Equalization of 2x2 Rayleigh Fading BPSK-Modulated MIMO Channels with Performance Comparison

In this document, we implement and analyze equalization techniques for 2x2 Rayleigh fading MIMO channels using BPSK modulation, comparing the performance of Zero-Forcing (ZF), Minimum Mean Square Error (MMSE), and Maximum Likelihood (ML) detection methods. The implementation involves calculating channel matrix inverses for ZF (using pseudo-inverse techniques like pinv() in MATLAB), applying regularization for MMSE (adding noise variance term to diagonal elements), and performing exhaustive search for ML detection (evaluating all possible symbol combinations). Through this study, we gain deeper insights into how different equalization approaches affect channel performance metrics, providing valuable references for future research. During experiments, we detail our experimental setup including SNR ranges, channel realization parameters, and evaluation metrics like Bit Error Rate (BER) and Symbol Error Rate (SER) to ensure result accuracy. Furthermore, we conduct in-depth analysis of experimental results to examine the trade-offs between computational complexity and performance for each method under various channel conditions, offering readers comprehensive perspectives on implementation considerations and practical applications. This enhanced documentation enables readers to thoroughly understand equalization techniques for 2x2 Rayleigh fading BPSK-modulated MIMO channels and provides inspiration for further research in related fields.