Towards Designing Systems with LargeNumber of Antennas for Range Extension in

Ground-to-Air CommunicationsHaneya Naeem Qureshi, Ali Imran

School of Electrical and Computer Engineering, University of Oklahoma, Tulsa, USAEmails: haneya@ou.edu, ali.imran@ou.edu

Abstract—Providing broadband connectivity to air-borne systems using ground based cellular networks isa promising solution as it offers several advantages oversatellite-based solutions. However, limited range of ter-restrial base stations is a key challenge in full realizationof this approach. This paper addresses this problem byproposing a mathematical framework for range extensionleveraging large number of antennas at the base station.In contrast to prior works where range is not consideredas a design parameter, we model the signal to noiseratio as a function of both number of antennas as wellas the range in line-of-sight ground-to-air systems. Thisallows us to derive analytical expressions to determinethe number of antennas required to increase range indifferent frequency bands and tracking and non trackingscenarios.

Index Terms—range extension, beamforming, ground-to-air, 3D antenna, tracking, signal-to-noise ratio

I. INTRODUCTION

Systems “above the clouds” [1] are the only re-maining areas today where broadband services are notfully available. Driven by users’ demand for seamlessconnectivity regardless of location and time, providingconnectivity in airborne systems is indispensable to thefuture of aircraft industry. According to a recent sur-vey, nearly 75% passengers are ready to switch airlinesto have access to faster internet and more than 20%passengers have already switched their airline for thesake of better in-flight internet access [2]. Like currentaircraft passengers, these high user expectations areequally anticipated for future users of ‘flying cars’as well as in unmanned aerial vehicle applications innext generation systems. This challenge is likely toaggravate in the next few years with increase in airtravel and smart devices carried by passengers.

To this end, solutions for air to ground communi-cations using ground based cellular networks is thesubject of several recent studies due to the multitudeof advantages offered by this approach as comparedto satellite-based connectivity [3]-[6]. While satellitecommunication has been used for voice communica-tion, its intrinsic capacity limits, high latency, lack ofscalability and cost make it unsuitable for carryingmultimedia and realtime traffic [4]. On the other hand,

utilizing a ground-based cellular system to create a di-rect link between the airborne systems and the groundfor broadband connectivity is a fast, scalable andan economical solution. Additionally, unlike satellitebased approach, terrestrial cellular approach allowsexpansion of the network capacity exactly where itis needed by adapting the cell sizes or increasing thenumber of cells [3].

However, limited range of ground-based cellularsystems hinders the full realization of this approach.This problem is more pronounced in parts of the world,such as Europe, where land masses are separated byseas. In such cases, base stations can only be deployedat most at the edges of the land masses, thus limitingthe range of service from ground to airborne system.In this paper, we propose a solution to this problemby leveraging large number of antennas at the basestation. While systems with large number of antennashave been widely studied in terrestrial networks, themain focus has been on capacity enhancement suchas in [7]-[8]. Range extension using large number ofantennas is not considered in terrestrial systems dueto the large number of multipaths. Therefore, Signal-to-Noise (SNR) is either computed at cell center, celledge or by averaging over all user locations drawnfrom a fixed distribution. However, two recent studies[9]-[10] have focused on cell coverage extension interrestrial systems. Authors in [9] propose a rate-basedcell coverage expansion scheme in ground-based sys-tems while authors in [10] leverage orthogonal randomprecoding in Massive MIMO terrestrial systems. Onthe other hand, we investigate the use of large numberof antennas itself for range extension in ground-to-aircommunications where line-of-sight is the dominantpath. The focus of this study is to investigate SNR asa function of both number of antennas as well as therange. To the best of authors’ knowledge, such threedimensional analysis leading to an SNR expressionas function of range, elevation angle and numberof antennas does not exist in current literature. Ourderived expressions also allow analysis of differentscenarios that stem from change in operational fre-

2018 IEEE 29th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC)

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Fig. 1: System model.

quency and tracking capability of the antenna systemand thus provides an essential tool for dimensioningsystems with large number of antennas for ground-to-air communications.

This paper is organized as follows: The systemmodel is described in Section II and a mathematicalframework for range extension is presented in SectionIII. Section IV presents the numerical results andanalysis and Section V concludes this paper.

