Scheduling and power adaptation for networks in the ultra wide band regime

The max-min fair scheduling problem in wireless ad hoc networks, in general, is a non-convex optimization problem. However in the limit of infinite bandwidth (W → ∞), the solution reduces to a simple simultaneous transmission (spread spectrum) of all links. Thus, having a very large bandwidth significantly simplifies the problem of scheduling. In This work, the scheduling problem is considered in the UWB regime (W ≫1 but finite), a model for certain practical radios. A quadratic (in 1/W) lower bound to the single link capacity function is developed. This approximation is applied to the general non-convex scheduling problem to obtain a dual problem, which involves a quadratic optimization sub-problem. A search algorithm is devised to find the optimal solution of the quadratic sub-problem. This solution is utilized to iteratively construct the schedule (sub-band sizes) and power allocation, thus optimally solving the UWB max-min fair scheduling problem, to within any desired precision. Simulations on medium sized networks demonstrate the excellent performance of this scheme. Thus, exploiting the UWB nature of the physical layer simplifies the wireless ad-hoc network scheduling problem.