Constant Wideband Compressive Spectrum Sensing for Sparse and Nonsparse Signals With Low-Rank Matrix Recovering and Prior Knowledge Mining

Abstract

In cognitive radios (CR), compressive spectrum sensing (CSS) is a promising technique to detect wideband spectrum holes with reduced sampling rate requirement of analog-to-digital converter (ADC). It is implied in compressive sensing (CS) that the minimum sampling rate is determined by the sparsity order of the observed wideband signal. Unfortunately, the sparsity order is previously unknown and dynamically varies. Meanwhile, CS technology fails to work efficiently for the nonsparse spectrum case. For example, the CSS performance degenerates significantly for low signal-to-noise ratio (SNR) scenarios since the observed signal becomes nonsparse in frequency domain. To overcome the above-mentioned challenges, we propose a novel CSS algorithm with temporally-correlated prior knowledge mining (TPKM-CSS) to detect spectrum holes without a prior sparsity order information. The proposed scheme can handle both the sparse and nonsparse spectrum cases. The proposed solution has three contributions: firstly, CR implements multiple parallel sampling simultaneously to acquire wireless spectrum signals, which have a low-rank spectrum matrix. Secondly, the temporal correlation between continuous CS data is further exploited to improve the estimation accuracy of the current spectrum. Finally, the theoretical performance of the proposed TPKM-CSS is evaluated, wherein the cumulative distribution function (CDF) of the spectrum reconstruction error is derived in the closed form. The simulation results show that the proposed scheme works well for both sparse and nonsparse spectrum scenarios. Compared with the CSS schemes that are based on low-rank matrix recovery (LMR-CSS), maximizing correlation (MC), iterative compressive filtering (ICF), or Bayesian CS (BCS), the proposed scheme yields the superior performance in terms of the probability of detection and the probability of false alarm, especially for nonsparse signals. Furthermore, the simulated statistical performance of the spectrum reconstruction error matches well the theoretical CDF curve.