![The air's attenuation at different frequency bands [35]. The white circle shows a minor attenuation of the low 5G frequency bands. Attenuation levels that are similar to the 4G cmWave bands are displayed in the green circles. The blue circles show high attenuation peaks; such bands are thus ideal for indoor communications with a minimal range.](https://www.researchgate.net/profile/Mohamed-Elmezughi-2/publication/353868290/figure/fig1/AS:1056201504743424@1628829470040/The-airs-attenuation-at-different-frequency-bands-35-The-white-circle-shows-a-minor_Q320.jpg)
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Received July 15, 2021, accepted July 29, 2021, date of publication August 6, 2021, date of current version August 12, 2021.
Digital Object Identifier 10.1109/ACCESS.2021.3102991
An Efficient Approach of Improving Path Loss
Models for Future Mobile Networks in
Enclosed Indoor Environments
MOHAMED K. ELMEZUGHI , (Student Member, IEEE),
AND THOMAS J. AFULLO , (Senior Member, IEEE)
Discipline of Electrical, Electronic and Computer Engineering, University of KwaZulu-Natal, Durban 4041, South Africa
Corresponding author: Mohamed K. Elmezughi (m.k.elmezughi@gmail.com)
ABSTRACT Path loss is the primary factor that determines the overall coverage of networks. Designing
reliable wireless communication systems requires accurate path loss prediction models. Future wireless
mobile systems will rely mainly on the super-high frequency (SHF) and the millimeter-wave (mmWave)
frequency bands due to the massive available bandwidths that will meet projected users’ demand, such as
the needs of the fifth-generation (5G) wireless systems and other high-speed multimedia services. However,
these bands are more sensitive and exhibit a different propagation behavior compared to the frequency bands
below 6 GHz. Hence, improving the existing models and developing new models are vital for characterizing
the wireless communication channel in both indoor and outdoor environments for future SHF and mmWave
services. This paper proposes an efficient improvement of the well-known close-in (CI) free space reference
distance model and the floating-intercept (FI) model. Real measured data was taken for both line-of-sight
(LOS) and non-line-of-sight (NLOS) communication scenarios in a typical indoor corridor environment at
three selected frequencies within the SHF band, namely 14 GHz, 18 GHz, and 22 GHz. The research finding
of this work reveals that the proposed models have better performance in terms of their accuracy of fitting
real measured data collected from measurement campaigns. In addition, this work studies the impact of the
angle of arrival and the antenna heights on the current and improved CI and FI models. The results show that
the improved models provide better stability and sensitivity to the change of these parameters. Furthermore,
the mean square error between the models and their improved versions were presented. Finally, this paper
shows that shadow fading’s standard deviation can have a notable reduction in both the LOS and NLOS
scenarios (especially in the NLOS), which means higher precision in predicting the path loss.
INDEX TERMS Path loss, 5G, 6G, channel modeling, millimeter-wave, propagation measurements, indoor
environments, angle of arrival, antenna height, radio propagation.
I. INTRODUCTION
Era after era, the demand for higher mobile data traffic is
exponentially increasing due to the tremendous revolution
in technologies relying totally on mobile networks and their
services. In 2019, Cisco reported that by 2022 the num-
ber of networked connections and devices would grow up
to 28.5billion, mobile-ready applications will reach up to
12.3billion of them [1], [2]. Also, it was expected that by
2022 the overall mobile data traffic would be increased to
approximately 77 exabytes per month, which is a seven-fold
increase over the year of 2017 [2]. Another vital issue that
The associate editor coordinating the review of this manuscript and
approving it for publication was Yi Ren .
will lead to more data needs is the current circumstances that
the world faces nowadays, such as the Coronavirus pandemic
that makes most of studying and work online, which leads
to enormous use of the internet connection. Of course, this
requires a massive amount of bandwidth [3]–[6].
Previously, the congestion of the spectrum below 6 GHz
was enough to meet the existing systems’ requirements.
On the contrary, these bands will not meet the necessities of
the fifth-generation (5G) cellular networks and many other
applications due to their relative shortage in the bandwidth
required [7]–[11]. Because of that, research has been done
to adopt the frequency regime above 6 GHz as a promising
solution to accomplish high peak data transmission rates up
to multi gigabits per second with the contribution of complex
110332 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ VOLUME 9, 2021
M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
modulation schemes and massive multiple-input multiple-
output (Massive-MIMO) systems and other advanced tech-
niques such as beamforming [12]–[18]. All these solutions
together will satisfy the requirements of the 5Gsystem.
To the best of our knowledge, the research beyond 5Gsys-
tems towards the sixth-generation (6G) cellular networks has
already been started by escaping the current solutions of the
5G systems aiming for better performance [1], [19].
In June 2018, the first commercial 5Gmobile communica-
tion standard (3GPP Release 15) was completed after many
years of research and development. In the middle of 2019,
some countries had already deployed 5Gcellular networks.
Meanwhile, the first 5G-enabled smart devices are now avail-
able on the market [1].
It is the norm to characterize and model the wireless
communication channel in the frequency bands used (or
expecting to be used) to better understand and accurately
deploy the upcoming systems. Many researchers focused on
this area by modeling the wireless channel’s behavior using
different ways: models based on theories, techniques such
as ray-tracing, and measurement campaigns. The latter looks
promising because of its accuracy and reliability since the
measurements are in real environments and communication
scenarios.
