ZHU Changju,SONG Maozhong,DANG Xiaoyu,and ZHU Qiuming

College of Electronic Information Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China

Abstract:A two-dimensional directional modulation (DM) technology with dual-mode orbital angular momentum (OAM) beam is proposed for physical-layer security of the relay unmanned aerial vehicle (UAV) tracking transmission.The elevation and azimuth of the vortex beam are modulated into the constellation,which can form the digital waveform with the encoding modulation.Since the signal is direction-dependent,the modulated waveform is purposely distorted in other directions to offer a security technology.Two concentric uniform circular arrays(UCAs) with different radii are excited to generate dual vortex beams with orthogonality for the composite signal,which can increase the demodulation difficulty.Due to the phase propagation characteristics of vortex beam,the constellation at the desired azimuth angle will change continuously within a wavelength.A desired single antenna receiver can use the propagation phase compensation and an opposite helical phase factor for the signal demodulation in the desired direction.Simulations show that the proposed OAM-DM scheme offers a security approach with direction sensitivity transmission.

Keywords:directional modulation (DM),orbital angular momentum (OAM),physical-layer security,directional sensitivity.

1.Introduction

Electromagnetic wave can carry orbital angular momentum (OAM),which makes vortex waves with different modes orthogonal to each other [1,2].Thus OAM provides a novel transmission dimension for wireless communication schemes [3].The radiation pattern of OAM beam can carry angle information [4],which has potential application in directional modulation (DM) technology for communication security.Recently,there are many studies for vortex wave generation [5-9].Since concentric uniform circular arrays (UCA) can flexibly generate vortex waves with different modes,it is widely used in OAM beam forming.

Wireless transmission messages are at risk of being intercepted without protective measures [10].Since DM can protect the digital transmission wave form in the prespecified direction to enhance transmission security,it is considered to be an effective approach to solve the physical-layer security problem [11,12].DM mainly considers the constellation distribution in the desired direction,which is different from traditional baseband modulation [13].The designed DM signal with dual beams in [14] is a spatial spread spectrum signal,where the angle and spread spectrum sequences are modulated together to form the specified signal constellation.The DM baseband signal in [15] adopts the artificial noise and the synthetic constellation can change dynamically,which eavesdroppers cannot monitor the law of the constellation distortion.On the basis of [15],the research in [16] extends dual-beam DM system to complex multibeam signal modulation and synthesis.

For the optical OAM security transmission,some researches are based on orthogonal OAM modes to ensure communication security [17-21].In the microwave field,OAM state is used as the waveform carrying parameter,and the modulated phase pattern has a helical phase front,where the angle-dependent signal waveform can be formed for physical-layer security transmission[22].Since vortex waves can carry elevation and azimuth information,the modulated OAM beam can be easier to achieve the two-dimensional direction physical-layer security.In recent years,conventional DM focusing on one-dimensional azimuth angle or elevation angle is common.However,the two-dimensional direction of the vortex wave radiation pattern is almost not fully utilized in OAM physical-layer security.

In the past few years,communication networks with fixed facilities are difficult to meet the increasing requirements of the fifth-generation (5G) quality-of-service(QoS).Therefore,unmanned aeriel vehicle (UAV) relay communication systems bring fundamental changes to wireless transmission which can promote the faster and more flexible deployment of communication equipment.In [23],the UAV-based line-of-sight (LOS) air-to-ground(A2G) channel model is established to accomplish OAM multiplexing for the A2G wireless transmission links.

Although OAM communication brings great benefits,the open wireless channel makes security information transfer a challenging issue and few studies can ensure that the transmission from the ground base station (GBS)is received only in one direction [24,25].The relay UAV,which communicates directly with GBS,can transmit the GBS information to UAV swarm [26].As a result,it is necessary to develop OAM physical-layer security technology.

