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Applications of Mathematical Analysis in Telecommunications-II
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Applications of Mathematical Analysis in Telecommunications-II

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

Deadline for manuscript submissions: closed (30 September 2023) | Viewed by 8564

Special Issue Editor

Prof. Dr. Konstantin Samouylov

E-Mail Website
Guest Editor
Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia
Interests: 5G; mobile communication; unmanned aerial vehicles; QoS; сomputer networks; wireless networks
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical analysis plays an indisputable role in almost all spheres of human activity. The global public telecommunications network is the largest technical object that humans have ever built. This network has been created since about the end of the 19th century and has survived all the stages of the development of industrial society. As of 2020, five generations of the telecommunication network have already been created, and the scientific community is already discussing the future 6th generation of the network. At all stages, starting from the tasks set by the outstanding mathematicians Agner Erlang and Aleksandr Khinchin, engineers turned to various mathematical theories and methods both to evaluate the performance of existing networks and to build models of future systems—even those that have not yet passed the laboratory research stage. Almost no scientific article devoted to the R&D of telecommunication systems and networks is complete without the construction of mathematical models and their mathematical analysis. The created methods in some cases served the development of purely mathematical disciplines such as queuing theory, coding theory, and some others.

We devote this Special Issue of Mathematics to the problems of the application of mathematical analysis in telecommunications and expect contributions from applied mathematicians from various profiles in the form of scientific articles showing their achievements and confirming the relevance of current and future research.

Prof. Dr. Konstantin Samouylov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (6 papers)

