When Is the Achievable Rate Region Convex in Two-User Massive MIMO Systems?

TL;DR

This paper analyzes the convexity of the achievable rate region in two-user Massive MIMO systems under Rayleigh fading and LoS conditions, providing conditions for when spatial multiplexing or orthogonal scheduling is optimal.

Contribution

It proves the convexity of the rate region under Rayleigh fading and identifies conditions affecting convexity in LoS scenarios based on system parameters.

Findings

Rate region is convex under Rayleigh fading.

Convexity in LoS depends on angular separation, antenna count, and SNR.

Spatial multiplexing is preferable when the region is convex.

Abstract

This letter investigates the achievable rate region in Massive multiple-input-multiple-output (MIMO) systems with two users, with focus on the i.i.d.~Rayleigh fading and line-of-sight (LoS) scenarios. If the rate region is convex, spatial multiplexing is preferable to orthogonal scheduling, while the opposite is true for non-convex regions. We prove that the uplink and downlink rate regions with i.i.d.~Rayleigh fading are convex, while the convexity in LoS depends on parameters such as angular user separation, number of antennas, and signal-to-noise ratio (SNR).