Complexity in 6G: Measures, Advanced Models and Mathematical Algorithms to Face New Challenges in the New Communication Paradigm Development

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: 30 November 2024 | Viewed by 7701

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Dipartimento di Ingegneria Elettrica, Elettronica ed Informatica (DIEEI), Universitá di Catania, 95125 Catania, Italy
Interests: bio-inspired models; ICT; telecommunications; social networks; complex networks; multilayer networks; social contagion; epidemic spreading; evolutionary game theory; data mining; machine learning; healthcare applications; cognitive networks

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Department of Clinical and Experimental Medicine c/o Dipartimento di Matematica e Informatica, University of Catania, Viale A. Doria 6, 95125 Catania, Italy
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Special Issue Information

Dear Colleagues,

The forthcoming 6th generation of communication networks (6G) will attempt to rewrite the communication networks’ perspective, focusing on a radical revolution in the way entities and technologies are conceived, integrated, and used. This will lead to innovative approaches with the aim of providing new directions to deal with future network challenges posed by the upcoming 6G. The analysis and modeling of networks as well as dynamical and temporal systems has attracted considerable multidisciplinary interest in research, giving birth to the interdisciplinary field of network science. Network science is the study of systems with many interdependent components, which may interact in several ways. Due to their size and the intrinsic complexity, such systems are defined as complex systems. Network science is providing new radical ways of understanding many different dynamical and temporal mechanisms and processes from the physical, social, engineering information, and biological sciences. Complex systems are characterized by emergent behaviors, largely determined by the nontrivial networks of interactions among their constituents. At a mesoscale level, recurrent patterns of interactions (motifs) determine the overall structure and organization of the system and may help to identify possible anomalies. This motivates the need of analytical methods to design a self-organized, resilient and cognitive network, suitable for many application fields (e.g., digital health or smart cities living scenarios).

In this context, random models are powerful tools to design networks with desired properties. 6G networks are intrinsically suitable to be modelled as multidimensional relational systems of different sub-networks, represented by various graphs that embed interacting elements in different ways. The multiplex or multilayer dimension offers a key change in structural perspective to investigate the emergence of complex network properties. The social aspects include human beings and devices as heterogeneous and interacting elements of a complex socio-technical ecosystem whose collective and evolutionary behavior plays a pivotal role for the design, forecasting, and monitoring of the communication network functions.

This Special Issue focuses on analytical methodologies, measures, and algorithms linked to the complex systems approach to facing challenges in 6G development. We are also interested in case studies based on different application fields, from health to smart cities. Through this Special Issue, we hope to encourage interdisciplinary collaboration between researchers in complex systems and networking from both academia and industry to present their novel and unpublished works in the domains explained above toward meeting the new challenging demands of 6G.

Dr. Marialisa Scatà
Dr. Salvatore Alaimo
Dr. Giovanni Micale
Guest Editors

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Keywords

  • complex systems and networks
  • multilayer networks
  • multiplex networks
  • temporal networks
  • motifs
  • 6G communication networks
  • mobile communication networks
  • computational methods
  • mathematical physics
  • nonlinear problems
  • dynamical systems
  • social networks
  • evolutionary game theory

Published Papers (5 papers)

