# 2009 Research Summary

## Spectrum Sharing between Wireless Networks

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Leonard Henry Grokop and David Tse

We consider the problem of two wireless networks operating on the same (presumably unlicensed) frequency band. Pairs within a given network cooperate with one another, but between networks there is competition for spectrum. To make the problem tractable, we assume transmissions are scheduled according to a random access protocol where each network chooses an access probability for its users. In this vein a game between the two networks is defined. We characterize the Nash Equilibrium behavior of the system. Three regimes are identified; a full-spread regime, where both networks choose to simultaneously schedule all transmissions; a partial-spread regime, where one network schedules all transmissions and the other only schedules a fraction; and a joint-spread regime, where both networks schedule a fraction of their transmissions. The regime of operation depends on the pathloss exponent. The joint-spread regime, which has a cooperative flavor, is attainable only for pathloss exponents greater than 4, which suggests that in certain environments there may be a natural incentive for rival wireless networks to cooperate.

Figure 1: The Nash equilibrium belongs to one of three regimes, depending on the density of wireless transmissions in each network and the pathloss exponent.

- [1]
- L. Grokop and D. N. C. Tse, "Spectrum Sharing between Wireless Networks,"
*IEEE INFOCOM,*Phoenix, AZ, April 2008 (submitted).