It is widely known that when a wireless communica-
tion system sends signals from the transmitting antenna(s),
the wireless signals will have a reduction of their power as
they travel through the wireless communication channel to
the receiving antenna(s). This signal loss is well-known as
path loss, which is the dominant component of the large-
scale fading effects. The path loss is a vital component that
must be modeled accurately to have reliable system design
and link budget analysis. Moreover, the knowledge of the
path loss provides statistically averaged (space and time)
radio channel conditions. Consequently, researchers need to
present more accurate path loss prediction models that can
precisely describe the reduction of the wireless signal levels
and accurately fit the real measured data collected in dif-
ferent indoor and outdoor environments over a wide range
of frequency regimes. The reason behind the inability of
the traditional models to be reliable models for the super-
high frequency (SHF) and the millimeter-wave (mmWave)
frequency bands and beyond is the significant sensitivity
of the signals at these frequency bands to the propagation
mechanisms in the communication channel. As an example,
the mmWave signals provide substantial path loss values in
the first meter away from the transmitting antenna and have
a significant penetration loss through solid materials such as
concrete walls [5], [20]–[23].
In general, the path loss can be modeled deterministi-
cally (theoretically), empirically (statistically), or stochasti-
cally [24]. The best understanding of the wireless channels’
propagation characteristics can be done based on measure-
ment campaigns in propagation’s real environments [24].
In this study, we adopted measurement-based (semi-
deterministic) models to predict the path loss taking into
account the propagation mechanisms such as reflections and
diffractions and the wave-guiding effect that occurs mainly in
enclosed indoor environments such as corridors.
Recently, most research aimed to characterize and model
the wireless channel has focused on specific path loss models
because of their suitability, such as the close-in (CI) free space
reference distance, floating-intercept (FI), and/or alpha-beta-
gamma (ABG) model [25]–[45]. The improvement of these
models in the literature was based on a consideration of some
factors like cross-polarization discrimination (XPD), taking
into account the mismatching of the antennas’ polarization
as in the models named CIX and ABGX models, which
are an improvement of the CI and ABG models, respec-
tively [23], [24]. Another improvement of the CI model is by
presenting the path loss exponent (PLE) term as a frequency-
dependent factor, as in the CIF model [23], [39], [46]–[48].
The last two factors (frequency-dependent PLE and XPD)
were considered in one model called the CIFX model [23].
In [49] and [50], a dual-slope CI path loss model was pre-
sented. This model provides higher precision in predicting
the path loss than the standard CI model. Note that all these
improvements can be implemented easily on the FI and ABG
models. Other improved models based on other different
concepts can be found in [20], [27], [47], [51]–[53]. However,
the question that has motivated this research is, how can
we improve the accuracy and reduce the standard deviation
of the shadow fading of these standard path loss models
without adding parameters that depend on something else like
antennas’ height or the XPD?.
This question is answered through a fundamental principle:
any linear equation is a polynomial equation with zero coef-
ficients in higher orders. It is well-known that the standard
path loss models (such as the CI and FI models) are a linear
equation of the path loss as a function of the logarithmic scale
of the separation distance between the transmitting and the
receiving antennas. We incorporate an additional parameter to
make these models a function of the transmitter-receiver (Tx-
Rx) separation distance’s squared logarithm. This adopted
improvement is simple (in the improved models’ equations,
the proposed additional parameter that improves the standard
models does not depend on anything like frequency and
antenna height, etc.) and provides more precision in predict-
ing the path loss, as will be proved in Section IV.
Many comparative studies between the existing path loss
prediction models show the CI and FI models’ preference
over other models like the ABG model [23], [39], [54], [55].
The CI and FI models offer a precise estimation of the
large-scale path loss as a function of the 3DTx-Rx sep-
aration distance over the SHF and mmWave frequency
regimes [24], [41], [55]. Hence, we hereby propose to fur-
ther improve these two models while avoiding a significant
increase in the models’ complexity to be used by engineers in
the wireless system design and calculations of the link-budget
since the total number of the improved models’ parameters is
within a suitable range as other well-known models such as
the ABG model have.
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M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
FIGURE 1. The air’s attenuation at different frequency bands [35]. The
white circle shows a minor attenuation of the low 5Gfrequency bands.
Attenuation levels that are similar to the 4GcmWave bands are displayed
in the green circles. The blue circles show high attenuation peaks; such
bands are thus ideal for indoor communications with a minimal range.
The rest of this paper is organized as follows. In section II,
a detailed derivation of the adopted path loss prediction mod-
els and their improvements are introduced and discussed.
The measurement setup and environment are described in
section III. The results and discussions of this research work
are presented in section IV. Finally, section V draws the main
conclusions and future aspects of this research.
II. LARGE-SCALE PATH LOSS PREDICTION MODELS
Generally, all path loss prediction models can be derived from
Friis’s equation [54], [55]:
FSPL(f,d)=(4πdf
c)2,(1)
where dis the Tx–Rx separation distance (in meters), fis
the frequency of the propagated signal (in Hz), and cis the
speed of light in the free space, which approximately equals to
3×108m/s. This simple equation in the linear scale (absolute
numbers) shows that the path loss between two isotropic
antennas aligned on boresight toward each other is mainly a
function of the operating frequency and the Tx-Rx separation
distance. As presented in Eq. (1), the path loss is distance-
and frequency-dependent; the increase in the frequency or the
distance will produce higher path loss values. However, this
is true when the wireless channel is in free space. In reality,
the wireless channel’s problems such as attenuation, inter-
ference, distortion, and noise in the communication schemes
have random behavior. For example, Fig. 1 represents the
attenuation in the air at different frequency bands in GHz.
