Sun, RuiWang, ChenLu, An-AnGao, XiqiXia, Xiang-Gen2024-05-212024-05-212024-02-12R. Sun, C. Wang, A. -A. Lu, X. Gao and X. -G. Xia, "Precoder Design for Massive MIMO Downlink With Matrix Manifold Optimization," in IEEE Transactions on Signal Processing, vol. 72, pp. 1065-1080, 2024, doi: 10.1109/TSP.2024.3364914.1941-0476https://udspace.udel.edu/handle/19716/34419This article was originally published in IEEE Transactions on Signal Processing. The version of record is available at: https://doi.org/10.1109/TSP.2024.3364914. © 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. See https://www.ieee.org/publications/rights/index.html for more information. This article will be embargoed until 02/12/2026.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.en-USlinear precodingmanifold optimizationper-antenna power constraintper-user power constrainttotal power constraintweighted sum-rateArticle