Deployment of UAV-mounted Access Points for VoWiFi Service with guaranteed QoS
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This document discusses the deployment of UAV-mounted access points for Voice over WiFi (VoWiFi) services, emphasizing the importance of ensuring Quality of Service (QoS) for users. It presents a mathematical formulation to optimize the number of UAVs needed for adequate coverage and QoS, acknowledging the limitations of traditional coverage-based models in WiFi networks. The study details analytical models and optimization techniques applied to enhance VoWiFi communication in scenarios lacking existing infrastructure.
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Deployment of UAV-mounted Access Points for VoWiFi Service with guaranteed
QoS
Vicente Mayor, Rafael Estepa, Antonio Estepa, and Germán Madinabeitia
Departament of Telematics Engineering, Universidad de Sevilla.
Abstract
Unmanned Aerial Vehicle (UAV) networks have emerged as a promising means to provide wireless coverage in open
geographical areas. Nevertheless, in wireless networks such as WiFi, signal coverage alone is not sufficient to guarantee
that network performance meets the quality of service (QoS) requirements of real-time communication services, as it
also depends on the traffic load produced by ground users sharing the medium access.
We formulate a new problem for UAVs optimal deployment in which the QoS level is guaranteed for real-time voice
over WiFi (VoWiFi) communications. More specifically, our goal is to dispatch the minimum number of UAVs possible
to provide VoWiFi service to a set of ground users subject to coverage and QoS constraints. Optimal solutions are found
using well-known heuristics that include K-means clusterization and genetic algorithms. Via numerical results, we show
that the WiFi standard revision (e.g. IEEE 802.11a/b/g/n/ac) in use plays an important role on both coverage and QoS
performance and hence, on the number of UAVs required to provide the service.
Keywords: Unmanned aerial vehicle (UAV), Wireless LAN, Voice over IP (VoIP), Quality of Service (QoS).
1. Introduction
The past decade has seen tremendous growth in the
use of unmanned aerial vehicles (UAVs). UAVs or so-
called drones have attracted significant interest for numer-
ous applications in the context of smart cities, collection
and dissemination of information, search and rescue, or
agriculture, just to name a few[1].
There is increasingly more research focused on the de-
ployment of UAVs for providing fast and temporal wire-
less communication infrastructure [2, 3]. A typical UAVs-
assisted communication example is the provision of reliable
connectivity between clustered non-directly communicated
users [4] (UAV-aided communication relays). Other appli-
cations include the deployment of quasi-stationary UAV-
mounted base stations to create a communication service,
deploying emergency infrastructure in disaster scenarios
[5, 6, 7], reaching remote areas that cannot be serviced
otherwise [8], or offloading existing base stations [9]. In the
aforementioned applications, optimal drone location prob-
lems typically minimize the number of drones deployed
(i.e. cost) to provide coverage to a set of ground users in
known positions [10].
UAV optimal deployment problems generally assume
that coverage (i.e. received signal strength) suffices for the
?Corresponding author. Tel.: +34 954487384. Address: C/
Camino de los descubrimiento s/n. 41092 Seville (Spain). E-mail ad-
dresses: {vmayor,rafa, aestepa, german}@trajano.us.es (Mayor V.,
Estepa R., Estepa A., Madinabeitia G.).
provision of communication services [11]. Nevertheless, al-
though this may hold for cellular networks (which includes
mechanisms to deal with congestion and QoS), the ability
of WiFi networks to guarantee QoS does not depends only
on coverage, but also on the traffic load generated by those
stations sharing the channel. Therefore, despite available
QoS mechanisms [12], a congested WiFi network may be
unable to meet the strict QoS requirements of interactive
real-time services such as VoIP [13] [14, 15, 16]. Unfortu-
nately, this fact is typically ignored in studies of UAV-AP
link performance[17, 18].
It is proven that there is an upper bound in the number
of voip traffic flows that an AP can handle with acceptable
performance, namely voip capacity [19]. As the authors
in[13] put it, above this upper bound, “One more VoIP
connection will jeopardize the performance of all voice con-
nections”. The voip capacity of an AP can be studied
through a model of the Medium Access Control (MAC)
sub-layer [19] which let us estimate the impact of voip
traffic in delay or packet loss [20, 21]. Applying the find-
ings from this research field to the problem of UAVs opti-
mal positioning would allow one to consider the maximum
number of simultaneous calls that each UAV-mounted AP
can take (i.e. voip capacity) to guarantee QoS require-
ments. Furthermore, voip capacity should also consider
statistical multiplexing in the service demand since it is
unlikely that all users associated to an AP use the voip
service concurrently. However, all this has been overlooked
in existing UAVs optimal location problems [22, 23]
In this work, we define and solve a new optimization
Preprint submitted to Elsevier June 26, 2022](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-3-320.jpg)
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UAV-to-Gateway
(distribution network)
VoIP Gateway
Internet /
PSTN
IEEE
802.11
(access
network)
Figure 1: Example scenario for VoWiFi.
problem that consists of finding the minimum number of
UAV-mounted APs that should be launched to provide
VoIP service with guaranteed QoS to a set of known users
in a scenario that lacks of alternative cellular or WiFi in-
frastructure on ground (see Figure 11
). More specifically,
our problem provides the minimum number of UAVs to be
deployed and their optimal location so that voip capacity
of any deployed AP is equal or greater than the number
of users associated to that AP who are expected to be
simultaneously talking.
Most handheld devices (e.g. smartphones, tables) have
WiFi. As such, deploying a temporary solution for voice
service can be of potential interest in situations where
users a expected to be confined in known areas such as
meeting points during search and rescue missions (e.g. dis-
aster scenario), for broadcast announcements, or voice ser-
vice during outdoor activities or missions in remote areas
that lack alternative communication infrastructure. In-
deed, in these contexts, a common VoIP application could
be downloaded by users from the UAV-deployed WiFi data
access network. We also provide a preliminar analysis of
the applicability of our problem where user mobility is
considered.
The contributions and originality of this paper are:
• We mathematically formulate a new optimal drone
location problem that takes into account the speech
quality perceived by ground users.
• We provide a mathematical model to predict speech
quality for a set of heterogeneous VoIP traffic sources,
and for different IEEE 802.11 standard amendments.
1Observe that the performance of the WiFi access network (see
Figure 1) is assumed to be critical for the feasibility of the QoS-
guaranteed service while UAV-to-UAV, or UAV-to-Infrastructure ei-
ther do not significantly impair QoS, or its impact can be added
to our model as a constant extra delay and/or loss. Therefore, the
scope of this paper is restricted to the IEEE 802.11 access network
to be deployed
• We propose a service model that takes advantage
of statistical multiplexing of users’s calls, providing
efficient use of resources.
2. QoS in VoIP over WiFi networks.
As indicated in ITU-R rec. M.1079, each communi-
cation service requires specific ranges of end-to-end delay,
loss and jitter to be met, and VoIP is no exception. In our
view, planning a VoIP service over IEEE 802.11 networks
requires to take into account two key aspects:
1. The speech quality of the VoIP service, defined by
the ITU-T rec. P.800 [24], which is measured through
surveys that rate a mean opinion score (MOS) rang-
ing from 1 (poor) to 5 (excellent).
2. The probability that a user is unable to place a new
call as a result of the exhaustion of the resources
of the (WiFi) network. This is also known as call-
blocking probability in the field of teletraffic.
According to ITU-T G.107, acceptable conversations
should exhibit MOS > 3.5, but in general, if the network
fails to underpin a minimum level MOSmin, the service
simply can not be provided[25].
At the planning stage, a method for MOS prediction
is needed. In VoIP, the most extended method is the E-
Model [26, 27], which combines additive impairments fac-
tors to measure speech quality R factor, ranging from 0
(poor) to 100 (excellent), that can be directly mapped to
MOS [28]. As Assem et al [29] put it, the E-Model is “a
repeatable way to assess if a network is prepared to carry
a VoIP call or not”. In its simplest form, the E-model can
be expressed as [30]:
R = 94.2 − Id − Ie−eff (1)
where for now, it suffices to know that Id represents all
impairments due to delay, and Ie−eff is a factor that ac-
counts for the impairments caused by low bit-rate cod-
ing and packet loss [31]. Both, delay and packet loss are
certainly affected by the performance of the IEEE 802.11
access network.
Figure 2 illustrates a system composed of a set of IEEE
802.11 stations associated to one UAV-mounted AP. Each
station is represented by its physical layer and its medium
access control (MAC) sub-layer. While all stations share a
common MAC protocol, each one auto-configures its Mod-
ulation and Coding Schema (MCS) according to the Re-
ceived Signal Strength Indicator (RSSI) from the AP and
a set of thresholds (i.e. minimum input sensitivity) de-
fined by the IEEE 802.11 standard in use [32]. An exam-
ple of different MCSs defined for OFDM modulations (e.g.
IEEE 802.11a/g) is shown in Table 1. Thus, each user ter-
minal is assumed to auto-configure its MCS to the greatest
bit-rate possible depending on the received signal power.
In VoWiFi, speech quality is strongly influenced by the
delay and loss of the downlink (i.e. from the access point
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Noisy Radio Channel
IEEE 802.11 MAC
IEEE 802.11 PHY
IEEE 802.11 MAC
IEEE 802.11 PHY
IEEE 802.11 MAC
IEEE 802.11 PHY
IEEE 802.11 MAC
IEEE 802.11 PHY
U1-VoIP
App
U2-VoIP
App
UN-VoIP
App
U1-VoIP
packets
U2-VoIP
packets
UN-VoIP
packets
MCS1 MCS2 MCSN
Figure 2: UAV-AP: IEEE 802.11 system under consideration
Modulation Coding rate
Data rate Sensitivity
(Mb/s) (dBm)
BPSK 1/2 6 -82
BPSK 3/4 9 -81
QPSK 1/2 12 -79
QPSK 3/4 18 -77
16-QAM 1/2 24 -74
16-QAM 3/4 36 -70
64-QAM 2/3 48 -66
64-QAM 3/4 54 -65
Table 1: 802.11 sensitivity relations for OFDM modulations with 20
MHz channels.
(AP) to VoIP terminals)[16]. Both factors depend on the
traffic load, which in turn depends on the speech codec
and the number and data bit-rate of users engaged on ac-
tive calls at a given moment2
. WiFi analytical models let
us capture the relation between the VoIP traffic volume
handled by an AP and the delay and loss that such traffic
will experience. There is a plethora of analytical models of
the IEEE 802.11 MAC behaviour [33, 34, 35, 36]. In most
models, the central variable is the probability that an ob-
served station attempts to transmit in a random time slot
(τ). However, different models apply different assumptions
to derive their analytical expression for τ. In this paper,
the following assumptions are considered:
• Heterogeneous traffic sources (two users may have
different physical data bitrate according to their RSSI).
• Non-saturated stations (sometimes there may be no
packets to be transmitted).
• Noisy channel (channel noise can corrupt packets).
But above analytical models, intuition suggests that
VoIP traffic increases with every new call, which in turn
2This assumes that either only VoIP traffic exists, or that VoIP
traffic is prioritized using IEEE 802.11e.
impacts on network delay and loss, deteriorating the QoS
of ongoing calls. As a result of the previous consideration,
a VoWiFi service with guaranteed QoS should not accept a
new call when this implies that calls in progress may turn
unacceptable (i.e. MOS < MOSmin). This is known as
Call Admission Control (CAC) function, typically imple-
mented either at the AP (as indicated in IEEE 802.11e),
or at the application level (e.g. VoIP gateway). Obviously,
this function requires to assess the maximum number of
concurrent calls that an AP can take so that the quality
experienced by active users is above MOSmin. This upper
bound is the voip capacity of an AP and will be denoted
by CCmax from now on. For example, in [16] it was found
that a maximum of 15 calls for 64kb/s CBR VoIP traffic,
or 38 calls for VBR VoIP traffic, can be held for IEEE
802.11b.
This leads us to the second factor deemed as key for di-
mensioning: the call-blocking probability, or, equivalently,
the probability that a new call is rejected as a result of
CCmax calls being already in progress. It is possible to find
such a probability if one takes a statistical model of the
user behaviour from the field of teletraffic. Assuming that
call attempts and calls duration follow exponential distri-
butions, the call-blocking probability for the users served
by an AP is given by the classical Engset formula [37]:
B(A, u, cc) =
u−1
cc
Acc
Pcc
i=0
u−1
i
Ai
(2)
where A stands for the traffic intensity (product of average
frequency and duration of calls), u is the number of users
associated to the access point, and cc is the number of
concurrent calls.
Then, provisioning VoWiFi with guaranteed QoS will
require that the following constraints are met:
• Speech quality level (MOS) higher than MOSmin.
• Call-blocking probability lower than
Bmax =B(A, u,CCmax).
which will be regarded as VoWiFi service QoS constraints
in the problem to be defined next.
3. Problem statement
In the scenario illustrated in Figure 1, we want to de-
ploy a set of drones to create a WiFi access network that
enables the VoWiFi service with guaranteed QoS. To make
the problem more tractable, the following assumptions are
made:
• The position of ground targets (i.e. users confined
in a known area) is known. User terminals run a
VoIP app which utilizes a known codec and standard
signaling.
• If a ground terminal could associate to more than
one AP, the one with maximum received power will
be selected.
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and the objective function is evaluated. Among potential
solutions with the same value of D, the one with the low-
est objective function is selected. The algorithm ends after
finding the optimal solution, or after trying unsuccessfully
with Dmax drones. The output of the algorithm is the set
of optimal UAVs locations and the value of the objective
function. A null location indicates that no solution has
been found.
Input: U, {wk}, Dmax, Cmin, Bmax, MOSmin
Output: L (location), ofmin (obj. function)
Initialization: D = 1, L = ∅, ofmin = Dmax + 1
1 while L = ∅ or D ≤ Dmax do
2 D++; // Increase number of UAVs
3 foreach possible value of X do
4 for j = 1 to D do
5 C(j) = associate(U, {wk}, X);
6 end
/* check first constraint */
7 if
PD
i=1 |C(i)|/U
≥ Cmin then
8 for j = 1 to D do
9 MOS(j) = QoS.eval(C(j), xj, {wk},
Bmax);
10 end
11 MOS = min
k=1..D
{MOS(k)};
12 if MOS ≥ MOSmin then
/* QoS constraints met */
13 of = D + (1 −
PD
i=1 |C(i)|/U);
14 if of ofmin then
15 ofmin = of; // solution
16 L = X; // UAVs position
17 end
18 end
19 end
20 end
21 end
Algorithm 1: Exhaustive search pseudocode
Next, we elaborate on the functions used for the assess-
ment of signal coverage and quality of service constraints.
4.1. Signal Coverage Evaluation: associate()
A ground terminal associates to an AP if its Signal to
Noise Ratio (SNR) and Received Signal Strength Indica-
tion (RSSI) are above minimum levels to properly demod-
ulate the received signal. In addition, if several APs were
available (e.g. D 1), each user will be associated to the
AP with maximum received power.
The UAV-to-ground path loss should generally consider
a combination of Line-of-Sight (LoS) and NLoS compo-
nents whose probability depend on the drone altitude and
ground terminal surroundings [38]. We adopt the model
presented in [39] (also used in [4]). According to such
model, the probability that a ground user has a LoS link
with the AP installed at a drone is:
PLoS(θ) =
1
1 + a1e−b1θ·180/π+b1a1
(4)
where θ is the elevation angle in degrees (between user and
drone), a1 and b1 are environment dependent constants
(e.g. rural, urban, etc.). Then, for user i located at wi
and the AP installed at drone j located at xj, RSSIij is
given by:
RSSIij =PT X + Gij − 20 log10
4πf · kwi − xjk
c
− PLoS(θij) · ηLoS − (1 − PLoS(θij)) · ηNLoS
(5)
Gij = 10 log10(10Gmax/20
· cos2
θij) (6)
where PT X (dBm) stands for the power delivered by
the transmitter antennas; Gij stands for the gain of the
antenna between user i and UAV j as indicated in (6);
kwi − xjk is the Euclidean distance between user i and
drone j;f (hertz) is the channel frequency; c(m/s) is the
speed of light; θij (radians) accounts for the elevation angle
between user’s position wi and UAV’s position xj; ηLoS(in
dB) and ηNLoS (in dB) are losses corresponding to LoS
and NLoS connections which depend on the environment
(a list of values can be found in [40]). Finally, constant
Gmax in(6) indicates the maximum power.
