Theoretical BER Performance of BPSK Coherent Demodulation in Single-Path Rayleigh Channel with Implementation Analysis

This document expands the original content while preserving core technical concepts through the following implementations: (1) We derive the theoretical BER performance for BPSK coherent demodulation in single-path Rayleigh channels, generating SNR-BER characteristic curves. The demodulation principle is explained with mathematical derivations showing how the BER formula P_b = 0.5*(1 - sqrt(γ/(1+γ))) is obtained for Rayleigh fading, where γ represents average SNR. Implementation involves using MATLAB's erf function and vectorized operations to compute theoretical values across SNR ranges from 0-30 dB, with plotting commands like semilogy() for logarithmic BER visualization. (2) We design a time-division pilot-assisted channel estimation scheme for single-path Rayleigh channel simulation. The Simulink model incorporates Rayleigh fading blocks, pilot insertion at predefined intervals, and LS (Least Squares) estimation algorithms. Key implementation includes configuring frame structure with 10% pilot overhead, using MATLAB Function blocks for channel estimation calculations, and employing Error Rate Calculation blocks for BER measurement. The comparative analysis involves running Monte Carlo simulations with 10^6 bits per SNR point, using hold on commands to overlay theoretical and practical curves on the same plot for performance gap assessment. Through these technical implementations, we enhance the original content with specific computational methods and simulation architectures while maintaining all critical theoretical foundations and analytical objectives.