1

Maximizing Indoor Wireless Coverage Using
UAVs Equipped with Directional Antennas

arXiv:1705.09772v1 [] 27 May 2017

Hazim Shakhatreh and Abdallah Khreishah

Abstract
Unmanned aerial vehicles (UAVs) can be used to provide wireless coverage during emergency
cases where each UAV serves as an aerial wireless base station when the cellular network goes down.
They can also be used to supplement the ground base station in order to provide better coverage and
higher data rates for the users. In this paper, we aim to maximize the indoor wireless coverage using
UAVs equipped with directional antennas. We study the case that the UAVs are using one channel, thus
in order to maximize the total indoor wireless coverage, we avoid any overlapping in their coverage
volumes. We present two methods to place the UAVs; providing wireless coverage from one building
side and from two building sides. In the first method, we utilize circle packing theory to determine the
3-D locations of the UAVs in a way that the total coverage area is maximized. In the second method,
we place the UAVs in front of two building sides and efficiently arrange the UAVs in alternating upsidedown arrangements. We show that the upside-down arrangements problem can be transformed from 3D
to 2D and based on that we present an efficient algorithm to solve the problem. Our results show that
the upside-down arrangements of UAVs, can improve the maximum total coverage by 100% compared
to providing wireless coverage from one building side.

Index Terms
Unmanned aerial vehicles, coverage, circle packing theory.

I. I NTRODUCTION
Cells on wheels (COW), are used to provide expanded wireless coverage for short-term
demands, when cellular coverage is either minimal, never present or compromised by the disaster [1]. UAVs can also be used to provide wireless coverage during emergency cases and
Hazim Shakhatreh and Abdallah Khreishah are with the Department of Electrical and Computer Engineering, New Jersey
Institute of Technology (email: {hms35,abdallah}@njit.edu)

2

special events (such as concerts, indoor sporting events, etc.), when the cellular network service
is not available or it is unable to serve users [2]–[5]. Compared to the COW, the advantage of
using UAV-based aerial base stations is their ability to quickly and easily move [6]. The main
disadvantage of using UAVs as aerial base stations is their energy capacity, the UAVs need to
return periodically to a charging station for recharging, due to their limited battery capacity.
In [7], the authors integrate the recharging requirements into the coverage problem and examine
the minimum number of required UAVs for enabling continuous coverage under that setting.
Directional antennas are used to improve the received signal at their associated users, and
also reduce interference since other- aerial base stations are targeting/serving other users in
other directions [8]. The authors in [9] study the optimal deployment of UAVs equipped with
directional antennas, using circle packing theory. The 3D locations of the UAVs are determined
in a way that the total coverage area is maximized. In [10], the authors investigate the problem
by characterizing the coverage area for a target outage probability, they show that for the case of
Rician fading there exists a unique optimum height that maximizes the coverage area. In [11], the
authors propose a heuristic algorithm to find the positions of aerial base stations in an area with
different user densities, the goal is to find the minimum number of UAVs and their 3D placement
so that all the users are served. However, it is assumed that all users are outdoor and the location
of each user represented by an outdoor 2D point. In [12], the authors use multiple UAVs to design
efficient UAV relay networks to support military operations. They describe the tradeoff between
connectivity among the UAVs and maximizing the covered area. However, they use the UAVs
as wireless relays and do not take into account their mutual interference in downlink channels.
In [13], the authors propose a computational method for positioning aerial base stations with the
goal of minimizing their number, while fully providing the required bandwidth over the disaster
area. It is assumed that overlapping aerial base stations coverage areas are allowed and they use
the Inter-Cell Interference Coordination (ICIC) methods to schedule radio resources to avoid
inter-cell interference. The authors in [4], [5] use a single UAV equipped with omnidirectional
antenna to provide wireless coverage for indoor users inside a high-rise building, where the
objective is to find the 3D location of a UAV that minimizes the total transmit power required to
cover the entire high-rise building. In [14], the authors use UAVs equipped with omnidirectional
antennas to minimize the number of UAVs required to cover the indoor users.
We summarize our main contributions as follows:
•

In order to maximize the indoor wireless coverage, we present two methods to place the

3

UAVs, providing wireless coverage from one building side and from two building sides.
In this paper, we study the case that the UAVs are using one channel, thus we avoid any
overlapping in their coverage volumes (to avoid interference). In the first method, we utilize
circle packing theory to determine the 3-D locations of the UAVs in a way that the total
coverage area is maximized. In the second method, we place the UAVs in front of two
building sides and efficiently arrange the UAVs in alternating upside-down arrangements.
•

We show that the upside-down arrangements problem can be transformed from 3D to 2D
and based on that we present an efficient algorithm to solve the problem.