II. SYSTEM MODEL

We consider a UAV equipped with single receiveantenna at a height of h meters being served by anactive antenna system (AAS) at the base station (BS)as shown in Fig 1. The range, which is distance fromthe center of the BS antenna array to the UAV isdenoted by d.

A. Antenna Array Model

We consider full dimension MIMO (FD-MIMO)utilizing an AAS with 2D planar antenna array struc-ture. Unlike conventional LTE systems, for FD-MIMO,3GPP proposes the organization of the radio resourceimplementation on the basis of antenna ports andantenna elements [11]-[12], where each column ofactive antenna elements in the array is referred to as anantenna port. We consider an M ×N array comprisingof N elements and M ports. Since all elements in theantenna array carry the same signal, each antenna portis perceived as a single antenna by the UAV.

The 3GPP proposed element radiation pattern isgiven by [12]:

AE(θ, ϕ) = Gm − min{−(Av(θ) + Ah(ϕ)), Am}(1)

where Gm is the maximum element gain, ϕ and θdenote the azimuth and vertical angles respectively. θand angle of elevation of the BS to UAV are comple-mentary angles. The radiation patterns in vertical andhorizontal directions are modelled as:

0 20 40 60 80 100 120 140 160 180

Vertical angle ( ) [o]

-60

-50

-40

-30

-20

-10

0

10

20

Ante

nna p

ort

pattern

(A

) [d

B]

N=20

N=10

N=5

Fig. 2: Antenna port radiation pattern for θtilt = 70o.

Av(θ) = − min

[12

(θ − 90θ3dB

)2

, Av

](2)

Ah(ϕ) = − min

[12

(ϕ

ϕ3dB

)2

, Am

](3)

where ϕ3dB and θ3dB are the half power beamwidthsin the azimuth and elevation domains respectively, Am

is the maximum attenuation and Av is the vertical sidelobe attenuation.

The array factor matrix for AAS, AF is given by[12] as

AF = W ◦ V (4)

where ◦ is the Hadamard product and V and W areN × M matrices containing the array responses ofindividual radiation elements and weights to be appliedto these elements respectively. Each entry of thesematrices in the rth row and cth column is given as[11]:

vr,c = exp(i2π

((c − 1)

dh

λsin ϕ sin θ + (r − 1)

dv

λcos θ

))(5)

wr,c =1√NM

exp(

− i2π(

(c − 1)dh

λsin ϕscan

sin θtiltc+ (r − 1)

dv

λcos θtiltc

))(6)

where dh is the horizontal separation between antennaports, dv is the vertical separation between antennaelements, ϕscan is the horizontal steering angle andθtiltc

is the downtilt angle for the cth port.The overall radiation pattern for cth antenna port

can now be represented as:

A(θ, ϕ, θtilt) = AE(θ, ϕ) + 20 log10 |AFc(θ, θtilt)|

(7)

where AFcis the sum of entries in cth column of the

matrix AF . In this work, we assume θtiltc= θtilt. The

antenna pattern is shown in Fig. 2 for θtiltc= 70o,

ϕ = 0o, Gm = 8dBi and ϕ3dB = θ3dB = 65o. Themain lobe shifts to the desired value of downtilt andbecomes narrower with increasing antenna elements.

B. 3D Channel

The channel gain between the transmitting antennaport and the receiver (UAV) can be represented as:

hc =N∑

(r∈port c)=1

wr,c(θtilt)√

G(θ, ϕ) vr,c(θ, ϕ) (8)

= wTc (θtilt)

√G(θ, ϕ)vc(θ, ϕ) (9)

for c = 1, . . . , M . wc and vc are the c-th columns ofthe matrices W and V respectively and G representsthe vertical and horizontal attenuation in linear scalegiven as:

G(θ, ϕ) = 10−1.2

((ϕ

ϕ3dB

)2+

(θ−90θ3dB

)2)

(10)

C. Downlink SNR

The received complex baseband signal at the user isgiven by:

y =√

PtF10Gm10 hH x̃ + n (11)

where Pt is the transmitted power, Gm is the max-imum antenna gain, h = [h1 . . . hM ] is the 1 × Mcomplex channel vector from the BS to the user givenby (9), x̃ is the precoded transmit signal from AAS,n is the additive white Gaussian noise with zero meanand variance equal to σ2

n and F is the free space pathloss given by:

