Impact of preconditioning on the convergence of numerical co-channel interference approximations in heterogeneous networks

Various low-power node technologies such as relays and femtocells are considered an integral part of the heterogeneous fourth generation radio access networks. However, due to different transmit power levels, antenna configurations, and network planning strategies of such nodes, the interference characteristics in heterogeneous deployments can be significantly different than the conventional macrocell-only deployments. The variations in experienced co-channel interference levels could affect the convergence of numerical interference modeling methodologies and significantly decrease their convergence rates. In this paper, different preconditioning approaches are proposed and their impact on the convergence of numerical co-channel interference approximations is analyzed. The evaluations are performed utilizing a flexible MGF-matching method which approximates the lognormal sum distribution by a lognormal random variable, a well-known approach to model the co-channel interference in mobile cellular networks. Simulations show that the proposed preconditioning approaches can substantially increase the computational efficiency of the MGF-matching method while ensuring the convergence of the method.