Int. J. Communications, Network and System Sciences, 2010, 3, 395-401
doi:10.4236/ijcns.2010.34050 Published Online April 2010 (http://www.SciRP.org/journal/ijcns/)
Radio Frequency Modelling for Future Wireless Sensor
Network on Surface of the Moon
Jayesh P. Pabari1, Yashwant B. Acharya1, Uday B. Desai2, Shabbir N. Merchant3, Barla Gopala Krishna4
1PLANEX, Physical Research Laboratory, Ahmedabad, India
2Indian Institute of Technology, Hyderabad, India
3Indian Institute of Technology Bombay, Mumbai, India
4Space Application Centre, Ahmedabad, India
Received January 6, 2010; revised February 8, 2010; accepted March 10, 2010
Abstract
In order to study lunar regolith properties, wireless sensor network is planned to be deployed on surface of
the Moon. This network can be deployed having few wireless sensor nodes capable of measuring soil prop-
erties and communicating results, as and when ready. Communication scenario on lunar surface is quite dif-
ferent as compared to that on the Earth, as there is no atmosphere and also there are lots of craters as well as
various terrain topologies. Since the deployment of sensors on the Moon is a challenging and difficult task, it
is advisable to predict the behaviour of communication channel on lunar surface. However, communication
models like Irregular Terrain Model used for terrestrial communication networks are not directly applicable
for Unattended Ground Sensor type sensor networks and need modifications according to lunar surface con-
ditions and lunar environment. Efforts have been put to devise a model of radio frequency environment on
the Moon using basic equations governing various physical phenomena occurring during radio propagation.
The model uses Digital Elevation Model of four sites of the Moon, measured by Terrain Mapping Camera on
board Chandrayan-1, a recent Indian mission to the Moon. Results presented in this paper can provide under-
standing of percentage area coverage for given minimum received signal strength, potential sites for sensor
deployment assuring wireless communication, decision whether a given sensor node can work and can pro-
vide suggestion for possible path of rover with cluster head to remain in contact with the nodes. Digital Ele-
vation Model based results presented here can provide more insight in to the communication scenario on the
Moon and can be very useful to mission planners.
Keywords: Wireless Model, Moon, DEM, Coverage
1. Introduction
In order to detect few regolith properties on lunar sur-
face, a Wireless Sensor Network (WSN) is planned to
be deployed near lunar South Pole, which utilizes wir-
eless sensors capable of working in harsh environ-
mental conditions. Main property of interest is permit-
tivity obtainable from impedance sensor. Since the de-
ployment of network on the Moon is a challenging and
difficult task, it is advisable to predict the behaviour of
communication channel on the lunar surface by some
channel model.
There have been various models for radio commu-
nication on the Earth, for example Irregular Terrain
Model (ITM) also known as Longley-Rice model given
by G. Hufford, A. Longley and W. Kissick [1] and
model given by Durkin [2,3]. ITM is a good model for
terrestrial communication network and it uses mini-
mum antenna height as 0.5 m for simulation while
Durkin’s model does not consider multipath effect in
the simulation. Hata [4] had proposed an empirical
formulation of graphical path loss valid from about 150
MHz to 1500 MHz and it was extended up to 2 GHz.
Walfisch and Bertoni [5] gave a model to consider im-
pact of rooftops and building height by using diffrac-
tion to predict average signal strength at street level.
Alberto Cerpa et al. [6] describes statistical model of
lossy links in wireless sensor networks. S. Willis and C.
J. Kikkert [7] have given radio propagation model for
long range wireless sensor networks. Chirag Patel [8]

