Multitarget Position-Sensitivity Security Transmission with OAM-DM Based on FDA

,emultitarget position-sensitivity security transmission scheme with orbital angular momentum (OAM) directional modulation (DM) waveform using the uniform circular frequency diverse array (FDA) is proposed.,e transmitter employs FDA to generate dual-mode range-dependent OAM beam pattern, and the direction information of OAM beam is modulated into the signal. According to the modulation method, orthogonal carrier frequency can be designed to realize multitarget position-dependent OAM pattern. In the undesired position, the intensity pattern and the phase front of the radio beam vary randomly with the digital transmission sequence. Because modulation waveform is position-dependent, the technique offers security, as the signal can be purposely distorted in other positions. ,e composite dual-mode OAM signal makes it more difficult for eavesdroppers to demodulate correct messages. ,e receiver with a single antenna employs the phase compensation and helical phase factor to restore the correct digital signal in the desired position. Numerical results show that multitarget position-sensitivity OAM-DM technology based on FDA offers the security transmission scheme.


Introduction
Wireless communication has the risk of being intercepted without physical-layer security measures [1]. DM technique, which can protect digitally modulated information signals in the prespecified spatial direction to lower the possibility of interception, has been proposed as a promising technique to address physical-layer security communication problems [2,3]. Most of DM technologies are based on phased array, which generates range-independent steering directions [4,5]. As compared with phased array, FDA can generate range-dependent beam pattern with a small frequency increment [6][7][8]. e range-dependent physical-layer security with FDA can be done in several ways [9][10][11][12][13][14][15][16][17][18]. e information code can be designed for FDA, which generates the specific radiation pattern. e transmission beam pattern is related to the range and the azimuth angle based on FDA element with the frequency increment for the DM technique, in which the transmitted symbols are purposely distorted to be unrecoverable except for the legitimate user. In [19], 2-bit phase control is used on a two-element FDA antenna, and the generated radiation pattern with directiondependent projects the phase modulation signal as a constellation for physical-layer security communication. FDA and DM are jointly exploited for point-to-point communication, which provides physical-layer security in both the range and angle dimensions [20]. Reference [21] combines DM technology and artificial noise matrix-aided Costas sequence matrix FDA in precoding systems for multicast communication scenario.
In the field of physical-layer security communication, there are some studies based on OAM for information security. Electromagnetic radiation can carry OAM, and vortex beams of different modes have orthogonality with each other [22][23][24]. us, OAM transmission technique is promising for communication scheme [25,26]. In the field of quantum and optics, OAM physical-layer security mainly employs the quantum key distribution protocol of entangled photon pairs, hybrid free space optics-THz technology, and OAM multiplexing [27][28][29][30]. So far, there are many methods to generate OAM beam [31][32][33][34][35][36], where the uniform circular array antenna (UCA) has been extensively studied for its flexibility in generating different OAM modes. In [37], the message is encoded on the OAM mode generated by the uniform circular FDA, and the security with OAM mode modulation is enhanced since the OAM mode can be observed in the desired region only. Due to the direction information carried by OAM beam, it has an application prospect in DM technology for physical-layer security. As compared with traditional DM, it is easier to achieve physical-layer security with the two-dimensional direction. At present, DM mostly focuses on the range and azimuth angle, where the sensitivity needs to be further improved. e vortex beam with two-dimensional direction and range is almost not fully utilized in security communication. OAM beam with range, elevation, and azimuth information, which is generated by FDA, has great potential in multitarget security.
In this paper, the uniform circular FDA element is excited by the designed signal to generate OAM beams related to the range, elevation, and azimuth. e modulated composite OAM-DM signal can be used for security transmission with the space position-sensitivity, and the designed orthogonal carrier frequency can realize multitarget communication. OAM beams generated by the uniform circular FDA with the random frequency offset can maintain the helical phase and the intensity pattern characteristics at the desired range. en, two-dimensional direction information of OAM beam radiation pattern is modulated into the signal to generate angle-dependent OAM-DM waveform. Because the frequency offset changes randomly with the transmission bit, the intensity pattern and phase front can be randomly distorted in the undesired position without disturbing the desired position. e receiver demodulates dual-mode OAM-DM signal with different modes and synthesizes them, which makes it more difficult for eavesdroppers to demodulate the correct message. Dual-mode OAM-DM signal emphasizes the position-sensitivity for multitarget security transmission and has a low requirement for communication capacity. Moreover, transmitting different modulation constellations in different space positions enables a single antenna receiver to restore the correct digital sequence in the desired position without requiring a larger aperture to receive the whole OAM signal at the farther range, which is different from the traditional OAM signal reception.
Actually, our proposed scheme is different from [37]. Firstly, the FDA generates the range-dependent OAM signal, and the confidential information is encoded on OAM modes in [37]. However, this scheme offers only one-dimensional range-dependent security transmission, which cannot be projected to a specific position in three-dimensional space. en, the vortex wave is used as a carrier to transmit information, in which the receiver is required to be a large aperture array antenna and aligned with the transmitter for OAM signal reception. Also, the frequency offset increasing regularly makes the wavefront distortion with range exist regularly to a certain extent, in which the signal has the risk of being monitored and restored. e proposed scheme's major contributions are listed as follows: (1) We introduce the phase integer ambiguity into the phase excitation of UCA's element, which does not affect the generation of vortex beam. e corresponding relationship between the phase excitation and the frequency offset is designed, which makes the frequency offset change irregularly in FDA. e wavefront with vortex wave characteristics can be generated at the desired range. e wavefront is randomly distorted at the undesired range, which reduces the eavesdropping risk on the wavefront variation law. However, the random frequency offset will not interfere with the vortex wavefront generation at the specific range, which can ensure security transmission at the desired range.
(2) We designed excitation signals for OAM-DM waveform generation in FDA. e range, elevation, and azimuth information carried by dual OAM beams are modulated into the signal constellation to generate OAM-DM signals, which can realize specific position-sensitivity security transmission in three-dimensional space. We design orthogonal carrier frequency for OAM-DM excitation signals to achieve multitarget security communication. e receiver can use a single antenna to demodulate OAM-DM signal related to specific range, elevation, and azimuth at the desired position, without requiring a large aperture array antenna to receive the complete wavefront.
(3) e traditional OAM signal uses a large aperture array antenna to measure the phase gradient at the receiver and requires the receiving array center to be aligned with the beam axis for OAM mode detection. We utilize two OAM-DM signals with different modes to transmit one digital sequence. e single antenna receiver can estimate the OAM mode through the relationship between the two received OAM-DM signals. Digital information in OAM-DM signals can be demodulated by the helix phase factor and compensating phase at the desired position. Further, two OAM-DM signals are synthesized into one signal to restore the correct digital information, which is conducive to reducing the eavesdropping risk.

