Optimal rate allocation and power control in wireless ad hoc networks with random access

For wireless ad hoc networks with random access, we propose an optimal rate allocation and power control mechanism. First, a network utility maximization problem and an energy minimization problem are given in this paper. Using multiobjective optimization theory, we then combine the two conflicting optimization problem together into a new optimization problem. Finally, the new optimization problem is vertically decomposed into three subproblems with the Lagrange dual decomposition: a rate allocation problem at the transport layer, a contention resolution problem at the medium access control (MAC) layer and a power control problem at the physical layer. We prove rigorously that the proposed algorithm can converge quickly. Theoretical analysis and simulation results are provided in support of our conclusions.