Abstract: With the continuously expanding of the advanced electronic information system applications, the bandwidth requirements of radar and communication are increasing, and the working frequency bands are constantly overlapping. To this end, an important issue arises with regard to the competition of the spectrum resources. Some papers have proposed the concept of the joint waveform to share the spectrum. Following this concept, the OFDM waveforms have arouse as the potential solutions. However, due to impact of the high randomness and the periodic characteristics of OFDM-based wireless communication signals, the point spread function for the radar sensing contains high side lobes and numerous fake peaks. In this paper, the intrinsic drawbacks of the OFDM-based joint radar and communication waveforms are analyzed from the perspective of ambiguity function. Following which, a novel side-lobe suppression algorithm using the mismatching is proposed by moving the ambiguous energy outside the radar observation window. With the algorithm, it becomes possible to realize the wireless communication and the radar sensing in a shared time-frequency plane. Theoretical analysis is validated by simulations.