In this paper, we consider a heterogeneous network (eg. Macrocells overlaid with small cells), where users associated with their respective base stations (BS) demand certain rates. These users interfere with each other and one needs an algorithm that satisfies the demands irrespective of the number of interferers and the amount of interference (whenever the demands are within the achievable limits). In our previous paper, we proposed one such iterative power allocation algorithm called UPAMCN (Universal power allocation algorithm for multicell networks), when all the agents update their power profiles at the same rate. Using two time scale stochastic approximation analysis, we analyze the same (UPAMCN) algorithm, when the heterogeneous agents update their power profiles at different rates. We obtain partial analysis of the algorithm using an ODE framework and demonstrate the convergence of the proposed algorithm via numerical examples and simulations.
