Location-Aided Mm Wave Train-to-Ground Beam Alignment: Optimal Beamformers and Performance Bounds.

The millimeter-wave (mmWave) train-to-ground (T2G) communications is an essential enabling technology for future intelligent railways, where the acquisition of beam alignment information is one of the most challenging and significant issues. Hence, in this paper, we investigate the optimal beamformers and performance bounds for the mmWave T2G beam alignment with the aid of train location information. We first propose a mmWave T2G system model, which can be used by arbitrary array geometry and identifies a clear relationship between the T2G scenario and the wireless channel. Then, based on the Cramer Rao bound (CRB), we provide two bounds characterizing the average and worst minimum mean square error (MMSE) of beam alignment with the bounded error model of train location. Next, two non-convex optimization problems are formulated aiming to find the transmitting beamformers that can minimize the bounds, which is solved optimally by relaxation and recovery techniques. Finally, numerical simulations are conducted to validate the proposed beamformers and bounds for the mmWave T2G beam alignment. In particular, the results show that the MSE performance of optimal beamformers converges to the bounds by applying the maximum likelihood estimator (MLE) in the high SNR regime.