A Bayesian recovery technique with Toeplitz matrix for compressive spectrum sensing in cognitive radio networks

Abstract

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-tonoise 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.

Metrics for Evaluating the Efficiency of Compressing Sensing Techniques

“…Recovery error, also called reconstruction error, is the norm of the difference between the original signal and the recovered signal divided by the original signal's norm [13] [15]. it can be expressed as…”

“…This metric is used to evaluate the variation of the recovery error of a recovery algorithm over time. It is mainly used for predictive modeling about a recovery algorithm for error estimation [15]. It measures the average magnitude of the squared difference between the original signal and the recovered signal.…”

“…Recovery time metric measures the time required by a recovery algorithm to solve the sparse recovery problem. It examines how fast is a recovery algorithm [13][14][15][16]. Moreover, we refer to the processing time when considering all the compressive sensing processes to evaluates how fast is a compressive sensing technique.…”

“…Signal to error ratio, also called signal to noise ratio, measures the strength of a signal over the noise [15][16][17]. In compressive sensing, this metric measures the strength of the original signal over the recovered signal.…”

“…Recovery signal to noise ratio metric measures the SNR level at the receiver by considering the original signal the input and the recovered signal the output [12][13][14][15][16]. It is expressed as…”