Stability Analysis of Interacting Wireless Repeaters

TL;DR

This work addresses the stability of networks with multiple interacting wireless repeaters performing in full-duplex amplify-and-forward mode, where inter-repeater interference creates a positive feedback loop. It casts the problem as an input-output stability task and derives an exact characterization of the maximum usable gain $\alpha_{\max}$, along with a computable, yet tight, lower bound $\alpha_G$ via the Gershgorin disc theorem. The analysis shows that the stability bound depends on the sum of inter-repeater channel amplitude gains rather than power, and validates the bound with circle and grid deployment case studies, offering practical deployment guidelines. The results enable safer design of repeater swarms for coverage extension in next-generation networks and highlight the need for cross-cell coordination in large-scale deployments.

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.

Figures (8)

• Figure 1: $N$ interacting single-antenna wireless repeaters.
• Figure 2: Block diagram corresponding to \ref{['eq: mimo system']}.
• Figure 3: Repeaters equally spaced on a circle.
• Figure 4: Stability test for repeaters on a circle.
• Figure 5: Illustration of coverage extension.

Theorems & Definitions (1)

• Remark 1