Outage Probability and Rate for $\kappa$ - $\mu$ Shadowed Fading in Interference Limited Scenario

The <inline-formula> <tex-math notation="LaTeX">$\kappa$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> shadowed fading model is a very general fading model as it includes both <inline-formula> <tex-math notation="LaTeX">$\kappa$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\eta$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> as special cases. In this paper, we derive the expression for outage probability when the signal-of-interest (SoI) and interferers both experience <inline-formula> <tex-math notation="LaTeX">$\kappa$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> shadowed fading in an interference limited scenario. The derived expression is valid for arbitrary SoI parameters, arbitrary <inline-formula> <tex-math notation="LaTeX">$\kappa$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> parameters for all interferers and any value of the parameter <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> for the interferers excepting the limiting value of <inline-formula> <tex-math notation="LaTeX">$m\rightarrow \infty$ </tex-math></inline-formula>. The expression can be expressed in terms of Pochhammer integral, where the integrands of integral only contains elementary functions. The outage probability expression is then simplified for various special cases, especially when SoI experiences <inline-formula> <tex-math notation="LaTeX">$\eta$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> or <inline-formula> <tex-math notation="LaTeX">$\kappa$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> fading. Furthermore, the rate expression is derived when the SoI experiences <inline-formula> <tex-math notation="LaTeX">$\kappa$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> shadowed fading with the integer values of <inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula>, and the interferers experience <inline-formula> <tex-math notation="LaTeX">$\kappa$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> shadowed fading with arbitrary parameters. The rate expression can be expressed in terms of sum of Lauricella’s function of the fourth kind. The utility of our results is demonstrated by using the derived expression to study and compare fractional frequency reuse and soft frequency reuse in the presence of <inline-formula> <tex-math notation="LaTeX">$\kappa$ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu$ </tex-math></inline-formula> shadowed fading. Extensive simulation results are provided and these further validate our theoretical results.