Optimality of the Discrete Fourier Transform for Beamspace Massive MU-MIMO Communication

TL;DR

This paper investigates the optimality of the discrete Fourier transform (DFT) in beamspace processing for massive MU-MIMO systems at mmWave frequencies, proposing algorithms to learn optimal transforms and analyzing their performance.

Contribution

It introduces algorithms to learn unitary beamspace transforms based on sparsity measures and studies their optimality both theoretically and through simulations.

Findings

DFT can be optimal under certain conditions for beamspace processing.

Proposed algorithms effectively learn unitary transforms that enhance sparsity.

Theoretical analysis supports the optimality of learned transforms in ideal and realistic channels.

Abstract

Beamspace processing is an emerging technique to reduce baseband complexity in massive multiuser (MU) multiple-input multiple-output (MIMO) communication systems operating at millimeter-wave (mmWave) and terahertz frequencies. The high directionality of wave propagation at such high frequencies ensures that only a small number of transmission paths exist between user equipments and basestation (BS). In order to resolve the sparse nature of wave propagation, beamspace processing traditionally computes a spatial discrete Fourier transform (DFT) across a uniform linear antenna array at the BS where each DFT output is associated with a specific beam. In this paper, we study optimality conditions of the DFT for sparsity-based beamspace processing with idealistic mmWave channel models and realistic channels. To this end, we propose two algorithms that learn unitary beamspace transforms using an $\ell^4$-norm-based sparsity measure, and we investigate their optimality theoretically and via simulations.