Different algorithms based on the consideration of eigenvectors and eigenvalues of the sample covariance matrix are widely used for signal detection and estimating the number of sources. But classic eigenvalue technique makes difficult the evaluation of the thresholds for eigenvalues at given false alarm probabilities. To find these thresholds, it is necessary to know eigenvalue distribution functions of the sample covariance matrix. For some important tasks of signal detection and signals resolution the knowledge of statistical characteristics of only two maximum eigenvalues is enough for the appropriate choice of the thresholds.

In this work the cumulative distribution function (CDF) for the first (maximum) eigenvalue of the sample correlation matrix has been found in explicit form for case when only internal noise presents (for the null hypothesis in detection task). Also the approximate CDF of the second eigenvalue has been found for asymptotic case of one powerful external signal (for the null hypothesis in resolution task).