MASSACHUSETTS INSTITUTE OF TECHNOLOGYLINCOLN LABORATORY

~ PHASED-ARRAY CALIBRATION BY ADAPTIVE NULLING

I1. M. A UMA NAF.G. W'ILLWERTII

G~roup 61

TECHNICAL REPORT 915

20 MAY 1991

Approved for public release; distribution is unlimited.

LEXINGTON MASSACHUSETTS

ABSTRACT

The limitations to ultra-low sidelobe performance are explored using a 32-element linear array. operating at L-band, containing transmit/receive (T/R) mod-ules with 12-bit attenuators and 12-bit phase shifters. With conventional far-fieldcalibrations, the average sidelobe level of the array was about -40 dB. In theory,considerably lower sidelobe performance is expected from such an array.

Initially, sidelobe performance was thought to be limited by inadequate cal-ibrations. An examination of individual array element patterns showed a mirror-symmetric ripple which could only be attributed to edge effects in a small array.Simulations indicated that more precise calibrations would not compensate for theseelement-pattern differences.

An adaptive calibration technique was developed which iteratively adjustedthe attenuator and phaser commands to create nulls in the antenna pattern in thedirection of the nulls of a theoretical antenna pattern. With adaptive calibrations,the average sidelobe level can be lowered to -60 dB. The technique can be usedfor interference suppression by implementing antenna patterns with deep nulls inspecified directions.

NTISi GRA&I

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TABLE OF CONTENTS

Abstract iiiList of Illustrations vii

1. INTRODUCTION

2. ANTENNA RANGE AND PHASED-ARRAY CHARACTERIS T CS 3

2.1 Antenna Test Range 32.2 Phased-Array Characteristics 32.3 Performance with Standard Calibrations 5

3. ADAPTIVE CALIBRATION TECHNIQUE 11

3.1 Theory 113.2 Mzasurement Selection 123.3 Ca'?:Tbration Procedure 13

4. PERFOR'MANCE WITH ADAPTIVE CALIBRATIONS 17

4.1 Sidelobe Suppression by Chebyshev Taper 174.2 Side!obe Suppression by Null Placement 17

5. SUMMARY 21

REtI ERENCES 23

v

LIST OF ILLUSTRATIONS

FigureNo. Page

1 Experimental phased array. 4

2 Antenna test range. 4

3 Antenna range geometry. 5

4 Typical array element patterns. 6

5 Typical attenuator characteristics. 7

6 Typical phaser characteristics. 7

7 Measured antenna pattern with standard calibrations. 8

8 Array sidelobe performance with standard calibrations. 8

9 Simulcted antenna pattern with standard calibrations. 9

10 Uncalibrated array pattern. 15

11 Array pattern with uniform illumination. 15

12 Comparison of insertion attenuation. 16

13 Comparison of insertion phase. 16

14 Excitation function for a 40-dB Chebyshev taper. 18

15 Array pattern with 40-dB Chebyshev taper. 18

16 Array pattern with 60-dB Chebyshev taper. 19

17 Array sidelobe performance with adaptive calibrations. 19

18 Adaptively calibrated antenna pattern with null. 20

vii

1. INTRODUCTION

One of the main advantages of a phased array is low sidelobe performance. Low sidelobesare beneficial for both clutter and interference suppression. However. aside from limitations due tomeasurement range and multipath effects, low sidelobe performance can be difficult to achieve formany reasons.

Quantization effects are often claimed to limit array sidelobe performance. The phased arraydescribed in this report contained 12-bit attenuators and phase shifters: quantization errors shouldbe insignificant.

It is desirable to build array components with sufficiently tight tolerances to make furtheralignment or calibrations unnecessary. In practice, amplitude and phase differences in the T/R

modules and transmission lines of the beamforming network are almost unavoidable. Array cali-brations are commonly used to compensate for these differences: however, the calibrations may notbe satisfactory if they are based on an inadequate array model.

