MIMO 2x2 Zero-Forcing (ZF) vs Minimum Mean Squared Error (MMSE) Equalizer Performance under Rayleigh Channel

This MATLAB implementation computes and compares the Bit Error Rate (BER) performance of Zero-Forcing (ZF) and Minimum Mean Squared Error (MMSE) equalizers in a 2x2 Multiple-Input Multiple-Output system operating over a Rayleigh fading channel. The code employs Monte Carlo simulation to evaluate both equalization techniques under identical channel conditions. Key implementation aspects include: 1. Rayleigh channel modeling using complex Gaussian random variables 2. ZF equalizer implementation through pseudo-inverse computation of channel matrix H 3. MMSE equalizer design incorporating noise variance estimation 4. Signal transmission and detection using QPSK modulation 5. BER calculation through error counting over multiple simulation iterations The algorithm structure involves: - Generating random transmit symbols - Applying channel effects with Rayleigh fading - Applying equalization using both ZF and MMSE approaches - Demodulating the equalized signals - Calculating and comparing BER performance curves The simulation provides quantitative comparison of both equalizers' performance, demonstrating MMSE's superior noise robustness compared to ZF in low SNR scenarios while showing their convergence at high SNR values.