[Paper Review] Interference Mitigation in Large Random Wireless Networks

Matthew Aldridge|arXiv (Cornell University)|Sep 6, 2011

Wireless Communication Security Techniques70 references3 citations

TL;DR

This paper establishes the asymptotic sum-capacity of large random dense Gaussian interference networks using ergodic interference alignment. It proves that as network size grows, the average per-user capacity converges in probability to $\frac{1}{2}\mathbb{E}\log(1+2\mathtt{SNR})$, under general power-law path loss and random node placement, resolving a key open problem in large-scale wireless network capacity limits.

ABSTRACT

A central problem in the operation of large wireless networks is how to deal with interference -- the unwanted signals being sent by transmitters that a receiver is not interested in. This thesis looks at ways of combating such interference. In Chapters 1 and 2, we outline the necessary information and communication theory background, including the concept of capacity. We also include an overview of a new set of schemes for dealing with interference known as interference alignment, paying special attention to a channel-state-based strategy called ergodic interference alignment. In Chapter 3, we consider the operation of large regular and random networks by treating interference as background noise. We consider the local performance of a single node, and the global performance of a very large network. In Chapter 4, we use ergodic interference alignment to derive the asymptotic sum-capacity of large random dense networks. These networks are derived from a physical model of node placement where signal strength decays over the distance between transmitters and receivers. (See also arXiv:1002.0235 and arXiv:0907.5165.) In Chapter 5, we look at methods of reducing the long time delays incurred by ergodic interference alignment. We analyse the tradeoff between reducing delay and lowering the communication rate. (See also arXiv:1004.0208.) In Chapter 6, we outline a problem that is equivalent to the problem of pooled group testing for defective items. We then present some new work that uses information theoretic techniques to attack group testing. We introduce for the first time the concept of the group testing channel, which allows for modelling of a wide range of statistical error models for testing. We derive new results on the number of tests required to accurately detect defective items, including when using sequential `adaptive' tests.

Motivation & Objective

• To determine the fundamental sum-capacity limit of large random dense wireless networks under realistic path loss and fading models.
• To resolve the open problem of characterizing the asymptotic per-user capacity in such networks.
• To demonstrate that ergodic interference alignment achieves optimal scaling in dense random networks.
• To provide a rigorous information-theoretic proof of capacity scaling using bottleneck link arguments and probabilistic counting.
• To generalize prior results on sum-capacity to broader spatial and fading models beyond uniform placement and Rayleigh fading.

Proposed method

• Models the network as an $n$-user Gaussian interference channel with time-varying fading coefficients and distance-dependent path loss.
• Uses ergodic interference alignment, where random phases in the channel coefficients allow interference to be aligned at receivers over time, enabling interference neutralization.
• Applies the bottleneck link argument from Jafar to upper-bound the sum-capacity by identifying critical links that constrain overall network throughput.
• Employs probabilistic counting to show that a large number of such bottleneck links exist with high probability in random networks.
• Derives a direct converse using the entropy power inequality and mutual information bounds on the capacity of bottleneck links.
• Uses a general power-law attenuation model where signal power decays as a function of distance, not restricted to uniform node placement.

Experimental results

Research questions

• RQ1 What is the asymptotic sum-capacity of a large random dense wireless network with general path loss and random node placement?
• RQ2 Can ergodic interference alignment achieve the optimal sum-capacity scaling in such networks?
• RQ3 How does the average per-user capacity behave as the number of users $n$ tends to infinity?
• RQ4 What is the role of bottleneck links in limiting the sum-capacity of large interference networks?
• RQ5 How do general fading models and non-uniform node distributions affect the capacity scaling law?

Key findings

• The average per-user capacity $C_{\Sigma}/n$ converges in probability to $\frac{1}{2}\mathbb{E}\log(1+2\mathtt{SNR})$ as $n \to \infty$ under general power-law attenuation and independent random node placement.
• The result holds for any spatial distribution of transmitters and receivers, not restricted to uniform placement on the unit square.
• Ergodic interference alignment achieves the optimal sum-capacity scaling, matching the theoretical upper bound derived via bottleneck link analysis.
• The proof establishes a tight converse using probabilistic counting of bottleneck links and information-theoretic bounds on their capacity.
• The result generalizes prior findings by Jafar and Johnson et al., extending them to non-uniform node distributions and arbitrary path loss functions.
• The asymptotic capacity is independent of network geometry and depends only on the expected signal-to-noise ratio $\mathtt{SNR}$, under the given fading and path loss assumptions.