The Society of Automotive Engineers (SAE) emphasizes that radars have become a critical technology. With the consideration of application scenarios and cost, increasing importance has been attributed to millimeter Wave (mmWave) radars. Because of the unique features of simultaneous detection and communication, Orthogonal Frequency- Division Modulation (OFDM) radars have been discussed frequently in the literature. In this paper, under the architecture of an OFDM radar, we propose a novel protocol which divides different radar users (i.e., different vehicles) into different logical channels by time and frequency. Following the rules of the protocol, a non- cooperative interference avoidance logical channel selection method is also proposed to choose a logical channel with the least inter-carrier interferences (ICIs). Simulation results show that the proposed logical channel selection method can choose a nearly optimal channel in a short time with a high probability.