Precoder Design for User-Centric Network Massive MIMO With Matrix Manifold Optimization

2024-04-11

IEEE Journal on Selected Areas in Communications

AI Summary

This paper addresses the precoding design problem for user-centric networking (UCN) massive MIMO downlink systems under per-base-station power constraints. We propose a low-complexity Riemannian manifold optimization framework. First, we rigorously establish that the set of feasible precoding matrices satisfying all individual base station power constraints forms a Riemannian submanifold embedded in a linear product manifold. Leveraging this geometric structure, we reformulate the constrained optimization problem as an unconstrained one on the manifold. Then, we develop a Riemannian conjugate gradient (RCG) algorithm that avoids large matrix inversions—employing orthogonal projection, retraction, and vector transport for efficient iteration. Compared with conventional methods, the proposed approach significantly reduces computational complexity by eliminating high-dimensional matrix inversions. Simulation results demonstrate superior spectral efficiency and faster convergence, thereby enhancing both the practicality and performance of UCN-based massive MIMO systems.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In this paper, we investigate the precoder design for user-centric network (UCN) massive multiple-input multiple-output (mMIMO) downlink with matrix manifold optimization. In UCN mMIMO systems, each user terminal (UT) is served by a subset of base stations (BSs) instead of all the BSs, facilitating the implementation of the system and lowering the dimension of the precoders to be designed. By proving that the precoder set satisfying the per-BS power constraints forms a Riemannian submanifold of a linear product manifold, we transform the constrained precoder design problem in Euclidean space to an unconstrained one on the Riemannian submanifold. Riemannian ingredients, including orthogonal projection, Riemannian gradient, retraction and vector transport, of the problem on the Riemannian submanifold are further derived, with which the Riemannian conjugate gradient (RCG) design method is proposed for solving the unconstrained problem. The proposed method avoids the inverses of large dimensional matrices, which is beneficial in practice. The complexity analyses show the high computational efficiency of RCG precoder design. Simulation results demonstrate the numerical superiority of the proposed precoder design and the high efficiency of the UCN mMIMO system.

Problem

• Design precoders for user-centric network massive MIMO systems.
• Transform constrained precoder design to unconstrained Riemannian submanifold optimization.
• Propose efficient Riemannian conjugate gradient method for precoder design.

Innovation

• Matrix manifold optimization for precoder design
• Riemannian conjugate gradient method avoids large matrix inverses
• User-centric network reduces precoder dimension complexity