Given RSSIij, the Signal to Noise Ratio (SNRij)(dB)
can be readily obtained by subtracting the receiver’s noise
figure (NF) and thermal noise (N) as indicated in (7)
and (8).
SNRij = RSSIij − NF − N (7)
N = −174 + 10 log10(CBW ) (8)
where CBW stands for signal bandwidth as specified by
the IEEE 802.11 standard in use.
For all i ∈ U and for all j ∈ D, let us define γij as
a boolean variable that indicates whether user i satisfies
minimum thresholds (i.e. SNRij ≥ SNRmin and RSSIij ≥
RSSImin) with respect to UAV j or not. Then, the function
associate() returns the set of users that meet minimum
thresholds and whose RSSI with drone j is greater than
with any other drone:
C(j) = {i ∈ U | γik = 1, RSSIij RSSIik ∀k 6= j} (9)
Recall from previous section that each ground user’s ter-
minal i sets its Modulation and Coding Scheme MCS(i)
according to its RSSI(i)
= max
j=1..D
{RSSIij} (see (5)), which
determines the data bit rate of the terminal.
4.2. VoWiFi service QoS evaluation: QoS.eval()
This function checks on VoWiFi service QoS constraints
described in Section 2 by following these two broad steps:
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Figure 4: for QoS assessment.
1. Find out how many users in C(j) can simultaneously
talk so that the call-blocking probability Bmax is not
exceeded (i.e. find CCmax). This can be readily done
by increasing the number of concurrent calls in (2)
as indicated in Algorithm 2.
Input: |C(j)| (set of users associated), A, Bmax
Output: CCmax (maximum concurrent calls)
1 for cc = 1 to |C(j)| do
2 if B(A, |C(j)|, cc) ≤ Bmax then // Eq. (2)
3 CCmax = cc;
4 cc++;
5 end
6 end
Algorithm 2: Finding CCmax within an AP
2. Estimate the MOS: Let M ⊂ C(j) be the subset
composed of the CCmax stations with the lowest
data bit rate in C(j). Stations in M are expected
to exhibit greater transmission/reception delay than
the rest and consequently, are regarded to be “worst
case” in terms of QoS. First, an analytical model of
the IEEE 802.11 mac sub-layer is applied to the sys-
tem composed of the set of stations M plus its AP
to estimate the delay and packet loss experienced by
VoIP traffic. Then, the E-model is used to finally
obtain speech quality level MOS. This is illustrated
in Figure 4. Next we elaborate on steps (a) and (b).
Delay and packet loss estimation. The set of stations in
M and its AP constitute a IEEE 802.11 system whose
performance has been largely studied in scientific litera-
ture [41, 42, 43, 44]. We have used a mix of different
analytical models from [33, 34, 35, 36] fitted for the follow-
ing assumptions: stations can have different bit rates (i.e.
heterogeneous traffic sources), stations are not-saturated3
,
3When the channel is idle a station may have no packets to trans-
mit.
and the channel is noisy. Due to the complexity of the
subject, and for the sake of clarity, we keep this section
as simple as possible. The reader is encouraged to read
more elaborated information in the corresponding refer-
ences and Appendix A.
The Distributed Coordination Function (DCF) of the
802.11 MAC sub-layer use CSMA/CA (Carrier Sense Mul-
tiple Access with Collision Avoidance) for medium access
control. Basically, each contending station must sense the
medium during a period of time in order to ensure that it
is idle before transmission. If the channel is busy, the sta-
tion waits a random backoff interval before trying again.
The backoff process is based on the Binary Exponential
algorithm. Time is discretized and the algorithm picks a
random number of time slots between 0 and 2i
Wo, where
Wo accounts for the minimum contention window value,
and i increases by one in each failed attempt up to a ceil-
ing m. After a maximum number of retransmissions is
reached (M), the packet is discarded.
Most analytical models based on Markov chains lay
on a central variable termed τ which represents the prob-
ability that an observed station attempts to transmit in
a randomly chosen time slot. In this paper we used the
expression in [33]:
τ =
1
η
1
1 − q
r2
Wo
(1 − p)(1 − (1 − r)Wo
− qr(1 − p)
(10)
where η is defined in (14), q is the probability of having
at least one packet queued at the transmission buffer, p
is the probability that a packet suffers any transmission
errors, and r is the probability that at least one packet
arrives during an idle state (load factor). Assuming non-
saturated stations and Poisson packet arrivals (with rate
λ) to the transmission queue, r and q can be expressed as:
r = 1 − e−λE[T ]
(11)
q = 1 − e−λE[T ]E[B]
(12)
where E[T] represents the expected average slot duration,
and E[B] is expected average number of back-off slots that
a packet waits before transmission. Due to its complexity,
a closed-form of E[T] is deduced in Appendix A (Equa-
tion (A.19)). E[B] can however, be expressed as in [36]:
E[B] =
Wo
2(1 − p)
1 − p − (2p)m
(1 − 2p)
− 2m
pM+1
(13)
Let τ(i)
, r(i)
, q(i)
, E[B(i)
] and λ(i)
denote τ, r, q, E[B]
and λ of station i in the system under consideration (i.e.
the subset M and its AP such as illustrated in Figure 2),
where i refers to either one user station {1, 2, ..|M|}, or
the AP (i = |M| + 1 = AP). Let p(i)
be the probability
of packet transmission error p for station i. Then, p(i)
can
be broken down as:
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η = (1 − r) +
r2
Wo(Wo + 1)
2(1 − (1 − r)Wo )
+
Wo + 1
2(1 − q)
r2
qWo
1 − (1 − r)Wo
+ rp(1 − q) − rq(1 − p)2
+
p
2(1 − q)(1 − p)
r2
Wo
1 − (1 − r)Wo
+ qr(1 − p)2
2Wo
1 − p − p(2p)m−1
1 − 2p
+ 1
(14)
p(i)
=
1 − P
(i)
i
∪ FER(i)
=
1 − P
(i)
i
+ FER(i)
−
1 − P
(i)
i
· FER(i)
(15)
where P
(i)
i accounts for the probability that the j-th sta-
tion finds the channel idle and FER(i)
stands for the Frame
Error Rate due to channel noise. The probability of finding
the channel idle, can be further expressed as:
P
(i)
i =
S
Y
j=1, i6=j
1 − τ(j)
(16)
Assuming that frames have a constant size of L bits
(L = preamble + header + data), it is possible to obtain
the FER of station i as:
FER(i)
= 1 − (1 − P(i)
e )L
(17)
where P(i)
e represents the codec bit error rate of station
i, which can be readily calculated4
if one knows user’s
modulation (i.e. MCS(i)
).
Finally, solving the non-linear equation system, the
packet loss of station i can be expressed as:
PL(i)
= 1 −
1 − FER(i)
τ(i)
Q|M|+1
j=1,j6=i 1 − τ(j)
λ(i) E[T]
(18)
Since we assume a very small buffer size, the queueing
delay can be neglected and the only delay component will
be the channel access delay. Then, the delay of station i
can be expressed as:
DEL(i)
= E[B(i)
] E[T] (19)
As justified in [16], the AP5
(i = AP) is the most
saturated station, leading the packet loss and delay in the
system. Thus, we can take its packet loss and delay as
representative of the worst case. Then, the output of this
step is:
PL = PL(AP )
(20)
DEL = DEL(AP )
(21)
4See equations in [45] and [46] for DSS and OFDM modulations
respectively.
5Observe that the AP is also part of the system and its MCS and
FER change dynamically according to its communication partner.
Our approach is to consider average values of its data bit-rate and
FER.
MOS estimation.. As stated in Section 2, the E-Model
rates the conversation quality R factor, which can be cal-
culated using (1) [29], whose terms were:
• Ie,eff is the effective impairment equipment param-
eter. It is a combination between impairment equip-
ment parameter at zero packet loss (Ie), and a func-
tion of Ie that is dependent on packet loss rate and
packet loss behaviour. It can be expressed as:
Ie,eff = Ie + (95 − Ie)
Ppl
Ppl
BurstR + Bpl
(22)
where Ie is a codec-dependent constant associated
with codec compression degradation6
, Ppl represents
the packet loss rate, BurstR accounts for the burst
ratio (i.e. equals 1 if packet loss if random and
greater otherwise), Bpl represents the codec packet
loss robustness, which also has a specific value for
each codec (listed in ITU-T Rec. G117 Appendix I).
• Id accounts for all impairments due to delay of com-
munication chain. A widely accepted approximation
for Id can be obtained from one-way delay in com-
munication path (d) as follows:
Id = 0.024d + 0.11(d − 177.3)H(d − 177.3), (23)
where H is the heavyside function (i.e. H(x) = 0
for x 0 and H(x) = 1 for x 0). This shows
that the effect of one-way delays under 100 ms can
be discarded.
In this paper we will use the G.711 codec (Ie = 0), with
BurstR = 1 and Bpl = 25, 1. So, assuming that Ppl = PL
(from (20)), and d = DEL (from (21)) + 20 ms (from the
VoIP codec packetization), R can be expressed7
as:
R = 93.72 − 95
PL
PL + 25, 1
− (0.024DEL + 0.11(DEL − 157.3)H(DEL − 157.3))
(24)
6A list of values from ITU-T codecs were presented in ITUT-T
Rec. G.113 Appendix I.
7The 20 ms of packetization delay has been taken into account in
the expression provided.
7](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-9-320.jpg)
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0
2
10
100
20
z
(m)
90
80 100
70 90
80
60
y (m)
70
50 60
1
x (m)
40 50
30 40
30
20 20
10 10
0 0
Drone
Associated users
Non covered users
Figure 5: Example solution (D = 2).
Finally, to obtain speech quality, the R factor can be
mapped to MOS [27] as:
MOS =
1, R 6.5
1 + 0.035 R + 7 · 10−6
R
· (R − 60) (100 − R), 6.5 ≤ R ≤ 100
4.5, R 100
(25)
4.3. Example solution
This section introduces a first example of the results
obtained after implementing Algorithm 1 in Matlab®
. The
scenario includes 25 ground users randomly distributed
within an area of 100 m×100 m. The parameters used in
the example are listed in Table 3. Unless otherwise spec-
ified, such parameters are common to all experiments in
this paper.
Figure 5 provides a graphical representation of the so-
lution obtained, showing by color users distribution among
UAVs. In this case, two drones were necessary to cover 24
out of 25 users8
(i.e. (|C(1)| + |C(2)|) /U = 0.96 Cmin)
using the IEEE 802.11n standard revision.
The solution represented in Fig. 5 has been simulated
with the network simulator ns-3 in order to validate the
IEEE 802.11 analytical model from Section 4.2. The ns-3
model YansWifiPhy with a transmission buffer size of one
packet has been used. The simulation has been repeated
30 times with different seeds and the results presented rep-
resent the average value with a 95% confidence interval.
Table 2 summarizes the results obtained, comparing
delay, packet loss and MOS from our analytical models
with those obtained with ns-3. It can be observed no sig-
nificant differences between the output of the analytical
models used and simulation results, particularly in terms
of predicted speech QoS. Note that delay is very small in
absolute terms, always under 1 ms as a result of a very
small buffer. The comparison of the MOS obtained with
our analytical models versus simulation suggests that the
method and models proposed in Section 4.2 are accurate
enough.
8Some ground terminals almost entirely overlap in the figure as
they were generated randomly.
Note that the X-Y discretization step in our example
was only 1m (which we consider the minimum safe for col-
lision avoidance), while Z step was 5m. In general, the
smaller grid steps the more accurate the solution will be
(i.e. closer to the optimal that would be found without
discretizing the flying space) but the more edges in P will
have to be assessed, increasing the computational load. In
general,
PD
d=1
|P|
d
possibilities will have to be assessed
when D drones are being evaluated. For example, the
grid defined in our example has |P| = 2 · 104
edges, thus
' 2·108
possible combinations of UAV locations have been
assessed. This fact suggests that exhaustive search may
be feasible only in very small scenarios since its computa-
tional complexity grows exponentially with D. For that
reason, heuristic search methods are commonly preferred
as a general way to find (semi) optimal solutions.
5. Heuristic Solution
A number of different metaheuristics can be used to
find (semi)optimal solutions. These include genetic al-
gorithms (GAs), particle swarms optimization, artificial
immune system, and simulated annealing. Furthermore,
other approaches such as optimal transport theory have
been also successfully applied to solve user-drone associa-
tion in similar scenarios
Our heuristic search method can be viewed as a re-
placement of lines 3-20 in Algorithm1 for a function call
(GAsearch) that returns the (semi)optimal solution found
for a specific number of drones D as shown in Algorithm3.
Input: U, {wk}, Dmax, Cmin, Bmax, MOSmin
Output: L (location), ofmin (obj. function)
Initialization: D = 0, L = ∅, ofmin = Dmax + 1
1 while (L = ∅ or D ≤ Dmax) do
2 D + +;
3 L,of =GAsearch(D,{wk},Bmax,Cmin,MOSmin)
4 end
Algorithm 3: Use of the heuristic search method
We have designed the genetic algorithm GAsearch()
using the Matlab®
R2017A Global Optimization Tool-
box [47]. Next we elaborate on the GA developed.
5.1. Individuals
An individual is a possible solution to the problem.
As such, each individual is a location of D drones X =
{x1, x2, .., xD|xi ∈ P, i ∈ D, xi 6= xj|∀j6=i}, where xi ∈ P
represents the 3D coordinates of drone i. For instance, an
individual composed of two drones {x1, x2} is given by the
sequence of genes {x1, y1, z1, x2, y2, z2}.
5.2. Algorithm steps
The algorithm performs the following steps:
8](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-10-320.jpg)
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Drone xi C(i)
B(i)
Algorithm 1 / Simulation
(%)
PL D MOS
(i) (%) (ms) [1 - 4.5]
1 (24, 36, 20) 12 1.58 0.45 / 0.32 ± 0.05 0.19 / 0.12 ± 0.002 4.39 / 4.40
2 (63, 67, 20) 12 1.58 0.36 / 0.26 ± 0.04 0.18 / 0.13 ± 0.002 4.39 / 4.40
Table 2: Comparison of algorithmic results with simulation
IEEE Standard Scenario Traffic Constraints
Revision 802.11n Users 25 Calls/hour/user 1 RSSImin -82 dBm
GI 800 ns Size 100×100 m Call length 180 s SNRmin 20 dB
Preamble Greenfield X-Y step 1 m VoIP codec G.711 MOSmin 3.5
Bandwidth 20 MHz Altitude layers {20, 25} m On/Off times CBR Cmin 0.9
Retries 7 Prop. Exponent 3.3 Packet interval 20 ms Bmax 0.05
Table 3: Example solution input parameters
1. An initial population is generated.
2. Each individual from the generation is evaluated
and ranked by assessing a raw fitness score based on
the objective function of the problem (3).
3. Individuals are selected as parents according to their
position in the ranking.
4. A new generation is created as follows:
• The top 5% of the ranking (elite individuals)
are copied to the new generation.
• Of the remaining individuals:
– 80% is created by Crossover-and-Mutation
(CM) combining the genes of two selected
parents (crossover) and applying a muta-
tion to these new individuals with a very
low probability pCM
m .
– 20% is created by an operation of muta-
tion of parents (termed self-reproduction
and mutation, SRM) with probability pSRM
m .
5. After each new generation the exit criteria is eval-
uated. The algorithm finishes when the lowest raw
fitness score found cannot be improved after MAXG
consecutive generations9
by at least 10−3
. If the exit
criteria is not met, go to step 2.