F =(

λ

4πd

)2

(12)

Assuming perfect channel state estimation at thetransmitter and employing conjugate precoding at thetransmitter, i.e., x̃ = h

||h||x, where x is the transmitsignal from AAS, (11) reduces to:

y =√

PtF10Gm10 ||h||x + n (13)

The downlink SNR, γ for the UAV is then given as:

γ =PtF10

Gm10 ||h||2

σ2n

(14)

III. MATHEMATICAL FRAMEWORK FOR RANGEEXTENSION

For range extension leveraging large number ofantennas, we derive an analytical expression for thenumber of antennas, M as a function of the range d,target SNR, γ and height of UAV, h by substituting(9) in (14):

γ =PtF10

Gm10

σ2n

∥∥ [wT

1

√Gv1 . . .wT

M

√GvM

] ∥∥2(15)

=PtF10

Gm10

σ2n

Tr

wT

1

√Gv1

...wT

M

√GvM

[wT

1

√Gv1 . . .wT

M

√GvM

]

=PtF10

Gm10

σ2n

Tr

(wT1

√Gv1)2 . . . w1wMGv1vM

.... . .

...wMGvMwT

1 v1 . . . (wTM

√GvM )2)

=

PtF10Gm10

σ2n

((wT

1

√Gv1)2 + . . . + (wT

M

√GvM )2

)(16)

In this study, we assume ϕscan = 0 as we areconcerned with elevation beamforming only. Hence(16) reduces to:

γ =PtF10

Gm10

σ2n

M(wT1

√Gv1)2

=PtF10

Gm10 MG

Nσ2n

exp(−i2π(1 − 1)dy

λ cos θtilt

...exp(−i2π(N − 1)dy

λ cos θtilt

T exp(i2π(1 − 1)dy

λ cos θ...

exp(i2π(N − 1)dy

λ cos θ

2

=PtF10

Gm10 MG

Nσ2n

N∑

k=1

exp(−i2π(k − 1)dy

λcos θtilt) exp(i2π(k − 1)

dy

λcos θ)︸ ︷︷ ︸

A

2

(17)

where Tr is the Trace operator. We further identifytwo cases of (17): tracking and no tracking. Trackingin airborne systems is the scenario when both θ andθtilt are aligned with each other as shown in Fig. 2,such that the UAV always receives main lobe gain asit moves. The second case of no tracking occurs whenthis type of dynamic beamforming is absent. Applyingexponential sum formulas to (17), the term A in (17)for both cases reduces to:

A =

{N θ = θtilt

sin(0.5Ma)sin(0.5a) exp

(ia(N−1)

2

)θ ̸= θtilt

(18)

where a = 2πdy

λ (cos θ − cos θtilt).From geometry in Fig. 1, θ can be expressed in

terms of h and d as: θ = cos−1(h/d). Substitutingthis θ in (17)-(18) and then performing algebraicmanipulation leads to the expression for number ofantennas in terms of range, height and target SNRin dB (γdb) given by (19), where ⌈.⌉ is the ceilingfunction.

IV. NUMERICAL RESULTS AND ANALYSIS

Fig. 3 shows the SNR in (17) as a function ofnumber of antennas and range for Pt = 30 dBm,f = 2.0 GHz and h = 1000m. In contrast to priorworks which depict SNR as a function of numberof antennas only, our study adds another dimensionof range into SNR expression. The effect of number

-100 3

0

100 2.5

10

2200

SN

R (

db) [

dB

]

Number of antennas (M) Range (d) [m]

104

20

1.5300

30

1400 0.5

500 0

0

5

10

15

20

25

30

35

SNR (db

)[dB]

Fig. 3: SNR as a function of number of antennas and range(with tracking).

0 0.5 1 1.5 2 2.5 3

Range (d) [m] 104

0

100

200

300

400

500

600

700

800

900

1000

Num

ber

of A

nte

nnas (

M) db

=10, from (18)

db=10, from simulation

db=15, from (18)

db=15, from simulation

db=20, from (18)

db=20, from simulation

Fig. 4: Number of antennas verses range for different targetSNRs at h = 1000m and f = 2GHz.

