论文标题
用于信号检测的大维随机矩阵的光谱理论
Spectral Theory of Large Dimensional Random Matrices Applied to Signal Detection
论文作者
论文摘要
随着尺寸的增加，随机矩阵的光谱行为的结果应用于检测撞击传感器阵列的源数量的问题。解决此问题的一种常见策略是估计来自样本协方差矩阵$ \ wideHat {r} $的空间协方差矩阵的最小特征值$ r $。现有的方法，例如基于信息理论标准的方法，依赖于$ \ widehat r $彼此之间的噪声特征值的亲密关系，因此，当来源数量很大时，样本量必须很大，以获得良好的估计。本报告中提供的分析重点是将$ \ wideHat {r} $的频谱分解为噪声和信号特征值。结果表明，当传感器数量较大时，可以用样本量估计的信号数量大大低于以前的方法所要求的。主要结果的实际意义在于，可以通过许多样品与大尺寸阵列处理中的传感器数量相当的样本来实现检测。
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the multiplicity of the smallest eigenvalue of the spatial covariance matrix $R$ of the sensed data from the sample covariance matrix $\widehat{R}$. Existing approaches, such as that based on information theoretic criteria, rely on the closeness of the noise eigenvalues of $\widehat R$ to each other and, therefore, the sample size has to be quite large when the number of sources is large in order to obtain a good estimate. The analysis presented in this report focuses on the splitting of the spectrum of $\widehat{R}$ into noise and signal eigenvalues. It is shown that, when the number of sensors is large, the number of signals can be estimated with a sample size considerably less than that required by previous approaches. The practical significance of the main result is that detection can be achieved with a number of samples comparable to the number of sensors in large dimensional array processing.
