Simulation Implementation of Minimum Mean Square Error (MMSE) Equalization Algorithm

In this article, we demonstrate how to implement Minimum Mean Square Error (MMSE) equalization algorithm using MATLAB simulation, and help understand the algorithm principles by eliminating Inter-Symbol Interference (ISI) caused by multipath propagation. The MMSE equalization algorithm is a widely used signal processing technique that improves signal transmission quality and reliability. Through MATLAB simulation, we can clearly illustrate the algorithm's working mechanism and effectiveness. The implementation typically involves calculating the MMSE equalizer coefficients using matrix operations, where the key mathematical formulation includes solving the Wiener-Hopf equation to minimize the mean square error between the transmitted and received signals. During the simulation process, we generate a series of input signals and process them through the MMSE equalization algorithm to eliminate ISI caused by multipath effects. The code implementation includes crucial steps such as channel estimation, noise variance calculation, and equalizer weight computation using MATLAB's matrix inversion capabilities (e.g., the 'inv' function or more stable 'pinv' function for ill-conditioned matrices). This practical example helps better understand and apply the MMSE equalization algorithm's role in communication systems, demonstrating how it effectively mitigates multipath distortion while maintaining computational efficiency through optimized matrix operations.