Double α -κ - μ Distribution: A New Model Characterizing Signal Fading in Non-Linear Environments

The existing channel models have limitations in accurately describing the statistical properties of electromagnetic wave signals with non-linear propagation effects in line-of-sight cascading channel environments. In this paper, we proposed a general double <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha-\kappa-\mu$</tex> model to capture these fading characteristics more precisely. Specifically, the exact expressions for the probability density function, cumulative distribution function and higher order moments based on signal-to-noise ratio are derived. The Monte Carlo simulation is conducted to validate the effectiveness of the newly proposed double <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha-\kappa-\mu$</tex> distribution. The simulation results show that the stability of the cascaded channel signals improves with higher values of the parameters <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha, \kappa$</tex>, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mu$</tex>. Furthermore, Our proposed double <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha-\kappa-\mu$</tex> distribution is highly versatile, allowing for the inclusion of many popular product distributions, such as double <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha-\mu$</tex>, double <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\kappa-\mu$</tex>, double Nakagami- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m$</tex>, double Weibull, double Rayleigh, and double Rician distributions.