Advances in Electrical Engineering
Volume 2015 (2015), Article ID 621306, 15 pages
http://dx.doi.org/10.1155/2015/621306

Research Article

Characterization and Modeling of Received Signal Strength and Charging 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 Arabia
²Systems Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
³Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 30 April 2014; Revised 11 October 2014; Accepted 28 October 2014

Academic Editor: Abdulkareem Adinoyi

Copyright © 2015 Uthman Baroudi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

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. Wireless energy transfer is another source that has attractive features that make it a promising candidate for supplying power to wireless sensor nodes. This paper is concerned with characterizing and modeling the charging time and received signal strength indicator for wireless energy transfer system. These parameters play a vital role in deciding the geometry of sensor network and the routing protocols to be deployed. The development of communication protocols for wireless-powered wireless sensor networks is also improved with the knowledge of such models. These two quantities were computed from data acquired at various coordinates of the harvester relative to a fixed position of RF energy source. Data was acquired for indoor and outdoor scenarios using the commercially available PowerCast energy harvester and evaluation board. Mathematical models for both indoor and outdoor environments were developed and analyzed. A few guidelines on how to use these models were suggested. Finally, the possibility of 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 unprecedented advancement in radio frequency (RF) based equipment, ranging from personal and medical devices to complex civil structures’ monitoring and military systems, all with reliably precise specifications. Several wireless systems have replaced their wired counterparts, for example, personal communication using cellular phones (significantly reducing the use of landline phones) and wireless data and computer communication networks (WLANS). The advent of extremely low power processors and energy efficient RF devices has further assisted drastic development and deployment of wireless sensor networks (WSN). Examples of such applications include structural health monitoring (SHM), healthcare systems, habitat monitoring, and precision agriculture [1]. A periodical battery charging/replacement of individual sensor nodes is, however, always needed to ensure the continuous operation of WSN. In practice, there are several WSN applications where the human approach to deployed sensor node is either too difficult or expensive. By this very nature of WSN applications, it is very cumbersome and sometimes very expensive to periodically attain this action of battery charging and/or replacement. Examples of such scenarios are SHM and border surveillance systems using unattended acoustic and seismic sensors. This problem has made the researchers look for alternatives for powering wireless sensor nodes [2]. The literature survey suggests that there are two possible alternative solutions to cope with the above-mentioned problem. The first alternative is to use some ambient sources of energy. Different energy harvesting schemes have been under consideration; they mainly include solar [3], piezoelectric [4], and ambient RF energy harvesting systems [5–9]. In cases where such energy harvesting is not possible, the second alternative is to charge a battery using directed transmission of RF energy as a wireless battery charging scheme [10]. This paper is concerned with the investigation of some important aspects of RF energy harvesting using both the ambient RF energy and directed RF energy transmission.

In both of the aforementioned alternatives, since the charging process is not instant, there are time intervals when a sensor node has not enough amount of energy to send data packets, and hence the communication is intermittent. Such a scenario creates the need for development of new protocols for communication among different nodes. The charging time and received signal strength RSSI are the major variables to influence the new communication protocols. Recently several papers have discussed different aspects of wireless powering of the WSNs and some new routing protocols [9, 11, 12]. However, to the best of our knowledge, there is no research work available in the literature considering the mathematical relationship of these two parameters with the spatial coordinates.

Our main contribution is the development of a 3D mathematical model that presents the real behavior of RSSI and at indoor and outdoor environments. Our mathematical models relate these variables or parameters (RSSI and ) to spatial coordinates. In order to study any communication protocol, we need a model to represent the signal behavior between the transmitter and receiver. Generally, a random channel model (Gaussian, Rician, etc.) is used. However, this approach does not always catch the real behavior of the suggested protocols that make them irrelevant. Consider designing a routing protocol for RF energy harvesting based WSN. In this case, our model can easily be used to quantify/estimate the charging time needed for each node and we can select the next hop accordingly. On the other hand, RSSI models can be exploited to test certain protocol under different channel coding, for example. Once, the expected RSSI for a given scheme is determined, we can use our model to find out the expected charging time at the intended receiver and neighboring nodes as well.

For data acquisition, a series of experiments were performed on P2110-EVAL-01 PowerCast Energy Harvesting Development Kit for Wireless Sensors. RF survey was also conducted to assess the capability of ambient RF energy for the purpose of energy harvesting by PowerCast energy harvester.

