Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

Digital Object Identifier 10.1109/ACCESS.2019.DOI

Nonlinearity-Based Single-ChannelMonopulse Tracking Method forOFDM-Aided UAV A2G CommunicationsXI PAN1, CHAOXING YAN2, (Member, IEEE), JIANKANG ZHANG3 (Senior Member, IEEE).1School of Mechatronical Engineering, Beijing Institute of Technology, Beijing, 100081, China (e-mail: panxi@bit.edu.cn)2Beijing Research Institute of Telemetry Beijing, 100076, China (e-mail: chaoxing@bit.edu.cn)3Electronics and Computer Science, University of Southampton, SO17 1BJ, U.K. (e-mail: jz09v@ecs.soton.ac.uk)

Corresponding author: C. Yan (e-mail: chaoxing@bit.edu.cn).

This research was supported in part by the the National Natural Science Foundation of China under Grant U1730109 and Grant 61571401.

ABSTRACT Unmanned aerial vehicles (UAVs) have attracted great interest in rapid deployment forboth civilian and military applications. The conventional UAV monopulse tracking technique requiresdedicated pulses which suffer from multipath effect in air-to-ground (A2G) link with low elevation angles,whereas the orthogonal frequency division multiplexing (OFDM) for A2G high rate communication underfrequency selective fading channel was not yet investigated for UAV target tracking at ground station.In this paper, we propose a single-channel monopulse tracking (SCMT) angle estimation method inOFDM tracking receiver exploiting square- and absolute-value nonlinear detection of amplitude-modulateddifference signals. Extensive simulations are conducted to validate the proposed estimation method in termsof estimation range and estimation root mean squared error (RMSE). Results show that, the proposed angleestimation method exhibits S-shaped curve characteristic under different angle errors, which is insensitiveto channels and modulations. The proposed method obtains angle estimation RMSEs smaller than 0.18◦

for antenna element distance d = 0.5 m with 10 MHz OFDM signals. For both square- and absolute-valuemethods, a maximum degradation of 0.02◦ for angle estimation RMSEs is observed under Rician channelscompared with the estimation under additive white Gaussian noise (AWGN) channels, whereas the absolute-value estimation outperforms the square-value estimation.

INDEX TERMS UAV target tracking, Air-to-ground communication, Single-channel monopulse tracking,OFDM signals, Frequency selective fading channel, Nonlinear detection

I. INTRODUCTION

Unmanned aerial vehicles (UAVs) have tremendous potentialin both military and civilian applications, including disastersearch and rescue operations, surveillance, remote sensing,traffic monitoring, and goods transportations [1]–[3]. Posi-tion and orientation can greatly impact UAV link quality [4],formation control [5], path planning [6], and collision avoid-ance [7]. Targets tracking has found wide applications inradar, mobile satellite communication, and UAV remote sens-ing. Existing localization methods include global positioningsystem (GPS), beacon (or anchor) nodes and proximity-basedlocalization, etc [8]. As we classified in [4], the unmannedaerial systems (UASs) differ one to each other for size andstructure, like long-endurance UAVs of Predator and Globalhawk, short-range small UAV of Scout, and very close-rangeone of Raven. UAV regulations in most countries usually

require to equip with a GPS and an inertial measurementunit (IMU) for providing position information at any time [9].When the GPS signal of conventional satellite-based systemsis weak, ground-based positioning systems can be used inthe context of indoor navigation [10]–[12], wireless emer-gency services and tactical military operations [13]. With therapid development of wireless communication techniques,the communication signals available can be utilized andshared by UAV and ground station (GS) cooperatively to cal-culate the UAV location and tracking the moving target [14],[15].

A. UAV POSITIONING AND TRACKING

Generally, the airborne and ground stations have omnidirec-tional antennas or directional antennas for UAV communica-tions [4]. Relatively large UAS often uses directional highly

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X. Pan et al.: Nonlinearity-Based Single-Channel Monopulse Tracking Method for OFDM-Aided UAV A2G Communications

focused beams to achieve connectivity with more distinctsystems. Directional antennas usually require node locationinformation for beam pointing. UAV communication linkscan be broadly classified into two aspects namely, air-to-ground (A2G) communications and air-to-air (A2A) com-munications [16], [17]. In multi-UAV networks, the UAVposition can be determined based on the ranging estimatefrom different transmitters, whereas the UAV position canalso be calculated using ranging and angle information ofsingle target.

