Precoder Design for Massive MIMO Downlink with Matrix Manifold Optimization

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...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 72; pp. 1 - 15
Main Authors: Sun, Rui, Wang, Chen, Lu, An-An, Gao, Xiqi, Xia, Xiang-Gen
Format: Journal Article
Language:English
Published: New York IEEE 01.01.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Codes
Complexity theory
Constraints
Downlinking
Euclidean geometry
Euclidean space
Interference
Linear precoding
manifold optimization
Manifolds
Manifolds (mathematics)
Massive MIMO
Mathematical analysis
Matrices (mathematics)
Maximization
MIMO communication
Optimization
per-antenna power constraint
per-user power constraint
Signal to noise ratio
total power constraint
Transforms
weighted sum-rate
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2024.3364914