The Derivation of The Probability of Error for BPSK, 16-QAM and 64-QAM in Rayleigh Fading Channel: A Unified Approach

Understanding the probability of error is paramount in the design and analysis of digital communication systems, particularly in Rayleigh fading channels where signal impairments are prevalent. This article presents a unified approach for deriving the probability of error formulations applicable to Binary Phase Shift Keying (BPSK), 16-Quadrature Amplitude Modulation (16-QAM), and 64-QAM in Rayleigh fading channels. This article presents a general approach to derive the probability of error formulations applicable to Binary Phase Shift Keying (BPSK), 16-Quadruple Amplitude Modulation (16-QAM) and 64-QAM in Rayleigh fading channels. The derivation process encompasses the unique characteristics of each modulation scheme and the statistical properties of Rayleigh fading providing a comprehensive framework to analyze error performance. By establishing a unified formulation, this approach simplifies the analysis and facilitates a deeper understanding of error probability behavior across different modulation schemes. The derived formulations offer insights into the impact of fading-induced impairments on system performance, allowing for accurate prediction and optimization of communication systems in real-world fading environments. The insights and techniques presented herein serve as a valuable resource for researchers, engineers, and practitioners engaged in the design and optimization of communication systems operating in challenging fading environments.