Optimal grouping algorithm for a group decision feedback detector in synchronous CDMA communications

The group decision feedback (GDF) detector is studied in this letter. Given the maximum group size, a grouping algorithm is proposed. It is shown that the proposed grouping algorithm maximizes the symmetric energy of the multiuser detection system. Furthermore, based on a set of lower bounds on asymptotic group effective energy (AGEE) of the GDF detector, it is shown that the proposed grouping algorithm, in fact, maximizes the AGEE lower bound for every group of users. The theoretical analysis of the grouping algorithm enables the offline estimation of the computational cost and the performance of a GDF detector. The computational complexity of a GDF detector is exponential in the largest size of the groups. Simulation results are presented to verify the theoretical conclusions. The results from this letter can be applied to the decision feedback detector by setting the maximum group size to one.