•

We demonstrate through simulation results that the upside-down arrangements of UAVs, can
improve the maximum total coverage by 100% compared to providing wireless coverage
from one building side.

The rest of this paper is organized as follows. In Section II, we describe the system model. In
Section III, we show the appropriate placement of UAVs that maximizes the total indoor wireless
coverage. Finally, we present our numerical results in Section IV and make concluding remarks
in Section V.
II. S YSTEM M ODEL
A. System Settings
Consider a 3D building, as shown in Figure 1, where N UAVs must be deployed to maximize
wireless coverage to indoor users located within the building. The dimensions of the high-rise
building, in the shape of a rectangular prism, be [0, xb ] × [0, yb] × [0, zb ]. Let (xk , yk , zk ) denote
the 3D location of UAV k∈ N, and let (Xi , Yi , Zi ) denote the location of user i. Also, let
dout,i be the distance between the UAV and indoor user i, and let din,i be the distance between
the building wall and indoor user i. Each UAV uses a directional antenna to provide wireless
coverage where the antenna half power beamwidth is θB . The authors in [15] use an outdoor
directional antenna to provide wireless coverage for indoor users. They show that the highest
RSRP (Reference Signal Received Power) and throughput values are measured along the main
beam direction, thus the radiation pattern of a directional antenna is a cone and the indoor
volume covered by a UAV is a truncated cone, as shown in Figure 2. Here, ri is the radius of
the circle that is located at yz-rectangular side ((0,0,0), (0,0,zb ) , (0,yb ,zb ), (0,yb ,0))), rj is the

4

Fig. 1: System model

radius of the circle that is located at yz-rectangular side ((xb ,0,0), (xb ,0,zb ) , (xb ,yb ,zb ), (xb ,yb ,0))
and xb is the horizontal width of the building. The volume of a truncated cone is given by:
1
V = πxb (ri2 + rj2 + ri rj )
3

B. UAV Power Consumption
In [16], the authors show that significant power gains are attainable for indoor users even in
rich indoor scattering conditions, if the indoor users use directional antennas. Now, consider a
transmission between k-th UAV located at (xk , yk , zk ) and i-th indoor user located at (Xi , Yi ,
Zi ). The received signal power at i-th indoor user location can be given by:
Pr,ik (dB) = Pt + Gt + Gr − Li
where Pr,ik is the received signal power, Pt is the transmit power of UAV, Gt is the antenna
gain of the UAV. It can be approximated by Gt ≈

29000
2
θB

with θB in degrees [17], [18] and Gr is

the antenna gain of indoor user i, which is given by [16]:
Gr (dB) = Gr,dir + Gr,omni − GRF

5

Fig. 2: 3D Dimensions of the truncated cone

Fig. 3: Building sides

where Gr,dir and Gr,omni are free-space antenna gains of a directive and an omnidirectional
antenna respectively and GRF is the decrease in gain advantage of a directive over an omnidirectional antenna, due to the presence of clutter.
Also, Li is the path loss which for the Outdoor-Indoor communication is:
Li = LF + LB + LI = (w log10 d3D,i + w log10 fGhz + g1 )
+(g2 + g3 (1 − cos θi )2 ) + (g4 d2D,i )
where LF is the free space path loss, LB is the building penetration loss, and LI is the indoor
loss. In the path loss model, we also have w=20, g1 =32.4, g2 =14, g3 =15, g4 =0.5 [19] and fGhz
is the carrier frequency.
C. Placement of UAVs
Choosing the appropriate placement of UAVs will be a critical issue when we aim to maximize
the indoor wireless coverage. In this paper, we assume that we can place the UAVs in front of
building sides A, B and above the building C as shown Figure 3. We also assume that the UAVs

