New 64-QAM Golay Complementary Sequences

A generalized Boolean function generator for complementary sequences

“…They were generalized to complementary sets in [2] and polyphase sequences in [3,4]. More recently, QAM complementary sequences were studied in, for example, [5][6][7][8]. We distinguish two different families of algorithms for generation of complementary sequences.…”

“…Davis and Jedwab [9] gave the corresponding algorithm for M-PSK sequences (later improved by Paterson [10]) and showed that complementary sequences are closely related to Reed-Muller codes. This approach was later followed by all researchers in the field of QAM complementary sequences as in [5][6][7][8]. Golay also introduced an alternative family of algorithms.…”

“…These are recursive algorithms that generate longer sequences from shorter ones. The first recursive algorithm for generating standard polyphase sequences (including M-PSK) was introduced in [11] and was soon followed by a recursive algorithm for generating multilevel sequences [12], which is related to QAM algorithms that appeared much later [5][6][7][8]. These early recursive algorithms were all formulated in time domain.…”

“…For 64-QAM it generates new sequences that are not generated by [6,7]. It can also generate many new 256-QAM, 1024-QAM, etc., sequences compared to any other published algorithm.…”

Number of Distinct 16-QAM Periodic Complementary Sequence Sets

“…More clearly, it is investigated that the super bounds of PMEPR of several constructions of QAM sequences without CS pairs [1]- [4], whose results show that only QAM Golay CS pair results in the lowest super bound of PMEPR in an orthogonal frequency division multiplexing (OFDM) communication system. And 16-QAM and 64-QAM Golay CS pairs are constructed by [5]- [9]. As the development of investigation of QAM CS sequences, QAM CS pair is generalized to QAM CS set and QAM Golay CS pair is expanded to QAM periodic CS sets [10]- [13].…”