Compressive sensing has been proposed as a low-cost solution for dynamic wideband spectrum sensing in cognitive radio networks. It aims to accelerate the acquisition process and minimize the hardware cost. It consists of directly acquiring a sparse signal in its compressed form that includes the maximum information using a minimum number of measurements and then recovering the original signal at the receiver. Over the last decade, a number of compressive sensing techniques have been proposed to enable scanning the wideband radio spectrum at or below the Nyquist rate. However, these techniques suffer from uncertainty due to random measurements, which degrades their performances. To enhance the compressive sensing efficiency, reduce the level of randomness, and handle uncertainty, signal sampling requires a fast, structured, and robust sampling matrix; and signal recovery requires an accurate and efficient reconstruction algorithm. In this paper, we proposed a method that addresses the previously mentioned problems by exploiting the Bayesian model strengths and the Toeplitz matrix structure. The proposed method was implemented and extensively tested. The simulation results were analyzed and compared to those of the 2 techniques: basis pursuit and orthogonal matching pursuit algorithms with Toeplitz and random matrix. To evaluate the efficiency of the proposed method, several metrics were used, namely, sampling time, sparsity, required number of measurements, recovery time, processing time, recovery error, signal-to-noise ratio, and mean square error. The results demonstrate the superiority of our proposed method over the 2 other techniques in speed, robustness, recovery success, and handling uncertainty.
