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Ambient RF (Radio Frequency) energy harvesting technique has recently been proposed as a potential solution to provide proactive energy replenishment for wireless devices. This paper aims to analyze the performance of a battery-free wireless sensor powered by ambient RF energy harvesting using a stochastic geometry approach. Specifically, we consider the point-to-point uplink transmission of a wireless sensor in a stochastic geometry network, where ambient RF sources, such as mobile transmit devices, access points and base stations, are distributed as a Ginibre α-determinantal point process (DPP).The DPP is able to capture repulsion among points, and hence, it is more general than the Poisson point process (PPP). We analyze two common receiver architectures: separated receiver and time-switching architectures. For each architecture, we consider the scenarios with and without co-channel interference for information transmission. We derive the expectation of the RF energy harvesting rate in closed form and also compute its variance. Moreover, we perform a worst-case study which derives the upper bound of both power and transmission outage probabilities. Additionally, we provide guidelines on the setting of optimal time-switching coefficient in the case of the time-switching architecture. Numerical results verify the correctness of the analysis and show various tradeoffs between parameter setting. Lastly, we prove that the sensor is more efficient when the distribution of the ambient sources exhibits stronger repulsion.

The Ginibre point process is one of the main examples of determinantal point processes on the complex plane. It forms a recurring model in stochastic matrix theory as well as in practical applications. Since its introduction in random matrix theory, the Ginibre point process has also been used to model random phenomena where repulsion is observed. In this paper, we modify the classical Ginibre point process in order to obtain a determinantal point process more suited for simulation. We also compare three different methods of simulation and discuss the most efficient one depending on the application at hand.Mathematics Subject Classification: 60G55, 65C20.

Ambient RF (Radio Frequency) energy harvesting technique has recently been proposed as a potential solution to provide proactive energy replenishment for wireless devices. This paper aims to analyze the performance of a battery-free wireless sensor powered by ambient RF energy harvesting using a stochastic-geometry approach. Specifically, we consider a random network model in which ambient RF sources are distributed as a Ginibre α-determinantal point process which recovers the Poisson point process when α approaches zero. We characterize the expected RF energy harvesting rate. We also perform a worstcase study which derives the upper bounds of both power outage and transmission outage probabilities. Numerical results show that our upper bounds are accurate and that better performance is achieved when the distribution of ambient sources exhibits stronger repulsion.Index terms-RF energy harvesting, sensor networks, determinantal point process, Poisson point process, Ginibre model .

RF-enabled wireless power transfer and energy harvesting has recently emerged as a promising technique to provision perpetual energy replenishment for low-power wireless networks. The network devices are replenished by the RF energy harvested from the transmission of ambient RF transmitters, which offers a practical and promising solution to enable selfsustainable communications. This paper adopts a stochastic geometry framework based on the Ginibre model to analyze the performance of self-sustainable communications over cellular networks with general fading channels. Specifically, we consider the point-to-point downlink transmission between an access point and a battery-free device in the cellular networks, where the ambient RF transmitters are randomly distributed following a repulsive point process, called Ginibre α-determinantal point process (DPP). Two practical RF energy harvesting receiver architectures, namely time-switching and power-splitting, are investigated. We perform an analytical study on the RF-powered device and derive the expectation of the RF energy harvesting rate, the energy outage probability and the transmission outage probability over Nakagami-m fading channels. These are expressed in terms of so-called Fredholm determinants, which we compute efficiently with modern techniques from numerical analysis. Our analytical results are corroborated by the numerical simulations, and the efficiency of our approximations is demonstrated. In practice, the accurate simulation of any of the Fredholm determinant appearing in the manuscript is a matter of seconds. An interesting finding is that a smaller value of α (corresponding to larger repulsion) yields a better transmission outage performance when the density of the ambient RF transmitters is small. However, it yields a lower transmission outage probability when the density of the ambient RF transmitters is large. We also show analytically that the power-splitting architecture outperforms the time-switching architecture in terms of transmission outage performances. Lastly, our analysis provides guidelines for setting the time-switching and power-splitting coefficients at their optimal values. Index terms-Wireless energy harvesting, self-sustainable communications, wireless powered communication networks, simultaneous wireless information and power transfer, Nakagami-m fading, Internet of things, time-switching, powersplitting, determinantal point process, Ginibre model.

Determinantal point processes (DPP) serve as a practicable modeling for many applications of repulsive point processes. A known approach for simulation was proposed in [5], which generate the desired distribution point wise through rejection sampling. Unfortunately, the size of rejection could be very large. In this paper, we investigate the application of perfect simulation via coupling from the past (CFTP) on DPP. We give a general framework for perfect simulation on DPP model. It is shown that the limiting sequence of the time-to-coalescence of the coupling is bounded by O E

The Poisson point process (PPP) has been widely employed to model wireless networks and analyze their performance. The PPP has the property that nodes are conditionally independent from each other. As such, it may not be a suitable model for many networks where there exists a repulsion among the nodes. In order to address this limitation, we adopt a Poisson hard-core process (PHCP) in which no two nodes can be closer than a repulsion radius from one another. We consider two-tier heterogeneous networks where the spatial distributions of transmitters in the first-tier and the second-tier networks follow a PHCP and a PPP, respectively. To alleviate inter-tier interference, we consider a guard zone for the first-tier network and presume that the second-tier transmitters located in the zone are deactivated. Under this setup, the activated secondtier transmitters form a Poisson hard-core hole process. We first derive exact computable expressions of the coverage probability and introduce a method to efficiently evaluate the expressions. Then, we provide approximations of the coverage probability which have lower computational complexities. Additionally, as a special case, we investigate the coverage probability of single-tier networks by modeling the locations of transmitters as a PHCP.

Abstract. The goal of this paper is to generalize most of the moment formulae obtained in [Pri11]. More precisely, we consider a general point process µ, and show that the relevant quantities to our problem are the so-called Papangelou intensities. Then, we show some general formulae to recover the moment of order n of the stochastic integral of a random process. We will use these extended results to study a random transformation of the point process.