APS-2 1-6
ADAPTIVE NGLLING IN YCNOPULSE K'ITTENNAS
Randy L. Haupt
E l e c t r o m a g n e t i cS c i e n c e sD i v i s i o n
Rome Air DevelopmentCenter
Hanscom AFB, MA 01731
Introduction
I n a ni n t e r f e r e n c ee n v i r o n m e n t ,
a monopulse r a d a r mustmaini t s d e t e c t i o na b i l i t y .
Thus, a n
t a i n i t s t r a c k i n ga sw e l la s
a d a p t i v ea n t e n n a must be c a p a b l e of p l a c i n g n u l l s i n b o t h t h e
sum
i s s e r i o u s l y dea n dd i f f e r e n c ep a t t e r n s . [ l lT r a c k i n gp e r f o r m a n c e
sum channel.
graded when t h e i n t e r f e r e n c e i s c a n c e l l e d i n o n l y t h e
This p a p e rd e s c r i b e s a f u l l ya d a p t i v ep h a s e - o n l yg r a d i e n ts e a r c h
algorithmthatsimultaneouslyplacesnullsinthe
sum and d i f f e r e n c ep a t t e r n s of a low sidelobemonopulseantenna.Experiment a l r e s u l t s a r e shown t o v e r i f y t h e t h e o r y .
GradientSearchAlgorithm
The g r a d i e n t s e a r c h a l g o r i t h m a s s u m e s t h a t t h e p h a s e s h i f t s
This a s s u m p t i o np r e v e n t st h ea d a p t e dp h a s e
a r er e l a t i v e l ys m a l l .
settingsfromsignificantlydistortingthefarfieldantennapatt e r n .I np a r t i c u l a r ,t h e
low s i d e l o b es p e c i f i c a t i o n s mustbekept
w i t h i na na c c e p t a b l et o l e r a n c e .S m a l lp h a s es h i f t sa l s op r e v e n t
c a n c e l l a t i o n of t h e main beam s i g n a l .
Hence, a b u i l t - i n main beam
c o n s t r a i n te x i s t si nt h ea l g o r i t h m .
S i n c e t h e main b e a m s i g n a l i s k e p t f a i r l y c o n s t a n t , t h e s i d e l o b e i n t e r f e r e n c e may be reduced by m i n i m i z i n g t h e t o t a l o u t p u t
i s t h eg r a d i e n ts e a r c h
powerof
a n N elementarray.Equation(1)
algorithm
N
E
w
i = new phase s h i f t e r s e t t i n g f o r e l e m e n t
where W
k'OLDi = o l d p h a s e s h i f t e r s e t t i n
LI = g r a d i e n t s t e p s i z e = APH /TP
for
h:
TP = (E APWRi2)1/2
i=1
APH = p h a s e s e t t i n g s t e p s i z e
Ami = Change i n o u t p u t powerdue t o a d d i n g
i
tophaseshifter
i
k
I nt h i se q u a t i o n ,
e n tv e c t o rf o re l e m e n t
CH20-13-8~84:0000-0819501.00C
APH
APWRiIAPH i s t h e componentof
t h eg r a d i i. A f t e ri n c r e m e n t i n gt h ep h a s es h i f t e ra t
1984 IEEE
819
element i by a constant step size (APH), the
change in output power
is measured (Ami), the approximation formed(AFWRi/APH), and the
phase shifter returned to its original state. This process of
finding the gradient component is repeated for N elements. When
adaptation occurs only in the sum channel the gradient
is formed
from APWRi given by
APWRi
=
NEWSUMi
-
OLDSUMi
(2)
where NFNSUMi= sum channel output
phase shifter i by
OLDSUMi = sum channel output
phase shifter i by
power after incrementing
APH
power before incrementing
APH
A modification to this equation must made
be to incorporatethe
difference channel. The modified equation takes the form of
APWRi = [(NEWSUMi
X
NEWDIFi)
-
1 /2
(OLDSUMi x OLDDIFi)]
(3)
where NEWDlFi= difference channel output power after incrementing phase shifter by
i APH
OLDDIFi = difference channel output power before incrementing phase shifter by
i APH
Adaptive performance is judged by
NEWPM
<
(4)
OLDPM
When Eq ( 4 ) is not true, APH is decremented and the adaptive pro= 0.
&Ithe other hand,
if Eq ( 4 ) is true,
cess repeated until APH
APH stays the same and the adaptive process repeated.
When the adaptive process is performed
in the sum channel, then
NEWPBW
OLDPOW
and
= s1
(5)
= SO
In the case of nulling
in both channels, then
NEWPOW = S1
+
Dland
OLDPOW = S O
+ DO
to
where S1 = sum output power due WNEW
Dl = difference output power due
to WNEW
SO = sum output power due to WOLD
D O = difference power due to WOLD
Experimental
Results
The algorithm was experimentally verified using
an 80 element low sidelobe linear array with
8 bit phase shifters. Fig-
820
ures l a and l b show the antenna'squiescent far fieldsun aud
L' jammer was placed at an
difference patterns respectively.A C
angle of 23". Q. (11, ( 2 ) , ( 4 ) ) and (5) were used in the adaptive algorithm to place
a n u l l in the sum far field pattern (Figure 2a).
Note that a correspondingnull was not placed in the
difference pattern (Figure2b). In order t o simultaneously cancel
the jammer in both channels, Eq ( l ) , (3), ( 4 ) , and ( 6 ) are used in
the algorithm. The results from these modifications are shown in
Figures 3a and3b.
References
1.
Haupt, R.L. "Simultaneous Nulling in the Sum and Difference
Patterns of a Monopulse Antenna." RUC-TR-82-274,
Oct 1982.
0
10
20
30
0
40
Figure la.
Pattern
Qiescent Sum
10
20
30
40
A W E
AHOLEO
Figure l b . Qiescent Difference Pattern
82 1
0
10
eo
30
40
ANOLE'
MBLE
Figure 2a. Sum Pattern
after Adapting in theSum
Channel
Figure 2b. Difference Pattern
after Adapting in the Sum
Channel
1
0
IO
20
30
0
40
K)
20
30
40
ANOLE
ANGLEo
Figure 3a. Sum Pattern
Figure 3b.
after
Simultaneous
Adaptive
after
Simultaneous
Adaptive
Nulling
Nulling
822
Difference Pattern