This study investigates the efficiency of a new method of powering remote sensors by the means of wireless energy transfer. The increased use of sensors for data collection comes with the inherent cost of supplying power from sources such as power cables or batteries. Wireless energy transfer technology eliminates the need for power cables or periodic battery replacement. The time and cost of setting up or expanding a sensor network will be reduced while allowing sensors to be placed in areas where running power cables or battery replacement is not feasible. This paper models wireless channels for power and data separately. Smart scheduling for the data channel is proposed to avoid transmitting data on a noisy channel where the probability of data loss is high to improve power efficiency. Analytical models have been developed and verified using simulations

Abedi, Ali

Almaghasilah, Ahmed

Veilleux, Shaun

Wilkerson, DeLisa

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1Stochastic Modelling of Wireless Energy Transfer
Shaun Veilleux, Ahmed Almaghasilah, Ali Abedi, DeLisa Wilkerson1
Wireless Sensor Network (WiSe-Net) Lab
Electrical and Computer Engineering Department
University of Maine, Orono, ME, USA
Shaun.Veilleux@Maine.edu
1Electronics Systems Branch
NASA Marshall Space Flight Center
Huntsville, AL, USA
Abstract—This study investigates the efficiency of a new
method of powering remote sensors by the means of wireless
energy transfer. The increased use of sensors for data collection
comes with the inherent cost of supplying power from sources
such as power cables or batteries. Wireless energy transfer
technology eliminates the need for power cables or periodic
battery replacement. The time and cost of setting up or expanding
a sensor network will be reduced while allowing sensors to
be placed in areas where running power cables or battery
replacement is not feasible.
This paper models wireless channels for power and data
separately. Smart scheduling for the data channel is proposed to
avoid transmitting data on a noisy channel where the probability
of data loss is high to improve power efficiency. Analytical models
have been developed and verified using simulations.
I. INTRODUCTION
Wireless energy transfer will allow for sensors to receive
power and transmit data without the use of the wires or the
need to exchange batteries. This energy transmission method is
ideal for sensors that have a low sampling rate, quick sampling
time, and a varying sampling period. This technology is able
to power multiple sensors at once and allow for changing the
position of the sensor(s), and add additional sensors to the
network with relative ease.
Technologies such as WiFi, cellular, and television (TV)
that are considered abandoned wireless energy sources. They
can be put in use to power and charge wireless sensors and
batteries. For example, a TV signal is harvested and converted
from a RF signal to DC using a RF-DC converter circuit, to
power microcontroller and transceiver relay [1]. The wireless
energy harvesting beacon system (WEH) is able to capture
energy from the TV signal with a range of over 6.5 km.
Technologies, such as microwave power transfer (MPT) and
mobile communication offloading are designed to extend the
mobile device’s battery life [2]. The simultaneous wireless
information and power transfer (SWIPT) field is a combination
of two technologies with a goal of increasing the efficiency of
the MPT.
This paper investigates the effects of smart scheduling on
wireless sensors outage (the amount of time the sensor is not
operational due to low energy). Smart scheduling is a method
to determine when to transmit data based on the amount of
stored energy in the sensor and the noise levels on the data
channel. If there is too much noise on the wireless channel it
is highly likely that the transmitted data will fail and be lost.
If the sensor has low energy and the data channel has a high
level of noise it would be best to preserve the energy and wait
until either the sensor has more energy or the channel has less
noise.
II. PROBLEM FORMULATION
Research on wireless energy transfer will allow for sensors to
