The high-speed of train (HST) in combination with the high carrier frequency of HST systems leads to the severe inter carrier interference (ICI) in the HST orthogonal frequency division multiplexing (HST-OFDM) systems. To avoid the complexity in OFDM receiver design for ICI eliminations, the OFDM system parameters such as symbol duration, signal bandwidth, and the number of subcarriers should be chosen appropriately. This paper aims to propose a process of HST-OFDM system performance investigation to determine these parameters in order to enhance spectral efficiency and meet a given quality-of-service (QoS) level. The signal-to-interference-plus-noise ratio (SINR) has been used as a figure of merit to analyze the system performance instead of signal-to-noise ratio (SNR) as most of recent research studies. Firstly, using the non-stationary geometry-based stochastic HST channel model, the SINR of each subcarrier has been derived for different speeds of the train, signal bandwidths, and number of subcarriers. Consequently, the system capacity has been formulated as the sum of all the single channel capacity from each sub-carrier. The constraints on designing HST-OFDM system parameters have been thoughtfully analyzed using the obtained expressions of SINR and capacity. Finally, by analyzing the numerical results, the system parameters can be found for the design of HST-OFDM systems under different speeds of train. The proposed process can be used to provide hints to predict performance of HST communication systems before doing further high cost implementations as hardware designs