1. Blind Beamforming for Cyclostationary Signals
Array Processing Project
Preeti Nagvanshi
Aditya Jagannatham

2. 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

3. Cyclostationary Statistics
b(K) is random, s(t) does not contain first order periodicities
b2(t) = 1 (BPSK), s2(t) is periodic
Spectral Lines at  = (±2fc ± mf b)

4. Data Model: Data Model:
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

5. Cyclic Conjugate Correlation:
Cyclic Correlation:
- time average over infinite observation period
no is some time shift,  is the cycle frequency
Cyclic Conjugate Correlation:

6. Cyclic Adaptive Beamforming(CAB):
wCAB is a consistent estimate of d()
Multiple desired signals (same )...

7. Constrained Cyclic Adaptive Beamforming(C-CAB):
True DOA of the desired signal is unknown, wCAB  d()
C-CAB  MPDR with d() replaced by wCAB
Robust Cyclic Adaptive Beamforming(R-CAB):

8. Fast Adaptive Implementation:
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)

9. Simulation: 2 BPSK signals 100% cosine rolloff Data rate - 5Kbps
Experiment1-Carrier Recovery
2 BPSK signals
100% cosine rolloff
Data rate - 5Kbps
Carrier - 5MHz
Carrier offset
s =40º, I =120º
 = 0
M = 4 (array size)

10. Simulation (contd.): Sampling - 150K samples/s s =40º - 130º
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

11. Simulation (contd.):
Experiment2-Moving source DOA estimation (contd.)

12. Simulation (contd.): s1 =30º, s2 =40º, I =120º SNR1 = 15 dB
Experiment3-Multipath signals
s1 =30º, s2 =40º, I =120º
SNR1 = 15 dB
SNR2 = 12 dB
SNRI = 1 dB
M = 10 (array size)

13. Simulation (contd.): s1 =130º, s2 =60º, I =10º SNR1 = 15 dB
Experiment4-Multiple signals
s1 =130º, s2 =60º, I =10º
SNR1 = 15 dB
SNR2 = 9 dB
SNRI = 1 dB
M = 15 (array size)

14. Conclusions… References…
Achieved blind beamforming exploiting the cyclostationarity property of the communication signal
Using structure of the signals better signal processing techniques can be developed
References…
“Blind Adaptive Beamforming for Cyclostationary Signals”- Trans. SP, 1996
“Statistical spectral analysis – A non probabilistic theory”- William A. Gardner