A Projected Gradient Descent Algorithm for Designing Low-Resolution Finite-Alphabet Equalizers in All-Digital Massive MU-MIMO Communication Systems

Incorporating low-resolution finite-alphabet equalizers into all-digital base station architectures is a promising approach to enhance energy efficiency and cost-effectiveness in massive multi-user multiple-input multiple-output uplink systems. These equalizers represent the spatial equalization matrix using low-resolution coefficients. However, designing these coefficients to achieve the desired bit error rate (BER) performance is a computationally challenging task that is classified as NP-hard. A previous study used Riemannian manifold optimization (RMO) to design a low-resolution spatial equalization matrix to address this challenge. Although the RMO-assisted equalizer provides excellent BER performance, it has high computational complexity and runtime. In this study, we propose a computationally efficient algorithm based on the projected gradient descent (PGD) framework to simultaneously reduce the computational time and complexity of the equalization algorithm while maintaining the same BER performance as the RMO-assisted equalizer. Our simulation results demonstrate that the proposed PGD-assisted equalizer achieves almost the same performance as the RMO-assisted equalizer with significantly lower computational complexity. Notably, the proposed PGD-based algorithm has a faster convergence rate than RMO, running approximately 151.75 times faster.