396 J. P. PABARI ET AL.
has described wireless channel modeling in his thesis.
Vishwanath Chukkala et al. [9] and Anirudh Daga et al.
[10] gave modeling and simulation of Radio Frequency
(RF) environment of Mars.
In case of present application scenario, operating fre-
quency is to be 2.4 GHz and sensors are to be deployed
on lunar surface, where operating conditions are dif-
ferent than that on the Earth. It is known that there is
no atmosphere on the Moon and there exists very high
vacuum of the order of 10-12 Torr [11,12]. The com-
munication models used for terrestrial communication
networks are not directly applicable to Unattended
Ground Sensor (UGS) type sensor network, like that
planned on the Moon and need modification according
to lunar surface condition. This has motivated us to
carry out the work presented in this paper. Efforts have
been put to derive modeling of radio frequency envi-
ronment on the Moon, using basic equations governing
various physical phenomena occurring during radio
propagation. Our work uses Digital Elevation Model
(DEM) of four sites of the Moon, measured by Terrain
Mapping Camera (TMC) on board Chandrayan-1, a
recent Indian mission to the Moon. Results presented
in this paper can provide understanding of percentage
area coverage for given minimum received signal
strength, potential sites for sensor deployment assuring
wireless communication, decision whether a given sen-
sor node could be used and suggestion for possible
path of rover (carrying cluster head) to remain in con-
tact with the nodes.
Section 2 presents suitability of existing propagation
models for lunar application, Section 3 describes phy-
sical phenomena which can occur on the Moon and as-
sociated path losses, Section 4 gives lunar wireless
model, Section 5 gives details of DEM of selected sites
on lunar surface, Section 6 shows results and paper
ends with conclusion.
2. Suitability of Existing Propagation Models
for Lunar Application
It is expected that the communication would be better
on the Moon as compared to that on the Earth, due to
absence of atmosphere on the Moon. Few existing pro-
pagation models were developed for communication on
the Earth and need to be reviewed for the Moon in
view of their applicability.
2.1. Irregular Terrain Model
Irregular Terrain Model (ITM) was suggested by Rice
et al. [13] and is also known as Longley-Rice model.
Hufford [14] informed that it can be used in area predic-
tion mode and point-to-point mode. ITM takes terrain
and other parameters as input and produces output as
signal distribution in a given area. There are certain
limitations of ITM that it can be used for minimum an-
tenna height of 0.5 metre and minimum distance for
communication as 1 km. The Point-To-Point (PTP)
model given by Wong [15] is based on Longley-Rice
model. However, PTP model describes method to obtain
diffraction loss. As the wireless sensor network involves
deployment of sensors on the ground with very small
antenna heights especially at 2.4 GHz operating fre-
quency, the ITM can’t be used for such applications.
2.2. Two-Ray Model
For a line-of-sight communication, a two-ray model was
given by Neskovic et al. [16]. This theoretical model
incorporates reflection by the reflection coefficient,
which is calculated from incidence angle, dielectric con-
stant, surface conductivity and polarization of antenna.
The signal strength at the receiver as given in (1) is
shown in Willis [7] using free space loss and reflection.
22
12
212
11
|exp()()exp() |
16
ttr
r
PG Gλ
Pjkdψjkd
dd
π



(1)
where and are lengths of first and second path
respectively. The two ray model is mostly used for direct
and ground reflected rays. In case of lunar wireless sensor
net- work, sensor nodes are to be the surface with very
small antenna heights and therefore ground reflected
signal is not expected at the receiver.
1
d2 d
2.3. VSS Multipath Model
Signals reflected from reflectors would reach the receiver
with different strengths and phases with reference to di-
rect signal. At receiver, equivalent signal strength is equ-
al to superposition of varying amplitude and phase sig-
nals and it is possible to get overall signal strength as
reduced or improved. The multipath channel model in
AWR Visual System Simulator [17] uses Equations (2)
and (3) to obtain signal strength for a sample k. The mul-
tipath model was implemented by Willis [18] in MAT-
LAB.
1
() (,)
N
i
x
kpathk

i (2)
2
(,)( )exp()
ci
ii
jπVf Cosθ
path kiAx kdC
 

(3)
where ()
x
k is kth sample, is number of multipath
signals,
N
(,)
p
ath k i is contribution of ith multipath sig-
nal determined by (3), i
A
is gain of ith path, ()
i
x
kd