It is clear from the figure that the attenuation of the air does
not follow a specific behavior. This means that some low fre-
quencies have large path loss values in outdoor environments
because of air attenuation and atmospheric absorption. This
issue and many other problems have accelerated the research
to cover all frequency bands by conducting measurement
campaigns in typical indoor and outdoor environments to
have reliable semi-deterministic channel models.
It is more convenient to present the path loss equations
in the logarithmic scale. Hence, Eq. (1) can be written as
follows:
FSPL(f,d)[dB]=32.4+20 log10 (f)+20 log10(d).(2)
The value 32.4 comes from 10 log10(4π×109
c)2, and the
value 109is to have values of frequencies directly in GHz (i.e.,
fin Eq. (2) is the operating frequency in GHz). The variable
din the previous equation represents the Tx-Rx separation
distance in meters.
The existing path loss models can be categorized as single-
frequency (like the CI and FI models) or multi-frequency
(like the ABG model). For single-frequency models, the term
20 log10(f) is constant and can be added to the first term of
Eq. (2). The result is a constant term that depends on the
value of the frequency (single-frequency path loss models
have a pure dependence on the frequency presented as a
parameter). The representation of this parameter differs from
one model to another. Let us name this parameter k1. The term
20 log10(d) is basically 2 times the distance in the logarithmic
scale, where the value 2 is the free space path loss exponent
(FSPLE), which indicates that the path loss changes with the
square of the Tx-Rx distance in the free space. However,
this value will change significantly, depending mainly on the
medium’s nature between the Tx and Rx. In general, it will
be easier to denote it as k2. Hence, Eq. (2) can be simplified
as:
PL(d)[dB]=k1+k2×10 log10 (d),(3)
where the coefficient k1is measured in dB, and k2is unitless.
It is clear from the previous equation that the power of the
propagated signal decreases by 1
dk2. This means that higher
values of k2will lead to stronger dependency of the path loss
on the separation distance between the Tx and Rx. Depending
on the techniques used to evaluate the values of these coef-
ficients, different path loss models exist. This paper adopted
from those several models in the literature two well-known
path loss models, the CI and FI models, and our improvement
on these models. The parameters of these semi-deterministic
models are based on the real measured values of the received
signal levels collected from measurement campaigns. The
received signal power at the Rx side mainly depends on the
strength of the transmitted signal (Pt), the path loss of the
propagated signal (PL), and the gain of the transmitting and
the receiving antennas (Gtand Gr), as presented in Eq. (4):
Pr(d)[dBm]=Pt−PL(d)+Gt+Gr.(4)
In the previous equation, Pr(d) and Ptare in dBm,Gtand
Grare in dBi, and PL(d) is in dB.
A. THE CLOSE-IN (CI) FREE SPACE REFERENCE DISTANCE
PATH LOSS PREDICTION MODEL
The CI model can be written from Eq. (3) by replacing k1by
the value of the free space path loss at the operating frequency
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M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
(f) and the reference distance (d0), and replacing k2by the
PLE (n) as described in the following equation:
PLCI (d)[dB]=FSPL (f,d0)+10nlog10(d)+XCI
σ,(5)
where XCI
σis a Gaussian random variable with zero mean and
a standard deviation σin dB [6]. This term represents the
shadow fading (SF), representing the large-scale fluctuations
of the path loss values because of obstructions and other ran-
dom propagation effects [56]. Having fewer values of the SF
standard deviation means that the path loss models are more
accurate. The SF’s importance for researchers and engineers
lies in the fact that it can establish standards that include large-
scale fading statistical models without detailed knowledge of
the characteristics of a site-specific environment [6].
In this work, we adopted the physically-based reference
distance to be 1 mfor the reason that the wireless signals
at the frequency bands above 6 GHz exhibit significant path
loss values in the first meter of the propagation away from the
transmitting antenna [29]. Also, it will be easier to compare
our work with other works as most of the researches in the
open literature use 1 mreference distance. The free space path
loss expressed in the dB scale at a reference distance d0=1
mis given by:
FSPL(f,1m)=10 log10 (4πf
c)2.(6)
Note that the CI model depends on one main parameter
to be optimized, which is the PLE (n). The dependency of
the path loss model on the 3DTx-Rx separation distance is
characterized by this unitless parameter (PLE). This model
depends on a physical anchor that catches path loss near the
transmitting antenna. It is clear that the CI model has an
intrinsic dependency on the frequency of propagation that
exists in the FSPL term. This term’s values vary from 48 to
82 dB when the frequency range is between 6 and 300 GHz,
respectively. The CI model is suitable for single- and multi-
frequency situations and can estimate the path loss from both
co- and cross-polarization cases [57].
The minimum mean square error (MMSE) technique is
used to optimize the CI model’s parameter (i.e., the PLE).