Array element patterns are assumed to be uniform. Mutual coupling and edge effects maydistort array element patterns, thus compromising the array calibrations and excitation-functioncalculations. Standard array calibrations cannot compensate for element-pattern difference:.

Rather than attempting to minimize the various error sources, the phased-array calibraticntechnique described in this report concentrates on achieving the lowest pu__,.le sAdelobe perfor-mance under the given conditions.

2. ANTENNA RANGE AND PHASED-ARRAY CHARACTERISTICS

2.1 Antenna Test Range

Phased-array calibrations and antenna-pattern measurements were carried out using the lineararray shown in Figure 1 on a 100-ft. ground-reflection antenna range, shown in Figure 2. The rangegeometry is shobwn in Figure 3; knowledge of the range and array dimensions is essential to thealignment process.

The antenna range did not meet the conventional far-field criterion given by 2D 2 'A. "hisformula limits the maximum phase distortion at the face of the array to 22.5 degrees. For the testarray with a source at 100 ft.. the maximum phase distortion is 75 degrees. In either case, focusingthe arrav will be necessary. The alignment process described in this report autonratically includesarray focusing.

2.2 Phased-Array Characteristics

The experimental array, operating at L-band, measured 15 ft. by 2 ft. and contained 36identical waveguide-radiating elements. Two elements on either end of the array were terminatedto reduce edge effects. The remaining 32 elements were connected to Ti"R moducs.

Half-height. open-ended waveguide-radiating elements were choen. primariiy because they areinexpensive and have a broad. aspect-angle-insensitive radiat;on pattern. Typical elemen, patternsare shown in Figure 4. In the center of the array. the element pai.terns were nearly identical:however, at the ends of the array the element patterns exhibited a rniror-symnine-ric ripple thatwas attributed to edge diffraction.

Array align lent is usually performed with the array at broaAde. Each rray elemet isthen examined individually and the array insertion attenuation and phase -re adjusted 11i thebrodside re ..- :se of all eicments is the same. This can be achievei at ny speciflic angle: however.at any other aigle. comparison of the element patterns in Figu'e 4 suggests that the insert;onattenuation might be 2-3 dB in error. Thus, standard array calibrttios cannot compensate fordifferences in the element patterns.

Good sidelobe performance in a small array requires TjiR modules with very rrmcise a:ten-uation and phase control. In the past, arrav sidelobe perloirnance at L-band wams usualiy !inuitedby quantization effects in the T/i'R modules. Commonly avaiiable L-band attenuators 4snd phaseshifters are limited to 5-6 bits of control; however, each module in the test array had 12 bits ofamplitude and phase control. This was achieved by using voltage-controlled devices operating atar, intermediate freq )encv :T. Tv-pical characteristics are shown in Figures 5 and 6. A nominalquadratic approximat. i ade,,.uatel¢ vescribed the attenuator and -haser characteristics. There isa weak attenuator and phaser interaction; a change in attenuation will result in a significant changein phase, and vice versa. This interacticn is not easily accounted for 1., a closed-form expression:however, it is corrected by tL, iterative aligriment technique.

3

Figure 1. Experimenztal phased array.

Figure 2. Antenna test range.

4

• -7993 2

SOURCE

R= 100ft0 = 6 ind=4.3inN=32A=9.3 in

R

ARRAY'

N CENTER OF ROTAT."IN

Figure 3. Antenna range geometru.

2.3 Performance with Standard Calibrations

The standard array calibrations described in Section 2.2 were carried out with the arrayat broadside: all active elements were terminatcd and the characteristics of each elemet weredetermined. An example of an antenna pattern with such calibrations is given in Figure 7. Althoughthe measured average sidelobe level of -39 dB was considered quite good. with 12-bit quantizationthe sidelobe level should have been -45 dB.

One way of determining the limits of array sidelobe performance is to measure the averagesidelobe level as increasingly severe array tapers are commanded. Figure 8 shows that with standardcalibrations the array sidelobe performance was limited to about -40 dB.

