Rate-Constrained Wireless Networks with Fading Channels: Interference-Limited and Noise-Limited Regimes

TL;DR

This paper investigates the maximum number of active links in a wireless network with fading channels, proposing strategies that approach the theoretical upper bounds and operate efficiently in interference- and noise-limited regimes.

Contribution

It introduces a modified decentralized link activation strategy that nearly achieves the optimal scaling law in fading wireless networks.

Findings

Upper bound scales as (1/λ) log n

Modified strategy is asymptotically optimal for extreme λ values

Network can operate in noise-limited regime with reduced throughput scaling

Abstract

A network of $n$ wireless communication links is considered in a Rayleigh fading environment. It is assumed that each link can be active and transmit with a constant power $P$ or remain silent. The objective is to maximize the number of active links such that each active link can transmit with a constant rate $\lambda$. An upper bound is derived that shows the number of active links scales at most like $\frac{1}{\lambda} \log n$. To obtain a lower bound, a decentralized link activation strategy is described and analyzed. It is shown that for small values of $\lambda$, the number of supported links by this strategy meets the upper bound; however, as $\lambda$ grows, this number becomes far below the upper bound. To shrink the gap between the upper bound and the achievability result, a modified link activation strategy is proposed and analyzed based on some results from random graph theory. It is shown that this modified strategy performs very close to the optimum. Specifically, this strategy is \emph{asymptotically almost surely} optimum when $\lambda$ approaches $\infty$ or 0. It turns out the optimality results are obtained in an interference-limited regime. It is demonstrated that, by proper selection of the algorithm parameters, the proposed scheme also allows the network to operate in a noise-limited regime in which the transmission rates can be adjusted by the transmission powers. The price for this flexibility is a decrease in the throughput scaling law by a multiplicative factor of $\log \log n$.