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 expression, we present 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.