UNIMODULAR WAVEFORM DESIGN WITH LOW CORRELATION LEVELS: A FAST ALGORITHM DEVELOPMENT TO SUPPORT LARGE-SCALE CODE LENGTHS

We deal with the problem of unimodular waveform(s) design with low correlation levels for the case of large-scale code lengths that can reach tens of thousands. Our primary goals are to reduce the resulting complexity with high efficiency, and meanwhile, to ensure an integrated sidelobe level (ISL) or weighted ISL (WISL) of waveforms as low as possible. To this end, we study a generic model for the minimization of ISL/WISL, wherein the objective function is formulated to embed a Hadmard product into a high-order matrix norm. Our major contributions lie in the transformation of the objective into a proper form via multiple shift matrices and the reformulation of problem in order to use alternating direction method of multipliers (ADMM) technique. In particular, we introduce a virtual matrix to form an additional equality constraint for ADMM, whose augmented Lagrangian is elaborated to help derive a fast algorithm that iterates with closed-form solutions. Simulation results verify the superiority of our algorithm over existing state-of-the-art algorithms in different aspects.