Abstract: Binary Phase Shift Keying (BPSK) represents a fundamental modulation technique extensively utilized within digital communication systems. The present study presents an analytical examination of BPSK modulation, with a specific focus on its theoretical aspects, MATLAB implementation, and performance analysis. The article commences by providing an introduction to modulation techniques and a concise overview of BPSK, emphasizing its significance and applications. Theoretical foundations encompassing the mathematical representation, key parameters, and characteristics of BPSK are thoroughly deliberated upon. Performance metrics, namely the bit error rate (BER) and signal-to-noise ratio (SNR), are scrutinized, incorporating theoretical derivations and analysis. Following this, the implementation of BPSK modulation and demodulation in MATLAB is expounded, supplemented by coding algorithms and code snippets. Empirical results acquired from the MATLAB implementation are presented and scrutinized, alongside a comparison to the theoretical analysis. The article concludes by summarizing the principal findings and contributions, accentuating the advantages and limitations associated with BPSK modulation, and suggesting potential avenues for future research within this domain. By concentrating on the theoretical aspects and providing comprehensive derivations and mathematical analysis, this research enhances our understanding and exploration of BPSK modulation, thereby circumventing the reliance on simulation-based methodologies
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