In this paper,we contribute that the legitimate relay UAV can receive the correct information in the desired two-dimensional direction.OAM beam generated by UCAs can be combined with DM technology to design OAM-DM signal wave form,which can transmit different modulation constellations related to elevation and azimuth.The dual-mode OAM beam is used for the ground-to-air (G2A) relay UAV communication,which emphasizes the security transmission in a fixed direction rather than channel capacity.Moreover,modulated constellations in different directions enable a single antenna receiver to restore the original digital waveform in the desired direction without a large aperture receiving array.In summary,the contributions of this paper are listed as follows:

(i) In the UAV swarm transmission system,one of UAVs can be used as a relay receiver,which can transmit control instruction to the short-range UAV.When a relay UAV acts as a legitimate user,the open space around the GBS facilitates the signal reception for the eavesdropper and the desired receiver.Therefore,there is a potential risk of eavesdropping.In this context,it is urgent to investigate security schemes for G2A relay UAV tracking transmission.

(ii) We combine dual OAM beams generated by UCAs with DM technology to design OAM-DM signal waveform,which transmits different modulation constellations related to elevation and azimuth.Since radiation pattern information of vortex wave is modulated into the signal,the transmission waveform with direction information can distort the constellation in all eavesdropping directions.Due to the composite OAM-DM signal,the eavesdropper will demodulate incorrect digital sequence.Moreover,the beam axis direction and the rotation phase can be controlled to adjust the desired direction for the relay UAV tracking transmission.

(iii) We utilize the single antenna to receive two composite OAM for OAM mode detection.Since the receiver does not require the large aperture receiving array to align with OAM beam axis,the relay UAV attitude does not affect the signal reception.Additionally,we employ the helix phase factor,the desired azimuth angle and the compensating phase for digital sequence demodulation in the desired direction,which can further protect the transmission security.

2.Directional modulation with dual OAM beams

2.1 UCA design for OAM beam generation

Since the method based on phase UCA has the advantages of strong flexibility and easy control,we divide antenna arrays into inner UCAInnerand outer UCAOuter.2Mantennas in UCAInnerand UCAOuterare fed and the phase differenceφbetween adjacent elements in each array is 2πl(wèi)/M,whereldenotes the OAM mode andl＜M/2.

Fig.1 shows that UCAs are employed to generate dual vortex waves.The phase wavefront of OAM beam is shown in Fig.2(a).Radii of UCAInnerand UCAOuterare set asR1=λandR2=1.5λrespectively,whereλis the wavelength.Each element in arrays is full-wavelength dipole and the antenna length isλ.In Fig.1,elements in UCAInnerand UCAOutercan be excited bys(t) and the phase shift exp[j(lβm+θ)],whereβmis the azimuth angle of themth element andθis the rotation phase.The phase wavefront can be rotatedθas a whole in Fig.2(b),which is to align the azimuth angle with the legitimate receiver.

Fig.2 Diagram of phase wavefront

2.2 OAM-DM signal design

Two sets of excitation signals are designed for UCAInnerand UCAOuter,which can modulate the phaseθinto the signal.In Fig.1,Melements in UCAInnerare excited by the excitation signals1(t)=b11cos(ωct)+b12sin(ωct) and the phase exp[j(l1βm+θ1)] respectively,whileMelements in UCAOuterare excited bys2(t)=b21cos(ωct)+b22sin(ωct)and the phase exp[j(l2βm+θ2)] respectively.Hereωcis the signal carrier angular frequency,cij(n)∈[-1,0,1] (i,j=1,2)is the encoding matrix element,θx∈[-180,180] (x=1,2).

The signal,which is mapped to the constellation point on the real and imaginary coordinate system,can be given as

whereg1(δ,γ) andg2(δ,γ) donate radiation patterns of OAM beams in UCAInnerand UCAOuterrespectively,δandγare the elevation and azimuth respectively,XI(δ,γ) andXQ(δ,γ) are orthogonal equivalent baseband signals.Without losing generality,the rotation angleθ1can be set to 0 as the reference phase.The equivalent baseband signal is given by

whereα=θ2.The far-field radiation pattern of OAM beam generated by UCA can be expressed as

wherek=2π/λ,(δ1,γ1) is the direction of the vortex beam axis andf(δ,γ) denotes the radiation pattern of each array element.

