Performance Comparison of LMS and RLS Adaptive Filtering Algorithms

LMS (Least Mean Square) and RLS (Recursive Least Squares) are two classical adaptive filtering algorithms that exhibit significant differences in weight convergence speed, computational complexity, and adaptability to dynamic environments. From an implementation perspective, LMS typically uses a simple iterative update rule while RLS requires matrix inversion operations.

Weight Convergence Comparison LMS algorithm gradually adjusts weights through gradient descent, featuring slower convergence but lower computational load, making it suitable for scenarios with less stringent real-time requirements. In code implementation, LMS uses a straightforward weight update formula: w(n+1) = w(n) + μ*e(n)*x(n), where μ is the step size. RLS employs recursive least squares to directly approach the optimal solution, achieving faster weight convergence, particularly when input signals exhibit strong correlation. However, RLS requires maintaining an inverse correlation matrix, resulting in higher computational complexity of O(N²) compared to LMS's O(N) per iteration.

Influence of Forgetting Factor The forgetting factor is a unique parameter in RLS that controls the decay rate of historical data weights. A larger forgetting factor (close to 1) allows stronger memory of old data, suitable for stationary environments. Smaller values enhance tracking capability for sudden changes but may cause oscillation due to excessive sensitivity. In RLS implementation, this factor directly affects the inverse covariance matrix update. LMS lacks this mechanism - while its step-size parameter influences convergence speed, its overall adaptability to non-stationary environments is weaker than RLS's.

Application Scenario Summary LMS is appropriate for systems with limited computational resources and slowly varying signals. RLS performs better when rapid convergence or non-stationary signal processing is required, but requires careful consideration of computational overhead. The key functions in practical implementation include: for LMS - step size optimization; for RLS - efficient matrix inversion techniques and forgetting factor tuning. Actual selection should comprehensively consider hardware constraints and dynamic performance requirements.