Fast Optimal and Suboptimal Any-Time Algorithms for CWMA Multiuser Detection

– A fast optimal algorithm based on the branch and bound method, coupled with an iterative lower bound update, is proposed for the joint detection of binary symbols of K users in a synchronous correlated waveform multiple-access (CWMA) channel with Gaussian noise. The proposed method significantly decreases the average computational cost and the Decision Feedback Detector (DFD) [2] is proved to be the Þrst order approximation to the optimal algorithm. Furthermore, a suboptimal algorithm using the Probabilistic Data Association (PDA) is also proposed. It is shown that the suboptimal algorithm gives a near-optimal performance at a computational cost of O(K). I. Problem Formulation and The Optimal Algorithm A discrete-time equivalent model for the matched-Þlter outputs at the receiver of a CWMA channel is given by the Klength vector [1] y = Hb+ n (1) where E[nn ] = σH is the colored Gaussian noise. Suppose H = LL is the Cholesky decomposition of H. DeÞne ˜ y = L−1 T y, D = Lb, and denote the kth component of D and ˜ y by Dk and ˜ yk, respectively. The optimal solution of (1) can be written as φML : ˆb = arg min b∈{−1,+1}K K !