Ellipsoidal Manifold Optimization for Distributed Antenna Beamforming

2026-03-24

AI Summary

This work addresses the weighted sum-rate maximization problem under per-cluster power constraints in downlink distributed antenna systems. By exploiting the fact that optimal beamformers lie in the low-dimensional subspace spanned by the channels of their respective antenna clusters, the original high-dimensional constrained optimization problem is reformulated—for the first time—as an unconstrained optimization over a product of ellipsoidal manifolds. The authors systematically develop the Riemannian geometry of this manifold, including its tangent space, metric, projection, and retraction operators, and design a tailored Riemannian conjugate gradient algorithm. The proposed method achieves solution quality comparable to that of WMMSE and conventional manifold-based approaches while significantly improving computational efficiency and scalability, with pronounced advantages as the number of antenna clusters increases.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper addresses the weighted sum-rate (WSR) maximization problem in a downlink distributed antenna system subject to per-cluster power constraints. This optimization scenario presents significant challenges due to the high dimensionality of beamforming variables in dense antenna deployments and the structural complexity of multiple independent power constraints. To overcome these difficulties, we generalize the low-dimensional subspace property--previously established for sum-power constraints--to the per-cluster power constraint case. We prove that all stationary-point beamformers reside in a reduced subspace spanned by the channel vectors of the corresponding antenna cluster. Leveraging this property, we reformulate the original high-dimensional constrained problem into an unconstrained optimization task over a product of ellipsoidal manifolds, thereby achieving significant dimensionality reduction. We systematically derive the necessary Riemannian geometric structures for this specific manifold, including the tangent space, Riemannian metric, orthogonal projection, retraction, and vector transport. Subsequently, we develop a tailored Riemannian conjugate gradient algorithm to solve the reformulated problem. Numerical simulations demonstrate that the proposed algorithm achieves the same local optima as standard benchmarks, such as the weighted minimum mean square error (WMMSE) method and conventional manifold optimization, but with substantially higher computational efficiency and scalability, particularly as the number of antenna clusters increases.

Problem

• weighted sum-rate maximization
• distributed antenna system
• per-cluster power constraints
• beamforming
• downlink

Innovation

• Ellipsoidal manifold optimization
• Distributed antenna systems
• Weighted sum-rate maximization
• Riemannian conjugate gradient
• Per-cluster power constraints