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16 pages, 668 KiB  
Article
Optimizing Lifetime of Internet-of-Things Networks with Dynamic Scanning
by Seung-Kyu Choi, Woo Hyun Kim and Illsoo Sohn
Mathematics 2023, 11(23), 4768; https://doi.org/10.3390/math11234768 - 25 Nov 2023
Viewed by 749
Abstract
With the development of Internet-of-Things (IoT) technology, industries such as smart agriculture, smart health, smart buildings, and smart cities are attracting attention. As a core wireless communication technology, Bluetooth Low Energy (BLE) is gaining a lot of interest as a highly reliable low-power [...] Read more.
With the development of Internet-of-Things (IoT) technology, industries such as smart agriculture, smart health, smart buildings, and smart cities are attracting attention. As a core wireless communication technology, Bluetooth Low Energy (BLE) is gaining a lot of interest as a highly reliable low-power communication technology. In particular, BLE enables a connectionless mesh network that propagates data in a flooding manner using advertising channels. In this paper, we aim to optimize the energy consumption of the network by minimizing the scanning time while preserving the reliability of the network. Maximizing network lifetime requires various optimizing algorithms, including exhaustive searching and gradient descent searching. However, they are involved with excessive computational complexity and high implementation costs. To reduce computational complexity of network optimization, we mathematically model the energy consumption of BLE networks and formulate maximizing network lifetime as an optimization problem. We first present an analytical approach to solve the optimization problem and show that finding the minima from the complicated objective function of the optimization problem does not guarantee a valid solution to the problem. As a low-complexity solution, we approximate the complicated objective function into a convex form and derive a closed-form expression of the suboptimal solution. Our simulation results show that the proposed suboptimal solution provides almost equivalent performance compared to the optimal solution in terms of network lifetime. With very low computational complexity, the proposed suboptimal solution can extensively reduce implementation costs. Full article
(This article belongs to the Special Issue Applications of Mathematical Analysis in Telecommunications-II)
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21 pages, 1888 KiB  
Article
Retrial Queueing System for Analyzing Impact of Priority Ultra-Reliable Low-Latency Communication Transmission on Enhanced Mobile Broadband Quality of Service Degradation in 5G Networks
by Elena Makeeva, Irina Kochetkova and Reem Alkanhel
Mathematics 2023, 11(18), 3925; https://doi.org/10.3390/math11183925 - 15 Sep 2023
Cited by 3 | Viewed by 1471
Abstract
Fifth generation (5G) networks support ultra-reliable low-latency communications (URLLC) and enhanced mobile broadband (eMBB). The coexistence of URLLC and eMBB is often organized by non-orthogonal multiple access (NOMA), giving priority to URLLC and resulting in eMBB quality of service (QoS) degradation. In this [...] Read more.
Fifth generation (5G) networks support ultra-reliable low-latency communications (URLLC) and enhanced mobile broadband (eMBB). The coexistence of URLLC and eMBB is often organized by non-orthogonal multiple access (NOMA), giving priority to URLLC and resulting in eMBB quality of service (QoS) degradation. In this paper, we address the issue of joint URLLC and eMBB transmission, focusing on the problem from the perspective of delay-tolerant eMBB. Due to the priority given to URLLC, we assume that an eMBB session may be interrupted if there are no free resources available for URLLC or delayed when a new eMBB session arrives. To make the scheme more flexible, we propose that interrupted and delayed eMBB sessions periodically check for free resources, rather than continuously. To analyze this scenario, we propose a retrial queuing system with two retrial buffers (orbits) for interrupted and delayed eMBB sessions. The stationary probability distribution, provided in matrix form by recursive formulas, is presented. The paper concludes with a numerical example showing that the scheme with two buffers, compared to one buffer, practically doubles the average number of active eMBB sessions while keeping the interruption probability below 0.001. We provide an illustration of the configuration of eMBB retrial rates to meet its QoS requirements. Full article
(This article belongs to the Special Issue Applications of Mathematical Analysis in Telecommunications-II)
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18 pages, 2785 KiB  
Article
Spatio-Temporal Coherence of mmWave/THz Channel Characteristics and Their Forecasting Using Video Frame Prediction Techniques
by Vladislav Prosvirov, Amjad Ali, Abdukodir Khakimov and Yevgeni Koucheryavy
Mathematics 2023, 11(17), 3634; https://doi.org/10.3390/math11173634 - 23 Aug 2023
Cited by 1 | Viewed by 1421
Abstract
Channel state information in millimeter wave (mmWave) and terahertz (THz) communications systems is vital for various tasks ranging from planning the optimal locations of BSs to efficient beam tracking mechanisms to handover design. Due to the use of large-scale phased antenna arrays and [...] Read more.
Channel state information in millimeter wave (mmWave) and terahertz (THz) communications systems is vital for various tasks ranging from planning the optimal locations of BSs to efficient beam tracking mechanisms to handover design. Due to the use of large-scale phased antenna arrays and high sensitivity to environmental geometry and materials, precise propagation models for these bands are obtained via ray-tracing modeling. However, the propagation conditions in mmWave/THz systems may theoretically change at very small distances, that is, 1 mm–1 μm, which requires extreme computational effort for modeling. In this paper, we first will assess the effective correlation distances in mmWave/THz systems for different outdoor scenarios, user mobility patterns, and line-of-sight (LoS) and non-LoS (nLoS) conditions. As the metrics of interest, we utilize the angle of arrival/departure (AoA/AoD) and path loss of the first few strongest rays. Then, to reduce the computational efforts required for the ray-tracing procedure, we propose a methodology for the extrapolation and interpolation of these metrics based on the convolutional long short-term memory (ConvLSTM) model. The proposed methodology is based on a special representation of the channel state information in a form suitable for state-of-the-art video enhancement machine learning (ML) techniques, which allows for the use of their powerful prediction capabilities. To assess the prediction performance of the ConvLSTM model, we utilize precision and recall as the main metrics of interest. Our numerical results demonstrate that the channel state correlation in AoA/AoD parameters is preserved up until approximately 0.3–0.6 m, which is 300–600 times larger than the wavelength at 300 GHz. The use of a ConvLSTM model allows us to accurately predict AoA and AoD angles up to the 0.6 m distance with AoA being characterized by a higher mean squared error (MSE). Our results can be utilized to speed up ray-tracing simulations by selecting the grid step size, resulting in the desired trade-off between modeling accuracy and computational time. Additionally, it can also be utilized to improve beam tracking in mmWave/THz systems via a selection of the time step between beam realignment procedures. Full article
