In this paper, we propose an attractive method to jointly design discrete phase radar sequence and receive Doppler filter with the aim of enhancing Signal to Interference and Noise Ratio (SINR) in a cognitive radar system. Towards this, we consider minimizing the output power of interference under Capon constraint, when transmitting $M$-ary Phase Shift Keying (MPSK) sequences. This minimization results in a multi-variable and non-convex optimization problem. To tackle the problem we propose an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) to optimize the Doppler filter and waveform alternatively. The problem with respect to filter is convex enabling a closed-form solution, while the problem is non-convex with regards to the waveform. We propose a Coordinate Descent (CD) framework to address this aspect and illustrate some numerical results.