MIMO radar plays a key role in autonomous driving, and the similarity waveform constraint is an important constraint for radar waveform design. However, the joint constant-modulus and similarity constraint is a difficult constraint. Only the special case with $\infty$-norm similarity and constant-modulus constraints is tackled by the semidefinite relaxation (SDR) and the successive quadratic refinement (SQR) methods. In this paper, the joint constant-modulus and any p-norm (1<= p<=$\infty$) similarity constraint is tackled by the proposed relax-and-retract algorithm. In particular, the nonconvex constant-modulus constraint is first relaxed to convex constraint, and then the retract operation is guaranteed to recover a constant-modulus solution within a fixed iteration number. Extensive simulation results show that full range similarity control and constant-modulus constraints are satisfied under different $p$-norms. For the special case with $1$-norm, it is firstly found to be a constant-modulus-inducing norm. For the special case with $\infty$-norm, the proposed relax-and-retract method has less computational time than the SDR and SQR methods.
Shenzhen University, Hanshan Normal University, China. May/2021.