Frequency-domain wideband compressive spectrum sensing

The authors study the power spectrum density (PSD) estimation of wideband wide-sense stationary (WSS) signals with sub-Nyquist sampling rate. Owing to the large bandwidth, Nyquist rate sampling of such signals needs very high rate analogue-to-digital converters. It is important to note that PSD estimation does not necessarily require reconstruction of the original signal. Indeed, the power spectrum can be directly obtained from sub-Nyquist samples. In this study, a new method for reconstructing the power spectrum in the frequency domain for WSS signals is presented. The main idea is to divide the whole spectrum into N equal-length segments and calculate the average PSD in each segment using a frequency-domain representation of sub-Nyquist samples. In addition, the capability of the proposed method, as a detector of spectrum holes, is studied using receiver operating characteristic (ROC) curves. Then, the analysis of false alarm probability is provided. Simulation results for the additive white Gaussian noise channel and the slowly fading frequency selective channel show that the proposed method considerably outperforms available techniques.