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Optimizing power limits for white space devices under a probability constraint on aggregated interference

This paper presents a solution to the problem of setting power limits for white space devices sharing a spectrum band. It is desired to utilize the available white space efficiently while also protecting the primary system from harmful interference. Power limits are set individually for each white space device by maximizing a joint utility measure, e.g., sum capacity. The aggregated interference caused by the white space devices to the primary system is controlled by constraining the probability of harmful aggregated interference to be below a defined threshold. First, the problem of single white space channel sharing is given a mathematical formulation in the form of an optimization problem. Under the common assumption of lognormal fading the distribution of the aggregate interference is unknown and the optimization problem becomes infeasible to solve. A computationally feasible approximation of the initial optimization problem is formulated in which the distribution of the aggregated interference is modeled using the Fenton-Wilkinson approximation. We derive the expressions needed for efficiently solving the simplified optimization problem with a numerical solver, including the gradients of the constraint and objective functions. We show by means of simulations that the solutions to the simplified optimization problem typically fulfill the original probability constraints with good precision. Further, the resulting sum-capacity values are higher than what can typically be obtained by using fixed margins for coping with the aggregate interference. We also discuss multi channel extensions which are able to handle not only interference to primary systems operating on adjacent channels, but also the joint problem of selecting the channels for white space operation and deciding the associated power limits.