Designing Unimodular Sequence with Low Peak of Sidelobe Level of Local Ambiguity Function

This paper considers the problem of designing unimodular sequence with low peak of sidelobe level of local ambiguity function. The optimization problem is difficult because of the mixed nonconvex unimodulus and highly nonlinear fourth-order polynomial-like constraints. To solve the problem, we propose a hybrid lagrange programming neural network-alternating direction method of multipliers (LPNN-ADMM) approach. To separately deal with the complex nonconvex and nonlinear constraints, we introduce auxiliary variables to transfer the fourth-order polynomials from the nonlinear constraints into the Lagrange function. As a result, the original optimization variables and auxiliary variables are updated alternately in the ADMM framework. Especially, the original optimization variables are updated from the newly formed nonlinear objective function together with the unimodular constraints via the LPNN method, in which an adaptive selection scheme of the penalty parameter is developed to minimize the corresponding Lagrange function while satisfying the constraints. The performance of the proposed method is demonstrated via numerical examples.