Cooperative compressive wideband power spectrum sensing

Compressive sampling is a popular approach to relax the rate requirement on the analog-to-digital converters and to perfectly reconstruct wideband sparse signals sampled below the Nyquist rate. However, there are some applications, such as spectrum sensing for cognitive radio, that demand only power spectrum recovery. For wide-sense stationary signals, power spectrum reconstruction based on samples produced by a sub-Nyquist rate sampling device is possible even without any sparsity constraints on the power spectrum. In this paper, we examine an extension of our proposed power spectrum reconstruction approach to the case when multiple sensors cooperatively sense the power spectrum of the received signals. In cognitive radio networks, this cooperation is advantageous in terms of the channel diversity gain as well as a possible sampling rate reduction per receiver. In this work, we mainly focus on how far this cooperative scheme promotes the sampling rate reduction at each sensor and assume that the channel state information is available. We concentrate on a centralized network where each sensor forwards the collected measurements to a fusion centre, which then computes the cross-spectra between the measurements obtained by different sensors. We can express these cross-spectra of the measurements as a linear function of the power spectrum of the original signal and attempt to solve it using a least-squares algorithm.