Optimal grouping and user ordering for sequential group detection in synchronous CDMA

The sequential group detection technique is a generalization of the decision feedback detector: in the latter, users are successively demodulated and cancelled one-by-one, while in the former this basic operation is performed simultaneously on groups of users. The computational complexity of a group decision feedback detector (GDFD) is exponential in the largest size of the groups; thus instead of using the partition of users as design parameters, choosing the "maximum group size" is more reasonable in practice. Given the maximum group size, a grouping algorithm is proposed. It is shown that the proposed grouping algorithm maximizes the asymptotic symmetric energy (ASE) of the multiuser detection system. Furthermore, based on a set of lower bounds on the asymptotic group symmetric energy (AGSE) of the GDFD, it is shown that the proposed grouping algorithm, in fact, maximizes the AGSE lower bound for every group of users. Together with a fast computational method based on branch-and-bound, the theoretical analysis of the grouping algorithm enables the offline estimation of the computational cost and the performance of GDFD. Simulation results are presented to verify the theoretical results.