Distributed Compressive Power Spectrum Sensing for Cognitive Radio

In cognitive radio (CR) networks, secondary users (SUs) might be required to gauge a wide frequency band to find frequency holes that they can use for signal transmission. When this spectrum sensing process is conducted digitally, a high sampling rate might be needed to satisfy the Nyquist rate. However, the existence of the frequency holes can be concluded by simply constructing the power spectral density (PSD) instead of the original signal. In fact, the Nyquist criterion is not applicable when we aim to reconstruct the PSD (and not the original analog signal). This paper introduces a distributed wideband power spectrum sensing using multiple SUs to first estimate the power spectrum of signals received from sources in a collaborative manner. Each SU samples the received signal at sub-Nyquist rate and reconstructs the local PSD estimate based on the received digital samples. The local PSD estimate is then exchanged between SUs based on the consensus approach without fusion center. Once convergence on the PSD is reached, the detection on the existence of PUs is conducted. We found that for a PU signal power of 4 mW, noise power of 1 mW, and Rayleigh fading with the variance of -1 dB, the probability of detection can be at least 0.9 for the probability of a false alarm of 0.1 if the number of SUs is at least 40 or the compression rate is at least 0.4.