Performance Analysis of Clustered Wireless-Powered Ad Hoc Networks via ß-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 ß-Ginibre Point Processes (ß-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 ß-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.
? The ambient RF sources, such as mobile sensor networks, cellular base stations, exhibit repulsion behaviors, and thus there exists a form of correlation among the RF sources.
? Therefore, modeling the spatial distribution of RF sources as a PPP may not be sufficient for characterizing the performance of the practical networks.
? Most previous works on ambient RF energy harvesting networks have assumed that the ambient RF sources follow a PPP due to its analytical tractability.
? In this paper, we model the spatial distribution of ambient RF sources as a Ginibre point process (GPP) which is one of the most practical examples of two-dimensional DPPs.
? The main problem with these point processes is their limited analytical tractability, which makes it difficult to analyze the properties of these repulsive point processes, thus limiting their applications in wireless networks.
? As ß increases, the repulsiveness between the nodes will reduce the impact of the path-loss model and the interference from the far nodes decreases as a increases.
? The reason is that the inter-distance between nodes is not large enough to reduce the impact of the path-loss due to the relatively high intensity 1/p of the GPP.
? Increasing the former one will result in the decrease of the mean interference while increasing the latter one will cause the mean interference to increase instead.
• In this paper, we propose the Ginibre point process (GPP) as a model for wireless networks whose nodes exhibit repulsion.
• The GPP, one of the main examples of determinantal point processes on the complex plane, has recently been proposed as a model for cellular networks in.
• In this paper, we proposed a wireless network model based on the thinned and re-scaled GPP, which is a repulsive point process.
• A power splitting technique for an RF energy harvesting interference channel was proposed in.
• The works in characterized tradeoff between the information rate and the harvested energy for two-user and K-user interference channels, respectively.
? The spatial structure of transmitters in wireless networks plays a key role in evaluating the mutual interference and hence the performance.
? The spatial distribution of transmitters is critical in determining the power of the received signals and the mutual interference, and hence the performance, of a wireless network.
? Another attractive feature of the GPP is that it has some critical properties that other soft-core processes do not share, which enables us to obtain expressions or bounds of important performance metrics in wireless networks.
? The first two are classical statistics in stochastic geometry, while the last one is a key performance metric of cellular networks.
? Our objective of fitting is to minimize the vertical average squared error between the metrics obtained from the experimental data and those of the ß-GPP.
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