Research ArticleCharacterization and Modeling of Received Signal Strength andCharging Time for Wireless Energy Transfer
Uthman Baroudi,1 Amin-ud-din Qureshi,2 and Samir Mekid3
1Computer Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia2Systems Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia3Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Correspondence should be addressed to Uthman Baroudi; [email protected]
Received 30 April 2014; Revised 11 October 2014; Accepted 28 October 2014
Wireless sensor networks can provide effective means for monitoring and controlling a wide range of applications. Recently,tremendous effort was directed towards devising sensors powered from ambient sources such as heat, wind, and vibration.Wirelessenergy transfer is another source that has attractive features that make it a promising candidate for supplying power to wirelesssensor nodes. This paper is concerned with characterizing and modeling the charging time and received signal strength indicatorfor wireless energy transfer system. These parameters play a vital role in deciding the geometry of sensor network and the routingprotocols to be deployed. The development of communication protocols for wireless-powered wireless sensor networks is alsoimproved with the knowledge of such models. These two quantities were computed from data acquired at various coordinatesof the harvester relative to a fixed position of RF energy source. Data was acquired for indoor and outdoor scenarios using thecommercially available PowerCast energy harvester and evaluation board. Mathematical models for both indoor and outdoorenvironments were developed and analyzed. A few guidelines on how to use these models were suggested. Finally, the possibilityof harvesting the energy from the ambient RF power to energize wireless sensor nodes was also investigated.
1. Introduction
The previous two decades have witnessed an unprecedentedadvancement in radio frequency (RF) based equipment,ranging from personal and medical devices to complex civilstructures’ monitoring and military systems, all with reliablyprecise specifications. Several wireless systems have replacedtheir wired counterparts, for example, personal communi-cation using cellular phones (significantly reducing the useof landline phones) and wireless data and computer com-munication networks (WLANS). The advent of extremelylow power processors and energy efficient RF devices hasfurther assisted drastic development and deployment ofwireless sensor networks (WSN). Examples of such applica-tions include structural healthmonitoring (SHM), healthcaresystems, habitat monitoring, and precision agriculture [1]. Aperiodical battery charging/replacement of individual sensornodes is, however, always needed to ensure the continuous
operation of WSN. In practice, there are several WSNapplications where the human approach to deployed sensornode is either too difficult or expensive. By this very nature ofWSNapplications, it is very cumbersome and sometimes veryexpensive to periodically attain this action of battery chargingand/or replacement. Examples of such scenarios are SHMand border surveillance systems using unattended acousticand seismic sensors. This problem has made the researcherslook for alternatives for powering wireless sensor nodes [2].The literature survey suggests that there are two possiblealternative solutions to cope with the above-mentioned prob-lem. The first alternative is to use some ambient sources ofenergy. Different energy harvesting schemes have been underconsideration; theymainly include solar [3], piezoelectric [4],and ambient RF energy harvesting systems [5–9]. In caseswhere such energy harvesting is not possible, the secondalternative is to charge a battery using directed transmissionof RF energy as a wireless battery charging scheme [10].
Hindawi Publishing CorporationAdvances in Electrical EngineeringVolume 2015, Article ID 621306, 15 pageshttp://dx.doi.org/10.1155/2015/621306
2 Advances in Electrical Engineering
This paper is concerned with the investigation of someimportant aspects of RF energy harvesting using both theambient RF energy and directed RF energy transmission.
In both of the aforementioned alternatives, since thecharging process is not instant, there are time intervals whena sensor node has not enough amount of energy to send datapackets, and hence the communication is intermittent. Sucha scenario creates the need for development of new protocolsfor communication among different nodes. The chargingtime 𝑇
𝑐and received signal strength RSSI are the major
variables to influence the new communication protocols.Recently several papers have discussed different aspects ofwireless powering of the WSNs and some new routing pro-tocols [9, 11, 12]. However, to the best of our knowledge, thereis no research work available in the literature considering themathematical relationship of these two parameters with thespatial coordinates.
Our main contribution is the development of a 3D math-ematical model that presents the real behavior of RSSI and𝑇𝑐at indoor and outdoor environments. Our mathematical
models relate these variables or parameters (RSSI and 𝑇𝑐)
to spatial coordinates. In order to study any communicationprotocol, we need a model to represent the signal behaviorbetween the transmitter and receiver. Generally, a randomchannel model (Gaussian, Rician, etc.) is used. However,this approach does not always catch the real behavior ofthe suggested protocols that make them irrelevant. Considerdesigning a routing protocol for RF energy harvesting basedWSN. In this case, our model can easily be used to quan-tify/estimate the charging time needed for each node andwe can select the next hop accordingly. On the other hand,RSSI models can be exploited to test certain protocol underdifferent channel coding, for example. Once, the expectedRSSI for a given scheme is determined, we can use our modelto find out the expected charging time at the intended receiverand neighboring nodes as well.
