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.

翻译：随着尺寸的增加,随机矩阵的光谱行为结果被应用于探测影响一系列传感器的源数的问题。解决这一问题的一个共同战略是估计空间共变矩阵最小值的多重性。从样本共变矩阵中测得的数据,其最小值为$R$美元。现有的方法,如基于信息理论标准的方法,取决于相互之间超大R$的噪声电子值的近距离,因此,当源数大以获得良好的估计值时,样本规模必须相当大。本报告中的分析侧重于将$\百拉特{R}的频谱分割成噪音和信号电子值。显示,当传感器数量大时,信号的数量可以用比以往方法要求的样本大小大大降低来估计。主要结果的实际意义是,检测可以用与大型处理阵列的传感器数量相近的样本进行。