Using this approach, we can achieve the least error of fit-
ting the real measured data by minimizing the SF standard
deviation.
B. IMPROVED CI PATH LOSS PREDICTION MODEL
To predict the path loss with more accuracy and sensitivity to
the small changes of the propagation environments, we add
an independent parameter to the CI model’s equation. The
improved model has two terms that depend on the 3DTx-Rx
separation distance. This means that the path loss exponent
principle exists in two parameters (n1and n2), as presented
in the following equation:
PLImp.CI (d)[dB]=FSPL (f,d0)+10n1log10(d)
+10n2(log10(d))2+XImp.CI
σ,d>1m,
(7)
where n1and n2are the first order and second order of the
PLE, respectively. This improvement of the CI will increase
the opportunity to fit the real measured data collected from
measurement campaigns and present more details in char-
acterizing the wireless channel. Changing the environment
where the signal can propagate, or the propagation’s commu-
nication scenario (LOS or NLOS, etc.) will lead to a notable
change in the values of n1and n2. To have the closed-form
of these parameters, let us assume that A=FSPL(f,d0),
B=PLImp.CI (d), D=10 log10 (d), and E=10(log10(d))2,
then, the SF of Eq. (7) can be expressed as:
XImp.CI
σ=B−A−n1D−n2E.(8)
The SF standard deviation (σImp.CI ) can be determined
from the experimental data using:
σImp.CI =sP(XImp.CI
σ)2
N,(9)
where Nis the number of the Tx-Rx separation distances (i.e.,
the total number of the average path loss samples recorded).
Now, we have to differentiate the numerator of Eq. (9) with
respect to both n1and n2and equate the result to zero to have
the optimum value of these parameters that will lead to the
minimum value of the standard deviation as follows:
∂
∂n1
(X(B−A−n1D−n2E)2)=0,(10)
∂
∂n2
(X(B−A−n1D−n2E)2)=0.(11)
After the differentiation and simplification of the previous
two equations, we have two linear equations which can be
expressed as:
XD2n1+X(DE)n2=X(BD)−AXD,(12)
X(DE)n1+XE2n2+ = X(BE)−AXE.(13)
The matrix form of the equations (12) and (13) can be
written easily as:
PD2P(DE)
P(DE)PE2n1
n2=P(BD)−APD
P(BE)−APE.(14)
Finally, the closed-form of n1and n2can be found from the
previous matrix.
C. THE FLOATING-INTERCEPT (FI) PATH LOSS PREDICTION
MODEL
The FI model has been widely used in 3GPP and WINNER II
standards [5], [23], [24], [48], [56]. It does not depend on
the physical anchor point constraint that catches the path loss
near the transmitting antenna. However, it depends on the
mathematical curve that fits the measured path loss values.
As a linear equation, the FI model has two parameters, which
are the intercept (denoted by α) and slope (indicated by β) of
the path loss line as presented in the following equation:
PLFI (d)[dB]=α+10βlog10 (d)+XFI
σ,d>1m,(15)
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M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
where PLFI (d) is the path loss in dB, and XFI
σis a Gaussian
random variable with zero mean and a standard deviation
σFI . In the previous expression, both XFI
σand σFI are in dB.
It is worth noting that the FI model’s parameters are unlike
the CI model (αis unlike FSPL, and βis unlike the PLE).
However, the models have comparable overall performance
in predicting the path loss with a preference of one over
the other depending on the operating frequency as well as
the environment and communication scenario of the wireless
communication system [10], [57], [58].
D. IMPROVED FI PATH LOSS PREDICTION MODEL
In this model, we follow the same principle as we used for
the improved CI model, which is adding an independent
parameter that will be the coefficient of the square of the
logarithm of the 3DTx-Rx separation distance as presented
in the following equation:
PLImp.FI (d)[dB]=α+10β1log10 (d)
+10β2(log10(d))2+XImp.FI
σ,d>1m,
(16)
As seen from Eq. (16), this model has three parameters
to be known (α,β1, and β2). Using the MMSE approach
and following the same derivation we used for the improved
CI model, the solution matrix of these parameters can be
expressed as:
NPDPE
PDPD2P(DE)
PEP(DE)PE2
α
β1
β2
=
PB
P(BD)
P(BE)
,(17)
where B=PLImp.FI (d), D=10 log10 (d), and E=
10(log10(d))2. The closed-forms of the parameters are found
from the previous matrix. To validate the proposed models
given in equations (7) and (16), we used real measured data
of the path loss in a typical indoor corridor environment,
as explained in the next section.
III. MEASUREMENT SETUP AND DATA COLLECTION
METHOD
A detailed description of radio frequency (RF) propagation
measurement campaigns conducted in a typical enclosed
corridor environment is provided in this section. The cor-
ridor exists on the 5th floor of the Discipline of Electri-
cal, Electronic, and Computer Engineering, University of
KwaZulu-Natal, Howard College Campus, Durban 4001,
South Africa.
Before beginning the measurement campaigns, we ensured
that no other transmissions on the same experimental radio
frequency bands existed. Also, the measurement system was
carefully calibrated, and the measurements were repeated and
averaged to ensure high-quality data collection.
The wireless propagation channel is a corridor environ-
ment with dimensions of 30, 1.4, 2.63 meters as a length,
width, and height. Both sides of the corridor are made of
bricks and dry concrete with wooden doors to offices on
one side and an elevator and a staircase on the other side.
