Opportunistic Link Scheduling, Power Control, and Routing for Multi-hop Wireless Networks over Time Varying Channels

We consider a cross-layer optimization problem for multi-hop wireless networks over time varying channels. The system consists of L interfering links, where the transmission power and rate of link l (= 1, . . . , L) are specified in vectors ~ P = [P1 . . . PL] and ~ X = [X1 . . . XL] respectively. In every time slot, the scheduler schedules the transmissions by assigning a resource allocation vector ~ V = [~ P ~ X]T. We denote the expectation of ~ V by E(~ V ). Our objective is to find the optimal scheduling policy which minimizes the cost of average resource consumption while maintaining average service guarantees to each user. We develop a unified framework, in which the cost of the average resource consumption is given by a convex function f(E(~ V )) and the minimum average service guarantees are given by a set of convex constraints ~g(E(~ V )) ≤ 0. By means of convex optimization and stochastic approximation, we obtain the solution by solving the corresponding dual problem. An iterative algorithm is proposed and analyzed, which schedules the transmission powers and rates adapting to the channel variations. If the channel states are described by a finite-state mixing process, it is shown that our algorithm asymptotically attains the optimal cost.