The ranging-based localization methods in UAV commu-nication systems infers location information taking advan-tage of a distance-dependent parameter in radio signals ofmulti-UAV networks [18]–[20]. The methods of receivedsignal strength (RSS) [21], time of arrival (TOA) [22], [23],time difference of arrival (TDOA) [24], frequency differenceof arrival (FDOA) [25], and angle of arrival (AOA) [26]are the most popular types of measurements. Localizationschemes based on TOA or TDOA offer high precision,but this comes at the cost of a very complex process ofaccurate time synchronization among all users [27]. Thislocalization requires multiple receivers or stations [28]–[30]and its performance is also highly related to the receiver-target deployment [31]. Ultra-wide bandwidth-based systemsare commonly used in the localization community to obtaindesirable localization performance and simple multipath mit-igation without costly estimators but at the cost of a largebandwidth [32].

The other family member of self-positioning methodsin UAV systems, monopulse tracking method is designedfor tracking UAV target via a single array antenna on theground station [33]. Conventional monopulse techniquesusually require dedicated pulse to estimate the direction ofa UAV target in A2G communication system. Additional-ly, linear modulations, continuous phase modulations, anddirect-sequence spread-spectrum signals were also exploitedto design monopulse tracking benefitting from their constantenvelope characteristics [34], [35]. However, these signalswith high rate suffer from multipath effect for A2G link withlow elevation angles.

The airborne transmitter antenna is usually mounted on theunderside of the aircraft fuselage and the GS is equipped witha tracking antenna. Active phased arrays, passive phased ar-rays and switched multiple-beam antennas are the approach-es that enable electronically controlled beam steering andshaping. In order to achieve accurate UAV target pointing,the ground array antenna can provide pointing errors inelevation and azimuth related to the antenna beams of threetracking signals: the azimuth difference signal, the eleva-tion difference signal and the sum signal. The monopulsetracking receivers can be implemented in single-channel,two-channel, and three-channel configurations based onamplitude-modulated difference signals [36]–[39]. The num-ber of receiver channels of monopulse antennas is two forone-plane tracking and three for two-plane tracking [40].More specifically, Shang et al. [38] proposed a phase calibra-

tion method for single-channel monopulse tracking (SCMT)systems using error voltage’s convergence trajectory datawith the aid of the curve fitting technique. Champion [39]designed a three-channel monopulse tracking receiver forupgrading tracking stations relying on commercial off-the-shelf equipment. Zheng et al. [41] provided a mathematicalclosed-form solution for identifying two targets based on afour-channel monopulse including both phase and amplitudemonopulse measurement. Zhang et al. [42] suggested meth-ods to localize multiple unresolved extended targets. Jardaket al. [43] divided the antenna array into multiple overlappingsets each of four antennas to detects two targets at generalizedlocations. Moreover, Nickel [44] overviewed the monopulsetechniques and introduced the multi-dimensional generalizedmonopulse formula. For tracking requirement of communi-cation satellites, Lacheta et al. designed a generic digitalmonopulse tracking receiver in [45], where the receiver wascapable of being configured into single-channel and two-channel by adjusting the firmware. Conventional monopulsetracking systems are designed to operate with antenna arrays,whereas a multimode extractor for feed chain of monopulsetracking feed was presented at Ka band in [46]. In multi-mode monopulse tracking system, when the antenna receivesan incident wave, the output of the communication signalis maximum and the antenna points directly toward a targetsignal source. When the boresight axis of the antenna feed isnot in line with the target, higher order modes are activatedin the circular waveguide.

B. MOTIVATION AND CONTRIBUTIONFrom the brief review above, we can find that monopulsetechniques are well studied in both radar signal process-ing and target tracking literature. However, to the best ofour knowledge, there is no literature studying monopulsetracking method utilizing the OFDM signals in UAV A2Gcommunication systems. In the context of UAV A2G linkswith low elevation angles and multipath fading, OFDM isan effective solution to broadband communication resultingfrom its high spectral efficiency and robustness against fre-quency selective fading [47]–[50]. The amplitude-modulateddifference signals in conventional UAV monopulse track-ing system usually employ dedicated slave carrier pulses,spread-spectrum signals or single carrier linear modulation-s taking advantage of their approximately constant signalamplitudes, whereas the multicarrier OFDM signals withGaussian-like distribution were not yet investigated to gen-erate the amplitude-modulated difference signals for angleestimation. To fill this gap, this paper presents a novel SCMTmethod using the OFDM signals which was designed for highrate A2G telemetry and image data transmission, instead ofusing dedicated signals in UAV communication and trackingsystem. The monopulse tracking system in the ground stationoperates relying on a planar antenna array for developingtracking signals.