It is worth noting that these indoor corridors can be approxi-
mated as a rectangular air-filled waveguide with dimensions
immense compared to signals’ wavelength. This environment
is crucial and commonly used for many indoor applications.
The antennas used in this experiment are vertically-
polarized with directional radiation patterns. The Tx
antenna’s height was 160 and 230 centimeters above the floor
level, while the Rx height was 160 centimeters; which are the
average antenna heights for these indoor environments that
are adopted by many researchers [29], [59]–[61]. When the
Tx antenna height was 230 centimeters above the floor level,
we down tilted the Tx antenna to ensure that both antennas are
aligned on boresight for all the Tx-Rx measurement places
in the LOS communication scenario. Three frequencies in
the SHF band were considered in this work: 14, 18, and 22
GHz. Both antennas were pyramidal horn antennas with half-
power beamwidth values between 13 and 19.2degrees and
a directional gain ranging between 19.5 and 22.1dBi at the
operating frequencies. Throughout the campaigns, the intent
was to place the Tx at one end of the corridor and moving the
Rx away from the Tx, having a Tx-Rx separation distance of
2−24 meters with an incremental step of 2 meters a time. The
reference Tx-Rx distance was 1 meter, as is recommended
by most research experts in this field [62]–[66]. Note that to
satisfy the far-field requirements, the distance from the Tx
should be much greater than the wavelength of the lowest
operational frequency, which already exists since the wave-
length of the SHF signals is in the range of millimeters.
The measurements were performed under the conditions
of LOS and NLOS communication scenarios. In the LOS
scenario, both antennas were aligned on boresight, and there
were no obstacles in the direct propagation path between
them. In contrast, the Rx in the NLOS depends mainly on
diffractions, reflections, and waveguiding mechanisms in the
corridor environment since both antennas had no alignment
on boresight. Throughout the measurements, the transmit
power was fixed at 10 dBm. However, the received power
level range was between −41.33 and −19.05 dBm. The angle
of departure (AoD) was set at 0 degree, while the angle of
arrival (AoA) was in the range of 0 −360 degrees with an
incremental step of 10 degrees a time.
A Rohde and Schwarz SMF 100A signal generator work-
ing in continuous-wave (CW) mode was applied to feed the
transmitting antenna. The measured results are collected by
means of a Rohde and Schwarz FSIQ 40 Signal Analyzer.
This receiving equipment records 500 data sets of received
signal strength (RSS) per each AoA and Tx-Rx separation
distance. The RSS data were averaged to ensure accurate
detection of the CW signals. Both signal generator and signal
analyzer were directly connected to the antennas through
coaxial cables. Since the path loss is the difference value
between the Tx and Rx power, taking into account the anten-
nas’ gain and the coaxial cables’ loss, the measured path loss
PLmis calculated by:
PLm[dB]=Pt−Pr+Gt+Gr−Lcable,(18)
110336 VOLUME 9, 2021
M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
FIGURE 2. 3D floor plan of the indoor corridor environment.
FIGURE 3. Comparison of measured path loss, the fitted CI model, and the improved CI model for the LOS results at 14, 18, and 22 GHz.
where Lcable is the total coaxial cable loss of the measurement
system in dB. Fig. 2 represents the 3Dfloor plan of the indoor
corridor environment. The parameters of the measurement
setup used in this work are summarized in Table 1.
IV. RESULTS AND DISCUSSIONS
This section presents and discusses the main results obtained
from this research work. It is presented in two subsections,
each one compares a model with its improved version at the
three frequencies (14, 18, and 22 GHz) for both the LOS
and NLOS scenarios. Also, each subsection investigates the
behavior of the models’ parameters with the AoA and the
antenna’s height.
A. RESULTS AND DISCUSSIONS OF COMPARING THE CI
WITH IMPROVED-CI MODELS
Fig. 3 depicts the real measured path loss, the CI model, and
the Improved-CI model together for the LOS communication
scenario at the three frequencies. It is clear from the fig-
ure that both models fit the measured path loss adequately
and both have a comparable performance with a slight pref-
erence of the improved model. This also can be noted from
Table 2 that presents the values of the models’ parameters.
TABLE 1. Channel sounder specifications and parameters configuration.
Our proposed model minimizes the shadow fading’s standard
deviation at the three frequencies by 2.3%, 5.2%, and 10.7%
at 14, 18, and 22 GHz, respectively. We note that the reduction
of the standard deviation becomes higher as we go for high
frequency bands. This is because the higher frequency bands
suffer from many propagation effects and have higher path
loss values than lower bands. From Table 2, for the CI model,
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M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
FIGURE 4. Directional large-scale path loss prediction models for the LOS
communication scenario.
FIGURE 5. MSE between the CI and improved CI models in the LOS
communication scenario.
the path loss exponent is directly proportional to the operating
frequency. This leads to the general fact that higher frequency
bands have higher path loss values. All the PLE’s values are
under the value of the FSPLE. The reason behind that is
the constructive interference between the multipath signals
which makes the PLE lower than 2. For the improved-CI
model, as discussed previously, the concept of the PLE has
split into two parameters (i.e., n1and n2) as shown in Table 2.
