  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.
