Scheduling with Rate and Duty-Cycle Constraints for Wireless Networks over an Interference Channel

We consider the problem of finding a minimum energy transmission schedule for duty-cycle and rate constrained nodes transmitting over a AWGN interference channel. Since traditional optimization methods using Lagrange multipliers do not work well and are computationally expensive given the non-convex constraints, we develop polynomial time approximation schemes for finding optimal rate and duty-cycle constrained energy schedule by considering a restricted version of the problem using discrete power levels. We first show a simple dynamic programming solution that optimally solves the restricted problem using two fixed power levels. We then find a 2-factor approximation to the problem of finding the optimal fixed power level that generates the optimal (minimum) energy schedule. We then develop a (2,beta)-FPAS (fully polynomial time approximation scheme) for the problem that approximates the optimal power consumption and rate constraints to within factors of 2 and arbitrarily close beta, respectively. The running time of the FPAS is polynomial in 1/beta.