This technique gives the model more relaxation to accurately
fit the measured data. It is clear that the values of n1are higher
than the values of the CI model’s PLE. However, all the values
of n2are negative, which will compensate the increase of
n1values and make the model following the measured path
loss and counts all the possible signal effect. Fig. 4 offers a
graphical view of both models (CI and improved-CI) together
at 14, 18, and 22 GHz for the LOS communication scenario.
We plotted the MSE curves between the CI and improved CI
models with respect to the separation distance between the
Tx and Rx for the LOS scenario as depicted in Fig. 5. It is
worth noting that all the MSE values are in the range of 10−4
to 10−2with lower values around 14 to 16 meters (near the
breakpoint of the corridor) of the Tx-Rx separation distance.
In the NLOS communication scenario, as it is known,
the receiving antenna relies mainly on reflection, diffraction
and the effect of waveguiding in this enclosed environment
for capturing the signals from the Tx. The CI model’s PLE
TABLE 2. A comparison between the CI and Improved-CI models’
parameters in the LOS scenario.
TABLE 3. A comparison between the CI and Improved-CI models’
parameters in the NLOS scenario.
values here are 2.07, 2.38, and 2.26 at 14, 18, and 22 GHz,
respectively. Note that because there is no direct dominant
path from the transmitting to the receiving antennas, the val-
ues became notably high compared to the LOS results. How-
ever, they are still low compared to the communications in
outdoor environments where the fluctuations of the prop-
agated signals is much stronger. We find that in enclosed
indoor environments such as corridors, the PLE values will
not go much higher than the values of the FSPLE since the
maximum percentage jump is in 18 GHz band by 16%. This
frequency band (i.e., 18 GHz) has a higher sensitivity to the
wireless channel effects than the others for the frequencies
studied. The SF standard deviation of the CI model is seen
to rise to more than the double in the NLOS scenario as
shown in Table 3. This means that there is less precision in
predicting the path loss in NLOS scenarios than the LOS
ones. Nevertheless, the proposed model provides an attrac-
tive reduction of the standard deviation since it produces a
minimum reduction of 3.24 dB (54.2% less) as can be seen
in Table 3. This improvement is simple and highly efficient
since almost all the communication methods for indoor envi-
ronments are NLOS. The reason behind this improvement
is the fact that the current statistical NLOS models cannot
properly model the propagation mechanisms such as reflec-
tions and diffractions effects, which are captured better by the
new parameter in our improved model. Again, all the values
of the parameter n2are negative and n1values are larger
than the PLE value for the NLOS scenario as the LOS one.
Fig. 6 displays both models at the three selected frequency
bands. From this figure, it is clear that the path loss curves
of the improved CI model are away from the CI model’s
curves. The MSE between the CI and improved CI models are
outlined in Fig. 7 for the NLOS scenario. The figure shows
the increase in the MSE values compared to the LOS scenario
since for the NLOS, the MSE values are in the range of 10−2
to 100.
The behavior of the CI and Improved-CI models’ param-
eters with the AoA at 14, 18, and 22 GHz is presented in
detail in Table 4, Table 5, and Table 6, respectively. From the
Tables, it is clear that the PLE’s minimum values occur when
110338 VOLUME 9, 2021
M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
TABLE 4. The behavior of the CI and Improved-CI models’ parameters with the AoA at 14 GHz frequency band.
TABLE 5. The behavior of the CI and Improved-CI models’ parameters with the AoA at 18 GHz frequency band.
TABLE 6. The behavior of the CI and Improved-CI models’ parameters with the AoA at 22 GHz frequency band.
FIGURE 6. Directional large-scale path loss prediction models for the
NLOS communication scenario.
the AoA equals 30 and 330 degrees. The reason behind that
is that at these AoA values, the Rx antenna is still aligned
near the LOS path, and with the help of the propagation
mechanisms discussed above, the PLE’s value is minimized.
The maximum PLE values occur at 150 and 210 degrees of
the AoA. This shows that around these angles when the Rx is
in the opposite direction of the Tx, the propagated signal will
suffer from maximum path loss values before reaching the
Rx antenna. Note that when the AoA is exactly 180 degrees,
the PLE values are within a good range compared to other
AoA because of the back loops of the Rx antenna’s radiation
pattern as can be seen from Fig. 8. These findings give an
insight into what will happen in reality when the Tx or Rx
orientations might not be known and how the wireless signals
will be affected according to this issue in such enclosed
indoor corridor environments. When we compare the three
frequencies together, we observe that the fluctuations of the
PLE values are 6.8%, 10.4%, and 3.1% at 14, 18, and 22 GHz,
respectively. This means that the 22 GHz frequency band has
FIGURE 7. MSE between the CI and improved CI models in the NLOS
communication scenario.
an attractive behavior in terms of its stability to the AoA,
which leads to accurate modeling of the wireless propagation
channel in the NLOS communication scenario. For the SF’s
standard deviation values, the difference between the maxi-
mum and minimum values are 2.04, 3.1, and 1.3dB. It is clear
that the worst performance between the three frequencies is
at 18 GHz. For our proposed model, since the concept of
the PLE is divided into two parameters, it is clear from the
Tables that it outperforms the CI regarding the sensitivity and
stability of the model’s parameters with the AoA.
