Bridging the digital divide is one of the goals of mobile networks in the future, and further building IoT networks in rural areas is a feasible solution. This paper studies the downlink performance of rural wireless networks, where IoT devices we consider are battery-less and powered only by ambient radio-frequency (RF) signals. We model a rural area as a finite area that is far from the city center. The base stations (BSs) in the whole city and the access points (APs) in the finite network both act as sources of wireless RF signals harvested by IoT devices. We assume that BSs follow an inhomogeneous Poisson Point Process (PPP) with a 2D-Gaussian density, and a fixed number of APs are uniformly distributed inside the finite area following a Binomial Point Process (BPP). The IoT devices we consider can harvest energy and receive downlink signals in each time slot, which is divided into two parts: (1) a charging sub-slot, where the RF signals from BSs and APs are harvested by IoT devices, and (2) a transmission sub-slot, where each IoT device uses the harvested energy to receive and process downlink signals. We consider two main system requirements: minimum energy requirement and signal-to-interference-plus-noise ratio (SINR). Using these two parameters, we investigate the overall coverage probability (OCP) related to them. We first study the effect of remoteness in rural areas on energy harvesting performance. Then we analyze the influence of IoT device's location and the number of APs on coverage probability when the effect of BSs can be ignored. This paper shows that the IoT devices located inside the rural area can obtain about twice the ECP and OCP of IoT devices located near the edge. For the average downlink performance in rural areas with radii less than 100 m, more than 80% of the RF-powered IoT devices can be supported when there are 100 APs deployed.

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