Joint Routing and Resource Allocation via Superposition Coding for Wireless Data Networks

A wireless data network with static nodes is considered. The nodes communicate simultaneously over the same narrowband channel and each node uses superposition coding to broadcast independent messages to individual nodes in the network. The goal herein is to find optimal data routes and power allocations to maximize a weighted sum of the data rates injected and reliably communicated over the network. Two instances of this problem are considered. In the first instance, each node uses a fixed power budget, whereas in the second instance the power used by each node is adjustable. For the latter case, two variants are considered: in the first there is a constraint on the power used by each node and in the second there is constraint on the total power used by all nodes. It will be shown that while the instance in which the power of each node is fixed can be cast in the form of an efficiently solvable geometric program (GP), the second instance in which the node powers are adjustable cannot be readily cast in this form. To circumvent this difficulty, an iterative technique is proposed for approximating the constraints of the original optimization problem by GP-compatible constraints. Numerical simulations suggest that this technique converges to a locally optimal solution within a few iterations.