In this study, the deployment of UAV as aerial base station considers its deployment at a low altitude platform (LAP) [
27,
28] for two scenarios, namely, outdoor-to-outdoor and outdoor-to-indoor scenarios. In the outdoor-to-outdoor scenario, all users are located outdoors, whilst, in the outdoor-to-indoor scenario, users are located outdoors and indoors.
2.1. Outdoor-to-Outdoor Path Loss Model
The outdoor-to-outdoor scenario considers the deployment of UAV as an aerial base station in providing wireless coverage to outdoor users only. The air-to-ground (ATG) path loss model in [
24] predicts the path loss between LAP and a ground receiver. It is modeled by considering the probabilistic mean path loss, which is averaged over the Line-of-Sight (
) and Non-Line-of-Sight (
) conditions.
However, the probability of
in the path loss model of [
24] does not consider user’s antenna height. It was observed that the probability of
increased, as the user’s antenna height increased [
29]. Therefore, in this work, the
probability that takes into consideration the user’s antenna height is derived and included in the outdoor-to-outdoor path loss model.
Moreover, in this study, the effect of rain attenuation to 5G spectrum in Malaysia is studied. Therefore, the rain attenuation,
is derived and included in the outdoor-to-outdoor path loss model as follows:
where
is the carrier frequency,
c is the speed of the light,
h is the UAV height,
r is the horizontal distance between the UAV and the user,
and
are the average additional loss which depends on the environment, and
and
are given by Equations (
6) and (
11), respectively.
2.1.1. Line of Sight Probability
Figure 2 shows the system model to calculate the
considering the user’s antenna height, where the aerial base station antenna height is denoted by
, the user’s antenna height is referred to as
,
d is the horizontal distance from the aerial base station,
is the average street width and
is the building height. Using triangles similarity, the relationship between the building height,
and the aerial base station antenna height,
at the onset of
can be written as:
and
where
is the building height at the onset of
. Thus,
can be re-written as Equation (
4) by solving these two above equations, and eliminating
x:
One of the most important conditions in an urban environment is the layout and characteristics of the building. The parameter that describes the geometrical statistics of a certain urban area of which the RF signal propagates is
[
29]. This parameter describes the buildings heights distribution according to Rayleigh distribution function [
29]:
where
is the building height in meters.
Equation (
5) is used to plot
Figure 3. It is clear that increasing the value of
results in a higher range of building heights distribution. For
= 6, the building height at the onset of
can be calculated using Equation (
4), which gives the value of
= 0.06, which is illustrated as the vertical line in
Figure 3.
Thus, the probability of
equals the area under the curve from
= 0 to
=
, which is given as
The effects of user’s antenna and UAV height on the probability of
can be analyzed using Equations (
4) and (
6).
Line of Sight Probability Analysis and Validation
Figure 4a shows the
probability versus the UAV height for different values of the horizontal distance between the UAV and the user that are located within the UAV coverage area when the user antenna height is at the ground level,
= 6 and street average width of 20 m, which is an estimation for urban environment. This figure shows that the probability of
increases as the UAV height increases for the same horizontal distance between the UAV and the user. On the other hand, the probability of
decreases as the horizontal distance from the UAV increases for the same UAV height.
Figure 4b shows the effect of increasing the user’s antenna height on the probability of
keeping the height of the UAV constant at 50 m for the same parameters as
Figure 4a where
= 6 and street average width is 20 m. As the height of the user’s antenna increases, the probability of
increases and hence decreases the path loss, thus contributing as a gain factor as indicated in [
29]. The increase in
probability and hence reduction in path loss is more significant for lower values of horizontal distances between the UAV and the user.
The P(
) Equation (
6) is validated with the work by the authors in [
24]. The value of parameters in [
24] are substituted into their P(
) model to plot
Figure 5a–c. The dotted line in these figures shows the plot using Al-Hourani’s P(
) model of [
24], whereas the solid line shows the P(
) plot of Equation (
6). The value of variables
and
varies with different environments dense urban, urban, and suburban as shown in
Table 1.
It can be seen from
Figure 5a–c that the
of Equation (
6) is in agreement with that of Al-Hourani’s for dense urban environment. For the case of urban environment, the
of Equation (
6) is in agreement with that of Al-Hourani’s. Meanwhile, for the case of a suburban environment, the
of Equation (
6) is in close agreement with that of Al-Hourani’s.
2.1.2. Rain Attenuation
Based on ITU rain regions for Asia in [
30], Malaysia falls in the P region and the rainfall intensity exceeded in mm/h as a percentage of time of the year (with a 1-min integration time) for P region is shown in
Table 2.
Specific rain attenuation based on rain rates can be calculated following the procedure recommended by the ITU-R [
22,
30]. The specific attenuation
(dB/km) is obtained from the rain rate
R (mm/h) using the power-law relationship [
22,
30]:
where the value of the coefficients
k and
are given as function of frequency,
f (GHz), in the range from 1 to 1000 GHz, for different polarization tilt angle relative to the horizontal, and for a different path elevation angle from [
22].
