Monte Carlo Simulation of 4PSK Communication System

The Monte Carlo simulation requirements for the 4PSK communication system are as follows: First, generate and plot the four distinct phase modulation waveforms of 4PSK signals. This involves implementing a phase modulator that maps two-bit symbols (00, 01, 10, 11) to four equally spaced phases (0°, 90°, 180°, 270°) using trigonometric functions or complex exponential representations. Second, assuming an additive white Gaussian noise channel with zero mean and unit variance, simulate the transmission of 1000 symbols under different signal-to-noise ratio conditions and plot the Monte Carlo results. The implementation should include: generating random symbols, applying phase modulation, adding Gaussian noise using randn() function, implementing a maximum likelihood demodulator, and calculating error statistics. For the graphical representation, use signal-to-noise ratio (SNR) as the x-axis and bit error rate (BER) as the y-axis. The plot must display both the actual measured bit error rate (obtained through simulation counting) and the theoretical bit error rate (calculated using Q-function formulas for PSK systems). The simulation should be programmed using MATLAB or equivalent software tools, incorporating proper vectorization techniques for efficient Monte Carlo trials and statistical averaging across multiple noise realizations for each SNR point.