Blind Beamforming for Cyclostationary Signals
Array Processing
Project Preeti Nagvanshi
Aditya Jagannatham
Conventional Beamforming Based on DOA estimation
Intensive Computation, Calibration Based on known training signal
Synchronization, Sacrifice of bandwidth
Blind Beamforming No reference signal required No advance knowledge of the correlation properties No Calibration is necessary Selectivity is achieved using knowledge of cycle
frequency
Cyclostationary Statistics
b2(t) = 1 (BPSK), s2(t) is periodic Spectral Lines at = (±2fc ± mf b)
b(K) is random, s(t) does not contain first order periodicities
2 2 2( ) ( ) ( )k
s t b k g t kT
2( ) ( )
( ) ( ) ( )
cj f t
k
z t s t e
s t b k g t kT
Data Model:1
( ) ( ) ( ) ( ) ( )K
k kk
n s n n n
x d i v
sk(n), k= 1,…….,K K narrowband signals from DOA k
i(n) Interferers, v(n) white noise x(n) is Mx1 complex vector, M = array size
ˆ ( ) ( )Hk ks n nw x
Data Model:
Cyclic Correlation:
- time average over infinite observation period no is some time shift, is the cycle frequency
[.]
Cyclic Conjugate Correlation:
* 2
2*
( , ) if ( ) ( )ˆ( , ) if ( ) ( )
j nxx o o
xu j nxx o o
n u n x n n eR
n u n x n n e
])()([),( 2* nj
ooss ennsnsn
])()([),( 2
*nj
oossennsnsn
Cyclic Adaptive Beamforming(CAB):2 2
ˆˆ, ,
ˆmax | ( , ) | max | | : 1H H Hsv o xun
w c w cw R c w w c c
( ) : as CAB N w d
wCAB is a consistent estimate of d()
CAB ss CAB
CAB I CAB
SINR = H H
H
rw d dw
w R w
0, , {1, , }, Hk l k l K k l d d
Multiple desired signals (same )...
{1, , }kCAB k k K w d
Constrained Cyclic Adaptive Beamforming(C-CAB):
True DOA of the desired signal is unknown, wCAB d() C-CAB MPDR with d() replaced by wCAB
1ˆCCAB xx CAB
w R w
Robust Cyclic Adaptive Beamforming(R-CAB):
2 2| | | |max subject to , 1
H HH
H HI
w
w d w dw d
w R w w w
1( )I w R I d
Fast Adaptive Implementation:
11 12 1M
21 22 2M
M1 M2 MM
ˆ ˆ ˆ
ˆ ˆ ˆR̂ =
ˆ ˆ ˆ
xu
11 1
ˆ ˆTM M
CAB i Mii i
w
Rxu(N) is updated every sample
Use matrix inversion lemma to compute the inverse
Complexity wCAB(N) is O(M), wCCAB(N) is O(M2) compared to O(M3)
1
1( ) ( ) ( )
NH
xui
N n nN
R x u
Simulation:
2 BPSK signals 100% cosine rolloff Data rate - 5Kbps Carrier - 5MHz Carrier offset -
0.00314 s =40º, I =120º = 0 M = 4 (array size)
Experiment1-Carrier Recovery
Simulation (contd.):Experiment2-Moving source DOA estimation
Sampling - 150K samples/s
s =40º - 130º SNR = 8 dB SNRI = 4 dB M = 16 (array size) Updated every 0.1s Uses 60 symbols(300
Samp) Interferer at 30º
Simulation (contd.):Experiment2-Moving source DOA estimation (contd.)
Simulation (contd.):Experiment3-Multipath signals
s1 =30º, s2 =40º, I
=120º
SNR1 = 15 dB SNR2 = 12 dB SNRI = 1 dB M = 10 (array size)
Simulation (contd.):Experiment4-Multiple signals
s1 =130º, s2 =60º, I
=10º
SNR1 = 15 dB SNR2 = 9 dB SNRI = 1 dB M = 15 (array size)
Conclusions…
References…
“Blind Adaptive Beamforming for Cyclostationary Signals”- Trans. SP, 1996
“Statistical spectral analysis – A non probabilistic theory”- William A. Gardner
Achieved blind beamforming exploiting the cyclostationarity property of the communication signal
Using structure of the signals better signal processing techniques can be developed