The previous steps differ slightly from the traditional
sequential application of operations done by the canonical
GA, however convergence is improved according to [48, 49].
5.2.1. Initial Population
It is desirable to count with initial individuals prone to
be fit [50]. We created the following heuristic based on the
k-means clusterization method illustrated in Figure 6:
• In an area similar to the grid X-Y dimensions, D
clusters are created so that the mean distance from
9However, if within the first MAXG generations no individual
meets problem constraints, the algorithm returns L = ∅ to indicate
that no solutions can be found with that number of drones.
each ground user to its cluster centroid is minimized.
Then, we add the grid’s average altitude to the cen-
troid of each 2D region created previously, obtaining
3D centroids.
• The first individual of the initial population will lo-
cate its drones in those edges of the grid closest to
these 3D centroids.
• The other (p−1) individuals of the initial population
are created simply by distributing each individual’s
drones randomly among the spatial regions created
around each centroid. In particular, we define cubes
with a volume equals to the D-th part of the grid
volume10
. Note that drones are always located at
grid edges
We found experimentally that a population size p of
200 individuals provided results that could not be im-
proved in the scenarios tested.
To guarantee convergence, after creating the initial pop-
ulation, these 3D spatial regions are no longer taken into
consideration for next generations. This implies that genes
carried by individuals from next generations are not con-
strained by spatial regions and hence, could be at any edge
∈ P.
5.2.2. Operators
The following operators have been used:
1. Evaluation and ranking. Each individual is as-
signed a raw fitness score by evaluating the problem
objective function defined in (3). Since the genetic
algorithm is called to search for solutions with D
drones, individuals that do not meet the problem
constraints are assigned a higher score by adding a
penalty (between 1 and 2, according to the ratio of
10Observe that since the centroid of each cube was determined by
k-means clusterization, there could be overlapping regions or regions
out of the grid bounds such as those illustrated (in 2D) in Figure 6.
9](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-11-320.jpg)
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number of ground users whose traffic can be handled by
a single drone). In its upper bound however, D tends to
match the number of users U (e.g. in a large extension
with scattered users). Finally, using this upper bound, we
conclude that the computational complexity of our heuris-
tic method is upper bounded by O(U3
). However, if one
considers that D is constrained by the maximum number
of UAVs in the problem (constant Dmax), then the compu-
tational complexity would be O(U). At any rate, solutions
can be computed in polynomial time.
6. Numerical results
In this section we provide a numerical analysis of the
proposed UAV deployment method. Results are obtained
through the heuristics proposed in Section 5. The focus is
set on two different aspects: the impact of the IEEE 802.11
standard revision in use, and the impact of the constraints
bounds in the solutions.
6.1. Influence of IEEE 802.11 standard revision
A comprehensive summary of the challenges and impli-
cations of the various IEEE 802.11 amendments in long-
range outdoor WiFi deployments can be found in [23]. In
this section, we compare the performance of the IEEE 802.11
(b/g/a/n/ac) standard amendments shown in Table 6 and
evaluate their fitness to scenarios with specific character-
istics. In particular, we define two types of scenarios:
• Coverage-limited scenario: for a fixed number of ground
users U = 100, the terrain size is increased from
100 m2
to 10 000 m2
, obtaining values of user spar-
sity that range from 1 m2
to 100 m2
. In this kind
of scenario, it is expected that the number of drones
in the solutions is mainly determined by the need to
satisfy the coverage constraint Cmin (which depends
on the physical layer) and SNR of users.
• QoS-limited scenario: for a fixed very small terrain
size (5m × 5m) the number of users is increased
from 25 to 100, obtaining highly dense scenarios (1−
0.25 m2
/user). In this kind of scenario, it is expected
that all users are under coverage, and the number
of drones in the solutions is mainly determined by
the need to satisfy QoS constraints (Bmax, MOSmin)
(which depend on the mac-sublayer).
Frequency Channel Bandwidth Revision
2.4 GHz
22 MHz 802.11b
20 MHz 802.11g
40 MHz 802.11n
5 GHz
20 MHz 802.11a
160 MHz 802.11ac
Table 6: IEEE 802.11 standard revisions considered
Results presented in this section represent average val-
ues after repeating 30 times each experiments. 95% confi-
dence intervals obtained were small and have been omitted
in the figures presented for clarity.
6.1.1. Coverage-limited scenario
10 20 30 40 50 60 70 80 90 100
m 2
/U
0
5
10
15
20
objective
function
value
802.11b
802.11a
802.11g
802.11n | 40MHz
802.11ac | 160MHz
Figure 9: Solutions for various values of user geographic dispersion.
Figure 9 plots the value of the objective function of
the solutions found. It is noticeable that the physical bit
rate of IEEE 802.11b (11Mbps) results in higher demand
of drones due to the low throughput supported by each
AP. It can also be observed that when geographic disper-
sion increases, standards in the 5 GHz band (IEEE 802.11a
and 802.11ac) produce worse results (i.e. more UAVs are
needed) than those in the 2.4 GHz band. This can be at-
tributed to a higher propagation loss (see RSSI expression-
formula in (5)). Another noticeable effect is produced by
the channel bandwidth. Higher bandwidth exhibits higher
thermal noise (see N formula in (8)), which negatively
impacts on SNR and, consequently, on coverage. This is
clearly noticeable in the case of IEEE 802.11ac, and less ob-
vious in IEEE 802.11n, which performs a little worse than
IEEE 802.11g for areas greater than 70 m × 70 m in spite
of a greater data bit rate.
Finally, an interesting effect can be observed at the
leftmost part of the figure. Most revisions start with 4
drones and then fall to 3 for larger areas until it starts
increasing again. This is attributable to the own scenario
characteristics as in the most dense case (100 users in an
area of 10 m×10 m) it behaves like a QoS-limited scenario
where 100% of users are covered and the limiting factor
is their traffic. However, when the terrain size increases
(i.e. sparsity increases) some users are left uncovered (un-
til Cmin). This happens first in those standard revisions
that exhibit worse coverage properties (i.e. ac and a) and
as a consequence less drones are required. Nevertheless,
as the terrain size keeps on increasing, coverage constraint
is dominant, and the number of drones in the solutions
tend to increase with the terrain size in all standard revi-
sions but IEEE 802.11b due to the large number of drones
deployed.
12](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-14-320.jpg)
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6.1.2. QoS-limited scenario
Figure 10 shows the results obtained for the high user-
density QoS-limited scenario. To be consistent with the
previous case, we consider user sparsity (0, 25−1 m2
/user)
instead of density in the results shown. Results show that
all standard revisions (but IEEE 802.11b) exhibit a similar
behaviour, increasing the number of drones when QoS con-
straints are not met due to a high volume of traffic. This
suggest that the higher data bit rate exhibited by some
revisions is not fully exploited (except at 0.76 m2
/user) in
the very small scenario under consideration. As expected,
the insufficient physical bit-rate of IEEE 802.11b causes
an exponential growth in the number of drones required
to support very high users densities.
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
m 2
/U
0
2
4
6
8
10
12
objective
function
value
802.11b
802.11a
802.11g
802.11n | 40MHz
802.11ac | 160MHz
Figure 10: QoS limited scenario
From the two scenarios studied, it can be concluded
that revisions IEEE 802.11 g/n achieve the best results,
requiring only between 1 and 4 drones to cover between
90 and 100 users in an area ranging from 5 m × 5 m up
to 100 m × 100 m. Revisions using 5 Ghz however (a,ac),
exhibit more path loss and tend to require more drones
in large areas e.g. greater than 70 × 70 m. Finally, the
old IEEE 802.11b standard revision exhibits a poor per-
formance compared with the rest as a result of its poor
throughput.
6.2. Influence of the constraints
The selection of thresholds in the constraints also plays
an important role in the solutions obtained; very restric-
tive constraints may lead to unwanted results. In this sec-
tion, we show the results produced with the variation of
Cmin in a coverage-limited scenario (100 users in the great-
est terrain size: 10 000 m2
), and Bmax in a QoS-limited
scenario (100 users in the smallest terrain size: 25 m2
).
The value of MOSmin is always set to 3.5.
Figure 11 shows the influence of Cmin in the objec-
tive function for different IEEE 802.11 standard revisions.
As expected, the number of drones in the solutions in-
creases with Cmin. This growth is approximately linear un-
til Cmin = 0.9, where those standard revisions with higher
frequency (a, ac) or channel bandwidth (ac, n) exhibit a
steeper rise than b or g. Therefore, very demanding Cmin
values may cause exponential growth in the number of
0.5 0.6 0.7 0.8 0.9 1
Cmin
0
5
10
15
20
25
objective
function
value
802.11b
802.11a
802.11g
802.11n | 40MHz
802.11ac | 160MHz
Figure 11: Influence of Cmin in the value of the objective function.
0 0.02 0.04 0.06 0.08 0.1
Bmax
5
10
15
20
objective
function
value
802.11b
802.11a
802.11g
802.11n | 40MHz
802.11ac | 160MHz
Figure 12: Influence of Bmax in the value of the objective function.
UAVs needed for those standards. In such case, the max-
imum number of available UAVs in the problem (Dmax)
might limit the feasibility of finding valid solutions.
Figure 12 shows the influence of Bmax in the objec-
tive function for a very small area with a highly dense
crowd. Recall that Bmax = 0 means that all users as-
sociated to WiFi (i.e. covered) can simultaneously call,
whereas Bmax = 0.1 means that a covered user will be al-
lowed (by the CAC mechanism) to call with a probability
of 90%. In this case, those standards with better data bit
rate withstand more restrictive values of Bmax (i.e. simul-
taneous calls) with the same number of drones. As such,
we find that IEEE 802.11n/ac revisions achieve slightly
better results than the rest.
Finally, it is important to remark that our numerical
results are limited by several factors. First, only the high-
est data bit rate from each revision has been considered;
then, some features such as frame aggregation or MIMO
in 802.11n or 802.11ac have also been disregarded, as it
has been inter-channel interference. Besides, some recent
and promising revisions such as IEEE 802.11ah, specifi-
cally targeted for outdoor long-range at 900 Mhz serving
high density wireless stations [23] have not been included
due to lack of adoption in today’s user terminals. How-
ever, the most patent limit of our results is the fact that
the problem has been used just for the initial deployment
of UAVs. Next we provide a preliminary analysis of the
applicability of this problem to a scenario where ground
users are moving.
13](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-15-320.jpg)
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7. Application to moving targets
The problem defined in Equation 3 is aimed at solving
the problem of initial deployment of UAVs and as such, it
can also be applied for service provisioning when ground
users are gathered in specific known areas such as meeting
points. In this section we provide a brief analysis of its ap-
plicability when ground users are on the move, identifying
open issues which remain to be addressed in future work.
It is assumed that ground users position can be tracked.
In such case, every T seconds user’s position is updated
and our optimization problem is solved, relocating UAVs
accordingly in a process such as the one illustrated in Fig-
ure 13.
000
111
000
111 0000
1111 0
1
00
11
UAVs relocated UAVs relocated
UAVs relocation delay
0 T 2T 3T
time
...
UAVs deployed
solution computation delay
Figure 13: Dynamic of UAVs relocation
The key points in this process are:
• The observation period T. The minimum possible
value for T should be greater than the addition of:
– The time required to solve the problem (which
in turn depends on the performance of the algo-
rithm finally implemented, the scenario under
consideration and computational resources).
– The time required to relocate all UAVs accord-
ing to the new solution. This in turn depends
on the solution found, initial position, UAV speed
and the displacement strategy.
Practical values should be in the order of seconds.
Clearly, the longer T, the greater discrepancy be-
tween the theoretical and actual position of ground
users, increasing the error of the models and chances
of unsatisfying constraints.
• Relocation of UAVs. Moving UAVs may result in
transient periods of unsatisfied constraints. The de-
cision about which drones are displaced according to
the final solution and the trajectories followed is a
problem itself that should consider not only the de-
lay (e.g.[11]) but also service disruption to ground
users engaged in conversations. Examples of strate-
gies include minimizing the sum of all UAVs displace-
ments, the longest UAV displacement, or the number
of users affected by service outages. It would also be
interesting to explore techniques of machine learning
such as conceptor-based echo state networks (ESN)
[51] to predict user service request pattern and user
mobility pattern.
• Problem Objective function. Once the relocation
strategy is fixed, the cost of relocating drones should
be taken into account into the optimization problem
as a penalty factor added to the objective function.
Let us imagine a case in which two candidate solu-
tions exhibit the same number of drones and cover-
age (i.e. a similar value of the objective function)
but one solution implies a complex repositioning of
all drones while the other implies just a slight change
on a single drone. Thus, this penalty could include
aspects such as the relocation delay or the temporal
effect of impaired users as a result of drones relo-
cation, serving as a factor to break the deadlock in
favor of the less costly solution.
The aforementioned key points suggest that user’s move-
ment brings out new issues and implications that require
an extension to the problem defined in this paper including
the cost of UAVs relocation according to a specific strategy
as well as user mobility models. Furthermore, a centralised
approach such as the one suggested for initial deployment
might not hold of service continuity. These aspects15
are
left as open issues for further research. Nevertheless, as a
prospective exercise, we have performed a simulation with
users on the move using the coverage-limited scenario and
the parameters in Table 4 (but using a traffic profile of 5
calls/hour/user and altitude layers between 10 m and 40 m
with steps of 1 m).
In our coverage-limited scenario, the 100 users now
move according to a correlated random walk model. Each
ground user moves at a walking speed of 5.3 km/h with a
probability of 0.8 and in such case, the direction remains
unchanged with probability 0.8. Users rotate 180 degrees
when they reach the area bounds. Algorithm 3 is used for
the initial deployment and the number of drones deployed
D remains unchanged for the remainder of the simulation
(30 min). To achieve this we limit subsequent solutions to
the best possible found by our GA with D drones (even
though problem constraints were not satisfied). With ev-
ery new solution drones are relocated (considering a speed
of 60 Km/h) so that the sum of the distances traveled by
all drones is the minimum possible.
To study the transient effects of UAV’s relocation we
check every five seconds whether the problem constraints
(i.e. coverage and speech quality) are satisfied considering
the actual position of users. New solutions (and drones
relocation) have been recalculated every T ={15 s, 30 s,
45 s, 60 s} and in each case simulations are repeated 30
times. Figure 14 shows the percentage of the simulation
time when both constraints are satisfied. Results show
that problem constraints were satified above 92% of the
time in worst case (i.e. area of 10 000 m2
and T = 60 s).
As expected, the worse performance is obtained when users
are more scattered and, to a lesser extent, with longer T.
15Another open issue is to speed up the solution search by experi-
menting with other heuristics or at implementation level (e.g. using
low-level programming language)
14](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-16-320.jpg)
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10 20 30 40 50 60 70 80 90 100
m 2
/U
60
65
70
75
80
85
90
95
100
time
that
constraints
are
satisfied
(%)
T = 15
T = 30
T = 45
T = 60
Figure 14: Effect of UAV relocation in problem constraints.
But since users call according to a traffic profile of
5 calls/hour, it would be interesting to observe the im-
pairment that drones relocation cause in these calls. To
this end, we define a call disruption event when a call in
progress does not satisfy the speech quality constraint for
two consecutive samples (i.e. 10 seconds). The percent-
age of calls that experience a service free of disruption is
shown in Figure 15. According to our results, after the 30
minutes of simulation almost 95% of calls have not been
affected by disruption events. As in the previous case, re-
sults show a small decrease for larger scenarios with more
scattered users and to a lesser extent with T.
10 20 30 40 50 60 70 80 90 100
m 2
/U
60
65
70
75
80
85
90
95
100
calls
without
interruptions
(%)
T = 15
T = 30
T = 45
T = 60
Figure 15: Effect of UAV relocation in calls in progress.
A final experiment was done launching one extra drone
(D + 1) in the initial deployment (i.e. forcing one extra
iteration in Algorithm 3). The results obtained in this
case were promising since the effect of UAV relocation was
unnoticed (i.e. constraints were met 100% of the time
and no call was interrupted). This suggest that launching
extra drones16
can be a effective method to avoid service
degradation during UAVs relocation.
