A sequential constraint relaxation framework to design phase-coded sequences for radar systems

In this paper, the design of phase-coded sequences with good aperiodic autocorrelation properties including peak sidelobe level and integrated sidelobe level for radar systems is considered. The problem is formulated as a rank-one constraint optimization at the design stage. To tackle the resulting non-convex and generally NP-hard optimization problem, an iterative algorithm is developed based on the sequential rank-one constraint relaxation framework, which guarantees a local optimal rank-one solution. The proposed method requires solving a convex problem in each iteration. The procedure can be initialized by dropping the rank-one constraint or using a good sequence in terms of autocorrelation properties. Simulation results show that using the proposed method for finding phase-coded sequences leads to better peak sidelobe ratio and integrated sidelobe ratio for polyphase and binary phase codes compared to previous works in the literature.