The main contributions of this paper are summarized asfollows:

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X. Pan et al.: Nonlinearity-Based Single-Channel Monopulse Tracking Method for OFDM-Aided UAV A2G Communications

d

UAV target

A

D

B

C

A-D

B-C

A+D

B+C

(A+C)-(B+D)

(A+B)-(C+D)

A+B+C+D

(A+D)-(B+C)

azimuth error Az

elevation error El

! channel

Auto-tracking

antenna

AB

Antenna

boresight

d sin( )

Tracking receiverCoupler

gE(t)

gA(t)

Shifter

ADCServo system

Az El

C D

gA(n)

gE(n)

|·|

or

|·|2

Az

El

g(t)

Down

converter

Monopulse

comparator

y! (t)

z! (n)

Air-to-g

round li

nk

FIGURE 1: Target tracking architecture of monopulse technique exploiting UAV A2G communication signal.

• We propose an angle estimation method relying on thenonlinear detection for amplitude-modulated differencesignals exploiting the OFDM communication signals atUAV ground station, and the angle estimation expres-sions are derived using two nonlinearity functions ofsquare-value and absolute-value in SCMT receiver.

• We find that the proposed angle estimation methodexhibits S-shaped curve characteristic under differentangle errors, which is insensitive to channels and mod-ulations. The estimation range relies on the distancebetween antenna elements. The S-curve of the absolute-value estimation outperforms that of the square-valueestimation.

• Simulation results show that the angle estimation rootmean squared errors (RMSEs) will get smaller for in-creasing sampling rates and signal-to-noise ratios (S-NRs) of OFDM signal. A maximum degradation of0.02◦ of the angle estimation RMSEs will be observedunder Rician frequency selective channels comparedwith the estimation under additive white Gaussian noise(AWGN) channels for both square-value and absolute-value methods.

The remainder of this article is organized as follows. InSection II, we depict the diagram of the SCMT system inUAV A2G communication system. In Section III, we propose

a novel SCMT angle estimation method using nonlineardetection of OFDM signals. Simulation results and analysisare presented in Section IV, followed by our conclusions inSection V.

II. SIGNAL MODELThe monopulse tracking system consists of antenna-feedsystem, monopulse comparator, coupler, monopulse trackingreceiver and antenna servo system, as shown in Fig. 1.Generally, two feeders A and B are separated by a distance dwith parallel pointing directions for UAV target. The receivedsignals are utilized to produce a phase difference ∆ϕ basedon the angle-of-arrival θ, and we have ∆ϕ = 2πd sin(θ)/λ,where λ is the wavelength of carrier frequency. This can beimplemented with two antenna elements of the antenna arrayinstead of two independent antennas. Monopulse comparatorgenerates the sum signal (Σ), azimuth error signal (∆Az) andelevation error signal (∆El). For the two-channel mode, theazimuth error signal and the elevation error signal are com-bined [51], whereas for the single-channel mode, the azimutherror signal and the elevation error signal are multiplexedand coupled with the sum signal as the amplitude modulationsignal [38]. The SCMT system with single receiver channelrequires only one down converter and analog-to-digital con-verter (ADC) chain [45].

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X. Pan et al.: Nonlinearity-Based Single-Channel Monopulse Tracking Method for OFDM-Aided UAV A2G Communications

At the airborne transmitter in the UAV A2G link, the timedomain OFDM signal x(n) can be expressed as

x(n) =1√Ns

Ns−1∑k=0

X(k)ej2πkn/Ns , 0 ≤ n ≤ Ns − 1, (1)

where Ns is the size of inverse fast Fourier transform (IFFT),and X(k) represents the data sequence modulated on the k-th subcarrier with M-ary quadrature amplitude modulation(M-QAM) or M-ary phase shift keying (M-PSK). Throughdigital-to-analog converter (DAC) and power amplifier, theoutput of the transmitter is denoted as x(t). Considering theA2G radio channel, the OFDM signal received at the groundstation, s(t), can be expressed as

s(t) =

∫x(t− τ)h(τ)dτ + w(t), (2)