A simulation was carried out using measured element patterns as shown in Figure -1. Tileactual element patterns included range multipath as well as smali array effects. Perfectly im-plemented excitation functions were assumed: starting with standard calibrations, the excitationfunctions were applied A. th numerical precision. A typical simulated antenna pattern is shown inFigure 9. The resultin, .rx" sidelobe performance in Figure 8 was only a few dB better than thearray performance m° .i.-. u- d on the antunna range, indicating that the standard calibrations wereas good as could be ,..-pected.

5

2

0-

uJo -2I.

IL -4

w>-6I-

.u -8 FAR-FIELD MEASUREMENTSELEMENTS 1.2.3,4FREOUENCY = !.3 GHz

-10 1 i I

-90 -60 -30 0 30 60 90

2

w

.J

(b)<[_>-6

"U FAR-FIELD MEASUREMENTS, ELEMENTS 14. 15. !6. !7

FREQUENCY = .3 GH-Z-10 *

-90 -60 .-30 30 60 90

2 p p .. p ' ." ..

w

S-2

-,JCL -4 (c)

>-6

"j FAR-FIELD MEASUREMrt.;Scr -8 -ELEMENTS 29. 30. 31. 32

FREQUENCY = 1.3 GHz-1 . I I I I

-90 -60 -30 0 30 60 90AZOAUTH (deg)

Figure 4. Typical army enment patterns.

6

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1 70993 80 10

40-d0 CHEBYSHEV -WITH STANDARD-10 -FREQUENCY= 1.3 GHz CALIBRATIONS -10

-20 -THEORY -0

-30 -10 -10

IL-3

-50 -0a

-60 -- 40

-70 -50

-60 J___ --60-90 -60 -30 0 30 60 90

AZIMUTH tdeg)

Figure 7. Measured antennia pattern with standard calibrations.

0 FAR-FIELD MEASUREMENTS

-j-00 SIMULATION -10

LU -40-20 LU

-50 TER -30 2

Lu u

> FREQUENCY= 1.3 GHZ>AZIMUTH =O0deg

20 30 40 50 60

COMMANDED CHEBYSHEV TAPER (dB)

Figure 8. Array sidelobe performance with standard calibrations,

0 1709930

40-dB CHEBYSHEV - WITH STANDARD-10 - FREQUENCY= 1.3 GHz CALIBRATIONS - 10

-20 - THEORY - 0a U

1 30- - -10

- -20

-.50 -30 .

-60 I -40

-70 I- -50

-801 . 1 11 --60-90 -60 -30 0 30 60 90

AZIMUTH (deg)

Figure 9. Stmulated antenna pattern with standard calibrations.

9

3. ADAPTIVE CALIBRATION TECHNIQUE

A technique for calibrating a phased array from the far-field pattern has been describedby Patton [2]. The process consists of calculating the far-field pattern of an array by Fouriertransformation of planar near-field measurements. The array element excitations are then computedby inverse Fourier transformation of the far-field pattern back to the aperture plane.

The array calibration technique described in this report is based on iteratively forming nullsin the antenna pattern [3]. The calibrations are considered adaptive in that the actual antennapattern is adjusted to match a theoretical model. When the specified nulls correspond to the nullsof an array with uniform illumination, the technique yields the insertion attenuation and phase ofthe array elements. By specifying other null directions, different array illumination functions canbe implemented.

3.1 Theory

The excitation function of a phased array can be calculated from an observed far-field patternby the direct matrix-inversion method [4]. The pattern of a linear N-ele-lent array in the direction9 is given by

N

P() = wnzn(O) (1)n=1

zn(O) = -- n expj-27r R mc.

where wn is the complex excitation coefficients and En(On) is the element patterns. All arrayelements are assumed identical and the range geometry is such that

El1(01) = E2 (02) = ... = En,(On) -(2)

By measuring the antenna pattern in N directions, a set of linear equations can be written andsolved for the N excitation coefficients. These equations can be expressed in matrix form as

W = Z-1 P (3)

where

11

W2

W= W

WN

Z1 (01) Z2 (01) ... Z(2

z1(02) Z2(02) ... ZN(03)... ... .. . ..°°

z1(ON) Z2(ON) "" ZN(ON)

P(01)

P(02 )

P(ON)

In theory, measurements of the antenna pattern in any N directions could be chosen todetermine the array-excitation function. In practice, the quality of results obtained from a single"back transformation" has not been satisfactory, as the assumption of identical element patternsis of limited validity and the range geometry is not sufficiently known. Thus, an iterative solution,with careful selection of the measurement directions, will be required.

