 3BUS importanit in trackinig systemiis, sin-ce it distorts the

leading edge of the pulse.+. : < These patterni distortionis can be reduced by com-14-

I pensating the capacitances with inductances, and the4I response of the network can be analyzed in the same

manner. A better solution is to form the real and imagi-BEAM nary parts of (15) in separate resistive networks and to

OUTPUT combine their outputs in a broad-band quadratureFig. 15-Simplified RC beam-forming network forming one phase-shifter, as in Fig. 17. The pattern distortions of

squinted beam. this network, which are essentially due to the quad-rature phase-shifter, can be analyzed by the same

+ a+ method. In this way, a beam-forming network whichwill handle a wide-bandwidth signal without pattern or

I9 X /


where a, is the taper coefficienit (applied after the non- NORMALIZATION LEVELlinear operation), I, is the nth elementary signal and Oo LARGERis the phase gradient for beam steering. If only a single TARGETsignal is present, and if noise is neglected, I1, = 1o exp (jnk)and F(I,) = F(Io) exp (jnq5) due to phase preservationin the receiver. The received pattern is then 40

F(I()) E a, exp (jnO) exp - (jn0o), (20) TRUE,& ~~~~~~~~ ~ ~ ~~~IMAGE OFl /SMALL ER

SMALLER\ l 1> F STARGETTARGET 20 -aj~ ~ TRGEwhich is exactly the linear-antenna pattern with ampli- TARGET

tude F(1o). If F(I) = 1 for all I (inifinite clipper), then a /normalized pattern is obtained for aily input-signalamplitude.

If two slgnals are present, then -48 -24 0 24 48In = II exp (jn0l) + I2 exp (jlt2) ELEVATION IN DEGREES PHASE SHIFT PER ELEMENT

,exp (jnj) [I a exp (jna) r Fig. 18-Compuited pattern of 61-elemenit linear array with clippilngIIlexp(1nAl)Ll + a exp (yzae) , at each receiver. No taper. Peak output with a single strong signalwotuld appear at "normalization level." Target voltage ratio is 0.6.

where IA is the larger signal, a =12/Il and a=42-+1. Inthis case, the signal no longer has equal amplitudeand linearly increasing phase across the aperture, but - _has amplitude An= [1+2acosna+a2J]12 and phase - 0 ___ _ ___On=n4b,+arc tanl [a sin na/l+a cos nca] at the nth ele- 10-l s __ment. The received pattern with infinite clipping is now ,

D-200__

an, exp (jO9) exp (-110). (21) E-2a-30

Coherenit addition will be obtainied only when 6,,=nO o oi-4zfor some 0. Since exp (JOn) is periodic with period 27r, it o -402:cain be expalnded in a Fourier series I< l\1\i\g n

-50+0O

exp (J9,) = exp (jn4:).)- C>(a) exp (jpn), (22) 5a-4--'~ 60

p--10~~~~~~~~~~~~~14anid the received pattern is 7015 3

0 -5 -10 -15 -20 -25 -30+0 { a,, ex 0ju 4+pcKvexp [Jno]}* INPUT RATIO- O (db)

P=--0o n Fig. 19-Angle harm-onic amiplitudes with two signals and noiseneglected. The larger target is at i, the true smialler target at61 + a, the first image at 01 -a, etc.The patterni thus consists of the original patterin with

"angle harmnonics" having phase gradients which are lo-cated uniformly about the larger signal. Each "angle the signials will have a ranidom distributioni of ampli-harmonic" is the linear pattern. Fig. 18 shows a com- tudes rather than equal amplitude before tapering. Theputed pattern of a linear array with clippinig. The true measured pattern of the array will have a random side-targets are at 0 and 24, while the peaks at

-24, +48, lobe level and will be below the normalization level byetc. are spurious.36 about the signal-to-noise ratio at the clippers.A plot of the "angle harmonic" amplitudes C,(a) as Analysis of more complex situations is difficult, but

functions of a is shown in Fig. 19. The weaker signal is experimental simulation is possible using distinct fre-suppressed about 6 db. The "image" at q,-a has ap- quencies into a clipper.37 This is formally equivalent toproximately the same amplitude as the true smaller the clipped array with multiple signals, with thetarget. "pattern" appearing as a frequency spectrum. The com-

If the signals are below the noise at the clipper, which puted results of Fig. 19 were verified. Signals belowis usually the case in a large array, then the resultant noise at the clippers were simulated with a broad-bandof signlal anld nloise will be nlormalized rather than the noise source and clipper followed by a nlarrow band-passsignlal itself. The signlal-to-nloise ratio inl each channlel filter before spectrum- mlealsuremlenlt. If two signals arewill be redulced by about 1 dlb. The signals will still add presenlt, both below nloise at the clipper, the syrstem- be-coherenltlyr, sinlce phase is preserved by the clipper, but comnes mlore nlearly linlear inl the senlse that the relative

