AD-AI15 105 OHIO STATE UNIV COLUMBUS ELECTROSCIENCE LAB F/6 9/5POWER INVERSION IN A TAPPED DELAY-LINE ARRAY.(U)MAR 75 1 LAO. R T COMPTON N00019-7-C-OIt4

UNCLASSIFIED ESL-3832-2 NL

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j ' -POWER INVERSION IN A TAPPED DELAY-LINE ARRAY

F Ich-Kien Lao and R.T. Compton, Jr.

ElectroScience LaboratoryDeportment of Electrical Engineering

Columbus, Ohio 43212

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QUARTERLY TECHNICAL REPORT 3832-2

March 1975

Contract N00019-74-C-0141

APpI~oVM. FOR PUBLIC RWEISDiSTMBgUT"~ uwn.,,,.

Department of the Navy'!"-'dIk [;

Naval Air Systems Command IEWashington, D.C. 20361 JUlwl 198 I

82 06 01 "074

NOTICES

When Government drawings, specifications, or other data areused for any purpose other than in connection with a definitelyrelated Government procurement operation, the United StatesGovernment thereby incurs no responsibility nor any obligationwhatsoever, and the fact that the Government may have formulated,furnished, or ir any way supplied the said Jawinqs, eciica-ic.s,or o-cne oata, i.s not to be regarded by :,icaior or . asin any rianner licensing the holder or any other person or corporation,or conveying any rights or permission to manufacture, use, or sellany patented invention that may in any way be related thereto.

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UNCLASSIFIED .__SEC UNW' C. ASSIFICATICN OF I -I.S PAGL '1, Der Ib F I -rr J,

- i !READ INSTR L:CT:ON\SREPORT DOCUMENTATION PAGE IBEFI- COMPLETINCGFKORM

* I. F EPORT NUMBER ,2 GOVT ACCESSION NO. 'S CATALGO NUMBER

4 TITLE Cand Subtitle) 5 TYPE OF REPORT & PERIOD COVERED

Quarterly Report

POWER INVERSION IN A TAPPED DELAY-LINE ARRAY December 1973-March 19746 PERFORMING ORG. REPORT NUMBER

_ _ _ ESL 3832-2* 7. AUTHOR(s) S. CONTRACT OR GRANT NUMBER(.)

Ich-Kien Lao N00019-74-C-0141R.T. Compton, Jr.

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT. TASK

The Ohio State University ElectroScience Lab AREA& WORK UNIT NIUMBERS

Department of Electrical EngineeringColumbus, Ohio 43212

II. C:NTR0,.ING OFFICE NAME ANC A .RESS 12. PLP Nr CATE

Department of the Navy March 1975, Naval Air Systems Command 13. NUMBER OF PAGES

Washington, D.C. 20361 1614 MONITORING AGENCY N AME 6 ADDRESSlf different from Corntrolhni Office) IS. SECURITY CLASS. (of this report)

UNCLASSIFIED,Sa DECLASSI FIC ATION,ODCWNGRADIN G

t SCHEDULE

S16. DISTRIBUTION STATEMENT (of this Report)

APPROVED FOR PUBLIC RELEA.DISTRIBUTION UNLIMITED

17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, If different from Report)

18. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse aide if necessary and idenlify by block number)&Arrays

Adaptive arrays1Interference protection

Null steering antennas

70. ABSTRACT (Continue on reverse side It necessary and identify by block number)

This report discusses recent studies on adaptive arrays for theNavy ITACS system. The report considers the power inversion behavior

of an adaptive array with tapped delay-line processing behind eachelement. Typical output signals from the array are shc.wn when apulsed desired signal is received in the presence of a continuous inter-

ference. The effect of feedback loop gain constants on array performanceis briefly discussed.

D RM 1473 EDITION OF I NOV65 IS OBSOLETE UNCLASSIFIED

SF.CURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

TABLE OF CONTENTS

PageI. INTRODUCTION

III. REVIEW OF BASIC THEORY

1III. RESULTS

6IV. CONCLUSIONS

8REFERENCES

14

Appendix

COMPUTER PROGRAM 15

-ii

ii

I. INTRODUCTION

In this report we discuss recent studies on adaptive arrays forthe Navy ITACS system. The goal of this research is to develop anadaptive antenna system compatible with the ITACS signaling waveform,so that a weak ITACS signal can be received in the presence of a stronginterfering signal .