3.2 Measurement Selection

Any measured antenna pattern will be affected by the specific range geometry. Thus, Figure 3should be used to carefully calculate the range geometry, specifically focusing corrections. Equation(1) also indicates that differences in the amplitude and phase of individual element patterns anderrors in the excitation function have similar effects on the antenna pattern. This interaction canbe minimized by making measurements in the directions of the pattern nulls.

For commonly used array tapers, the excitation function can be written in factored form.Consequently, the null locations of the far-field pattern are explicitly known [5]; the null locationswere probably used to specify the array sidelobe level. For an N-element arra3, there can be atmost N - 1 nulls in the antenna pattern. Ideally, if the main lobe is at Op and the nulls are at01, 02,..., eN-1, then the normalized pattern values are

12

P(OP) 1[ : = 0 (4)

P(ON-1) 0

and the matrix inversion in Equation (3) will return the theoretical excitation function WT.

As a result of the assumption made in Equation (2), the nulls in the antenna pattern areentirely determined by the array factor, and the above calculation will not be affected by the shapeof the element patterns.

Because the array-under-test and the measurement range are not perfect, the measured an-tenna response will not be zero at the null locations; that is,

P(Op) 1

P(Oi) (1

P(ON-) - EN-1

However, Equations (5) and (3) can be used to obtain an estimate WE of the applied excitationfunction. In the following calibration procedure, attenuation and phase commands will be adjusteduntil differences between the estimated and theoretical excitation function are at minimum. Whenthis is accomplished, the nulls of the measured and theoretical antenna patterns have been matched.

In general, the sidelobe peaks rather than the nulls of an antenna pattern are of interest. Byforcing the antenna pattern to have nulls in the proper directions, a well-formed antenna patternis virtually assured,

It should be noted that the process is mathemat 2ally identical to adaptive nulling by sam-ple watiAx inversion [6], in which the array receives a desired signal from a given direction andsuppresses vndesirpd signals in N - 1 carefully specified other directions.

3.3 Calibration Procedure

The first step mi ph-tsed array calibrations is to correct for element insertion attenuation andphase differences. Initially, au e:xcitptio f,-nction Wc is commanded without corrections to yielda uniform illumination WT

13

WC = Wr= (6)

The resulting antenna pattern of the uncalibrated test array is shown in Figure 10. The amplitudeand phase of the antenna pattern is measured at broadside and at the null locations correspondingto a uniform illumination. An estimate of the applied excitation function WE() is obtained fromEquation (3). This estimate is then used to update the commanded excitation function or the nextiteration as follows:

WC(i + 1) = WC(i) IWTk (7)

where k < 1 is a gain constant. The actual commands have to be expressed in counts based onnominal attenuator and phaser characteristics. The above process is repeated until

WE() WT (8)

and there is no further improvement in the null depths; Figure 11 shows the final antenna pattern.The array element insertion attenuation and phase are given by the reciprocal of WC. The inser-tion attenuation and phase as determined by standard calibrations and as measured by adaptivecalibrations are shown in Figures 12 and 13, respectively. Standard array calibrations are usuallycarried out with a source at broadside; Figure 3 shows that the element patterns are not identicalat all angles. Adaptive calibrations include element pattern differences and therefore yield slightlydifferent calibration results.

In the experiments, the iterative process was stopped when the null depths exceeded 60 dB.For k = 0.7 this was usually achieved after five or six iterations. As with any feedback algorithm,there is concern with convergence; for example, an instability may occur if the Z-matrix does notadequately model the array and range geometry. Another cause for instability may be a lack ofmonotonicity in the attenuator and phaser characteristics.