e Uniform Circular Array Antenna.
We consider that the OAM beam generation based on UCA is much flexible and easily controlled. M (M � 8) antennas in UCA are fed with the phase difference 2πl/M between each elements, where l denotes the integer OAM mode value and l < M/2. In Figure 1(a), UCA can be used to generate OAM beams, where d is the range, δ is the elevation angle, c is the azimuth angle, and R is the radius of UCA. e helical phase front of OAM beam is shown in Figure 1(b). Each array element is full-wavelength dipole, and the length of each antenna is λ, where λ is the wavelength. In Figure 1(a), all elements in UCA can be excited by s (t) and the phase exp (jlβ m + jθ), where β m is the azimuth angle of the mth element, and θ is the rotational phase. e helical phase front will deflect θ integrally in Figure 1(c), which can adjust the azimuth angle.

Range-Dependent OAM Beam Pattern Generated by the Uniform Circular FDA.
For the mth antenna element in Figure 1(a), the radiation frequency can be given by where f w denotes the central carrier frequency of wth target, and Δf m,x denotes the frequency offset of the mth antenna element. Since the FDA transmission mode is time varying [21,37], we design the corresponding relationship between frequency offset and phase excitation for mth antenna element at certain time t. For the uniform circular FDA generating OAM beam, the relationship between frequency offset Δf m,x and excitation phase φ m,x is designed as where d 0 is the desired range, δ 0 is the desired elevation angle, c is the speed of light, t is set to 2d 0 cosδ 0 /c and the parameter N x is an integer randomly generated at certain time t. e azimuth angle β m,x of the mth element is expressed as e phase of each element plus (θ x + 2πN x ) can make the phase front rotate θ x without affecting the generation of vortex beam. According to the principle of UCA generating OAM beam, the phase difference between adjacent array elements can be written as e phase difference of adjacent array elements is the sum of a fixed value, which satisfies the generation condition of the vortex wave. From equations (2)-(4), the frequency offset Δf m,x can be expressed as e frequency difference between adjacent array elements can be written as In FDA-related literature [34], Δf m,x is required to satisfy e relationship between the frequency offset Δf m,x and the integer N x from equation (5) can be expressed as where e desired range d 0 and the integer N x can constrain each other. e limited range of the frequency offset Δf m,x satisfies |Δf m,x | ≤ 20 MHz and c is 3 × 10 8 m/s. From equation (8), the relationship between N x and the desired range can be obtained by In equation (10), when |l| � 1, 2 and N x is generated randomly, the frequency offset |Δf m,x | is less than 20 MHz at the desired range. As shown in Figure 2, with the increase of the desired range, N x can take more values randomly. In Figure 3, when d 0 cosδ 0 � 60 m and N x is generated randomly with the transmission bit, |Δf m,x | is always less than 20 MHz. In Figure 4, when θ x � 0, the minimum desired range is greater than 14 m 13 m, 25 m, and 26 m, respectively, which can ensure that |Δf m,x | is always less than 20 MHz. In fact, with the change of θ x , the minimum desired range has a certain difference. In the uniform circular FDA, the array radius R satisfies where λ m,x is the wavelength of the beam generated by the mth element. e array radius is affected by the frequency offset. In this paper, R is set to 0.7 max {λ m,x }.

