基于Gerschgorin理论稀疏度估计的宽带频谱感知算法

Wide-band spectrum sensing algorithm using sparsity estimation based on Gerschgorin theorem

针对在低信噪比(SNR)情况下稀疏度欠估计和高信噪比情况下稀疏度过估计的问题,提出了一种基于Gerschgorin理论稀疏度估计的宽带频谱感知算法。首先,该算法利用Gerschgorin理论分离信号圆盘与噪声圆盘得到稀疏度估计值;然后,利用正交匹配追踪(OMP)算法得到频谱支撑集;最后,完成宽带频谱感知。仿真结果表明,所提算法、AIC-OMP算法和MDL-OMP算法频谱感知的检测概率达到95%信噪比分别需要4.6 d B、8.5 d B和9.7 d B;所提算法频谱感知的虚警概率在信噪比大于13 d B时趋近于0,明显低于BPD-OMP和GDRI-OMP算法的虚警概率,因此,所提算法对于压缩感知(CS)的信号稀疏度估计兼顾了低信噪比和高信噪比时的稀疏度估计性能,频谱感知性能优于AIC-OMP算法、MDL-OMP算法、BPD-OMP算法和GDRI-OMP算法。

To solve the problems of under-estimation of sparsity at low Signal-to-Noise Ratio（ SNR） and over-estimation of sparsity at high SNR, a wide-band spectrum sensing algorithm using sparsity estimation based on Gerschgorin theorem was proposed. Firstly, Gerschgorin theorem was used to separate the signal disk and noise disk in order to estimate the sparsity.Then, the spectrum support set was obtained by using Orthogonal Matching Pursuit（ OMP） algorithm. Finally, the wide-band spectrum sensing was accomplished. The simulation results show that, the SNR of the proposed algorithm, AIC-OMP（ Akaike Information Criterion-Orthogonal Matching Pursuit） algorithm and MDL-OMP（ Minimum Description Length-Orthogonal Matching Pursuit） algorithm need 4. 6 d B, 8. 5 d B and 9. 7 d B respectively while their detection probability reaching to 95%;the false alarm probability of the proposed algorithm tends to 0 when the SNR is higher than 13 d B, which is far lower than that of BPD-OMP（ Bayesian Predictive Density-Orthogonal Matching Pursuit） algorithm and GDRI-OMP（ Gerschgorin Disk Radii Iteration-Orthogonal Matching Pursuit） algorithm. Therefore, the proposed algorithm takes account of sparsity estimation performances under both low SNR and high SNR, and the spectrum sensing performance of the proposed algorithm is better than that of AIC-OMP algorithm, MDL-OMP algorithm, BPD-OMP algorithm and GDRI-OMP algorithm.