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5W& Bit c0?y AD-A171 894


Naval Research Laboratory

Washington, DC 20375-8000 NHL Report 8081 July 28, 1086


I 8981



Adaptive Digital Processing Investigation of
DFT Subbanding vs Transversal Filter Canceler


w. F. Gabriel

Electromagnetics Branch
Radar Division


DTIC



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11 TITLE (include Security Clmifictvon)

Adaptive Digital Processing Investigation of DFT Subbanding vs Transversal Filter Canceler


12 PERSONAL AuThOR(S)

Gabriel, William F .
134 TYPE OF REPORT

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1 14 DATE Of REPORT \Yt*r. Moon. Ocy) IIS RAGE COUNT

1986 July 2k 1 22


17 _ COSATi CODES _18 SUBJECT terms (Continue on revert* if necetttry tnd identify by block number)

_ FiEj) _ group SU B group Adaptive filters Digital processing

_ DFT Subbanding Tapped delay 1 lues

_____ ____ Digital fi lters Tiansvers.il filters

19 ABSTRACT (Continue on reverse if necetttry tnd identify by Clock number)

A performance cl .nparison investigation has been carried out for two multiple-weight, adaptive,
canceler techniques; the discrete Fourier transform (DFT) band partitioning approach and the
transversal filter canceler (TFC) approach A simple two-channel canceler model was utilized, with all-
digital processing, and four diflerent types of channel error were included. For differential delay errors
ana amphtude/phasc ripple errors, the TFC performance is generally far superior to the DFT subband
system, for the same number or degrees of freedom. For quadrature er.ors and sample/hold jitter
errors, there was essentially no difference in performance between the two, and performance did not
improve as the degrees of freedom were increased The superior performance of the TFC system is
attributed to more effective utilization of its adaptive degrees of freedom and the fact that it is
inherently suited to differential delay compensation The DFT canceler has no differential delay
compensation

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CONTENTS


INTRODUCTION. 1

SINGLE WEIGHT CANCELER. 4

DFT SUBBAND CANCELER. 5

TRANSVERSAL FILTER CANCELER. 13

FURTHER COMPARISON OF DFT VS TRANSVERSAL FILTERS. 14

CONCLUSIONS. 18

REFERENCES. 18



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ADAPTIVE DIC TAL PROCESSING INVESTIGATION OF
DFT SUBBANDING VS TRANSVERSAL FILTER CANCELER


INTRODUCTION

One of the most important and widely used ECCM techniques is the sidelobe canceler (SLC) [1-
3]. Although simple in concept and relatively economical in implementation, the SLC performance is
limited by a variety of factors, including:

• Multipath delay, often expressed in terms of delay-bandwidth product

• Aperture-frequency dispersion, often expressed in terms of aperture-bandwidth product

• Differing receiver channel responses, often referred to as channel mismatch errors

• Quadrature error in synchronous detectors

• Digital receiver channel errors such as analogue-to-digital (A/D) quantization, sample/hold
(S.'H) jitter, and dc offset

• Nonlinear effects, intermods, temperature drifts, etc.

To help overcome these limitations, particularly those related to bandwidth, multiple adaptive
weight systems have been proposed (over the years) that involve either a tapped delay line transversal
filter approach [4-7] or a band-partitioning filter approach such as the discrete Fourier transform (DFT)
[8-11]. Despite the fact that both of these multiple-weight adaptive filter approaches are well known,
the literature does not have much information that permits a direct performance comparison between
the two [11]. Therefore, this report attempts to address that need.

