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 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)

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

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

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

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):

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)

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 - 0.00314 s =40º, I =120º  = 0 M = 4 (array size)

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

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

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)

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)

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