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Inspired by recent advances in multiple-input multiple-output (MIMO) radar, we apply orthogonal phase coded waveforms to MIMO radar system in order to gain better range resolution and target direction finding performance. We provide and investigate a generalized MIMO radar system model using orthogonal phase coded waveforms. In addition, we slightly modify the system model to improve the system performance. Accordingly, we propose the concept and the design methodology for a set of ternary phase coded waveforms that is the optimized punctured zero correlation zone (ZCZ) sequence-pair set (ZCZPS). We also study the MIMO radar ambiguity function of the system using phase coded waveforms, based on which we analyze the properties of our proposed phase coded waveforms which show that better range resolution could be achieved. In the end, we apply our proposed codes to the two MIMO radar system models and simulate their target direction finding performances. The simulation results show that the first MIMO radar system model could obtain ideal target direction finding performance when the number of transmit antennas is equal to the number of receive antennas. The second MIMO radar system model is more complicated but could improve the direction finding performance of the system.