where h(t) is the channel impulse response and w(t) repre-sents the zero-mean complex AWGN with zero mean and thevariance of σ2

w.At the ground station, the signal arriving at antenna ele-

ments A, B, C and D in Fig. 1 can be written as

yA(t) = Ams(t) sin(ωt+πd

λsin θA +

πd

λsin θE), (3)

yB(t) = Ams(t) sin(ωt− πd

λsin θA +

πd

λsin θE), (4)

yC(t) = Ams(t) sin(ωt− πd

λsin θA −

πd

λsin θE), (5)

as well as

yD(t) = Ams(t) sin(ωt+πd

λsin θA −

πd

λsin θE), (6)

respectively, where Am is the signal gain, ω represents thefrequency, λ is the wavelength, and d denotes the distancebetween A (C) and B (D), or between A (B) and D (C).Moreover, θA and θE denote the angle of azimuth error andelevation error, respectively.

III. NONLINEARITY-BASED UAV TRACKING METHODWITH OFDM SIGNALSIn this section, we commence with angle estimation basedon square-value nonlinearity using OFDM signals receivedat tracking receiver. Then, we analyze the practical imple-mentation approximation and propose an alternative methodbased on absolute-value nonlinearity.

A. SQUARE-VALUE-BASED ANGLE ESTIMATIONIn the SCMT receiver, the sum signal and difference signalscan be expressed as (7) – (9), where the difference slope µis the scaling factor designed in monopulse antenna and it isassumed to be µ = 1 here. In terms of small azimuth andelevation angle errors θA and θE , because of the approxima-tion cos(πdλ sin θA) ≈ 1 and sin(πdλ sin θA) ≈ πd

λ θA, we canrewrite (7) – (9) as (10) – (12).

yΣ(t) ≈ 4Ams(t) sin(ωt), (10)

y∆A(t) ≈ 4Amµs(t)

πd

λθA cos(ωt), (11)

y∆E(t) ≈ 4Amµs(t)

πd

λθE cos(ωt). (12)

These azimuth error (∆Az) and elevation error (∆El) inFig. 1 are multiplied with the azimuth/elevation scan (AES)pulses gA(t) and gE(t),

gA(t) =

+1, 0 < t ≤ T

2,

−1,T

2< t ≤ T,

and gE(t) = gA(t+T

4).

(13)where T is the period of pulses.

The multiplied signals y∆A(t)gA(t) and y∆E

(t)gE(t) arecoupled with the sum signal through a π/2 phase shifterwhich aligns the sum signal yΣ′(t) in order to get the max-imum signal at the output. The sum signal can be expressedas,

yΣ′(t) = 4Ams(t) cos(ωt). (14)

The coupler output signal yΣ∆(t) of (15) is an amplitudemodulation signal and the modulation index is proportionalto the coupling factor G [45].

The amplitude modulation signal is down-converted andthen is filtered with low-pass filter to the baseband digitalsampling signal zΣ∆(n), where n is the sampling index. Thedigital tracking receiver detects the sampling signal using theAES pulses gA(n) and gE(n). Thus, we obtain the envelopedetection expressions rA(n) and rE(n) as follows,

rA(n) = E{gA(n) |zΣ∆(n)|2

}, (16)

rE(n) = E{gE(n) |zΣ∆(n)|2

}, (17)

where E{·} denotes the expectation. Then, rA(n) and rE(n)can be written as (18) and (19), respectively. Bearing in mindthat the expectations of pulses gA, gE in (13) can be given as

E{gA(n)gE(n)} = 0, (20)

E{g2A(n)} = {g2

E(n)} = 1, (21)

we derive the rA(n), rE(n) in (16) – (17) as

rA(n) = 16A2mG

πd

λµθAE{|s(n)|2}, (22)

rE(n) = 16A2mG

πd

λµθEE{|s(n)|2}. (23)

Therefore, the proposed angle estimations θA, θE relyingon OFDM signals s(n) can be formulated as

θA =rA(n)λ

16A2mµGπdE{|s(n)|2}

, (24)

andθE =

rE(n)λ

16A2mµGπdE{|s(n)|2}

. (25)

Define the secondary moment M2 , E{|zΣ∆(n)|2}, we cancalculate M2 as (26), where we have (Gπdµθ/λ)2 � 1

