Spatially Embedded Networks

Lead Research Organisation: University of Oxford
Department Name: Engineering Science

Abstract

The complexity of wireless communication networks has grown considerably in recent years. This has been driven in part by academic research that has started to define the information theoretic boundaries and advantages of certain complex networking topologies and protocols. On the other hand, the demands from consumers and industry have pushed wireless networks towards more sophisticated architectures and solutions, primarily in order to ensure a broad range of services can be delivered using a common infrastructure. This is particularly true of 4/5G technologies, which many believe should support all things for all people, including voice, data, public safety, distributed sensing and monitoring, etc. However, similar beliefs and trends can be found in other sectors, such as smart grid networks and even satellite networks.

It is important that engineers understand the global properties of complex networks, and how these properties arise from local structure. Such information can be fed into models and optimisation routines so that practical networks can be designed to perform as well as possible. A common approach to tackling complex problems is to exploit randomness and statistical properties of the underlying system. Probabilistic approaches to network modelling are not without their difficulties, and some of the main problems that researchers have struggled with over the years arise from the fact that networks are finite entities with physical boundaries.

Recent research by the investigators has focused on the effects that boundaries have on connectivity when networks are embedded in some finite spatial domain. Analytic expressions for the overall connection probability have been obtained. These formulae quantify the intuitive phenomenon that nodes near the boundary are more likely to disconnect, and thus they explain how the network outage probability behaves at high node densities. This work has been extended considerably to explore notions of resilience (k-connectivity), the effects of node directivity, diversity and power scaling laws, complicated geometric bounding domains (both convex and non-convex), and even the interplay between higher layer trust protocols and the physical network set-up and spatial domain.

In this project, the probabilistic formalism alluded to above will be exploited further to study several key concepts that influence the structure of spatially embedded networks. The following four topics will be treated:

- continuum models of spatially embedded networks, including the investigation of spectral and centrality properties of random networks;
- mobility models in spatially embedded networks, including random waypoint and Levy flight processes;
- trust models in spatially embedded networks, including trust dynamics and protocol design;
- temporal models of spatially embedded networks, including dynamical node and link (edge) models.

The work will take a mathematical approach, but will always maintain a focus on practical implications and designs.

Planned Impact

A number of parties and sectors will benefit from this research. These range from graduate students to industry leaders, and from private enterprise to spectrum regulators. Engagement with potential beneficiaries will largely take place through summer schools, workshops, and meetings with private industry.

Academic beneficiaries -- including Penrose (Bath), Win (MIT), Haenggi (Notre Dame) and many other academic institutions that are presently active in random graph/network research -- will no doubt create further scientific advances related to this research. New techniques and know how will be developed, and new results will of course be disseminated through scientific publications. Due to the timeliness of this research, its academic reach will be international.

Postdoctoral researchers and graduate students will benefit from skills training through an annual summer school and workshop programme. This training will strengthen the national pool of mathematically able engineers and problem solvers and attract others with similar skills to the UK for employment in the medium to long term. It is widely recognised that having a large number of skilled professionals such as these is of great importance to the UK in this age of information and technology, particularly with interest in electrical, electronic and computer engineering on the decline (Perkins' Review).

Industrial R&D facilities will feed research output into established businesses and markets by developing new products and services related to the Internet of Things and 5G cellular systems. They may also seek to create new businesses based on novel discoveries made in this project. R&D organisations are well represented on the panel of project partners (Toshiba, NEC, BT TSO), and thus it is envisaged that the time required for technology uptake will be minimal (2-3 years). In addition, due to the UK's reputation as a place for excellence in network research, which will be strengthened by this project, will bring further inward investment from companies like Toshiba and NEC.

Network operators and vendors will also utilise the output from this research. Network architectures will be able to be optimised by using techniques and theories developed in this project, thus enabling the delivery of new products that will enhance the end users' quality of life. Examples may include the exploitation of statistical connectivity or centrality information coupled with data analytics to offer users personalised services, or enable ad hoc device-to-device networks to form reliably.

Public sector organisations including health, police, and fire/rescue services will benefit from this research since it will aid with the development of enhanced public safety networks built on secure, ad hoc protocols and optimised network architecutres. The research will influence the design of truly intelligent transport systems (e.g., multihop vehicle-to-vehicle and vehicle-to-infrastructure), which will lead to safer UK road and rail networks.

Regulators are working hard to facilitate the creation of higher bandwidth next generation wireless services without allowing crippling levels of interference to affect transmissions. Interference is, however, a random quantity, being dependent upon the geographical locations of transmitting and receiving devices, the propagation medium and the likelihood that devices access the medium concurrently. Such random systems will be described by the proposed research, and thus the findings of this project will influence policy related to spectrum usage in the UK and further afield. In addition to these interference considerations avenues for influencing government policy may appear in other markets and technologies. Indeed, initial work by the investigators was used by Toshiba several years ago to inform and influence government policy on suitable communication network architectures for smart electricity meters.

