Performance Analysis of Clustered Wireless-Powered Ad Hoc Networks via β-Ginibre Point Processes

Abstract

We consider a wireless-powered ad hoc network with clustered Power Beacons (PBs). The wireless-powered transmitters (WP-Txs) only activate stochastically deployed PBs within the circles centered at their locations. The PBs transmit radio frequency (RF) signals, which are harvested by the WP-Txs to transmit information to their target receivers. The nodes are modeled as following <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> -Ginibre Point Processes ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> -GPP), which incorporate repulsion among PBs or active WP-Txs. Lacking analytical mathematical tools to describe the distribution of clustered PBs, we establish lower and upper bounds on the energy outage probability, as well as an approximated expression of it. We then derive the information outage probability, an approximate expression of it by approximating the reduced Palm distribution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> -GPP as an inhomogeneous Poisson point process (IPPP), and an analytical approximate expression of it by further ignoring the small-scale fading of interfering WP-Tx links. Finally, the transmission capacity is obtained based on the overall outage probability. The simulation results show that the derived theoretical expressions accurately reflect the performance of the wireless-powered ad hoc networks and the performance gap introduced by approximations is negligible. Transmission capacity optimization based on the derived expressions is also possible and demonstrated.