Stability Analysis of Interacting Wireless Repeaters

TL;DR

This paper analyzes the stability of wireless networks with multiple repeaters, deriving bounds on amplification gain to prevent instability caused by inter-repeater interference, and offers deployment insights.

Contribution

It introduces a stability bound for repeater amplification gain using Gershgorin disc theorem, linking it to channel gains and providing practical deployment guidance.

Findings

Maximum gain is limited by the sum of channel amplitudes.

The derived bound effectively predicts stability thresholds.

Deployment strategies influence system stability.

Abstract

We consider a wireless network with multiple single-antenna repeaters that amplify and instantaneously re-transmit the signals they receive to improve the channel rank and system coverage. Due to the positive feedback formed by inter-repeater interference, stability could become a critical issue. We investigate the problem of determining the maximum amplification gain that the repeaters can use without breaking the system stability. Specifically, we obtain a bound by using the Gershgorin disc theorem, which reveals that the maximum amplification gain is restricted by the sum of channel amplitude gains. We show by case studies the usefulness of the so-obtained bound and provide insights on how the repeaters should be deployed.