A Construction of General QAM Golay Complementary Sequences

• Published in: IEEE transactions on information theory Vol. 56; no. 11; pp. 5765 - 5771
• Main Author: Li, Ying
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-11-2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Boolean functions; Coding, codes; Constellations; Construction; Correlation; Enumeration; Exact sciences and technology; Frequencies; Frequency division multiplexing; Golay complementary sequences; Information systems; Information theory; Information, signal and communications theory; Modulation, demodulation; Multiplexers; Multiplexing; OFDM; orthogonal frequency-division multiplexing (OFDM); peak-to-mean envelope power ratio (PMEPR); Phase shift keying; Quadrature amplitude modulation; quadrature amplitude modulation (QAM); Quadrature phase shift keying; quadrature phase shift keying (QPSK); Signal and communications theory; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Upper bound; Upper bounds; Golay complementary sequences; Upper bound; quadrature phase shift keying (QPSK); Quadrature amplitude modulation; peak-to-mean envelope power ratio (PMEPR); quadrature amplitude modulation (QAM); Golay codes; Orthogonal frequency division multiplexing; orthogonal frequency-division multiplexing (OFDM); Quadrature phase shift keying
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2010.2070151

A construction of general quadrature amplitude modulation (QAM) Golay complementary sequences based on quadrature phase shift keying Golay-Davis-Jedwab sequences (GDJ sequences) is described. Existing constructions of 16- and 64-QAM Golay sequences are extended to 4 q -QAM sequences of length 2 m , for q ≥ 1, m ≥ 2. This construction gives [(m + 1)4 2(q - 1) - (m + 1)4 (q - 1) + 2 q - 1 ](m! / 2)4 (m + 1) Golay complementary sequences. A previous offset pair enumeration conjecture for 64-QAM Golay sequences is proved as a special case of the enumeration for 4q-QAM Golay sequences. When used for orthogonal frequency-division multiplexing signals, the peak-to-mean envelope power ratio upper bound is shown to be 6(2 q - 1)/ (2 q + 1), approaching 6 as the QAM constellation size increases.