From (1),the complex baseband signalp(δ,γ) can be written as

From (8),the direction information of the dual-beam radiation pattern can be modulated into the OAM-DM signal.

2.3 DM principle with dual OAM beams

In (9),the designed coding method can maps the modulation matrixFto the corresponding digital sequencezn,andzn=0,1,2,3.

There is a complex baseband signal in thenth frame,and one channel of digital information is transmitted through two frames of signals respectively,which can be expressed as

From (10),two complex signals can be synthesized into one quadrature phase shift keying (QPSK) signal at the receiver.Two signals can be written as

From coding and modulation of the digital sequence,the matrix elementbij(n) of thenth frame signala(1,δ,γ,n)can be given by

The matrix elementbij(n-1) of the (n-1)th frame signala(2,δ,γ,n-1) is

Two QPSK signals can be obtained by coding.The mapping relationship between the two signals andznis obtained in

Fig.3 shows OAM-DM signal synthesis and he spatial parameters of constellations.When sequencesznandzn-1are transmitted,the OAM-DM signal constellation is distorted.The receiver can synthesizea(1,δ,γ,n) anda(2,δ,γ,n-1) intoasyn(δ,γ) in (17),which can be related to elevation and azimuth.

Fig.3 Constellation diagrams of dual OAM-DM signals

Table 1 shows the received vector and the binary bit of OAM-DM signal,where four constellation points are related to direction (δ,γ).We write (17) as and the constellation distribution of the received signal can be related to the elevation angle.

Table 1 Received vectors corresponding to different data sets

From (18),the transmission waveform is restricted by the beam radiation pattern,and constellations of two QPSK signals are distorted independently in different twodimensional directions.Whena(1,δ,γ,n) anda(2,δ,γ,n-1)are synthesized intoasyn(δ,γ),the constellation distortion degree will be related to elevation and azimuth.Among them,the synthetic constellation in the desired twodimensional direction is a standard QPSK constellation,while constellations in other directions are distorted by the joint effect of elevation and azimuth.

Whenl2=±1 andl1≠l2,there is only one desired azimuth angle and OAM beam with model1causes the eavesdropper to receive the distorted constellation.From (18),the synthetic signalasyn(δ,γ) is only associated withg2(δ,γ).Therefore,θ2can be used to align the desired azimuth,andθ1=0°.

When the horizontal axis represents sinδcosγand the vertical axis represents sinδsinγ,normalized intensity patterns of OAM beams with different modes are shown in Fig.4.The main beam broadens with the increase oflx,indicating that the energy spread becomes worse with the increase oflx.Therefore,we can setlxto ±1,±2 andl1≠l2in this paper.

Fig.4 Normalized intensity patterns of OAM beams

The QPSK constellation is obtained by modulating and coding the two groups of orthogonal signals.Through DM,two signals carrying OAM direction information can be combined and QPSK signal constellations with different distortion degrees are transmitted in all directions,which can prevent eavesdroppers from getting the correct message.As a result,the distribution of the signal constellation indicates that OAM-DM signals can realize secure transmission in the desired two-dimensional direction.

3.Signal reception

According to the transmission theory of vortex wave,the receiver can utilize the opposite helical phase factor exp(-jlxγ) of the vortex signal to achieve OAM signal demodulation [27,28].From the helical phase factor,the mode detection of vortex waves is a key step at the receiver.However,a challenging problem in OAM communication is that the receiving antenna has a larger aperture at a farther range,which increases the difficulty of beam reception and OAM mode detection.In this study,the phase of OAM wavefront is modulated into the constellation and corresponds to the azimuth angle of the receiver,where the receiver can only obtain standard QPSK constellation points at a specific azimuth angle.Therefore,the single antenna receiver can demodulate the vortex signal at the desired azimuth angle without requiring a large aperture array to receive the vortex wave completely.The approach of OAM-DM signal demodulation can be given below.

