The downlink communication channel from high-altitude platform (HAP) to high-speed train (HST) in the Ka-band is a slowly time-varying Rician distributed flat fading channel with 10-25 dB Rician K factor. In this respect, the received signal is mainly affected by the Doppler shift of the line-of-sight (LOS) link. In order to increase receiver performance, we propose to firstly compensate the Doppler shift of the received signal before least-squares (LS) adaptive filtering is pursued. Implementing the proposed method requires a priori knowledge of the time-varying phase of the LOS component. This is justified since signalling between the train and the controller exists such that the train velocity and location are predictable. Implementing the proposed method to the recursive LS (RLS) received beamforming algorithm shows reduction of mean square error (MSE) and bit error rate (BER)