J. P. PABARI ET AL. 397
is delayed sample associated with path and exponen-
tial term represents doppler shift due to receiver move-
ment. This model may be used for moving nodes, which
is not the case for lunar wireless sensor network.
i
2.4. Multipath Signal Distribution
Instantaneous receiver signal strength (envelope) is rep-
resented by either Rayleigh or Rician distribution as sho-
wn by Hernando et al. [19]. Rayleigh distribution con-
siders only multipath components available and does not
take direct path. However, Rician distribution considers
direct as well as multipath components. Communication
on lunar surface is expected to be line-of-sight and also
multipath due to reflections from terrain and therefore,
Rician distribution is more suited for lunar application.
Rician distribution is shown by Hernando et al. [19] and
given below:
22
0
22
()exp[]( 2
2
rr a
pr I
σσ

 

)
ra
σ

for 0r
(4)
where 0
I
is modified 0th order Bessel function and va-
lue of depends on direct component. The Rician fun-
ction is usually expressed in terms of carrier-to-multipath
ratio or factor as
a
k
2
2
2
ca
kmσ 

(5)
where and are strengths of carrier and multipath
components respectively. As increases, received sig-
nal strength increases and for larger values of ,
becomes Gaussian.
c m
k
k()pr
2.5. Willis Multipath Model
Willis [18] has given extended version of two ray model
as multipath model, shown in Equation (6) for terrestrial
application on the Earth.
2
2
2
nndn
1
1
111d
2
2
rtt
r
|)jkdexp(
d
1
)(L
...)jkdexp(
d
1
)(L|
16
GGP
P









(6)
3. Physical Phenomena and Path Loss on the
Lunar Surface
Since the Earth based model cannot be directly used for
lunar applications, we have examined various physical
phenomena occurring during wave propagation in gen-
eral and those applied to wave propagation on the Moon.
Such phenomena and losses associated with them are
given below and we have combined them to arrive at the
path loss given in Section 4.
3.1. Free Space Loss
The plan is to use compact wireless impedance sensors
(along with other types of sensors) for detection of elec-
trical properties of lunar Regolith having small size
quarter wave antenna (3.125 cm). The idea is to use line
of sight propagation technique for small distances of up
to few hundred metres. Under ideal communication con-
ditions, the power radiated from antenna is omni direc-
tional in the plane of interest, which is horizontal here
and power is inverse square function of the distance for
free space wave propagation given below [19] by Friis
formula.
2
22
16
ttr
r
PG G
λ
P
πd

 (7)
where and are transmitter and receiver powers,
and are gains of transmitter and receiver anten-
nas,
t
P
G
r
P
t
Gr
λ
is wavelength of operation and is distance
from the transmitter. Free space loss is a basic loss for
communication on the lunar surface, since there is a
vacuum on the Moon.
d
3.2. Reflection
For communication on the Earth, there can be factors
like steady and moving reflectors and scatterers, atmos-
pheric absorption etc and can lead to multipath compo-
nents at the receiver. Due to multipath components, sig-
nal strength can vary at the receiver due to moving scat-
terers. However, in case of lunar application, there are no
moving objects on the surface and therefore there can be
multipath signals at the receiver due to surface topogra-
phy, but received signal strength is not expected to vary
randomly due to steady terrain, but it can show periodic
variations due to signals travelling in different time dura-
tions. Also, there is no atmosphere on the Moon and
therefore there are no atmospheric losses, which are pre-
sent on the Earth. The main possibility of signal getting
affected is that of the surface reflections due to uneven
terrain structure. This can cause multipath propagation
and signal reaching at the receiver by direct path will be
modified due to multipath components. The expected nu-
mber of multipath components is few as the mission lan-
der should land on comparatively plane or smooth sur-
face, where rover can move easily. The wavelength of
signal is 12.5 cm at 2.4 GHz wireless operation and ob-
jects should be of larger size to cause the reflection. Par-
sons [20] derived the received signal strength using re-
flection coefficient () from the reflector as given below.

