A Unimodular Fractional Optimization Framework and Its Applications to Joint Design of SAR Waveform and Receive Filter

Optimizing a fractional form over the unimodular vector set arises in radar waveform design, various active sensing scenarios and communication applications, which is usually NP-hard. In this paper, an optimization framework is proposed, which guarantees that the objective function converges to the strict local optimum. It employs the Dinkelbach's method and semidefinite programming (SDP) to convert a fractional objective function into a quadratic one, and deal with various nonconvex constraints, respectively. The iterative rank minimization is then introduced to force the rank of SDP variable to be zero, so that the original problem is split into a series of solvable subproblems with polynomial-time complexity. The optimization procedure is applied to joint design of synthetic aperture radar (SAR) waveform and receive filter. The formulation is established by taking the mutual information (MI) between range profile and target scattering characteristics as the objective, subject to high resolution, low sidelobe level, and unimodular constraints. The resultant MI maximization problem is boiled down to fractional unimodular optimization with a complicated mathematical structure. Based on a cyclic maximizer, it is decomposed into a series of subproblems, followed by application of the proposed optimization framework to customize the solving procedure. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed framework.