Abstract
In cognitive radio (CR) networks, eigenvalue-based detectors (EBDs) have attracted much attention due to their good performance of detecting secondary users (SUs). In order to further improve the detection performance of EBDs with short samples, we propose two new detectors: average circulant matrix-based Roy’s largest root test (ACM-RLRT) and average circulant matrix-based generalized likelihood ratio test (ACM-GLRT). In the proposed method, the circulant matrix of samples at each time instant from SUs is calculated, and then, the covariance matrix of the circulant matrix is averaged over a short period of time. The eigenvalues of the achieved average circulant matrix (ACM) are used to build our proposed detectors. Using a circulant matrix can improve the dominant eigenvalue of covariance matrix of signals and also the detection performance of EBDs even with short samples. The probability distribution functions of the detectors undernull hypothesis are analyzed, and the asymptotic expressions for the false-alarm and thresholds of two proposed detectors are derived, respectively. The simulation results verify the effectiveness of the proposed detectors.
Highlights
We first show the influence of a circulant matrix on the eigenvalues of the covariance matrix as well as the histogram of proposed methods under binary hypothesis
We proposed two detectors, the average circulant matrix (ACM)-Roy’s largest root test (RLRT) and ACM-generalized likelihood ratio test (GLRT), based on the circulant matrix technique for the known and unknown noise variances
The simulation results show that the circulant matrix technique can enhance the dominant eigenvalue of the covariance matrix, which would broaden the range between the probability density function (PDF) of the detectors’
Summary
Eigenvalue-based detection (EBD) techniques has good application prospects because they do not require prior knowledge of the primary user signal and have a good detection performance [4,5,6,7,8]. In order to characterize the performance of the detectors, the theoretical thresholds are analyzed under the assumption that the sample number of received signal by SUs is large and even goes to infinity [21,22] This assumption is relevant in many applications in cognitive radio networks. We proposed two detectors to improve the detection performance of EBDs with small samples based on the average circulant matrix. From the numerical simulation results, using a circulant matrix can improve the dominant eigenvalue of covariance matrix of signals and obtain a better detection performance of EBDs even with small samples.
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