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