MMSE Multiuser Receiver Design for Uniformly Quantized Synchronous CDMA Systems

This project conducts comprehensive analysis and design of a minimum mean-square error (MMSE) multiuser receiver for uniformly quantized synchronous code division multiple access (CDMA) signals operating in additive white Gaussian noise (AWGN) channels. The core methodology employs a gain-plus-additive-noise model to represent uniform quantization, enabling systematic algorithm development through numerical computation. Using this model, we derive the MMSE receiver's weight vector via matrix inversion operations (e.g., implementing Wiener solution through MATLAB's inv() or pinv() functions) and calculate the output signal-to-interference ratio (SIR) to quantify performance metrics.

A critical investigation focuses on quantization effects on MMSE receiver performance, characterized through a single parameter termed "equivalent noise variance." This parameter is computed algorithmically by analyzing quantization error statistics, allowing performance degradation assessment through Monte Carlo simulations. Furthermore, we determine the optimal quantizer stepsize that maximizes the MMSE receiver's output signal-to-noise ratio (SNR) using gradient-based optimization techniques (e.g., fminsearch in MATLAB), ensuring peak system performance under constrained quantization resolution.

Through rigorous theoretical analysis supported by numerical simulations implementing the gain-plus-additive-noise model, this research provides significant contributions to MMSE receiver design for uniformly quantized synchronous CDMA systems in AWGN environments, with verifiable results through reproducible code implementations.