Proof of convergence for the distributed optimal rate assignment algorithm

Previous work has discussed maximization of reverse link throughput of a multi-service CDMA system by jointly optimizing powers and rates. That was for a single cell optimization with the effect of other cells entering only as independent other-cell interference. One can try to extend the approach to multiple cells, but this becomes very complex. This paper assumes that each base station does its optimization independently of the other base stations. The different base stations will be affecting each other through other cell interference, continually being modified by the separate optimizations. There is then the question of stability and convergence of such uncoordinated optimizations. We prove that the algorithm nevertheless converges.