8. Conclusions and further work
In this paper we dealt with the problem of optimal
placement of UAVs in order to provide VoWiFi service
16Although we used one extra drone, the optimal number will end
up depending on users density and terrain extension, which is also
left for further research.
with guaranteed QoS to a set of static users. We formu-
lated a optimization problem that minimizes the number
of drones required to provide such service and the ratio
of uncovered users. An algorithm to find solution through
exhaustive search was proposed, but due to the high com-
putational complexity, we also proposed efficient heuristics
as a general way to solve the optimization problem.
Numerical results suggest that large area scenarios with
highly disperse users (coverage-limited) will benefit from
IEEE 802.11 g/n standards, as less drones will be needed
to provide the service. However, in very small scenarios
with a highly dense crowd, the limiting factor will be QoS,
and less drones will be required by using IEEE 802.11 stan-
dards with higher bit rate.
The next step in our work is to include the energy of
the communication and the blocking probability as part
of the objective function in a combination customizable
by the designer. It is also left for further work the full
extension of this problem to ground users on the move
exploring relocation strategies and launching extra drones.
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Appendix A. Expected time per slot: E[T]
The expected time per slot represents the expected
length of each state of the Markov chain modeling the
IEEE 802.11 system. To obtain a closed-form expression
of E[T], we follow the approach presented in [35] (but
adapted to the terms and concepts defined in Section 4.2)
which considers the probability of being on each of the
following states:
• Idle state, when nobody attempts to transmit.
• Success state, when only a single station attempts to
transmit with no channel related errors.
• Error state, when a single station attempts to trans-
mit but channel errors occur.
• Collision state, when more than one station attempts
to transmit simultaneously (same slot).
E[T] can be obtained by weighting the time spent on
each of the previous states respectively as follows:
E[T] = TI + TS + TE + TC (A.1)
The factors in (A.1) can be calculated as follows:
• TI can be expressed as:
TI = PI σ (A.2)
where σ stands for the time slot duration as defined
in the corresponding IEEE 802.11 revision. PI is the
probability that the channel is idle in a randomly
chosen slot, which can be expressed as
PI =
S
Y
j=1
1 − τ(j)
(A.3)
where S is the number of stations in the system un-
der consideration . Let us define this set as S =
M ∪ AP. Then, S = |S| = |M| + 1.
• The time spent on successful (TS) and erroneous
(TE) slots can be expressed as:
TS =
S
X
j=1
P(j)
s (1 − FER(j)
) T(j)
s (A.4)
TE =
S
X
j=1
P(j)
s FER(j)
T(j)
e (A.5)
where T
(j)
s and T
(j)
e represent the average time that
station j spends in successful and erroneous trans-
missions, respectively. Their actual value depend on
the IEEE 802.11 standard revision used and physical
data rate of stations. They can be expressed as:
T(j)
s = DIFS + 2 · PLCP(j)
+
(Header(j)
+ Data(j)
)/R
(j)
b + SIFS + Tack + 2δ
(A.6)
T(j)
e = DIFS + PLCP(j)
+
(Header(j)
+ Data(j)
)/R
(j)
b + EIFS + δ
(A.7)
Where R
(j)
b represents the physical data rate (given
by the MCS used by the station), DIFS, SIFS, EIFS
are inter-frame periods as specified by the 802.11
standard and PLCP(j)
, Header(j)
and Tack correspond
with the PLCP header, the IEEE 802.11 header and
the duration of an ack frame in the IEEE 802.11
standard17
, and δ is the propagation delay.
In equations (A.4) and (A.5), P
(j)
s stands for the
probability that only an observed station j attempts
to transmit while the rest remain silent, which can
be expressed as:
P(j)
s = τ(j)
S
Y
k=1, k6=j
1 − τ(k)
(A.8)
• The time spent in collided transmissions TC can be
deduced as follows. Each station j exhibits an aver-
age collision time, T
(j)
c which can be can be approx-
imated by the time spent in a erroneous transmis-
sion T
(j)
e (i.e. T
(j)
c =T
(j)
e ). Nevertheless, when pack-
ets sent by two different station collide, the time to
be considered corresponds with the longest average
collision time. To address this concern, stations in
the system (i.e. set S) are grouped in traffic classes
according to their collision time (i.e. all stations with
the same average collision time belong to the same
class). Then, the following subsets of S can be de-
fined:
N(i)
i∈1..S
=
n
j ∈ S | T(j)
c = T(i)
c , j /
∈ N(k), k ≤ i
o
(A.9)
Where N(i) is a subset of S that includes those sta-
tions whose collision time is T
(i)
c (only if such sta-
tions are not yet in other group N(j) with j
17Note that in the AP station these times are averaged considering
the physical data rate and/or codec of every user in M
17](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-19-320.jpg)
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i). Notice that (A.9) defines multiple groups (e.g.
N(1), N(2), .., N(S)), and since each station can only
belong to one group (or class), some of the previous
classes may be empty sets. Therefore, let us define
a new set which can be used to identify non-empty
sets as:
E = {i | N(i) 6= ∅} (A.10)
The number of non-empty classes will be finally given
by Nc = |E|.
Considering N(d) as the set of stations that belong
to class d ∈ E, let us define L(d) as the set of sta-
tions whose collision time is longer than T
(d)
c (i.e.
their data bit rate is slower), and H(d) as the set
of stations whose collision time is shorter than T
(d)
c
(i.e. their data bit rate is faster). H(d) and L(d) can
be formally defined as:
L(d) =
n
i ∈ S | T(i)
c T(d)
c
o
(A.11)
H(d) =
n
i ∈ S | T(i)
c T(d)
c
o
(A.12)
Now the probability that at least one station that
belongs to class d ∈ E transmits is:
P
N (d)
tx = 1 −
Y
j∈N (d)
(1 − τ(j)
) (A.13)
And the probabilities that at least one station from
a higher or lower class transmits are:
P
H(d)
tx = 1 −
Y
j∈H(d)
1 − τ(j)
(A.14)
P
L(d)
tx = 1 −
Y
j∈L(d)
1 − τ(j)
(A.15)
Due to the fact that lower classes slow down higher
ones as a result of longer transmission times, TC can
be calculated as:
TC =
Nc
X
d=1
PN (d)
c + PH(d)
c
T(d)
c (A.16)
where T
(d)
c is the average time that any station from
class d spends on collision state, and P
N (d)
c repre-
sents the probability that any collision occurs be-
tween stations from the same class d:
PN (d)
c =
1 − P
H(d)
tx
·
1 − P
L(d)
tx
·
P
N (d)
tx −
X
j∈N (d)
P(j)
s
(A.17)
and P
H(d)
c accounts for the probability that class d is
involved in a collision with at least one station from
a higher class.
PH(d)
c = P
N (d)
tx · P
H(d)
tx ·
1 − P
L(d)
tx
(A.18)
Finally, substituting the expressions of TI, TS, TE, and
TC in (A.1), the closed-form expression of E[T] presented
in (A.19) is obtained .
Appendix B. Raw fitness criteria evaluation
Assessing raw fitness scores entails solving both signal
coverage (e.g. RSSI and SNR) and the analytical models
to estimate QoS. This appendix provides a pseudocode in
Algorithm 4 that can be used as a guidance for implemen-
tation and also to estimate the computational complexity
of this step.
The algorithm can be divided in the following parts:
• Lines 1-6: RSSI and SNR are calculated for each pair
ground user-drone.
• Lines 7-15: Each ground user station is associated
to a specific drone, creating C(i).
• Lines 19-24: The maximum number of concurrent
calls CCmax is calculated for each drone k, which
depends on the blocking probability constraint Bmax.
• Lines 25: The set of stations S = M∪AP, is created
selecting the CCmax slowest ground users stations
and the AP.
• Lines 26-42: The non-linear equation system is solved
iteratively, the output is the estimation of the MOS
experienced by users associated to drone k.
18](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-20-320.jpg)
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E[T] = σ ·
S
Y
j=1
1 − τ(j)
| {z }
TI ,
+
S
X
j=1
τ(j)
S
Y
k=1, k6=j
(1 − τ(k)
)
(1 − FER(j)
) T(j)
s
| {z }
TS
+
S
X
j=1
τ(j)
S
Y
k=1, k6=j
(1 − τ(k)
)
FER(j)
T(j)
e
| {z }
TE
+
Nc
X
d=1
Y
j∈H(d)
1 − τ(j)
Y
j∈L(d)
1 − τ(j)
1 −
Y
j∈N (d)
1 − τ(j)
−
X
j∈N (d)
τ(j)
S
Y
k=1, k6=j
(1 − τ(k)
)
· T(d)
c
| {z }
TC
+
Nc
X
d=1
1 −
Y
j∈N (d)
(1 − τ(j)
)
1 −
Y
j∈H(d)
1 − τ(j)
1 −
1 −
Y
j∈L(d)
1 − τ(j)
· T(d)
c
| {z }
TC (continued)
(A.19)
19](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-21-320.jpg)
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Input: U = {1, . . . , U}, D = {1, . . . , D},
{wi | i ∈ U}, {xk | k ∈ D}
Initialization: ffitness = D + 2
Output: ffitness
1 for i = 1 to U do
2 for j = 1 to D do
3 calculate RSSIi,j; // Eq. (5)
4 calculate SNRi,j; // Eq. (7)
5 end
6 end
7 for i = 1 to U do
8 for k = 1 to D do
9 if RSSIi,k ≥ RSSImin and
SNRi,k ≥ SNRmin then
10 if RSSIi,k RSSIi,j, ∀j 6= k then
11 C(k) = C(k) ∪ i;
12 end
13 end
14 end
15 end
16 if
PD
i=1 |C(i)|/U ≥ Cmin then
17 for k = 1 to D do
18 calculate CCmax; // Algorithm 2
19 build set S = M ∪ AP;
20 for j = 1 to |S| do
21 calculate T
(j)
s , T
(j)
c , T
(j)
e ;
22 calculate FER(j)
; // Eq. (17)
23 end
24 τ
(j)
next = T
(j)
c , ∀j;
25 while diff ∆ do
26 τ(j)
= τ
(j)
next;
27 calculate E[T]; // Appendix Appendix
A
28 for j = 1 to |S| do
29 calculate E[B(j)
]; // Eq. (13)
30 calculate r(j)
, q(j)
;
// Eqs. (11),(12)
31 calculate p(j)
; // Eq. (15)
32 calculate τ
(j)
next; // Eq. (10)
33 end
34 diff = max
|τ
(j)
next − τ(j)
|
, ∀j;
35 end
36 calculate MOS(k); // Eq. (25)
37 end
38 if MOS(k) ≥ MOSmin, ∀k ∈ {1, . . . , D} then
39 ffitness = D +
1 −
PD
k=1 |C(k)|/U
;
40 else
41 ffitness = D + 1 +
1 −
PD
k=1 |C(k)| [MOS(k) MOSmin] /U
;
42 end
43 end
Algorithm 4: Fitness function evaluation
20](https://image.slidesharecdn.com/1-s2-221207150621-d503e26c/85/Deployment-of-UAV-mounted-Access-Points-for-VoWiFi-Service-with-guaranteed-QoS-22-320.jpg)
Deployment of UAV-mounted Access Points for VoWiFi Service with guaranteed QoS
- 1. See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/361595878 Deployment of UAV-mounted Access Points for VoWiFi Service with guaranteed QoS Article in Computer Communications · June 2022 DOI: 10.1016/j.comcom.2022.06.037 CITATIONS 0 READS 41 4 authors: Some of the authors of this publication are also working on these related projects: Rafa Estepa View project Vicente Mayor 7 PUBLICATIONS 42 CITATIONS SEE PROFILE Rafael Estepa Universidad de Sevilla 47 PUBLICATIONS 236 CITATIONS SEE PROFILE Antonio Estepa Universidad de Sevilla 45 PUBLICATIONS 341 CITATIONS SEE PROFILE Germán Madinabeitia Universidad de Sevilla 30 PUBLICATIONS 114 CITATIONS SEE PROFILE All content following this page was uploaded by Rafael Estepa on 04 July 2022. The user has requested enhancement of the downloaded file.
