Precoder Design for Massive MIMO Downlink with Matrix Manifold Optimization

TL;DR

This paper introduces a matrix manifold optimization framework for designing weighted sum-rate maximization precoders in massive MIMO downlink systems, effectively handling various power constraints with reduced computational complexity.

Contribution

It develops a unified Riemannian manifold approach for precoder design under different power constraints, transforming the problem into an unconstrained optimization on manifolds.

Findings

Riemannian methods outperform traditional algorithms in computational efficiency.

Proposed algorithms achieve higher sum-rate performance.

Framework is adaptable to multiple power constraint scenarios.

Abstract

We investigate the weighted sum-rate (WSR) maximization linear precoder design for massive multiple-input multiple-output (MIMO) downlink. We consider a single-cell system with multiple users and propose a unified matrix manifold optimization framework applicable to total power constraint (TPC), per-user power constraint (PUPC) and per-antenna power constraint (PAPC). We prove that the precoders under TPC, PUPC and PAPC are on distinct Riemannian submanifolds, and transform the constrained problems in Euclidean space to unconstrained ones on manifolds. In accordance with this, we derive Riemannian ingredients, including orthogonal projection, Riemannian gradient, Riemannian Hessian, retraction and vector transport, which are needed for precoder design in the matrix manifold framework. Then, Riemannian design methods using Riemannian steepest descent, Riemannian conjugate gradient and Riemannian trust region are provided to design the WSR-maximization precoders under TPC, PUPC or PAPC. Riemannian methods do not involve the inverses of the large dimensional matrices during the iterations, reducing the computational complexities of the algorithms. Complexity analyses and performance simulations demonstrate the advantages of the proposed precoder design.