0 0.5 1 1.5 2 2.5 3

Range (d) [m] 104

0

20

40

60

80

100

Num

ber

of A

nte

nnas (

M) f=2.0 GHz

f=2.5 GHz

f=3.0 GHz

f=3.5 GHz

Fig. 5: Number of antennas verses range with differentfrequencies for target SNR of 5dB at h = 1000m.

of antennas in tandem with range can be observedfor SNR in Fig. 3. Although SNR increases withincreasing number of antennas, as expected rangeextension causes degradation in SNR.

The proposed framework also allows to design thesystem for a target received signal strength or receivedSNR. More specifically, for given design constraintsgoverned by the target SNR, our model allows todetermine the number of antennas required to increasethe range from d to md, where m can be any realnumber. This is depicted in Fig. 4. For higher targetSNRs, number of antennas increases to achieve the

2 2.5 3 3.5 4

Range (d) [m] 104

0

20

40

60

80

Vert

ical A

ngle

()

Num

ber

of A

nte

nnas (

M)

, h=1000 m

, h=7000 m

, h=10000 m

M, h=1000 m

M, h=7000 m

M, h=10000 m

Fig. 6: Number of antennas and vertical angle verses rangewith different UAV heights for target SNR of 5dB at f =

2GHz.

-400

-20

10000

0

100

SN

R (

db)

[dB

]

Number of antennas (M)

8000

20

Range (d) [m]

6000

40

2004000

300 2000

Fig. 7: SNR as a function of number of antennas and rangeat θtilt = 70o (no tracking).

-300

-20

-10

10000

0

100

SN

R (

db)

[dB

]

10

8000

Number of antennas (M)

20

Range (d) [m]

6000

30

2004000

300 2000

Fig. 8: SNR as a function of number of antennas and rangeat θtilt = 85o (no tracking).

same range extension. Our derived expression in (19)is also corroborated through simulations in Fig. 4.

Our proposed framework can be extended for anyfrequency and UAV heights. Fig. 5 quantifies theincrease in number of antennas with increase in fre-quency, owing to the increased free space path lossat higher frequencies. The number of antennas alsoincrease at higher UAV heights as shown in Fig. 6.Although the main lobe radiation pattern is in linewith the tilt angle through beamforming or tracking,higher UAV heights result in higher vertical angleswhich in turn increase antenna attenuation in (2),leading to decrease in amplitude of main lobe from

M(γdb, d, h) =

⌈10

γdb10 4πdσ2

n

NPtλ210Gm10 10

−1.2

((ϕ

ϕ3dB

)2+

( cos−1(hd )−90

θ3dB

)2) ⌉

θ = θtilt

⌈10

γdb10 4πdσ2

nN sin(0.5a)

sin(0.5Na)Ptλ210Gm10 10

−1.2

((ϕ

ϕ3dB

)2+

( cos−1(hd )−90

θ3dB

)2) ⌉

θ ̸= θtilt

(19)

(1). Hence, more antennas are required to compensatefor the decreased antenna gain. Dynamically adjustableradiation patterns in an antenna array system can berealized through smart antenna techniques [13]-[15].

Next, we investigate the case when θ ̸= θtilt i.e.,tracking-less scenario. Figures 7 and 8 show this casefor two different values of θtilt, 70o and 85o. Ascompared to the case with tracking, θ is no longer inline with tilt angle of antenna as range varies. In Fig. 7,maximum SNR at around 3000m can be attributed themaximum value of antenna gain at 3000m, since a tiltangle of 70o roughly corresponds to θ at a distance of3000m. Similarly, in constrast to Fig. 3, SNR increaseswith range in Fig. 8 as the vertical angle increases withrange and attains a maximum value where θ equalsθtilt = 85o (at d = 10000m).