When the relay UAV communicates with GBS,UAV transmits the space position (δ,γ,D) to the transmitter.Then OAM-DM transmission system can be aligned with the desired direction of the relay UAV.The phase front of vortex waves varies 2πl(wèi)in a wavelength.Therefore,the phase of the OAM beam can adopt the wavelengthλand the transmission distance to establish a conversion relationship with the azimuth angle of the receiver.We establish the phase propagation model of the vortex wave with distance,and the relationship can be written as

wherex=1,2.Dis the distance between the receiver and the UCA center.

The propagation phase of the OAM beam at the receiver isψ1(lx,γ).As shown in Fig.5,the relationship in(20) can be obtained from phase propagation.

Fig.5 Diagram of phase wavefront

Before transmitting the digital sequence,it is necessary to detect the vortex wave mode andθx=0.We design the coding matrix elementbijas (21) and (22) for OAM mode detection at the receiver.

The smaller wavelength of OAM beam can make the distance error affect the phaseψ0(lx,γ,D) greatly.To eliminate the influence of distance error on OAM mode detection,(20) can be expressed as

wherel2=±1 andl1≠l2.Thusl1andl2can be mapped by the mode ratio from (23).As shown in Table 2,the OAM mode has multiple values.In order to determine the sign of the mode value,(20) can be written as

Table 2 Mapping relationship of OAM mode

whereB≥1.Whenγ＞0,lxandQare the same sign.Whenγ＜0,lxandQare different signs.Since OAM modes are integers in our study,the estimated mode value can be rounded.

After the receiver detects the OAM mode,the transmitter can align the direction of the receiver by changingθ2.The complex signal with the normalized radiation pattern in the direction (δ,γ) can be written as

The vortex signal carrying direction information can be expressed as

The signalrMux(δ,γ,n,t) is divided into two signalsr(1,δ,γ,n-1) andr(2,δ,γ,n),which are used to calculateα.Since the reference phaseθ1is set to 0,the rotation phaseθ2equalsα.When the receiver is located in the desired direction (δ0,γ0),δ=δ0andγ=γ0.In (29),the relationship can be obtained from two received signals and (25).

In the process of vortex wave propagation,the desired azimuth angle can change with the phase rotation.Therefore,the phase of the signal needs to be compensated,which can rotate the constellation to the desired direction for the digital sequence demodulation.When the distance between the receiver and the UCA center isD,the influence ofθxon the phase can be eliminated by combining(20),and the azimuth compensation can be obtained by(31),which can eliminate the distance parameter.

Therefore,OAM-DM signal can be demodulated by the helix phase factor exp(-jlxγ0) and the phase compensation exp(-jlxγ1) with a single antenna.

Two OAM-DM signals from (32) can be obtained by the signal demodulation with the mode value.

When two frame signals are demodulated in (33),two QPSK signals are combined into one QPSK signalrQPSK(δ,γ) for the digital sequence restoration.

When the receiver is located at the desired azimuth angle,the standard QPSK constellation is obtained byx=2 for the signal demodulation.The restored digital sequencezncan be given by

At the desired elevation angle,the signal amplitude is 2I2and the standard QPSK signal constellation is transmitted.Thus the bit error rate (BER) performance is the best.

As a result,the composite OAM-DM signal and switching modes can prevent illegitimate receivers from eavesdropping on transmission messages.Moreover,the legitimate receiver employs the desired azimuth angle to estimate OAM mode,and the single antenna receiver can demodulate OAM-DM signals waveform.When two OAM-DM constellations are combined into one signal constellation in the desired direction,the legitimate user can receive the correct digital sequence.

4.Numerical simulations and results

The radiation pattern can reflect the signal waveform in different directions and the BER is an important performance to measure physical-layer security performance of the DM signal.The low BER can be required in the desired direction [13-16],and most environments are additive white Gaussian noise (AWGN) channel in all spatial directions [15,16].It is noted that the initial OAM research takes the orthogonal vortex wave as the carrier,which means that the influence of signal attenuation and atmospheric turbulence on the helical wavefront reception is the factor to analyze the BER performance [29,30].In other words,the communication quality depends on the impact of the channel on the helical phase wavefront.