receive energy and transmit data without the use of wires or
the need to change batteries. As a wireless signal is transmitted
it is reflected, scattered, and corrupted from the environment
which prevents it from fully reaching the receiver. Three
widely used channel models, AWGN, Rayleigh, and Rician are
used to simulate the various cases detailed in Table I. The data
and power are individually simulated through three channels.
AWGN channel is suited for static charging situation, Rician
channel is suited for mobile charging with a line of sight
(LOS), and Rayleigh channel is used to model for mobile
sensors with no dominant LOS.
A sensor takes time to receive and store enough energy to
successfully transmit the sensor’s data. The available energy
for wireless energy transfer is limited, therefore, the imple-
mentation of smart scheduling is used to avoid wasting energy.
If the noise on the data channel is above a threshold the sensor
will not transmit or waste energy transmitting data that may
not be received. Additionally, if the sensor’s stored energy is
below a threshold the sensor will not transmit to prevent an
outage. For each unit of time, the power channel represents the
amount of energy received. If the noise on the data channel is
below a set threshold, the sensor will transmit.
III. SIMULATION RESULTS AND MATHEMATICAL
REPRESENTATIONS
Simulations are modeled in MATLAB 2016b to display the
effects of varying power and data channels between AWGN,
Rayleigh, and Rician, detailed in Table I. The outage percent-
age versus the threshold with the inclusion of smart scheduling
is represented in Figure 1. The first channel name corresponds
to the power channel while the second is the data channel. If
smart scheduling is not included the outage will be constant
and equal to the max outage seen in Figure 1
It might not be possible to choose the environment the
system is in, but the threshold can be chosen to maximize the
https://ntrs.nasa.gov/search.jsp?R=20170012427 2019-08-30T16:46:19+00:00Z
2TABLE I
MODELLED WIRELESS CHANNEL COMBINATIONS AND REAL WORLD EXAMPLES OF WHERE THEY MAY BE USED.
Power/Data AWGN Rayleigh Rician
AWGN [1] Static sensor Static charging for a mobile sensor Static charging for a mobile sensor withLOS[2]
Rayleigh Mobile charging for a static sensor Mobile sensor Mobile charging for a mobile sensorwith LOS
Rician Mobile charging with LOS for a staticsensor
Mobile charging with LOS for a mobile
sensor Mobile sensor with LOS
[1] AWGN - Additive White Gaussian Noise.
[2] LOS - Line of sight.
Fig. 1. The resultant outage vs threshold for modelled power channel and
data channel
number of successful transmissions and minimize the outage.
To choose the threshold a mathematical expression for the
outage versus threshold is preferred over a simulation. When
the threshold is low the sensor never transmits and therefore
never uses energy, the result is an outage of zero percent. When
the system has a high threshold the sensor will transmit every
at time interval resulting in a maximum outage probability.
To make the calculation of the max outage easier, the effects
of the sensors energy storage will be ignored. Therefore the
outage will be equal to the probability that the received power
between each transmission is less than the required transmit
power. For the case where the power channel is modeled using
an AWGN channel the outage can be calculated using (1) -
(3), where (1) is the probability density function (PDF) of a
normal distribution.
N(µ, σ2) = 1√
2piσ2
e−
(x−µ)2
2σ2 (1)
where µ is the mean and σ is the variance of an AWGN
channel.
σ =
√
10− SNR10 (2)
The outage is equal to the probability the received power is
less than the power required to transmit, hence,
outage =
∫ x
−∞
N(µ, σ2)
=
1
2
[
1 + er f
(
x − µ
σ
√
2
)] (3)
where x is the power required to transmit. Simulation results
represented in Figure 2 verify where the power channel is
modeled using an AWGN channel, and the data channel is
modeled using a Rayleigh channel.
Fig. 2. The simulated outage vs the calculated max outage
As seen in Figure 2, calculating the maximum outage can
be accurately accomplished using the cumulative density func-
