基于随机矩阵非渐近谱理论的协作频谱感知算法研究

将随机矩阵的非渐近谱理论应用到协作频谱感知中，对接收信号样本协方差矩阵的最大特征值和最小特征值进行分析，该文提出一种精确的最大最小特征值差(Exact Maximum Minimum Eigenvalue Difference, EMMED)的协作感知算法。对于任意给定的协作用户个数K和采样点数N，首先推导了最大最小特征值之差的精确概率密度函数(Probability Density Function, PDF)和累积分布函数(Cumulative Distribution Function, CDF)，然后利用该分布函数设计了所提算法的判决阈值。理论分析表明，EMMED算法的判决阈值较已有的渐进最大最小特征值差(Asymptotic Maximum Minimum Eigenvalue Difference, AMMED)检测更为精确，算法无需主用户信号特征并且能够对抗噪声不确定度影响。仿真结果表明，存在噪声不确定度的感知环境下，EMMED算法较已有的精确最大特征值(Exact Maximum Eigenvalue, EME)和EMMER等频谱感知算法具有更好的检测性能。

Study on Cooperative Spectrum Sensing Algorithm Based on Random Matrix Non-asymptotic Spectral Theory

The non-asymptotic spectral theory of random matrix is applied to cooperative spectrum sensing, the maximum eigenvalue and the minimum eigenvalue of the sampled signal covariance matrix are analyzed and an Exact Maximum Minimum Eigenvalues Difference (EMMED) algorithm is proposed. For any given numbers of cooperative users K and sampling points N, the exact Probability Density Function (PDF) and Cumulative Distribution Function (CDF) of the difference between the maximum and minimum eigenvalues are derived. Then, an accurate decision threshold is designed by using the distribution function. Theoretical analysis shows, the EMMED algorithm has the characteristics that the decision threshold is more accurate than the existing Asymptotic Maximum Minimum Eigenvalue Difference (AMMED) algorithm, without the characteristics of the main user signal and not affected by noise uncertainty. In addition, the simulation results show that the EMMED algorithm has better detection performance than the existing Exact Maximum Eigenvalue (EME) and EMMER algorithms in the real sensing environment with noisy uncertainty.