This investigation has been restricted to digital processing systems exclusively because of the com¬
puter simulation convenience and, also, because analogue filter systems contain additional errors that
would increase the modeling burden. Further, cancellation limitation effects have been investigated by
use of a simple two-channei canceler model derived from a typical multichannel receiver system of the
type shown in Fig. 1. This system includes radio-frequency (RF) antenna elements and circulators, RF
local oscillators (LO), intermediate frequency (IF) amplifiers, synchronous baseband detection with in-
phase and quadrature (I&Q) video signal output, baseband video amplifiers with low-pass filters,
snapshot sample and hold (S/H) circuits, and analogue to digital (A/D) converters. The output signals
consist of digital complex-data (I&Q) samples occurring at a sampling rate related to the Nyquist rate
[ 12 ].


Manuscript approved March 26. 1986.


1


MV I tjABRIl.L



Fig. 1 — Multichannel receiver system
feeding digital processor


Figure 2 represents the resultant two-channel canceler model, configured for a single adaptive
weight. In this model, we accommodate the insertion of five different types of adaptive processor
channel errors.

• Differential delay

• Filter passband ripple errors

• Quadrature error in synchronous detectors

• S/H jitter error

• A/D quantization and offset errors.

Many other types of errors exist in any practice! system implementation, but they were net considered
in this initial investigation because of time considerations.

A critical choice in any digital data processing system is the patliculat type of analogue lowpass
niter utilized to band-limit the input signal energy without introducing excessive linear or nonlinear dis¬
tortion. This is a critical operation because in the following stage when the filter’s output signal is sam¬
pled, any frequencies above one-half the sampling frequency will be folded or "aliased" and appear as
signal contributions [121. In practice, a computer-aided filter design program is often used to prodt. ee
between a sixth- end eleventh-order design incorporating active filter elements. For the purposes of
our simple cancellation performance behavior discussed herein, we assume an ideal Chebyshev f pole


2








NRL REPORT 8“>8I


Y.(ui) input


auxiliary

channel


SYNCHRONOUS!

DETECTOR


LOWPASS

FILTER


c


A/D S CONV.


V(ui)\^


adaptive

weight

T


Y(u>) output


main
I channel


differential j

delay error '

DELAY T



quadrature I

error |

SYNCHRONOUS

DETECTOR




amp./phase
ripple error

LOWPASS

FILTER



jitter

quantization
offset errors

S/H

A/D CONV.




'S(ul)


Fig. 2 — Two-channel canceler model with
a single adaptive weight


lowpass filter that has a cutoff frequency point selected to be 25% of the sampling frequency. The filter
function and its various parameters may be summarized.


T . L.-

a 13 u tv oamj/i 11 igy pvi IVU.

/j - -y is the sampling rate.

/ r — 0.25 / 5 is the lowpass filter "cutoff frequency.

cu “ 2a (///,) is the angular frequency, normalized to the sampling rate

H (wj is the filter function.

I -njizrr I * 1 +<1 “ shI I M coslr ' \t\ 11 <0

t < \ t 1 I J i

where e 2 is the lowpass ripple magnitude factor and M is the number of po<es or filter o r der.

Figure 3 shows a plot of the filter function | H (o>) | ? vs angular frequency in Z-plane degrees,
where Z - e lw , computed for « 2 « 0.156 and M - 6. Both f c and the sharp filter skirt roll-off charac¬
teristic were deliberately chosen to give us an "oversampled" system, avoid aliasing problems and yet
represent a lowpass characteristic that could bs implemented in practice. Recall that the Nyquist rale is
half of the sampling rate (12], which equals 180" in the Z-plane and bounds our frequency plot region.*


* Angular frequency <o is represented in terms of the complex Z plane equivalent, Z - e , “, because of the importance of the Z-
transform in analysis of discrete-time signals and systems 112). This representation of w involves a natural geometric angle (in
degrees*, the accommodation of "negative" frequencies, and a clear picture of the periodic/repetitious nature of discrete^ime
sampled system behavior vs w For convenience, the term "fiequency” is used in place of "angular frequency" throughoc. the
remainder of the report.