For a rain rate exceeding 0.01% of the time, the attenuation due to rain
in dB can be calculated using the formula:
where
d is the link distance in km and the coefficient
r is calculated as follows:
and the coefficient
in km for
100 mm/h is given by:
where for
> 100 mm/h, the
value of 100 mm/h is substituted in Equation (
10). For percentages of time
p other than 0.01, the attenuation is calculated using Equation (
11), which is suitable for Malaysia:
where
p ranges from 0.001 to 1%.
The specific rain attenuation analysis is performed using Equation (
11).
Figure 6 shows the dependence of the rain attenuation on the rain rate for the frequencies of interest of the mobile network in Malaysia. It also shows that increasing the carrier frequency leads to an increase in the attenuation value, whereas
Figure 7 shows the dependence of the rain attenuation on the frequencies of interest, for the different rain rates registered in Malaysia for one year that ranges from 0 to 250 mm/h [
30].
At low frequencies, a different value of rain rate does not significantly cause rain attenuation, but it will be noticeable at higher frequencies (mm Waves). The propagation loss through rain reaches a value of 40 dB/km at 24.9 GHz operating frequency which is high and should be taken into consideration in any design problem of UAV deployment at 5G frequencies in Malaysia.
2.2. Outdoor to Indoor Path Loss Model
The outdoor-to-indoor scenario considers the deployment of UAV as an aerial base station in providing wireless coverage to outdoor and indoor users. The path loss model discussed in
Section 2.1 is not appropriate for providing a coverage for indoor users, where this model assumes that all users are outdoor and located at 2D points. The outdoor-to-indoor path loss model that is certified by the International Telecommunication Union (ITU) [
31] when considering the case of providing wireless coverage for indoor receivers only.
However, in the case of operating frequencies at higher bands, the wall penetration loss,
, is derived and included in the outdoor-to-indoor path loss model. Moreover, in this study, the effect of rain attenuation to 5G spectrum in Malaysia is studied. Therefore, the rain attenuation,
of Equation (
11) is also included in the outdoor-to-outdoor path loss model as follows: the path loss for an outdoor-to-indoor model that considers wall penetration loss is given as:
where
is given by Equation (
23).
,
is the horizontal distance between the incidence on building wall and the indoor user.
is given by:
where
is the 3D distance between the UAV and an indoor user.
2.2.1. Wall Penetration Loss
This section presents the derivation of wall penetration loss by analyzing the two mechanisms causing this additional loss which are transmission at the air dielectric interface, and the absorption that occurs when the wave traverses the wall. In this work, the derivation of wall penetration loss considers operating frequency at higher bands. In addition, the derivation of wall penetration loss assumes that a wall consists of two materials, namely concrete and glass.
The wall transmission loss will be analyzed assuming a single interface between air and the wall material where the transmission coefficient depends on the frequency and the real part of the dielectric constant of the wall material [
32]. On the other hand, absorption coefficient is caused by the imaginary part of the dielectric constant [
32].
The real part of the relative permittivity varies with frequency according to:
where
f is the frequency in GHz, and
a and
b are factors depending on the wall material as shown in [
29,
32].
The imaginary part of the relative permittivity is related to the material conductivity
as follows:
where
is the permittivity of free space and
varies with frequency according to:
where
f is the frequency in GHz, and
c and
d are factors depending on the wall material as shown in [
32].
The attenuation rate in dB/m of the dielectric material is given as:
The attenuation due to the conductivity of wall material will be:
where
d is the wall thickness and
is the angle of incidence on the wall. The total loss due to wall penetration (assuming circular polarization) is given as:
where
and
are power transmission coefficient of the magnetic and electric fields, respectively [
32].
Equation (
19) and parameters value in
Table 3 are used to plot
Figure 8a,b.
Figure 8a shows the penetration loss of a concrete wall of thickness 30 cm as a function of the angle of incidence at different frequencies, whereas
Figure 8b shows the penetration loss of glass material of thickness 2 cm as a function of the angle of incidence at different frequencies.
The penetration loss of a concrete wall and glass material, respectively, which can be represented in the form of:
From
Figure 8a,b, and in the frequency range from 1 to 60 GHz, the coefficients b1 and b2 are approximated as:
The value of parameters
,
,
, and
for concrete, and glass materials are derived from
Figure 8a,b and are listed in
Table 4.
For a wall area divided in the ratio
p% glass and (1 −
p)% concrete, wall penetration in dB can be approximated as [
25,
33]:
Wall Penetration Loss Validation
Penetration loss of Equation (
20) is validated by comparing it with the results presented by the authors in [
34] at 60.5 GHz for indoor-to-indoor and outdoor-to-indoor mobile scenarios. More specifically, in [
34], the attenuation versus incidence angle attenuation for two different materials (single layer), namely, wood, and glass were plotted. The thickness of the single-layered wood and glass materials was set as 45 mm and 9.5 mm, respectively.
Figure 9 shows Equation (
20) curves for wood and glass material at 60.5 GHz, which is in agreement with that of [
34]. Thus, this validates the derivation of penetration loss term of Equation (
20).
