Periodic Reporting for period 4 - NEMO (Network Motion)
Reporting period: 2023-07-01 to 2024-12-31
Stochastic geometry emerges as the main tool for the system level design of large wireless communication networks. It provides a universal tool allowing one to design and imension such networks, notably cellular networks, device-to-device networks, self-organized WiFi networks, vehicular networks, non-terrestrial networks, etc.
One can see stochastic geometry as a spatial extension of the representation of queuing networks as functional of one dimensional point processes. Here, the system level properties of large cellular communication networks are represented as functionals of two or three dimensional point processes leveraging, e.g. shot noise fields to represent interference, and Voronoi tessellations to represent association cells. This leads to the definition and the explicit computation of global metrics such as the area spectral efficiency of such networks, based on statistical physics type analyses. This representation by stochastic geometry can then be used to determine the architectures optimizing these metrics.
This approach leads to a system level assessment of major paradigms to be used in the forthcoming generations of communication networks such as Reconfigurable Intelligent Surfaces, Joint Communication and Sensing, cell free architectures and non-terrestrial networks, and of their interplay. By interplay, we mean here a range of activities from joint economic analysis to joint deployment optimization, to the design both new real time and non real time controllers for all these new paradigms.
NEMO is at the interface of mathematics, primarily stochastic geometry and random graph theory, and networking, as illustrated in the examples listed above. Its objective is to improve the mathematical understanding of large random networks and of their dynamics in order to analyze the concrete communication network problems listed above, among others. Interestingly, the developed mathematical machinery applies to other and at first glance completely different large networks such as social networks or biological networks.
One can see stochastic geometry as a spatial extension of the representation of queuing networks as functional of one dimensional point processes. Here, the system level properties of large cellular communication networks are represented as functionals of two or three dimensional point processes leveraging, e.g. shot noise fields to represent interference, and Voronoi tessellations to represent association cells. This leads to the definition and the explicit computation of global metrics such as the area spectral efficiency of such networks, based on statistical physics type analyses. This representation by stochastic geometry can then be used to determine the architectures optimizing these metrics.
This approach leads to a system level assessment of major paradigms to be used in the forthcoming generations of communication networks such as Reconfigurable Intelligent Surfaces, Joint Communication and Sensing, cell free architectures and non-terrestrial networks, and of their interplay. By interplay, we mean here a range of activities from joint economic analysis to joint deployment optimization, to the design both new real time and non real time controllers for all these new paradigms.
NEMO is at the interface of mathematics, primarily stochastic geometry and random graph theory, and networking, as illustrated in the examples listed above. Its objective is to improve the mathematical understanding of large random networks and of their dynamics in order to analyze the concrete communication network problems listed above, among others. Interestingly, the developed mathematical machinery applies to other and at first glance completely different large networks such as social networks or biological networks.
The mathematical part of the project is centered on the development of the theories of unimodular random graphs, point processes, and stochastic geometry, with an emphasis on dynamics on such random structures. Instances of mathematical tools involved, beyond unimodularity, are ergodic theory, mean-field techniques, spectral analysis, coupling techniques, and Palm calculus. The mathematical work on unimodular random networks is meant to analyze networks which are not necessarily embedded in the Euclidean space: how to define such random objects? how to evaluate their dimensions? what type of computational tools can one rely on to analyze them quantitatively? what classes of dynamics can they harbor? Instances of dynamics considered are navigations on graphs, optimizations on graphs, random walks and migrations on graphs, epidemics on graphs, scheduling and queuing on graphs, interference on graphs.
The application part of the project has a central component in communication networks. The mastering of the complexity of this class of systems is a major challenge worldwide. NEMO focused on the mastering of this complexity by stochastic geometry and random graph theory. It was based on a strong collaboration with Nokia Bell Laboratories Paris (NBLP). The first class of problems considered with NBLP concerned the interplay between beam management and user motion. The second class was the analysis of 5/6G cellular networks enhanced with Reconfigurable Intelligent Surfaces. A third class of questions concerned resource sharing with real-time constraints, which is of central importance for both the industrial applications of 5/6G networks and of WiFi type networks. The fourth set of questions concerned the analysis of non-terrestrial and in particular low Earth orbit satellite communication networks.
Another broad application domain investigated is that of biological networks. Three main directions of research were selected: neural network dynamics, epidemics on networks, and classification of phylogenetic networks.
The dissemination effort was thorough: 8 workshops were organized. 52 research papers were published, with a good equilibrium between math journal publications and IEEE type publications. One book on point processes was posted and another one on unimodularity is under preparation. 72 dissemination events (from poster to keynote lectures to radio interviews) were organized. The research achievements of the project members were recognized through two international and one national award, with, again, a good equilibrium between mathematics and communications. The work in NEMO also had an impact on the scientific policy concerning communication networks both in France (through two reports of the French Academy of Sciences) and at the European level. (through contributions to the SRIA).
