Blind Beamforming for Cyclostationary Signals

1
Blind Beamforming for Cyclostationary Signals

• Array Processing Project
• Preeti Nagvanshi
• Aditya Jagannatham

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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

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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)

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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

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Cyclic Correlation

• - time average over infinite observation
  period
• no is some time shift, ? is the cycle frequency

Cyclic Conjugate Correlation
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Cyclic Adaptive Beamforming(CAB)

• wCAB is a consistent estimate of d(?)

Multiple desired signals (same ?)...
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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)
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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)

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Simulation
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)

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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

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Simulation (contd.)
Experiment2-Moving source DOA estimation (contd.)
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Simulation (contd.)
Experiment3-Multipath signals

• ?s1 30º, ?s2 40º, ?I 120º
• SNR1 15 dB
• SNR2 12 dB
• SNRI 1 dB
• M 10 (array size)

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Simulation (contd.)
Experiment4-Multiple signals

• ?s1 130º, ?s2 60º, ?I 10º
• SNR1 15 dB
• SNR2 9 dB
• SNRI 1 dB
• M 15 (array size)

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Conclusions

• 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