  In this work, we propose and analyze a class of distributed algorithms
performing the joint optimization of radio resources in heterogeneous cellular
networks made of a juxtaposition of macro and small cells. Within this context,
it is essential to use algorithms able to simultaneously solve the problems of
channel selection, user association and power control. In such networks, the
unpredictability of the cell and user patterns also requires distributed
optimization schemes. The proposed method is inspired from statistical physics
and based on the Gibbs sampler. It does not require the concavity/convexity,
monotonicity or duality properties common to classical optimization problems.
Besides, it supports discrete optimization which is especially useful to
practical systems. We show that it can be implemented in a fully distributed
way and nevertheless achieves system-wide optimality. We use simulation to
compare this solution to today's default operational methods in terms of both
throughput and energy consumption. Finally, we address concrete issues for the
implementation of this solution and analyze the overhead traffic required
within the framework of 3GPP and femtocell standards.
