Broad Coverage Precoding Design for Massive MIMO With Manifold Optimization

In this paper, we design the precoding matrix with broad coverage for massive multi-input multi-output public channels. In order to guarantee the efficient use of power amplifiers and improve the achievable ergodic rate, equal transmit power per-antenna and semi-unitary constraints on the precoding matrix are considered simultaneously. Within the framework of manifold optimization, the precoding matrix design under the above two constraints becomes an optimization problem over the intersection of the oblique manifold and the Stiefel manifold. We propose to use the steepest descent method on the intersection of these two manifolds to obtain the optimal solution. By using the alternating projections method, the search direction of the steepest descent method is derived. Meanwhile, the convergence analysis for the proposed approach is also provided. The proposed approach can be used for both omnidirectional and sector-shaped power pattern design. Simulation results show that the power pattern of our designed precoder has less variation in different spatial directions within the cell coverage compared with the existing Zadoff–Chu scheme.