Publications

10 25 50

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Chen G (2017) Secrecy Outage Analysis for Downlink Transmissions in the Presence of Randomly Located Eavesdroppers in IEEE Transactions on Information Forensics and Security

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Chen G (2018) Secure Routing for Multihop Ad Hoc Networks With Inhomogeneous Eavesdropper Clusters in IEEE Transactions on Vehicular Technology

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Coon JP (2018) Entropy of spatial network ensembles. in Physical review. E

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Dang S (2018) Lexicographic Codebook Design for OFDM With Index Modulation in IEEE Transactions on Wireless Communications

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Dang S (2018) Adaptive OFDM With Index Modulation for Two-Hop Relay-Assisted Networks in IEEE Transactions on Wireless Communications

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Dang S (2018) Multicarrier Relay Selection for Full-Duplex Relay-Assisted OFDM D2D Systems in IEEE Transactions on Vehicular Technology

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Dettmann CP (2016) Random geometric graphs with general connection functions. in Physical review. E

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Etemadi Tajbakhsh S (2018) Network Coding for Physical Layer Secrecy in IEEE Wireless Communications Letters

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Knight G (2016) Counting Geodesic Paths in 1D VANETs in IEEE Wireless Communications Letters

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Tajbakhsh SE (2017) Accessibility and delay in random temporal networks. in Physical review. E

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Thanh TL (2016) System-level analysis of receiver diversity in SWIPT-enabled cellular networks in Journal of Communications and Networks

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Tu Lam T (2016) System-Level Analysis of SWIPT MIMO Cellular Networks in IEEE Communications Letters

 
Description 1. A key result in this project has been the development of a mathematical framework for analysing spatial network complexity. This framework brings together tools from information theory, probability theory, and geometry to capture the effect that the space in which a network is embedded has on the uncertainty and complexity of the network topology. This has opened up a new avenue for exploration and potential exploitation, e.g., in the context of designing better protocols and algorithms for wireless communication networks.

2. A second result of notable importance has been the successful application of analytical methods to study security in wireless networks that operate in the presence of eavesdropping devices, the locations of which are unknown to the legitimate users. In this example, networks confined to operate within a given region have been analysed using the probabilistic tool of stochastic geometry. Applications of the theory include visible light communication (VLC) networks and networks of unmanned aerial vehicles (UAVs).

3. The third key result relates to inferring trust in networks. Specifically, we developed a new way of inferring the trustworthiness of agents in a network of distributed devices, which may be useful in future blockchain and IoT networks.

4. We constructed analytic methods for predicting the reachability of certain devices in a network after a given period of time. This result enables the study of delay in distributed networks.

5. Finally, we developed analytical tools and techniques that can be used to optimise the placement of cellular base stations and/or WiFi access points in network planning tasks. These tools can also be exploited to devise optimal ways to turn on/off resources (access points) with a view to maximising the energy efficiency of the network.
Exploitation Route Network operators (e.g., energy, telecomms) will be able to adopt and adapt the findings of the project to predict network performance, simulate and analyse particular deployment scenarios, and design better systems. Specifically, the security of wireless networks can be studied, predicted, and improved based on project results. Furthermore, temporal changes in network structure and reachability can be analysed in practical scenarios. The likelihood of network failures or changes can be investigated using the tools developed in this project.

Regarding trustworthiness, our results can be applied in blockchain and IoT networks (among others) to improve security and information fidelity.
Sectors Aerospace, Defence and Marine,Digital/Communication/Information Technologies (including Software),Energy,Manufacturing, including Industrial Biotechology,Transport

URL http://www.eng.ox.ac.uk/sen/
 
Description US ARMY RESEARCH OFFICE - BROAD AGENCY ANNOUNCEMENT FOR BASIC AND APPLIED SCIENTIFIC RESEARCH
Amount $96,200 (USD)
Organisation US Army 
Sector Public
Country United States
Start 03/2019 
End 02/2020
 
