Robust Precoder Design for Massive MIMO High-Speed Railway Communications With Matrix Manifold Optimization

In high-speed railway (HSR) communications, the channel suffers from severe Doppler and channel aging effects caused by the high mobility, making the channel outdated quickly. To address this issue, we investigate the robust precoder design against channel aging and prediction inaccuracy in massive multiple-input multiple-output (MIMO) systems with matrix manifold optimization. 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 of interest can achieve a higher accuracy by channel prediction with the estimated QB domain channel. To further improve the performance while save the pilot overhead, we predict the forthcoming QB domain channel and integrate the prediction inaccuracy within the a posterior QB domain statistical channel model. Then, we consider the robust precoder design aiming to maximize the upper bound of the ergodic weighted sum-rate (WSR) on the Riemannian submanifold formed by the precoders satisfying the total power constraint (TPC). Riemannian ingredients are derived for matrix manifold optimization, with which the Riemannian conjugate gradient (RCG) method is proposed to solve the unconstrained 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 robust precoder design against channel aging and prediction inaccuracy.