The rest of the paper is organized as follows. Section 2 describes the ambient RF survey. Section 3 describes the experimental setup. Section 4 analyzes the data of outdoor experiments. Section 5 describes the indoor experiments and its outcomes. Mathematical modeling is considered in Section 6. The paper is concluded in Section 7.

2. RF Survey

The RF survey is performed to investigate the possibility of harvesting the energy from the ambient RF energy due to several sources like cellular mobile transmitters, radio stations, Wi-Fi networks, and so forth. This survey was performed by scanning the available RF power spectrum at six different locations inside the King Fahd University campus using GW Instek spectrum analyzer. Instead of showing the spectral peaks recorded at all six locations, we have shown them only for one location. In the following data, Table 1 lists the observed spectral peaks while powers along several bands are mentioned separately. It should be noticed here that the minimum power requirement for a PowerCast power harvester is −10 dBm and that it is optimally designed to receive power in 902–928 MHz band.

Table 1: Spectral power peaks.

Peak number
Peak frequency (MHz)
Peak power (dBm)

952
−37

2
939.5998
−39

3
922.24
−43.9

4
177
−42.7

5
178
−42.7

6
179
−42.7

7
181
−42.9

8
183
−43.2

9
184
−43.4

All of the following readings are taken using PowerCast omnidirectional (dipole) antenna.

Power through the system:

(1)whole spectrum (1 MHz–2.7 GHz) = −14.4 dBm;(2)band (900 MHz–950 MHz) = −31.0 dBm;(3)band (902 MHz–928 MHz) = −33.8 dBm;(4)band (500 MHz–1500 MHz) = −20.0 dBm.

From the spectral peaks and powers across several bands, it was observed that none of them is even close to −10 dBm from which we may conclude that PowerCast harvester is not capable of harvesting from ambient RF energy.

It is important to note that these measurements were collected via an antenna which is optimally designed for the band 902 MHz–928 MHz. Promising measurements can be observed if an array of antennas is used, expecting the power of magnitude to be −10 dBm or even more, making the energy harvesting possible from ambient RF energy. The interested readers may read the recent paper [8] and references therein for a review of attempts made in this regard.

3. Experimental Setup

The following subsections describe the hardware, experiment scenarios, data acquisition, and analysis tools followed by outdoor and indoor experiments. The parameters of interest are shown graphically as well as in tabular form.

3.1. Hardware

The hardware components used in the experiments are listed as follows:

(1)P2110-EVAL-01 PowerCast Energy Harvesting Development Kit for Wireless Sensors;(2)LabJack U6 data acquisition card;(3)notebook computer.

The constituent components of P2110-EVAL-01 PowerCast Energy Harvesting Development Kit are listed as follows:

(1)915 MHz, 3 W transmitter;(2)915 MHz directional (patch) antenna;(3)915 MHz omnidirectional (dipole) antenna;(4)wireless sensor board (WSN-EVAL-01);(5)access point: Microchip 16-bit XLP Development Board (DM240311);(6)2.4 GHz, IEEE 802.15.4 radio: Microchip MRF24J40 PICtail/PICtail Plus Daughter Board (AC164134-1).

Figure 1 shows the hardware listed above. For further details and operation of the P2110-EVAL-01 Development Kit, the interested reader should refer to the corresponding user manual at http://www.powercastco.com/.

Figure 1: Hardware components used in data acquisition.

3.2. Scenarios

The data acquisition was performed for two different scenarios: outdoor free-field and indoor reverberant environment.

The outdoor scenario is straightforward to imagine where there is no source of reflection for the transmitted energy reaching the harvester, except the negligible ground reflections. Such situation can be termed as an ideal one for the RF energy harvesting with no obstacle amid transmitter-receiver and zero reflections.

The indoor data acquisition is performed in two rooms of different dimensions. The smaller room has dimensions 20.5 × 9 × 8.5 ft while the larger room has dimensions 40 × 25 × 8.5 ft. Both rooms are carpeted. Two faces of each room are concrete walls with the other two faces made of steel partitions. All of these four faces are enameled. Ceilings of both rooms are made of stainless steel. Both rooms with such five faces out of total six have certain reflection coefficients with significant magnitudes, thereby making them reverberant for RF signals.

