Low Correlation Sequences over QAM and AM-PSK Constellations

— A construction for a family, Q M 2 , of low-correlation sequences over QAM alphabet of size M 2 = 2 2m is presented with maximum nontrivial normalized correlation parameter bounded above by a √ N , where N is the period of the sequences in the family and where a ranges from 2.10 in the case of 64-QAM modulation to 2.76 for large m. Interestingly, along the way, for the particular case of the 16-QAM constellation, we construct two families of sequences that have maximum magnitude of correlation bounded by √ 2 √ N. Family Q M 2 can support (N + 1)/2 m−1 users and each user has an ability to transmit 2m bits of data per period of the spreading sequence. The Euclidean distance between the signals assigned to a particular user, corresponding to different data symbols, is larger than the corresponding value for the case when M 2-PSK, M = 2 m , modulation and spreading is used. Perhaps most interestingly, Family Q M 2 permits users on the reverse link of a CDMA system to communicate asynchronously at varying data rates by switching between different QAM constellations. Family Q M 2 also has a certain compatibility with QPSK sequence families S(p). Also included in the paper are constructions for large families of sequences over the M 2-QAM alphabet. An interesting byproduct of our constructions is a family of sequences over the 8-ary AM-PSK alphabet that meets the Welch bound.