Physical Model Based Method to Generate Channel Coefficients for Nakagami-m Distribution
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Physical Model Based Method to Generate Channel Coefficients for Nakagami‑m Distribution Brijesh Kumbhani1 · Jatin Gaur1 Accepted: 14 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we discuss physical model based method to generate channel coefficients for Nakagami-m distribution. We consider the phase envelope joint distribution so that the phase of the faded signal is also considered. Mainly, the coefficients are generated by exploring the physical model that relates the Nakagami-m fading distribution with Gaussian and gamma distributions for which generation of coefficients is available in commonly used simulation tools. The empirical probability density function (PDF) of generated coefficients are compared with the theoretical values and they are found in excellent agreements. The empirical PDFs for envelope and phase of the generated coefficients are validated using the Kolmogorov–Smirnov test. Keywords Fading channel coefficients · Gamma distribution · Nakagami-m distribution
1 Introduction Generation of fading channel coefficients is an essential part of the simulation of wireless communication systems. It helps in the simulation of fading channels. There have been reports of simulation of fading channels for various distributions using different techniques among which rejection method has been the most popular [1–3]. But, physical models have not been used in any of the available literature to the best of our knowledge. Using physical model has another advantage that it gives relation of Nakagami-m distributed random variable with Gaussian distributed or gamma distributed variants, the generation of which is readily available in commonly used software tools for simulations of wireless communication systems. Moreover, Nakagami-m distribution is a parametric distribution whose phase is not uniformly distributed unlike Rayleigh fading distribution [4, 5], i.e. it is important to consider the phase of the channel coefficients of Nakagami-m fading channels. However, most of the articles have reported the results considering only envelope distribution [6–8]. The effect of phase may not be significant in the systems like maximal ratio combining * Jatin Gaur [email protected] Brijesh Kumbhani [email protected] 1
Department of Electrical Engineering, Indian Institute of Technology Ropar, Rupnagar, India
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or selection combining because of co-phasing of the received signals before processing them further. But, it is shown in [9] that the phase of faded signal affects performance of multiple input multiple output (MIMO) systems with spatial modulation (SM). Recently, researchers have reported performance analysis of various communication systems, like space shift keying, cognitive radio and power line communications over Nakagami-m fading channels/noise but none of them reported about the distribution of phase of Nakagamim fading channel coefficients [10–12]. The contribution of this paper lies
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