3


i









WF GABRIEL



-180 -120 -60 0 60
FREQUENCY (Z-ptww d«g)


120


180


Fig. 3 — Chjbyshev 6-pole lowpass filter with 0.25 cutoff point
and 0.156 ripple magnitude factor


The representation of filter passband ripple errors in amplitude and phase was chosen to follow
the error model described in Ref. 6. Let us define a ripple error function E (co ),


£ (co) — A ( w)e'* M for |u | ^



( 2 )


where A (co) " 1.0 + a cos (cm),
£ (co) •* b cos (cm),
a is peak amplitude error,
b is peak phase error, and
c is cycles of error ripple.


E (co) multiplies the filter function in the auxiliary channel to iryect the ripple errors: i.e., the main
channel is considered the reference here. We assume that / and Q lowpass filters in a given channel
are identical pairs, such that the error exists only between the two channels.


Quadrature phase error is introduced mainly by the quadrature hybrid circuit that sets up the 90°
phase difference for the / and Q synchronous video detectors. Figure 4 illustrates the effect, where "Q
Signal" denotes the actual posiiiuu of the Q axis. The quadrature error £ is the deviation of the Q axis
from the true orthogonal Y axis. The "/ Signal" axis is always assumed to be in perfect alignment with
the A' axis by definition. Therefore, a true signal vector of magnitude f3 and phase angle ¥ is con¬
verted by the receiver to another vector, «, which is in error both in amplitude and phase.


S/H jitter error refers to the uncertainty in the timing of the sampling window when the command
is given to sample a signal. For the purposes of this report, we assume that jitter error occurs indepen¬
dently in the / and Q signals of both channels, with uniform random distribution.


SINGLE WEIGHT CANCELER


To gain an initial appreciation for the sensitivity of cancellation degradation to the various types of
errors across the filter band, let us review the cancellation performance of the Fig. 2 circuit when single
weight W - -1. The canceler output, Y 0 (co), divided by the input, Y, (co), is

Y 0 (co)
y, (co)


5 (co) - V (co)
y,(co)


(3)


4


NRL REPORT 8981



where 5 («) and V (w) are the main channel and auxiliary-channel signals being subtracted. Note that
if no err rs are present in the two channels, then Eq. (3) results in perfect cancellation across the entire
Filter bandwidth.


Figure 5 illustrates the cancellation degradation for the different types of errors. In Fig. 5(a),
delay errors of r — 0.04, 0.2, and 1.0 sampling period have been inserted in the main channel, and the
response graphically demonstrates that perfect cancellation occurs only at band center; at all other fre¬
quencies across the band, the phase error is equal to <ar. In Fig. 5(b), amplitude ripple error of 0.1
peak and 2.5 cycles (see Eq. (2)) has been inserted in the auxiliary channel; we note the cyclic behavior
in accordance with the ripple, with a peak degradation of —20 dB. The same exact cyclic behavior is
produced for a phase ripple error of 0.1 radian (5.72°) peak. In Fig. 5(c), synchronous detector quadra¬
ture errors of 2.5° (rather typical rf such circuits) have been inserted in the main and auxiliary chan¬
nels (total error of 5°), and we see that cancellation degrades to about -21 dB across the filter
passband. Figure 5(d) illustrates the behavior for a jitter error with uniform random distribution
between peak values of ±2", added independently io / and Q signals ui both channel s. Jitter is s
delay-type of error and has similar behavior across the passband (compare with Fig. 5(a)).


Figure 6 is a universal plot of cancellation in dB vs amplitude or phase errors, based on Eq. (3).
It illustrates the considerable precision (small errors) required to achieve large cancellation dynamic
ranges.


