Fundamental Channel Capacity Analysis for Novel Modified Nakagami-n Fading SIMO Wireless Channels

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.