OAM-DM Based on FDA
3.1. OAM Signal Design and Direction Modulation. Two excitation signals are designed for the uniform circular FDA.
In Figure 1(a), mth element is driven by s 1 (t) and s 2 (t).
where c ij is the element of the encoding matrix and c ij ∈ [−1, 0, 1] (i, j � 1, 2). e radiation pattern of each antenna element in the uniform circular FDA is expressed as e far-field OAM beam radiation pattern without phase front rotation can be expressed as where k � 2πf/c, t � 2d 0 cosδ 0 /c. e complex digital symbol with the magnitude and phase, which can be viewed as a constellation point on the real-imaginary coordinate system, is written as e rotation angle θ 1 is set to 0 as the reference phase. Equation (15) is written as Equation (16) is written as 4 Security and Communication Networks   In each bit period [kT, (k + 1)T], wth and (w + 1)th carrier frequencies are designed to be orthogonal, and then When f w,m + f w+1,m and f w,m − f w+1,m are integral multiples of 1/T, the integral result in equation (18) is 0, which can obtain orthogonal OAM signals. Moreover, f w,m − f w+1,m � 1/T is the minimum frequency difference. us, multiple orthogonal signals can be generated to realize multitarget communication. e signal on the wth carrier is coded and modulated. From equation (16), the constellation can be expressed as From the modulation matrix K, the dual-mode OAM beam pattern with the range, elevation, and azimuth can be modulated into the signal. where

OAM Signal
Coding. e digital information can be modulated into the signal by coding the modulation matrix K. Designed coding matrix P (n) with the data sequence z n can be given by where μ � exp jπ z n + 1 mod3 2 , where z n � 0, 1, 2, 3. Coding matrix H is designed for the nth frame and the (n − 1)th frame signals. e nth frame and the (n − 1)th frame signals are obtained from In equation (24), the dual-mode OAM beam radiation pattern with the position information can be modulated into the signal. Two complex signals (1, n) and a (2, n − 1) in equation (25) can be obtained.
Two frame signals a (1, n) and a (2, n − 1) are equivalent complex signals, which can generate two QPSK signals. e corresponding relationship between two QPSK signals and data sequence can be given by When transmitting sequences z n and z n−1 (z n � z n−1 ), the receiver synthesizes two QPSK signals into a syn (d, δ, c, t), which is related to position. a syn (d, δ, c, t) � a(1, n) + a(2, n − 1). Table 1 shows the receive vectors of the OAM-DM signal, along with the binary bit and created by the four sets of values in the position (d, δ, c).where According to equation (28), constellation distortion degree of the received signal can be correlated with the elevation angle. At the desired position, constellation phase states of two signals are 0, π/2, π and 3π/2. Phase states of the synthesized constellation are π/4, 3π/4, 5π/4 and 7π/4. When N x is generated randomly with the transmission bit, the phase state is almost stationary at the desired position. In the undesired position, the random N x can make the signal phase state change irregularly. As shown in Figure 5(a), phase states always remain unchanged at the desired range. However, random N x can distort phase states of constellation points at other ranges. When the position changes, N x , elevation and azimuth angle can affect the distortion degree of the constellation. In Figure 5(b), N x makes the constellation phase state change irregularly at the undesired range, the change of the azimuth angle can make the constellation phase rotation, and the elevation angle can affect the signal amplitude. Due to the position-dependent OAM beam pattern, constellations of two QPSK signals obtained by modulation and code will be distorted to varying degrees in different positions, which can interfere with the eavesdropper to get the correct information. erefore, dualmode OAM-DM signal with position-sensitivity can achieve security transmission in the desired position.
When l 2 � ±1 and l 1 ≠ l 2 , the desired azimuth angle is unique, and OAM beam with mode l 1 can interfere with the eavesdropper to demodulate dual-mode OAM-DM signal. In equation (29), the synthesized signal is related to g 2 and the desired azimuth angle can be adjusted by changing θ 2 . Intensity patterns of OAM beams are shown in Figure 6. It is seen that the main beam will broaden as l x increases, which indicates that the energy diffusion becomes worse with increasing l x . In this paper, l x can be set to ±1, ±2 and l 1 ≠ l 2 .

