Matrix Manifold Precoder Design for Massive MIMO High-Speed Railway Communications with Channel Prediction

In high-speed railway (HSR) communications, the channel suffers from severe channel aging effect caused by the high mobility. To address this issue, we investigate the precoder design against channel aging in massive multiple-input multiple-output (MIMO) systems with channel prediction. First of all, we introduce the concept of the quadruple beams (QBs), and establish a QB based channel model with sampled quadruple steering vectors. Then, the upcoming space domain channel can achieve a higher accuracy by channel prediction. We consider the precoder design on the Riemannian submanifold formed by the precoders satisfying the total power constraint (TPC). The Riemannian conjugate gradient (RCG) method is proposed to solve the problem on the manifold. The RCG method mainly involves the matrix multiplication and avoids the need of matrix inversion of the transmit antenna dimension. The simulation results demonstrate the effectiveness of the proposed channel model and the superiority of the RCG method for precoder design against channel aging.