Large-Dataset Statistical Modeling of Empirical SNR in 851 MHz Cellular Channels Using Classical, Generalized, and Composite Fading Models

Accurate modeling of instantaneous signal-to-noise ratio (SNR) statistics is important for characterizing wireless fading channels and predicting communication-system performance. The 851 MHz band is an important part of the sub-GHz spectrum used for cellular communications and is also relevant to emerging Internet of Things (IoT) applications, where favorable propagation at these frequencies supports broad coverage and signal penetration in obstructed environments. Despite this practical relevance, measurement-based studies of composite fading environments that directly evaluate statistical fading models against SNR observations at 851 MHz remain limited. To the best of our knowledge, this work provides the first measurement-based statistical modeling of a composite fading environment at 851 MHz using empirical SNR observations. Nearly one million measurements collected in an indoor non-line-of-sight (NLOS) cellular environment are used to evaluate a broad set of classical, generalized, and composite fading distributions directly in the SNR domain. Model agreement is quantified using a bin-probability mean-squared-error (MSE) methodology that compares empirical and analytical probability masses over logarithmically spaced SNR intervals under a common goodness-of-fit criterion. The results show that the generalized α–μ distribution provides the best fit among the evaluated models, achieving a bin-probability MSE of 5.72×10−7 (−62.43 dB), followed by the Weibull and SNR-domain generalized-K distributions. The α–μ model also outperforms the evaluated composite fading models, showing that greater model complexity does not necessarily lead to better agreement with the measured SNR statistics. Additional domain-consistency experiments illustrate the consequences of applying envelope-domain formulations directly to power-like SNR observations without the required variable transformation. By providing compact analytical representations of the measured SNR statistics, the resulting models can support communication-system performance analysis without relying exclusively on time-consuming Monte Carlo simulations using the complete measurement dataset. While the reported model performance is specific to the propagation environment considered in this study, the assessment framework can be applied to measurements collected under other propagation conditions.