A theoretical analysis of multiuser zero forcing relaying with noisy channel state information

We consider a wireless ad hoc network with single antenna nodes under a two-hop relay traffic pattern. Some of the nodes in the network form source/destination pairs, while the other nodes serve as amplify and forward relays. The relay gains are assigned such, that the interference between different source/destination links is nulled (multiuser zero forcing relaying) [A. Wittneben et al., 2005]. This essentially realizes a distributed spatial multiplexing gain with single antenna nodes. The main contribution of this paper is an analysis of multiuser ZF relaying, which takes noisy channel state information, phase noise and quantization noise into account. Our analytical expressions are tight for the parameter space of practical interest The system imperfections essentially introduce an additive noise component at the destinations. We show, that the variance of this component is proportional to the number of source/destination pairs. Finally we observe, that for perfect channel state information the sum rate of the system grows beyond any limit as the number of nodes tends to infinity. For noisy CSI however this asymptotic sum rate becomes finite.