Simulation of 2x2 MIMO System with Water-Filling Theorem Implementation

In this document, I provide a detailed explanation of the 2x2 MIMO simulation and the water-filling theorem implementation. First, let's understand the fundamentals of MIMO technology. MIMO, which stands for Multiple-Input Multiple-Output, is a wireless communication technique that utilizes multiple antennas for simultaneous data transmission and reception. The 2x2 configuration specifically refers to a MIMO system employing 2 transmit antennas and 2 receive antennas, which can be implemented in code through channel matrix initialization and signal processing operations.

Next, we explore the water-filling theorem concept with implementation details. The water-filling theorem is a fundamental principle in information theory that determines the optimal power allocation strategy to achieve maximum channel capacity in bandwidth-limited communication channels. In our simulation code, this is typically implemented through eigenvalue decomposition of the channel matrix and iterative power distribution algorithms that assign more power to subchannels with better signal-to-noise ratios.

This documentation includes comprehensive simulation results for the 2x2 MIMO system, demonstrating how the water-filling algorithm can be programmed using matrix operations and optimization techniques. The implementation typically involves calculating channel capacity through singular value decomposition and applying the water-filling solution using convex optimization methods. These technical insights will help you better understand both the theoretical concepts and practical implementation of MIMO systems and the water-filling theorem in modern wireless communications.