(This article belongs to the Special Issue Applications of Mathematical Analysis in Telecommunications-II)
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13 pages, 757 KiB  
Article
Optimizing Service Areas in 6G mmWave/THz Systems with Dual Blockage and Micromobility
by Elizaveta Golos, Anastasia Daraseliya, Eduard Sopin, Vyacheslav Begishev and Yuliya Gaidamaka
Mathematics 2023, 11(4), 870; https://doi.org/10.3390/math11040870 - 8 Feb 2023
Cited by 4 | Viewed by 1171
Abstract
The modern 5G millimeter wave (mmWave) New Radio (NR) systems as well as future terahertz (THz) radio access technologies (RAT) will heavily rely on beamforming to combat the excessive path losses. Additionally, both RATs target similar bandwidth-greedy non-elastic traffic and are affected by [...] Read more.
The modern 5G millimeter wave (mmWave) New Radio (NR) systems as well as future terahertz (THz) radio access technologies (RAT) will heavily rely on beamforming to combat the excessive path losses. Additionally, both RATs target similar bandwidth-greedy non-elastic traffic and are affected by the blockage phenomena. To improve service reliability in these systems multiconnectivity can be utilized to dynamically hand over the ongoing sessions between two technologies. In this article, we investigate the association strategies in collocated deployments of mmWave/THz systems and evaluate the impact of the utilized antenna arrays. Our results show that accepting sessions to THz BS that may experience outage in blocked conditions is preferable when multiconnecitvity is utilized as compared to accepting them to mmWave BS. However, extending the coverage of THz base station (BS) by increasing the number of antenna elements slightly affects performance metrics. Nevertheless, there is still non-negligible probability of dropping sessions accepted for service, implying that in 6G deployments the support of fully reliable microwave technology such as sub-6 GHz NR is vital. Full article
(This article belongs to the Special Issue Applications of Mathematical Analysis in Telecommunications-II)
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15 pages, 575 KiB  
Article
UVCS: Unit Virtual Coordinate System for UAV Intra-Swarm Routing in GPS-Denied Environment
by Yuliya Gaidamaka and Konstantin Samouylov
Mathematics 2023, 11(3), 694; https://doi.org/10.3390/math11030694 - 30 Jan 2023
Viewed by 1496
Abstract
Wireless ad hoc networks are the solution for providing network connectivity in challenging environments with a lack or absence of infrastructure. Data transmission in such networks typically adopts geographic routing protocols, which use geographic coordinates as addresses of network devices. However, geographic coordinates [...] Read more.
Wireless ad hoc networks are the solution for providing network connectivity in challenging environments with a lack or absence of infrastructure. Data transmission in such networks typically adopts geographic routing protocols, which use geographic coordinates as addresses of network devices. However, geographic coordinates are not always obtainable, as traditional localization systems (GNSS, Wi-Fi, terrestrial infrastructure) might not be available due to signal loss. In this paper, we propose a method that assigns virtual coordinates to network nodes, which can be used as input for geographic routing protocols. The numerical results demonstrate the high topological similarity between the physical and the virtual network. Our method exhibits convergence advantages over conventional approaches and outperforms them in terms of the total number of discovered paths. Full article
(This article belongs to the Special Issue Applications of Mathematical Analysis in Telecommunications-II)
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14 pages, 621 KiB  
Article
Statistical Method Based Waveform Optimization in Collocated MIMO Radar Systems
by Ahmad Kamal Hassan, Ubaid M. Al-Saggaf, Muhammad Moinuddin and Mohamed K. Alshoubaki
Mathematics 2023, 11(3), 680; https://doi.org/10.3390/math11030680 - 29 Jan 2023
Cited by 2 | Viewed by 1351
Abstract
Multiple-input multiple-output (MIMO) radar has acquired considerable attention as it offers an additional degree of freedom which results in performance gains when contrasted with the regular single antenna element radar system. Waveform optimization in MIMO radar is essential as it can offer tremendous [...] Read more.
Multiple-input multiple-output (MIMO) radar has acquired considerable attention as it offers an additional degree of freedom which results in performance gains when contrasted with the regular single antenna element radar system. Waveform optimization in MIMO radar is essential as it can offer tremendous improvements in target detection which are quantified in terms of reductions in the symbol error rate and improvements in target detection probability. In this work, we foster a strategy for the optimization of transmitter and receiver waveform in a collocated MIMO radar by only considering the second order statistics, thus relaxing the information of the instantaneous target states. Our contributions are primarily two-fold. First, we find a closed-form expression of the outage probability of an unknown target under clutter environment. For this prospect, we model the signal-to-interference-plus-noise ratio in a canonical quadratic structure, and then utilize the modern residue theory approach to characterize the distribution function. Secondly, we propose constrained and unconstrained optimization problems for the reduction in outage probability using algorithmic techniques such as interior-point, sequential-quadratic programming, and the active-set method for the optimization of the transmitter and receiver waveform. We also provide simulated re-enactments to validate our hypothetical deductions. Full article
(This article belongs to the Special Issue Applications of Mathematical Analysis in Telecommunications-II)
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