Wideband Spectrum Sensing Using Compressive Sensing

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) x(t) AIC y[m]

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

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=120sparsity ratio = 30% (# of non-zeros = 77)# of iterations=3 Beta=5

11. n=256 m=85sparsity 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: ZhiTian;   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 : MihailoStojnic, FarzadParvaresh, and BabakHassibi “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 QunWan, “Compressive Wideband Spectrum Sensing for Fixed Frequency Spectrum Allocation”, arxiv, 2010