DFT SUBBAND CANCELER


One option for extending the single-weight system of Fig. 2 to a multiple-weight canceler is to
partition the passband into a number of filter subbands and then provide one adaptive weight for each
filter subband (8-11]. A discrete Fourier transform (DFT) filter is a logical method for achieving this
band partitioning in a digital processor, and Fig. 7 shows typical subband filter responses for seven taps
input/output. The DFT filter requires a sequence of data samples at its inputs, in a manner equivalent


5








W I CiAIIKILL










NKL RI.I'OR 1 8V81



-45


-60


-120 -60 0 CO

FREQUENCY (2-(jl»ne d<XJ>

(c) Synchronous detector quadrature error of 5.0°


120


180


0


1


-15


\


co



-180 -120 -60 0 60 120 180
FREQUENCY (Z-plane deg)


(dl Rjndom jitter error of 2.0° peak. both l&Q

t ig 5 (Continued! — Cancellation degradation lor various errors,
two-channel cancelcr using single weight of value H — — I


7



















NRL RF.PORT 8981


to a tapped delay line, such that we arrive at the overall system schematic illustrated in Fig. 8. The
individual subband adaptive we.ghts W k are computed from the simple relationship for a pair of signals
[ 131 ,


K --


I («,) »'*•(*„)

n — 0


N

I

#i — 0


Vk GO


where (N + 1) is the total number of data samples,
S k (ai„) is the k th subband output, main, and
F. (w„) is the Ac th subband output, auxiliary.


V lc.j) input


auxiliary


I


mam

channel




channel



differential

DELAY t I



delay error


— 1

SYNCHRONOUS

quadrature

synchronous

DETECTOR

error

DETECTOR






L'Ji/VPASS

amp /phase

LOWPASS

FILTER

ripple error

FILTER

1


1

1 S,H

litim

S/H


A/D CONV


A/D CONV



V L) output


Fig 8 — Multiple weight tancclcr using DFT filter subbund
pjrlilionmg. with one adaptive weight per subbund


( 4 )


to

i


B


hr*




I




. v- C-. r. I . ff . «•. Pit. !*•. tv r.l, S. C. y. ev I*. 1*. if. au if. WOJ«rWs


■r.f-


r»


















W.F GABRIEL


The subband outputs derive from the DFT operations.


S (<,.„) - B'S (<u„)
V («,) - B'V ( w „)


(5)

(6)


where S (o> r ) and V (w rt ) are the main and auxiliary input vector signals to the DFT, and
S(a>„) and V («>„) are the main und auxiliary subband output veetot signals resulting from the DFT
operation. ( denotes a matrix transpose. The DFT transformation matrix B has individual row-column
matrix elements containing discrete phase-shifts of the form.


*«A


vF exp


2ir . A' + I
A 2



(7)


where m is the input tap index, k is the subband output index, and K is
subbands.


*..

*21

*31


*12 I
*22 I

*32 I


I *IX

i b 2K
I *U


the total number of taps or


B -


I - i

I I
I I


( 8 )


*A1 *A 2 *A A


Digital signals are used in the simulations, based on a "sweep" sequence of {N + I) frequencies stepped
from -ii to +77 in the Z-plane. The nth frequency may be expressed


ui


n




n


(2tt)

/V


/n\

V7/


where n — 0, 1, 2, 3, 4, .... A. Note the direct relationship to a> as defined for Eq. (1). Each unit-
amplitude signal is given a random start-phase, such that we have a digital equivalent of clipped wide¬
band noise input. This swept noise-like signal characteristic is evidenced in Fig. 5(c) because quadra¬
ture error cancellation degradation happens to be sensitive to the particular phases of the individual sig¬
nals. (The reader may verify this phase sensitivity with the help of Fig. 4.)


The canceler output Y„ (o>) is the summation of subband adapted outputs,

y ° {w) “ A i ^ %)+Wk ** (w) l • (10)

If no errors are present, then Eq. (4) results in all IF* — — 1 and perfect cancellation occurs across the
entire filter bandwidth.