- 2. Journal Pre-proof Deployment of UAV-mounted Access Points for VoWiFi Service with guaranteed QoS Vicente Mayor, Rafael Estepa, Antonio Estepa, Germán Madinabeitia PII: S0140-3664(22)00239-0 DOI: https://doi.org/10.1016/j.comcom.2022.06.037 Reference: COMCOM 7183 To appear in: Computer Communications Received date : 4 March 2019 Revised date : 16 July 2019 Accepted date : 22 June 2022 Please cite this article as: V. Mayor, R. Estepa, A. Estepa et al., Deployment of UAV-mounted Access Points for VoWiFi Service with guaranteed QoS, Computer Communications (2022), doi: https://doi.org/10.1016/j.comcom.2022.06.037. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
- 3. J o u r n a l P r e - p r o o f Journal Pre-proof Deployment of UAV-mounted Access Points for VoWiFi Service with guaranteed QoS Vicente Mayor, Rafael Estepa, Antonio Estepa, and Germán Madinabeitia Departament of Telematics Engineering, Universidad de Sevilla. Abstract Unmanned Aerial Vehicle (UAV) networks have emerged as a promising means to provide wireless coverage in open geographical areas. Nevertheless, in wireless networks such as WiFi, signal coverage alone is not sufficient to guarantee that network performance meets the quality of service (QoS) requirements of real-time communication services, as it also depends on the traffic load produced by ground users sharing the medium access. We formulate a new problem for UAVs optimal deployment in which the QoS level is guaranteed for real-time voice over WiFi (VoWiFi) communications. More specifically, our goal is to dispatch the minimum number of UAVs possible to provide VoWiFi service to a set of ground users subject to coverage and QoS constraints. Optimal solutions are found using well-known heuristics that include K-means clusterization and genetic algorithms. Via numerical results, we show that the WiFi standard revision (e.g. IEEE 802.11a/b/g/n/ac) in use plays an important role on both coverage and QoS performance and hence, on the number of UAVs required to provide the service. Keywords: Unmanned aerial vehicle (UAV), Wireless LAN, Voice over IP (VoIP), Quality of Service (QoS). 1. Introduction The past decade has seen tremendous growth in the use of unmanned aerial vehicles (UAVs). UAVs or so- called drones have attracted significant interest for numer- ous applications in the context of smart cities, collection and dissemination of information, search and rescue, or agriculture, just to name a few[1]. There is increasingly more research focused on the de- ployment of UAVs for providing fast and temporal wire- less communication infrastructure [2, 3]. A typical UAVs- assisted communication example is the provision of reliable connectivity between clustered non-directly communicated users [4] (UAV-aided communication relays). Other appli- cations include the deployment of quasi-stationary UAV- mounted base stations to create a communication service, deploying emergency infrastructure in disaster scenarios [5, 6, 7], reaching remote areas that cannot be serviced otherwise [8], or offloading existing base stations [9]. In the aforementioned applications, optimal drone location prob- lems typically minimize the number of drones deployed (i.e. cost) to provide coverage to a set of ground users in known positions [10]. UAV optimal deployment problems generally assume that coverage (i.e. received signal strength) suffices for the ?Corresponding author. Tel.: +34 954487384. Address: C/ Camino de los descubrimiento s/n. 41092 Seville (Spain). E-mail ad- dresses: {vmayor,rafa, aestepa, german}@trajano.us.es (Mayor V., Estepa R., Estepa A., Madinabeitia G.). provision of communication services [11]. Nevertheless, al- though this may hold for cellular networks (which includes mechanisms to deal with congestion and QoS), the ability of WiFi networks to guarantee QoS does not depends only on coverage, but also on the traffic load generated by those stations sharing the channel. Therefore, despite available QoS mechanisms [12], a congested WiFi network may be unable to meet the strict QoS requirements of interactive real-time services such as VoIP [13] [14, 15, 16]. Unfortu- nately, this fact is typically ignored in studies of UAV-AP link performance[17, 18]. It is proven that there is an upper bound in the number of voip traffic flows that an AP can handle with acceptable performance, namely voip capacity [19]. As the authors in[13] put it, above this upper bound, “One more VoIP connection will jeopardize the performance of all voice con- nections”. The voip capacity of an AP can be studied through a model of the Medium Access Control (MAC) sub-layer [19] which let us estimate the impact of voip traffic in delay or packet loss [20, 21]. Applying the find- ings from this research field to the problem of UAVs opti- mal positioning would allow one to consider the maximum number of simultaneous calls that each UAV-mounted AP can take (i.e. voip capacity) to guarantee QoS require- ments. Furthermore, voip capacity should also consider statistical multiplexing in the service demand since it is unlikely that all users associated to an AP use the voip service concurrently. However, all this has been overlooked in existing UAVs optimal location problems [22, 23] In this work, we define and solve a new optimization Preprint submitted to Elsevier June 26, 2022
- 4. J o u r n a l P r e - p r o o f Journal Pre-proof UAV-to-Gateway (distribution network) VoIP Gateway Internet / PSTN IEEE 802.11 (access network) Figure 1: Example scenario for VoWiFi. problem that consists of finding the minimum number of UAV-mounted APs that should be launched to provide VoIP service with guaranteed QoS to a set of known users in a scenario that lacks of alternative cellular or WiFi in- frastructure on ground (see Figure 11 ). More specifically, our problem provides the minimum number of UAVs to be deployed and their optimal location so that voip capacity of any deployed AP is equal or greater than the number of users associated to that AP who are expected to be simultaneously talking. Most handheld devices (e.g. smartphones, tables) have WiFi. As such, deploying a temporary solution for voice service can be of potential interest in situations where users a expected to be confined in known areas such as meeting points during search and rescue missions (e.g. dis- aster scenario), for broadcast announcements, or voice ser- vice during outdoor activities or missions in remote areas that lack alternative communication infrastructure. In- deed, in these contexts, a common VoIP application could be downloaded by users from the UAV-deployed WiFi data access network. We also provide a preliminar analysis of the applicability of our problem where user mobility is considered. The contributions and originality of this paper are: • We mathematically formulate a new optimal drone location problem that takes into account the speech quality perceived by ground users. • We provide a mathematical model to predict speech quality for a set of heterogeneous VoIP traffic sources, and for different IEEE 802.11 standard amendments. 1Observe that the performance of the WiFi access network (see Figure 1) is assumed to be critical for the feasibility of the QoS- guaranteed service while UAV-to-UAV, or UAV-to-Infrastructure ei- ther do not significantly impair QoS, or its impact can be added to our model as a constant extra delay and/or loss. Therefore, the scope of this paper is restricted to the IEEE 802.11 access network to be deployed • We propose a service model that takes advantage of statistical multiplexing of users’s calls, providing efficient use of resources. 2. QoS in VoIP over WiFi networks. As indicated in ITU-R rec. M.1079, each communi- cation service requires specific ranges of end-to-end delay, loss and jitter to be met, and VoIP is no exception. In our view, planning a VoIP service over IEEE 802.11 networks requires to take into account two key aspects: 1. The speech quality of the VoIP service, defined by the ITU-T rec. P.800 [24], which is measured through surveys that rate a mean opinion score (MOS) rang- ing from 1 (poor) to 5 (excellent). 2. The probability that a user is unable to place a new call as a result of the exhaustion of the resources of the (WiFi) network. This is also known as call- blocking probability in the field of teletraffic. According to ITU-T G.107, acceptable conversations should exhibit MOS > 3.5, but in general, if the network fails to underpin a minimum level MOSmin, the service simply can not be provided[25]. At the planning stage, a method for MOS prediction is needed. In VoIP, the most extended method is the E- Model [26, 27], which combines additive impairments fac- tors to measure speech quality R factor, ranging from 0 (poor) to 100 (excellent), that can be directly mapped to MOS [28]. As Assem et al [29] put it, the E-Model is “a repeatable way to assess if a network is prepared to carry a VoIP call or not”. In its simplest form, the E-model can be expressed as [30]: R = 94.2 − Id − Ie−eff (1) where for now, it suffices to know that Id represents all impairments due to delay, and Ie−eff is a factor that ac- counts for the impairments caused by low bit-rate cod- ing and packet loss [31]. Both, delay and packet loss are certainly affected by the performance of the IEEE 802.11 access network. Figure 2 illustrates a system composed of a set of IEEE 802.11 stations associated to one UAV-mounted AP. Each station is represented by its physical layer and its medium access control (MAC) sub-layer. While all stations share a common MAC protocol, each one auto-configures its Mod- ulation and Coding Schema (MCS) according to the Re- ceived Signal Strength Indicator (RSSI) from the AP and a set of thresholds (i.e. minimum input sensitivity) de- fined by the IEEE 802.11 standard in use [32]. An exam- ple of different MCSs defined for OFDM modulations (e.g. IEEE 802.11a/g) is shown in Table 1. Thus, each user ter- minal is assumed to auto-configure its MCS to the greatest bit-rate possible depending on the received signal power. In VoWiFi, speech quality is strongly influenced by the delay and loss of the downlink (i.e. from the access point 2
- 5. J o u r n a l P r e - p r o o f Journal Pre-proof Noisy Radio Channel IEEE 802.11 MAC IEEE 802.11 PHY IEEE 802.11 MAC IEEE 802.11 PHY IEEE 802.11 MAC IEEE 802.11 PHY IEEE 802.11 MAC IEEE 802.11 PHY U1-VoIP App U2-VoIP App UN-VoIP App U1-VoIP packets U2-VoIP packets UN-VoIP packets MCS1 MCS2 MCSN Figure 2: UAV-AP: IEEE 802.11 system under consideration Modulation Coding rate Data rate Sensitivity (Mb/s) (dBm) BPSK 1/2 6 -82 BPSK 3/4 9 -81 QPSK 1/2 12 -79 QPSK 3/4 18 -77 16-QAM 1/2 24 -74 16-QAM 3/4 36 -70 64-QAM 2/3 48 -66 64-QAM 3/4 54 -65 Table 1: 802.11 sensitivity relations for OFDM modulations with 20 MHz channels. (AP) to VoIP terminals)[16]. Both factors depend on the traffic load, which in turn depends on the speech codec and the number and data bit-rate of users engaged on ac- tive calls at a given moment2 . WiFi analytical models let us capture the relation between the VoIP traffic volume handled by an AP and the delay and loss that such traffic will experience. There is a plethora of analytical models of the IEEE 802.11 MAC behaviour [33, 34, 35, 36]. In most models, the central variable is the probability that an ob- served station attempts to transmit in a random time slot (τ). However, different models apply different assumptions to derive their analytical expression for τ. In this paper, the following assumptions are considered: • Heterogeneous traffic sources (two users may have different physical data bitrate according to their RSSI). • Non-saturated stations (sometimes there may be no packets to be transmitted). • Noisy channel (channel noise can corrupt packets). But above analytical models, intuition suggests that VoIP traffic increases with every new call, which in turn 2This assumes that either only VoIP traffic exists, or that VoIP traffic is prioritized using IEEE 802.11e. impacts on network delay and loss, deteriorating the QoS of ongoing calls. As a result of the previous consideration, a VoWiFi service with guaranteed QoS should not accept a new call when this implies that calls in progress may turn unacceptable (i.e. MOS < MOSmin). This is known as Call Admission Control (CAC) function, typically imple- mented either at the AP (as indicated in IEEE 802.11e), or at the application level (e.g. VoIP gateway). Obviously, this function requires to assess the maximum number of concurrent calls that an AP can take so that the quality experienced by active users is above MOSmin. This upper bound is the voip capacity of an AP and will be denoted by CCmax from now on. For example, in [16] it was found that a maximum of 15 calls for 64kb/s CBR VoIP traffic, or 38 calls for VBR VoIP traffic, can be held for IEEE 802.11b. This leads us to the second factor deemed as key for di- mensioning: the call-blocking probability, or, equivalently, the probability that a new call is rejected as a result of CCmax calls being already in progress. It is possible to find such a probability if one takes a statistical model of the user behaviour from the field of teletraffic. Assuming that call attempts and calls duration follow exponential distri- butions, the call-blocking probability for the users served by an AP is given by the classical Engset formula [37]: B(A, u, cc) = u−1 cc Acc Pcc i=0 u−1 i Ai (2) where A stands for the traffic intensity (product of average frequency and duration of calls), u is the number of users associated to the access point, and cc is the number of concurrent calls. Then, provisioning VoWiFi with guaranteed QoS will require that the following constraints are met: • Speech quality level (MOS) higher than MOSmin. • Call-blocking probability lower than Bmax =B(A, u,CCmax). which will be regarded as VoWiFi service QoS constraints in the problem to be defined next. 3. Problem statement In the scenario illustrated in Figure 1, we want to de- ploy a set of drones to create a WiFi access network that enables the VoWiFi service with guaranteed QoS. To make the problem more tractable, the following assumptions are made: • The position of ground targets (i.e. users confined in a known area) is known. User terminals run a VoIP app which utilizes a known codec and standard signaling. • If a ground terminal could associate to more than one AP, the one with maximum received power will be selected. 3
- 6. J o u r n a l P r e - p r o o f Journal Pre-proof • Channelization between adjacent APs is done in such a manner that interferences are negligible. • A CAC mechanism is in place to limit the maximum number of concurrent calls at each AP. 3.1. Terminology We discretize the flying zone as illustrated in Figure 15. The set P represents the set of R3 coordinates of each edge of the grid (i.e. potential locations of UAVs). The follow- ing terms and definitions will be used for the remainder of this paper: Figure 3: Grid edges in a deployment scenario. • Users are denoted by the set U = {1, 2, ..., U} and at known locations given by {wk|k ∈ U}, where wk∈ R3 represents the 3D coordinates of user k. • Drones are denoted by the set D = {1, 2, ..., D} and at known locations given by the set X = {x1, x2, .., xD|xi ∈ P, i ∈ D, xi 6= xj|∀j6=i}, where xi∈ P represents the 3D coordinates of dron i. • C(i) ⊂ U represents the set of users associated to the access point at drone i ∈ D. • The number of ground users associated to the WiFi network is C = PD i=1 |C(i)| . • B(i) represents the call-blocking probability for users associated to the access point at drone i ∈ D. • MOS(i) represents the speech quality level for users associated to the access point at drone i ∈ D. Figure 2, illustrates a scenario with 12 users (U = 12) and two drones (D = 2). The UAVs flying space has been discretized using a grid P with 30 edges. The set D = {1, 2} is composed by the leftmost drone (located at x1 ∈ P) and the rightmost drone (at x2 ∈ P). Then, C(1) and C(2) would be composed of the set of users associated to drones 1 and 2 respectively, and the ratio of users as- sociated to the WiFi network would be P2 i=1 |C(i)|/U = 11/12. 3.2. Problem definition Our goal is to minimize the number of drones deployed. Among solutions with the same number of drones, we chose the one that minimizes the ratio of uncovered users (i.e. terminals not associated to the WiFi network). This can be formulated as follows: min X D + 1 − D X i=1 |C(i)|/U ! subject to D X i=1 |C(i)|/U ≥ Cmin B(i) ≤ Bmax , ∀i ∈ D MOS(i) ≥ MOSmin , ∀i ∈ D xi ∈ P , ∀i ∈ D D ≤ Dmax (3) where D represents the cardinality of D (which is bounded by Dmax), and (1 − PD i=1 |C(i)|/U) is the ratio of ground users uncovered. Constants Cmin, Bmax, MOSmin are thresh- olds for their respective constraints. According to ITU-T G.107 recommendation, an acceptable call should exhibit a MOS ∼ 3.5. But one could decide to raise that lower bound to provide a higher quality service. This would im- pact on the number of drones deployed (e.g. more UAVs may be necessary to provide the voice service as the voip capacity of APs is decreased). Finally, observe that the objective function is com- posed of an integer (i.e. number of UAVs, D ≥ 1), and a decimal (the ratio of uncovered users 1). Thus, its integer part indicates the minimum number of UAVs that meet all constraints. 4. Finding solutions with exhaustive search The exhaustive search approach involves assesing (3) for all possible UAV(s) positioning within the grid (P) for an incremental number of drones until the optimal solu- tion is found (or a maximum number of UAVs Dmax is reached). This procedure is described in Algorithm 1. It takes as input the set of ground users U and their loca- tion, the set of edges P, Dmax, and the coverage and QoS constraints. For an incremental number of drones (D), all possible combination of UAVs locations are checked. The algorithm starts by estimating the set of users associated to the WiFi network given by D drones located at X. If the first constraint (i.e. coverage) is met, then QoS constraints are assessed (considering the worst case among all UAVs). If both constraints are met, a potential solution is found 4
