Asaf Barel Eli Ovits Supervisor: Debby Cohen June 2013 High speed digital systems laboratory Technion - Israel institute of technology department of Electrical Engineering

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 Sampling MWC system ~~ ~~

Background: Sub-Nyquist Sampling Digital Processing

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 Original support: Reconstructed support: Original support is not contained! Original support: Reconstructed support: Original support is contained!

Cyclostationary Signals

[Gardner, 1994]

Cyclostationary Signals [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 For a Stationary SignalFor a Cyclostationary Signal

SCF Reconstruction – Mathematical derivation

Algorithm Pseudo Code

Pseudo Code

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 )

Gantt Chart