ZF, MMSE, and ML Equalizers for MIMO Systems with Implementation Codes

This documentation provides four MATLAB codes implementing Zero-Forcing (ZF), Minimum Mean Square Error (MMSE), and Maximum Likelihood (ML) equalizers, along with a detailed document focusing on linear detection techniques for MIMO systems. The MATLAB implementations include separate functions for each equalizer type, featuring matrix inversion operations for ZF, noise variance estimation for MMSE, and exhaustive search algorithms for ML detection.

These equalizers simulate the signal equalization process during data transmission in MIMO systems, aiming to recover transmitted data at the receiver side. The ZF equalizer employs least squares optimization to compute equalizer coefficients through pseudoinverse matrix calculations. The MMSE equalizer determines coefficients based on minimum mean square error criteria, incorporating channel state information and noise statistics. The ML equalizer utilizes maximum likelihood criterion with optimal detection algorithms that compare all possible transmitted symbol combinations.

Additionally, we provide comprehensive documentation on linear detector-based MIMO systems. Linear detectors represent fundamental MIMO reception techniques that facilitate data recovery in complex communication environments. The document elaborates on the theoretical principles of linear detection, implementation methodologies including matrix operations and signal processing algorithms, and practical applications in modern MIMO communication systems. The implementation showcases how linear detectors process received signals through weighting matrices to mitigate interference and enhance signal detection performance.