V. CONCLUSION

The problem of range extension in ground-to-aircommunications is addressed by leveraging large num-ber of antennas at the base station. In contrast toprevious works, where SNR as a function of numberof antennas is computed at fixed distances or aver-aged over possible user positions, in this work, weadd a new dimension of range to SNR derivation.The proposed mathematical framework allows dimen-sioning of systems with large number of antennasin terms of number of antennas for a given rangeand SNR threshold and vice versa. The frameworkalso allows analysis of effect of different frequencybands and tracking and non-tracking scenarios. Whileresults for tracking scenario provide quantification ofintuitively expected trend where SNR increases withnumber of antennas and then saturates, non-trackingscenarios characterize counter-intuitive insights whichcan include both increasing and decreasing patterndepending on tilt angle. Thus the proposed frameworkprovides a basic new tool for dimensioning systemswith large number of antennas for ground-to-air com-munication, which can be extended to multiple usersas well. Such investigations of multi-user interferenceusing the proposed model can be focus of a futurestudy.

ACKNOWLEDGEMENT

This work is supported by the National Science Foun-dation under Grant Number 1619346 and Grant Num-

ber 1718956.

REFERENCES

[1] A. Jahn, M. Holzbock, J. Muller, R. Kebel, M. de Sanctis,A. Rogoyski, E. Trachtman, O. Franzrahe, M. Werner, andF. Hu, “Evolution of aeronautical communications for personaland multimedia services,” IEEE Communications Magazine,vol. 41, no. 7, pp. 36–43, July 2003.

[2] Honeywell, “Honeywell survey: Airlines risk losingpassengers due to poor Wi-Fi,” Available [Online]:https://www.honeywell.com/newsroom/pressreleases/2016/07/honeywell-survey-airlines-risk-losing-passengers-due-to-poor-wifi, 2016.

[3] Nokia, “Using air-to-ground LTE for in-flight ultra-broadband,” Strategic white paper, 2017.

[4] N. Tadayon, G. Kaddoum, and R. Noumeir, “Inflight broad-band connectivity using cellular networks,” IEEE Access,vol. 4, pp. 1595–1606, 2016.

[5] D. Xu, X. Yi, Z. Chen, C. Li, C. Zhang, and B. Xia, “Coverageratio optimization for hap communications,” in 2017 IEEE28th Annual International Symposium on Personal, Indoor, andMobile Radio Communications (PIMRC), Oct 2017, pp. 1–5.

[6] E. Dinc, M. Vondra, S. Hofmann, D. Schupke, M. Prytz,S. Bovelli, M. Frodigh, J. Zander, and C. Cavdar, “In-flightbroadband connectivity: Architectures and business models forhigh capacity air-to-ground communications,” IEEE Commu-nications Magazine, vol. 55, no. 9, pp. 142–149, 2017.

[7] E. Bjrnson, E. G. Larsson, and M. Debbah, “Massive MIMOfor maximal spectral efficiency: How many users and pilotsshould be allocated?” IEEE Transactions on Wireless Commu-nications.

[8] H. N. Qureshi, I. H. Naqvi, and M. Uppal, “Massive MIMOwith quasi orthogonal pilots: A flexible solution for TDDsystems,” in IEEE Vehicular Technology Conference Fall 2017,Toronto, Canada.

[9] G. Hattab and D. Cabric, “Rate-based cell range expansionfor downlink massive MIMO heterogeneous networks,” IEEEWireless Communications Letters, vol. PP, no. 99, pp. 1–1,2017.

[10] N. T. Nguyen and K. Lee, “Cell coverage extension withorthogonal random precoding for massive MIMO systems,”IEEE Access, vol. 5, pp. 5410–5424, 2017.

[11] Q. U. A. Nadeem, A. Kammoun, M. Debbah, and M. S.Alouini, “Design of 5G full dimension massive MIMO sys-tems,” IEEE Transactions on Communications, vol. PP, no. 99,pp. 1–1, 2017.

[12] 3rd Generation Partnership Project, “TR37.840 v12.0.0: Studyof radio frequency and electromagnetic compatibility require-ments for active antenna array system (AAS) base station ,”Tech. Rep., March 2013.

[13] V. R. Rentapalli and Z. J. Khan, “MIMO and smart antennatechnologies for 3G and 4G,” 2011.

[14] J. H. Winters, “Smart antenna techniques and their applicationto wireless ad hoc networks,” IEEE wireless communications,vol. 13, no. 4, pp. 77–83, 2006.

[15] C. Behroozi, E. Teller, and R. W. DeVaul, “Dynamicallyadjusting width of beam based on altitude,” May 10 2013,US Patent 20140333491A1.