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X. Pan et al.: Nonlinearity-Based Single-Channel Monopulse Tracking Method for OFDM-Aided UAV A2G Communications

yΣ(t) = yA(t) + yB(t) + yC(t) + yD(t) = 4Ams(t) cos

(πd

λsin θA

)cos

(πd

λsin θE

)sin(ωt), (7)

y∆A(t) = yA(t)− yB(t)− yC(t) + yD(t) = 4Amµs(t) sin

(πd

λsin θA

)cos

(πd

λsin θE

)cos(ωt), (8)

y∆E(t) = yA(t) + yB(t)− yC(t)− yD(t) = 4Amµs(t) cos

(πd

λsin θA

)sin

(πd

λsin θE

)cos(ωt), (9)

yΣ∆(t)=yΣ′(t) +G [y∆A(t)gA(t) + y∆E

(t)gE(t)]=4Ams(t) cos(ωt)

[1 +G

(πd

λµθAgA(t) +

πd

λµθEgE(t)

)]. (15)

for small value of θ =√θ2A + θ2

E . Hence, by neglecting(Gπdµθ/λ)2 in (26), we have the approximation

M2 ≈ 8A2mE{|s(n)|2}. (27)

Thus, we achieve the updated angle estimation θA, θE as,

θA =rA(n)λ

2µGπdM2, (28)

andθE =

rE(n)λ

2µGπdM2, (29)

which are expressed as normalization by OFDM signal powerE{|s(n)|2}.

For conventional UAV tracking receiver in low rate datatransmission system using direct-sequence spread-spectrum,the signal s(n) is replaced with the constant envelope spread-spectrum sequence c(n′) and the fact that |c(n′)| = 1will eliminate the influence of signal amplitude. However,OFDM signal for high rate data transmission will benefitfrom its robustness against A2G multipath fading channeland it is capable of achieving desired angle estimation by ourproposed algorithm.

B. IMPLEMENTATION AND ALTERNATIVE ESTIMATIONWITH ABSOLUTE-VALUEConsidering the practical implementation, we can approxi-mate the expectation rA(n) (16), rE(n) (17) over a period ofT in (13) as the accumulation,

rA(n) ≈∑T

gA(n) |zΣ∆(n)|2 , (30)

rE(n) ≈∑T

gE(n) |zΣ∆(n)|2 . (31)

Similarly, the secondary moment M2 is approximated as theaccumulation,

M2 ≈∑T

|zΣ∆(n)|2 . (32)

Accordingly, we approximate the angle estimations (28) and(29) relying on the signal power as θ′A, θ′E ,

θ′A ≈λ∑T gA(n) |zΣ∆(n)|2

2µGπd∑T |zΣ∆(n)|2

, (33)

and

θ′E ≈λ∑T gE(n) |zΣ∆(n)|2

2µGπd∑T |zΣ∆(n)|2

. (34)

which are expressed as normalization by OFDM signal powerΣT |zΣ∆(n)|2 over a period of T .

Alternative Estimation with Absolute-Value. After investi-gating the estimations θA, θE above, we hereby present alter-native angle estimation solutions (35) – (36) using absolute-value instead of the square-value in (16) and (17).

rA1(n) = E{gA(n) |zΣ∆(n)|

}, (35)

rE1(n) = E{gE(n) |zΣ∆(n)|

}. (36)

Define the first moment M1 = E{|zΣ∆(n)|}. we thendirectly derive the angle estimation expressions as,

θA1 =rA1(n)λ

µGπdM1, θE1 =

rE1(n)λ

µGπdM1. (37)

We approximate the angle estimations θA1, θE1 as (38) and(39) relying on normalization by the absolute value of OFDMsignal ΣT |zΣ∆(n)|, i.e.

θ′A1 ≈λ∑T gA(n) |zΣ∆(n)|

µGπd∑T |zΣ∆(n)|

, (38)

andθ′E1 ≈

λ∑T gE(n) |zΣ∆(n)|

µGπd∑T |zΣ∆(n)|

. (39)

It is very challenging to derive the theoretical performanceof (33)–(39) for multicarrier OFDM signals. In the followingsection, we will evaluate the angle estimation performance ofthe proposed method through extensive simulations.

