Fast Algorithms for Designing Unimodular Waveform(s) With Good Correlation Properties

We develop new fast and efficient algorithms for designing single or multiple unimodular waveforms with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding problems can quickly grow to a large scale with increasing the code length and the number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. The difficulty is also that the corresponding optimization problems are nonconvex, but the required accuracy is high. Therefore, we formulate the ISL and WISL minimization problems as nonconvex quartic optimization problems in frequency domain, and then simplify them into quadratic problems via majorization-minimization technique, which is one of the basic techniques for addressing large-scale and/or nonconvex optimization problems. While designing our fast algorithms, we explore and use the inherent algebraic structures in objective functions to rewrite them into quartic forms, and in the case of WISL minimization, to derive additionally an alternative quartic form that allows us to apply the quartic-quadratic transformation. Our algorithms are applicable to large-scale unimodular waveform design problems as they are proved to have lower or comparable computational burden (analyzed theoretically) and faster convergence speed (confirmed by comprehensive simulations) than the state-of-the-art algorithms. In addition, the waveforms designed by our algorithms demonstrate better correlation properties compared to their counterparts.