In this research work, we employ the small limit argument approximation (SLAA) to derive an analytically tractable model of the conventional Nakagami-n fading channel in single-input single-output (SISO) and single-input multiple-output (SIMO) system models. By applying the SLAA to the zerothorder modified Bessel function of the first kind, we facilitate the analysis of the resulting channel in the low signal-to-noise ratio (SNR) regime. We derive closed-form expressions for channel capacity in both SISO and SIMO systems, which are quantitatively validated and shown to be exceptionally precise. The analysis confirms that the approximation achieves high accuracy for channels with weak line-of-sight (LOS) components, exhibiting a root mean square error (RMSE) on the order of 10⁻³. However, it also indicates that the accuracy deteriorates as the LOS component becomes dominant, thereby clarifying the range of applicability. Our analysis reveals that for a SISO system with an instantaneous SNR of 20 dB and a Nakagami-n fading parameter of 0.05, the channel capacity reaches 7.4 bits/s/Hz. Furthermore, we demonstrate that SIMO systems exhibit significant increases in channel capacity as the number of receiver antennas grows. Specifically, at an SNR of 20 dB, SIMO configurations with two and four receiver antennas achieve channel capacities of 8.3 bits/s/Hz and 10.0 bits/s/Hz, respectively. We thus provide a validated and computationally efficient analytical solution for system designers to analyze channel capacity within well-defined fading scenarios.

Heaviside’s approach to deriving electromagnetic waves from the Maxwell equations is detailed by Nahin (P. J. Nahin: OLIVER HEAVISIDE, The Johns Hopkins University Press, 2002). In this session, we will follow Nahin’s approach to show how Heaviside derived electromagnetic waves. Namely, the current I(x) is obtained from H using the inverse of Ampere’s law. Since electromagnetic fields and electromagnetic waves satisfy duality, the voltage −V(x) is obtained from E using the inverse of Faraday’s law of induction. The current and voltage obtained here are complex functions because the operator method is used; they are not real functions (trigonometric functions) used in vector analysis and tensor analysis. Also, these complex functions of the current and voltage are the wave equations, slightly different from telegrapher’s equations, and the mathematics involved differs somewhat from Hilbert’s or Fourier’s mathematics. In this session, we refer to this mathematics as Heaviside’s extension. Since Heaviside’s extension does not involve the behavior of electrons, the behavior of electrons remains a future research topic.