# 2008 Research Summary

## Spectrum Sharing between Wireless Networks

View Current Project Information

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).