Fast Algorithms for Designing Multiple Unimodular Waveforms With Good Correlation Properties

摘要

In this paper, we develop new fast and efficient algorithms for designingsingle/multiple unimodular waveforms/codes with good auto- andcross-correlation or weighted correlation properties, which are highly desiredin radar and communication systems. The waveform design is based on theminimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) ofwaveforms. As the corresponding optimization problems can quickly grow to largescale with increasing the code length and number of waveforms, the main issueturns to be the development of fast large-scale optimization techniques. Thedifficulty is also that the corresponding optimization problems are non-convex,but the required accuracy is high. Therefore, we formulate the ISL and WISLminimization problems as non-convex quartic optimization problems in frequencydomain, and then simplify them into quadratic problems by utilizing themajorization-minimization technique, which is one of the basic techniques foraddressing large-scale and/or non-convex optimization problems. While designingour fast algorithms, we find out and use inherent algebraic structures in theobjective functions to rewrite them into quartic forms, and in the case of WISLminimization, to derive additionally an alternative quartic form which allowsto apply the quartic-quadratic transformation. Our algorithms are applicable tolarge-scale unimodular waveform design problems as they are proved to havelower or comparable computational burden (analyzed theoretically) and fasterconvergence speed (confirmed by comprehensive simulations) than thestate-of-the-art algorithms. In addition, the waveforms designed by ouralgorithms demonstrate better correlation properties compared to theircounterparts.