Efficient construction of polyphase sequences with optimal peak sidelobe level growth

Sequences with good correlation properties form an integral part of many active sensing and communication systems. Although polyphase sequence sets with optimal peak sidelobe level (PSL) growth have been known for years, it has been a long-standing problem to construct polyphase sequences with small PSL growth. In this paper, we introduce a new polynomial-time construction approach to design polyphase sequences with optimal PSL growth from sequence sets with small cross-correlation. The proposed construction approach is based on the observation that if the PSL of the sequence set grows optimally, the constructed polyphase sequence will also enjoy an optimal correlation sidelobe growth. Several numerical examples are provided to illustrate the performance of the construction method.