Open-Loop and Closed-Loop MIMO Channel Capacity Simulation with Water-Filling Algorithm

This simulation program calculates and compares the ergodic channel capacity of open-loop and closed-loop MIMO systems using the water-filling algorithm. The implementation models system performance under various antenna configurations (Nt x Nr MIMO setups) and channel state conditions. The water-filling algorithm optimizes power allocation across eigenchannels by solving the convex optimization problem: allocate more power to stronger subchannels while satisfying total power constraints. The simulation includes key functions for: - Generating random MIMO channel matrices with Rayleigh fading - Calculating singular value decomposition (SVD) for channel matrix decomposition - Implementing iterative water-filling power allocation across eigenmodes - Computing ergodic capacity through Monte Carlo averaging over channel realizations Open-loop systems (no channel state information at transmitter) and closed-loop systems (with perfect CSIT) represent two fundamental transmission schemes in wireless communications. By comparing their ergodic capacities under different SNR conditions and antenna configurations, researchers can evaluate their performance trade-offs. The water-filling algorithm enhances system capacity and robustness by optimally distributing transmission power, effectively "injecting" power into stronger channel dimensions. This simulation provides researchers with a powerful tool for analyzing and optimizing wireless communication system performance, featuring configurable parameters for antenna numbers, SNR ranges, and channel correlation settings. The code structure allows easy extension to include practical constraints like imperfect channel estimation or limited feedback scenarios.