Power allocation in wireless multihop networks with application to virtual antenna arrays

We examine a network consisting of a source-destination pair that want to communicate at a fixed transmission rate with the possibility of using an arbitrary number of nodes as relays. This network model forms a building block for cooperative diversity and coding systems. Fixing the transmission rate, we formulate the power allocation problem as a nonlinearly constrained optimization problem for a class of cooperative accessing schemes and we present results for two practically motivated network geometries. The first network geometry is the regular linear model where the relay nodes are allocated equidistantly on the line joining the source to the destination. The second network geometry is the clustered network model where the relay nodes form a cluster of closely packed nodes which act as a virtual antenna array. The presented analysis gives useful insights to the design of practical wireless multihop networks with deterministic properties and finite number of relay nodes.