Simulation of Two Channel Estimation Algorithms: LS and MMSE

This document presents simulation experiments for channel estimation using two algorithms: Least Squares (LS) and Minimum Mean Square Error (MMSE). In our experiments, we use Mean Square Error (MSE) as the performance metric to evaluate both algorithms. First, we introduce the principle and implementation method of the LS algorithm. The LS estimator operates by minimizing the sum of squared differences between received and transmitted signals, implemented in MATLAB through simple matrix operations: H_LS = Y/X where Y is the received signal and X is the known pilot sequence. We conduct simulation experiments demonstrating LS implementation with different signal-to-noise ratio conditions. Next, we explain the MMSE algorithm principle and its implementation approach. The MMSE estimator incorporates statistical channel information and noise covariance to minimize the expected estimation error. The implementation involves matrix calculations: H_MMSE = R_hy * inv(R_yy) * Y, where R_hy is the cross-covariance matrix and R_yy is the auto-covariance matrix of received signals. We perform comparative simulations showing MMSE's noise suppression capabilities. By comparing simulation results from both algorithms, we evaluate and contrast their performance characteristics. The analysis includes MSE performance curves, computational complexity comparisons, and robustness assessments under varying channel conditions, leading to conclusive recommendations for practical applications.