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
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
Background: Sub-Nyquist SamplingMWC system
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Background: Sub-Nyquist SamplingDigital Processing
System OutputFull signal reconstruction, or support
recovery using Energy DetectionThe problem: Noise is enhanced by Aliasing
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!
Cyclostationary SignalsWide sense Cyclostationary signal: mean and
autocorrelation are periodic with
Cyclostationary SignalsThe Autocorrelation can be expanded in a
fourier series:
Cyclostationary SignalsSpecral Correlation Function (SCF):
[Gardner, 1994]
Cyclostationary SignalsThe Cyclic Autocorrelation function can also
be viewed as cross correlation between frequency modulations of the signal:
[Gardner, 1994]
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.
SCF ReconstructionUsing the latter definition for cyclic
Autocorrelation, we can get Autocorrelation from a signal:
For a Stationary Signal
For a Cyclostationary Signal
SCF Reconstruction – Mathematical derivation
Discarding zero elements from :
B
Algorithm Pseudo Code
Pseudo Code
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 )
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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