Spectral convolution of star-like transformation semigroups for modeling telecommunication signal strength and user experience in Gombe state, Nigeria

Authors

  • Sulaiman Awwal Akinwunmi
    Department of Mathematics and Statistics, Federal University of Kashere, Gombe, Nigeria
  • David Opeoluwa Oyewola
    Department of Mathematics and Statistics, Federal University of Kashere, Gombe, Nigeria

Keywords:

Spectral convolution, Signal strength, Telecommunication networks, Star-like transformation, Semigroup, Gombe state

Abstract

An efficient and mathematically sound method for simulating the distributions of telecommunication signals is the star-like semigroup convolution model. A rigorous operator-theoretic measure of signal strength is provided by the (S3I), which is obtained via semigroup transformations. This study combines empirical field data with the mathematical tools of spectral convolution and star-like transformation semigroups to create a corrective-predictive model for the functioning of telecommunication networks in Gombe State, Nigeria.  A poll on signal strength and Quality of Experience (QoE) was conducted using an 11-point star-like scale with 615,510 respondents spread over 11 Local Government Areas (LGAs) and three major providers (MTN, GLO, and Airtel). A star-like signal spectral index (S3I) that generalizes empirical RSS distributions under a continuous semicharacter model was derived by analyzing the data using both formal statistical measures and semigroup-based spectral transformations. Semigroup theory is used with actual telecom data to provide a mathematically sound but practically useful model of network resilience.While GLO urgently needs infrastructure densification, MTN is demonstrated to dominate across LGAs, and Airtel exhibits localized strengths in Billiri and Shongom. Regulators such as the Nigerian Communications Commission are urged to use (S3I) as an impartial performance metric. The model guarantees that transformational semigroups can direct predictive modeling of large-scale communication systems and can be extended to additional Nigerian states and next-generation (5G) networks.

 

Dimensions

[1] M. Burgin, “Information theory: a multifaceted model of information”, Entropy 5 (2003) 146. https://doi.org/10.3390/entropy.

[2] U.G. Danbatta, “The role of the telecommunications sector in the diversification of the Nigerian economy- achievements, prospects and challenges: presentation of inaugural lecture to Bayero University Kan” 2 (2017) 25. https://www.ncc.gov.ng/sites/default/files/2025-02/Speeches-The-Role-of-Telecoms-Sector-to-Diversification-of-the-Nigerian-Economy.pdf.

[3] Z. Zhao, “The Fourier transform and its applications”, Highlights in Science, Engineering and Technology 38 (2023) 768. https://doi.org/10.54097/hset.v38i.5943.

[4] F. Pourkamali-anaraki, J. F. Husseini & S. E. Stapleton, “Probabilistic neural networks (PNNs) for modeling aleatoric uncertainty in scientific machine learning”, IEEE Acess 35 (2024) 35087. https://doi.org/10.1109/ACCESS.2024.3508735.

[5] J. Rhodes & B. Steinberg, The q-theory of finite semigroups. Springer, Berlin Heidelberg NewYork. Hong Kong London. Milan Paris Tokyo. 2007. https://doi.org/10.1007/978-0-387-09781-7.

[6] A. D. Adeshola, S. O Akande, G. R. Ibrahim, & J. O. Lawal, Characterization of quasi idempotent in semigroups of full contraction mappings, Proceedings of the Nigerian Society of Physical Sciences 1 (2024) 88. https://doi.org/10.61298/pnspsc.2024.1.88.

[7] Z. Qian, “Web testing generation: A stream X-machine based approach”, Journal of Software Engineering and Applications 5 (2012) 7. https://doi.org/10.4236/jsea.2012.51002.

[8] N. Kumar, & B. Kumar, “Some fundamental properties of semigroups and their classifications”. International Journal of Mathematics Trends and Technology 70 (2024) 8. https://doi.org/10.14445/22315373/IJMTT-V70I9P102.

[9] A. H. Clifford, “Semigroups admitting relative inverses”, Annals of Mathematics 42(1941) 1037. https://www.jstor.org/stable/1968781.

[10] K. Engel, & R. Nagel, “One-parameter semigroups for linear evolution equations”, Semigroup forum 63 (2001) 278. https://doi.org/10.1007/s002330010042.

[11] A. I. Komech & E. A. Kopylova, “On dynamical semigroup for damped driven Jaynes-cummings equations”, 1 (2026) 17553. https://arxiv.org/abs/2603.17553v1.

[12] M. M. El-borai, “The fundamental solutions for fractional evolution equations of parabolic type”, Journal of Applied Mathematics and Stochastic Analysis 3 (2004) 197. http://dx.doi.org/10.1155/S1048953304311020.

[13] M. Pu¨schel & J. M. F. Moura “Algebraic signal processing theory”, IEEE transactions on signal processing 56 (2006) 8. http://arxiv.org/abs/cs/0612077.

[14] S. A. Akinwunmi, M. M. Mogbonju & G. R. Ibrahim, “Some characterizations of equivalence relation on contraction mappings”, Scientific African 10 (2020) e00643. https://doi.org/10.1016/j.sciaf.2020.e00643.

[15] A. O. Adeniji, “Spectrum convolution of full transformation semigroup”, Honam Mathematical Journal 41 (2019) 505. https://doi.org/10.5831/HMJ.2019.41.3.505.

[16] M. Sliti, & M. Garai, “Performance analysis of FSO communication systems under different atmospheric conditions”, Asia Pacific Conference on Communications (APCC) 28 (2023) 19. https://doi.org/10.1109/APCC60132.2023.10460727.

