RF energy harvesting: an analysis of wireless sensor networks for reliable communication

Over the last few years, the industrial wireless sensor network (IWSN) has become one of the most interesting topics in the research community due to flexible installation and easy maintenance. Accordingly, many standards such as WirelessHART, WIA-PA, and ISA100.11a have been proposed [1, 2, 3, 4, 5, 6, 7]. More specifically, a dynamic power allocation policy for a wireless sensor network has been studied in [5] to improve the throughput and reduce energy consumption. In [6], authors investigated a strategy to set the time length in LEACH protocol to prolong the lifetime and increase throughput of wireless sensor network. In [7], an experiment study to understand the impact of interference among users on packet delivery ratio and throughput has been analyzed for wireless body sensor networks. Although, there are many works focusing on wireless sensor networks, but to fulfill demands on high reliability and timeliness is not easy because the wireless channels are often subject to interference and fading [3, 8]. Additionally, as the size of sensor network increases, replacing or recharging the batteries takes time and costs. This work becomes dangerous for humans in hazardous environments such as nuclear reactors, toxic environments. Moreover, devices implant inside the human body are more difficult or impossible to replace. To overcome these drawbacks, the radio frequency (RF) energy harvesting for wireless sensor networks has been considered as a promising solution to prolong the sensor’s lifetime and to enhance reliable communication [9, 10].

Recently, wireless power technologies have made a great progress to enable the wireless power transfer (WPT) for real wireless applications [11, 12, 13, 14]. The wireless power can be harvested from natural sources such as solar, wind, TV broadcast signals, or a dedicated power transmitter [11]. In [12], a prototype of the RF energy harvesting device has been developed for experimental purposes. In [15, 16], authors have shown that the harvested energy can be stored in a supercapacitor, which can be charged very fast and the lifetime may be prolonged for many years with charging and discharging cycles. However, the power of the supercapacitor is often leaked out due to its self-discharge process, and it is not possible to store the harvested energy long enough for the next communication round. Without doubt, the applications of the RF energy harvesting will be used widely in near future, and this technology is still an open problem demanding more research.

In the light of RF energy harvesting ideas, many researchers have investigated on the problems of simultaneous information transmission and WPT in order to improve reliable communication, accordingly theoretical models, protocols, and system designs, have been proposed [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28]. Specifically, in [17], an outage minimization with energy harvesting for point-to-point communication over fading channels has been studied. Employing a Markov model, the impact of packet retransmission, energy harvesting, and detection on the outage performance for a wireless power sensor network (WPSN) have been illustrated. Regarding to point-to-multipoint communications, Tiangquing et al. have focused on the problem of energy harvesting with cooperation beam selection for wireless sensors [18]. Closed-form expression for the distribution function of harvested energy in a coherent time is derived to analyze the system performance. In [20], the impact of energy harvesting on the packet loss probability and the average packet delay for overlaying wireless sensor networks has been considered. Also, the optimal design of energy storage capacity in the sensors has been proposed. Taking the advantages of cooperative communication, works reported in [26] have shown an interesting result that the harvested energy from a wireless source can obtain the same diversity multiplexing tradeoff as if the relay is attached to a fixed power supply. In [27], a protocol for the WPSN is proposed, and the characteristics of a full-duplex wireless-powered relay have been studied. The results have shown a fact that the throughput of the proposed protocol can be improved significantly when it is compared to the existing ones. In [29], authors have applied zero-forcing beamforming to optimize the energy harvesting capability and enhance the system performance. Given delay constraints, optimal stochastic power control for energy harvesting system has been investigated in [30, 31, 32]. Most recently, transmit power minimization for wireless networks with energy harvesting relays have been analyzed in [33].

The remainders of this paper are presented as follows. In Sect. 2, the system model, assumptions, and WPT protocols for the sensor network are introduced. In Sect. 3, the performance metrics for a single sensor node and whole system are introduced. Accordingly, closed-form expressions for the packet outage probability, system reliability, and system outage probability are derived in Sect. 4. In Sect. 5, the numerical results and discussions are provided. Finally, the conclusion is given in Sect. 6.

In this section, we introduce the system model, channel assumptions, and WPT schemes for the considered WPSN.