For data acquisition, a series of experiments were per-formed on P2110-EVAL-01 PowerCast Energy HarvestingDevelopment Kit for Wireless Sensors. RF survey was alsoconducted to assess the capability of ambient RF energyfor the purpose of energy harvesting by PowerCast energyharvester.
The rest of the paper is organized as follows. Section 2describes the ambient RF survey. Section 3 describes theexperimental setup. Section 4 analyzes the data of outdoorexperiments. Section 5 describes the indoor experimentsand its outcomes. Mathematical modeling is considered inSection 6. The paper is concluded in Section 7.
2. RF Survey
The RF survey is performed to investigate the possibilityof harvesting the energy from the ambient RF energy dueto several sources like cellular mobile transmitters, radiostations, Wi-Fi networks, and so forth. This survey wasperformed by scanning the available RF power spectrumat six different locations inside the King Fahd Universitycampus using GW Instek spectrum analyzer. Instead of
Table 1: Spectral power peaks.
Peak number Peak frequency (MHz) Peak power (dBm)952 −37
showing the spectral peaks recorded at all six locations, wehave shown them only for one location. In the following data,Table 1 lists the observed spectral peaks while powers alongseveral bands are mentioned separately. It should be noticedhere that the minimum power requirement for a PowerCastpower harvester is −10 dBm and that it is optimally designedto receive power in 902–928MHz band.
All of the following readings are taken using PowerCastomnidirectional (dipole) antenna.
Power through the system:
(1) whole spectrum (1MHz–2.7GHz) = −14.4 dBm;(2) band (900MHz–950MHz) = −31.0 dBm;(3) band (902MHz–928MHz) = −33.8 dBm;(4) band (500MHz–1500MHz) = −20.0 dBm.
From the spectral peaks and powers across several bands,it was observed that none of them is even close to −10 dBmfromwhich wemay conclude that PowerCast harvester is notcapable of harvesting from ambient RF energy.
It is important to note that these measurements werecollected via an antenna which is optimally designed for theband 902MHz–928MHz. Promising measurements can beobserved if an array of antennas is used, expecting the powerofmagnitude to be−10 dBmor evenmore,making the energyharvesting possible from ambient RF energy. The interestedreaders may read the recent paper [8] and references thereinfor a review of attempts made in this regard.
3. Experimental Setup
The following subsections describe the hardware, experimentscenarios, data acquisition, and analysis tools followed byoutdoor and indoor experiments. The parameters of interestare shown graphically as well as in tabular form.
3.1. Hardware. The hardware components used in the exper-iments are listed as follows:
(1) P2110-EVAL-01 PowerCast Energy Harvesting Devel-opment Kit for Wireless Sensors;
(2) LabJack U6 data acquisition card;(3) notebook computer.
Advances in Electrical Engineering 3
The constituent components of P2110-EVAL-01 Power-Cast EnergyHarvestingDevelopmentKit are listed as follows:
Figure 1 shows the hardware listed above. For furtherdetails and operation of the P2110-EVAL-01DevelopmentKit,the interested reader should refer to the corresponding usermanual at http://www.powercastco.com/.
3.2. Scenarios. The data acquisition was performed for twodifferent scenarios: outdoor free-field and indoor reverberantenvironment.
The outdoor scenario is straightforward to imagine wherethere is no source of reflection for the transmitted energyreaching the harvester, except the negligible ground reflec-tions. Such situation can be termed as an ideal one for the RFenergy harvesting with no obstacle amid transmitter-receiverand zero reflections.
The indoor data acquisition is performed in two roomsof different dimensions. The smaller room has dimensions20.5 × 9 × 8.5 ft while the larger room has dimensions 40 ×25 × 8.5 ft. Both rooms are carpeted. Two faces of eachroom are concrete walls with the other two faces madeof steel partitions. All of these four faces are enameled.Ceilings of both rooms are made of stainless steel. Bothrooms with such five faces out of total six have certainreflection coefficients with significant magnitudes, therebymaking them reverberant for RF signals.
Before the description of experimental details for bothscenarios, in the following, the spatial coordinates areexplained where the data acquisition was performed.
In order to characterize the power harvesting, a sphericalcoordinate system was chosen, since the radiation patternsare well described in this coordinate system.The characteris-tics are more meaningful without any confusion.
The power harvester system was tested along certainradial lines, that is, for fixed azimuth (𝜑) and elevation (𝜃)with different radial distances from origin.
As compared to [13], new radial lines are also includedfor enhanced data acquisition. Details of these radial linesare given in Table 2 and visualized in Figure 2. It shouldbe noted that the radiation pattern of the transmitter issymmetric about 𝑥-𝑦 plane and hence it can be argued thatthe results obtained for radial lines corresponding to azimuth16.29∘ and 30∘ can be equally associated with the radial linescorresponding to azimuth −16.29∘ and −30∘. Hence there areeffective twelve radial lines for data acquisition.
