Optimal muting and load balancing for eICIC

In heterogeneous networks, a macro cell can cause excessive interference to users in co-channel pico cells. In Release 10 of 3GPP's LTE system, enhanced Inter-Cell Interference Coordination (eICIC) has been introduced to reduce the interference experienced by pico users by having the macro mute some of its subframes. This is a tradeoff, because the benefit to pico users comes at the cost of the macro sacrificing a portion of its resources. This tradeoff is also influenced by the determination of which users are offloaded from the macro to the pico. We formulate the joint optimization of the proportion of muted sub-frames and the assignment of users to macro and pico cells as a network-wide utility maximization problem, and obtain an analytical characterization of the optimal solution. We propose an iterative algorithm that successively improves the assignment of users to cells and the muting proportion, and prove its convergence to the optimal solution.