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

2. 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

3. Background: Sub-Nyquist Sampling MWC system ~~ ~~

4. Background: Sub-Nyquist Sampling Digital Processing

5. System Output Full signal reconstruction, or support recovery using Energy Detection The problem: Noise is enhanced by Aliasing

6. Energy Detection: simulation SNR = 10 dB SNR = -10 dB Original 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! 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!

7. Cyclostationary Signals

9. [Gardner, 1994]

10. Cyclostationary Signals [Gardner, 1994]

11. 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.

12. SCF Reconstruction For a Stationary SignalFor a Cyclostationary Signal

13. SCF Reconstruction – Mathematical derivation

14. Algorithm Pseudo Code

15. Pseudo Code

16. 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 )

17. Gantt Chart