3.3. Data Acquisition and Analysis Tools. In order to charac-terize the power harvester the time taken by the capacitors to
Receiving antennasdipole and patch P2110 evaluation
board
Access point Wireless sensorboard
915 MHz powercaster transmitter
LabJack U6 data acquisition card
Figure 1: Hardware components used in data acquisition.
010
2030
400
1002468
1012
−10x (ft)
y (ft)
z(ft
)
Figure 2: Spherical coordinates of test points (red lines for 𝜃 = 0∘and blue lines for 𝜃 = 5∘).
get charged, denoted by𝑇𝑐, and the signal strength received by
the harvester, denoted by RSSI, are needed, both for changingharvester coordinates. Experiments were performed for twotypes of antennas used by the harvester: the low-gain omni-directional antenna and high-gain directional antenna.Thesetwo parameters are obtained from the data packets sent bythe sensor node attached to the harvester to the access pointthrough HyperTerminal as text file. A portion of such a file isshown in Figure 3. A packet is sent whenever the capacitorsare charged with an amount corresponding to enough energyto send a packet of data. This packet includes, among others,the 𝑇𝑐and RSSI, which are parameters of interest to us. For
further analysis, themean value of RSSI obtained from severalpackets was taken. However for 𝑇
𝑐it was preferred to exploit
the charging waveform of the capacitors acquired throughLabJack data acquisition card and its software utility. Powerspectrum (which is the FFT of the autocorrelation) of thiswaveform gave a direct measure of the 𝑇
𝑐by finding the
frequency of dominant peak along the spectrum and theninverting it. Power spectrum is a universally accepted tool forfinding the fundamental or dominant time period (𝑇
𝑐in this
case) of a signal (the charging waveform in our case). The
4 Advances in Electrical Engineering
Table 2: Spherical coordinates for testing harvester (𝑟,G, 𝜑).
Figure 3: A snapshot of data received at access point.
waveform is acquired at a sampling interval of 10ms, muchsmaller than the fastest charging time, as will be seen in thenext sections. A charging waveform and the correspondingspectrum are shown in Figure 4 when the omnidirectionalantenna was used. It should be emphasized here that sincethe waveform is always positive, the signal is preprocessedby detrending it, thereby showing the true peak other thantheDC component by power spectrum.The signal processingwas performed offline in MATLAB.
4. Outdoor Experiments
The outdoor experiments were performed in one of thefootball grounds inside King Fahd University. The data wasacquired for both types of antennas. In the following, weanalyze the acquired data for each radial line one by one.Numerical values of the evaluated parameters are shown intables and their trends are shown graphically. The standarddeviations for mean RSSI values are also mentioned in brack-ets just below them in the tables.The reader should follow theconvention in Table 2 for naming different coordinates, thatis, radial line number and point number. The acronym “NC”stands for “no charging” which means that “at this point theharvester could not charge.” Although the data was analyzedfor both of the antennas, results in the graphical form will beshown only for the directional (patch) antenna for the sake
50 100 150 200 250
1.1
1.2
1.3Harvested voltage waveform
50 100 150 200 250
0
0.1Detrended harvested voltage waveform
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
Frequency (Hz)
Pow
er (d
B)
Power spectrum
Time (s)
Volta
ge(V
)Vo
ltage
(V)
(AC
part
onl
y)−0.1
Time (s)
−60
−40
−20
Figure 4: Charging waveform and its power spectrum.
Figure 5: The outdoor experiment setup. The RF harvester withomnidirectional antenna and 14.1mF charging capacitor.
of brevity. A plot corresponding to a particular radial line issketched to the point beyond which it could not charge.
It will be found in Tables 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,13, and 14 that sometimes numerical values of 𝑇
𝑐and RSSI
are shown for only one point, which means that the antennacould charge only at that very point. Figure 5 shows the out-door experiment setup.
Advances in Electrical Engineering 5
Table 3: Parameters for radial line 1 in the outdoor experiment, azimuth = elevation = 0∘.
Serial number Radial distance𝑟 [ft]
RSSI [mW](directionalantenna)
RSSI [mW](omnidirectional
antenna)
𝑇𝑐[s]
(directionalantenna)
𝑇𝑐[s]
(omnidirectionalantenna)
1 10 1.0003(0.00025)
0.4000(0.00033) 3.7 9.1
2 15 0.4191(0.00047)
0.2012(0.00013) 8 21.3
3 20 0.2770(0.0002) NC∗ 16 NC
4 25 0.1857(0.00006) NC 32 NC
5 30 0.13(0) NC 197.8 NC
∗No charging.
Table 4: Parameters for radial line 2 in the outdoor experiment, azimuth = 0∘, elevation = 5∘.
Figure 6: RSSI versus radial distance using directional antenna inthe outdoor scenario.