2.3. Optimum 3D Placement of UAV
The problem of finding the optimum UAV 3D placement is formulated with the objective to minimize the total path loss between UAV and users and is given as:
minimize | |
| |
subject to |
|
|
whereas
is the maximum path loss of all the users.
The formulated problem is non-convex, and, due to its intractability, two algorithms are developed based on gradient descent (GD) and particle swarm optimization (PSO) algorithms.
Gradient descent is an optimization algorithm that is used when training a machine learning model. It is based on a convex function and tweaks its parameters iteratively to minimize a given function to its local minimum. For example, in the case of an upside parabola, for gradient descent to reach the local minimum and avoid bouncing, a learning rate is set to an appropriate value.
Gradient descent starts at the initialized point, and it takes one step after another in the steepest downside direction until it reaches the point where the cost function is as small as possible. In this study, the input values are the initial location of UAV, the step size which is the learning rate, gradient termination tolerance, minimum allowed perturbation, and the maximum allowed number of iterations. It begins to calculate the derivative of cost function from which then the learning rate will be updated.
The pseudo-code of the steps of this technique is given in Algorithm 1. During the while loop, the new location is calculated by multiplying the derivative of cost function with
, which is the step size shown in step 7 of Algorithm 1. The while loop will be terminated if the derivative of the cost function is larger than or equal to tolerance, difference of previous location from new location larger than or equal to the allowed change (
), or when it reaches the end of the maximum allowed number of iterations shown in step 8 of Algorithm 1.
Algorithm 1 Optimum 3D placement of UAV base station using Gradient Descent algorithm |
- 1:
Input: - 2:
The 3D locations of the users and the cell dimensions - 3:
The step size , minimum allowed perturbation , and the gradient termination tolerance . - 4:
The maximum number of iterations - 5:
Initialize: - 6:
For to - 7:
- 8:
IF and - 9:
Return: End FOR
|
PSO is based on the paradigm of the swarm intelligence, and it is inspired by the social behavior of animals like flocks of birds, and schools of fish, which move together when searching for food [
35]. Thus, in this work, the PSO algorithm is assumed to have a certain number of virtual UAVs which is randomly distributed in the area where the simulation is examined. These virtual UAVs constitute the members of the swarm which will move and communicate together towards the best solution with the aim to minimize the objective function.
Algorithm 2 presents the pseudo code of the PSO algorithm to find the optimized UAV 3D placement in providing wireless coverage.
Step 1 in Algorithm 2 presents the inputs of the algorithm, namely, defines the population of candidate solutions (virtual UAVs) of the algorithm, W refers to the inertia weight, while and denote the two random numbers uniformly distributed random in a range between 0 and 1, and and are the acceleration coefficients.
In the initialization step, the values of constriction factor,
, cognitive parameter,
, and the social parameter,
must be selected, where
, and
[
35], which results in finding the efficient solution for the formulated problem. The PSO algorithm is initialized with a group of random solutions for all particles’ positions and particles’ velocities, as in steps 4 to 11 of Algorithm 2. Then, in every iteration, the local best location and the velocity for each particle are updated. In addition, the global best location is updated also, as in steps 12 to 22 of Algorithm 2. This is expected to move the virtual UAV swarm towards the best solution.
Algorithm 2 Optimum 3D placement of UAV base station ( ) using Particle Swarm Optimization algorithm |
- 1:
Input:: Lower bound decision variable. : Upper bound decision variable. and : acceleration coefficients. , . : Number of iterations. : Population size. (): Construction coefficients - 2:
Initialization:, globalbest.cost=∞ - 3:
for i = 1: - 4:
location(t) = unifrnd() - 5:
velocity(t) = zeros() - 6:
cost = costfunction(location) - 7:
best.location(t) = location(t) - 8:
best.cost(t) = cost(t) - 9:
if best.cost(t) < globalbest.cost - 10:
globalbest = best.cost(t) end if end - 11:
PSO Loop: - 12:
for t = 1: - 13:
for i = 1: - 14:
particle(t + 1).velocity = W*particle(t).velocity +**(particle(t).best.position -particle(t).position) +**(globalbest.position-particle(t).position) - 15:
location(t + 1) = location(t)+ velocity(t+1) - 16:
cost(t) = costfunction(location(t)) - 17:
if cost(t) < best.cost(t) - 18:
best.location(t) = location(t) - 19:
best.cost(t) = cost(t) - 20:
if best.cost(t) < globalbest.cost - 21:
globalbest = best.cost(t) end if end if end end
|
The optimum path loss is then used to calculate the transmit power using the Shannon theorem. Shannon theorem is given as:
where
C is the bit rate available for a user,
B is the allocated bandwidth to each user,
is the noise power superimposed on the signal received by the user’s cellular phone, and
is the received power by the user’s cellular phone.
Focusing on the user with the worst condition, whose path loss is maximum, and with threshold value for bit rate,
, then the user minimum received power is given as:
Then, the minimum UAV transmit power is given as:
where
is the maximum loss encountered by the worst case user in the coverage area served by the UAV.