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X. Pan et al.: Nonlinearity-Based Single-Channel Monopulse Tracking Method for OFDM-Aided UAV A2G Communications

rA(n) = 8A2mE

{gA(n)|s(n)|2

[1 +G

πd

λµ(θAgA(n) + θEgE(n))

]2}, (18)

rE(n) = 8A2mE

{gE(n)|s(n)|2

[1 +G

πd

λµ(θAgA(n) + θEgE(n))

]2}. (19)

M2 = 8A2mE

{|s(n)|2

[1 +G

πd

λµ(θAgA(n) + θEgE(n))

]2}

= 8A2mE

{|s(n)|2

[1 +

(Gπdµθλ

)2]}, (26)

TABLE 1 Parameters setting in simulations

Parameter ValuesAntenna monopulseFrequency 1.5 GHzElement distance, d 0.5 m, 0.9 mCoupling factor, G 1/4Slope, µ 1Pulse period, T 1 msNs of OFDM 1024OFDM sampling rate 5.12, 10.24, 20.48 MHzModulation 4QAM, 16QAMChannel Rician, AWGNRice factor, K 10 dB

IV. RESULTS AND DISCUSSIONSIn this section, we will evaluate our proposed method interms of angle estimation range as well as the estimationRMSE performance using OFDM signals in both AWGN andfrequency-selective channel.

A. SIMULATION SETTINGFollowing the target tracking architecture described in Fig. 1,we set the simulation frequency for monopulse trackingantenna to be L-band (1.5 GHz) and the antenna elementdistance is d = 0.5 m or 0.9 m with coupling factor G =1/4, difference slope µ = 1 and AES pulse period T = 1 ms.Our OFDM system has an IFFT/FFT length of Ns = 1024,where the edge IFFT bins are not used. The spacing betweentwo subcarriers is 10 kHz with each subcarrier mapped byM-QAM. The sampling rate of OFDM signals is 10.24 MHz.The Rician fading channel used is modelled as 10 paths withpath delays τn of n =1, 2, ..., 10 samples, exponentiallydecaying path gains of e−τn/3 and K factor of 10 dB [52].The parameters are summarized in Table 1.

Following the setting above, we express the proposedangle estimations of (33) and (34) as

θ′A =2λ∑T gA(n) |zΣ∆(n)|2

πd∑T |zΣ∆(n)|2

, (40)

and

θ′E =2λ∑T gE(n) |zΣ∆(n)|2

πd∑T |zΣ∆(n)|2

. (41)

The corresponding absolute-value estimation in (38) and (39)can be expressed as,

θ′A1 =4λ∑T gA(n) |zΣ∆(n)|

πd∑T |zΣ∆(n)|

, (42)

and

θ′E1 =4λ∑T gE(n) |zΣ∆(n)|

πd∑T |zΣ∆(n)|

. (43)

To the best of our knowledge, there is no literature study-ing monopulse tracking taking advantage of OFDM signals.Therefore, we present our simulation results in the frame-work of angle estimation range and RMSE performance forour proposed methods (40) – (43) without comparisons withother methods.

B. ANGLE ESTIMATION RANGEFigure 2 shows the angle estimation performance of proposedmethod versus different azimuth or elevation angle errorswith 4-QAM modulation and antenna element distance d =0.5 m, 0.9 m. The angle error estimation results can becharacterized by an ‘S-shape’ curve, which is independentof channels and modulations. From (40) – (43), we can findthat the S-curve will only rely on wavelength λ, antennaelement distance d and receiving OFDM signal. The zero-crossing point angle errors of the S-curve are the equilibri-um states of auto-tracking system. The zero-crossing points±6.4◦, ±11.5◦ in Fig. 2 are the maximum acquisition anglevalues for the auto-tracking antenna using proposed method.We can find that the maximum azimuth or elevation angleestimation φ decreases for increasing d, i.e. for d = 0.5 m,0.9 m, φ = ±11.5◦, ±6.4◦, respectively. The azimuth (orelevation) angle estimation S-curve can be defined as theaverage estimator output in the range of |θe| ≤ |φ|, i.e.,

S(θe) = E[θA(n)|∀n : |θe| ≤ |φ|]. (44)

The 3 dB beamwidths for antenna can be approximatedas 2θh ≈ 70◦ × λ/Da where Da is antenna equivalentaperture [53]. Our monopulse array antenna has Da = 2d.Thus we have 2θh ≈ 14◦ and 7.7◦ for d = 0.5 m, 0.9 m,respectively. To further analyze the estimation performance,

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X. Pan et al.: Nonlinearity-Based Single-Channel Monopulse Tracking Method for OFDM-Aided UAV A2G Communications