Tables 3 through 8 show the numerical values of theparameters of interest while Figures 6 and 7 show thevariations of RSSI and 𝑇
𝑐versus radial distance. We have
observed that charging time and RSSI are affected by radialdistance as well as azimuth and elevations. It is observedthat charging time is significantly increased when patchtype directional antenna is used. The maximum harvesting
10 12 14 16 18 20 262422 28 30Radial distance from transmitter, r (ft)
20
40
60
80
100
120
140
160
180
200
0
Radial line 1Radial line 2Radial line 3
Radial line 4Radial line 5Radial line 6
Tc
(s)
Figure 7: Charging time 𝑇𝑐versus radial distance using directional
antenna in the outdoor scenario.
range is found to be 30 ft when directional antenna isused along the zero azimuth and elevation, while it isonly 15 ft in the case of dipole antenna. At azimuthsother than zeros, it is only 15 ft. In addition, as it canbe expected, RSSI is inversely proportional to the dis-tance between transmitter and harvester. From Figure 6,we can infer that the parameters such as the charging
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time and RSSI follow trends similar to the inverse squarelaw.
5. Indoor Experiments
In a room with the dimensions 40 × 25 × 8.5 ft, the experi-ments were performed along the same radial lines as in thecase of outdoor experiments and the results are documentedin the same way in the following. Tables 9 through 14 showthe numerical values of the parameters of interest obtainedfrom indoor experiments, while Figures 8 and 9 show thevariations of RSSI and 𝑇
𝑐versus radial distance.
The indoor experiments exhibit very interesting observa-tions. As compared to outdoor experiments, the maximumrange is 35 ft for both antennas. The trends of these param-eters with respect to radial distance are not as regular asthose for the outdoor experiments.The parameters have verypoor values at some points nearer to the transmitter andvery good values at farther points. This can be attributedto the fact that five faces of the room out of six are highlyreflective and caused multiple reflections of the transmittedwaves.These reflections might cause complete cancellation ata nearer point while allowing enhancement of the signal atsome farther points.
6. Mathematical Modeling of 𝑇𝑐
and RSSI
As compared to battery powered WSN, the placement ofindividual sensor nodes in wireless-powered WSN requiresspecial attention. Firstly, the charging range of wireless powertransmitter is limited by its power as well as radiation pattern.RSSI at a certain node is pragmatically supposed to besignificantly different from those of others. This difference isfurther propagated into several communication parameterslike data rate, range of transmission, and so forth. Secondly,wireless charging of the sensor nodes contributes to theintersample delay of a sensor node because a node cannottransmit a packet of data unless it is charged with enoughenergy, which takes a certain amount of time. Keeping thesefacts in view, the mathematical models of 𝑇
𝑐and RSSI are of
significant importance in WSN applications because of thefollowing reasons.
(a) Geometry of the Sensor Network. With the knowledgeof a closed formmathematicalmodel, describingRSSIas a function of Cartesian coordinates, locations ofsensor nodes can be optimally decided.
(b) Sampling Interval of Data. The mathematical modelof 𝑇𝑐as a function of geometrical coordinates will
give a measure of the charging time of a certain nodeand thus interval between two data points can beanticipated prior to the actual operation.
It should be emphasized here that our work is muchdifferent from channel modeling. Channel modeling dealswith the variation of different parameters of a signal indue course of propagation from transmitter to the receiver.Channel models are simply unable to give the information
10 20 302515 35 40
1
2
3
4
5
6
0
RSS
I (m
W)
Radial line 1Radial line 2Radial line 3
Radial line 4Radial line 5Radial line 6
Radial distance from transmitter, r (ft)
Figure 8: RSSI versus radial distance using directional antenna inthe indoor scenario.
0
50
100
150
Tc
(s)
10 20 302515 35 40
Radial line 1Radial line 2Radial line 3
Radial line 4Radial line 5Radial line 6
Radial distance from transmitter, r (ft)
Figure 9: 𝑇𝑐versus radial distance using directional antenna in the
indoor scenario.
required in the scenario of wireless-powered WSNs. Forexample, it is not possible to compute charging time fromchannel model.
The models were obtained through data from direc-tional antenna as described previously. A separate modelis developed for each set of data with constant elevation,both for 𝑇
𝑐and RSSI. For the sake of clarity and easiness in
modeling, spherical coordinates of data points are convertedto Cartesian coordinates.The surface fitting tool of MATLABis utilized to fit our data into mathematical models. Different
Advances in Electrical Engineering 9
Table 15: Mathematical model of RSSI0(outdoor, elevation = 0∘).
Model
RSSI0= 𝑝00+ 𝑝20𝑥2
+ 𝑝02𝑦2
+ 𝑝30𝑥3
+ 𝑝12𝑥𝑦2
+ 𝑝40𝑥4
+ 𝑝22𝑥2
𝑦2
Coefficients𝑝00= 1.929
𝑝02= −0.05405
𝑝12= 0.005695
𝑝20= −0.01803
𝑝22= −0.0001521
𝑝30= 0.0009966
𝑝40= −1.542𝑒 − 5
Goodness of fit
SSE 0.009726 𝑅-square 0.9939
Adjusted 𝑅-square 0.9913 RMSE 0.02636
Table 16: Mathematical model of 𝑇𝑐0(outdoor, elevation = 0∘).