Before the description of experimental details for both scenarios, in the following, the spatial coordinates are explained where the data acquisition was performed.

In order to characterize the power harvesting, a spherical coordinate system was chosen, since the radiation patterns are well described in this coordinate system. The characteristics are more meaningful without any confusion.

The power harvester system was tested along certain radial lines, that is, for fixed azimuth () and elevation () with different radial distances from origin.

As compared to [13], new radial lines are also included for enhanced data acquisition. Details of these radial lines are given in Table 2 and visualized in Figure 2. It should be noted that the radiation pattern of the transmitter is symmetric about - plane and hence it can be argued that the results obtained for radial lines corresponding to azimuth 16.29° and 30° can be equally associated with the radial lines corresponding to azimuth −16.29° and −30°. Hence there are effective twelve radial lines for data acquisition.

Table 2: Spherical coordinates for testing harvester ().

Point number
Line number

1
2
 3
4
5
6

1
(10, 0, 0)
(10, 5, 0)
(10, 0, 16.29)
(10, 0, 30)
(10, 5, 16.29)
(10, 5, 30)

2
(10, 0, 0)
(15, 5, 0)
(15, 0, 16.29)
(15, 0, 30)
(10, 5, 16.29)
(15, 5, 30)

3
(10, 0, 0)
(20, 5, 0)
(20, 0, 16.29)
(20, 0, 30)
(10, 5, 16.29)
(20, 5, 30)

4
(10, 0, 0)
(25, 5, 0)
(25, 0, 16.29)
(25, 0, 30)
(10, 5, 16.29)
(25, 5, 30)

5
(10, 0, 0)
(30, 5, 0)
(30, 0, 16.29)
(30, 0, 30)
(10, 5, 16.29)
(30, 5, 30)

6
(10, 0, 0)
(35, 5, 0)
(35, 0, 16.29)
(35, 0, 30)
(10, 5, 16.29)
(35, 5, 30)

Figure 2: Spherical coordinates of test points (red lines for   and blue lines for ).

3.3. Data Acquisition and Analysis Tools

In order to characterize the power harvester the time taken by the capacitors to get charged, denoted by , and the signal strength received by the harvester, denoted by RSSI, are needed, both for changing harvester coordinates. Experiments were performed for two types of antennas used by the harvester: the low-gain omnidirectional antenna and high-gain directional antenna. These two parameters are obtained from the data packets sent by the sensor node attached to the harvester to the access point through HyperTerminal as text file. A portion of such a file is shown in Figure 3. A packet is sent whenever the capacitors are charged with an amount corresponding to enough energy to send a packet of data. This packet includes, among others, the and RSSI, which are parameters of interest to us. For further analysis, the mean value of RSSI obtained from several packets was taken. However for it was preferred to exploit the charging waveform of the capacitors acquired through LabJack data acquisition card and its software utility. Power spectrum (which is the FFT of the autocorrelation) of this waveform gave a direct measure of the by finding the frequency of dominant peak along the spectrum and then inverting it. Power spectrum is a universally accepted tool for finding the fundamental or dominant time period ( in this case) of a signal (the charging waveform in our case). The waveform is acquired at a sampling interval of 10 ms, much smaller than the fastest charging time, as will be seen in the next sections. A charging waveform and the corresponding spectrum are shown in Figure 4 when the omnidirectional antenna was used. It should be emphasized here that since the waveform is always positive, the signal is preprocessed by detrending it, thereby showing the true peak other than the DC component by power spectrum. The signal processing was performed offline in MATLAB.

Figure 3: A snapshot of data received at access point.

Figure 4: Charging waveform and its power spectrum.

4. Outdoor Experiments

The outdoor experiments were performed in one of the football grounds inside King Fahd University. The data was acquired for both types of antennas. In the following, we analyze the acquired data for each radial line one by one. Numerical values of the evaluated parameters are shown in tables and their trends are shown graphically. The standard deviations for mean RSSI values are also mentioned in brackets just below them in the tables. The reader should follow the convention in Table 2 for naming different coordinates, that is, radial line number and point number. The acronym “NC” stands for “no charging” which means that “at this point the harvester could not charge.” Although the data was analyzed for both of the antennas, results in the graphical form will be shown only for the directional (patch) antenna for the sake of brevity. A plot corresponding to a particular radial line is sketched 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 and RSSI are shown for only one point, which means that the antenna could charge only at that very point. Figure 5 shows the outdoor experiment setup.

