Block-Diagonalization-Based Precoding Algorithm

This document presents a comprehensive implementation of a block-diagonalization-based precoding algorithm, which comprises three core components: bit error rate calculation, encoding procedures, and likelihood decoding methods. The algorithm utilizes matrix decomposition techniques to transform the channel matrix into block-diagonal form, effectively eliminating inter-user interference in multi-user MIMO systems. The implementation includes numerical methods for computing the bit error rate (BER) through Monte Carlo simulations, where transmitted symbols are compared with received symbols after applying the precoding matrix. The encoding process involves constructing the precoding matrix using singular value decomposition (SVD) or similar matrix factorization techniques to achieve channel diagonalization. The likelihood decoding module employs maximum likelihood detection algorithms to optimize symbol recovery from noise-affected signals. This precoding optimization technique significantly reduces bit error rates in data transmission by exploiting channel state information to pre-compensate for channel distortions. The algorithm's adaptive nature allows for optimization across various communication environments, accommodating different channel characteristics and network conditions through parameter tuning and threshold adjustments. With its robust performance and flexibility, this algorithm demonstrates substantial application potential in wireless communications, data transmission systems, and related fields where reliable signal processing is critical.