Figure 9 illustrates the cancellation degradation for the various types of errors. In Fig. 9(a), a
delay error of r •* 1.0 sampling period has been inserted in the main channel, and the response is plot¬
ted for A — 1, 7, and 15 DFf subbands. We note that the performance improves as A increases, but
it is evident that DFT subband cancellation is seriously degraded by this type of error. In Fig. 9(b),
amplitude ripple error of 0.1 peak and 2.5 cycles has been inserted in the auxiliary channel for A — 1,
7, and 15. Here again, the degradation does improve as A increases, but the ripple error remains seri¬
ous. In Fig. 9(c), synchronous detector quadrature errors of 2.5° have been inserted in the main and
auxiliary channels (total of 5°) for A - 1, 7, and 15. Quadrature error degradation remains essentially
constant vs frequency and cannot be improved by increasing the number of subbands. Performance is
about 6 dB better than Fig. 5(c) only because the weights here are adaptive and compensate for half of
the quadrature error. Figure 9(d) illustrates the behavior for a jitter error with uniform random distri¬
bution between peak values of ±2°, added independently tu I and Q signals in both channels. Jitter
error degradation is similar to quadrature error in that it cannot be improved by increasing the number
of subbands. Note the similarity to Fig. 5(d).


10





FREQUENCY (Z-plan« deg)

(b> Ampiiiude ripple error of 0 1 peak end 2 5 cycles



ig 9 — Cancellation degradation Tor various errors, DFT subband
cancclcr. ploucd lor I, 7. and 15 subbands





POWER <dB) POWER <dB)


W.F. GABRIUL



-120 -60 0 60
FREQUENCY (Z-piane d*g)

(c) Synchronous detector quadrature error of 5 O’


120


180


-15


-30



-180 -120 -60 0 60 120 TOO

FREQUENCY (Z-plarva degl

(d) Random inter error of 2.0“ peak, both l&Q

Fig. 9 (Continued) — Cancellation degradation for various errors.

DFT subband canccler. plotted for i, 7. and IS subbands


12





























NRL KkPORT 8981


Note that for the purposes of this investigation, we deliberately nave not taken ar. inverse DFT at
the output, as would be necessary to obtain a final output pulse in the time domain. Rather, the inves¬
tigation of cancellation behavior has been restricted to the frequency domain.

TRANSVERSAL FILTER CANCELER

The second multiple-weight digital filter to be examined is a transversal filler canceler (TFC),
shown in Fig. 10. This circuit is identical in configuration to a one-step 'inear prediction filter and,
also, to the generic "sidelobe canceler" 114]. The optimal weights may be arrived at by any of the
current adaptive processing algorithms, with the choice determined primarily by system performance
requirements. For our investigation purposes, it was convenient to employ the familiar sidelobe can¬
celer algorithm based on a covariance matrix inverse [31,

W«R l A (11)

where W is the adaptive weights vector for the TFC, R is the signal covariance matrix, and A is the
equivalent "steering vector."



t ig 10 — Multiple weight canceler using transversal filter,
with one adaptive weight per delay line tap


13












W.F. GABRIEL


1


I S m ((•>,,) V * (&„)


<* +»>,-0


( 12 )


(13)


where S„, (<o„) is the main channel signal at the output summer. V (&>„) is the auxiliary signal vector
front the tapped delay line, 8 2 represents a small "pseudonoise" power term of-60 dB level to facilitate
matrix inversion, I is the identity matrix, and is the nth frequency defined in Eq. (9).


S„, (<*»„) - S (ci„)e

v k (<*.„) - v (w n )c


(14)


-,<.„U-I>


where m


K - \


is the midpoint index for the delay line, A is the delay line tap index, V (to„) is


the auxiliary channel signal input to the delay line, S (<u„) is the main channel signal that already incor¬
porates differential delay error « n r, if r ** 0. Note that F.q. (14) implies unit delay between taps; i.e.,
r- i.


The TFC output is the summation of S m («a) plus the weighted auxiliary delay line tap outputs.


Y„ (u,) - S„ (a>) + £ W k V k (ca)

k - i


(15)


If no errors are present, then all W k - 0 except for W m — -1, and perfect cancellation occurs across
the entire filter bandwidth for an odd number of taps.


