# Coverage Probability Analysis of Device-to-Device Communication Underlaid Cellular Networks in Uplink Over $$\kappa -\mu$$/$$\eta -\mu$$ Fading Channels

Article

## Abstract

Device-to-device (D2D) communication is an emerging technique for future cellular networks to extend the network coverage. In D2D communication, two nearby mobile users can communicate directly without involving the base-station by sharing the uplink/downlink resource with cellular users. The performance of wireless communication deteriorates due to multipath fading and shadowing. Two generalized fading distributions namely $$\kappa -\mu$$ and $$\eta -\mu$$ have been proposed to characterize the line-of-sight and non-line-of-sight propagation effects respectively. In this paper, the expression of coverage probability for D2D communication, when D2D direct link undergoes $$\kappa -\mu$$ fading with random values of $$\kappa$$ and $$\mu$$, and interferers undergo $$\eta -\mu$$ fading with random values of $$\eta$$ and $$\mu$$ has been derived. The stochastic geometry has been utilized to derive the expression of D2D coverage probability. The Lauricella’s function, a special mathematical function has been used to represent the expression of D2D coverage probability which is easy to calculate numerically. The effects of fading parameters over coverage probability have been analyzed. Further, using the properties of Lauricella’s function and particular values of fading parameters, D2D coverage probability expression has been simplified for four special cases. The D2D coverage probability results obtained from the analytical analysis have been validated through Monte-Carlo simulation.

## Keywords

Device-to-device communication Coverage probability Uplink resource General $$\kappa -\mu$$ fading distribution General $$\eta -\mu$$ fading distribution Stochastic geometry

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## Authors and Affiliations

• Indrasen Singh
• 1
• Niraj Pratap Singh
• 1
1. 1.Department of Electronics and Communication EngineeringNational Institute of Technology KurukshetraKurukshetraIndia