We design orthogonal excitation signals for two UCAs to modulate dual-mode OAM direction information into QPSK signals.Actually,constellations have QPSK characteristic related to direction,where the receiver only focuses on QPSK signal reception in a fixed direction without paying attention to the overall helical phase wavefront.Therefore,we consider QPSK signal transmission in the AWGN channel for the simulation.

We simulate and analyze OAM-DM radiation pattern,the phase pattern and the BER performance.The BER performance can be calculated by randomly generating a data stream of 106QPSK symbols in the AWGN channel.OAM-DM system parameters are specified in Table 3.

Table 3 Parameters for OAM-DM system

The direction of the beam axis can be controlled to adjust the desired elevation angle.Without losing generality,the rotation phaseθ2and the beam axis direction are set to 60° and 0° respectively.

When the radiation pattern is modulated to QPSK signal,the desired elevation angle is 11° and the normalized OAM-DM radiation pattern related to the elevation angle at the desired azimuth angle is shown in Fig.6(a) and Fig.7(a),where the desired azimuth angle is 105°.The negative half axis of the abscissa plots the radiation pattern with the desired azimuth angle of -75°.Two OAMDM radiation patterns obtained by the combination with various OAM modes are different,and the maximum radiation direction of |asyn(δ,γ)| pattern is the desired elevation angle which depends on the pattern |g2(δ,γ)|.From(18),|asyn(δ,γ)| pattern is independent ofθ2.It is revealed in (15) and (16) that radiation patterns ofa(1,δ,γ,n) anda(2,δ,γ,n-1) are related to rotation phaseθ2.Moreover,the beam axis direction can vary the desired elevation.

Fig.6 OAM-DM radiation pattern (l2≠l1, l2=±1, l1=±1, ±2)

Fig.7 OAM-DM radiation pattern (l2≠l1, l2=±2, l1=±1, ±2)

Fig.6 (b) and Fig.7(b) show OAM-DM radiation pattern at the undesired azimuth angle.The positive and negative half axes of the abscissa plot the radiation pattern with azimuth angles of 75° and -125° respectively.The synthetic signal |asyn(δ,γ)| pattern remains unchanged and is not affected by the azimuth angle.However,radiation patterns of |a(1,δ,γ,n)| and |a(2,δ,γ,n-1)| vary at the undesired azimuth angle.From (32),Fig.6 and Fig.7,the receiver is required to be located at the desired direction for the signal reception.Therefore,dual OAM-DM patterns with the rotation phaseθ2can interfere with the eavesdropper to obtain the correct constellation at the undesired direction.

We set the beam axis direction to 0° andθ2is 60°.The single antenna on a rotatable plane is used to pick up the circle phase which is perpendicular to the beam axis.As shown in Fig.8,phases ofa(1,δ,γ,n) anda(2,δ,γ,n-1)cannot form the standard constellation phase of QPSK signals at different azimuth angles,which contributes to the protection of information security.OAM-DM signal phase patterns,generated by the positive and negative values ofl2,are mirror symmetric,which the security performance of the legitimate receiver is the same.However,switching OAM modes can interfere with eavesdroppers.From Fig.8(c) and Fig.8(d),the phase of the synthetic signalasyn(δ,γ) has multiple values withl2=±2,which means that the same QPSK signal phase as the desired azimuth angle (γ0=105°) appears in the undesired azimuth angle (γ=-75°).Whenl2=±1,the phase has a unique value(γ0=105°) in Fig.8(a) and Fig.8(b),which avoids the possibility of information leakage in the undesired direction.Thusl2is set to ±1 (l2≠l1) in our OAM-DM system.

Fig.8 OAM-DM signal phase pattern

In the same UCA with other parameters unchanged,the helical phase of OAM beam with positive and negative mode values is opposite,while elevation information of the radiation pattern is the same.Switching OAM mode can be used to interfere with the eavesdropper to obtain the correct information without affecting the desired receiver to demodulate the digital sequence.