Table 3: Parameters for radial line 1 in the outdoor experiment, azimuth = elevation = 0°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

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°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

1
10
0.8311 (0.047)
0.3317 (0.00029)
3.7
12.8

2
15
0.4063 (0.00093)
NC
8
NC

3
20
0.2216 (0.00011)
NC
25.6
NC

Table 5: Parameters for radial line 3 in the outdoor experiment, azimuth = 16.29°, elevation = 5°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

1
10
0.9309 (0.0027)
0.2522 (0.00039)
3.2
16

2
15
0.3778 (0.0012)
0.155 (0.00068)
10.6
64

3
20
0.2050 (0.00011)
NC
21.3
NC

Table 6: Parameters for radial line 4 in the outdoor experiment, azimuth = 30°, elevation = 5°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

1
10
0.6528 (0.001)
0.2036 (0.0001)
5.3
32

2
15
0.2379 (0.000012)
NC
21.3
NC

3
20
NC
NC
NC
NC

Table 7: Parameters for radial line 5 in the outdoor experiment, azimuth = 16.29°, elevation = 5°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

1
10
0.8885 (0.0607)
0.320 (0.0155)
3.5
17.3

2
15
0.4557 (0.0231)
0.1667 (0.0115)
17.2
150.3

3
20
0.2000 (0.01)
NC
95.5
NC

4
21
0.19 (0.01)
NC
187
NC

Table 8: Parameters for radial line 6 in the outdoor experiment, azimuth = 30°; elevation = 5°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

1
10
0.75 (0.0346)
0.2175 (0.0126)
4.3
31.5

2
12
0.5672 (0.0222)
0.1875 (0.0096)
7.6
27.3

3
14
0.3843 (0.0222)
0.1100 (0)
10.9
114

4
15
0.2929 (0.0111)
NC
12.5
NC

5
20
0.222 (0.011)
NC
20.6
NC

6
22
0.15 (0.01)
NC
94.5
NC

Table 9: Parameters for radial line 1 in the indoor experiment, azimuth = elevation = 0°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

1
10
5.0410 (0.26)
1.5561 (0.0087)
1.6
0.5

2
15
0.9243 (0.0078)
0.3683 (0.00092)
10.6
2.7

3
20
0.2506 (0.000711)
0.17 (0.00013)
64
16

4
25
0.2818 (0.0014)
0.3807 (0.0015)
10.6
12.8

5
30
0.2116 (0.00083)
0.7040 (0.0020)
5.3
21.3

6
35
0.7767 (0.0031)
0.9802 (0.0040)
3.7
4

Table 10: Parameters for radial line 2 in the indoor experiment, azimuth = 0°, elevation = 5°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

1
10
0.5809 (0.0027)
0.4023 (0.0024)
5.8
9.1

2
15
0.2452 (0.00027)
0.19 (0.2111)
18.2
32

3
20
0.2182 (0.00025)
NC
21.3
NC

4
25
0.2107 (0.00025)
NC
32
NC

5
30
0.2146 (000.11)
0.244 (0.00035)
32
16

6
35
NC
NC
NC
NC

Table 11: Parameters for radial line 3 in the indoor experiment, azimuth = 16.29°, elevation = 5°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

1
10
0.2614 (0.0006)
0.3713 (0.0007)
9.1
21.3

2
15
0.1975 (0.0024)
0.2127 (0.0002)
21.3
128

3
20
0.5585 (0.0016)
0.2071 (0.0001)
21.3
5.8

4
25
0.2783 (0.0015)
0.2327 (0.0006)
21.3
16

5
30
0.6685 (0.0043)
0.4124 (0.0008)
9.1
4.5

Table 12: Parameters for radial line 4 in the indoor experiment, azimuth = 30°; elevation = 5°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional antenna)
[s]
(omnidirectional antenna)

1
10
2.4960 (0.0164)
0.2256 (0.00031)
1
21.3

2
15
0.9080 (0.0011)
0.1487 (0.0008)
3.3
64

3
20
NC
0.4183 (0.00047)
NC
8

Table 13: Parameters for radial line 5 in the indoor experiment, azimuth = 16.29°, elevation = 0°.