Model𝑇𝑐0= 𝑝00+ 𝑝10𝑥 + 𝑝
20𝑥2
+ 𝑝02𝑦2
+ 𝑝30𝑥3
+ 𝑝12𝑥𝑦2
+𝑝40𝑥4
𝑝22𝑥2
𝑦2
+ 𝑝04𝑦4
Coefficients𝑝00= −3381
𝑝10= 866.2
𝑝20= −79.7
𝑝02= 20.75
𝑝30= 3.138
𝑝12= −2.927
𝑝40= −0.04471
𝑝22= 0.105
𝑝04= −0.0129
Goodness of fit
SSE 1.991 𝑅-square 0.998
Adjusted 𝑅-square 0.997 RMSE 0.5334
Table 17: Mathematical model of RSSI5 (outdoor, elevation = 5∘).
ModelRSSI5 = 𝑝00 + 𝑝10𝑥 + 𝑝01𝑦 + 𝑝20𝑥
2
+ 𝑝02𝑦2
+ 𝑝30𝑥3
+ 𝑝12𝑥𝑦2
+𝑝40𝑥4
+ 𝑝04𝑦4
Coefficients𝑝00= −11.38
𝑝10= 3.535
𝑝20= −0.3588
𝑝02= 0.01644
𝑝30= 0.01511
𝑝12= −0.00748
𝑝40= −0.0002276
𝑝04= −8.596𝑒 − 5
Goodness of fit
SSE 0.009726 𝑅-square 0.9939
Adjusted 𝑅-square 0.9913 RMSE 0.02636
model forms can be selected to fit the data. The polyno-mial form was chosen as it is the most general form andencompasses a large number of functions becausemost of thefunctions can be decomposed into polynomials using Taylor’sseries, including exponentials and sinusoids. The models ofRSSI and 𝑇
𝑐are generally described as
RSSI𝜃= 𝑓𝜃
RSSI (𝑥, 𝑦) ,
𝑇𝑐𝜃= 𝑓𝜃
𝑇𝑐
(𝑥, 𝑦) ,
(1)
Table 18: Mathematical model of 𝑇𝑐5(outdoor, elevation = 5∘).
Model𝑇𝑐5= 𝑝00+ 𝑝10𝑥 + 𝑝
20𝑥2
+ 𝑝02𝑦2
+ 𝑝30𝑥3
+ 𝑝12𝑥𝑦2
+ 𝑝40𝑥4
+𝑝22𝑥2
𝑦2
+ 𝑝04𝑦4
Coefficients𝑝00= 114.4
𝑝10= −30.14
𝑝20= 2.957
𝑝02= −1.307
𝑝30= −0.1278
𝑝12= 0.2142
𝑝40= −0.002207
𝑝22= −0.007837
𝑝04= 0.002548
Goodness of fit
SSE 1.163Adjusted 𝑅-square 0.9987
𝑅-square 0.9993RMSE 0.3813
Table 19: Mathematical model of RSSI (indoor, elevation = 0∘).
ModelRSSI0 = 𝑝00 + 𝑝10𝑥 + 𝑝20𝑥
2
+ 𝑝02𝑦2
+ 𝑝30𝑥3
+ 𝑝12𝑥𝑦2
+ 𝑝40𝑥4
+𝑝22𝑥2
𝑦2
+ 𝑝04𝑦4
Coefficients𝑝00= −10.3
𝑝10= 3.283
𝑝20= −0.2823
𝑝02= −0.1685
𝑝30= 0.0093
𝑝12= 0.01243
𝑝40= −0.0001045
𝑝22= −0.0002286
𝑝04= 0.000234
Goodness of fit
SSE 10.53Adjusted 𝑅-square 0.2972
𝑅-square 0.52219993RMSE 0.7873813
Table 20: Mathematical model of 𝑇𝑐(indoor, elevation = 0∘).
ModelRSSI0 = 𝑝00 + 𝑝10𝑥 + 𝑝20𝑥
2
+ 𝑝02𝑦2
+ 𝑝30𝑥3
+ 𝑝12𝑥𝑦2
+ 𝑝40𝑥4
+𝑝22𝑥2
𝑦2
+ 𝑝04𝑦4
Coefficients𝑝00= 380.6
𝑝10= −97.3
𝑝20= 8.502
𝑝02= 1.042
𝑝30= −0.2932
𝑝12= −0.1329
𝑝40= 0.003456
𝑝22= 0.002338
𝑝04= 0.004663
Goodness of fit
SSE 1513Adjusted 𝑅-square 0.6477
𝑅-square 0.7605RMSE 9.433
where the subscript 𝜃 indicates that themodel corresponds tothat elevation only.