OAM-DM Signal Reception
When two combined vortex signals are transmitted, it is achieved by multiplying the opposite helical phase factor exp (−l x c) to receive OAM signals for demodulation [38]. erefore, OAM mode detection is an important step. One of the challenging problems in OAM communication is the transmission range. When the transmission is farther, the receiving antenna has a larger aperture, which makes it more difficult for the receiver to detect OAM mode at a long distance. In this paper, OAM azimuth information is modulated into the signal, in which the receiver can demodulate correct information with desired azimuth angle. us, when the transmission is farther, the single antenna receiver can demodulate OAM signal without a large aperture. e desired receiver transmits the position (d 0 cosδ 0 , δ 0 , c 0 ) to the transmitter, which can align the desired position of OAM-DM system with the receiver. e receiver can detect the propagation phase ψ (l x ,c) of OAM beam, and the relationship in equation (29) can be obtained.
When the transmitter switches OAM mode, θ x is set to 0. From equation (12), the encoding matrix c ij can be designed as equation (30), and the signal amplitude weighting factor is set to 1 for detecting OAM mode in the desired position.
For determining the sign of OAM mode value, equation (29) is written as In order to reduce the influence of azimuth angle error on mode detection, equation (31) can be written as  1 10 where l 2 � ±1 and l 1 ≠ l 2 . us, l 1 and l 2 can be mapped by OAM mode ratio in Table 2 and equation (31) can be used to judge the sign of the mode value. When the desired receiver detects OAM mode, the normalized radiation pattern information of OAM beam at (dcosδ, δ, c) can be expressed as where In the desired position, equation (33) can maintain the vortex beam characteristic. e vortex signal can be expressed as From Figure 1(c), θ x makes the phase front rotate as a whole.
us, the relationship between compensation azimuth angle c 1 and θ x is l x c 1 � l x θ x . us, the compensation azimuth angle c 1 can be expressed as When the receiver is in the desired position (d 0 cosδ 0 , δ 0 , c 0 ), i.e., d � d 0 , δ � δ 0 and c � c 0 , OAM-DM signal can be demodulated by multiplying the helix phase factor exp (−l x c 0 ) and compensating phase exp (−l x c 1 ) with a single antenna.
Two signals in equation (38) can be obtained by demodulating the signals with l 1 and l 2 , respectively.
Two frame signals can be demodulated from equation (38) and synthesized into the QPSK signal V QPSK for eliminating the influence of θ x on the signal demodulation.
In the desired position (d � d 0 , δ � δ 0 and c � c 0 ), the desired receiver can restore correct signal constellation with l x � l 2 . e data sequence can be calculated by the traditional QPSK signal demodulation method.
Since equation (22) disturbs the distribution of the digital sequence from equation (40) is not the correct data sequence.
e constellation needs the specific phase rotation to demodulate the original digital sequence z n . e correct digital sequence z n can be obtained by Moreover, when the receiver is located at the desired elevation angle δ 0 , the signal amplitude 2I 2 is the largest, and the bit error rate (BER) performance will be the best. e composite mode of OAM-DM signal and the changing OAM mode can make it more difficult for the eavesdropper to demodulate OAM-DM signals. e desired receiver can estimate the OAM mode using the azimuth angle relative to the transmitter, which enables the single antenna receiver to demodulate dual-mode OAM-DM signal. When two signals are synthesized into one signal, the receiver uses the special demodulation method to restore the correct digital information in the desired position.
Since the wave propagates with time, the beam cannot dwell for a long time. is implies that the eavesdropper can receive the same signal as the legitimate user, when they are both in the same position. From our design of OAM-DM signal in random FDA, the signal demodulation depends on OAM mode value, and the transmitter can flexibly switch OAM modes to interfere with eavesdropping. However, OAM-DM signal generated by the random frequency causes OAM mode value to be detected only at the desired range. e eavesdropper must accurately obtain the desired range before it is possible to monitor modes of randomly varying dual OAM beams. Even if the eavesdropper can obtain OAM mode value at the desired range, it must be located at the desired elevation and azimuth to restore correctly two OAM-DM signal constellations. In other words, the eavesdropper must exactly be consistent with the spatial coordinates of the desired receiver to restore the desired signal constellation with correct information, which is extremely difficult for the eavesdropper.