Description CNRS-OXFORD 
Organisation National Center for Scientific Research (Centre National de la Recherche Scientifique CNRS)
Department IN2P3 CNRS
Country France 
Sector Public 
PI Contribution This has mostly been a research partnership. Collaborative research has been undertaken and several papers have been published. Also, Marco Di Renzo at CNRS co-directs (with Justin P Coon at Oxford) the IEEE SIG on Heterogeneous Ultra-Dense Networks. Finally, Dr Di Renzo assisted with three summer schools and symposia that Prof. Coon and Prof. Carl Dettmann (Bristol) organised in Oxford (Sep 2016, Sep 2017) and Bristol (Sep 2018).
Collaborator Contribution This has largely been agile and bilateral.
Impact Four publications have been accepted: Chen, G., Coon, J. P., & Di Renzo, M. (2017). Secrecy outage analysis for downlink transmissions in the presence of randomly located eavesdroppers. Information Forensics & Security, IEEE Transactions on, (to appear). Lam, T., Di Renzo, M., & Coon, J. P. (2016). System-Level analysis of receiver diversity in SWIPT-enabled cellular networks. Journal of Communications and Networks, (to appear). Lam, T., Di Renzo, M., & Coon, J. P. (2016). System-Level analysis of SWIPT MIMO cellular networks. Communications Letters, IEEE, 20(10), 2011-2014. Chen, G., Coon, J. P., & Di Renzo, M. (2016, December). Secrecy enhancement by antenna selection and FD communication with randomly located eavesdroppers. In 2016 IEEE Global Communications Conference (GLOBECOM). IEEE. A summer school and symposium were successfully organised (http://www.eng.ox.ac.uk/sen/events.html). Further funding has been applied for to further this collaboration (PICS - a CNRS-Oxford focused scheme).
Start Year 2016
 
Description Toshiba-Oxford 
Organisation Toshiba Research Europe Ltd
Country United Kingdom 
Sector Private 
PI Contribution Our team contributed expertise to this collaboration.
Collaborator Contribution The partner contributed their expertise and some research effort as well as a LINUX based simulation cluster to explore numerical results.
Impact The partnership has mostly been a research collaboration. Three papers have been accepted/published jointly with the partner since the project commenced: [1] J. P. Coon, O. Georgiou, and C. P. Dettmann, "Connectivity scaling laws in wireless networks," IEEE Wireless Commun. Lett., vol. 4, no. 6, pp. 629-632, Dec. 2015. [2] M. Z. Bocus, O. Georgiou, J. P. Coon and D. A. Hedges, "Location-based coverage probability for distributed antenna systems in finite-area networks," in Communications, 2017. ICC '17. IEEE International Conference on, May 21-25, 2017, pp. 1-5. [3] J. P. Coon, C. P. Dettmann, and O. Georgiou, "Entropy of spatial network ensembles," Phys. Rev. E, vol. 97, no. 4, 042319, Apr. 2018. Toshiba has begun to develop some of the methods based on spatial network entropy for its own purposes. It is too early to tell if this will have impact.
Start Year 2015
 
Description Wellington-Oxford 
Organisation Victoria University of Wellington
Department School of Mathematics and Statistics
Country New Zealand 
Sector Academic/University 
PI Contribution Expertise on network theory was contributed. Specifically, I contributed to a paper on mobile network connectivity that will be presented at ICC in May. I also contributed to a grant application that was recently submitted to the Royal Society of New Zealand.
Collaborator Contribution Expertise on statistics was contributed. Specifically, my collaborator, Prof. Pete Smith, contributed to a paper that was presented at ICC 2017. He also assisted with the preparation of an EPSRC Established Career Fellowship proposal that I submitted in November 2017.
Impact The collaboration resulted in two accepted conference contributions: J. P. Coon and P. J. Smith, "Topological entropy in wireless networks subject to composite fading," in Communications, 2017. ICC '17. IEEE International Conference on, May 21-25, 2017, pp. 1-5. and P. J. Smith and J. P. Coon, "Connectivity times for mobile D2D networks," in International Conference on Communications, 2018. ICC '18. IEEE, May 20-24, 2018, pp. 1-5.
Start Year 2016
 
Description Graph entropy lecture (Aston) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact This was an invited academic lecture to physicists and engineers at Aston University. Approximately 10 graduate students and academics attended. Through the discussion that ensued, it was clear that the topic lectured on opened the eyes of some attendees to new problems.
Year(s) Of Engagement Activity 2016
 
Description Graph entropy lecture (Newcastle) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact This was an invited academic lecture to engineers at Newcastle University. Approximately 50 graduate students and academics attended. Through the discussion that ensued, it was clear that the topic lectured on opened the eyes of some attendees to new problems, and I was able to advise on the work of others. Moreover, this lecture stimulated a discussion about a follow-on collaborative research proposal to EPSRC involving Oxford, Newcastle and Durham. This activity is in the proposal-writing stage at present.
Year(s) Of Engagement Activity 2016
 
Description Graph entropy lecture (York) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact This was an invited academic lecture to engineers at York University. Approximately 15 graduate students and academics attended. Through the discussion that ensued, it was clear that the topic lectured on opened the eyes of some attendees to new problems. Additionally, this discussion factored into an initiative to write a new H2020 grant proposal, which was submitted on 8 Nov and is currently in review.
Year(s) Of Engagement Activity 2016
 