In the modeling process, an attempt is made to reducethe number of coefficients to a possible minimum withacceptable goodness of fit. The following tables detail theobtained models. Tables 15, 16, 17, 18, 19, 20, 21, and 22 givethe numerical details of the models while Figures 10–13 givethe pictorial description of the fitted models. Note that SSEand RMSE stand for sum of squared errors and root meansquare error, respectively.
10 Advances in Electrical Engineering
Table 21: Mathematical model of RSSI (indoor, elevation = 5∘).
ModelRSSI0 = 𝑝00 + 𝑝10𝑥 + 𝑝20𝑥
2
+ 𝑝02𝑦2
+ 𝑝30𝑥3
+ 𝑝12𝑥𝑦2
+ 𝑝40𝑥4
+𝑝22𝑥2
𝑦2
+ 𝑝04𝑦4
Coefficients𝑝00= 24.41
𝑝10= −5.708
𝑝20= 0.4696
𝑝02= 0.1692
𝑝30= −0.01618
𝑝12= −0.01498
𝑝40= 0.000199
𝑝22= 0.0003446
𝑝04= −0.0001921
Goodness of fit
SSE 0.886 𝑅-square 0.8981
Adjusted 𝑅-square 0.8165 RMSE 0.2977
Table 22: Mathematical model of 𝑇𝑐(indoor, elevation = 5∘).
ModelRSSI0 = 𝑝00 + 𝑝10𝑥 + 𝑝20𝑥
2
+ 𝑝02𝑦2
+ 𝑝30𝑥3
+ 𝑝12𝑥𝑦2
+ 𝑝40𝑥4
+𝑝22𝑥2
𝑦2
+ 𝑝04𝑦4
Coefficients𝑝00= −271.1
𝑝10= 63.45
𝑝20= −5.129
𝑝02= 0.5736
𝑝30= −0.01159
𝑝12= −0.01982
𝑝40= 0.002266
𝑝22= 0.0005403
𝑝04= 0.01159
Goodness of fit
SSE 7.647 𝑅-square 0.9922
Adjusted 𝑅-square 0.9922 RMSE 0.8745
6.1. Outdoor Model. The RSSI model for outdoor environ-ment is illustrated in Figure 10. The reciprocal relationshipbetween the signal strength and the distance from the emitteris obvious. In addition, for the same elevation, we canobserve huge variations in the signal strength due to theunequal gain of directional antenna used in the experiment.Hence, in order to obtain the same RSSI, we need to placethe sensor closer to the antenna compared to the directsituation. Figure 11 describes the relationship between thecharging time and the sensor position from the emitter andits complements in Figure 10. Again, we can easily observethe reciprocal relationship between the charging time and thedistance.The farther the distance from the emitter, the longerthe time needed to obtain enough energy to activate/transmitthe sensor board.
Figures 12 and 13 illustrate the obtained models for RSSIand charging time for 5∘ elevation scenarios, respectively.Again, the reciprocal relation is very clear. However, we canobserve local minima (e.g., 𝑥 = 16) and even maxima (e.g.,𝑥 = 22). Knowing this behavior helps the sensor networkarchitect in placing the sensors in the best positions to obtainthe best performance. Moreover, this knowledge helps also indesigning/selecting the routes for delivering data over suchnetwork.We can also notice that due to lower RSSI compared
−100
10 15 20 25 30
100
0.2
0.4
0.6
0.8
1
RSSI
(mW
)
x (ft)y (ft)
RSSI versus x, yFitted surface
Figure 10: The fitted surface for RSSI0(outdoor, elevation = 0∘).
2510 15 20010
0
200
400
600
800
1000
1200
1400Tc
(s)
−10
Fitted surface
x (ft)y (ft)
Tc versus x, y
Figure 11: The fitted surface for 𝑇𝑐0(outdoor, elevation = 0∘).
to 0∘ elevation, the feasible charging region is smaller butsmoother. As expected, the signal strength at 0∘ elevationshows higher level (>1mw) than 5∘ elevation (<0.9mw).
Figures 14 and 19 provide a comparison of experimentaland fitted parameters for a couple of radial lines. The fittedcurves show perfect matching with experimental data.
6.2. Indoor Model. Indoor modeling is very challenging andcomplex due to the surrounding environment. Our model,as described above, is simple and it can lend itself easily tosimilar environment like wholesale yard and so on. Figure 15shows an interesting behavior where closer positions tothe emitter suffer lower RSSI than some farther positions.
Advances in Electrical Engineering 11
10 12 14 16 18 20 220 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fitted surfaceRSSI5 versus x, y
−5
x (ft)y (ft)
RSSI
5(m
W)
Figure 12: The fitted surface for RSSI5(outdoor, elevation = 5∘).
Tc5 versus x, y
1015
2025
05
100
10203040506070
−5−10
Tc5
(s)
x (ft)y (ft)
Fitted surface
Figure 13: The fitted surface for 𝑇𝑐5(outdoor, elevation = 5∘).
Furthermore, the farther positions near the walls exhibithigher RSSI than the middle of the room.
