Perfect 16-QAM Sequences and Arrays

Fanxin ZENG  Xiaoping ZENG  Zhenyu ZHANG  Guixin XUAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.10   pp.1740-1748
Publication Date: 2012/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.1740
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
perfect arrays,  perfect sequences,  16-QAM constellation,  synchronization,  

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This paper investigates construction methods of perfect 16-QAM sequences and arrays, since such sequences and arrays play quite an important role in synchronization of communication systems making use of 16-QAM signals. The method used for obtaining the results is to establish a relationship between the known perfect quaternary sequences/arrays and the required ones so that the former is transformed into the latter. Consequently, the sufficient conditions for implementing the required transformations are derived, and several examples are given. Our methods can provide perfect 16-QAM sequences with lengths 2, 4, 8, and 16, which are given in Table A·1 and infinite families of perfect 16-QAM arrays, whose existing sizes up to dimension 5 and volume 2304 are listed in Tables A·2 and A·3.