tion (CDF) of the modeled power channel. Without the data
channel and threshold taken into consideration the calculation
is inaccurate when the threshold is not high. To calculate a
better equation at any time interval, one needs to look at the
energy received and amount needed to transmit. If the energy
received is less than the amount needed to transmit and the
noise on the data channel is less than the specified threshold,
there will be an outage. Since the power channel and data are
independent, the probability of an outage occurring are the
probabilities multiplied together. For the case where the power
channel is modelled using an AWGN channel, the data channel
is modelled using a Rayleigh channel, the probability that the
received energy is less than the energy needed to transmit is
presented in (3). The probability that the noise on the data
3channel is less than the threshold can be calculated using (4)
and (5).
f (x, σ) = x
σ2
e
−x
2σ2 (4)
where x is the threshold and σ is the variance.
F(x, σ) =
∫ x
0
f (x, σ)
= 1 − e −x
2
2σ2
(5)
Therefore the total outage can be calculated as
outage =
(∫ x1
−∞
N(µ, σ21 )
)
∗
(
F(x2, σ22 )
)
=
1
2
[
1 + er f
(
x1 − µ
σ1
√
2
)]
∗ ©­«1 − e
−x22
2σ22
ª®¬
(6)
where x1 is the required transmit energy and x2 is the
threshold. Simulation in Figure 3 verifies (6) and with a tighter
maximum outage bound.
Fig. 3. The simulated outage vs the calculated max outage
The maximum outage bound calculated in (6) neglects the
effects of the sensors energy storage. Figure 4 shows the
simulation with the inclusion of the sensor energy storage,
alongside the analytical result from (6).
IV. CONCLUSION
With the increased use of sensors, it is desired to be able
to decrease the setup time and maintenance cost. Wireless
energy transfer technology helps achieve both of these. Sensors
will no longer need expensive power cables or batteries to
be periodically changed. This will allow for larger sensor
networks to be established as well as reduction in time
deployment. This paper focused on how to model a wireless
stochastic network and the effects that smart scheduling has
on a sensor’s run time.
Three types of channels are investigated, AWGN, Rayleigh,
and Rician as well and smart scheduling is examined to
Fig. 4. The simulated outage with a battery vs the calculated max outage
without a battery
decrease the outage percentage of a given sensor. Additionally,
this paper has proposes a way to calculate the upper bound on
the outage that a channel will see versus the threshold.
V. REFERENCES
[1] Hansen, R.C., J. McSpadden, and J.N. Benford. "A Uni-
versal Power Transfer Curve". IEEE Microwave and Wireless
Components Letters 15.5 (2005): 369-371. Web. 1 Oct. 2016.
[2] You, Changsheng, Kaibin Huang, and Hyukjin Chae.
"Energy Efficient Mobile Cloud Computing Powered By Wire-
less Energy Transfer". IEEE Journal on Selected Areas in
Communications 34.5 (2016): 1757-1771. Web. 1 Nov. 2016.
[3] C. Bergsrud, S. Noghanian, J. Straub, D. Whalen and R.
Fevig, "Orbit-to-ground Wireless Power Transfer test mission,"
2013 IEEE Aerospace Conference, Big Sky, MT, 2013, pp. 1-
11.
[4] C. R. Valenta and G. D. Durgin, "Harvesting Wireless
Power: Survey of Energy-Harvester Conversion Efficiency
in Far-Field, Wireless Power Transfer Systems," in IEEE
Microwave Magazine, vol. 15, no. 4, pp. 108-120, June 2014.
[5] D. Belo and N. B. Carvalho, "Harmonic spaced multisines
for efficient wireless power transmission," 2015 IEEE Wireless
Power Transfer Conference (WPTC), Boulder, CO, 2015, pp.
1-4.
[6] D. Niyato, P. Wang and D. I. Kim, "Admission control
policy for wireless networks with RF energy transfer," 2014
IEEE International Conference on Communications (ICC),
Sydney, NSW, 2014, pp. 1118-1123.
[7] G. Wild and S. Hinckley, "Wireless acoustic communica-
tions and power supply for in vivo biomedical devices," 2010
IEEE International Ultrasonics Symposium, San Diego, CA,
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[8] A. Biason and M. Zorzi, "Joint Transmission and Energy
Transfer Policies for Energy Harvesting Devices With Finite
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