一种基于特征值极限分布理论的盲多天线频谱感知算法

当信道空闲时接收信号取样协方差矩阵的特征值在数值上均近似等于噪声方差，而主用户信号的出现则改变了这些特征值的大小。基于这一事实，论文提出一种基于取样协方差矩阵特征值的频谱感知算法。该算法以取样协方差矩阵的最大特征值与其他特征值的和之比作为感知判决量。基于大维随机矩阵理论的特征值极限分布理论，分析了算法的理论虚警性能，在此基础上提出了理论判决门限的计算方法。新算法在感知判决过程中无需事先知道噪声方差、主用户信号和信道增益等先验信息。因而，新算法属于一种全盲多天线频谱感知算法，具有广泛的适用范围。进一步的数值仿真结果验证了新方法的有效性。

A Blind Multiple Antenna Spectrum Sensing Algorithm Based on the Limiting Distribution Theory of Eigenvalues

The eigenvalues of the sampling covariance matrix of the received signal approximately equal to the noise variance when the channel is idle, while the presence of the primary user signal changes the values of these eigenvalues. Based on this fact, an eigenvalue based multiple antenna spectrum sensing algorithm is proposed in this paper. The proposed algorithm takes the ratio of the maximum eigenvalue of the sample covariance matrix to the sum of other eigenvalues as the test statistic. By utilizing the limiting distribution theory of eigenvalues of the large dimensional random matrix, the probability of false-alarm and the decision threshold are theoretically analyzed. The proposed algorithm does not need to know the prior information of noise variance, primary user signal and channel gain in advance. Therefore, the new algorithm is a fully blind multiantenna spectrum sensing algorithm, which has wide application scope. Further numerical simulation results verify the effectiveness of the new method.