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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