2.1 System model

Let us consider a WPSN as shown in Fig. 1 in which K sensor nodes are scheduled to harvest the energy and send packets to the HAP. The HAP is assumed to have \(M+1\) antennas in which one special antenna is designed for the downlink wireless energy transfer (DWET) and the M antennas are used to receive the ULIT. Here, the HAP can employ either the SC or the MRC technique to process the received information. Due to the limited energy, the sources need to be charged by the HAP following a specific protocol (see Sects. 2.2 and 2.3). The channel gain of the ULIT from the sensor node \(S_k\) to the jth antenna of the HAP is denoted by \(g_{kj}\), \(j \in \{1,2,\ldots , M\}\). The channel gain of the DWET from the HAP to the sensor node \(S_k\) is expressed by \(f_{k}\) or \(h_{k}\), \(k \in \{1,2,\ldots , K\}\) depending on the energy harvesting protocol. Note that the sensors are often equipped with a battery to start the energy harvesting process and they also use such a battery as a backup energy source [10]. However, the analysis of the battery consumption is out of scope of this paper.

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To make the line with recent publications [34, 35, 36, 37], we assume that all channel coefficients are modeled as Rayleigh blocked flat fading, i.e., the channels remain constant during transmission of one packet but they may independently change thereafter. Accordingly, the channel gains are random variables (RVs) distributed following an exponential distribution, and the probability density function (PDF) and cumulative distribution function (CDF) are formulated, respectively, as,

$$f_{X}(x)=\frac{1}{\Omega _{X}}\exp \left( - \frac{x}{\Omega _X} \right) ,$$

(1)

$$F_{X}(x)=1- \exp \left( - \frac{x}{\Omega _X} \right) ,$$

(2)

where X is the RV refers to the channel gain, and \({\Omega _X}={{\mathrm{{\mathbf {E}}}}}[X]\) is the channel mean gain. In the considered system, the channel mean gains of RVs \(f_k\), \(h_{k}\), and \(g_{kj}\) are denoted by \(\Psi _{k}\), \(\Omega _k\), and \(\beta _{k}\), respectively.

2.2 HHT protocol

This protocol employs the TDMA approach as shown in Fig. 2 in which a time block T is separated into K timeslots, and each timeslot is assigned for one sensor node \(S_{k}\) with the period of \((t_{0k}+t_{k})T\). Here, the header of each timeslot \(t_{0k}T\) is used for the DWET while the remainder \(t_{k}T\) is dedicated to send the data packet to the HAP. In other words, the total time block of the energy harvesting and information transfer can be expressed as

$$\sum \limits _{k=1}^{K}t_{0k}T+ \sum \limits _{k=1}^{K}t_{k}T=T,$$

(3)

i.e., \(\sum \limits _{\tau =0}^{K} t_{\tau } = 1\), \(t_{\tau }\) is a fraction of timeslot T which satisfies \(0<t_{\tau } < 1\), and \(t_{0}\) denotes the total time for the energy harvesting, defined by

$$t_{0}=\sum \limits _{k=1}^{K} t_{0k},\quad 0<t_{0k}<1,\quad \forall k \in \{1,2,\ldots , K\},$$

(4)

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In the period \(t_{0k}T\), the HAP uses one special antenna to transfer the energy to the sensor node \(S_{k}\), and hence the harvested energy at the \(S_{k}\) can be expressed as follows

$$E_{k}=\eta _{k} t_{0k}T P f_{k} d^{-\alpha }_{k},\quad \forall k \in \{1,2,\ldots , K\},$$

(5)

where P is the transmission power of the HAP, \(d_{k}\) is distance from the HAP to the node \(S_{k}\), \(\alpha\) is the path-loss exponent, and \(\eta _{k} \in (0,1)\) is the energy conversion efficiency coefficient which depends on the harvesting circuitry [38, 39]. After energy harvesting period, the sensor node \(S_{k}\) uses its harvested energy to send the data packet to the HAP with the power given by

$$\begin{aligned} P_k=\frac{E_k}{ t_{k}T}=\frac{\eta _{k} t_{0k} P f_{k}d^{-\alpha }_{k}}{t_k},\quad \forall k \in \{1\ldots K\}. \end{aligned}$$

(6)

