Impact of Doppler shift error on least-squares MIMO channel estimation for high-speed railway

Owing to the availability of Doppler shift measurement and the existence of dominant line-of-sight (LOS) path in high-speed railway (HSR) communications, Doppler shift is often pre-compensated on the received signal before performing further processing. In this study, the authors address the impact of erroneous Doppler shift measurement on the tracking performance of least-squares multiple-input multiple-output (MIMO) channel estimation for HSR. The closed-form tracking mean-square error (MSE) is derived over time-varying Rician fading channel assuming Gaussian distributed Doppler shift measurement. By transforming the Gaussian distributed measurement into its characteristic function and performing approximations with practical considerations, the tracking MSE of the approach with Doppler shift pre-compensation is written as a function of that with no pre-compensation, contributed from the previous research. Accordingly, they are able to develop a simple relation between MSE gain and MSE loss for channels with dominant LOS path. It is revealed that erroneous Doppler shift measurement impacts stronger LOS or faster time-varying channel more severely. However, if the measurement is perfect, the presence of a dominant LOS path provides tremendous gain approximately equal to the Rician factor in high signal-to-noise ratio (SNR) regime.