A separation algorithm based on mirror image matrix for weak correlated signals

Signal correlation is widely present in communication systems. The current blind source separation (BSS) algorithms are mostly based on the assumption that source signals are mutually independent. This paper proposes a weakly correlated source signal separation algorithm. Firstly, according to the matrix decomposition method, the correlation matrix of the source signal is decomposed into the sum of a matrix with all elements outside the main diagonal being zero and a matrix in which all elements except those on the main diagonal are non-zero. Then introduce the corresponding mirror matrix to establish the objective function. Through iterative optimization of the objective function, it is demonstrated that as the objective function approaches zero, the separation matrix converges to a decomposable form, enabling the recovery of source signals from mixed signals. The effectiveness of this BSS algorithm can be verified by simulation results.