MIMO Radar Optimization With Constant-Modulus and Any p-Norm Similarity Constraints

He Xin(hx66hxgmail.com)

Abstract: 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.

Keywords: MIMO Radar, Constant-Modulus, Unit-Modulus, $p$-Norm, Similarity Constraint, Relax-and-Retract.

Category 1: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

Category 2: Convex and Nonsmooth Optimization (Convex Optimization )

Category 3: Applications -- OR and Management Sciences (Telecommunications )

Citation: Shenzhen University, Hanshan Normal University, China. May/2021.

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Entry Submitted: 05/22/2021
Entry Accepted: 05/28/2021
Entry Last Modified: 05/22/2021

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