Golay complementary set (GCS) plays a vital role in reducing peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency division multiplexing (OFDM). A more general version of GCS is a multiple shift complementary set (MSCS), where by relaxing the condition of zero auto-correlation sum throughout all the non-zero time shifts to the integer multiples of some fixed time shift, more sequence sets can be made available. In this paper, we propose direct constructions of MSCSs with flexible and arbitrary lengths and flexible set sizes, by using multivariable functions, which have not been reported before.

翻译：戈莱互补集（GCS）在正交频分复用（OFDM）中降低峰均包络功率比（PMEPR）方面起着至关重要的作用。GCS的一种更一般形式是多重移位互补集（MSCS），通过将零自相关和条件从所有非零时移放宽到某个固定时移的整数倍，可以获取更多序列集。本文利用多变量函数，提出了具有灵活任意长度和灵活集合大小的MSCS的直接构造方法，该结果此前尚未见报道。