The application part of the project has a central component in communication networks. The mastering of the complexity of this class of systems is a major challenge worldwide. NEMO focused on the mastering of this complexity by stochastic geometry and random graph theory. It was based on a strong collaboration with Nokia Bell Laboratories Paris (NBLP). The first class of problems considered with NBLP concerned the interplay between beam management and user motion. The second class was the analysis of 5/6G cellular networks enhanced with Reconfigurable Intelligent Surfaces. A third class of questions concerned resource sharing with real-time constraints, which is of central importance for both the industrial applications of 5/6G networks and of WiFi type networks. The fourth set of questions concerned the analysis of non-terrestrial and in particular low Earth orbit satellite communication networks.
Another broad application domain investigated is that of biological networks. Three main directions of research were selected: neural network dynamics, epidemics on networks, and classification of phylogenetic networks.
The dissemination effort was thorough: 8 workshops were organized. 52 research papers were published, with a good equilibrium between math journal publications and IEEE type publications. One book on point processes was posted and another one on unimodularity is under preparation. 72 dissemination events (from poster to keynote lectures to radio interviews) were organized. The research achievements of the project members were recognized through two international and one national award, with, again, a good equilibrium between mathematics and communications. The work in NEMO also had an impact on the scientific policy concerning communication networks both in France (through two reports of the French Academy of Sciences) and at the European level. (through contributions to the SRIA).
Mathematical Contributions: The main achievements in unimodular graphs are (1) the completion of the mathematical definition of the unimodular Hausdorff and the Minkowski dimensions of random networks; (2) the definition of point processes and Palm calculus on unimodular spaces; (3) the identification of the Gromov-Hausdorff type distances to be used on the space of general undimodular metric spaces. Several instances of graph and point process dynamics were also studied using the unimodular framework: (a) renewal type point-shifts; (b) Circle packing problems; (c) record vertex shifts on processes with stationary increments; (d) random binary trees; (e) balanced allocations; (f) spectral properties of random directed networks. Euclidean stochastic geometry has also progressed a lot during the project. The main contributions bear on optimal marking, stabilization, and high dimensional tessellations. Several instances of stochastic geometric problems were also studied using this machinery: (a) point process-based space occupation games; (b) optimal marking on point processes; (c) contact processes on point processes; and (d) contention processes on point processes. These topics are covered in a new book.
Communication Networks: A thorough stochastic geometry analysis of 5G networking was conducted in collaboration with Nokia Bell Labs. The main results bear on (1) beam management, (2) the gains consecutive to bandwidth partitioning, (3) the analysis of Reconfigurable Intelligent Surfaces. The proposed approaches, which are all based on stochastic geometry, answer core questions in 5/6G networking and are leveraged by Nokia for standardization purposes. The two main further achievements in this domain are (4) the definition of a new spatial network calculus and (5) the design of a new methodology for the system level analysis of non-terrestrial networks.
Biological Networks: Replica mean field techniques were introduced and studied for Galves-Loecherbach neural networks. The work on contagion migration processes allows one to better understand the behavior of the thresholds separating the survival and the non-survival of epidemics. The ongoing work on the connections between unimodularity and evolution provided several structural results on the possible types of evolutionary trees.
Social Networks: Opinion dynamics of the noisy bounded confidence type was investigated. Another important result was the design and analysis of the phase transitions of a new community detection model leveraging additional distance-type data.
Communication Networks: A thorough stochastic geometry analysis of 5G networking was conducted in collaboration with Nokia Bell Labs. The main results bear on (1) beam management, (2) the gains consecutive to bandwidth partitioning, (3) the analysis of Reconfigurable Intelligent Surfaces. The proposed approaches, which are all based on stochastic geometry, answer core questions in 5/6G networking and are leveraged by Nokia for standardization purposes. The two main further achievements in this domain are (4) the definition of a new spatial network calculus and (5) the design of a new methodology for the system level analysis of non-terrestrial networks.
Biological Networks: Replica mean field techniques were introduced and studied for Galves-Loecherbach neural networks. The work on contagion migration processes allows one to better understand the behavior of the thresholds separating the survival and the non-survival of epidemics. The ongoing work on the connections between unimodularity and evolution provided several structural results on the possible types of evolutionary trees.
Social Networks: Opinion dynamics of the noisy bounded confidence type was investigated. Another important result was the design and analysis of the phase transitions of a new community detection model leveraging additional distance-type data.