The work here is a continuation of earlier research on powerinversion by Compton, Lee, and Schwegman [1,2,3,4]. This work differsfrom previous studies in that we consider here the power inversionbehavior of an array with tapped delay-line processing behind theelements, rather than quadrature hybrid processing. Tapped delay-line processing allow-s the adaptive array to operate over a muchwider bandwidth than does quadrature hybrid processing, and thus allowsthe array to protect a communication system from broadband interference.

In a power inversion array, no reference signal is provided, andthe array feedback uses a low-pass filter to prevent weight shutdown [1,3].This approach is especially attractive for time-division multiple accesssystems when the important interference threat is a continuous broadbandsignal. In this situation, the steady presence of the interferencesignal allows the array to null it effectively, while the pulsed natureof the desired signal allows one to depend on array time constants toprevent desired signal nulling.

Although our ultimate interest is in broadband interference, thisreport is a preliminary study in which we consider only CW interference.The more general case of broadband noise interference will be discussedin a later report.

In Section II we define the tapped delay-line array and thefeedback loop under s~tudy, and discuss the problem of determiningsuitable values for the feedback constants. In Section III, we applythese results to a two-element array and show some typical preliminaryresults.

II. REVIEW OF BASIC THEORY

Figure 1 indicates the basic configuration of a 2-elementadaptive array [1,3]. The feedback loop is based on a steepest-

* descent minimization of the mean-square error signal, c (t). Ingeneral, c(t) is obtained by subtracting the output of the array from

* a reference signal R(t). However, in a power inversion array, R(t)is zero so that c(t) is just the array output [1]. The incomingsignal from each element is split in a tapped delay-line into n com-ponents. Each of these components is multiplied by a weighting coef-ficient wi and then summed to yield the array output. The weights ina power inversion array are controlled by the system of equations [3]:

IA

LTAPPED WIY2() DELAY-LINE- t

FEEDBACK SR(t=O

________________ERROR REFERENCE

Fig. 1. Basic adaptive feedback system.

dw - K 2 ( t

where w is a column vector whose components are the array weights,

is

DELAY-LNE nt

an initial offset w vector, and Vw[Et)] denotes the gradientWof the mean-square error .,, (t) with respect to the weights. KI and K2are loop gain constants that must be chosen so the array nulls a high-power interfering signal sufficiently without nulling the weaker desired

signal. The dw/dt term in the equation provides the smoothing necessary

2

to limit the frequency response of the weights, and the proportionalterm w, results in steady-state weights that have the desired powerinversion behavior. [1,3] The feedback loop corresponding to Eq. (1)is shown in Fig. 2.

SIGNALS FROMOTHER CHANNELS

xi t 41)-+ 1;HANNEL5 s

WWW

KI S + K2

Fig. 2. The power inversion feedback loop.

r

& If the reference signal R(t) is 0, the error signal becomes:

2n(3) C(t) = -s(t) =- I wi xi(t)

i=l

Hence the mean square error is

2n 2n(-- iL j~l wi xi(t)x (t)

Differentiation of Eq. (4) yields:

I 52 3 x(txj(t)awi j I

so

31

I.

(6) Vw[c-t) ] : ¢w

where 0 is a 2n x 2n matrix defined by

x I t) xt) x1(t) X2(t) x 1(t) x 2n(t)

(7)

X -n- (t) x1(t) X2n (t X2n(t)

Substituting Eq. (6) into Eq. (4), we have

(8) K2 - + [I + 2K0]w = wo

The ith component of this equation is

dw. 2n U

(9) K2 -+ Wi + 2K L xit)xj(t) w =jdlj 1710

where wi is the ith component of vector wo . This is a coupled system ofdifferenyial equations.

We may obtain an understanding of the effects of K1 and K2 on thesolutions by considering a one-dimensional version of Eq. (9):w(10) dw-- I 2K 2 (t) 10

xIf XTl(t) is constant, the solution for w in Eq. (10) will have a finalvalue given by:

4

(11) Wfinal = W0

1 + 2K1 x1 (t)

and the time constant of the transient term will be

K(12) T

1 + 2K1 xl(t)

From Eqs. (11) and (12), one can see how the constants Kl and K2

are to be chosen. For a given signal power xl(t), Kl must be largeenough so that Wfinal is sufficiently different from wlO to allowadequate interference nulling. After KI is selected, K2 may be chosento give a desirable array response time.

The design problem is complicated, however, by the fact that the

optimum choice for K1 depends on the signal power x2(t), since it is

really the product Klxl(t) that determines the loop gain. (Normally22Klx2(t) >> 1.) One must select a value for K1 giving adequate inter-

ference nulling for the weakest interference signal for which protectionis needed. Then for larger interference, the protection will be greater.However, the array will perform satisfactorily only up to the point wherethe time constant of the loops becomes too short. When the array timeresponse is too fast, other problems may occur; for example, the arrayweights may affect the desired signal modulation.