Fig. 9 depicts the CI and improved-CI models’ parame-
ters at two different practical antenna heights (i.e., 1.6 and
2.3m) for both the LOS and NLOS communication scenarios.
Generally, the figure shows the increase of the parameters’
values when the Tx antenna height is 2.3mcompared to
1.6 Tx antenna height because of the mismatching of the
antennas’ heights. Moreover, it can be seen from the fig-
ure that our proposed model provides more sensitivity to
the antenna height and capture more accurately the wireless
VOLUME 9, 2021 110339
M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
FIGURE 8. The behavior of the CI and improved CI models’ parameters with the AoA.
FIGURE 9. The parameters of the CI and improved-CI models at two different Tx antenna heights.
FIGURE 10. Comparison of measured path loss, the fitted FI model, and the improved FI model for the LOS results at 14, 18, and 22 GHz.
propagation characteristics caused by the mismatching of the
Tx and Rx antenna heights. Furthermore, it reveals that the
antenna height’s impact is minimum at 22 GHz and maximum
at 14 GHz for both the CI model and our proposed model.
However, when we look at the SF’s standard deviation values,
we observe that the proposed model outperforms the standard
CI model depending on the antennas’ heights. It is worth
noting that the antenna height might not be an essential factor
in the specific investigations presented in this work. However,
the antenna locations, patterns, and relative orientation are
significant factors, especially at high frequencies, mmWave
and above. These performance studies will help engineers in
designing reliable communication systems in such scenarios
and have an accurate understanding and modeling of the
wireless channel’s behavior.
B. RESULTS AND DISCUSSIONS OF COMPARING THE FI
WITH IMPROVED-FI MODELS
Fig. 10 shows the curves of the real measured data,
the FI model, and the improved-FI model for the LOS
110340 VOLUME 9, 2021
M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
FIGURE 11. Directional large-scale path loss prediction models for the
LOS communication scenario.
FIGURE 12. MSE between the FI and improved FI models in the LOS
communication scenario.
communication scenario at the three frequency bands adopted
for this work. The figure shows that both models accurately
fit the real measured data with the minimum possible MSE
between the models and the data. As a comparison between
the three frequencies, the best fit occurs at the 22 GHz fre-
quency band. It must be emphasized that any path loss model
will always depend on the operating frequency, no matter how
they are derived. Maybe simplifications could come from
the fact that the exact carrier frequency is not needed, and
only the knowledge of the band (e.g., 14 GHz, 18 GHz, and
22 GHz) is enough. The models’ parameters are represented
in Table 7. It is observed that our proposed model slightly bet-
ters the standard FI model in terms of the performance since
it reduces the standard deviation values by 3.2%, 13.7%, and
1.8% at 14, 18, and 22 GHz. Note that the best improvement
applies at 18 GHz, contrary to what happened between the
CI and improved-CI models. Also, note that the values of
the parameter αare not far between both models. A notable
improvement can be observed from Table 8 since the percent-
age reduction goes up to 44% in the NLOS communication
scenario. Upon comparing the four models, it is noted that the
best model that fits the real measured data is the improved-
FI model. Fig. 11 presents both FI and improved-FI models
together at the three frequencies selected. The curves of
the two models in the figure are almost the same, as also
confirmed from the values in Table 7. We have plotted the
MSE between both models to show how these models behave
FIGURE 13. Directional large-scale path loss prediction models for the
NLOS communication scenario.
FIGURE 14. MSE between the FI and improved FI models in the NLOS
communication scenario.
TABLE 7. A comparison between the FI and Improved-FI models’
parameters in the LOS scenario.
when the Tx-Rx separation distance increases. It is noted that
from Fig. 12, the correlation between the models is high since
the values of the MSE are in the range of 10−6and 10−2
with minimum values around the breakpoint. Nevertheless,
Fig. 13 and Fig. 14 show a highly notable difference between
both models in terms of their performance in the NLOS
scenario since the models’ curves are far away from each
other in Fig. 13, and have MSE values higher than the ones
we got from Fig. 12.
Fig. 15 represents the FI and improved-FI models’ param-
eters versus the AoA of the receiving antenna at 14, 18,
and 22 GHz for the NLOS communication scenario. This
figure shows that while both models provide a valuable
stability to the change of the AoA, our proposed model
shows slight advantage. This advantage is seen clearly from
Tables 9, 10, and 11, where the models’ parameters are pre-
sented. The impact of the antenna heights on the models’
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FIGURE 15. The behavior of the FI and improved FI models’ parameters with the AoA.
FIGURE 16. The parameters of the FI and improved-FI models at two different Tx antenna heights.
TABLE 8. A comparison between the FI and Improved-FI models’
parameters in the NLOS scenario.
parameters is presented in Fig. 16. As for the behavior of the
CI model and the proposed improved version, when there is a
change in the antenna’s height, there will be a corresponding
change in the models’ parameters, and the worst behavior
is seen to occur when there is a mismatch in the antenna’s
heights. However, the performance of our proposed model is
better than the performance of the standard FI model.
From the previous analysis, we observed that it is possible
to provide valuable improvements to the existing wireless
channel models without a notable increase in the models’
complexity. In fact, with the demand for more and more data
traffic, we will always need to go for higher frequency bands
to meet future requirements. These higher frequency bands
have smaller wavelengths, they then suffer more from the
wireless propagation channel. Hence, improving the existing
110342 VOLUME 9, 2021
M. K. Elmezughi, T. J. Afullo: Efficient Approach of Improving Path Loss Models for Future Mobile Networks
TABLE 9. The behavior of the FI and Improved-FI models’ parameters with the AoA at 14 GHz frequency band.