14

0UNIFORM ILLUMINATION - WITHOUTFREQUENCY= 1.3 GHz CALIBRATIONS

-10

-20

-4o0 - _... : i ,

-90 -60 -30 0 30 60 90AZIMUTH (dog)

Fipre 10. Uncalibrated array pattern.

t70993-l2

0 I

32 ELEMENTS - WITH ADAPTIVEFREQUENCY 1.3 GHz CALIBRATIONS

.10 . THEORY

Z-20 -

w

S-20

-90 -60 -30 0 30 60 90AZIMUTH (dg)

Iigure 11. Array pattern with uniform illumination.

15

1703-14

6 ,- -rFREt.. ' . '3GHzA. ' .do

4

1- 2

> -2

l -4 0 STANDARD CALIBRAT'ONScc 0 ADAPTIVE CALIBRATIONS 1-6 - I I

0 4 8 12 16 20 24 28 32

ELEMENT NUMBER

Figure 12. Comparison of insertion attenuation.

170993-13180 ' 1 i I

FREQUENCY= 1.3 GHz120 AZIMUTH O dog

~-60

-120 0 STANDARD CALIBRATION.4 -

0 ADAPTWE CAL AlONS

0 ., 8 12 16 20 24 28 32

ELEMENT NUMBER

Figure 13. Comparison of insertion phase.

16

4. PERFORMANCE WITH ADAPTIVE CALIBRATIONS

4.1 Sidelobe Suppression by Chebyshev Taper

The calibration technique is not limited to a uniform illumination. For example, Figure 14shows the adaptively determined excitation function required to implement a 40-dB Chebyshevtaper. A parabolic phase distortion necessary to phase focusing is clearly evident. Althoughthe differences between standard and adaptively determined excitation functions are usually quitesmall. the resulting array pattern in Figure 15 represents a considerable improvement over thecorresponding pattern with standard calibrations shown in Figure 7.

With adaptive calibrations, exceedingly low sidelobe performance can be demonstrated. Fig-ure 16 shows an antenna pattern with a 60-dB Chebyshev taper. At that level, the 40-dB dynamicrange of the attenuators becomes the limiting factor.

Figure 17 shows the sidelobe performance with adaptive calibrations. With adaptive calibra-tions, the array performance comes much closer to the theoretical array performance expected froman array with 12 bits of amplitude and phase control.

1.2 Sidelobe Suppression by Null Placement

In the previous section the antenna pattern nul directions were chosen to correspond to astandard Chebyshev taper; this resulted in predictable array performance. However, uniformly lowsidelobes may not be required in all applications. Rather than accepting the loss in efficiency andbroadening of the mainlobe, selective null placement in the direction of a known interference sourcemay be the preferred approach.

For example, Figure 18 shows an adaptively calibrated array pattern with a 30-dB ChebysLevtaper and an additional null at -30 degrees. Again, sidelobes in the direction of the interferencehave been suppressed by 60 dB.

17

0 1700-15180

150

- -10 ATrENUATIONm 120

z40-dB CHEBYSHEV

06

-2m FREQUENCY= a .3 GHz 90 Uj

o ADAPTIVE CAIRTIONS

-30 HASE30

-40 100 4 8 12 16 20 24 28 32

ELEMENT NUMBER

Figure 14. Excitation function for a 40-dB Chebyshev taper.

17033-16

0 1 11 120

40-dB CHEBYSHEV - WIH ADAPTIVE-10 FREQUENCY, 1.3 GHz CALIBRATIONS - 10

-20- .... THEORY 0m

a-3 -10 V

40 -4--0

a -50 - -300I-. w -40

-70 -

-90 -60 -30 0 30 60 90

AZMU"H (dog)

Figure 15. Army pattern udth 40-dB Chebpshev taper.

