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.

翻译：本文研究基于矩阵流形优化的用户中心网络大规模多输入多输出下行链路预编码器设计。在UCN mMIMO系统中，每个用户终端由基站子集而非全部基站提供服务，这降低了系统实现复杂度并缩减了待设计预编码器的维度。通过证明满足每基站功率约束的预编码器集合构成线性乘积流形的一个黎曼子流形，我们将欧氏空间中的约束预编码设计问题转化为该黎曼子流形上的无约束问题。进一步推导了该黎曼子流形上的黎曼几何要素，包括正交投影、黎曼梯度、收缩映射与向量传输，在此基础上提出黎曼共轭梯度设计方法以求解无约束问题。所提方法避免了大维矩阵求逆运算，具有实际应用优势。复杂度分析表明RCG预编码器设计具有较高的计算效率。仿真结果验证了所提预编码器设计的数值优越性及UCN mMIMO系统的高效性。