# Throughput Limits of Wireless Networks With Fading Channels

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## Date

2007-12-21T18:08:42Z

## Authors

Ebrahimi Tazeh Mahalleh, Masoud

## Advisor

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## Publisher

University of Waterloo

## Abstract

Wireless Networks have been the topic of fundamental research in recent years with the aim of achieving reliable and efficient communications. However, due to their complexity, there are still many aspects of such configurations that remain as open problems. The focus of this thesis is to investigate some throughput limits of wireless networks. The network under consideration consists of $n$ source-destination pairs (links) operating in a single-hop fashion. In Chapters 2 and 3, it is assumed that each link can be active and transmit with a constant power P or remain silent. Also, fading is assumed to be the
dominant factor affecting the strength of the channels between transmitter and receiver terminals. The objective is to choose a set
of active links such that the throughput is maximized, where the rate of active links are either unconstrained or constrained. For the unconstrained throughput maximization, by deriving an upper bound and a lower bound, it is shown that in the case of Rayleigh fading: (i) the maximum throughput scales like $\log n$, (ii) the maximum throughput is achievable in a distributed fashion. The upper bound is obtained using probabilistic methods, where the key point is to upper bound the throughput of any random set of active links
by a chi-squared random variable. To obtain the lower bound, a threshold-based link activation strategy (TBLAS) is proposed and
analyzed. The achieved throughput of TBLAS is by a factor of four larger than what was obtained in previous works with centralized
methods and with multihop communications. When the active links are constrained to transmit with a constant rate $\lambda$, an upper bound is derived that shows the number of active links scales at most like $\frac{1}{\lambda} \log n$. It is proved that TBLAS \emph{asymptotically almost surely(a.a.s.)} yields a feasible solution for the constrained throughput maximization problem. This solution, which is suboptimal in general, performs close to the upper bound for small values of $\lambda$. To improve the suboptimal solution, a double-threshold-based link activation strategy (DTBLAS) is proposed and analyzed based on some results from random graph theory. It is demonstrated that DTBLAS performs very close to the optimum. Specifically, DTBLAS is a.a.s. optimum when $\lambda$ approaches $\infty$ or $0$. The optimality results are obtained in an interference-limited regime. However, it is shown that, by proper selection of the algorithm parameters, DTBLAS 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 factor of $\log \log n$. In Chapter 4, the problem of throughput maximization by means of power allocation is considered. It is demonstrated that under individual power constraints, in the optimum solution, the power of at least one link should take its maximum value. Then, for the special case of $n=2$ links, it is shown that the optimum power allocation strategy for throughput maximization is such that either both links use their maximum power or one of them uses its maximum power and the other keeps silent.

## Description

## Keywords

Wireless network, Fading channel, Throughput, Scaling law, Random graph