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