Random fibonacci sequences and capacity/power scaling in cooperative multihop networks

Abstract

In this paper, we analyze capacity and power scaling in multihop cooperative AF relay networks. An analytical framework for this task is developed by drawing a correspondence between random Fibonacci sequences and the end-to-end multihop system model. It turns out, the exponential growth rate of these interesting sequences can be employed to establish scaling laws, from which we conclude that it is possible to construct multihop cooperative AF networks that simultaneously avoid 1) exponential capacity decay and 2) exponential transmit power growth across the network. This is done by ensuring the network's Lyapunov exponent (a key observable studied in random dynamical system theory) is zero, which can be achieved by appropriately selecting the amplification factors at each of the relay nodes. Our results apply to both fixed-gain and variable-gain relaying. To conclude our work, we demonstrate the presented theory through numerical simulations.