- 7. J o u r n a l P r e - p r o o f Journal Pre-proof and the objective function is evaluated. Among potential solutions with the same value of D, the one with the low- est objective function is selected. The algorithm ends after finding the optimal solution, or after trying unsuccessfully with Dmax drones. The output of the algorithm is the set of optimal UAVs locations and the value of the objective function. A null location indicates that no solution has been found. Input: U, {wk}, Dmax, Cmin, Bmax, MOSmin Output: L (location), ofmin (obj. function) Initialization: D = 1, L = ∅, ofmin = Dmax + 1 1 while L = ∅ or D ≤ Dmax do 2 D++; // Increase number of UAVs 3 foreach possible value of X do 4 for j = 1 to D do 5 C(j) = associate(U, {wk}, X); 6 end /* check first constraint */ 7 if PD i=1 |C(i)|/U ≥ Cmin then 8 for j = 1 to D do 9 MOS(j) = QoS.eval(C(j), xj, {wk}, Bmax); 10 end 11 MOS = min k=1..D {MOS(k)}; 12 if MOS ≥ MOSmin then /* QoS constraints met */ 13 of = D + (1 − PD i=1 |C(i)|/U); 14 if of ofmin then 15 ofmin = of; // solution 16 L = X; // UAVs position 17 end 18 end 19 end 20 end 21 end Algorithm 1: Exhaustive search pseudocode Next, we elaborate on the functions used for the assess- ment of signal coverage and quality of service constraints. 4.1. Signal Coverage Evaluation: associate() A ground terminal associates to an AP if its Signal to Noise Ratio (SNR) and Received Signal Strength Indica- tion (RSSI) are above minimum levels to properly demod- ulate the received signal. In addition, if several APs were available (e.g. D 1), each user will be associated to the AP with maximum received power. The UAV-to-ground path loss should generally consider a combination of Line-of-Sight (LoS) and NLoS compo- nents whose probability depend on the drone altitude and ground terminal surroundings [38]. We adopt the model presented in [39] (also used in [4]). According to such model, the probability that a ground user has a LoS link with the AP installed at a drone is: PLoS(θ) = 1 1 + a1e−b1θ·180/π+b1a1 (4) where θ is the elevation angle in degrees (between user and drone), a1 and b1 are environment dependent constants (e.g. rural, urban, etc.). Then, for user i located at wi and the AP installed at drone j located at xj, RSSIij is given by: RSSIij =PT X + Gij − 20 log10 4πf · kwi − xjk c − PLoS(θij) · ηLoS − (1 − PLoS(θij)) · ηNLoS (5) Gij = 10 log10(10Gmax/20 · cos2 θij) (6) where PT X (dBm) stands for the power delivered by the transmitter antennas; Gij stands for the gain of the antenna between user i and UAV j as indicated in (6); kwi − xjk is the Euclidean distance between user i and drone j;f (hertz) is the channel frequency; c(m/s) is the speed of light; θij (radians) accounts for the elevation angle between user’s position wi and UAV’s position xj; ηLoS(in dB) and ηNLoS (in dB) are losses corresponding to LoS and NLoS connections which depend on the environment (a list of values can be found in [40]). Finally, constant Gmax in(6) indicates the maximum power. Given RSSIij, the Signal to Noise Ratio (SNRij)(dB) can be readily obtained by subtracting the receiver’s noise figure (NF) and thermal noise (N) as indicated in (7) and (8). SNRij = RSSIij − NF − N (7) N = −174 + 10 log10(CBW ) (8) where CBW stands for signal bandwidth as specified by the IEEE 802.11 standard in use. For all i ∈ U and for all j ∈ D, let us define γij as a boolean variable that indicates whether user i satisfies minimum thresholds (i.e. SNRij ≥ SNRmin and RSSIij ≥ RSSImin) with respect to UAV j or not. Then, the function associate() returns the set of users that meet minimum thresholds and whose RSSI with drone j is greater than with any other drone: C(j) = {i ∈ U | γik = 1, RSSIij RSSIik ∀k 6= j} (9) Recall from previous section that each ground user’s ter- minal i sets its Modulation and Coding Scheme MCS(i) according to its RSSI(i) = max j=1..D {RSSIij} (see (5)), which determines the data bit rate of the terminal. 4.2. VoWiFi service QoS evaluation: QoS.eval() This function checks on VoWiFi service QoS constraints described in Section 2 by following these two broad steps: 5
- 8. J o u r n a l P r e - p r o o f Journal Pre-proof Figure 4: for QoS assessment. 1. Find out how many users in C(j) can simultaneously talk so that the call-blocking probability Bmax is not exceeded (i.e. find CCmax). This can be readily done by increasing the number of concurrent calls in (2) as indicated in Algorithm 2. Input: |C(j)| (set of users associated), A, Bmax Output: CCmax (maximum concurrent calls) 1 for cc = 1 to |C(j)| do 2 if B(A, |C(j)|, cc) ≤ Bmax then // Eq. (2) 3 CCmax = cc; 4 cc++; 5 end 6 end Algorithm 2: Finding CCmax within an AP 2. Estimate the MOS: Let M ⊂ C(j) be the subset composed of the CCmax stations with the lowest data bit rate in C(j). Stations in M are expected to exhibit greater transmission/reception delay than the rest and consequently, are regarded to be “worst case” in terms of QoS. First, an analytical model of the IEEE 802.11 mac sub-layer is applied to the sys- tem composed of the set of stations M plus its AP to estimate the delay and packet loss experienced by VoIP traffic. Then, the E-model is used to finally obtain speech quality level MOS. This is illustrated in Figure 4. Next we elaborate on steps (a) and (b). Delay and packet loss estimation. The set of stations in M and its AP constitute a IEEE 802.11 system whose performance has been largely studied in scientific litera- ture [41, 42, 43, 44]. We have used a mix of different analytical models from [33, 34, 35, 36] fitted for the follow- ing assumptions: stations can have different bit rates (i.e. heterogeneous traffic sources), stations are not-saturated3 , 3When the channel is idle a station may have no packets to trans- mit. and the channel is noisy. Due to the complexity of the subject, and for the sake of clarity, we keep this section as simple as possible. The reader is encouraged to read more elaborated information in the corresponding refer- ences and Appendix A. The Distributed Coordination Function (DCF) of the 802.11 MAC sub-layer use CSMA/CA (Carrier Sense Mul- tiple Access with Collision Avoidance) for medium access control. Basically, each contending station must sense the medium during a period of time in order to ensure that it is idle before transmission. If the channel is busy, the sta- tion waits a random backoff interval before trying again. The backoff process is based on the Binary Exponential algorithm. Time is discretized and the algorithm picks a random number of time slots between 0 and 2i Wo, where Wo accounts for the minimum contention window value, and i increases by one in each failed attempt up to a ceil- ing m. After a maximum number of retransmissions is reached (M), the packet is discarded. Most analytical models based on Markov chains lay on a central variable termed τ which represents the prob- ability that an observed station attempts to transmit in a randomly chosen time slot. In this paper we used the expression in [33]: τ = 1 η 1 1 − q r2 Wo (1 − p)(1 − (1 − r)Wo − qr(1 − p) (10) where η is defined in (14), q is the probability of having at least one packet queued at the transmission buffer, p is the probability that a packet suffers any transmission errors, and r is the probability that at least one packet arrives during an idle state (load factor). Assuming non- saturated stations and Poisson packet arrivals (with rate λ) to the transmission queue, r and q can be expressed as: r = 1 − e−λE[T ] (11) q = 1 − e−λE[T ]E[B] (12) where E[T] represents the expected average slot duration, and E[B] is expected average number of back-off slots that a packet waits before transmission. Due to its complexity, a closed-form of E[T] is deduced in Appendix A (Equa- tion (A.19)). E[B] can however, be expressed as in [36]: E[B] = Wo 2(1 − p) 1 − p − (2p)m (1 − 2p) − 2m pM+1 (13) Let τ(i) , r(i) , q(i) , E[B(i) ] and λ(i) denote τ, r, q, E[B] and λ of station i in the system under consideration (i.e. the subset M and its AP such as illustrated in Figure 2), where i refers to either one user station {1, 2, ..|M|}, or the AP (i = |M| + 1 = AP). Let p(i) be the probability of packet transmission error p for station i. Then, p(i) can be broken down as: 6
- 9. J o u r n a l P r e - p r o o f Journal Pre-proof η = (1 − r) + r2 Wo(Wo + 1) 2(1 − (1 − r)Wo ) + Wo + 1 2(1 − q) r2 qWo 1 − (1 − r)Wo + rp(1 − q) − rq(1 − p)2 + p 2(1 − q)(1 − p) r2 Wo 1 − (1 − r)Wo + qr(1 − p)2 2Wo 1 − p − p(2p)m−1 1 − 2p + 1 (14) p(i) = 1 − P (i) i ∪ FER(i) = 1 − P (i) i + FER(i) − 1 − P (i) i · FER(i) (15) where P (i) i accounts for the probability that the j-th sta- tion finds the channel idle and FER(i) stands for the Frame Error Rate due to channel noise. The probability of finding the channel idle, can be further expressed as: P (i) i = S Y j=1, i6=j 1 − τ(j) (16) Assuming that frames have a constant size of L bits (L = preamble + header + data), it is possible to obtain the FER of station i as: FER(i) = 1 − (1 − P(i) e )L (17) where P(i) e represents the codec bit error rate of station i, which can be readily calculated4 if one knows user’s modulation (i.e. MCS(i) ). Finally, solving the non-linear equation system, the packet loss of station i can be expressed as: PL(i) = 1 − 1 − FER(i) τ(i) Q|M|+1 j=1,j6=i 1 − τ(j) λ(i) E[T] (18) Since we assume a very small buffer size, the queueing delay can be neglected and the only delay component will be the channel access delay. Then, the delay of station i can be expressed as: DEL(i) = E[B(i) ] E[T] (19) As justified in [16], the AP5 (i = AP) is the most saturated station, leading the packet loss and delay in the system. Thus, we can take its packet loss and delay as representative of the worst case. Then, the output of this step is: PL = PL(AP ) (20) DEL = DEL(AP ) (21) 4See equations in [45] and [46] for DSS and OFDM modulations respectively. 5Observe that the AP is also part of the system and its MCS and FER change dynamically according to its communication partner. Our approach is to consider average values of its data bit-rate and FER. MOS estimation.. As stated in Section 2, the E-Model rates the conversation quality R factor, which can be cal- culated using (1) [29], whose terms were: • Ie,eff is the effective impairment equipment param- eter. It is a combination between impairment equip- ment parameter at zero packet loss (Ie), and a func- tion of Ie that is dependent on packet loss rate and packet loss behaviour. It can be expressed as: Ie,eff = Ie + (95 − Ie) Ppl Ppl BurstR + Bpl (22) where Ie is a codec-dependent constant associated with codec compression degradation6 , Ppl represents the packet loss rate, BurstR accounts for the burst ratio (i.e. equals 1 if packet loss if random and greater otherwise), Bpl represents the codec packet loss robustness, which also has a specific value for each codec (listed in ITU-T Rec. G117 Appendix I). • Id accounts for all impairments due to delay of com- munication chain. A widely accepted approximation for Id can be obtained from one-way delay in com- munication path (d) as follows: Id = 0.024d + 0.11(d − 177.3)H(d − 177.3), (23) where H is the heavyside function (i.e. H(x) = 0 for x 0 and H(x) = 1 for x 0). This shows that the effect of one-way delays under 100 ms can be discarded. In this paper we will use the G.711 codec (Ie = 0), with BurstR = 1 and Bpl = 25, 1. So, assuming that Ppl = PL (from (20)), and d = DEL (from (21)) + 20 ms (from the VoIP codec packetization), R can be expressed7 as: R = 93.72 − 95 PL PL + 25, 1 − (0.024DEL + 0.11(DEL − 157.3)H(DEL − 157.3)) (24) 6A list of values from ITU-T codecs were presented in ITUT-T Rec. G.113 Appendix I. 7The 20 ms of packetization delay has been taken into account in the expression provided. 7
- 10. J o u r n a l P r e - p r o o f Journal Pre-proof 0 2 10 100 20 z (m) 90 80 100 70 90 80 60 y (m) 70 50 60 1 x (m) 40 50 30 40 30 20 20 10 10 0 0 Drone Associated users Non covered users Figure 5: Example solution (D = 2). Finally, to obtain speech quality, the R factor can be mapped to MOS [27] as: MOS = 1, R 6.5 1 + 0.035 R + 7 · 10−6 R · (R − 60) (100 − R), 6.5 ≤ R ≤ 100 4.5, R 100 (25) 4.3. Example solution This section introduces a first example of the results obtained after implementing Algorithm 1 in Matlab® . The scenario includes 25 ground users randomly distributed within an area of 100 m×100 m. The parameters used in the example are listed in Table 3. Unless otherwise spec- ified, such parameters are common to all experiments in this paper. Figure 5 provides a graphical representation of the so- lution obtained, showing by color users distribution among UAVs. In this case, two drones were necessary to cover 24 out of 25 users8 (i.e. (|C(1)| + |C(2)|) /U = 0.96 Cmin) using the IEEE 802.11n standard revision. The solution represented in Fig. 5 has been simulated with the network simulator ns-3 in order to validate the IEEE 802.11 analytical model from Section 4.2. The ns-3 model YansWifiPhy with a transmission buffer size of one packet has been used. The simulation has been repeated 30 times with different seeds and the results presented rep- resent the average value with a 95% confidence interval. Table 2 summarizes the results obtained, comparing delay, packet loss and MOS from our analytical models with those obtained with ns-3. It can be observed no sig- nificant differences between the output of the analytical models used and simulation results, particularly in terms of predicted speech QoS. Note that delay is very small in absolute terms, always under 1 ms as a result of a very small buffer. The comparison of the MOS obtained with our analytical models versus simulation suggests that the method and models proposed in Section 4.2 are accurate enough. 8Some ground terminals almost entirely overlap in the figure as they were generated randomly. Note that the X-Y discretization step in our example was only 1m (which we consider the minimum safe for col- lision avoidance), while Z step was 5m. In general, the smaller grid steps the more accurate the solution will be (i.e. closer to the optimal that would be found without discretizing the flying space) but the more edges in P will have to be assessed, increasing the computational load. In general, PD d=1 |P| d possibilities will have to be assessed when D drones are being evaluated. For example, the grid defined in our example has |P| = 2 · 104 edges, thus ' 2·108 possible combinations of UAV locations have been assessed. This fact suggests that exhaustive search may be feasible only in very small scenarios since its computa- tional complexity grows exponentially with D. For that reason, heuristic search methods are commonly preferred as a general way to find (semi) optimal solutions. 5. Heuristic Solution A number of different metaheuristics can be used to find (semi)optimal solutions. These include genetic al- gorithms (GAs), particle swarms optimization, artificial immune system, and simulated annealing. Furthermore, other approaches such as optimal transport theory have been also successfully applied to solve user-drone associa- tion in similar scenarios Our heuristic search method can be viewed as a re- placement of lines 3-20 in Algorithm1 for a function call (GAsearch) that returns the (semi)optimal solution found for a specific number of drones D as shown in Algorithm3. Input: U, {wk}, Dmax, Cmin, Bmax, MOSmin Output: L (location), ofmin (obj. function) Initialization: D = 0, L = ∅, ofmin = Dmax + 1 1 while (L = ∅ or D ≤ Dmax) do 2 D + +; 3 L,of =GAsearch(D,{wk},Bmax,Cmin,MOSmin) 4 end Algorithm 3: Use of the heuristic search method We have designed the genetic algorithm GAsearch() using the Matlab® R2017A Global Optimization Tool- box [47]. Next we elaborate on the GA developed. 5.1. Individuals An individual is a possible solution to the problem. As such, each individual is a location of D drones X = {x1, x2, .., xD|xi ∈ P, i ∈ D, xi 6= xj|∀j6=i}, where xi ∈ P represents the 3D coordinates of drone i. For instance, an individual composed of two drones {x1, x2} is given by the sequence of genes {x1, y1, z1, x2, y2, z2}. 5.2. Algorithm steps The algorithm performs the following steps: 8
