Compressive Sparsity Order Estimation for Wideband Cognitive Radio Receiver

Compressive sensing (CS) has been widely investigated in the cognitive radio (CR) literature in order to reduce the hardware cost of sensing wideband signals assuming prior knowledge of the sparsity pattern. However, the sparsity order of the channel occupancy is time-varying and the sampling rate of the CS receiver needs to be adjusted based on its value in order to fully exploit the potential of CS-based techniques. In this context, investigating blind sparsity order estimation (SOE) techniques is an open research issue. To address this, we study an eigenvalue-based compressive SOE technique using asymptotic random matrix theory. We carry out detailed theoretical analysis for the signal plus noise case to derive the asymptotic eigenvalue probability distribution function (aepdf) of the measured signal's covariance matrix for sparse signals. Subsequently, based on the derived aepdf expressions, we propose a technique to estimate the sparsity order of the wideband spectrum with compressive measurements using the maximum eigenvalue of the measured signal's covariance matrix. The performance of the proposed technique is evaluated in terms of normalized SOE Error (SOEE). It is shown that the sparsity order of the wideband spectrum can be reliably estimated using the proposed technique for a variety of scenarios.