We investigate the weighted sum-rate (WSR) maximization linear precoder design for massive MIMO downlink 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). Particularly, we prove that the precoders under TPC, PUPC and PAPC are on different 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 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 are free of the inverse of large dimensional matrix, which is of great significance for practice. Complexity analysis and performance simulations demonstrate the advantages of the proposed precoder design.
翻译:----
基于矩阵流形优化的大规模MIMO预编码器设计
Translated abstract:
本文研究了大规模MIMO下行链路的加权和速率(WSR)最大化线性预编码器设计,并提出了适用于总功率约束(TPC)、每用户功率约束(PUPC)和每天线功率约束(PAPC)的统一矩阵流形优化框架。特别地,我们证明了TPC、PUPC和PAPC下的预编码器处于不同的黎曼子流形上,并将欧几里得空间中的约束问题转化为流形上的无约束问题。应此,我们推导出欲在流形框架中设计预编码器所需的黎曼因素,包括正交投影、黎曼梯度、黎曼海森、回退和向量传输。然后,我们提供了在流形上设计WSR最大化预编码器的黎曼方法,包括黎曼最速降(Riemannian steepest descent)、黎曼共轭梯度(Riemannian conjugate gradient)和黎曼信任域(Riemannian trust region)方法。黎曼方法不涉及高维矩阵求逆,这在实践中具有重要意义。复杂度分析和性能模拟表明了所提出的预编码器设计的优越性。