On the Capacity of Memoryless Relay Networks

In a relay network, the signal processing at the relay significantly affects the capacity benefits of cooperation. In this work, we explore the optimal relay functionality for capacity maximization in a memoryless relay network, i.e. a network where, during each channel use, the signal transmitted by a relay depends only on the last received symbol at that relay. By relating some of the existing memoryless forwarding strategies to the fundamental signal processing operations of estimation and detection, we develop a new scheme that forwards the unconstrained minimum mean square error (MMSE) estimate obtained at the relay to the destination. For a single relay system, we derive the characterization of the optimal relay function and show that the relay function of EF (estimate and forward) satisfies the optimality condition. For the multiple relay case, we consider both parallel and serial relay networks and show that EF performs better than both AF (amplify and forward) and DF (demodulate and forward). For hybrid networks that contain both serial and parallel elements, and when robust performance is desired at all SNR, the advantage of EF over the best of AF and DF is found to be significant.