BER Performance for BPSK in ISI Channel with MMSE Equalization Analysis

This document discusses the performance of BPSK signal transmission through ISI-impaired channels using MMSE equalization technology, where BER serves as a critical metric for analysis. The implementation typically involves modeling the ISI channel using finite impulse response (FIR) filters and designing MMSE equalizers through statistical signal processing approaches. Key MATLAB functions like `lscov` or custom matrix inversion algorithms can be employed to compute equalizer weights by solving the Wiener-Hopf equation (R_xx * w = R_xy), where R_xx represents the autocorrelation matrix of received signals and R_xy denotes the cross-correlation between transmitted and received symbols. We further explore the fundamental principles of MMSE equalization and examine how BPSK signal transmission is affected by ISI channels, characterized by parameters such as delay spread and channel impulse response. The discussion includes comparative analysis between MMSE equalization and alternative techniques (e.g., Zero-Forcing, Decision Feedback Equalizers) regarding their computational complexity, robustness to noise enhancement, and performance under varying channel conditions characterized by different signal-to-noise ratios (SNRs) and multipath profiles. Through comprehensive understanding of these aspects, we can better optimize BPSK transmission performance in interference-prone environments using techniques like adaptive filter tuning and channel estimation algorithms.