Low-Correlation Sequences Over the QAM Constellation

This paper presents the first concerted look at low correlation sequence families over quadrature amplitude modulation (QAM) constellations of size and their potential applicability as spreading sequences in a code-division multiple-access (CDMA) setting. Five constructions are presented, and it is shown how such sequence families have the ability to transport a larger amount of data as well as enable variable-rate signaling on the reverse link. Canonical family has period , normalized maximum-correlation parameter bounded above by , where ranges from in the 16-QAM case to for large . In a CDMA setting, each user is enabled to transfer bits of data per period of the spreading sequence which can be increased to bits of data by halving the size of the sequence family. The technique used to construct is easily extended to produce larger sequence families and an example is provided. Selected family has a lower value of but permits only -bit data modulation. The interleaved 16-QAM sequence family, has and supports 3-bit data modulation. The remaining two families are over a quadrature-pulse amplitude modulation (Q-PAM) subset of size of the -QAM constellation. Family has a lower value of in comparison with Family , while still permitting -bit data modulation. Interleaved Family , over the 8-ary Q-PAM constellation, permits 3-bit data modulation and interestingly achieves the Welch lower bound on .