The Golay complementary set (GCS) has been applied in OFDM systems because of its desirable property of low peak-to-average power ratios (PAPRs). A generalization of GCS which is called the multiple-shift complementary set (MSCS) was also introduced to have bounded PAPRs. In addition, the MSCSs can be used to construct GCSs. In this letter, we first provide a more generalized construction of GCSs with non-power-of-two length. Then, a direct construction of MSCSs of non-power-of-two length is proposed based on the generalized Boolean functions. Moreover, a connection between the constructed GCSs and MSCSs is provided and hence the PAPR upper bound of the constructed MSCSs is derived. The proposed GCSs and MSCSs can have various lengths, set sizes, and bounded PAPRs.

中文翻译：

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具有非二次幂长度和有界 PAPR 的 Golay 互补集和多班互补集


Golay互补集(GCS)因其具有低峰均功率比(PAPR)的理想特性而被应用于OFDM系统。还引入了称为多班互补集 (MSCS) 的 GCS 推广，以具有有界 PAPR。此外，MSCS可用于构建GCS。在这封信中，我们首先提供了一种更通用的非二次幂长度的 GCS 结构。然后，提出了一种基于广义布尔函数的非二次方长度MSCS的直接构造方法。此外，提供了所构建的GCS和MSCS之间的连接，因此导出了所构建的MSCS的PAPR上限。所提出的 GCS 和 MSCS 可以具有各种长度、集合大小和有界 PAPR。