Abstract: Aiming at the problem of cross interference between automotive frequency modulated continuous wave radars, a interference mitigation method based on CFAR-ProxSGD is proposed in this paper. Firstly, the radar received signal with interference is converted to time-frequency domain by short-time Fourier transform. The one-dimensional CFAR detector along each frequency point is used to detect the interference position and the amplitude correction method is used to initially suppress the interference. Then, combining the time-domain sparsity of the interference signal and the frequency-domain sparsity of the target echo, the residual interference is iteratively optimized by using the proximal subgradient descent method, and the interference signal is ultimately eliminated and the signal is reconstructed. To verify the performance of the algorithm, numerical simulations in multi-target and multi-interference source scenarios were conducted on the software platform, and real measurement data were obtained based on the AWR1843 millimeter-wave radar and DCA1000 data acquisition system. The experimental results show that the proposed algorithm can effectively suppress the interference signal, reduce the frequency-domain background noise and improve the target detection capability of the millimeter-wave radar system in the traffic environment.