Bit Error Rate Analysis of BPSK Modulation over AWGN and Rayleigh Fading Channels

This study focuses on calculating the Bit Error Rate (BER) of Binary Phase Shift Keying (BPSK) modulation over both Additive White Gaussian Noise (AWGN) and Rayleigh Fading channels. In communication systems, Bit Error Rate serves as a crucial performance metric that quantifies the probability of errors occurring in received signals at the receiver end. BPSK represents a fundamental modulation scheme widely employed in digital communication systems due to its simplicity and robustness. The AWGN channel models an ideal communication scenario characterized by Gaussian noise, while the Rayleigh Fading channel simulates real-world multipath propagation conditions commonly encountered in wireless communications. Through computational analysis of BPSK performance across these channel models, we can evaluate its behavioral characteristics under different environmental conditions and implement necessary optimizations and improvements. Implementation typically involves MATLAB simulations using key functions such as: - awgn() for adding Gaussian noise to transmitted signals - rayleighchan() for creating Rayleigh fading channel objects - biterr() for comparing transmitted and received bits to calculate BER - Monte Carlo simulations for statistical averaging of error rates The theoretical BER for BPSK in AWGN follows Q(sqrt(2*Eb/N0)), while Rayleigh fading requires integration over the fading distribution, typically resulting in closed-form expressions involving exponential functions and signal-to-noise ratios.