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

|The Group Decision Feedback (GDF) detector is studied in this paper. The computational complexity of a GDF detector is exponential in the largest size of the groups. 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 Asymptotic Group Symmetric Energy (AGSE) of the GDF detector, 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 thegrouping algorithm enables the o2ine estimation of the computational cost and the performance of GDF detector. Simulation results on both small and large size problems are presented to verify the theoretical conclusions. All the results in this paper can be applied to the Decision Feedback (DF) detector by simply setting the maximum group size to 1. Keywords| Multiuser detection, decision feedback, optimization methods, code division multiple access.