Spectral Theory of Large Dimensional Random Matrices Applied to Signal Detection
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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 R. Existing approaches, such as that based on information theoretic criteria, rely on the closeness of the noise eigenvalues of 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 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.
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