TABLE 10. The behavior of the FI and Improved-FI models’ parameters with the AoA at 18 GHz frequency band.
TABLE 11. The behavior of the FI and Improved-FI models’ parameters with the AoA at 22 GHz frequency band.
models and developing new models that accurately describe
the wireless propagation channel will always be needed.
V. CONCLUSION
In this paper, a simple and efficient improvement of two well-
known path loss prediction models, namely the CI and FI
models, was presented and discussed in detail. The validation
of the models’ performance was given by applying the CI
and FI models and their improvement to fit real measured
data. The data was collected in a typical indoor corridor
environment at three frequencies in the SHF band, which are
14, 18, and 22 GHz. Both the LOS and NLOS communi-
cation scenarios were considered in this research. The main
findings of this work are that our proposed models generally
outperform the existing standard models in terms of several
factors such as the accuracy of predicting the path loss with
the lowest possible value of the MSE, minimizing the SF’s
standard deviation for both LOS and NLOS conditions (with
better improvements in the NLOS scenario), and providing
better sensitivity and stability of the models’ parameters with
the change of the AoA and antenna height. The improvement
of the models was effected through a simple and valuable
approach. There is no notable increase in the models’ com-
plexity to be used by the planning engineers for wireless
systems’ deployment and calculations of the link budget.
Finally, this work shows that the proposed models can be
trusted as accurate and reliable models for predicting the path
loss at frequency bands above 6 GHz in enclosed indoor envi-
ronments such as corridors since they provide better accuracy,
sensitivity, and stability than well-known standard path loss
prediction models such as the CI and FI models. Further
studies and investigations need to be conducted to achieve
greater accuracy in predicting the path loss since it is the
dominant component that determines the networks’ overall
coverage.
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Jun. 10, 2021, doi: 10.1109/LCOMM.2021.3088264.
MOHAMED K. ELMEZUGHI (Student Mem-
ber, IEEE) was born in Tripoli, Libya, in 1995.
He received the bachelor’s degree (Hons.) in elec-
trical engineering from the University of Tripoli,
Libya, in 2017, and the master’s degree (cum
laude) in electronic engineering from the Univer-
sity of KwaZulu-Natal (UKZN), Durban, South
Africa, in 2020, where he is currently pursuing
the Ph.D. degree under the supervision of Prof.
Thomas J. Afullo. The focus of his Ph.D. research
is on millimeter-wave channel modeling for 5G mobile communication
systems and beyond. His research interests include millimeter-wave systems,
wireless channel modeling, signal detection, antennas design, radio propaga-
tion, and channel parameters estimation.
THOMAS J. AFULLO (Senior Member, IEEE)
received the B.Sc. degree (Hons.) in electri-
cal engineering from the University of Nairobi,
Kenya, in 1979, the M.S.E.E. degree through a
Fulbright-Hays Scholarship from West Virginia
University, Morgantown, USA, in 1983, and
the Bijzondre License in Technology and the
Ph.D. degree in telecommunication engineering
from Vrije Universiteit Brussel (VUB), Belgium,
in 1989. From 1979 to 1986, he promoted from
a rank of a Pupil (Trainee) Engineer to a Senior Executive Engineer in
charge of transmission and radio planning with Kenya Posts and Telecom-
munication Corporation. From 1987 to 1994, he promoted from a rank of
a Tutorial Fellow to a Senior Lecturer and the Head of the Department
of Electrical and Communications Engineering, Moi University, Eldoret,
Kenya. From 1996 to 2002, he was a Lecturer in telecommunication with the
Department of Electrical Engineering, University of Botswana, Gaborone.
He joined the University of Durban-Westville, as an Associate Professor
of electrical engineering, in 2003. Since 2012, he has been a Professor of
telecommunications engineering with the Discipline of Electrical, Electronic
and Computer Engineering, University of KwaZulu-Natal (UKZN), Durban.
He is also the Director of the Telkom Centre for Radio Access & Rural
Technologies (CRART). He has spent Sabbatical Leave with Prof. Emilio
Matriciani and Prof. Carlo Riva with Politechnico di Milano (POLIMI),
in 2017, with Prof. Rajarathnam Chandramouli with Stevens Institute of
Technology, New Jersey, in 2017, and the Department of Electronics, Uni-
versity of Kaiserslautern, Germany, in 1996, on a DAAD Fellowship. He has
successfully supervised 16 Ph.D. and 28 master’s students, as well as co-
supervised two Ph.D. students. His research interests include microwave
and millimeter-wave propagation, power line communications (PLC), and
free space optics (FSO). He is a Registered Engineer with the Engineering
Council of South Africa (ECSA). He is a fellow of the South African
Institute of Electrical Engineering (SAIEE), and a Rated Researcher with
the South African National Research Foundation (NRF). He was a member
of Eta-Kappa Nu (Beta-Rho Chapter), in 1982. Since 2016, he has been a
Faculty Advisor and a member of the IEEE-Eta-Kappa Nu (Mu Eta Chapter).
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