asaf barel eli ovits supervisor: debby cohen june 2013 high speed digital systems laboratory...
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Cyclostationary Feature Detection of Sub-Nyquist Sampled Sparse Signals
Asaf Barel Eli Ovits
Supervisor: Debby CohenJune 2013
High speed digital systems laboratoryTechnion - Israel institute of technologydepartment of Electrical Engineering
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Project MotivationCommunication Signals are wideband with
very high Nyquist rateCommunication Signals are Sparse, therefore
subnyquist sampling is possiblePossible application: Cognitive RadioCurrent system suffers from low noise
robustness Project goal: implementing algorithm for
cyclic detection with high noise robustness
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Background: Sub-Nyquist SamplingMWC system
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Background: Sub-Nyquist SamplingDigital Processing
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System OutputFull signal reconstruction, or support
recovery using Energy DetectionThe problem: Noise is enhanced by Aliasing
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Energy Detection: simulation
SNR = 10 dB SNR = -10 dBOriginal support: 24 35 117 135 217 228
Reconstructed support: 24 87 107 217 232 168 228 165 145 35 20 84
Original support is not contained!
Signal:
Original support:8 72 90 162 180 244
Reconstructed support: 90 180 244 21 200 241 162 72 8 231 52 11
Original support is contained!
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Cyclostationary SignalsWide sense Cyclostationary signal: mean and
autocorrelation are periodic with
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Cyclostationary SignalsThe Autocorrelation can be expanded in a
fourier series:
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Cyclostationary SignalsSpecral Correlation Function (SCF):
[Gardner, 1994]
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Cyclostationary SignalsThe Cyclic Autocorrelation function can also
be viewed as cross correlation between frequency modulations of the signal:
[Gardner, 1994]
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Cyclic Detection Signal Model: Sparse, Cyclostationary signal.
No correlation between different bands.
The goal: blind detection
Support Recovery: instead of simple energy detection, we will use our samples to reconstruct the SCF, and then recover the signal’s support.
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SCF ReconstructionUsing the latter definition for cyclic
Autocorrelation, we can get Autocorrelation from a signal:
For a Stationary Signal
For a Cyclostationary Signal
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SCF Reconstruction – Mathematical derivation
Discarding zero elements from :
B
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Algorithm Pseudo Code
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Pseudo Code
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Further ObjectivesMATLAB implementation of the Algorithm
Simulation of the new system, including Comparison to the Energy Detection system (Receiver operating characteristic (ROC) in different SNR scenarios )
Comparison to Cyclic detection at Nyquist rate (mean square error )
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Gantt Chart
Adaptation of exisiting algorithm to the cyclic case
Implementing MATLAB code for SCF reconstruction
Adding signal detecion from the SCF
Simulations and comparison
Optional: Implementing cyclic detection in Hardware simulating enviroument
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