Technion - Israel institute of technology department of Electrical Engineering High speed digital systems laboratory Cyclostationary Feature Detection of Sub-Nyquist Sampled Sparse Signals AsafBarel Eli Ovits Supervisor: Debby Cohen June 2013
Project Motivation • Communication Signals are wideband with very high Nyquist rate • Communication Signals are Sparse, therefore subnyquist sampling is possible • Possible application: Cognitive Radio • Current system suffers from low noise robustness • Project goal: implementing algorithm for cyclic detection with high noise robustness
~ ~ ~ ~ Background: Sub-Nyquist SamplingMWC system
System Output • Full signal reconstruction, or support recovery using Energy Detection • The problem: Noise is enhanced by Aliasing
Energy Detection: simulation SNR = 10 dB SNR = -10 dB Signal: • Original support: 2435117135217228 • Reconstructed support: 24 87 107 217 232 168 228 165 145 35 20 84 Original support is not contained! • Original support: 8 72 90 162 180 244 • Reconstructed support: 90180244 21 200 241 162728 231 52 11 Original support is contained!
Cyclostationary Signals • Wide sense Cyclostationary signal: mean and autocorrelation are periodic with
Cyclostationary Signals • The Autocorrelation can be expanded in a fourier series:
Cyclostationary Signals • Specral Correlation Function (SCF): [Gardner, 1994]
Cyclostationary Signals • The 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 Reconstruction • Using 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
Further Objectives • MATLAB 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 )