Online Wideband Spectrum Sensing Using Sparsity

Wideband spectrum sensing is an essential part of cognitive radio systems. Exact spectrum estimation is usually inefficient as it requires sampling rates at or above the Nyquist rate. Using prior information on the structure of the signal could allow near exact reconstruction at much lower sampling rates. Sparsity of the sampled signal in the frequency domain is one of the popular priors studied for cognitive radio applications. Reconstruction of signals under sparsity assumptions has been studied rigorously by researchers in the field of Compressed Sensing (CS). CS algorithms that operate on batches of samples are known to be robust but can be computationally costly, making them unsuitable for cheap low power cognitive radio devices that require spectrum sensing in real time. On the other hand, on line algorithms that are based on variations of the Least Mean Squares (LMS) algorithm have very simple updates so they are computationally efficient and can easily adapt in real time to changes of the underlying spectrum. In this paper we will present two variations of the LMS algorithm that enforce sparsity in the estimated spectrum given an upper bound on the number of non-zero coefficients. Assuming that the number of non-zero elements in the spectrum is known we show that under conditions the hard threshold operation can only reduce the error of our estimation. We will also show that we can estimate the number of non-zero elements of the spectrum at each iteration based on our online estimations. Finally, we numerically compare our algorithm with other on line sparsity-inducing algorithms in the literature.