The legitimate receiver employs our designed OAMDM signal reception method to demodulate digital sequence.As shown in Fig.9,the BER performance of the desired receiver demodulating OAM-DM signals is simulated in all directions.Whenθ2=0° and (δ1,γ1)=(0°,0°),l1=2 andl2=1,the desired direction (δ,γ) is(11°,45°).In Fig.9(a),the BER performance is the best at(11°,45°) and deteriorates in other directions.When the desired direction is set to (11°,105°) and (20°,105°),the BER performance is shown in Fig.9(b) and Fig.9(c).It is noted that the azimuth angle will not change the synthetic pattern |a(1,δ,γ,n)|,where the trend of Fig.9(c) is similar to that of Fig.9(b).In Fig.9(c),the elevation angle adjustment can transform the radiation pattern and the BER trend without affecting the signal phase and the maximum radiation in the desired direction.Therefore,the legitimate user can remain the lowest BER in the desired direction.

Fig.9 BER performance of the legitimate user (SNR=12 dB)

It can be observed from Fig.9 that the BER ripple observed in unsecured directions is smoothed,which indicates that it is difficult for the eavesdropper to receive the correct transmission message.

Since the synthetic OAM-DM patternasyn(δ,γ) is only related tog2(δ,γ),l2is set to ±1 andl2≠l1,where synthetic patterns ofl2=±1 are equivalent.Without losing generality,we setl2to 1 andl2to 2.Fig.10 shows the BER offset in all directions relative to the desired direction,which indicates the influence degree of direction sensitivity on the BER is obtained by our designed demodulation method,and the BER offset is the smallest in the desired direction.

Fig.10 BER offset when SNR=12 dB, the desired direction (δ0,γ0)is (11°,45°), l1 =2 and l2=1

Fig.11 shows BER performance of the desired receiver demodulating OAM-DM signals under different SNRs.When the elevation and azimuth of the legitimate user deviate from the desired direction by 1° and 2°,the BER performance reduces to a certain extent.The BER performance decreases sharply when the legitimate receiver direction deviates from the desired direction by 3°.Therefore,the legitimate receiver is required to be located in the desired direction to obtain the best BER performance,which can enhance the security transmission.

Fig.11 BER performance under different SNRs when desired direction (δ,γ) is (11°,45°), l1 =2, l2=1

It is noted that most traditional DM technologies add artificial noise to distort the signal constellation in undesired directions [15,16].Any illegitimate user can receive the correct digital waveform in the desired direction.Moreover,the beamforming of DM is utilized to optimize the beamwidth [13,14],and yet eavesdroppers can demodulate the signal as the legitimate user within the beam irradiation range.In addition,the large aperture array is used to receive the signal with OAM carrier,and the receiver is required to be located in the specific alignment position for security transmission [22],which is not conducive to the mobility of the receiver.When the illegitimate user is aligned with the center of the transmitter,the mode value can be estimated for information eavesdropping.

Compared with current OAM and DM security transmission schemes,the eavesdropper can receive our OAMDM signal waveform on each frame and employs QPSK demodulation to obtain the digital sequence in all directions.As shown in Fig.12,the BER performance deteriorates sharply,where the illegitimate user eavesdrops on error messages in all directions.Therefore,our OAM-DM scheme provides a novel dimension for physical-layer security.

Fig.12 BER performance of the eavesdropper in all directions(SNR=12 dB)

5.Conclusions

The OAM-DM signal design and demodulation scheme are proposed for the relay UAV security transmission.Radiation pattern information of the vortex beam is modulated into the signal,which makes the modulated waveform carry elevation and azimuth information to distort the constellation in all directions except that of the desired receiver.OAM-DM beams of composite modes can make it more difficult for eavesdroppers to demodulate digital information.The phase spiral propagation of the vortex beam makes the distortion of constellation change with the propagation distance,which makes it difficult for the receiver to demodulate the digital information correctly.Methods of OAM mode estimation and phase compensation are proposed to demodulate OAMDM signal.In the desired two-dimensional direction,the receiver can use a single antenna to demodulate digital signals.