Power-space functions in high speed railway wireless communications

To facilitate the base station planning in high speed railway communication systems, it is necessary to consider the functional relationships between the base station transmit power and space parameters such as train velocity and cell radius. Since these functions are able to present some inherent system properties determined by its spatial topology, they will be referred to as the power-space functions in this paper. In light of the fact that the line-of-sight path persists the most power of the received signal of each passing train, this paper considers the average transmission rate and bounds on power-space functions based on the additive white Gaussian noise channel (AWGN) model. As shown by Monte Carlo simulations, using AWGN channel instead of Rician channel introduces very small approximation errors, but a tractable mathematical framework and insightful results. Particularly, lower bounds and upper bounds on the average transmission rate, as well as transmit power as functions of train velocity and cell radius are presented in this paper. It is also proved that to maintain a fixed amount of service or a fixed average transmission rate, the transmit power of a base station needs to be increased exponentially, if the train velocity or cell radius is increased, respectively.