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.
In this letter, we study the performance of network coding (NC)-aided cooperative communications in large scale networks, where the relays are able to harvest energy emitted by wireless transmissions. In particular, we derive theoretical expressions for key network performance metrics, i.e., the probability of successful data exchange and the network lifetime gain. The proposed analytical expressions are verified via extensive Monte Carlo simulations, demonstrating the potential benefits of the energy harvested by the wireless transmissions. In this paper, the application of wireless information and power transfer to cooperative networks is investigated, where the relays in the network are randomly located and based on the decode-forward strategy. For the scenario with one source-destination pair, three different strategies for using the available relays are studied, and their impact on the outage probability and diversity gain is characterized by applying stochastic geometry. By using the assumptions that the path loss exponent is two and that the relay-destination distances are much larger than the source-relay distances, closed form analytical results can be developed to demonstrate that the use of energy harvesting relays can achieve the same diversity gain as the case with conventional self-powered relays. For the scenario with multiple sources, the relays can be viewed as a type of scarce resource, where the sources compete with each other to get help from the relays. Such a competition is modeled as a coalition formation game, and two distributed game theoretic algorithms are developed based on different payoff functions. Simulation results are provided to confirm the accuracy of the developed analytical results and facilitate a better performance comparison. Microwave power transfer (MPT) delivers energy wirelessly from stations called power beacons (PBs) to mobile devices by microwave radiation. This provides mobiles practically infinite battery lives and eliminates the need of power cords and chargers. To enable MPT for mobile recharging, this paper proposes a new network architecture that overlays an uplink cellular network with randomly deployed PBs for powering mobiles, called a hybrid network. The deployment of the hybrid network under an outage constraint on data links is investigated based on a stochastic-geometry model where single-antenna base stations (BSs) and PBs form independent homogeneous Poisson point processes (PPPs) with densities λb and λp, respectively, and single-antenna mobiles are uniformly distributed in Voronoi cells generated by BSs. In this model, mobiles and PBs fix their transmission power at p and q, respectively; a PB either radiates isotropically, called isotropic MPT, or directs energy towards target mobiles by beamforming, called directed MPT. The model is used to derive the tradeoffs between the network parameters (p, λb, q, λp) under the outage constraint. First, consider the deployment of the cellular network. It is proved that the outage constraint is satisfied so long as the product pλbα 2 is above a given threshold where α is the path-loss exponent. Next, consider the deployment of the hybrid network assuming infinite energy storage at mobiles. It is shown that for isotropic MPT, the product qλpλbα 2 has to be above a given threshold so that PBs are sufficiently dense; for directed MPT, zmqλpλbα 2 with zm denoting the array gain should exceed a different threshold to ensure short distances between PBs and their target mobiles. Furthermore, similar results are derived for the case of mobiles having small energy storage. Wireless networks can be self-sustaining by harvesting energy from ambient radio-frequency (RF) signals. Recently, researchers have made progress on designing efficient circuits and devices for RF energy harvesting suitable for low-power wireless applications. Motivated by this and building upon the classic cognitive radio (CR) network model, this paper proposes a novel method for wireless networks coexisting where low-power mobiles in a secondary network, called secondary transmitters (STs), harvest ambient RF energy from transmissions by nearby active transmitters in a primary network, called primary transmitters (PTs), while opportunistically accessing the spectrum licensed to the primary network. We consider a stochastic-geometry model in which PTs and STs are distributed as independent homogeneous Poisson point processes (HPPPs) and communicate with their intended receivers at fixed distances. Each PT is associated with a guard zone to protect its intended receiver from ST's interference, and at the same time delivers RF energy to STs located in its harvesting zone. Based on the proposed model, we analyze the transmission probability of STs and the resulting spatial throughput of the secondary network. The optimal transmission power and density of STs are derived for maximizing the secondary network throughput under the given outage-probability constraints in the two coexisting networks, which reveal key insights to the optimal network design. Finally, we show that our analytical result can be generally applied to a non-CR setup, where distributed wireless power chargers are deployed to power coexisting wireless transmitters in a sensor network. Energy harvesting (EH) from ambient radio-frequency (RF) electromagnetic waves is an efficient solution for fully autonomous and sustainable communication networks. Most of the related works presented in the literature are based on specific (and small-scale) network structures, which although give useful insights on the potential benefits of the RF-EH technology, cannot characterize the performance of general networks. In this paper, we adopt a large-scale approach of the RF-EH technology and we characterize the performance of a network with random number of transmitter-receiver pairs by using stochastic-geometry tools. Specifically, we analyze the outage probability performance and the average harvested energy, when receivers employ power splitting (PS) technique for "simultaneous" information and energy transfer. A non-cooperative scheme, where information energy are conveyed only via direct links, is firstly considered and the outage performance of the system as well as the average harvested energy are derived in closed form in function of the power splitting. For this protocol, an interesting optimization problem which minimizes the transmitted power under outage probability and harvesting constraints, is formulated and solved in closed form. In addition, we study a cooperative protocol where sources' transmissions are supported by a random number of potential relays that are randomly distributed into the network. In this case, information energy can be received at each destination via two independent and orthogonal paths (in case of relaying). We characterize both performance metrics, when a selection combining scheme is applied at the receivers and a single relay is randomly selected for cooperative diversity.