Low-Complexity Pareto-Optimal 3D Beamforming for the Full-Dimensional Multi-User Massive MIMO Downlink

TL;DR

This paper proposes a low-complexity 3D beamforming method for multi-user massive MIMO systems that outperforms traditional 2D beamforming and approaches full-dimensional performance, with some cases surpassing full-dimensional beamforming.

Contribution

Introduction of a new class of FD beamforming based on the sum of two outer products, offering reduced complexity and improved performance over existing methods.

Findings

Outperforms 2D beamforming relying on a single outer product.

Approaches the performance of full-dimensional beamforming in key metrics.

Can be outperformed by improper Gaussian signaling in some cases.

Abstract

Full-dimensional (FD) multi-user massive multiple input multiple output (m-MIMO) systems employ large two-dimensional (2D) rectangular antenna arrays to control both the azimuth and elevation angles of signal transmission. We introduce the sum of two outer products of the azimuth and elevation beamforming vectors having moderate dimensions as a new class of FD beamforming. We show that this low-complexity class is capable of outperforming 2D beamforming relying on the single outer product of the azimuth and elevation beamforming vectors. It is also capable of performing close to its FD counterpart of massive dimensions in terms of either the users minimum rate or their geometric mean rate (GM-rate), or sum rate (SR). Furthermore, we also show that even FD beamforming may be outperformed by our outer product-based improper Gaussian signaling solution. Explicitly, our design is based on low-complexity algorithms relying on convex problems of moderate dimensions for max-min rate optimization or on closed-form expressions for GM-rate and SR maximization.