6

Fig. 4: Placing two UAVs in front of building side A

Fig. 5: Placing two UAVs in front of two building sides A and B

are using one channel. In this section, we demonstrate why avoiding the overlapping between
UAV’s coverage volumes will strengthen the total indoor wireless coverage.
1) Overlapping between UAV’s coverage volumes is allowed: Now, when we place two UAVs
in front of building sides A as shown in Figure 4 (the UAVs have different z-coordinates and
same x- and y- coordinates), the indoor users located in G1 ’s and G2 ’s locations will have high
SINR. On the other hand, the indoor users located in G3 ’s location will have low SINR. This
is because the dependency of SINR on the location of indoor user. Similarly, when we place two
UAVs in front of two building sides A and B as shown in Figure 5 (the UAVs have different xcoordinates and same y- and z- coordinates), the indoor users located in G1 ’s and G2 ’s locations
will have high SINR. On the other hand, the indoor users located in G3 ’s location will have
low SINR. In Figure 6 (the UAVs have same y-coordinates and same x- and z- coordinates),

7

Fig. 6: Placing one UAV in front of building side A and one UAV above the building C

Fig. 7: UAVs with small antenna half power beamwidth θB

when we place one UAV in front of building side A and one UAV above the building C, the
indoor users located in G1 ’s and G2 ’s locations will have high SINR. On the other hand, the
indoor users located in G3 ’s location will have low SINR. From the previous examples, we can
conclude that allowing the UAVs coverage volumes to overlap will result in that some users are
not satisfied. In the next section, we place the UAVs in a way that maximizes the total coverage,
and avoids any overlapping in their coverage volumes.
2) Overlapping between UAV’s coverage volumes is not allowed: In Figure 7, we avoid the
overlapping between UAV’s coverage volumes by using UAVs with small antenna half power
beamwidths θB . Actually, this is impractical way to cover the building, due to the high number
of UAVs required to cover the building. In Figure 8, we place the UAVs in front of two building
sides and efficiently arrange the UAVs in alternating upside-down arrangements. We can notice

8

that this method will maximize the indoor wireless coverage where the uncovered holes are
minimized and the overlapping between UAV’s coverage volumes is not allowed.
III. M AXIMIZING I NDOOR W IRELESS C OVERAGE
In this section, the UAVs are assumed to be symmetric having the same transmit power, the
same horizontal location xk , the same channel and the same antenna half power beamwidth θB .
We show two methods to place the UAVs in a way that tries to maximize the total coverage,
and avoids any overlapping in their coverage volumes.
A. Providing Wireless Coverage from one building side
In this method, we place all UAVs in front of one building side (side A, side B or side C). The
objective is to determine the three-dimensional location of each UAV k∈ N in a way that the
total covered volume is maximized. Now, consider that we place the UAVs in front of building
side A, then the projection of UAV’s coverage on the building side B is a circle as shown in
Figure 9. Our problem can be formulated as:
max |N| ⋆

1
⋆ π ⋆ xb ⋆ (ri2 + rj2 + ri rj )
3

subject to
q

(yk − yq )2 + (zk − zq )2 ≥ 2rj , k 6= q ∈ N

zb − (zk + rj ) ≥ 0, k ∈ N
(zk − rj ) ≥ 0, k ∈ N
yb − (yk + rj ) ≥ 0, k ∈ N
(yk − rj ) ≥ 0, k ∈ N
The objective is to maximize the indoor wireless coverage (covered volume). Constraint set
(1) guarantees that truncated cones cannot overlap each other. Constraint sets (2-5) ensure that
UAV k should not cover outside the 3D building, see Figure 9. We model this problem by
utilizing the well-known problem, circle packing problem. In this problem, N circles should be
packed inside a given surface such that the packing density is maximized and no overlapping
occurs [20], note that the surface in our problem is a rectangle.
The authors of [20] tackle this problem by solving a number of decision problems. The
decision problem is:

9

Fig. 8: UAVs in alternating upside-down arrangements

Given N circles of radius rj and a rectangle of dimension d1 × d2 , whether is it possible
to locate all the circles into the rectangle or not.

In [20], the authors introduce a nonlinear model for this problem. Finding the answer for the
decision problem will depend on finding the global minimizer of a nonconvex and nonlinear
optimization problem. In each decision problem, they investigate the feasibility of packing N
identical circles. If this is feasible, N is incremented by one and the decision problem is solved
again. The algorithm will stop when the decision problem yields an infeasible packing [21]. The
pseudo code of the algorithm is shown in Algorithm 1. In the next section, we utilize the two
building sides to maximize the indoor wireless coverage. This will allow us to extend the indoor
wireless coverage compared with providing wireless coverage from one building side, because
the holes induced by the cones of the UAVs in one side can be filled by the cones induced by
the UAVs in the other side without causing overlap among the two sets of cones.
B. Providing Wireless Coverage from two building sides
In this method, we place the UAVs in front of two building sides (side A and side B) and
efficiently arrange the UAVs in alternating upside-down arrangements (see Figures 10 and 11).
In Theorem 1, we find the horizontal location of the UAV xU AV that guarantees the upside-down
arrangements of the truncated cones. In Theorem 2, we prove that if the truncated cones do not
intersect in 3D, then the circles do not intersect in building sides (A and B), and vice versa. In