Figure 11 illustrates the cancellation degradation for the various types of errors. In Fig. 11(a), a
delay error of t - 1 0 sampling period has been inserted in the main channel, and the response is plot¬
ted for a — i, 4, and 8 delay line taps. The improvement in performance as K increases is far supe¬
rior to the DFT filter (compare with Fig. 9(a)), despite the fact that an even number of taps represents
the worst case for a TFC with r ~ 1.0. Note that for an odd number of taps where A > 3, the TFC
gives perfect cancellation performance because there exists one tap for which the delay is precisely
equal to the main channel delay. We expand upon this discussion of delay errors in the next section by
comparing performance as a function of the delay-bandwidth product.

Figure 11(b) illustrates the degradation caused by an amplitude ripple error of 0.1 peak and 2.5
cycles, for K — 1 and 7 delay line taps. Here again, the improvement in performance as K increases is
far superior to the DFT filter (compare with Fig. 9(b)). What is demonstrated here is that the TFC
uses its degrees of freedom (DOF) far more effectively within the lowpass filter bandwidth than dees

tKo OCT an^rAonl*
iiiv a uppivsuvu.


In Fig. 11(c), synchronous detector quadrature errors of 2.5° have been inserted in both the main
and auxiliary channels (total of 5.0° error) for K = 7, Quadrature degradation remains essentially con¬
stant as K increases, except for a 6 dB ripple that appears across the passband (compare with Fig. 9(c)).
Figure 11 (d) illustrates the behavior for a jitter error with uniform random distribution between peak
values of ±2.0°, added independently to I&Q signals in both channels. Jit’er error degradation is simi¬
lar to quadrature error in that it cannot be improved by increasing the number of taps (compare with
Fig. 9(d)).

FURTHER COMPARISON OF DFT VS TRANSVERSAL FILTERS

In the previous sections, we have noted the following comparisons between a DFT filter subband
canceler and a transversal filter canceler (TFC) for these errors;

• Delay errors—TFC is far superior but requires additional performance criteria, such as odd vs
even number of taps for a given r.


14












W.F. GABRIEL



FREQUENCY (Z-plane dagl

(c) Synchronous detector quadrature erior of 5.0°



FREQUENCY (Z-plane deg)

(d) Random jitter error of 2.0° peak, both l&Q

Fig. 11 (Continued) — Cancellation degradation for various errors, transversal
filter ciiP.ccl^r, ploucti for ], 4. or 8 idns


• Amplitude/phase ripple errors—TFC is far superior because of more effective use of its adap¬
tive DOF.

• Quadrature error—Essentially no difference exists between DFT and TFC performance. This
error cannot be removed via adaptation but, rather, requires calibration and I&Q signal correction in
each channel.

• Jitter error—Essentially no difference exists between DFT and TFC performance. This error
cannot be removed via adaptation and requires high-quality S/H components to keep the error as small
as possible.

Of these, the delay error is examined in more detail in this section. We begin by demonstrating
the significance of the lowpass filter in achieving good adaptive performance. Figure 12 shows the can¬
cellation degradation resulting from a delay error of 0.5 sampling period, using K - 7 subbands or taps,






NRL REPORT 8981




(b) Including Chebyshev 6-pole lowpass niter

Tig 12 — Cancellation ucgiuuaiion Tor deiuy error of 0.5 sampling period,
both DFT niter and transversal niter, for K ” 7

when the lowpass filter is omitted or included. When omitted as in Fig. 12(a), there is little difference
between DFT and TFC performance for this case and, in fact, both perform poorly. The poor perfor¬
mance occurs because our "clipped wideband noise" input fills the entire frequency range with this tor
error. However, when our Chebyshev 6-pole lowpass filter of Fig. 2 is included as in Fig. 12(b), then
the performance of the TFC improves dramatically across the passband. The DFT improves somewhat,
but not nearly as much.