On the other hand, though we have carried out severaltrials to enhance the correlation coefficient, the best obtainedcorrelation coefficient is the one presented in Table 19 that islow indicating a poor data fitting. The same thing applies onFigure 16, but with a better coefficient. These results manifestthe difficulty in modeling the indoor RSSI/𝑇
𝑐behavior.
Considering the RSSI/𝑇𝑐behavior for indoor with ele-
vation 5∘, Figures 17 and 18 depict these two relationships.It is interesting to notice that we were able to reach goodfitness models that have almost unity correlation coefficients.Moreover, we have a better RSSI and lower charging timecompared to the 0∘ elevation. This result can be attributed tothe elevation where we minimize the ground floor reflections
and the received signal has lower attenuation and conse-quently higher RSSI. In addition, we can observe almost aperfect symmetry. Figure 15 shows a good matching betweenthe fitting model and the experimental data points.
6.3. Comparison between Indoor and Outdoor Behaviours.Having studied the indoor and outdoor models, we willsummarize the differences between the two models in thefollowing points.
(i) The P2110-EVAL-01 Development Kit works well forboth environments.
(ii) However, the kit is optimized to work for indoor asit is observed in the obtained readings for RSSI andcharging time.
12 Advances in Electrical Engineering
10 15 20 25 30
0.5
1
1.5
0
RSSI
(mW
)
ExperimentalFitted
Radial distance (ft)
(a)
10 15 20 25
10
20
30
40
0
ExperimentalFitted
Tc
(s)
Radial distance (ft)
(b)
10 15 20
0.4
0.6
0.8
1
0.2
RSSI
(mW
)
Radial distance (ft)
ExperimentalFitted
(c)
5 10 15 20 25
10
20
30
40
0
Radial distance (ft)
Tc
(s)
ExperimentalFitted
(d)
Figure 14: Comparison of (outdoor) experimental and fitted values of the parameters for radial line 1 (a, b) and radial line 5 (c, d).
(iii) The harvesting can cover larger outdoor area com-pared to the indoor area. Nevertheless, the qualityof the signal for indoor is better over the shortrange.
6.4. Guidelines toUseTheseModels. In the section, we presenta few guidelines to use the above models.
(i) The RSSI models complement the 𝑇𝑐models.
(ii) For given position coordinates (𝑥, 𝑦, 𝜃), we can deter-mine the correspondingRSSI value and𝑇
𝑐value using
both models.(iii) If we want to use the same kit, we can use these
models to find the optimal positions for placing the
sensors by simply differentiating RSSI with respect to𝑥, 𝑦 or both and then we find the corresponding 𝑇
𝑐.
Alternatively, we can do the opposite, which is morepractical.
(iv) For routing design, we can integrate our models withthe route selection function.
(v) For a given RSSI, which can be extracted from anychannel model, we can easily find the corresponding𝑇𝑐. In this case, the position coordinates (𝑥, 𝑦, 𝜃)
are not relevant. We just used them to establish therelationship between RSSI and 𝑇
𝑐. This makes our
model applicable to a wide range of channel models.
Advances in Electrical Engineering 13RS
SI0
(mW
)
10 15 20 25 30 35 40
05
10
0
1
2
3
4
5
6
x (ft)
y(ft
)
−5−10
Fitted surfaceRSSI0 versus x, y
Figure 15: The fitted surface for RSSI0(indoor, elevation = 0∘).
30 35 0x (ft) y (ft)−10
10 15 20 2540
100
20
40
60
80
100
Fitted surface
Tc0
(s)
Tc0 versus x, y
Figure 16: The fitted surface for 𝑇𝑐0(indoor, elevation = 0∘).
7. Conclusion
This paper describes a series of data acquisition experimentsand modeling of two important parameters for RF pow-ered WSNs. These parameters are the charging time of acapacitor/battery powering the sensor node and the receivedsignal strength indicator at a node.Themathematical modelsof these parameters are important in designing the routingprotocols andWSN geometry. Extensive data are acquired inboth indoor and outdoor environments. A detailed experi-mental procedure is explained in the paper. Modeling resultsare presented and discussed in detail. Then, a few guidelinesfor the usage of these models are suggested.
Additionally, the RF survey and the experimental resultsusing PowerCast power harvester suggested that it is prac-tically impossible to harvest sufficient energy for running
x (ft) y (ft)−5−10
10 15 20 25 300 5
1000.5
1
1.5
2
2.5
3
3.5
4
Fitted surface
RSSI
5(m
W)
RSSI5 versus x, y
Figure 17: The fitted surface for RSSI5(indoor, elevation = 5∘).
0−5
−10
x (ft)10 15 20 25 30
Tc5 versus x, y
y(ft)
10
5
0
10
20
30
40T
(s)
Fitted surface
Figure 18: The fitted surface for 𝑇𝑐5(indoor, elevation = 5∘).
the associated application with PowerCast. However, anoptimized multiband antenna with further improvements inthe electronics of the harvesting circuitry can be realized inthe future to improve the level of harvested energy.