Serial number
Radial distance
[ft]
RSSI [mW]
(directional antenna)
RSSI [mW]
(omnidirectional antenna)
[s]
(directional
antenna)
[s]
(omnidirectional antenna)

1
10
1.0604 (0.0504)
NC
2.5
NC

2
15
0.64 (0.0390)
0.4000 (0.0232)
5
8.1

3
20
0.2318 (0.0272)
0.1367 (0.0115)
26.7
92.3

4
25
NC
NC
NC
NC

5
30
NC
NC
NC
NC

6
39
0.1786 (0.0146)
0.2980 (0.0179)
46.5
14.5

Table 14: Parameters for radial line 6 in the indoor experiment, azimuth = 30°; elevation = 0°.

Radial distance
[ft]
RSS [mW]
(directional antenna)
[s]
(directional antenna)
Radial distance
, [ft]
RSSI [mW]
(omnidirectional antenna)
[s]
(omnidirectional antenna)

10
0.4900 (0.0230)
6.61
10
0.3 (0.0132)
13.4

15
0.2880 (0.0132)
14
11
0.48 (0.0150)
7.1

16
0.6900 (0.0339)
6.3
12
0.23 (0.0141)
17.5

17
0.8462 (0.0375)
3.7
16
0.1940 (0.0114)
25.25

18
0.2325 (0.0175)
23.25
18
0.222 (0.011)
19.6

19
0.2590 (0.0173)
18.4
20
0.1310 (0.0208)
99.6

Figure 5: The outdoor experiment setup. The RF harvester with omnidirectional antenna and 14.1 mF charging capacitor.

Tables 3 through 8 show the numerical values of the parameters of interest while Figures 6 and 7 show the variations of RSSI and versus radial distance. We have observed that charging time and RSSI are affected by radial distance as well as azimuth and elevations. It is observed that charging time is significantly increased when patch type directional antenna is used. The maximum harvesting range is found to be 30 ft when directional antenna is used along the zero azimuth and elevation, while it is only 15 ft in the case of dipole antenna. At azimuths other than zeros, it is only 15 ft. In addition, as it can be expected, RSSI is inversely proportional to the distance between transmitter and harvester. From Figure 6, we can infer that the parameters such as the charging time and RSSI follow trends similar to the inverse square law.

Figure 6: RSSI versus radial distance using directional antenna in the outdoor scenario.

Figure 7: Charging time versus radial distance using directional antenna in the outdoor scenario.

5. Indoor Experiments

In a room with the dimensions 40 × 25 × 8.5 ft, the experiments were performed along the same radial lines as in the case of outdoor experiments and the results are documented in the same way in the following. Tables 9 through 14 show the numerical values of the parameters of interest obtained from indoor experiments, while Figures 8 and 9 show the variations of RSSI and versus radial distance.

Figure 8: RSSI versus radial distance using directional antenna in the indoor scenario.

Figure 9: versus radial distance using directional antenna in the indoor scenario.

The indoor experiments exhibit very interesting observations. As compared to outdoor experiments, the maximum range is 35 ft for both antennas. The trends of these parameters with respect to radial distance are not as regular as those for the outdoor experiments. The parameters have very poor values at some points nearer to the transmitter and very good values at farther points. This can be attributed to the fact that five faces of the room out of six are highly reflective and caused multiple reflections of the transmitted waves. These reflections might cause complete cancellation at a nearer point while allowing enhancement of the signal at some farther points.

6. Mathematical Modeling of and RSSI

As compared to battery powered WSN, the placement of individual sensor nodes in wireless-powered WSN requires special attention. Firstly, the charging range of wireless power transmitter is limited by its power as well as radiation pattern. RSSI at a certain node is pragmatically supposed to be significantly different from those of others. This difference is further propagated into several communication parameters like data rate, range of transmission, and so forth. Secondly, wireless charging of the sensor nodes contributes to the intersample delay of a sensor node because a node cannot transmit a packet of data unless it is charged with enough energy, which takes a certain amount of time. Keeping these facts in view, the mathematical models of and RSSI are of significant importance in WSN applications because of the following reasons.