398 J. P. PABARI ET AL.
22
22|1exp( )|
16
tt r
r
PG Gλ
P
πd


j
(8)
where
2
2
()cos
()cos
r
r
aSinψεjx ψ
aSinψεjx ψ



is reflection
coefficient
 = phase shift created due to reflected signal
a = 1 or for horizontal or vertical polari-
zation respectively
(
r
εjx)
ψ = angle of incidence with vertical from transmitter
antenna to the reflector
r
ε = relative dielectric constant of the ground
0
2
σ
xπfε  
σ= conductivity of the ground
f
= frequency of operation
0
ε= free space permittivity
It is also possible to calculate received signal strength
by the Equation (9) given by Hernando et al. [19] de-
rived from two ray model for longer link distances and
lower antenna heights at both ends having direct visibil-
ity of each other.
22
4
ttrt r
r
PG Ghh
P
d
 (9)
where and are heights of transmitter and receiver
antennas respectively. However, for sensors being on
surface, Equation (9) may not be used. Reflections are
expected from nearby ground terrain on the Moon. Infact
the major component for channel fading on the Moon is
due to multipath created by reflections from craters and
surface irregularities. Also, transceiver used for ground
sensors should not use horizontal polarization; otherwise
signal would be attenuated [21] very near the transmitter.
Instead, vertical polarization should be used, which can
provide sufficient signal at farther distances.
t
hr h
3.3. Reflection Scattering
When signal is reflected from lunar surface, it is likely
that the ray may be scattered due to dispersed signal.
Gibson [22] has suggested this specular reflection and
stated that roughness of a surface can be classified by
Rayleigh criterion given below:
8cos
c
i
λ
hθ  (10)
where is angle of incidence at the reflector. Gibson
[22] gave a parameter , which represents minimum to
maximum deviation about mean terrain height. If ,
then terrain is considered as rough terrain and the loss for
it is considered by multiplying reflection coefficient by a
scattering loss factor
i
θ
h
c
hh
s
ρ
calculated by Bothias’ equa-
tion as below:
22
0
cos
hi
θcos
exp[8( )][8( )]
hi
s
πσπσ θ
ρI
λλ
  (11)
where is standard deviation of surface height about
the mean surface height and
h
σ
0
I
is the 0th order Bessel
function of the first kind. On the lunar surface, the re-
gions are mostly rough and may have varying sized ob-
jects, which can lead to scattering losses.
3.4. Diffraction
For line of sight communication, if an obstacle of size
comparable to wavelength is present in between trans-
mitter and receiver, then diffraction loss can occur at the
edge of an obstacle. The signal may be scattered and at-
tenuated before reaching to the receiver. Diffraction from
knife-edge obstacle can cause signal to bend and Wong
[15] stated that bending of signal due to knife-edge obsta-
cle causes higher signal strength as compared to that due
to rounded. On the lunar surface it is likely to have such
obstacles in between transmitter and receiver, which may
be considered only for direct path but the deployment is
supposed to be in almost plane terrain for smooth move-
ment of the rover and hence possibility of occurrence of
such loss is rare and may be neglected.
4. Lunar Wireless Model
Equation (6) given by Willis [18] does not include possi-
bility of direct path, but it is expected to be present in
case of wireless sensor networks. Also, diffraction loss
given by Wong [15] may be considered for direct path
from transmitter to receiver and not for multipath for
operation at 2.4 GHz frequency. Considering diffraction
loss only for direct path and including reflection scatter-
ing loss factor, following equation is given for obtaining
area coverage by wireless sensor network on the lunar
surface:
2
2
11 11
22 22
2
1
|exp()
16
() xp()
(xp() ...
() exp()|
ttr dd
d
s
s
sn nnn
PG Gλjkd
d
π
ρψ jkd
ρψ jkd
ρψ jkd

 

 
 
 
1
2
1e
1
) e
1
rd
n
PL
d
d
d
(12)

