Iterative Multiuser Decoding with an Unknown Number of Users: Large-System Analysis

We study iterative multiuser detection in large randomly spread code division multiple access systems under the assumption that the number of users accessing the channel is unknown by the receiver. In particular, we focus on the factor graph representation and iterative algorithms based on belief propagation. We build an iterative scheme that detects the encoded data and the users’ activity. By using the replica method from statistical physics, we characterize the density evolution of the iterative detector when the number of potential users is large. As a result, we provide a general fixed-point equation where the nature of the exchanging probabilities depends on to the users’ activity. Finally, we show that the structure of the users’ codes yields a multiuser efficiency fixed-point equation that is equivalent to the case of all-active users with a system load scaled by the activity rate. A. Tauste Campo and A. Guillén i Fàbregas are with the Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK, e-mail: [email protected], [email protected].