10

Fig. 9: Circle packing in a rectangle

Theorem 3, we prove that if we maximize the percentage of covered area of building sides (A
and B), then we maximize the percentage of covered volume of building, and vice versa. These
theorems help us to transform the geometric problem from 3D to 2D and present an efficient
algorithm that maximizes the indoor wireless coverage.
Theorem 1. The horizontal location of the UAV xU AV that guarantees the upside-down arrangements of the truncated cones will be equal to 0.7071xb regardless of the antenna half power
beamwidth angle θB .
Proof. The radius of the smaller circular face ri is given by:
ri = rj

xU AV
xb + xU AV

(1)

Now, we divide the building sides A and B to square cells (as shown in Figures 10 and 11),

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Algorithm 1 Circle packing in a rectangle
1: N ←− 1
2: Solve the decision problem for N circles
3: If Answer = YES
4: Then N ←− N + 1
5: Return to step 2
6: If Answer = NO
7: n ←− N − 1
8: End
9: Output n

the large circle in Figure 10 and the small circle in Figure 11 will represent the projections of
UAV’s coverage on building sides A and B when the UAV is placed in front of building side
B. Similarly, the four small circles quarters in Figure 10 and the four large circles quarters in
Figure 11 will represent the projections of UAVs coverage on building sides A and B when the
UAV is placed in front of building side A. From Figures 10 and 11, the diagonal of the square
cell is:
D = 2rj + 2ri
where rj is the radius of the larger circular face and ri is the radius of the smaller circular face.
By applying the pythagoreans theorem, we get:
√
4rj2 + 4rj2 = (2rj + 2ri )2 =⇒ 8rj = 2rj + 2ri =⇒
√
8−2
ri =
rj = γrj
2

(2)

From equations
√ (1) and (2), we get:
√
√
8−2
xU AV
=
=⇒ 2xU AV = xb ( 8 − 2) + xU AV ( 8 − 2) =⇒
xb + xU AV √ 2
( 8 − 2)
√ = 0.7071xb

xU AV = xb
(4 − 8)
Thus, to guarantee the upside-down arrangements of the truncated cones, we must place the
UAVs at horizontal distance equals to 0.7071xb . Theorems 2 and 3 help us to transform the
geometric problem from 3D to 2D and present an efficient algorithm that maximizes the indoor
wireless coverage.

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Fig. 10: The square cell in side A

Fig. 11: The square cell in side B

Fig. 12: Four circles (with

Fig. 13: Four circles (with

radius rj ) in building side A

radius ri ) in building side B

Theorem 2. The truncated cones do not intersect in 3D iff The circles do not intersect in building
sides (A and B).
Proof. First, we prove that if the truncated cones do not intersect in 3D, then the circles do
not intersect in building sides (A and B). Assume that we have a set of truncated cones G =
{1, 2, ..., N} and they do not intersect in 3D space. Each truncated cone n ∈ G can be represented
by a number of 2D circles {c1n , c2n , ..., c|h|n}, where |h| is the height of the truncated cone, c1n
is the smaller circular face and c|h|n is the larger circular face. It is obvious that if the |G|
truncated cones do not intersect in 3D space then the smaller and larger circular faces do not
intersect in building sides (A and B).

13

Second, we prove that if the circles do not intersect in building sides (A and B), then the
truncated cones do not intersect in 3D. Assume that four circles (with large radius rj ) not
intersect in building side A (see Figure 12), then the circles (with small radius ri ) in building
side B will appear as shown Figure 13. Now, we need to do two steps: 1) Connect the lines
between these points (A|h| with A1 , B|h| with B1 , C|h| with C1 and D|h| with D1 ). 2) Draw
circles that pass through four points Ak , Bk , Ck and Dk where k ∈ h. After these two steps, the
circles that have been drawn in step two will represent a truncated cone that his circular bases
do not intersect with the four circles in building sides (A and B). Also, the truncated cones do
not intersect in 3D space.