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Research

20 pages, 1683 KiB  
Article
A Complex Insight for Quality of Service Based on Spreading Dynamics and Multilayer Networks in a 6G Scenario
by Marialisa Scatá and Aurelio La Corte
Mathematics 2023, 11(2), 423; https://doi.org/10.3390/math11020423 - 13 Jan 2023
Cited by 1 | Viewed by 1277
Abstract
Within the 6G vision, the future of mobile communication networks is expected to become more complex, heterogeneous, and characterized by denser deployments with a myriad of users in an ever-more dynamic environment. There is an increasing intent to provide services following the microservice [...] Read more.
Within the 6G vision, the future of mobile communication networks is expected to become more complex, heterogeneous, and characterized by denser deployments with a myriad of users in an ever-more dynamic environment. There is an increasing intent to provide services following the microservice architecture, thus gaining from higher scalability and significant reliability. Microservices introduce novel challenges and the level of granularity impacts performances, due to complex composition patterns. This openness in design demands service requirements be heterogeneous and dynamic. To this end, we propose a framework and a mathematical approach to investigate the complex quality of services. We exploit the temporal multilayer network representation and analysis jointly, with the spreading dynamics of user experience. We study the joint impact of structural heterogeneity and the evolutionary dynamics of the temporal multilayer quality network, composed of networked parameters, and a temporal multilayer social network, populated by a social layered structure of users. We conducted simulations to display our findings on how this modeling approach enables evaluation of otherwise-overlooked information on quality arising from a profound investigation of the structural-complexity and social-dynamics measurements. Full article
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11 pages, 552 KiB  
Article
Ergodic Capacity Analysis of Downlink Communication Systems under Covariance Shaping Equalizers
by Ubaid M. Al-Saggaf, Ahmad Kamal Hassan and Muhammad Moinuddin
Mathematics 2022, 10(22), 4304; https://doi.org/10.3390/math10224304 - 17 Nov 2022
Cited by 2 | Viewed by 835
Abstract
Advances in higher-end spectrum utilization has enabled user equipment to dock multiple antenna elements, and hence make use of selectivity via equalization in new generation of mobile networks. The equalization can exploit channel statistics to shape covariance matrices, and hence improve network performance [...] Read more.
Advances in higher-end spectrum utilization has enabled user equipment to dock multiple antenna elements, and hence make use of selectivity via equalization in new generation of mobile networks. The equalization can exploit channel statistics to shape covariance matrices, and hence improve network performance at the physical layer of these networks by projecting segregated signals to non-overlapping subspaces. We propose to establish the promise of covariance shaping method by incorporating the equalizers in the modelling of a downlink multi-user multiple-input multiple-output (MU-MIMO) systems and thereby characterizing a key performance indicator, namely, the sum ergodic capacity. This is achieved by utilizing a residue theory approach which can account for indefinite eigenvalues. The system modelling is generic in a sense that it requires the base station (BS) to only have second order statistics of the channel rather than instantaneous knowledge. Furthermore, the BS incorporates a transmit beamformer design to enhance the ergodic capacity and feedforward the information of covariance shaping equalizers. Search method for transmit beamforming is also proposed which shows a promising three fold increase in sum ergodic capacity at signal-to-noise ratio of 10 dB for the considered MU-MIMO system. Proposed characterization of the system is authenticated using simulation means, and a comparative analysis of transmit beamformer designs on the sum ergodic rate is showcased. Full article
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21 pages, 3372 KiB  
Article
Multi-User Massive MIMO System with Adaptive Antenna Grouping for Beyond 5G Communication Network
by Shakti Raj Chopra, Akhil Gupta, Sudeep Tanwar, Calin Ovidiu Safirescu, Traian Candin Mihaltan and Ravi Sharma
Mathematics 2022, 10(19), 3621; https://doi.org/10.3390/math10193621 - 03 Oct 2022
Cited by 1 | Viewed by 1875
Abstract
Error-correcting codes with limited errors and higher spectral efficiency are the main concern for wireless communications. In the current situation, research is increasing daily to satisfy the growing demand for users with improved QoS. Adaptive Antenna Grouping (AAG) with a multilevel space–time trellis [...] Read more.
