Detection of Signal-Like Interference Based on the Analysis of Eigenvalues of the Sample Correlation Matrix

We obtain an analytical expression for the decision statistics for detecting signal-like active interference based on an estimate of the eigenvalues of a sample correlation matrix. The exact decision statistic is derived from a rigorous expression for the likelihood ratio and obtained on the basis of the generalized likelihood ratio including that for short samples. Using the exact decision statistic, we obtain detection curves (the dependence of the probability of correct detection on the signal-to-noise ratio) for various process-sample lengths. Dependences of the probability of correct detection on the phase-fluctuation value are given and it is shown that signal-to-noise ratio for detecting the signal-like interference in the case of a given probability of correct detection significantly increases with decreasing phase fluctuations of the interference.