The application of the Maximum Likelihood Estimation principle in communication systems

Abstract

This paper examines the application of Maximum Likelihood Estimation (MLE) in digital communication systems, with particular emphasis on Binary Phase Shift Keying (BPSK) modulation. The discussion opens with an overview of MLE fundamentals and its asymptotic properties—consistency and efficiency—that establish its suitability for optimal signal detection. The central contribution lies in the derivation of an MLE-based detection algorithm for BPSK transmission over an Additive White Gaussian Noise (AWGN) channel, yielding a transparent optimal decision rule. To substantiate the theoretical framework, a full-scale MATLAB R2024b simulation was developed and executed. The simulation encompasses the complete baseband BPSK transceiver: pulse shaping, carrier modulation, AWGN channel impairment, coherent demodulation, and matched filtering. Performance assessment involves comparing empirically measured Bit Error Rate (BER) against theoretical predictions across varying signal-to-noise ratios. The findings indicate that empirical BER approaches the theoretical bound as the number of simulated bits grows, confirming both the validity and practical efficacy of the derived MLE algorithm. These results underscore the continued relevance of MLE in communication signal detection and furnish a concrete reference for both instructional and engineering contexts.