Monte Carlo Simulation of M=4 PSK Communication System

This experiment conducts Monte Carlo simulation of M=4 PSK communication system to analyze BPSK and 4PSK modulation performance over Gaussian channels and compare with theoretical results. Implementation details include: The simulation employs MATLAB's random number generator for bit sequence creation, with BPSK mapping bits to ±1 symbols and 4PSK using QPSK constellation points (phase shifts of 0°, 90°, 180°, 270°). AWGN channel implementation uses randn() function for noise generation with variance calculated from SNR. Performance curves include theoretical error probability plots using Q-function for BPSK and approximate expressions for 4PSK, alongside empirical curves from Monte Carlo trials. The simulation repeats each SNR point 10,000+ times for statistical reliability. SNR ranges are set as BPSK (0dB-10dB) and 4PSK (0dB-14dB) with 1dB increments, allowing early termination when BER approaches 10^-6. SNR calculation follows: SNR=10log(Es/N0)=10log(REb/N0), where R represents code rate. Key functions include symbol mapping/demapping modules, correlation-based detectors, and error counting modules comparing decoded symbols with original bit sequences. The simulation architecture ensures proper Eb/N0 scaling relationship between modulation schemes.