Cooperative compressive power spectrum estimation in wireless fading channels

This paper considers multiple wireless sensors that cooperatively estimate the power spectrum of the signals received from several sources. We extend our previous work on cooperative compressive power spectrum estimation to accommodate the scenario where the statistics of the fading channels experienced by different sensors are different. The signals received from the sources are assumed to be time-domain wide-sense stationary processes. Multiple sensors are organized into several groups, where each group estimates a different subset of lags of the temporal correlation. A fusion centre (FC) combines these estimates to obtain the power spectrum. As each sensor group computes correlation estimates only at a subset of lags, the sampling rate per sensor can be less than the Nyquist rate. The conditions required for uniqueness of the least-squares estimator are derived based on our previous results. The sensors are combined into clusters in such a way that all sensors within the same cluster experience approximately the same fading statistics. We find that, as long as the number of sensors of each group is the same across clusters, the resulting power spectrum estimate computed by the FC converges to the power spectrum of the transmitted signal scaled by the averaged fading statistics. In a simulation study, we also investigate the performance of our approach when the aforementioned assumption is not true, i.e., when the number of sensors of each group is not the same across clusters. The simulation study shows degradation in the performance of our approach for this case.