An Adaptive Blind Separation Algorithm for Co-frequency Overlapping Signals Using RLS Approach

In the fields of wireless communication and signal processing, the separation of co-frequency overlapping signals remains a highly challenging problem. Adaptive blind separation algorithms can achieve signal separation using only observed signals without prior knowledge of source signals or mixing matrices. Among these, the RLS (Recursive Least Squares)-based adaptive blind separation algorithm has gained significant attention due to its superior convergence rate and stability characteristics.

The core concept of the RLS algorithm involves recursively minimizing the weighted sum of squared errors through iterative updates. Compared to traditional LMS (Least Mean Square) algorithms, RLS demonstrates faster convergence in dynamic signal environments, making it particularly suitable for non-stationary signal processing. For co-frequency overlapping signals, RLS gradually approaches the optimal solution by adaptively adjusting the coefficients of the separation matrix, thereby achieving blind separation of mixed signals. In code implementation, the RLS algorithm typically involves weight vector updates using a gain vector and covariance matrix recursion, with key operations including matrix inversion lemma applications for computational efficiency.

In practical applications, the performance of the RLS algorithm depends on critical parameter settings such as the forgetting factor and regularization parameters. Proper parameter selection balances the algorithm's convergence speed and steady-state error, ensuring high separation accuracy even in complex signal environments. From a programming perspective, the forgetting factor (usually denoted as lambda) controls the memory length of the algorithm, while regularization parameters prevent numerical instability in matrix inversion operations. Furthermore, combining RLS with other signal processing techniques like Independent Component Analysis (ICA) can further enhance separation performance, making it valuable in applications such as multi-user detection and speech enhancement. A typical implementation would involve initializing the weight matrix, computing the Kalman gain vector, and updating the inverse covariance matrix through rank-1 updates at each iteration.