Estimating the number of signals by chi-square statistics

An examination is made of the use of hypothesis testing on the problem of estimating the number of signals. The asymptotic distribution of the likelihood ratio test (LRT) statistics is derived for when the underlying distribution of the observation vectors is complex multivariate normal. An algorithm is proposed using the P-value (observed significance level) of the LRT. This algorithm does not need a subjective threshold selection as required by the traditional hypothesis testing approach. Results of computer simulation are included to demonstrate the capability of this algorithm