Bandwidth and power allocation for cooperative strategies in Gaussian relay networks

In a relay network with a single source-destination pair, we examine the achievable rates with amplify-and-forward (AF) relaying strategy. Motivated by applications in sensor networks, we consider power-constrained networks with large bandwidth resources and a large number of nodes. We show that the AF strategy does not necessarily benefit from the large available bandwidth. We characterize the optimum AF bandwidth and show that transmitting in the optimum bandwidth allows the network to operate in the linear regime where the achieved rate increases linearly with the available network power. We then present the optimum power allocation among the AF relays. The solution, which can be viewed as a form of maximum ratio combining, indicates the favorable relay positions in the network. Motivated by the large bandwidth resources we further consider a network that uses orthogonal transmissions at the nodes. While the above result for the optimum bandwidth still holds, a different set of relays should optimally be employed. In this case, the relay power solution can be viewed as a form of water-filling. The optimum AF bandwidth and the relay powers can be contrasted to the decode-and-forward (DF) solution. In a network with unconstrained bandwidth, the DF strategy will operate in the wideband regime to minimize the energy cost per information bit (S. Verdu, 2002), (O. Oyman et al., 2004). The wideband DF strategy requires again a different choice of relays; in the case of orthogonal signaling, the data should be sent through only one DF relay (I. Maric et al., 2004). Thus, in general, in a large scale network, a choice of a coding strategy goes beyond determining a coding scheme at a node; it also determines the operating bandwidth as well as the best distribution of the relay power.