Much of the focus in dynamic spectrum access has been on detection of primary users prior to channel occupation by secondary users as well as expediently vacating channels in the event that primary users reappear. These efforts are necessary, though reactionary in nature. We propose that, in addition to these efforts, the topology of the secondary network be optimized in order to proactively minimize the potential for primary user outages should primary users either appear while the channel is in use by the secondary network, or go undetected due to the stochastic nature of signal detection. The topology control problem that we describe is based on outage probability using a lognormal shadowing path loss model and incorporates the effects of a CSMA-like MAC protocol. Additionally, we assume that the secondary network has learned from past observations of primary user behavior and maintains this knowledge in the form of an outage potential map, which is similar to the occupancy grid concept used in robot navigation [1]. Brute force search is clearly impractical for this problem and the existence of an efficient algorithm for finding the optimal solution is questionable due to the need for enumerating maximal independent sets. There are three main sources of complexity of this topology control problem, namely the exponential number of feasible connected topologies, the exponential number of maximal independent sets of the conflict graph, and the difficulty of computing outage probability for sums of lognormal random variables. We propose a heuristic that addresses each of these three issues and compare its performance against the optimal solution as well as two other topology control aglorithms, one focused on minimizing total power and the other focused on minimizing interference.
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