Implementation of LMS Channel Estimation Algorithm under AWGN Noise with Enhancements

Implementation of LMS channel estimation algorithm under AWGN noise conditions, along with my algorithmic enhancements. In AWGN (Additive White Gaussian Noise) environments, using adaptive algorithms for channel estimation is a common approach. The LMS (Least Mean Squares) algorithm serves as a classical adaptive filtering method suitable for channel estimation applications. However, to enhance algorithm performance, I have implemented several improvements to the standard LMS approach. My enhancements include extending the sliding window length and introducing weight adjustment factors. These modifications aim to improve both the accuracy and stability of channel estimation. The implementation typically involves initializing filter coefficients, calculating the error signal between desired and estimated outputs, and iteratively updating weights using the LMS update rule: w(n+1) = w(n) + μ * e(n) * x(n), where μ represents the step size parameter. My improved version incorporates a dynamic window mechanism that adjusts the observation period based on signal characteristics, and a weighting factor that prioritizes recent samples for better tracking capability in time-varying channels. The code structure would include: - Noise generation module using AWGN characteristics - LMS core algorithm with adjustable step size - Enhanced window management system - Weight adaptation logic with forgetting factors - Performance evaluation metrics (MSE, convergence rate) Through these enhancements, the modified algorithm demonstrates improved convergence behavior and reduced estimation error compared to conventional LMS implementations, particularly in scenarios with non-stationary channel conditions.