The fifth generation (5G) wireless communication is currently a hot research topic and wireless communication systems on high speed railways (HSR) are important ap-plications of 5G technologies. Existing stud-ies about 5G wireless systems on high speed railways (HSR) often utilize ideal channel parameters and are usually based on simple scenarios. In this paper, we evaluate the down-link throughput of 5G HSR communication systems on three typical scenarios including urban, cutting and viaduct with three different channel estimators. The channel parameters of each scenario are generated with tapped delay line (TDL) models through ray-tracing sim-ulations, which can be considered as a good match to practical situations. The channel estimators including least square (LS), linear minimum mean square error (LMMSE), and our proposed historical information based ba-sis expansion model (HiBEM). We analyze the performance of the HiBEM estimator in terms of mean square error (MSE) and evaluate the system throughputs with different channel es-timates over each scenario. Simulation results are then provided to corroborate our proposed studies. It is shown that our HiBEM estimator outperforms other estimators and that the sys-tem throughput can reach the highest point in the viaduct scenario.