Forwarding strategies for Gaussian parallel-relay networks

For reliable and unreliable forwarding in a parallel-relay network that allows orthogonal transmissions, we maximize the achievable rate under the total power constraint over all nodes. In such a network, the energy cost per information bit [S. Verdu, 1990] during the reliable forwarding is minimized in the wideband regime. For the wideband decode-and-forward (DF) strategy, we show that the optimum parallel-relay solution is to send the data through one relay that is in the "best" position. On the other hand, as observed in [B.E. Schein, 2001], the benefit of unreliable amplify-and-forward (AF) strategy diminishes in the wideband regime. We characterize the optimum bandwidth for AF and show that transmitting in the optimum bandwidth allows the network to operate in the linear regime where the achieved rate increases linearly with transmit power. We identify the best subset of AF relay nodes and characterize the optimum power allocation per dimension among relays.