(a) Geometry of the Sensor Network. With the knowledge of a closed form mathematical model, describing RSSI as a function of Cartesian coordinates, locations of sensor nodes can be optimally decided.(b) Sampling Interval of Data. The mathematical model of as a function of geometrical coordinates will give a measure of the charging time of a certain node and thus interval between two data points can be anticipated prior to the actual operation.

It should be emphasized here that our work is much different from channel modeling. Channel modeling deals with the variation of different parameters of a signal in due course of propagation from transmitter to the receiver. Channel models are simply unable to give the information required in the scenario of wireless-powered WSNs. For example, it is not possible to compute charging time from channel model.

The models were obtained through data from directional antenna as described previously. A separate model is developed for each set of data with constant elevation, both for and RSSI. For the sake of clarity and easiness in modeling, spherical coordinates of data points are converted to Cartesian coordinates. The surface fitting tool of MATLAB is utilized to fit our data into mathematical models. Different model forms can be selected to fit the data. The polynomial form was chosen as it is the most general form and encompasses a large number of functions because most of the functions can be decomposed into polynomials using Taylor’s series, including exponentials and sinusoids. The models of RSSI and are generally described as

where the subscript indicates that the model corresponds to that elevation only.

In the modeling process, an attempt is made to reduce the number of coefficients to a possible minimum with acceptable goodness of fit. The following tables detail the obtained models. Tables 15, 16, 17, 18, 19, 20, 21, and 22 give the numerical details of the models while Figures 10–13 give the pictorial description of the fitted models. Note that SSE and RMSE stand for sum of squared errors and root mean square error, respectively.

Table 15: Mathematical model of (outdoor, elevation = 0°).

Model

Coefficients

Goodness of fit

SSE 0.009726
-square 0.9939

Adjusted -square 0.9913
RMSE 0.02636

Table 16: Mathematical model of (outdoor, elevation = 0°).

Model

Coefficients

Goodness of fit

SSE 1.991
-square 0.998

Adjusted -square 0.997
RMSE 0.5334

Table 17: Mathematical model of RSSI₅ (outdoor, elevation = 5°).

Model

Coefficients

Goodness of fit

SSE 0.009726  
-square 0.9939  

Adjusted -square 0.9913
RMSE 0.02636

Table 18: Mathematical model of (outdoor, elevation = 5°).

Model

Coefficients

Goodness of fit

SSE 1.163 
Adjusted -square 0.9987
-square 0.9993 
RMSE 0.3813

Table 19: Mathematical model of RSSI (indoor, elevation = 0°).

Model

Coefficients

Goodness of fit

SSE 10.53 
Adjusted -square 0.2972
-square 0.52219993 
RMSE 0.7873813

Table 20: Mathematical model of (indoor, elevation = 0°).

Model

Coefficients

Goodness of fit

SSE 1513  
Adjusted -square 0.6477
-square 0.7605 
RMSE 9.433

Table 21: Mathematical model of RSSI (indoor, elevation = 5°).

Model

Coefficients

Goodness of fit

SSE 0.886
-square 0.8981

Adjusted -square 0.8165
RMSE 0.2977

Table 22: Mathematical model of (indoor, elevation = 5°).

Model

Coefficients

Goodness of fit

SSE 7.647
-square 0.9922

Adjusted -square 0.9922
RMSE 0.8745

Figure 10: The fitted surface for RSSI₀ (outdoor, elevation = ).

Figure 11: The fitted surface for (outdoor, elevation = ).

Figure 12: The fitted surface for RSSI₅ (outdoor, elevation = ).

Figure 13: The fitted surface for (outdoor, elevation = ).

6.1. Outdoor Model

The RSSI model for outdoor environment is illustrated in Figure 10. The reciprocal relationship between the signal strength and the distance from the emitter is obvious. In addition, for the same elevation, we can observe huge variations in the signal strength due to the unequal gain of directional antenna used in the experiment. Hence, in order to obtain the same RSSI, we need to place the sensor closer to the antenna compared to the direct situation. Figure 11 describes the relationship between the charging time and the sensor position from the emitter and its complements in Figure 10. Again, we can easily observe the reciprocal relationship between the charging time and the distance. The farther the distance from the emitter, the longer the time needed to obtain enough energy to activate/transmit the sensor board.

