Bandwidth and Power Allocation for Cooperative Strategies in Gaussian Relay Networks

Achievable rates with amplify-and-forward (AF) and decode-and-forward (DF) cooperative strategies are examined for relay networks. Motivated by sensor network applications, power-constrained networks with large bandwidth resources and a large number of nodes are considered. It is shown that AF strategies do not necessarily benefit from the available bandwidth. Rather, transmitting in the optimum AF bandwidth allows the network to operate in the linear regime where the achieved rate increases linearly with the available network power. The optimum power allocation among the AF relays, shown to be a form of maximal ratio combining, indicates the favorable relay positions. Orthogonal node transmissions are also examined. While the same optimum bandwidth result still holds, the relay power allocation in this case can be viewed as a form of water-filling. In contrast, the DF strategy will optimally operate in the wideband regime and is shown to require a different choice of relays. Thus, in a large scale network, the choice of a coding strategy goes beyond determining a coding scheme at a node; it also determines the operating bandwidth, as well as the set of relays and best distribution of the relay power.