Finding suitable compromise values for K1 and K2 would not bedifficult for the one-dimensional weight equation in Eq. (10). However,the full array is described by the set of 2n coupled equations in Eq. (9),in which the coefficients xi(t)xi(t) are time varying. For this reason,the most practical method of choosing K1 and K2 in a computer simulationhas been to use a trial-and-error approach, taking into account theeffects described above.

In the next section, we examine the performance of a two-elementpower inversion array with tapped delay-lines.

5&' '

III. RESULTS

In this section we show some typical response curves for a two-element adaptive array with tapped delay-lines when a high power inter-ference signal and a pulsed desired signal are incident. The array isshown in Fig. 3. Each element is followed by a two-section tapped

DESIRED SIGNALIei8d INTERFERENCE

SIGNAL

y2 (t), y,(t

x5 (1) X2 (t)

xs(t) x 3 lt)

Fig. 3. Two-element array with tapped delay-lines.

delay-lihe* with taps spaced one-quarter wavelength at the desiredsignal carrier frequency. The desired and the interference signalsare assumed incident on the array from angles Od and ei , respectively,as shown in Fig. 3. The two elements are spaced a half wavelengthapart at the desired signal frequency (L=Ad/2). The interface isassumed to be on a slightly different frequency than the desiredsignal.

The element signals are given by

(13) yl(t) = A(t) cos(wit) + B cos(w 2t)

*The number of delays needed behind each element depends on the band-

width of the signals. A subsequent report will discuss this subject,and will explain why 2 delays are appropriate with the ITACS waveform.

6

and

(14) Y2 (t) = A(t) cos(wlt-Yd) + B cos(W2t -Yi)

where A(t) is the pulse envelope of the desired signal, B is theamplitude of the interference signal,

(15) d L sin d =T sin ed

and

(16) sin e . = y - sin ei

since-L = d/2 We assume B >> A(t).

The outputs of the tapped delay-lines are given by

(17) xl(t) = A(t)cos[wt] + B cos[w2 t]

(18) x2 (t) = A(t-TI)cos[l (t-T1 )] + B cos[w 2 (t-T1)]

(19) x3 (t) = A(t-2T1 )cos[wl(t-2Tl)] + B cos[w 2 (t-tTl)]

(20) x4 (t) = A(t) cos[wlt-yd] + B cos[ 2t-'Yi

(21) x5 (t) = A(t-T 1)cos[wl(t-Tl )-yd] + B cos[w2 (t-T 1 )-Yi]

(22) x6 (t) = A(t-2Tl)cos[wl(t-2Tl)-yd] + B cos[ 2 (t-2Tl)--yi].

The offset weight vector is chosen to be

0

(23) wo =

~0

This choice makes the quiescent pattern of the array omnidirectional.

7

A computer program has been written to simulate the time behavioror tne array shown in Fig. 3 with feedback loops as shown in Fig. 2.The array weights are controlled by an iterative routine that is asampled data equivalent of Eq. (1). The program is shown in theAppendix.

Figures 4 and 5 show a typical output from the array as the weightsadapt. In Fig. 4, the high power interference signal is turned on att=O, and the array weights change with time to suppress this signal.Figure 5 is a continuation of the run shown in Fig. 4 with the verticalscale amplified, and the desired sional pulse cccur jmri:c the tir.eshoy.%n in Fiq. 5. It may be seer hcl, tne rteeer e %_: , Qe

(in Fig. 4), and remains suppressed t;, en tr-e ces re Ei,, a I seoccurs (in Fig. 5). The desired signal power at tie array output ishigher than the interference power, even though the interference is40 dB higher than the desired signal at the array input. The feed-back loop gain constants K1 and K2 used in Figs. 4 and 5, which havebeen chosen by trial-and-error to produce a suitable response, areK1 = .5, K2 = 1.25 x 10

-4 . (KI/K 2 = 4 x 103). The effect of reducing

K1 may be seen by compari~ng Figs. 4 and 5 with Figs. 6 and 7, whereK1 = .05, K2 = 1.25 x lO

- , and with Figs. 8 and 9, where K1 = .005 andK2 = 1.25 x 10-6. (In all three sets of curves, K1/K2 = 4 x 1O3, so thearray time constant is the same in each case.) In Fiqs. 8 and 9, K1 istoo small for satisfactory interference rejection; the residual inter-ference present at the array output beats with the desired signal pulseto produce an amplitude modulation.