Theorem 3. We maximize the percentage of covered area of building sides (A and B) iff We
maximize the percentage of covered volume of building
Proof. First, we divide the building sides A and B to square cells (as shown in Figures 10
and 11). The percentage of covered volume is given by:
(yb ∗ zb )
⌋ ∗ 2 ∗ ( π3 ∗ xb ∗ (ri2 + ri rj + rj2 ))
2
4rj
V =
(xb ∗ yb ∗ zb )
⌊

(3)

Where:
(yb ∗ zb )
⌊
⌋: the number of square cells in the building side.
4rj2
2: the number of truncated cones in the square cell (see Figures 7 and 8).
π
3

∗ xb ∗ (ri2 + ri rj + rj2 ): the volume of truncated cone.

(xb ∗ yb ∗ zb ): the volume of the building.
Now, from equations (2) and (3), we get:
(yb ∗ zb )
) ∗ (γ 2 + γ + 1)rj2
⌋ ∗ ( 2π
3
4rj2
(yb ∗ zb ) 2
⌋rj
= K1 ⌊
V =
(yb ∗ zb )
4rj2
⌊

(4)

Where:
( 2π )(γ 2 + γ + 1)
K1 = 3
(yb ∗ zb )
The percentage of covered area of building sides (A and B) is given by:
(yb ∗ zb )
(yb ∗ zb )
(yb ∗ zb )
⌋ ∗ (πri2 + πrj2 ) ⌊
⌋ ∗ (πri2 + πrj2 )
⌋ ∗ 2π(ri2 + rj2 )
⌊
2
2
4rj
4rj
4rj2
W =
+
=
(yb ∗ zb )
(yb ∗ zb )
(yb ∗ zb )
⌊

(5)

14

Now, from equations (2) and (5), we get:
(yb ∗ zb )
⌋ ∗ 2π(γ 2 + 1)rj2
2
4rj
(yb ∗ zb ) 2
⌋rj
= K2 ⌊
W =
(yb ∗ zb )
4rj2
⌊

(6)

Where:
(2π)(γ 2 + 1)
K2 =
(yb ∗ zb )
To prove that maximizing the percentage of covered volume of building is equivalent to maximizing the percentage of covered area of building sides (A and B). From equations (4) and (6),
(yb ∗ zb ) 2
(yb ∗ zb ) 2
⌋rj is equivalent to maximizing K2 ⌊
⌋rj where K1 and
maximizing V = K1 ⌊
2
4rj
4rj2
K2 are constants.
To prove that maximizing the percentage of covered area of building sides (A and B) is
equivalent to maximizing the percentage of covered volume of building. From equations (4) and
(yb ∗ zb ) 2
(yb ∗ zb ) 2
⌋rj is equivalent to maximizing K1 ⌊
⌋rj where K1
(6), maximizing W = K2 ⌊
2
4rj
4rj2
and K2 are constants.

In Algorithm 2, we maximize the covered volume by placing the UAVs in alternating upsidedown arrangements. First, we find the horizontal distance between the building and the UAVs
xU AV = 0.7071xb (see Theorem 1) that guarantees the alternating upside-down arrangements.
Then, we divide the building sides A and B to square cells and place one UAV in front of the
square cell. In steps (8-16), we find the 3D locations of UAVs that cover the building from side
B. On the other hand, steps (17-25) find the 3D locations of UAVs that cover the building from
side A. Finally, the algorithm will output total number of UAVs and the total covered volume.
IV. SIMULATION RESULTS
Let the dimensions of the building, in the shape of a rectangular prism, be [0, xb = 30]×[0, yb =
40] × [0, zb = 60]. We use three methods to cover the building using UAVs. In the first method,
we place all UAVs in front of one building side (A or B) (FOBS). In the second method, we
place all UAVs above the building (C) (ABS). In the third method, we arrange the UAVs in
alternating upside-down arrangements (AUDA). For the first and second methods, we utilize
the circle packing in a rectangle approach [22] to maximize the covered volume. For the third
method, we apply Algorithm 2 to maximize the covered volume. In Figure 14, we find the
maximum total coverage for different antenna half power beamwidth angles θB . As can be seen
from the simulation results, the maximum total coverage is less than half for the FOBS and

