Considering a nonlinear high power amplifier(HPA) and a predistorter, we have designed a four-dimensional 8-ary phase shift keying trellis-coded modulation(4D-8PSK-TCM) system, which is recommended for X-band satellite communications. Subsequently, we have evaluated and analyzed the spectrum, constellation characteristics, and BER performance of the system. In satellite communications, owing to the limited power, nonlinear characteristics that determine the operating point of the HPA must be analyzed because the HPA consumes high power. We herein report the design of the 4D-8PSK-TCM system, with efficiencies of 2 and 2.25 bits/channel-symbol. The simulation results confirmed that a 0.35 roll-off value is effective, considering the low peak-to-average power ratio(PAPR) characteristic and the narrow occupation bandwidth of the spectrum. It also confirmed that approximately 15~20 dB of output backoff(OBO) value is required at the HPA when the predistorter is not used, and approximately 1 dB of the OBO value is required when the predistorter is used.