Moreover, the transmission time of the sensor node \(S_{k}\) for one packet with size of L bits can be formulated as the ratio of packet size to the transmission rate as follows [40, 41, 42, 43, 44]

$$\begin{aligned} T^{(v)}_{k}=\frac{{\widetilde{B}}_{k}}{\ln \left( 1+\rho _k \gamma ^{(v)}_{k}\right) }, \quad \forall k \in \{1,2,\ldots , K\}, \end{aligned}$$

(7)

where \({\widetilde{B}}_{k}=\frac{L\ln (2)}{Wt_k}\), W is the system bandwidth, and \(\rho _k\) is a constant related to a specific target bit error rate of M-ary quadrature amplitude modulation (MQAM), \(\rho _k=-\frac{1}{\log (5*BER_k)}\) [45, 46]. Accordingly, the SNR \(\gamma ^{(v)}_{k}\) can be expressed as (see Appendix 1)

$$\begin{aligned} \gamma ^{(v)}_{k}=\frac{P_k g^{(v)}_k d^{-\alpha }_{k}}{WN_0}=\frac{\eta _{k} t_{0k} \gamma _{0} f_{k} g^{(v)}_k d^{-2\alpha }_{k} }{t_k }, \end{aligned}$$

(8)

where \(\gamma _{0}=\frac{P}{WN_0}\), \(v \in \{SC,MRC\}\) technique, and if the HAP employs the SC technique, i.e. \(v=SC\), \(g^{(v)}_{k}\) can be formulated as

$$\begin{aligned} g^{(SC)}_{k}=\max \limits _{j \in \{1,2,\ldots , M\}} \{ g_{kj}\}, \end{aligned}$$

(9)

otherwise if the HAP uses the MRC technique to process the received signal, i.e. \(v=MRC\), then \(g^{(v)}_{k}\) can be given by

$$g^{(MRC)}_{k}=\sum \limits _{j=1}^{M} g_{kj}.$$

(10)

2.3 HDT protocol

In contrast with the HHT protocol, in the HDT protocol, the HAP uses a dedicated timeslot, \(t_0\), at the beginning of the block to harvest the energy, while other timeslots are only used for ULIT (see Fig. 3). Accordingly, the sensor node \(S_{k}\) can harvest the energy over the downlink \(h_k\) as

$$\begin{aligned} E_{k}=\eta _{k} P d^{-\alpha }_{k} h_{k} t_{0}T,\quad \forall k \in \{1,2,\ldots , K\}. \end{aligned}$$

(11)

After the energy harvesting period, the sensor nodes wait for their assigned timeslot to send the packet to the HAP with the power given by

$$\begin{aligned} P_k=\frac{E_k}{t_kT}=\frac{ t_{0}\eta _{k}h_k P d^{-2\alpha }_{k} }{t_k},\quad \forall k \in \{1\ldots K\}. \end{aligned}$$

(12)

Accordingly, the SNR at the HAP when the sensor node \(S_k\) used its harvested energy to transmit the packet to the HAP is given as

$$\begin{aligned} \gamma ^{(v)}_{k}=\frac{P_k g_k d^{-\alpha }_{k}}{WN_0}=\frac{\eta _{k}t_{0} \gamma _{0} h_k g^{(v)}_k d^{-2\alpha }_{k}}{t_k}. \end{aligned}$$

(13)

In this protocol, the total time including the wireless energy transfer and communication transmission time for one block is also normalized to one as given in (3).

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In this section, we introduce performance metrics for a single user and for a complete system.

In the following section, we use the results of Lemma 1 to analyze the performance of the considered system for both HDT and HHT protocols.

In this paper, two WPT protocols for wireless sensor networks were proposed and compared. More specifically, the analytical expressions of the packet time probability and reliable communication for the proposed protocols over Rayleigh fading channels are derived. These obtained performance metrics were subsequently used to compare the performance of proposed protocols with respect to the SC and MRC techniques. Further, these obtained expressions can be useful tools for a fast evaluation and parameter optimization of the WPSN implementations. Numerical examples showed that the proposed HDT protocol using the MRC technique outperforms all other simulated scenarios. The performance of the proposed HDT protocol can be further improved when the number of antennas at the HAP increases. Thus, the HDT protocol using MRC technique can be a promising solution for wireless sensor networks with high reliability demands. In the future research, we will utilize the advantage of RF energy harvesting and study the performance of multi-hop communication and the impact of interference on communication links with high reliability demands.