[17] A. Umar, “Some combinatorial in the theory of partial transformation semigroups”, Algebra and Discrete Mathematics 17 (2014) 110. http://mi.mathnet.ru/adm462.

[18] A. Laradji & A. Umar, “On certain finite semigroups of order-decreasing transformations”, Semigroup Forum 69 (2004) 184. https://doi.org/10.1007/s00233-004-0101-9.

[19] M. M. Zubairu , & Z. D. Lawan, “On the monoid of all order preserving full contractions with a fixed set”, Open Journal of Discrete Mathematics 15 (2025) 55. https://doi.org/10.4236/ojdm.2025.153004.

[20] S. A. Akinwunmi, M. M. Mogbonju & A. O. Adeniji, “Multiplicative invertibility characterizations on star-like cyclicpoid CyPωn∗ finite partial transformation semigroups”, Hikari Journal of Pure Mathematical Science 10 (2021) 45. https://doi.org/10.12988/pms.2021.91276.

[21] U. G. Garba, M. J. Ibrahim & A. T. Imam, “On certain semigroups of full contraction maps of a finite chain”, Turkish Journal of Mathematics. 41 (2017) 500. https://doi.org/10.3906/mat-1602-52.

[22] A. Bashir, A. Umar & M. Z. Muhammad, “Regularity and Green’s relations for the semigroups of partial and full contractions of a finite chain”, Scientific African 21 (2023) e01890. https://doi.org/10.1016/j.sciaf.2023.e01890.

[23] S. A. Akinwunmi, G. R. Ibrahim, A. O. Adeniji & D. O. Oyewola, “On the multiplicity order of spinnable star-like transformation semigroup”, Journal of the Nigerian Society of Physical Sciences 6 (2024) 1692. https://doi.org/10.46481/jnsps.2024.1692.

[24] A. Bappi, I. A. Jimoh, K. Idoma, J. Musa, & A. A. Abdurrahman, “Accessibility analysis of primary healthcare facilities using geo-spatial techniques in kwami local government area of gombe state, nigeria”, Gombe Journal of Geography and Environmental Studies (GOJGES) 2 (2022) 551. http://www.gojgesjournal.com.

[25] G.S.M. Galadanci, & S.B. Abdullahi, “Performance Analysis of GSM Networks in Kano Metropolis of Nigeria”, American Journal of Engineering Research (AJER) 7 (2018) 69. https://www.researchgate.net/profile/Abdullahi-Sunusi-2/publication/325131258_Performance_Analysis_of_GSM_Networks_in_Kano_Metropolis_of_Nigeria/links/5afa088caca272e730299996/Performance-Analysis-of-GSM-Networks-in-Kano-Metropolis-of-Nigeria.pdf?__cf_chl_tk=m7nrL9XE1ZDVqD.Y6C1sGkTh3g9toCLan.x8Z.syEos-1777604154-1.0.1.1-HDW.e.g7nIQmleOC2dQSyYgt_4XJ1WZFoLCufGTweD0.

[26] Nigerian Communications Commission (NCC), Annual report on consumer complaints and QoS. Abuja, Nigeria, 2022. https://www.ncc.gov.ng/documents/855-2022-annual-report/file.

[27] A. F. Mongi, “A conceptual framework for QoE measurement and Management in networked systems”, International Journal of Computer Applications 112 (2015) 0975. https://www.ijcaonline.org.

[28] T. R. Joseph, Performance evaluation of mobile network services in shiroro power stattion, Nigeria. A thesis submitted to the university of technology minna, Nigeria, for the award of master degree of engineering (2021). http://irepo.futminna.edu.ng:8080/jspui/bitstream/123456789/14384/1/JOSEPH%20Tunde%20Raphael.pdf.

[29] M. Pu¨schel & J. M. F. Moura, “Algebraic signal processing theory:Cooley-Tukey type algorithms for DCTs and DSTs”, IEEE Transactions on Signal Processing 56 (2008) 1502. https://doi.org/10.1109/TSP.2007.907919.

[30] P. Kurasov “Operator theory: advances and applications”, Springer-Verlag GmbH, DE eidelberger Platz 3, 14197 Berlin, Germany. 10 (2024) 5. https://doi.org/10.1007/978-3-662-67872-5.

[31] S. A. Akinwunmi & D. O. Oyewola, Synthetic dataset for star-like semi-group modeling of telecommunication signals in Gombe State, Nigeria. [Data set]. (2026) Zenodo. https://doi.org/10.5281/zenodo.18115574.

11 Point Star-like Scale for QoE

Published

2026-05-04

How to Cite

Spectral convolution of star-like transformation semigroups for modeling telecommunication signal strength and user experience in Gombe state, Nigeria. (2026). Journal of the Nigerian Society of Physical Sciences, 8(2), 3129. https://doi.org/10.46481/jnsps.2026.3129

Issue

Volume 8, Issue 2, May 2026

Section

Mathematics & Statistics
Copyright & Licensing

Copyright (c) 2026 Sulaiman Awwal Akinwunmi, David Opeoluwa Oyewola (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Spectral convolution of star-like transformation semigroups for modeling telecommunication signal strength and user experience in Gombe state, Nigeria. (2026). Journal of the Nigerian Society of Physical Sciences, 8(2), 3129. https://doi.org/10.46481/jnsps.2026.3129

Similar Articles

111-120 of 277

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)