Page 415 - Kaleidoscope Academic Conference Proceedings 2024

Innovation and Digital Transformation for a Sustainable World

value of the excessive path loss, and the propagation group is approximated as a Sigmoid function (S-curve). The
(i.e. LoS or NLoS ) is referred to as ξ (ξ ∈ {LoS, NLoS}). parameters of this S-curve, p and q, are related to the α, β
The path loss incurred due to the scattering and shadowing is and γ values. The Sigmoid function is expressed as:
modelled as a mean value here. Any fluctuations due to rapid
1
variations in channel are not taken into consideration in this P(LOS, θ) = (6)
channel. 1 + p exp(−q[θ − p])
h
with tan θ = .
Substituting the FSPL expression considering Friss free r
space equation with isotrppic radiators into eq.(1), the path
C. Power Model
loss can be written as
The power consumed by an UAV depends on several

4π factors, including internal and external ones. Internal factors
PL ξ = 20 log d + 20 log f + 20 log + η ξ (2)
c represent the weight of the platform including chassis, motors,
circuitry, batteries and payload, while external factors involve
Where, f denotes the carrier frequency and d denotes the
the density of the air at flight altitude and any wind or air re-
distance between the UAV and the ground user, c is the speed
sistance to the platform’s vertical or horizontal movement. The
of light, f is the frequency of the system under consideration.
electronic circuitry that controls the platform, processes data
and establish communication links consumes tens of Watts
A LAP having a common angle of elevation θ with the
on average. Thereby, the total power consumption consists of
ground users/receivers has path loss as given in Eq. (1). For
hovering and communication powers.
this PL, the expectation Γ is given as
1) Hovering Power: The hovering power is related to the
X
Γ = PL ξ P(ξ, θ) (3) height of the flying station as: [14]
ξ
µ 0 h
P req = P 0 e 2 (7)
Here, P(ξ, θ) represents the occurrence probability of a where P 0 is the power consumption of UAV at zero altitude,
group of ground receivers at elevation θ. Also, the groups which is constant and µ 0 = 9.7 x 10 −5 . As can be seen that
probabilities are related as the value of µ 0 is so low that for the altitude range between
0 to 5000 meters, the power consumption for a single UAV is
P(NLoS, θ) = 1 − P(LOS, θ) (4)
assumed to be constant (i.e. P 0 ).
In [13], International Telecommunication Union (ITU) puts 2) Communication Power: The power required to transmit
forth an approach for determining the probability of the LoS the signals to all the users inside the UAV cell is modeled
in an urban use case between an aerial transmitter at an as the sum of the analog beam forming power required by
elevation h t x, and a ground-based receiver with height h r x. the antenna array and the power consumed by the other
Three statistical constants associated to the urban environment intermediate equipment like phase splitter, power amplifier,
influence this probability: multiplexer, digital to analog converter, phase shifter, etc.
• Constant α: represents the ratio of the land area that is In this paper, it is assumed that the antenna array always
constructed to the total land area. transmits the maximum possible power (P T (Total)), for any
• Constant γ: illustrates the distribution of building heights value of UAV elevation. Thus, the communication power
using the Rayleigh probability density function (PDF). required by a UAV is assumed to be constant with the height
• Constant β: denotes the average number of structures per of the UAV. Further, this value is much smaller than the
square kilometer of area. hovering power for typical altitude and modelling these minor
The probability for the LoS communication is expressed in variations is unnecessary.
terms of height of transmitter (h ( t x )) and height of receiver
(h ( r x )) in [13]. Simplifying it for the scenario depicted in Fig. Considering the UAV altitude as the optimization variable,
1, P(LOS) can be represented as and deducing swarm size as a function of h, for constant
pathloss PL max , the coverage radius deduced from (6) can
2
 

1
(n+ )h be approximated by a second order equation below as:
2
m+1
M   
Y
P(LoS) = 1 − exp h −  (5) 2



2γ 2 R COV = mh + nh + o (8)
n=0   
where m, n and o are constants whose value depends upon
√
where M = floor(r αβ − 1). r is the distance separating the the PL max , A, B, p and q. Here, (8) is approximated by a
ground user from the center of the cell. second order linear equation.
Further, in [12], the expression of the LoS probability If the total available area that needs to be provided the
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