The effect of changing K2 without changing Kl may be seen bycomparing Figs. 4 and 5 with Figs. 10 and 11 and with Figs. 12 and 13.In all cases Kl = .5 In Figs. 4-5, K2 = 1.25 x 10

-4 , in Figs. 10and 11, K2 = 5 x 1O

- 4 , and in Figs. 12 and 13, K2 =.5 x 10- . The

larger K2, the longer the transient during which the interference isbeing nulled out, as predicted by Eq. (12).

IV. CONCLUSIONS

This is a preliminary report on power inversion in a widebandadaptive array using delay-line processing. The power inversionconcept in a tapped-delay line array has been discussed and a computerprogram written to simulate array behavior. Some typical results forCW interference and pulsed desired signal have been shown, and theinfluence of the feedback loop constants on the performance have beenillustrated. A subsequent report will discuss the power inversioncharacteristics of such an array in more detail and will show systemperformance with wideband interference signals.

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REFERENCES

I. Compton, R.T., Jr., "Adaptive Arrays - On Power Equalization withProportional Control," Report 3234-1, December 1971, Electro-Science Laboratory, Department of Electrical Engineering, TheOhio State University; prepared under Contract N00019-71-C-0219for Naval Air Systems Command.

2. Lee, D.W. and R.T. Compton, Jr., "The Transient Response of aPower Equalization Array with Coherent CW Signals," Report 3234-2,T1arch 1972, ElectroScience Laboratory, Department of ElectricalEngineering, The Ojiio State Universitv; pravared under ContractN0019-71-C-02.1 for N'aval Air Systems Uco);.and.

3. Schwegman, C.W. and R.T. Compton, Jr., "Power Inversion in aTwo-Element Adaptive Array," Report 3433-3, December 1972,

.ElectroScience Laboratory, Department of Electrical Engineering,The Ohio State University; prepared under Contract N00019-72-C-0184 for Naval Air Systems Command.

4. Schwegman, C.W., "Adaptive Arrays - Interference Suppression ofMultiple Interfering Signals," Report 3576-1, December 1973,ElectroScience Laboratory, Department of Electrical Engineering,The Ohio State University; prepared under Contract N00019-73-C-0195 for Naval Air Systems Command.

14

APPENDIXCOMPUTER PROGRAM

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39 17 OrE=IwuP]*FkEl*l40 Ii(ONET.GT.7mfOPI) (C 1O 11141 60 70 10142 111 OME7:0MI-76OPI43 IFCOMET.L.T.T60PI) GO TO IlI44 lei Y(I):Dt.SIG4ICa.*SIN(OMOIT45 Y(4) :IJESIGDC+10.sSljd( uMEh:-BETA)46 S Ul:@.47 DO03 K:1,646 SUtI:W(X).Y(K,,SUI49 3 CONTINUE50 IF(J.LE.60I) G0 70 5iZ251 IF(.uT.135od) 1.0 T, 50352 (L0 T0 54353 502 S UKA(J) :SUM

54 s Ti7,MEW) =ToFRED

55 G)0TO 54

5 0 r 13i

57 S Ulij A =51U

V .. ... _

c5 Y():Y()

67 1 (5):Y(4)68 2 C ONI1 tWUE7t CALL PLSUA(SU1,Ii MEJ

71 CALL LAIT

73 C7,4 S U, ki[; J 7" f. i P L;SU L#Sfl, ;

76 CALL PLOTS (ILUFL,.,.3)77 CALL PLO] (J.,5.5,-3)78 CALL A.IS ( . . . .,.,i.,3 . 5,i.,)79 CkLL AXIS (X.,-4. ,3 .Jf3 S..,-'..- L,, *| ,

CA i L, Y/ ,

f;; 4 X n

8, CALL PLI ,7 7 CO:,T1 NUE

98 CALL PLOT 5.,-5.5,99)89 PETJkA

91 C92 SUtsROUINTE PLSU(SUM, T)93 D) ,;E,-Sl N l(U..I ),rJM'(6VI),IdUF( 101b)

94 CALL PLOTS (IbUF,Iv,,5)

.95 CALL PLOT (I .,5.5,-3)

. 6 CALL AXIS , 5...,3 .5,)oE)

97 CALL AXIS ,98 X:()/sz.c99 y :S UMj( ) /. 5Izz CALL PLOT (X.Y,3)Ib1 DO 68 , SZtlI 22 A,:T(i)/3e.i 5

1 ,,3 Y :S JM(iS) / .5104 CALL PLOT (AY,?),,5 8B C ON IIN UElob CALL PLOT (5.,-5.5,;9)IZ7 ETUkh108 itwD

LOG

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16