基于Wishart矩阵极限特征值比分布的协作频谱感知
Cooperative Spectrum Sensing based on the Limiting Eigenvalue Ratio Distribution in Wishart Matrices
摘要：
随机矩阵理论的最新进展促使认知无线电中采用基于特征值的检测技术进行协作频谱感知。大多数这样的技术使用接收信号协方差矩阵的最大和最小特征值之间的比率来推断主信号的存在或不存在。迄今为止，在这一领域中得出的结果是基于渐近假设，由于在表征的确切分布的特征值比的困难。利用复Wishart矩阵最小特征值极限分布的一个新结果，本文导出了极限特征值比分布的表达式，它在非渐近区域也比以前的近似值精确得多.然后，直接应用该结果来计算作为虚警的目标概率的函数的判决阈值。数值模拟表明，该检测规则提供了一个显着的性能改善相比，其他基于特征值的算法。
英文摘要：
Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. Most of such techniques use the ratio between the largest and the smallest eigenvalues of the received signal covariance matrix to infer the presence or absence of the primary signal. The results derived so far in this field are based on asymptotical assumptions, due to the difficulties in characterizing the exact distribution of the eigenvalues ratio. By exploiting a recent result on the limiting distribution of the smallest eigenvalue in complex Wishart matrices, in this paper we derive an expression for the limiting eigenvalue ratio distribution, which turns out to be much more accurate than the previous approximations also in the non-asymptotical region. This result is then straightforwardly applied to calculate the decision threshold as a function of a target probability of false alarm. Numerical simulations show that the proposed detection rule provides a substantial performance improvement compared to the other eigenvalue-based algorithms.
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