1. Wideband Spectrum Sensing Using Compressive Sensing

2. Spectrum sensing Number of wireless devises is growing every day  spectrum has become valuable The most of allocated bands are unoccupied more than 90% of the time PUs pay for the spectrum bands and no SU can use those bands to avoid interference CR  maximize the efficiency of a wireless system by detecting ad transmitting on underused bands while avoiding interference No need to any pre-assigned Frequencies to operate  numerous commercial and military benefits

3. Challenges Sampling and hardware sampling CRs are used in a restricted frequency range  limits in usefulness If wideband  sampling at Nyquist rate In practice, impossible to operate over wideband frequency band  Compressive sensing

4. Compressive Sensing in Spectrum Sensing Recover certain signals from far fewer samples Conditioned on : signal should be sparse in a particular domain Principle of sparsity: information rate of a continuous time signal is much smaller than suggested by its bandwidths. Sampling in Sub-Nyquist rate  AIC (ADC+CS) AIC x(t)y[m]y[m]

5. Analog to Information Cnonverter x(t)x(t) p(t)p(t) y(t)y(t)y[m]y[m]

6. Compressive sensing x is in time domain and sparse in frequency domain l0 minimization  (NP-hard) L1-minimization: – measurement matrix should have RIP –

7. l1/l2 minimization The received signal is block sparse For a licensed user, its operating spectrum is a certain band Using the priori information of the spectrum boundaries between PUs, we can use l1/l2 minimization instead of l1 minimization

8. Threshold-Iterative Support Detection (Threshold-ISD) Reduced requirement on the number of measurements compared to the classical l1 minimization Recovers the signal iteratively (but a few iterations) Algorithm farmework: 1. s=0: l1-minimization, 2. while stopping criteria isn’t met: – where – Solve truncated BP : – j  j+1 Truncated BP

9. n=256 m=140 sparsity ratio = 30% (# of non-zeros = 77) # of iterations=3 Beta=5

10. n=256 m=120 sparsity ratio = 30% (# of non-zeros = 77) # of iterations=3 Beta=5

11. n=256 m=85 sparsity ratio = 30% (# of non-zeros = 77) # of iterations=3 Beta=5

12. Performance of 4 algorithms n = 256 sparsity ratio = 30% (# of non-zeros = 77) # of runs=75 per each m

13. Future works Spectrum has correlation in consequent time slots, so we can search over the frequency bands which are more likely to be unoccupied  Achieve better performance and less complexity -Adaptive ISD : each iteration of ISD can be done in each time slot. (threshold should be constant) -Extend to the distributed cognitive radio networks -Using sparse measurement matrix to be able to use verification based algorithms whose complexity is much smaller than classic l1- minimization

14. References First work on spectrum sensing using compressive sensing: Zhi Tian; Giannakis, G.B., “Compressed Sensing for Wideband Cognitive Radios”, ICCASP, June 2007 ISD : Yilun Wang and Wotao Yin “Sparse Signal Reconstruction via Iterative Support Detectio”, SIAM Journal on Imaging Sciences, pp. 462-491, August 2010 L1-l2 : Mihailo Stojnic, Farzad Parvaresh, and Babak Hassibi “On the reconstruction of block-sparse signals with an optimal number of measurements”, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 57, NO. 8, August 2009 Applying 11/l2 in spectrum sensing contex: Yipeng Liu and Qun Wan, “Compressive Wideband Spectrum Sensing for Fixed Frequency Spectrum Allocation”, arxiv, 2010