-10 -5 0 5 10Azimuth or elevation angle error (°)

-15

-10

-5

0

5

10

15

Ang

le e

rror

est

imat

ion

(°) d=0.5 m

d=0.9 m

zero-crossing points

FIGURE 2: Angle error estimation output S-curve for proposedmethod (40) or (41) versus different azimuth or elevation angleerrors θe, d = 0.5 m, 0.9 m.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2Normalized angle error

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Nor

mal

ized

ang

le e

rror

est

imat

ion

d=0.5 m

d=0.9 m

FIGURE 3: Normalized angle estimation output S-curve for pro-posed method (45), d = 0.5 m, 0.9 m.

we then normalize the angle estimation θA and θE by θh, andget the normalized estimation values, θA and θE , i.e.

θA =θAθh, θE =

θEθh. (45)

Simulation results for normalized estimations (45) are pre-sented in Fig. 3, where the estimation S-curves for d = 0.5 m,0.9 m have identical characteristic. The angle estimationrange φ is proportional to θh and their relationship can beapproximately expressed as |φ| ≈ 1.65 θh.

We also studied the estimation performance of the pro-posed absolute-value method (42), (43) for d = 0.5 m,as shown in Fig. 4. Results show that the absolute-valuemethod exhibits larger estimation values than the square-value method for the same angle errors. The proposed SCMTangle estimation method will feed the angle estimation re-sults to auto-tracking antenna servo system and construct aclosed loop for tracking target. This absolute-value methodwill enhance the auto-tracking antenna sensitivity to chang-

-10 -5 0 5 10

Azimuth or elevation angle error (°)

-15

-10

-5

0

5

10

15

Ang

le e

rror

est

imat

ion

(°)

Absolute

Square

FIGURE 4: Angle estimation performance for proposed absolute-value method (42) or (43) versus different azimuth or elevationerrors θe, d = 0.5 m.

ing angle errors of UAV target. We will next examine theproposed method from the view of the RMSE performance.

C. ANGLE ESTIMATION RMSEThe angle estimation RMSEs under both frequency selectivefading channels and AWGN channels are given in Fig. 5,Fig. 6 for antenna element distance d = 0.5 m, 0.9 m,respectively. The estimation RMSEs under our Rician chan-nels show degradation of 0.01◦ – 0.02◦ compared with theestimation under AWGN channels for both square-value andabsolute-value methods. Under AWGN channels, the pro-posed square-value method exhibits robust RMSE perfor-mance with σθ < 0.17◦, 0.11◦, respectively, within the SNRregion from 0 dB to 20 dB. In the case of the absolute-valuemethod, we can find that it has decreasing RMSEs, i.e. σθ <0.16◦, 0.09◦ for d = 0.5 m, 0.9 m, respectively.

The absolute-value estimation outperforms the square-value estimation because the high-order moment of basebandsignal

∑T |zΣ∆(n)|2 in (40) and (41) enlarges influence of

noise and interference in zΣ∆(n) compared with the low-order one

∑T |zΣ∆(n)| in (42) and (43).

Figure 7 presents the estimation RMSEs of the proposedsquare-value method under AWGN channels with differentOFDM sampling rates of 5.12 MHz, 10.24 MHz and 20.48MHz for d = 0.5 m. We can find that, compared with 10.24MHz, the RMSEs for 5.12 MHz degrade by about 0.07◦,whereas the RMSEs for 20.48 MHz outperform the caseof 10.24 MHz by about 0.07◦. For higher-order mappingscheme, i.e. 16-QAM, with sampling rate 10.24 MHz, amaximum RMSE degradation of 0.05◦ is observed as shownby the dot-line in Fig. 7, although their S-curves in Fig. 2 havethe same characteristics. Not that, the rich multipath scenarioof UAV air-to-ground communication with high mobility andlow elevation imposes restrictions on employing high-ordermapping schemes. Therefore, 10 MHz OFDM signals with4-QAM mapping and square-value estimation are recom-mended for practical implementation in UAV communication

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X. Pan et al.: Nonlinearity-Based Single-Channel Monopulse Tracking Method for OFDM-Aided UAV A2G Communications

0 2 4 6 8 10 12 14 16 18 20SNR (dB)

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

Est

imat

ion

root

mea

n sq

uare

d er

ror

(°)

Square, RicianSquare, AWGNAbsolute, RicianAbsolute, AWGN

FIGURE 5: Estimation RMSE performance versus SNR under Ri-cian channel and AWGN channel for proposed square- and absolute-value methods, d = 0.5 m.

