  We investigate the possible performance gains of power control in multi-layer
cellular systems where microcells and picocells are distributed within
macrocells. Although multilayers in cellular networks help increase system
capacity and coverage, and can reduce total energy consumption; they cause
interference, reducing the performance of the network. Therefore, downlink
transmit power levels of multi-layer hierarchical cellular networks need to be
controlled in order to fully exploit their benefits. In this work, we present
an analytical derivation to determine optimum power levels for two-layer
cellular networks and generalize our solution to multi-layer cellular networks.
We also simulate our results in a typical multi-layer network setup and observe
significant power savings compared to single-layer cellular networks.
