Ambient radio frequency (RF) energy harvesting technique has recently been proposed as a potential solution for providing 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 @math -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 RF-powered sensor performs better when the distribution of the ambient sources exhibits stronger repulsion.
Other than RF energy harvesting, stochastic geometry approaches have also been applied to address other types of energy harvesting systems. Reference @cite_31 investigates the network coverage of a hexagonal cellular network, where the base stations are powered by renewable energy, and the mobiles are distributed as a PPP. The authors in @cite_13 explore the network coverage in a relay-assisted cellular network modeled as a PPP. Each relay node adopt an energy harvesting module, the energy arrival process of which is assumed to be an independent and identical poisson process. @cite_35 , the authors provides a fundamental characterization of the regimes under which a multiple-tier heterogeneous network with genetic energy harvesting modules fundamentally achieves the same performance as the ones with reliable energy sources. Different from above studies, our previous in @cite_17 adopts a determinantal point process model to analyze the downlink transmission performance from an access point to a sensor powered by ambient RF energy.
@cite_35 @cite_31 @cite_13 @cite_17
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We develop a new tractable model for K-tier heterogeneous cellular networks (HetNets), where each base station (BS) is powered solely by a self-contained energy harvesting module. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power and deployment density. Since a BS may not always have enough energy, it may need to be kept OFF and allowed to recharge while nearby users are served by neighboring BSs that are ON. We show that the fraction of time a k^ th tier BS can be kept ON, termed availability ρ_k, is a fundamental metric of interest. Using tools from random walk theory, fixed point analysis and stochastic geometry, we characterize the set of K-tuples (ρ_1,ρ_2,…ρ_K), termed the availability region, that is achievable by general uncoordinated operational strategies, where the decision to toggle the current ON OFF state of a BS is taken independently of the other BSs. If the availability vector corresponding to the optimal system performance, e.g., in terms of rate, lies in this availability region, there is no performance loss due to the presence of unreliable energy sources. As a part of our analysis, we model the temporal dynamics of the energy level at each BS as a birth-death process, derive the energy utilization rate, and use hitting stopping time analysis to prove that there exists a fundamental limit on ρ_k that cannot be surpassed by any uncoordinated strategy. Powering a radio access network using renewables such as wind and solar power promises dramatic reduction of the network operation cost and of the networks' carbon footprints. However, the spatial variation of the energy field can lead to fluctuation in power supplied to the network and thereby affects its coverage. To quantify the effect, the paper considers a cellular downlink network with hexagonal cells and powered by harvesting energy. The network coverage of mobiles is specified by an outage constraint. A novel model of the energy field is developed using stochastic geometry. In the model, fixed maximum energy intensity occurs at Poisson distributed locations, called energy centers; the intensities fall off from the centers following an exponential-decay function of squared distance; the energy intensity at an arbitrary location is given by the decayed intensity from the nearest energy center. First, consider single harvesters deployed on the same sites as base stations (BSs). The mobile outage probability is shown to decrease exponentially with the product of the energy-field parameters: the energy-center density and exponential rate of the energy-decay function. Next, consider distributed harvesters whose generated energy is aggregated and then re-distributed to BSs. As the number of harvesters per aggregator increases, the power supplied to each BS is shown to converge to a constant proportional to the number of harvesters per BS, which counteracts the randomness of the energy field. The advance in RF energy transfer and harvesting technique over the past decade has enabled wireless energy replenishment for electronic devices, which is deemed as a promising alternative to address the energy bottleneck of conventional battery-powered devices. In this paper, by using a stochastic geometry approach, we aim to analyze the performance of an RF-powered wireless sensor in a downlink simultaneous wireless information and power transfer (SWIPT) system with ambient RF transmitters. Specifically, we consider the point-to-point downlink SWIPT transmission from an access point to a wireless sensor in a network, where ambient RF transmitters are distributed as a Ginibre α-determinantal point process (DPP), which becomes the Poisson point process when a approaches zero. In the considered network, we focus on analyzing the performance of a sensor equipped with the power-splitting architecture. Under this architecture, we characterize the expected RF energy harvesting rate of the sensor. Moreover, we derive the upper bound of both power and transmission outage probabilities. Numerical results show that our upper bounds are accurate for different value of a.