A Study on Cooperative Compressive Wideband Power Spectrum Sensing

In the wideband regime, direct spectrum estimation requires the use of power hungry high-rate analog-to-digital converters to satisfy the required high Nyquistrate. While compressive sampling is popular for perfect reconstruction of sparse signals sampled below the Nyquist rate, for some applications, such as spectrum sensing for cognitive radio, perfect signal reconstruction is an overkill since only power spectrum recovery is required. For wide-sense stationary signals, it is possible to reconstruct the power spectrum based on samples produced by a sub-Nyquist rate sampling device without any sparsity constraints on the power spectrum. In general, up to a certain compression rate, it is possible to present the power spectrum recovery problem as an over-determined system, which is solvable using a least-squares method. In this paper, we study a possible extension of our proposed power spectrum reconstruction approach to the case where multiple sensing receivers cooperatively sense the power spectrum of the original signals. In cognitive radio networks, this cooperation is desirable since the signals from the primary users might suffer from wireless fading, which impedes an individual sensing receiver to reach the required performance. In the wideband regime, this cooperative sensing is not only advantageous in terms of the channel diversity gain but also in terms of a possible sampling rate reduction per receiver. We focus more on how far this cooperative scheme promotes the sampling rate reduction at each sensing receiver and assume that the channel state information is available. We concentrate on a centralized network where each sensing receiver forwards the collected measurements to a fusion centre, which later computes the correlations between the measurements obtained by different sensing receivers. We then express these correlations of the measurements as a linear function of the power spectrum of the original signal and we attempt to solve this linear system using least-squares.