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This paper studies the performance and design of high speed railway (HSR) communication systems that employ a large number of antennas at both the transmitter and re ceiver. User on board a train communicate with the BS by using distributed antennas mounted on top of the train as a gateways. One of the main challenges in HSR system design is the fast time-varying fading, the estimation and tracking of which demand large overheads in terms of pilot systems, especially for systems with a large number of transmit antennas. We derive an analytical uplink ergodic capacity by considering a large number of system parameters, such as large scale and small scale channel propagations, the percentage of pilot symbols among the transmitted symbols, the overhead caused by hardware consumptions, and the geometric configuration of the train, etc.In recognition of the fact that more transmit antennas means a higher multiplexing gain or diversity gain but more overhead, we identify the optimum number of transmit antennas by using the analytical results. Both analytical and simulation results demonstrate that less transmit antennas should be used at higher speed.Index Terms-Distributed MIMO (D-MIMO), high speed rail way, uplink capacity

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