15

Algorithm 2 Maximizing Indoor Wireless Coverage Using UAVs
1: Input:
2: The dimensions of building xb , yb and zb
3: The radius of the larger circular face rj
4: Initialization:
√
8−2
5: ri =
rj
2
6: xU AV = 0.7071xb
7: u = q = 0
8: The 3D locations of UAVs that cover the building from
side B are given by:
yb
9: For k1 = 1 : ⌊ ⌋
2rj
zb
10:
For s1 = 1 : ⌊
⌋
2rj
11:
u=u+1
12:

xq = xU AV + xb

13:

yu = (2k1 − 1)rj

14:

zu = (2s1 − 1)rj

15:

End

16: End
17: The 3D locations of UAVs that cover the building from
side A are given by:
yb
18: For k2 = 1 : ⌊ ⌋
3rj
zb
⌋
19:
For s2 = 1 : ⌊
3rj
20:
q =q+1
21:

xq = −xU AV

22:

yq = (2k2 )rj

23:

zq = (2s2 )rj

24:

End

25: End
26: Output:
27: The number of UAVs= u + q + 2k1 + 2s1
28: The covered volume=(u)(2)( π3 ∗ xb ∗ (ri2 + ri rj + rj2 ))

16

Total coverage (Normalized)

1
FOBS
ABS
AUDA

0.8
0.6
0.4
0.2
0

5
10
15
The antenna half power beamwidth (

20
θ )
B

Fig. 14: Total coverage vs. θB

100
FOBS
ABS
AUDA

Number of UAVs

80
60
40
20
0

8

10
12
14
16
18
The antenna half power beamwidth (

20
θ )

22

B

Fig. 15: Number of UAVs vs. θB

ABS methods, this is because providing wireless coverage from one building side will only
maximize the covered area of the building side. On the other hand, we improve the maximum
total coverage by applying the AUDA, this is because AUDA will allow us to use a higher
number of UAVs to provide wireless coverage compared with providing wireless coverage from
one building side, as shown in Figure 15.
In order to provide full wireless coverage for the building, we use UAVs with different channels
to cover the holes in the building. In Figure 16, we find the total number of UAVs required to

17

300
FOBS
ABS
AUDA

Number of UAVs

250
200
150
100
50
0

8

10
12
14
16
18
The antenna half power beamwidth (

20
θ )

22

B

Fig. 16: Number of UAVs vs. θB

provide full coverage. As can be seen from the figure, FOBS and ABS need high number of
UAVs to guarantee full wireless coverage for the building, due to the irregular shapes of the holes
in the building. Here, we can easily specify the number of UAVs required to cover each hole in
the building, due to the small projections of the holes in the building side. On the other hand,
AUDA needs fewer number of UAVs to provide full wireless coverage, due to the small-regular
shapes of the uncovered spaces inside the building. Here, we need only one UAV to cover each
hole. In Figure 17, we find the total transmit power consumed by UAVs when the building is
fully covered. Here, we assume that the threshold SNR equals 25dB, the noise power equals
-120dBm, the frequency of the channel is 2GHz and the antenna gain of each indoor user is
14.4 dB [16]. As can be seen from the figure, the total transmit power in all methods is very
small, due to the high gain of the directional antennas. Also, we can notice that the total power
consumed in FOBS and ABS is higher than that of AUDA. This is because the number of UAVs
required to fully cover the building in AUDA is fewer than that for FOBS and ABS.
V. C ONCLUSION
Choosing the appropriate placement of UAVs will be a critical issue when we aim to maximize
the indoor wireless coverage. In this paper, we study the case that the UAVs are using one channel,
thus in order to maximize the total indoor wireless coverage, we avoid any overlapping in their
coverage volumes. We present two methods to place the UAVs; providing wireless coverage from

18

Total transmit power consumed
by UAVs (Watts)

×10

-4

1.2
1
0.8
0.6
0.4
FOBS
ABS
AUDA

0.2
0

8

10
12
14
16
18
The antenna half power beamwidth (

20
θ )

22

B

Fig. 17: Total transmit power vs. θB

one building side and from two building sides. In the first method, we utilize circle packing theory
to determine the 3-D locations of the UAVs in a way that the total coverage area is maximized.
In the second method, we place the UAVs in front of two building sides and efficiently arrange
the UAVs in alternating upside-down arrangements. We show that the upside-down arrangements
problem can be transformed from 3D to 2D and based on that we present an efficient algorithm
to solve the problem. Our results show that the upside-down arrangements, can improve the
maximum total coverage by 100% compared to providing wireless coverage from one building
side.
ACKNOWLEDGMENT
This work was supported in part by the NSF under Grant CNS-1647170.
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