Strictly Positive and Continuous Random Fibonacci Sequences and Network Theory Applications

TL;DR

This paper introduces continuous random Fibonacci sequences and demonstrates their application in deriving capacity and power scaling laws for multihop cooperative relay networks, ensuring stable network performance.

Contribution

It establishes a novel connection between random Fibonacci sequences and network theory, enabling the design of networks with zero Lyapunov exponent for optimal scaling.

Findings

Capacity can be maintained without exponential decay.

Transmit power growth can be avoided across the network.

Lyapunov exponent zero condition ensures network stability.

Abstract

We motivate the study of a certain class of random Fibonacci sequences - which we call continuous random Fibonacci sequences - by demonstrating that their exponential growth rate can be used to establish capacity and power scaling laws for multihop cooperative amplify-and-forward (AF) relay networks. With these laws, we show 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 achieved by ensuring the network's Lyapunov exponent is zero.