Wideband spectrum sensing from compressed measurements using spectral prior information

Abstract—Wideband spectrum sensing (WSS) encompasses a collection of techniques intended to estimate or to decide over the occupancy parameters of a wide frequency band. However, broad bands require expensive acquisition systems, thus moti-vating the use of compressive schemes. In this context, previous works in compressive WSS have already realized that great compression rates can be achieved if only second-order statistics are of interest in spectrum sensing. In this paper, we go a step further by exploiting spectral prior information that is typically available in practice in order to reduce the sampling rate even more. The signal model assumes that the acquisition is done by means of an analog-to-information converter (A2I). The input signal is the linear combination of a number of signals whose second-order statistics are known and the goal is to estimate/de-cide over the coefficients of this combination. The problem is thus a particular instance of the well-known structured covariance estimation problem. Unfortunately, the algorithms used in this area are extremely complex for inexpensive spectrum sensors so that alternative techniques need to be devised. Exploiting the fact that the basis matrices are Toeplitz, we use the asymptotic theory of circulant matrices to propose a dimensionality reduction technique that simplifies existing structured covariance estimation algorithms, achieving a similar performance at a much lower computational cost. Index Terms—Analog-to-information converters, compressed sensing, covariance matching, wideband spectrum sensing