- 11. J o u r n a l P r e - p r o o f Journal Pre-proof Drone xi C(i) B(i) Algorithm 1 / Simulation (%) PL D MOS (i) (%) (ms) [1 - 4.5] 1 (24, 36, 20) 12 1.58 0.45 / 0.32 ± 0.05 0.19 / 0.12 ± 0.002 4.39 / 4.40 2 (63, 67, 20) 12 1.58 0.36 / 0.26 ± 0.04 0.18 / 0.13 ± 0.002 4.39 / 4.40 Table 2: Comparison of algorithmic results with simulation IEEE Standard Scenario Traffic Constraints Revision 802.11n Users 25 Calls/hour/user 1 RSSImin -82 dBm GI 800 ns Size 100×100 m Call length 180 s SNRmin 20 dB Preamble Greenfield X-Y step 1 m VoIP codec G.711 MOSmin 3.5 Bandwidth 20 MHz Altitude layers {20, 25} m On/Off times CBR Cmin 0.9 Retries 7 Prop. Exponent 3.3 Packet interval 20 ms Bmax 0.05 Table 3: Example solution input parameters 1. An initial population is generated. 2. Each individual from the generation is evaluated and ranked by assessing a raw fitness score based on the objective function of the problem (3). 3. Individuals are selected as parents according to their position in the ranking. 4. A new generation is created as follows: • The top 5% of the ranking (elite individuals) are copied to the new generation. • Of the remaining individuals: – 80% is created by Crossover-and-Mutation (CM) combining the genes of two selected parents (crossover) and applying a muta- tion to these new individuals with a very low probability pCM m . – 20% is created by an operation of muta- tion of parents (termed self-reproduction and mutation, SRM) with probability pSRM m . 5. After each new generation the exit criteria is eval- uated. The algorithm finishes when the lowest raw fitness score found cannot be improved after MAXG consecutive generations9 by at least 10−3 . If the exit criteria is not met, go to step 2. The previous steps differ slightly from the traditional sequential application of operations done by the canonical GA, however convergence is improved according to [48, 49]. 5.2.1. Initial Population It is desirable to count with initial individuals prone to be fit [50]. We created the following heuristic based on the k-means clusterization method illustrated in Figure 6: • In an area similar to the grid X-Y dimensions, D clusters are created so that the mean distance from 9However, if within the first MAXG generations no individual meets problem constraints, the algorithm returns L = ∅ to indicate that no solutions can be found with that number of drones. each ground user to its cluster centroid is minimized. Then, we add the grid’s average altitude to the cen- troid of each 2D region created previously, obtaining 3D centroids. • The first individual of the initial population will lo- cate its drones in those edges of the grid closest to these 3D centroids. • The other (p−1) individuals of the initial population are created simply by distributing each individual’s drones randomly among the spatial regions created around each centroid. In particular, we define cubes with a volume equals to the D-th part of the grid volume10 . Note that drones are always located at grid edges We found experimentally that a population size p of 200 individuals provided results that could not be im- proved in the scenarios tested. To guarantee convergence, after creating the initial pop- ulation, these 3D spatial regions are no longer taken into consideration for next generations. This implies that genes carried by individuals from next generations are not con- strained by spatial regions and hence, could be at any edge ∈ P. 5.2.2. Operators The following operators have been used: 1. Evaluation and ranking. Each individual is as- signed a raw fitness score by evaluating the problem objective function defined in (3). Since the genetic algorithm is called to search for solutions with D drones, individuals that do not meet the problem constraints are assigned a higher score by adding a penalty (between 1 and 2, according to the ratio of 10Observe that since the centroid of each cube was determined by k-means clusterization, there could be overlapping regions or regions out of the grid bounds such as those illustrated (in 2D) in Figure 6. 9
- 12. J o u r n a l P r e - p r o o f Journal Pre-proof + + + + + centroid ground user area for UAV positioning y x Figure 6: Example of 2D spatial regions where drones of initial pop- ulation are confined (D = 4) ground users that meet QoS constraints) to the value of their objective function. Appendix B details how the raw fitness score is calculated. Individuals are then sorted according to their raw fitness score. Finally, if an individual is in the n position in the ranking, it is assigned a new scored termed expectation value of 1/ √ n. 2. Parents Selection. We use a a stochastic uniform selection process among individuals according to their expectation value. In our case, 342 parents (152 × 2 CM + 38 SRM) are selected for crossover and/or mutation operations. Therefore, individuals in the top positions are chosen multiple times to be par- ents. 3. Crossover. The crossover operator combines the characteristics of two parents to create a new indi- vidual. We use a uniform crossover operation by generating a random binary vector which determines for each gene of the child whether it comes from one parent or the other. 4. Mutation. We apply a exchange-type uniform mu- tation that consists of changing one gene of an indi- vidual with a given probability11 (pCM m for those in- dividuals generated after crossover, or pSRM m for par- ents) for a random coordinate within the grid edges. 5.3. Heuristics performance To validate the proposed heuristic method, we have performed a series of experiments using the parameters listed in Table 4. In an area of 50 m×50 m, the number of users on ground has been increased from 10 to 60 so that the number of drones in the solutions is also increased. 11We set pSRM m = 1/(3 · D) in inverse proportion to the number of genes of individuals, and pCM m = 1/2 · pSRM m . We have performed 30 runs of each experiment (changing the layout of ground user randomly each time) and thus, values shown represent the average value obtained 5.3.1. Quality of the solutions Table 5 compares the results obtained with our heuris- tic method, the exhaustive search method, and the results obtained by simply using the first individual in our ini- tial population (i.e. k-means clusterization method). For each case we show the number of drones D, the num- ber of ground users associated to the WiFi network C, and the value of the objective function from (3). When greater than zero, the standard deviation is included be- tween parentheses. It can be observed that results ob- tained with our heuristic method are very close to the optimal found by exhaustive search, matching the num- ber of required drones in all cases. Solutions found by k-means clusterization however overestimate the number of required drones, providing poor results when compared to our heuristics. Results have been extended from 70 to 150 ground users for our heuristic method and k-means (such exten- sion poses a computational burden too high for exhaustive search with the grid under consideration, e.g. for D = 3 and |P| =2 500 edges, more than 15 · 109 possible UAV location combinations would have to be evaluated). Fig- ure 7 plots the value of the objective function in our ex- tended comparison. Results suggest that the number of drones obtained with our heuristics tends to grow linearly with the number of users in the scenario under considera- tion12 , outperforming the solutions found with k-means in the studied cases. Note that since the coverage constraint Cmin is 0.9, the value of objective function is almost en- tirely determined by the number of drones (which explains the steps in the plot). The value of the objective function exhibits greater confidence intervals in U = 90 as a re- sult of finding solutions with different number of drones (3 or 4) along the 30 repetitions, as user layout is randomly generated. 5.3.2. Convergence speed and complexity Figure 8 shows the number of generations produced by our heuristic search until a solution is found. Remember that D is increased (and a new call to GAsearch is made) only after failing to find an individual that meets the prob- lem constraints for MAXG consecutive generations13 . Re- sults show that the best individual is always found within the first five generations in all scenarios tested. This ex- plains that solutions with D drones (see Figures 7 and 8) 12The grid dimensions determine the density of ground users. Thus, for a a given area of sufficient dimensions (2500ṁ2 in our scenarios), the number of drones grows linearly with the density of users as shown in Figure 7 13MAXG was determined experimentally. We initially tried MAXG = 200 generations in an scenario of 100 m x 100 m and X-Y steps of 1m. But since solutions were always found in the first five generations, we decided to set MAXG = 50. 10
- 13. J o u r n a l P r e - p r o o f Journal Pre-proof IEEE Standard Scenario Traffic Constraints Revision 802.11n Users {10, . . . , 60} Calls/hour/user 1 RSSImin -82 dBm GI 800 ns Size 50×50 m Call length 180 s SNRmin 20 dB Preamble Greenfield X-Y step 1 m VoIP codec G.711 MOSmin 3.5 Bandwidth 20 MHz Altitude layers 20 m On/Off times CBR Cmin 0.9 Retries 7 Prop. Exponent 3.3 Packet interval 20 ms Bmax 0.05 Table 4: Heuristics validation input parameters U 10 20 30 40 50 60 exhaustive D 1 1 1 2 2 2 C 10 20 29.27 (0.45) 40 50 59.33 (0.52) of 1 1 1.024 (0.02) 2 2 2.01 (0.01) genetic D 1 1 1 2 2 2 C 10 20 29.23 (0.43) 40 50 57.87 (0.35) of 1 1 1.026 (0.01) 2 2 2.035 (0.01) k-means D 4.93 (0.64) 6.1 (0.84) 6.47 (0.63) 6.97 (0.72) 7.07 (0.64) 7.37 (0.67) C 10 19.43 (0.5) 28.5 (0.51) 37.63 (0.72) 46.93 (0.87) 56.27 (1.17) of 4.93 (0.64) 6.13 (0.84) 6.52 (0.63) 7.03 (0.72) 7.13 (0.64) 7.43 (0.67) Table 5: Comparison of exhaustive, heuristic, and k-means 20 40 60 80 100 120 140 U 0 2 4 6 8 10 12 objective function value exhaustive genetic k-means Figure 7: Comparing heuristics, exhaustive search and clusterization are commonly found after ∼ 50D generations (see our exit criteria). 20 40 60 80 100 120 140 U 0 50 100 150 200 250 300 350 generations Figure 8: Generations evaluated until exit criteria is met The fast convergence speed attained can be attributed to: • The first generation created exhibits excellent fit- ness. Both the k-means clusterization heuristic, and the large population size (p = 200) makes a first generation of 200 individuals prone to be good can- didates. • The characteristics of the scenarios tested. Consider- ing the finest-grained discretization X-Y step of 1 m, the number of grid edges that belong to each cluster (i.e. |P|/D ) is not too large compared to the pop- ulation size used. In general, this two factors will determine the convergence speed, and thus, for sce- narios covering a wider area (i.e. large |P|) a larger population is advised to attain fast convergence. The pseudocode used to evaluate the raw fitness func- tion for D drones (see Appendix Appendix B) can be computed in O(U · D) time14 . According to our previ- ous convergence analysis, the fitness function is evaluated a number of times that depends on the number of gen- erations created and population size as ∼ D · MAXG · p (e.g.∼ 10 000 · D in our scenario). Then, we could state that the computational complexity of our heuristic method is O(U · D2 ). However, the number of drones used is not independent of the number of ground users. In its lower bound, D is limited by U/U0 (where U0 is the greatest 14The pseudocode is composed by three main loops O(UD) + O(UD) + O(U) 11
- 14. J o u r n a l P r e - p r o o f Journal Pre-proof number of ground users whose traffic can be handled by a single drone). In its upper bound however, D tends to match the number of users U (e.g. in a large extension with scattered users). Finally, using this upper bound, we conclude that the computational complexity of our heuris- tic method is upper bounded by O(U3 ). However, if one considers that D is constrained by the maximum number of UAVs in the problem (constant Dmax), then the compu- tational complexity would be O(U). At any rate, solutions can be computed in polynomial time. 6. Numerical results In this section we provide a numerical analysis of the proposed UAV deployment method. Results are obtained through the heuristics proposed in Section 5. The focus is set on two different aspects: the impact of the IEEE 802.11 standard revision in use, and the impact of the constraints bounds in the solutions. 6.1. Influence of IEEE 802.11 standard revision A comprehensive summary of the challenges and impli- cations of the various IEEE 802.11 amendments in long- range outdoor WiFi deployments can be found in [23]. In this section, we compare the performance of the IEEE 802.11 (b/g/a/n/ac) standard amendments shown in Table 6 and evaluate their fitness to scenarios with specific character- istics. In particular, we define two types of scenarios: • Coverage-limited scenario: for a fixed number of ground users U = 100, the terrain size is increased from 100 m2 to 10 000 m2 , obtaining values of user spar- sity that range from 1 m2 to 100 m2 . In this kind of scenario, it is expected that the number of drones in the solutions is mainly determined by the need to satisfy the coverage constraint Cmin (which depends on the physical layer) and SNR of users. • QoS-limited scenario: for a fixed very small terrain size (5m × 5m) the number of users is increased from 25 to 100, obtaining highly dense scenarios (1− 0.25 m2 /user). In this kind of scenario, it is expected that all users are under coverage, and the number of drones in the solutions is mainly determined by the need to satisfy QoS constraints (Bmax, MOSmin) (which depend on the mac-sublayer). Frequency Channel Bandwidth Revision 2.4 GHz 22 MHz 802.11b 20 MHz 802.11g 40 MHz 802.11n 5 GHz 20 MHz 802.11a 160 MHz 802.11ac Table 6: IEEE 802.11 standard revisions considered Results presented in this section represent average val- ues after repeating 30 times each experiments. 95% confi- dence intervals obtained were small and have been omitted in the figures presented for clarity. 6.1.1. Coverage-limited scenario 10 20 30 40 50 60 70 80 90 100 m 2 /U 0 5 10 15 20 objective function value 802.11b 802.11a 802.11g 802.11n | 40MHz 802.11ac | 160MHz Figure 9: Solutions for various values of user geographic dispersion. Figure 9 plots the value of the objective function of the solutions found. It is noticeable that the physical bit rate of IEEE 802.11b (11Mbps) results in higher demand of drones due to the low throughput supported by each AP. It can also be observed that when geographic disper- sion increases, standards in the 5 GHz band (IEEE 802.11a and 802.11ac) produce worse results (i.e. more UAVs are needed) than those in the 2.4 GHz band. This can be at- tributed to a higher propagation loss (see RSSI expression- formula in (5)). Another noticeable effect is produced by the channel bandwidth. Higher bandwidth exhibits higher thermal noise (see N formula in (8)), which negatively impacts on SNR and, consequently, on coverage. This is clearly noticeable in the case of IEEE 802.11ac, and less ob- vious in IEEE 802.11n, which performs a little worse than IEEE 802.11g for areas greater than 70 m × 70 m in spite of a greater data bit rate. Finally, an interesting effect can be observed at the leftmost part of the figure. Most revisions start with 4 drones and then fall to 3 for larger areas until it starts increasing again. This is attributable to the own scenario characteristics as in the most dense case (100 users in an area of 10 m×10 m) it behaves like a QoS-limited scenario where 100% of users are covered and the limiting factor is their traffic. However, when the terrain size increases (i.e. sparsity increases) some users are left uncovered (un- til Cmin). This happens first in those standard revisions that exhibit worse coverage properties (i.e. ac and a) and as a consequence less drones are required. Nevertheless, as the terrain size keeps on increasing, coverage constraint is dominant, and the number of drones in the solutions tend to increase with the terrain size in all standard revi- sions but IEEE 802.11b due to the large number of drones deployed. 12
- 15. J o u r n a l P r e - p r o o f Journal Pre-proof 6.1.2. QoS-limited scenario Figure 10 shows the results obtained for the high user- density QoS-limited scenario. To be consistent with the previous case, we consider user sparsity (0, 25−1 m2 /user) instead of density in the results shown. Results show that all standard revisions (but IEEE 802.11b) exhibit a similar behaviour, increasing the number of drones when QoS con- straints are not met due to a high volume of traffic. This suggest that the higher data bit rate exhibited by some revisions is not fully exploited (except at 0.76 m2 /user) in the very small scenario under consideration. As expected, the insufficient physical bit-rate of IEEE 802.11b causes an exponential growth in the number of drones required to support very high users densities. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 m 2 /U 0 2 4 6 8 10 12 objective function value 802.11b 802.11a 802.11g 802.11n | 40MHz 802.11ac | 160MHz Figure 10: QoS limited scenario From the two scenarios studied, it can be concluded that revisions IEEE 802.11 g/n achieve the best results, requiring only between 1 and 4 drones to cover between 90 and 100 users in an area ranging from 5 m × 5 m up to 100 m × 100 m. Revisions using 5 Ghz however (a,ac), exhibit more path loss and tend to require more drones in large areas e.g. greater than 70 × 70 m. Finally, the old IEEE 802.11b standard revision exhibits a poor per- formance compared with the rest as a result of its poor throughput. 6.2. Influence of the constraints The selection of thresholds in the constraints also plays an important role in the solutions obtained; very restric- tive constraints may lead to unwanted results. In this sec- tion, we show the results produced with the variation of Cmin in a coverage-limited scenario (100 users in the great- est terrain size: 10 000 m2 ), and Bmax in a QoS-limited scenario (100 users in the smallest terrain size: 25 m2 ). The value of MOSmin is always set to 3.5. Figure 11 shows the influence of Cmin in the objec- tive function for different IEEE 802.11 standard revisions. As expected, the number of drones in the solutions in- creases with Cmin. This growth is approximately linear un- til Cmin = 0.9, where those standard revisions with higher frequency (a, ac) or channel bandwidth (ac, n) exhibit a steeper rise than b or g. Therefore, very demanding Cmin values may cause exponential growth in the number of 0.5 0.6 0.7 0.8 0.9 1 Cmin 0 5 10 15 20 25 objective function value 802.11b 802.11a 802.11g 802.11n | 40MHz 802.11ac | 160MHz Figure 11: Influence of Cmin in the value of the objective function. 0 0.02 0.04 0.06 0.08 0.1 Bmax 5 10 15 20 objective function value 802.11b 802.11a 802.11g 802.11n | 40MHz 802.11ac | 160MHz Figure 12: Influence of Bmax in the value of the objective function. UAVs needed for those standards. In such case, the max- imum number of available UAVs in the problem (Dmax) might limit the feasibility of finding valid solutions. Figure 12 shows the influence of Bmax in the objec- tive function for a very small area with a highly dense crowd. Recall that Bmax = 0 means that all users as- sociated to WiFi (i.e. covered) can simultaneously call, whereas Bmax = 0.1 means that a covered user will be al- lowed (by the CAC mechanism) to call with a probability of 90%. In this case, those standards with better data bit rate withstand more restrictive values of Bmax (i.e. simul- taneous calls) with the same number of drones. As such, we find that IEEE 802.11n/ac revisions achieve slightly better results than the rest. Finally, it is important to remark that our numerical results are limited by several factors. First, only the high- est data bit rate from each revision has been considered; then, some features such as frame aggregation or MIMO in 802.11n or 802.11ac have also been disregarded, as it has been inter-channel interference. Besides, some recent and promising revisions such as IEEE 802.11ah, specifi- cally targeted for outdoor long-range at 900 Mhz serving high density wireless stations [23] have not been included due to lack of adoption in today’s user terminals. How- ever, the most patent limit of our results is the fact that the problem has been used just for the initial deployment of UAVs. Next we provide a preliminary analysis of the applicability of this problem to a scenario where ground users are moving. 13
