Mixed Source Separation of Partially Correlated Source Based on Analytic CMA

The analytical constant modulus algorithm (ACMA) is an effective tool for separating and recovering statistically independent constant modulus (CM) signals. In previous ACMA studies, source signals are usually restricted to be statistically independent or statistically orthogonal. In this article, we no longer impose these restrictions on CM signals, but only require the CM signals to be partially independent or orthogonal. However, this will lead to the inability of ACMA to successfully separate these partially correlated source signals from the observed data. This article introduces a new method for separating partially correlated sources based on ACMA. We first analyzed that the biggest shortcoming of the original algorithm when dealing with partially correlated sources was that it could not estimate the number of source signals. Later, we found that the best range of the threshold value was a curve about SNR, which would not change greatly with the increase in the correlation coefficient. Therefore, we adopted the method of mixed estimation of the SNR of source signals and improved the threshold formula. The threshold performance of estimating the number of partially correlated sources is improved, and the ability of ACMA to estimate the number of partially correlated constant modulus sources is improved. We then estimate the source signal by reconstructing the covariance matrix of the signal to eliminate the associated effects. Simulation results show that this method can be used for nonindependent constant modulus signals with a correlation coefficient of less than 0.5.