Low Correlation Sequences over AM-PSK and QAM Alphabets

A construction for a family of sequences over the 8-ary AM-PSK constellation that has maximum nontrivial correlation magnitude bounded as thetas_max lsim radicN is presented here. The family is asymptotically optimal with respect to the Welch bound on maximum magnitude of correlation. The 8-ary AM-PSK constellation is a subset of the 16-QAM constellation. We also construct two families of sequences over 16-QAM with thetas_max lsim radic2radicN. These families are constructed by interleaving sets of sequences. A construction for a family of low-correlation sequences over QAM alphabet of size 2^2m is presented with maximum nontrivial normalized correlation parameter bounded above by lsim a radicN, where N is the period of the sequences in the family and where a ranges from 1.61 in the case of 16-QAM modulation to 2.76 for large m. When used in a CDMA setting, the family will permit each user to modulate the code sequence with 2m bits of data. Interestingly, the construction permits users on the reverse link of the CDMA channel to communicate using varying data rates by switching between sequence families associated to different values of the parameter m. Other features of the sequence families are improved Euclidean distance between different data symbols in comparison with PSK signaling and compatibility of the QAM sequence families with sequences belonging to the large quaternary sequence families {S(p)}.