361The existenlce of the "angle harmlonics'' was first poinlted out 37 This mlethod of simllUationl was sulggested by J. C. Nolen andby S. N. van Voorhis. The analysis given here iS dule to J. C. Nolen. carried out by R. Bensonl.


amplitudes of the spurious signals decrease. Withi three niques anid lead to better solutions of the inherentsignals present, the expected multiple harmonics occur. problems.When weak signals are present in a clipped array, the Oni the theoretical side, further work is needed on

array will be approximatelv liinear with a slight gain loss sy,niithesis of aperture distributions using unit elements.and small spurious responses. As the signials become Nonlinear receiving arravs are knowni to have interest-strong enough to capture the clippers, the weaker signials ing properties, and a general theory of gain aind resolu-will be suppressed by about 6 db anid large spurious re- tioin for themii would be of great interest. Further con-sponses will appear, leading to false target generationi sideratioin of the relationiships betweeni gaini, pattern,and angular ambiguity. The clipped array will eliminate receiving aperture and element coupling would be useful.an interfering signial inl the sidelobe region, but its ability The future of the array radar depends primarily onto see main-beam targets in the presence of inter- component development. The components used in anference in the sidelobes is somewhat poorer than that of array radar must meet all of the performance specifica-a conventional antenna with an unsaturated receiver. tions for conventional radar components, and in addi-

tion they must be matched over a band of frequenciesX. CONCLUSIONS anid must remain stable over long periods of time. A con-

Consideration of the radar requirements listed in siderable price reduction is also necessary if the largeSection I has led to the study of large steerable arrays array radar is to be economically feasible.with an amplifier for each element. These devices havethe desired properties, but require the use of hundreds XI. ACKNOWLEDGMENTor thousands of transmitters and receivers in parallel. The author wishes to thank his associates at theAttempts to circumvent the need for large nunmbers of Bendix Corporation, especially J. C. Nolen and J. H.amplifiers have in general been unsuccessful, although Best, and members of the engineering staff of Sanderssome of the techniques devised for this purpose are use- Associates, Inc., for much of the material presented inful in special situations. this paper. He also acknowledges his indebtedness toThe purpose of this paper has been to review the prini- D. D. King, S. J. Rabinowitz, and S. Falconer for their

cipal characteristics of such arrays and the major prob- useful suggestions, and to C. Mv. Tennant, M. A.lems encountered in their design. It is hoped that such a Abbott, and C. Mi. LaPorte for preparing the manuscriptreview may stimulate a wider interest in array tech- for publication.

Signal and Data-Process,ing Antennas*G. 0. YOUNGt, SENIOR MEMBER, IRE, AND A. KSIENSKIt, MEMBER, IRE

Summary-This paper treats the antenna as an information aperture distribution is uniform. When the image, or receiver, noiseprocessing device, and applies the concepts of modern information is zero, the useful output information content and rate are independ-theory to the design of antennas and to the optimization of their per- ent of the aperture distribution. An equation relating the signal andformance. The principal optimization criterion employed is maxi- noise spectra and the aperture distribution is derived which showsmization of information or data rate. the way in which the signal should be coded so as to maximize the

The general procedure is to treat the antenna as a spatial fre- information content. Processing is discussed generally, and aquency filter which is being optimized subject to a given set of con- specific nonlinear processing scheme is analyzed. The general con-trol inputs. Given these specifications, the information rate is maxi- clusion is that nonlinear processing degrades the useful informationmized with respect to the antenna system parameters subject to the rate when the SNR is low whereas it may improve the rate at highphysical constraints of the system. SNRs. Finally, a number of specific military and space applications of

It is shown that in a general antenna system where noise is intro- information processing antennas are considered.duced in both the object and image space, the optimum antenna

I . INTRODIUCTION* Received by the PGMIL, January 28, 1961. The research re- EvJaluation of Existing Data-Processing Systems

ported in this paper has been supported by the Electro)nics Res.Directorate of the AF Camubridge Res. Ctr.,ARDC, Bedford, Mass., ,{ VER the past few years the emphasis in antennaunder Contract No. AF19(604)-3508. Ii ) design has been shiftinlg from synthesizing pat-

t Aerospace Engrg. Div., Hughes Aircraft Co., Culver City, '+ yCalif., and Dept. of Elec. Engrg., UTniversity of Soulthern Californlia, terns to the design of efiMcient information proc-Los Angeles, Calif. essing devices. This emphasis has produced numerous

t Aerospace Engrg. Divr., Hughes Aircraft Co., Culver City, she s which climt exee the peforac ofcn

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Steerable Array Radars