MIMO radar design with joint constant-modulus and any p-norm similarity constraints

Abstract

MIMO radar plays a key role in many applications, e.g., autonomous driving, smart parking, and gesture recognition. The similarity waveform constraint is an important constraint for radar waveform design. However, the joint constant-modulus and similarity constraints pose a big challenge in MIMO radar design. Only the special case with ∞-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≤∞) similarity constraints are tackled by the proposed relax-and-retract algorithm. In particular, the nonconvex constant-modulus constraint is first relaxed to a 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 ∞-norm, the proposed relax-and-retract method has less computational complexity than the SDR and SQR approaches.