Numerical Results
In numerical simulation, BER is calculated by transmitting a data stream of random QPSK symbols in an additive white Gaussian noise (AWGN) channel. Calculating BER via the data stream approach makes Gray-code inspection for each symbol pair possible. When l 2 � ±1 and l 1 ≠ l 2 , a data stream with 10 6 random QPSK symbols can be used for the BER simulation. Intensity patterns, phase fronts, and multitarget BER performances of the position-sensitivity OAM-DM signal are evaluated. e desired position (d 0 cosδ 0 , δ 0 , c 0 ) is set to (60 m, 20°, 40°). In Figures 6(a) and 6(b), the intensity pattern of the radio wave is depicted at the desired range, which is not affected by N x . When the receiver is located at the undesired range, intensity patterns are shown in Figure 7. As shown in Figures 6(a), 6(b), and 7, the intensity pattern only keeps characteristic of vortex wave at the desired range, while intensity patterns at other ranges are distorted randomly with random N x . Figure 8 depicts phase fronts at different ranges. In Figures 8(a) and 8(c), the vortex phase front of the electric field can be easily recognized at the desired range, for both l � 1 and l � 2. When l � −1 and l � −2, the color changing from red to yellow, green, and blue back to red again indicates the phases changing from 0 to 2π. In Figures 8(b) and 8(d), it shows that the field obtained at the undesired range does not exhibit the helical phase fronts. In the desired position, the helical phases of OAM beam with positive and negative mode values are opposite, and elevation information of the radiation pattern is the same. e change of the OAM mode value is used to interfere with the eavesdropper to obtain the correct information without affecting the desired receiver to demodulate the digital information.
Multitarget desired positions are set to (50 m, 20°, 150°), (60 m, 20°, 40°), and (70 m, 20°, 120°), respectively. e mode of dual OAM-DM beams is set to l 1 � 2 and l 2 � 1. e signal-noise ratio (SNR) is 12 dB. As shown in Figure 9, BER performances with the position-sensitivity OAM-DM signal are simulated. e BER performance is the best in the desired position and varies with the change of the position. Numerical results in Figures 9(a), 9(b), and 9(c) show that the proposed communication scheme with the positionsensitivity OAM-DM pattern can generate a secure position in free space for the desired receiver without knowledge of the eavesdropper's channel state information.
random N x . e color changing from blue to green, yellow, and red back to blue again indicates the phases changing from 0 to 2π.  the desired receiver deviates from the desired position by 1 m and 1°, the BER performance reduces to a certain extent. If the position of the desired receiver deviates from the desired position by more than 1 m and 1°, the BER performance decreases sharply. Even if eavesdroppers have the ability to demodulate signals, it is difficult to obtain the accurate desired position. erefore, the position-sensitivity OAM-DM signal can still protect multitarget information security.

Conclusions
In this study, OAM-DM signal design based on the uniform circular FDA and vortex signal demodulation schemes are proposed for multitarget position-dependent security transmission. e radiation pattern is modulated into the signal, which makes the modulated waveform carry range, elevation, and azimuth information to distort the constellation in all directions except that of the desired position. e eavesdropper outside the desired range observes distorted intensity patterns, phase fronts, and modulation constellation. e phase and amplitude of the constellation point are distorted at the undesired elevation and azimuth angle. erefore, OAM-DM signal can correlate the positionsensitivity security transmission, in which the eavesdropper cannot recover OAM beam and messages. Moreover, composite signals with dual-mode OAM-DM beam can make it more difficult for eavesdroppers to demodulate OAM-DM signal. OAM mode estimation and the phase compensation enable multiple desired receivers to demodulate OAM-DM signal with a single antenna in the corresponding desired position.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this article.