Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), nonorthogonal and orthogonal selection decode-and-forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time (ST) code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay.

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 .

A construction for a family of sequences over the 8-ary AM-PSK constellation that has maximum nontrivial correlation magnitude bounded as thetasmaxlsim 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 thetasmaxlsim radic2radicN. These families are constructed by interleaving sets of sequences. A construction for a family of low-correlation sequences over QAM alphabet of size 22mis 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)}.

Cooperative relay communication in a fading channel environment under the orthogonal amplify-and-forward (OAF), non-orthogonal and orthogonal selection decode-and- forward (NSDF and OSDF) protocols is considered here. The diversity-multiplexing gain tradeoff (DMT) of the three protocols is determined and DMT-optimal distributed space-time code constructions are provided. The codes constructed are sphere decodable and in some instances incur minimum possible delay. Included in our results is the perhaps surprising finding that the OAF and NAF protocols have identical DMT when the time durations of the broadcast and cooperative phases are optimally chosen to suit the respective protocol. Two variants of the NSDF protocol are considered: fixed-NSDF and variable-NSDF protocol. In the variable-NSDF protocol, the fraction of time occupied by the broadcast phase is allowed to vary with multiplexing gain. In the two-relay case, the variable-NSDF protocol is shown to improve on the DMT of the best previously-known static protocol for higher values of multiplexing gain. Our results also establish that the fixed-NSDF protocol has a better DMT than the NAF protocol for any number of relays.