J. P. PABARI ET AL. 399
where is diffraction loss for direct path, is di-
dd
Ld d
rect path distance, is phase constant, k
s
n
ρ
is reflecti-
on scattering loss factor of nth multipath, is reflec-
tion coefficient of nth multipath, is angle of incid-
ence at nth reflector and is distance of nth multi-
path component.
n

n
ψ
n
d
5. Digital Elevation Model of Lunar Surface
Recent mission to the Moon from India, Chandrayan-1,
had Terrain Mapping Camera (TMC) on board for de-
riving Digital Elevation Model (DEM) of the Moon and
has provided good quality data during the mission time.
Four sample sites at various locations on the Moon have
been selected considering almost plane surface, region
with some peaks and region with few craters in order to
study lunar radio propagation model. Table 1 shows de-
tails of site used in deriving communication area cover-
age. DEM data for various sites were obtained during
different orbits and resolutions were different. Sites 1
and 2 have resolution of 56.1 m in both directions; site 3
has resolution of 122.67 m for horizontal (longitude)
direction and 53.34 m for vertical (latitude) direction,
while site 4 has 185.07 m for both directions. Figures
1(a) to 1(d) show images of all these four sites respec-
tively, taken by TMC on board Chandrayan-1.
6. Results
Lunar wireless model is given in Equation (12), which
considers all possible phenomena and losses for wireless
sensor network on the lunar surface. Diffraction loss is
expected to be very low in value as compared to direct
path and multipath reflections for targeted application.
Since, major interest is in establishing direct line-of-sight
communication between transmitter and receiver, such
loss is neglected. As readily available software cannot be
used for wireless sensor network for lunar applications,
MATLAB code was developed and DEM data were
taken as input in the programme along with values
shown in Table 2 and results of radio coverage are
Table 1. Lunar sites for RF model.
Site
No.
Crater Near the
Site Location Lunar Latitude Lunar Longitude
1 Catalan － 52.103 to
－ 52.40781
279.807 to
280.55313
2 Baade － 45.414 to
－ 45.71881
279.764 to
280.51013
3 Zsigmondy 60.548 to
60.101722
248.720 to
249.779051
4 Moretus － 70.5916 to
－ 71.708189
358.4305 to
360.645171
279.807 280.55313
-52.40781
-52.103
Longitude
Latitude
279.807 280.55313
-52.40781
-52.103
Longitude
Latitude
(a)
279.764 280.55013
-45.71881
-45.414
Longitude
Latitude
279.764 280.55013
-45.71881
-45.414
Longitude
Latitude
(b)
248.720 249.779051
6
0.101722
60.548
Longitude
Latitude
248.720 249.779051
6
0.101722
60.548
Longitude
Latitude
(c)
358.4305 360.645171
-71.708189
-70.591 6
Longitude
Latitude
358.4305 360.645171
-71.708189
-70.591 6
Longitude
Latitude
(d)
Figure 1. (a) Lunar site 1; (b) Lunar site 2; (c) Lunar site 3;
(d) Lunar site 4.
Table 2. Input parameters for lunar radio frequency model.
Parameter for Model Value
Moon Radius 1737.4 km
Transmitter Power 0 dBm
Transmitter Antenna Quarter Wave Monopole
Receiver Antenna Quarter Wave Monopole
Frequency of Operation 2.4 GHz
Lunar Regolith Dielectric Constant [24] 4
Lunar Regolith Conductivity [25] 10-8 s/m
Wave Polarization Vertical
Transmitter Location Middle Left

