Asymptotic analysis of proportional fair algorithm

It was previously shown (under simplifying assumptions) that the proportional fair algorithm gives equal power and time to users who only differ in their distance from the BS, their fading characteristics being the same (see Holtzman, J.M., Proc. VTC2000-Spring, p.1663-7, 2000). We give here a more general result for two classes of users with different fading characteristics. All other things being equal, the user class with more fading variability gets more throughput with a lower (but not much lower) fraction of time transmitting. We also demonstrate a separability property-the effects of variability and distance from the base station are separable.