18

0o 20

-0-60-dB CHEBYSHEV -FAR FIELD-0 FREQUENCYw 1. 3 Hz MEASUREMENTS -10

-- 10-D AVERAGE

-40 SIDEL ODE LEVEL -2

-- 30 w

.-60 -- -- 40-

-70 -50-s

-90 -.60 -30 0 30 60 90

AZIMUTH (dog)

Figure 16. Array pattern with 60-dB Chebyshev taper,

M703-10-20 0

0 FAR-FIELD MEASUREMENTS

-j

MICALIBRATI ONS

W-40 -20

MI ADAPTIVE 5-W 12-BIT .. CALIBRATIONS -30

OUANTIZATIN~-W-4

FREQUENCY. 1.3 GHzAZIMUTH - 0 deg

-701 1-- - -5020 30 40 50 60

COMMANDED CHEDYSHEV TAPER (dB)

Figure 17. Army sid$-lobe performanwe with adaptive calibration.

19

0 I0g-920

3-B CHEBYSHEV -WITH ADAPTWVE-10 -FREOIJENCV 1.3GHZ CALIBRATIONS -10

-2- INTERFERENCE -0

-- 0 - A

~ -40

-60

-0 -60 -30 0 30 60 90AZIMUTH (dog)

Figure 18. Adaptively calibrated antenna pattern tvith null.

20

5. SUMMARY

An adaptive calibration technique for a phased array was described. This technique allowsthe insertion attenuation and phase of the array elements to be determined directly from themeasured far-field pattern. Although not specifically discussed in this report, the technique canreadily i&-rtify failed T/R modules; no built-in-test capability is required.

The technique is applicable not only to implementing standard array tapers, but also toimplementing antenna patterns with deep nulls in specified directions.

21

REFERENCES

1. H.M. Aumann and F.G. Willwerth, "Intermediate Frequency Transmit/Receive Modules forLow Sidelobe Phased Array Application," 1988 IEEE National Radar Conference Proceedings,Ann Arbor, Michigan.

2. W.T. Patton, "Phased Array AlignmenAt with Planar Near-Field Scanning, or DeterminingElement Excitation fron, Planar Near-Field Data," 1981 Antenna Applications SymposiumProceedings, Allerton Park, Illinois.

3. H.M. Aumann and F.G. Wi1lwerth, "F. G. (1989) Measurement of Phased Array Patterns byNear-Field Focusing," 1989 Antenna Measurement and Techniques Conference Proceedings,Monterey California.

4. M. Hoffinan, "The Utility of the Array Pattern Matrix for Linear Array Computations. IRETrans. Ant. and Propag. Vol. AP-9, 97-100 (1961).

5. R.S. Elliot, Antenna Theory and Design, Englewood C!iffs, New Jersey: Prentice-Hall (1981).Ch. 5.

6. R.A. Monzingo and T.W. Miller, Introduction to Adaptive Arrays, New York: Wiley (1980).

23

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Phased-Array Calibration by Adaptive Nulling

6. C - F19628-90-C-00026AUTHOR(S) P- 227

PE - 63250FHerbert M. AumannFrancis G. Willwerth

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Lincoln Laboratory, MIT

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13. ABSTRACT (Maximum 200 words)

The limitations to ultra-low sidelobe performance are explored using a 32-element linear array, operating at L-band, containingtransmit/receive (TmR) modules with 12-bit attenuators and 12-bit phase shifters. With conventional far-field calibrations, theaverage sidelohe level of the array was about -40 dB. In theory, considerably lower sidelobe performance is expected from such anarray.

Initially, sidelobe performance was thought to be limited by inadequate calibrations. An examination of individual array elementpatterns showed a mirror-symmetrii ripple which could only be attributed to edge effects in a small array. Simulations indicated thatmore precise calibrations would riot comipensate for these element-pattern differences.

An adaptive calibration technique was developed which iteratively adjusted the attenuator and phaser commands to create nullsin the antenna pattern in the direction of the nulls of a theoretical antenna pattern. With adaptive calibrations, the average sidelobelevel can be lower to -60 dB. The technique can be used for interference suppression by implementing antenna patterns with deepnulls in specified directions.

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