Journal
IEEE COMMUNICATIONS LETTERS
Volume 25, Issue 9, Pages 2805-2809Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LCOMM.2021.3094580
Keywords
Peak to average power ratio; Correlation; Boolean functions; Upper bound; Time-domain analysis; Spectroscopy; Radar; Generalized Boolean function (GBF); Golay complementary set (GCS); multiple-shift complementary set (MSCS); peak-to-average power ratio (PAPR)
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Funding
- Ministry of Science and Technology, Taiwan [MOST 109-2628-E-006-008-MY3, 109-2813-C-006-012-E]
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This letter introduces a more generalized construction method for GCS and MSCS, which can be applied to sequences of non-power-of-two lengths and is based on generalized Boolean functions. A connection between the constructed GCS and MSCS is provided, leading to the derivation of the PAPR upper bound for the constructed MSCS.
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.
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