Generate Equiprobable Independent Binary Sequences and Plot Waveforms

This article presents a comprehensive implementation of digital communication system components through the following tasks:

1. Generate equiprobable independent binary sequences using random number generators (e.g., MATLAB's randi function with [0,1] parameters) and plot their time-domain waveforms using plotting functions like stem() or plot() to visualize the binary patterns.

2. Create additive Gaussian random noise with zero mean and unit variance using functions like randn() in MATLAB, which requires scaling by standard deviation (sqrt(variance)) to achieve the specified statistical properties.

3. Implement 8PSK modulation by mapping 3-bit symbol groups to phase shifts (0°, 45°, 90°, etc.) using constellation mapping, then plot the modulated waveforms showing both in-phase and quadrature components or the modulated carrier signal.

4. Perform Monte Carlo analysis by transmitting multiple random symbol sequences through simulated channels with noise, calculating error rates, and statistically evaluating system performance metrics like bit error rate (BER).

5. Demodulate 8PSK signals using phase detection algorithms (e.g., maximum likelihood detection) and plot eye diagrams by overlapping symbol periods using MATLAB's eyediagram() function to analyze timing synchronization and signal quality.

We will execute these steps systematically while documenting results at each stage. This analytical approach provides deeper insights into digital communication system characteristics and performance limitations.