Figures 12 and 13 illustrate the obtained models for RSSI and charging time for elevation scenarios, respectively. Again, the reciprocal relation is very clear. However, we can observe local minima (e.g., ) and even maxima (e.g., ). Knowing this behavior helps the sensor network architect in placing the sensors in the best positions to obtain the best performance. Moreover, this knowledge helps also in designing/selecting the routes for delivering data over such network. We can also notice that due to lower RSSI compared to elevation, the feasible charging region is smaller but smoother. As expected, the signal strength at elevation shows higher level (>1 mw) than elevation (<0.9 mw).

Figures 14 and 19 provide a comparison of experimental and fitted parameters for a couple of radial lines. The fitted curves show perfect matching with experimental data.

(a)

(b)

(c)

(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).

6.2. Indoor Model

Indoor modeling is very challenging and complex due to the surrounding environment. Our model, as described above, is simple and it can lend itself easily to similar environment like wholesale yard and so on. Figure 15 shows an interesting behavior where closer positions to the emitter suffer lower RSSI than some farther positions. Furthermore, the farther positions near the walls exhibit higher RSSI than the middle of the room.

Figure 15: The fitted surface for RSSI₀ (indoor, elevation = ).

On the other hand, though we have carried out several trials to enhance the correlation coefficient, the best obtained correlation coefficient is the one presented in Table 19 that is low indicating a poor data fitting. The same thing applies on Figure 16, but with a better coefficient. These results manifest the difficulty in modeling the indoor RSSI/ behavior.

Figure 16: The fitted surface for (indoor, elevation = ).

Considering the RSSI/ behavior for indoor with elevation , Figures 17 and 18 depict these two relationships. It is interesting to notice that we were able to reach good fitness models that have almost unity correlation coefficients. Moreover, we have a better RSSI and lower charging time compared to the elevation. This result can be attributed to the elevation where we minimize the ground floor reflections and the received signal has lower attenuation and consequently higher RSSI. In addition, we can observe almost a perfect symmetry. Figure 15 shows a good matching between the fitting model and the experimental data points.

Figure 17: The fitted surface for RSSI₅ (indoor, elevation = ).

Figure 18: The fitted surface for (indoor, elevation = ).

(a)

(b)

(c)

(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).

6.3. Comparison between Indoor and Outdoor Behaviours

Having studied the indoor and outdoor models, we will summarize the differences between the two models in the following points.

(i)The P2110-EVAL-01 Development Kit works well for both environments.(ii)However, the kit is optimized to work for indoor as it is observed in the obtained readings for RSSI and charging time.(iii)The harvesting can cover larger outdoor area compared to the indoor area. Nevertheless, the quality of the signal for indoor is better over the short range.

6.4. Guidelines to Use These Models

In the section, we present a few guidelines to use the above models.

(i)The RSSI models complement the models.(ii)For given position coordinates , we can determine the corresponding RSSI value and value 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 to or both and then we find the corresponding . Alternatively, we can do the opposite, which is more practical.(iv)For routing design, we can integrate our models with the route selection function.(v)For a given RSSI, which can be extracted from any channel model, we can easily find the corresponding . In this case, the position coordinates are not relevant. We just used them to establish the relationship between RSSI and . This makes our model applicable to a wide range of channel models.

7. Conclusion

This paper describes a series of data acquisition experiments and modeling of two important parameters for RF powered WSNs. These parameters are the charging time of a capacitor/battery powering the sensor node and the received signal strength indicator at a node. The mathematical models of these parameters are important in designing the routing protocols and WSN geometry. Extensive data are acquired in both indoor and outdoor environments. A detailed experimental procedure is explained in the paper. Modeling results are presented and discussed in detail. Then, a few guidelines for the usage of these models are suggested.

Additionally, the RF survey and the experimental results using PowerCast power harvester suggested that it is practically impossible to harvest sufficient energy for running the associated application with PowerCast. However, an optimized multiband antenna with further improvements in the electronics of the harvesting circuitry can be realized in the future to improve the level of harvested energy.

Our plan is to incorporate electromagnetic properties of reflecting walls to come up with similar models for the indoor scenario, which is much complicated as compared to the outdoor scenario.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

The authors would like to acknowledge the support provided by 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 part of the National Science Technology and Innovation Plan.

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