Our plan is to incorporate electromagnetic properties ofreflectingwalls to come upwith similarmodels for the indoorscenario, which is much complicated as compared to theoutdoor scenario.
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
14 Advances in Electrical Engineering
10 20 30 40
0
2
4
6RS
SI (m
W)
−2
ExperimentalFitted
Radial distance (ft)
(a)
10 20 30 40
0
50
100
Tc
(s)
−50
ExperimentalFitted
Radial distance (ft)
(b)
10 15 20 25 30
0
0.5
1
1.5
RSSI
(mW
)
−0.5
ExperimentalFitted
Radial distance (ft)
(c)
0
10
20
30
40
010 20 30
ExperimentalFitted
Radial distance (ft)
Tc
(s)
(d)
Figure 19: Comparison of (indoor) experimental and fitted values of the parameters for radial line 1 (a, b) and radial line 5 (c, d).
Acknowledgment
The authors would like to acknowledge the support providedby King Abdulaziz City for Science and Technology (KACST)through King Fahd University of Petroleum and Minerals(KFUPM) for funding this Project, no. 09ELE758-04, as partof the National Science Technology and Innovation Plan.
References
[1] Z. W. Sim, R. Shuttleworth, M. J. Alexander, and B. D. Grieve,“Compact patch antenna design for outdoor rf energy harvest-ing in wireless sensor networks,” Progress in ElectromagneticsResearch, vol. 105, pp. 273–294, 2010.
[2] D. Niyato, E. Hossain, M. M. Rashid, and V. K. Bhargava,“Wireless sensor networks with energy harvesting technologies:
a game-theoretic approach to optimal energy management,”IEEE Wireless Communications, vol. 14, no. 4, pp. 90–96, 2007.
[3] P. T. V. Bhuvaneswari, R. Balakumar, V. Vaidehi, and P.Balamuralidhar, “Solar energy harvesting for wireless sensornetworks,” in Proceedings of the 1st International Conferenceon Computational Intelligence, Communication Systems andNetworks (CICSYN ’09), pp. 57–61, July 2009.
[4] G. K. Ottman, H. F. Hofmann, A. C. Bhatt, and G. A. Lesieutre,“Adaptive piezoelectric energy harvesting circuit for wirelessremote power supply,” IEEE Transactions on Power Electronics,vol. 17, no. 5, pp. 669–676, 2002.
[5] D. Bouchouich, F. Dupont, M. Latrach, and L. Ventura, “Ambi-ent RF energy harvesting,” in Proceedings of the InternationalConference on Renewable Energies and Power Quality (ICREPQ’10), Granada, Spain, March 2010.
Advances in Electrical Engineering 15
[6] S. Kim, “RF energy harvesting techniques for wirelessly pow-ered devices,” in Proceedings of the IEEE MTT-S InternationalMicrowave Workshop Series on Intelligent Radio for FuturePersonal Terminals (IMWS-IRFPT ’11), 2011.
[7] M. Mi, M. H. Mickle, C. Capelli, and H. Swift, “RF energyharvesting with multiple antennas in the same space,” IEEEAntennas and Propagation Magazine, vol. 47, no. 5, pp. 100–106,2005.
[8] S. Mandal and S. K. Giri, “Comparison of antennas for radiofrequency energy harvesting in 0.2–2.4GHz range,” in Proceed-ings of the 3rd International Conference on Electronics ComputerTechnology (ICECT ’11), pp. 93–97, April 2011.
[9] M. Minami, T. Morito, H. Morikawa, and T. Aoyama, “SolarBiscuit. A battery-less wireless sensor network system forenvironmental monitoring applications,” in Proceedings of the2nd InternationalWorkshop onNetworked Sensing Systems, June2005.
[10] L. Tang and C. Guy, “Radio frequency energy harvesting inwireless sensor network,” in Proceedings of the InternationalConference onWireless Communications and Mobile Computing(IWCMC ’09), 2009.
[11] L. Xie, Y. Shi, Y. T. Hou, W. Lou, H. D. Sherali, and S. F. Midkiff,“On renewable sensor networks with wireless energy transfer:the multi-node case,” in Proceedings of the 9th Annual IEEECommunications Society Conference on Sensor,Mesh andAdHocCommunications and Networks (SECON ’12), pp. 10–18, Seoul,Republic of Korea, June 2012.
[12] M. Erol-Kantarci and H. T. Mouftah, “Suresense: sustainablewireless rechargeable sensor networks for the smart grid,” IEEEWireless Communications, vol. 19, no. 3, pp. 30–36, 2012.
[13] U. Baroudi, A.-U. Qureshi, S. Mekid, and A. Bouhraoua, “Radiofrequency energy harvesting characterization: an experimentalstudy,” in Proceedings of the 11th IEEE International Conferenceon Trust, Security and Privacy in Computing and Communica-tions (TrustCom ’12), pp. 1976–1981, Liverpool, UK, June 2012.