400 J. P. PABARI ET AL.
Longitude (Degree)
Latitude (Degree)
Pr (dBm)
279.807279.99213 280.17913 280.36613 280.55313
-52.103
-52.1778
-52.25447
-52.33114
-52.40781
-100
-95
-90
-85
-80
-75
-70
-65
Longitude (Degree)
Latitude (Degree)
Pr (dBm)
279.764279.94913 280.13613 280.32313280.51013
-45.414
-45.4888
-45.56547
-45.64214
-45.71881
-100
-95
-90
-85
-80
-75
-70
-65
(a) (b)
Longitude (Degree)
Latitude (Degree)
Pr (dBm)
248.720 248.981696 249.247481 249.513266 249.779051
60.548
60.437764
60.32575
60.213736
60.101722
-105
-100
-95
-90
-85
-80
-75
-70
-65
Longitude (Degree)
Latitude (Degree)
Pr (dBm)
358.4305358.979541 359.534751 360.089961 360.645171
-70.5916
-70.8661205
-71.14681
-71.4274995
-71.708189
-110
-105
-100
-95
-90
-85
-80
-75
-70
(c) (d)
Figure 2. (a) RF model for site 1; (b) RF model for site 2; (c) RF model for site 3; (d) RF model for site 4.
depicted in Figures 2(a) to 2(d) respectively; for sites 1,
2, 3 and 4. For a given area on the Moon, there can be
many multipath components depending up on terrain and
if all are allowed to contribute in the code, then compu-
tational complexity is increased highly due to involve-
ment of higher order matrix. Moreover, it needs highly
sophisticated computing facility and it takes very long
time for computation. Number of multipath components
may, therefore, be restricted to smaller numbers, which is
reasonably justified, as distance travelled by signal along
multipath is quite large in most of the regions as com-
pared to that for the direct path and hence the contribu-
tion of those multipath components would be very less as
compared to contribution from the direct path. Normally,
sensor node operating in 2.4 GHz ISM band has 0 dBm
as output power and its receiver has sensitivity of about
-100 dBm [23]. We have calculated radio coverage of the
sites as a ratio of occupied region having more than -100
dBm received signal strength to total region under con-
sideration. Table 3 shows percentage radio coverage of
all sites for 250 kbps link, effectively showing useful
area for sensor network deployment.
Sites 1 and 2 have been selected with comparatively
plane surface having lesser undulations on the surface,
while sites 3 and 4 have different profiles, for example,
site 4 is at the edge of Moretus crater near lunar South
Pole. Due to this, site coverage is very less for sites 3
and 4 as compared to that for sites 1 and 2, as expected.
From the derived radio coverage at selected lunar sites,
one can know the areas having more than some specific
value of received power, for example, region receiving
more than -100 dBm power. Results indicate the percen-
tage coverage of a given site with known topography
and also the possibility of checking if a given sensor no-
de would be useful on the Moon, as far as power is con-
cerned. Sensor nodes should preferably be deployed in
the region where sufficient amount of power is available
(pink in the coverage patterns). In case of lunar wireless
sensor network, rover is supposed to carry the cluster
Table 3. Site coverage.
Site Site Coverage
(250 kbps link)
1 11.27 %
2 10.02 %
3 2.73 %
4 1.01 %

J. P. PABARI ET AL. 401
head and radio coverage patterns can suggest possible
path for the rover to move, assuring intact communica-
tion link with the nodes.
7. Conclusions
In this paper, we have investigated that existing radio fre-
quency models cannot be directly applied to lunar wireless
sensor network and arrived at lunar wireless model from
fundamental physical phenomena occurring during wave
propagation on the Moon. We have presented radio signal
coverage patterns of four lunar sites by using actual DEM
data of the Moon. We have used 0 dBm transmitter power
at 2.4 GHz frequency with quarter wave antennas for
transmitter and receiver. The results show percentage cov-
erage for 250 kbps links on the lunar surface, suggesting
possible use of commercially available transceiver in sen-
sor node as well as possible deployment sites and rover
paths to assure wireless connectivity.
8. References
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[2] R. Edwards and J. Durkin, “Computer Prediction of Service
Areas for VHF Mobile Radio Networks,” Proceedings of
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[3] J. Durkin, “Computer Prediction of Service Areas for
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[4] M. Hata, “Empirical Formula for Propagation Loss in
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UHF Propagation in Urban Environments,” IEEE Tran-
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[6] C. A. E., Wong, J. L., Kuang, L. Potkonjak and M. D.
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versity of California Los Angeles, 2005. http://escho-
larship.org/uc/ item/4s2698fs
[7] S. L. Willis and C. J. Kikkert, “Radio Propagation Model
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