0 2 4 6 8 10 12 14 16 18 20SNR (dB)

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

Est

imat

ion

root

mea

n sq

uare

d er

ror

(°)

Square, RicianSquare, AWGNAbsolute, RicianAbsolute, AWGN

FIGURE 6: Estimation RMSE performance versus SNR under Ri-cian channel and AWGN channel for proposed square- and absolute-value methods, d = 0.9 m.

0 2 4 6 8 10 12 14 16 18 20SNR (dB)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Est

imat

ion

root

mea

n sq

uare

d er

ror

(°)

5.12 MHz10.24 MHz20.48 MHz16QAM 10.24 MHz

FIGURE 7: Estimation RMSE performance of proposed square-value methods in the context of different OFDM sampling ratesunder AWGN channels, d = 0.5 m.

system, whereas antenna element distance d and aperture Da

depend on the requirement of link budget and ground stationcoverage area.

V. CONCLUSIONSIn this paper, we construct an SCMT receiver architectureexploiting OFDM signals in UAV A2G communication sys-tem and then propose an angle estimation method usingsquare-value and absolute-value nonlinearities of amplitude-modulated OFDM difference signals. Extensive simulationsare conducted for evaluating the performance of our proposedangle estimation method in terms of the estimation rangeand RMSE. Results show that, the proposed angle estimationmethod has S-curve characteristic which is insensitive tochannels and modulations. The estimation RMSEs improvewith increasing OFDM signal sampling rates and SNRs,whereas a maximum degradation of 0.02◦ is observed underRician channels compared with the estimation under AWGNchannels. The estimation results of the proposed SCMT angleestimation method will finally be fed to auto-tracking antennaand a closed loop is constructed for tracking UAV target.

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XI PAN received the B.S., M.S. and Ph.D. degreesfrom the Beijing Institute of Technology, Beijing,China, in 1999, 2002 and 2007, respectively. Shewas a visiting scholar with the college of Engineer-ing and Computer Science, Australian NationalUniversity from 2011 to 2012. She is now an as-sociate professor with the school of MechatronicalEngineering, Beijing Institute of Technology. Shehas been working on a range of research projectsincluding four projects of NSFC, three Defence

Key Laboratory funds, two Advance Research Programs and she holds morethan ten patents. Her research interests include target tracking and rangingtechnique, short range radar signal processing.

CHAOXING YAN received his PhD degree inCommunication and Information System from theBeijing Institute of Technology, China, in 2012.Since March 2012, he has been with the BeijingResearch Institute of Telemetry, where he is now aSenior Engineer and Associate Project Manager.From July 2017 to December 2017, he was avisiting scholar in the Next-Generation WirelessGroup chaired by Prof. Lajos Hanzo, School ofElectronics and Computer Science, University of

Southampton, UK. He is selected into the Youth Outstanding Talent SupportProgram (2019) of China Aerospace Science and Technology Corporation(CASC). He is the author of several scientific papers and the holder ofover 30 patents. He serves as the Session Chair of IEEE/CIC ICCC 2018and a reviewer of several IEEE journals. His primary research interests arewireless communication and networking techniques in terrestrial networks,UAV datalinks, satellite and space communication networks.

JIANKANG ZHANG received the B.Sc. degree inMathematics and Applied Mathematics from Bei-jing University of Posts and Telecommunicationsin 2006, and the Ph.D. degree in Communicationand Information Systems from Zhengzhou Univer-sity in 2012. Dr Zhang was a lecturer from 2012 to2013 and an associate professor from 2013 to 2014in School of Information Engineering, ZhengzhouUniversity. From 2009 to 2011, Dr Zhang was avisiting PhD student in the School of Electronics

and Computer Science, the University of Southampton, UK. From 2013 to2014, he was a postdoctoral researcher in the McGill University, Canada.Currently, he is a Senior Research Fellow in the University of Southampton,UK. Dr Zhang is a recipient of a number of academic awards, includingExcellent Doctoral Dissertation of Henan Province, China, Youth Scienceand Technology Award of Henan Province, China. His research interests arein the areas of wireless communications and signal processing, aeronauticalcommunications and broadband communications. He serves as an AssociateEditor for IEEE ACCESS and a guest editor of a special issue on EURASIPJournal on Advances in Signal Processing.

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