On the Delay-Throughput Tradeoff in Distributed Wireless Networks

This paper deals with the delay-throughput analysis of a single-hop wireless network with $n$ transmitter/receiver pairs. All channels are assumed to be block Rayleigh fading with shadowing, described by parameters $(\alpha,\varpi)$, where $\alpha$ denotes the probability of shadowing and $\varpi$ represents the average cross-link gains. The analysis relies on the distributed on-off power allocation strategy (i.e., links with a direct channel gain above a certain threshold transmit at full power and the rest remain silent) for the deterministic and stochastic packet arrival processes. It is also assumed that each transmitter has a buffer size of one packet and dropping occurs once a packet arrives in the buffer while the previous packet has not been served. In the first part of the paper, we define a new notion of performance in the network, called effective throughput, which captures the effect of arrival process in the network throughput, and maximize it for different cases of packet arrival process. It is proved that the effective throughput of the network asymptotically scales as $\frac{\log n}{\hat{\alpha}}$, with $\hat{\alpha} \triangleq \alpha \varpi$, regardless of the packet arrival process. In the second part of the paper, we present the delay characteristics of the underlying network in terms of the packet dropping probability. We derive the sufficient conditions in the asymptotic case of $n \to \infty$ such that the packet dropping probability tend to zero, while achieving the maximum effective throughput of the network. Finally, we study the trade-off between the effective throughput, delay, and packet dropping probability of the network for different packet arrival processes.Comment: Submitted to IEEE Transactions on Information Theory (34 pages

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

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 $\log \log n$.Comment: Submitted to IEEE Trans. Information Theor

Throughput Scaling Laws for Wireless Networks with Fading Channels

A network of n communication links, operating over a shared wireless channel, is considered. Fading is assumed to be the dominant factor affecting the strength of the channels between transmitter and receiver terminals. 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 throughput over the selection of active links. 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 decentralized link activation strategy is proposed and analyzed.Comment: Submitted to IEEE Transactions on Information Theory (Revised