Perhaps the best further comparison criterion is to plot degradation performance vs delay-
bandwidth product Br, where B is defined as the channel bandwidth normalized to the sampling rate.
Such a plot is shown in Fig. 13 for an adaptive single weight, a DFT with K — 7 subbands, and a TFC
with K “ 7 taps. These plots are sensitive to the particular lowpass filter employed, and the data for
Fig. 13 were taken with the Chebyshev 6-pole lowpass filter of Fig. 2 incorporated. The curves are
derived from passband performance such as contained in Fig. 12(b) and, therefore, are approximate;


17







W.F. GABRIEL



Fig 13 — C.inccll.ilion degradation vs delay-bandwidth product, lor adaptive single
weight and multiple weight cancelers. using Chebyshev b-pnle lowpass lilier


the indicated range for each point is an upper value of 3 dB below the highest peak, and a lower value
equal to the next highest peak. Transversal filter performance is always cyclic vs Bt product, having a
sin (n Bt) behavior when K is odd and a cos (rr Bt) behavior when K is an even number of taps.
Performance improves as the value of K increases

Figure !3 serves to emphasize the considerable performance superiority of the TFC in comparison
with a DFT of the same K vaiue.

CONCLUSIONS

This investigation has shown that the TFC performance is generally far superior to the DFT sub¬
band system, for both differential delay errors and amplitude/phase passband ripple errors. This
marked superiority is attributed to more effective use of its adaptive DOF and the fact that the TFC is
inherently suited to differential delay compensation whereas the DFT is not. For quadrature errors and
S/H jitter errors, there was essentially no difference in performance between the two.

REFERENCES

1. P.W. Howells, "Explorations in Fixed and Adaptive Resolution at GE and SURC." IEEE Trans.,
AP-24, 575-584, Sept. 1976.

2. P.W. Howells, "Intermediate Frequency Side-Lobe Canceller," U.S Patent 3.202,990, Aug 1965.

3. S.P. Applebaum, "Adaptive Arrays," IEEE Trans. AP-24 585-598, Sept. 1976.

4. O.L. Frost 111, "An Algorithm for Linearly Constrained Adaptive Array Processing." Eroc. IEEE
60, 926-935, Aug. 1972.

5. L.E. Brennan, J.D. Mallet, and I.S. Reed, "Adaptive Arrays in Airborne MTI Rucar.” IEEE 7
AP-24, 607-615, Sept. 1976.


6.


R.A. Monzingo and T.W. Miller, Introduction to Adaptive Arrays (John Wiley and Sons, New York.

1980).








NRL REPORT 8981


7. D.R. Morgan anti A. Aridgidcs, "Adaptive Sidelobe Cancellation of Wideband Multipath Interfer¬
ence," IEEE Trans. AP-33, 908-917, Aug 1985.

8. B.L. Lewis and F.F. Kretschmer, Jr., NRL reports and communications of limited distribution
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9. B. Widrow and S.D. Stearns, Adaptive Signal Processing (Prentice-Fiall, Inc., Englewood Cliffs, NJ,
1985).

10. S.S. Natayan and A.M. Peterson, "Frequency Domain Least-Mean-Square Algorithm," Proc. IEEE
69, 124 126, Jan. 1981.

11. G.M. Dillard, 'Band Partitioning for Coherent Sidelobe Cancellation," Tech. Doc. 597, Naval
Ocean Systems Center, May 1983.

12. G.V. Oppenheirn and R.W, Schafer, Digital Signal Processing (Prentice Hall, Englewood Cliffs, N.l,
1975).

13. W.F. Gabriel, "Deriding Block for an Orthonormal-Laltice-Filter Adaptive Network," NRL Report
8409, July 1980

14. W.F. Gabriel, "Spectral Analysis and Adaptive Array Superresolution Techniques," Proc. IEEE 68,
654-066, June 1980


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