Error-correcting codes with limited errors and higher spectral efficiency are the main concern for wireless communications. In the current situation, research is increasing daily to satisfy the growing demand for users with improved QoS. Adaptive Antenna Grouping (AAG) with a multilevel space–time trellis coding scheme in the Multi-User Massive MIMO system is the better option to provide flexible data transfer speeds, encoding gains, and gain in diversity with improved spectral efficiency and low decoding complexity, including the power optimization by reduced SNR at the same Symbol Error Rate/Frame Error Rate (SER/FER). The prior aim of maintaining spectral efficiency is achieved by using Massive MIMO. This paper presents the AAG according to the channel state information in the Massive MIMO scenario. The impact of the proposed model on standard ITU-R M.2135 scenarios is also demonstrated in this paper. Full article
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10 pages, 643 KiB  
Article
Performance Analysis of Multi-Cell Association in Downlink MU-MIMO System with Arbitrary Beamforming
by Muhammad Moinuddin, Ahmad Kamal Hassan and Ubaid M. Al-Saggaf
Mathematics 2022, 10(15), 2611; https://doi.org/10.3390/math10152611 - 26 Jul 2022
Cited by 1 | Viewed by 1023
Abstract
This article deals with the analysis of the multi-cell association setup, and it exploits the possibility of enhancing coverage in the envisioned sixth generation (6G) large-scale cellular networks. Specifically, we propose a simple, effective approach for finding a closed-form solution to the coverage [...] Read more.
This article deals with the analysis of the multi-cell association setup, and it exploits the possibility of enhancing coverage in the envisioned sixth generation (6G) large-scale cellular networks. Specifically, we propose a simple, effective approach for finding a closed-form solution to the coverage probability of a given user in a multi-cell association regime of downlink multiple-user multiple-input multiple-output (MU-MIMO) systems. In particular, a Rayleigh fading channel is considered, wherein the transmitter has only the knowledge of the second-order statistics of the channel. The proposed work uses an indefinite quadratic formulation method and thereby investigates the effect of cell association in a correlated downlink broadcast channel with co-channel interference, additive white noise, and multiple transceiver antenna elements. In the results, we show that a predefined signal-to-interference-plus-noise ratio (SINR) threshold dictates an effective multi-cell association setup, and we identify the region in which a multi-cell association performs better that a single association-based network. The derived theoretical expressions in this paper are validated by the same means of simulation. Full article
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16 pages, 1024 KiB  
Article
Cognitive Load Balancing Approach for 6G MEC Serving IoT Mashups
by Barbara Attanasio, Andriy Mazayev, Shani du Plessis and Noélia Correia
Mathematics 2022, 10(1), 101; https://doi.org/10.3390/math10010101 - 28 Dec 2021
Cited by 5 | Viewed by 1521
Abstract
The sixth generation (6G) of communication networks represents more of a revolution than an evolution of the previous generations, providing new directions and innovative approaches to face the network challenges of the future. A crucial aspect is to make the best use of [...] Read more.
The sixth generation (6G) of communication networks represents more of a revolution than an evolution of the previous generations, providing new directions and innovative approaches to face the network challenges of the future. A crucial aspect is to make the best use of available resources for the support of an entirely new generation of services. From this viewpoint, the Web of Things (WoT), which enables Things to become Web Things to chain, use and re-use in IoT mashups, allows interoperability among IoT platforms. At the same time, Multi-access Edge Computing (MEC) brings computing and data storage to the edge of the network, which creates the so-called distributed and collective edge intelligence. Such intelligence is created in order to deal with the huge amount of data to be collected, analyzed and processed, from real word contexts, such as smart cities, which are evolving into dynamic and networked systems of people and things. To better exploit this architecture, it is crucial to break monolithic applications into modular microservices, which can be executed independently. Here, we propose an approach based on complex network theory and two weighted and interdependent multiplex networks to address the Microservices-compliant Load Balancing (McLB) problem in MEC infrastructure. Our findings show that the multiplex network representation represents an extra dimension of analysis, allowing to capture the complexity in WoT mashup organization and its impact on the organizational aspect of MEC servers. The impact of this extracted knowledge on the cognitive organization of MEC is quantified, through the use of heuristics that are engineered to guarantee load balancing and, consequently, QoS. Full article
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