- 16. J o u r n a l P r e - p r o o f Journal Pre-proof 7. Application to moving targets The problem defined in Equation 3 is aimed at solving the problem of initial deployment of UAVs and as such, it can also be applied for service provisioning when ground users are gathered in specific known areas such as meeting points. In this section we provide a brief analysis of its ap- plicability when ground users are on the move, identifying open issues which remain to be addressed in future work. It is assumed that ground users position can be tracked. In such case, every T seconds user’s position is updated and our optimization problem is solved, relocating UAVs accordingly in a process such as the one illustrated in Fig- ure 13. 000 111 000 111 0000 1111 0 1 00 11 UAVs relocated UAVs relocated UAVs relocation delay 0 T 2T 3T time ... UAVs deployed solution computation delay Figure 13: Dynamic of UAVs relocation The key points in this process are: • The observation period T. The minimum possible value for T should be greater than the addition of: – The time required to solve the problem (which in turn depends on the performance of the algo- rithm finally implemented, the scenario under consideration and computational resources). – The time required to relocate all UAVs accord- ing to the new solution. This in turn depends on the solution found, initial position, UAV speed and the displacement strategy. Practical values should be in the order of seconds. Clearly, the longer T, the greater discrepancy be- tween the theoretical and actual position of ground users, increasing the error of the models and chances of unsatisfying constraints. • Relocation of UAVs. Moving UAVs may result in transient periods of unsatisfied constraints. The de- cision about which drones are displaced according to the final solution and the trajectories followed is a problem itself that should consider not only the de- lay (e.g.[11]) but also service disruption to ground users engaged in conversations. Examples of strate- gies include minimizing the sum of all UAVs displace- ments, the longest UAV displacement, or the number of users affected by service outages. It would also be interesting to explore techniques of machine learning such as conceptor-based echo state networks (ESN) [51] to predict user service request pattern and user mobility pattern. • Problem Objective function. Once the relocation strategy is fixed, the cost of relocating drones should be taken into account into the optimization problem as a penalty factor added to the objective function. Let us imagine a case in which two candidate solu- tions exhibit the same number of drones and cover- age (i.e. a similar value of the objective function) but one solution implies a complex repositioning of all drones while the other implies just a slight change on a single drone. Thus, this penalty could include aspects such as the relocation delay or the temporal effect of impaired users as a result of drones relo- cation, serving as a factor to break the deadlock in favor of the less costly solution. The aforementioned key points suggest that user’s move- ment brings out new issues and implications that require an extension to the problem defined in this paper including the cost of UAVs relocation according to a specific strategy as well as user mobility models. Furthermore, a centralised approach such as the one suggested for initial deployment might not hold of service continuity. These aspects15 are left as open issues for further research. Nevertheless, as a prospective exercise, we have performed a simulation with users on the move using the coverage-limited scenario and the parameters in Table 4 (but using a traffic profile of 5 calls/hour/user and altitude layers between 10 m and 40 m with steps of 1 m). In our coverage-limited scenario, the 100 users now move according to a correlated random walk model. Each ground user moves at a walking speed of 5.3 km/h with a probability of 0.8 and in such case, the direction remains unchanged with probability 0.8. Users rotate 180 degrees when they reach the area bounds. Algorithm 3 is used for the initial deployment and the number of drones deployed D remains unchanged for the remainder of the simulation (30 min). To achieve this we limit subsequent solutions to the best possible found by our GA with D drones (even though problem constraints were not satisfied). With ev- ery new solution drones are relocated (considering a speed of 60 Km/h) so that the sum of the distances traveled by all drones is the minimum possible. To study the transient effects of UAV’s relocation we check every five seconds whether the problem constraints (i.e. coverage and speech quality) are satisfied considering the actual position of users. New solutions (and drones relocation) have been recalculated every T ={15 s, 30 s, 45 s, 60 s} and in each case simulations are repeated 30 times. Figure 14 shows the percentage of the simulation time when both constraints are satisfied. Results show that problem constraints were satified above 92% of the time in worst case (i.e. area of 10 000 m2 and T = 60 s). As expected, the worse performance is obtained when users are more scattered and, to a lesser extent, with longer T. 15Another open issue is to speed up the solution search by experi- menting with other heuristics or at implementation level (e.g. using low-level programming language) 14
- 17. J o u r n a l P r e - p r o o f Journal Pre-proof 10 20 30 40 50 60 70 80 90 100 m 2 /U 60 65 70 75 80 85 90 95 100 time that constraints are satisfied (%) T = 15 T = 30 T = 45 T = 60 Figure 14: Effect of UAV relocation in problem constraints. But since users call according to a traffic profile of 5 calls/hour, it would be interesting to observe the im- pairment that drones relocation cause in these calls. To this end, we define a call disruption event when a call in progress does not satisfy the speech quality constraint for two consecutive samples (i.e. 10 seconds). The percent- age of calls that experience a service free of disruption is shown in Figure 15. According to our results, after the 30 minutes of simulation almost 95% of calls have not been affected by disruption events. As in the previous case, re- sults show a small decrease for larger scenarios with more scattered users and to a lesser extent with T. 10 20 30 40 50 60 70 80 90 100 m 2 /U 60 65 70 75 80 85 90 95 100 calls without interruptions (%) T = 15 T = 30 T = 45 T = 60 Figure 15: Effect of UAV relocation in calls in progress. A final experiment was done launching one extra drone (D + 1) in the initial deployment (i.e. forcing one extra iteration in Algorithm 3). The results obtained in this case were promising since the effect of UAV relocation was unnoticed (i.e. constraints were met 100% of the time and no call was interrupted). This suggest that launching extra drones16 can be a effective method to avoid service degradation during UAVs relocation. 8. Conclusions and further work In this paper we dealt with the problem of optimal placement of UAVs in order to provide VoWiFi service 16Although we used one extra drone, the optimal number will end up depending on users density and terrain extension, which is also left for further research. with guaranteed QoS to a set of static users. We formu- lated a optimization problem that minimizes the number of drones required to provide such service and the ratio of uncovered users. An algorithm to find solution through exhaustive search was proposed, but due to the high com- putational complexity, we also proposed efficient heuristics as a general way to solve the optimization problem. Numerical results suggest that large area scenarios with highly disperse users (coverage-limited) will benefit from IEEE 802.11 g/n standards, as less drones will be needed to provide the service. 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- 19. J o u r n a l P r e - p r o o f Journal Pre-proof bernetics evolving to systems, humans, organizations, and their complex interactions’ (cat. no.0, Vol. 5, 2000, pp. 3816–3822 vol.5. doi:10.1109/ICSMC.2000.886605. [50] B. Dengiz, F. Altiparmak, A. E. Smith, Local search genetic algorithm for optimal design of reliable networks, IEEE Trans- actions on Evolutionary Computation 1 (3) (1997) 179–188. doi:10.1109/4235.661548. [51] M. Chen, M. Mozaffari, W. Saad, C. Yin, M. Debbah, C. S. Hong, Caching in the sky: Proactive deployment of cache- enabled unmanned aerial vehicles for optimized quality-of- experience, IEEE Journal on Selected Areas in Communications 35 (5) (2017) 1046–1061. doi:10.1109/JSAC.2017.2680898. Appendix A. Expected time per slot: E[T] The expected time per slot represents the expected length of each state of the Markov chain modeling the IEEE 802.11 system. To obtain a closed-form expression of E[T], we follow the approach presented in [35] (but adapted to the terms and concepts defined in Section 4.2) which considers the probability of being on each of the following states: • Idle state, when nobody attempts to transmit. • Success state, when only a single station attempts to transmit with no channel related errors. • Error state, when a single station attempts to trans- mit but channel errors occur. • Collision state, when more than one station attempts to transmit simultaneously (same slot). E[T] can be obtained by weighting the time spent on each of the previous states respectively as follows: E[T] = TI + TS + TE + TC (A.1) The factors in (A.1) can be calculated as follows: • TI can be expressed as: TI = PI σ (A.2) where σ stands for the time slot duration as defined in the corresponding IEEE 802.11 revision. PI is the probability that the channel is idle in a randomly chosen slot, which can be expressed as PI = S Y j=1 1 − τ(j) (A.3) where S is the number of stations in the system un- der consideration . Let us define this set as S = M ∪ AP. Then, S = |S| = |M| + 1. • The time spent on successful (TS) and erroneous (TE) slots can be expressed as: TS = S X j=1 P(j) s (1 − FER(j) ) T(j) s (A.4) TE = S X j=1 P(j) s FER(j) T(j) e (A.5) where T (j) s and T (j) e represent the average time that station j spends in successful and erroneous trans- missions, respectively. Their actual value depend on the IEEE 802.11 standard revision used and physical data rate of stations. They can be expressed as: T(j) s = DIFS + 2 · PLCP(j) + (Header(j) + Data(j) )/R (j) b + SIFS + Tack + 2δ (A.6) T(j) e = DIFS + PLCP(j) + (Header(j) + Data(j) )/R (j) b + EIFS + δ (A.7) Where R (j) b represents the physical data rate (given by the MCS used by the station), DIFS, SIFS, EIFS are inter-frame periods as specified by the 802.11 standard and PLCP(j) , Header(j) and Tack correspond with the PLCP header, the IEEE 802.11 header and the duration of an ack frame in the IEEE 802.11 standard17 , and δ is the propagation delay. In equations (A.4) and (A.5), P (j) s stands for the probability that only an observed station j attempts to transmit while the rest remain silent, which can be expressed as: P(j) s = τ(j) S Y k=1, k6=j 1 − τ(k) (A.8) • The time spent in collided transmissions TC can be deduced as follows. Each station j exhibits an aver- age collision time, T (j) c which can be can be approx- imated by the time spent in a erroneous transmis- sion T (j) e (i.e. T (j) c =T (j) e ). Nevertheless, when pack- ets sent by two different station collide, the time to be considered corresponds with the longest average collision time. To address this concern, stations in the system (i.e. set S) are grouped in traffic classes according to their collision time (i.e. all stations with the same average collision time belong to the same class). Then, the following subsets of S can be de- fined: N(i) i∈1..S = n j ∈ S | T(j) c = T(i) c , j / ∈ N(k), k ≤ i o (A.9) Where N(i) is a subset of S that includes those sta- tions whose collision time is T (i) c (only if such sta- tions are not yet in other group N(j) with j 17Note that in the AP station these times are averaged considering the physical data rate and/or codec of every user in M 17
- 20. J o u r n a l P r e - p r o o f Journal Pre-proof i). Notice that (A.9) defines multiple groups (e.g. N(1), N(2), .., N(S)), and since each station can only belong to one group (or class), some of the previous classes may be empty sets. Therefore, let us define a new set which can be used to identify non-empty sets as: E = {i | N(i) 6= ∅} (A.10) The number of non-empty classes will be finally given by Nc = |E|. Considering N(d) as the set of stations that belong to class d ∈ E, let us define L(d) as the set of sta- tions whose collision time is longer than T (d) c (i.e. their data bit rate is slower), and H(d) as the set of stations whose collision time is shorter than T (d) c (i.e. their data bit rate is faster). H(d) and L(d) can be formally defined as: L(d) = n i ∈ S | T(i) c T(d) c o (A.11) H(d) = n i ∈ S | T(i) c T(d) c o (A.12) Now the probability that at least one station that belongs to class d ∈ E transmits is: P N (d) tx = 1 − Y j∈N (d) (1 − τ(j) ) (A.13) And the probabilities that at least one station from a higher or lower class transmits are: P H(d) tx = 1 − Y j∈H(d) 1 − τ(j) (A.14) P L(d) tx = 1 − Y j∈L(d) 1 − τ(j) (A.15) Due to the fact that lower classes slow down higher ones as a result of longer transmission times, TC can be calculated as: TC = Nc X d=1 PN (d) c + PH(d) c T(d) c (A.16) where T (d) c is the average time that any station from class d spends on collision state, and P N (d) c repre- sents the probability that any collision occurs be- tween stations from the same class d: PN (d) c = 1 − P H(d) tx · 1 − P L(d) tx · P N (d) tx − X j∈N (d) P(j) s (A.17) and P H(d) c accounts for the probability that class d is involved in a collision with at least one station from a higher class. PH(d) c = P N (d) tx · P H(d) tx · 1 − P L(d) tx (A.18) Finally, substituting the expressions of TI, TS, TE, and TC in (A.1), the closed-form expression of E[T] presented in (A.19) is obtained . Appendix B. Raw fitness criteria evaluation Assessing raw fitness scores entails solving both signal coverage (e.g. RSSI and SNR) and the analytical models to estimate QoS. This appendix provides a pseudocode in Algorithm 4 that can be used as a guidance for implemen- tation and also to estimate the computational complexity of this step. The algorithm can be divided in the following parts: • Lines 1-6: RSSI and SNR are calculated for each pair ground user-drone. • Lines 7-15: Each ground user station is associated to a specific drone, creating C(i). • Lines 19-24: The maximum number of concurrent calls CCmax is calculated for each drone k, which depends on the blocking probability constraint Bmax. • Lines 25: The set of stations S = M∪AP, is created selecting the CCmax slowest ground users stations and the AP. • Lines 26-42: The non-linear equation system is solved iteratively, the output is the estimation of the MOS experienced by users associated to drone k. 18
- 21. J o u r n a l P r e - p r o o f Journal Pre-proof E[T] = σ · S Y j=1 1 − τ(j) | {z } TI , + S X j=1 τ(j) S Y k=1, k6=j (1 − τ(k) ) (1 − FER(j) ) T(j) s | {z } TS + S X j=1 τ(j) S Y k=1, k6=j (1 − τ(k) ) FER(j) T(j) e | {z } TE + Nc X d=1 Y j∈H(d) 1 − τ(j) Y j∈L(d) 1 − τ(j) 1 − Y j∈N (d) 1 − τ(j) − X j∈N (d) τ(j) S Y k=1, k6=j (1 − τ(k) ) · T(d) c | {z } TC + Nc X d=1 1 − Y j∈N (d) (1 − τ(j) ) 1 − Y j∈H(d) 1 − τ(j) 1 − 1 − Y j∈L(d) 1 − τ(j) · T(d) c | {z } TC (continued) (A.19) 19
- 22. J o u r n a l P r e - p r o o f Journal Pre-proof Input: U = {1, . . . , U}, D = {1, . . . , D}, {wi | i ∈ U}, {xk | k ∈ D} Initialization: ffitness = D + 2 Output: ffitness 1 for i = 1 to U do 2 for j = 1 to D do 3 calculate RSSIi,j; // Eq. (5) 4 calculate SNRi,j; // Eq. (7) 5 end 6 end 7 for i = 1 to U do 8 for k = 1 to D do 9 if RSSIi,k ≥ RSSImin and SNRi,k ≥ SNRmin then 10 if RSSIi,k RSSIi,j, ∀j 6= k then 11 C(k) = C(k) ∪ i; 12 end 13 end 14 end 15 end 16 if PD i=1 |C(i)|/U ≥ Cmin then 17 for k = 1 to D do 18 calculate CCmax; // Algorithm 2 19 build set S = M ∪ AP; 20 for j = 1 to |S| do 21 calculate T (j) s , T (j) c , T (j) e ; 22 calculate FER(j) ; // Eq. (17) 23 end 24 τ (j) next = T (j) c , ∀j; 25 while diff ∆ do 26 τ(j) = τ (j) next; 27 calculate E[T]; // Appendix Appendix A 28 for j = 1 to |S| do 29 calculate E[B(j) ]; // Eq. (13) 30 calculate r(j) , q(j) ; // Eqs. (11),(12) 31 calculate p(j) ; // Eq. (15) 32 calculate τ (j) next; // Eq. (10) 33 end 34 diff = max |τ (j) next − τ(j) | , ∀j; 35 end 36 calculate MOS(k); // Eq. (25) 37 end 38 if MOS(k) ≥ MOSmin, ∀k ∈ {1, . . . , D} then 39 ffitness = D + 1 − PD k=1 |C(k)|/U ; 40 else 41 ffitness = D + 1 + 1 − PD k=1 |C(k)| [MOS(k) MOSmin] /U ; 42 end 43 end Algorithm 4: Fitness function evaluation 20