Description Keynote lecture: On the entropy of wireless networks - Workshop on Advances in Wireless Com- munications, Chengdu and Nanjing, China 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Approximately 400 graduate students attended this keynote lecture, which was one of two at the workshop. This is an annual event where recognised experts in wireless communications lecture on topics of their choice.
Year(s) Of Engagement Activity 2018
 
Description Keynote lecture: Spatial graph entropy - Workshop on Spatial Stochastic Models for Wireless Networks, Shanghai, China 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact One of two keynote lectures at SpaSWiN, the premier workshop on spatial network modelling.
Year(s) Of Engagement Activity 2018
URL http://iwin.sjtu.edu.cn/wiopt2018/spaswin.html
 
Description Mailing list 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact A mailing list was set up to disseminate outputs of the Spatially Embedded Networks project to a wider audience. Newsletters are sent out quarterly. These give details of talks, publications, etc.
Year(s) Of Engagement Activity 2015
 
Description On the complexity of wireless networks (K eynote, CommNet2 Workshop on Commu- nications and Signal Processing for 5G++, Durham University, U.K.) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Keynote at a forward-looking workshop. Attendees from national universities were present.
Year(s) Of Engagement Activity 2018
 
Description On the entropy of network ensembles - University of Nottingham 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Postgraduate students
Results and Impact Invited lecture at the University of Nottingham.
Year(s) Of Engagement Activity 2018
 
Description On the entropy of spatial network ensembles (Imperial College London, U.K.) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Invited lecture at Imperial. Led to invited proposal from US ARO, which has now been funded.
Year(s) Of Engagement Activity 2018
 
Description Presentation on network modelling activities (BT) 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Local
Primary Audience Professional Practitioners
Results and Impact This was an invited lecture to engineers at BT labs in Martlesham. Approximately 10 engineers and managers attended. Through the discussion that ensued, it was clear that the topic lectured on opened the eyes of some attendees to new ways of solving problems.
Year(s) Of Engagement Activity 2016
 
Description ResearchGate Project 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact A 'project' was set up on ResearchGate to disseminate outputs of the Spatially Embedded Networks project to the wider community. The team has updated this project as new publications have been accepted.
Year(s) Of Engagement Activity 2016
URL https://www.researchgate.net/project/Spatially-Embedded-Networks-EPSRC-2
 
Description Short courses on aspects of random/spatial networks 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Postgraduate students
Results and Impact Prof. Justin Coon (Department of Engineering Science, Oxford University) and Prof. Carl Dettmann (School of Mathematics, Bristol University) organised and delivered two-day short courses to educate graduate students, postdocs and practicing engineers in the nuances of network theory in September of 2016, 2017, and 2018. The emphasis of this course was on spatial networks, i.e., spatial and geometric effects are considered, thus facilitating a study of networks from a physical layer perspective. Between 25 and 50 attendees participated from three continents. Feedback was excellent, with many researchers stating that the course would be useful for their personal areas of work.
Year(s) Of Engagement Activity 2016,2017,2018
URL http://www.eng.ox.ac.uk/sen/events.html
 
Description Spatial network models for wireless communication - Lectures to China Telecom 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Industry/Business
Results and Impact Two invited lectures on spatial network modelling of wireless systems were delivered to delegates from China Telecom in Oxford and Cambridge.
Year(s) Of Engagement Activity 2018
 
Description Symposium on Spatial Networks 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact Prof. Coon and Prof. Dettmann (Bristol) organised symposia related to spatial networks in 2016, 2017, and 2018. The symposium brought together experts from the mathematics, physics and engineering communities working on elements of graph theory, complex networks, information theory and communication theory. Keynote talks were given by the following leading international experts, including:

Marc Barthélemy, CEA Institut de Physique Theorique
Bartek Blaszczyszyn, INRIA-ENS
Anthony Bonato, Ryerson University
Marco Di Renzo, CNRS-SUPÉLEC-University of Paris-Sud XI
Mark Newman, University of Michigan

In all three years, discussions were plentiful, and feedback about the event was excellent. Attendees came to see these events as THE spatial networks event of the year.
Year(s) Of Engagement Activity 2016,2017,2018
URL http://www.eng.ox.ac.uk/sen/events.html
 
Description Website 
Form Of Engagement Activity Engagement focused website, blog or social media channel
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Other audiences
Results and Impact A project website was set up to give details of the project to the wider public. Material held on the website includes project news, publications, information about courses and symposia organised by the project participants, etc.
Year(s) Of Engagement Activity 2016
URL http://www.eng.ox.ac.uk/sen/