# A Spectrum Efficient Secure Transmission Scheme Based on Directional Polarization Modulation for Wireless Communication Systems

Authors: Zhongmin Pei; Zhangkai Luo; Bo Zou
Journal: Mathematical Problems in Engineering
 (2018)

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## Abstract

In this paper, a spectrum efficient secure transmission scheme based on directional polarization modulation (DPM) is proposed. Specifically, the polarized signals are divided into two parts, i.e., I and Q, and a dual-polarized antenna array is designed to form beams to transmit these signals. Naturally, the constellation structure is associated with the beam gain, which can be controlled to make the constellation structure distort in undesired directions. Thus the security is enhanced for the symbol error rate performance deteriorates in undesired directions. Additionally, a kind of directional modulation technique is utilized to transform one component of the polarized signal into QPSK signal and thus improves the modulation order without extra transmitting power consummation. Finally, theoretical analysis and simulation results demonstrate that the proposed scheme can improve the transmission efficiency and provide a security transmission method for wireless communication systems.


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## Body

## 1. Introduction

In order to meet the ever increasing high data rate demand, the fifth generation (5G) of wireless cellular communication systems is predicted to be available to the market by 2020 [1, 2]. To alleviate the scarcity of spectrum resources, 5G is suggested to be working in millimeter-wave (mm-wave) bands. However, in the mm-wave communication, the non-line-of-sight (NLOS) signals are very weak due to the large path loss. Thus, multiple-input multiple-output (MIMO) techniques are hard to be applied to improve the transmission efficiency, for MIMO gains depend on the decorrelation between channels [3]. Fortunately, polarization diversity is proved to be a feasible way to improve the transmission efficiency for it can provide two independent paths on the same frequency band in line-of-sight (LOS) channels [4, 5]. Furthermore, in addition to the traditional polarization diversity and polarization multiplexing, the polarization state is explored to carry information and the technology is called polarization modulation (PM), which can be combined with traditional modulation techniques without contradictions [6] and improve the energy efficiency [7].On the other hand, the transmit information is easy to be eavesdropped due to the openness nature of the wireless medium [8]. The information security is important and receives more and more attention in recently years. Transmission security is traditionally dependent on cryptographic techniques in the link and network layer. Challenges (and vulnerabilities) associated with key distribution and management, however, make cryptography a less than ideal solution [9]. Fortunately, new research on physical layer security brings new ways with great potential, which focus on preventing eavesdroppers from decoding any useful message intended to the desired user.In the traditional mode, modulated radio frequency (RF) signals go through a power amplifier to drive the transmit antenna or antenna array. It is noteworthy that there is a great possibility for a sufficiently sensitive eavesdropper to recover information from the signal that is transmitted through side lobes, whose only difference from the signal received in the main lobe is the signal’s power. To address this problem, in [10, 11], directional modulation (DM) is proposed, in which the transmit signal is direction-dependent and the signal can be purposely distorted in undesired directions. In [12], a dual-beam DM technique is introduced, which utilizes dual beams to form a secure link from the transmitter to the receiver. In [13–15], multipath directional modulation is proposed to provide multisecure links to receivers. However, the above researches are based on the scalar array and little literature reports the DM with the dual-polarized array.Motivated by the above, we propose a spectrum efficient directional polarization modulation (SEDPM) scheme in this paper, which can improve the transmission efficiency and security at the same time. In the SEDPM scheme, two components of the polarized signal are both divided into two data streams and transmitted by four orthogonal beams formed by the dual-polarized antenna array. In this way, the transmit signals’ constellation structure is associated with the array gain and only in the desired direction that the constellation structure is not distorted. Therefore, the security is enhanced due to the symbol error rate (SER) increases in undesired direction. Additionally, to maximize the spectrum efficiency, the component of the polarized signal that contains only the real number is transformed into the QPSK signal [12] and this kind of transformation has no influence on the demodulation of the PM signal; thus two kinds of modulation technique can be combined and the spectrum efficiency is improved.In this letter, we assume an AWGN channel, infinite XPD, and evaluate the achievable security performance of the proposed scheme. Although nonideal XPD is an important consideration for the proposed scheme, its effect is less in the Ku band and precompensation methods [17, 18] can also reduce the influence. In addition, we assume the equal transmission path length between two polarization channels and there is no frequency offset for these problems are solved in [19].


## 2. Signal Model

The electromagnetic wave emitted from the antenna iss0=Aej(wct+ϕ) [20], where A denotes the amplitude, wc denotes the carry frequency, and ϕ denotes the initial phase, which is set to 0 for simplifying the analysis. Two components of the polarized signal can be denoted as(1)st=s1s2=cos⁡γsin⁡γejηs0,where γ∈0,π/2,η∈0,2π are polarization parameters. s1 and s2 denote the two components, respectively.Indeed, the polarized signal’s polarization state (PS) is determined byγ,η, and M1-th order constellation points can be represented as PSk:γk,ηk,k=1,2,⋯,M1. For the k-th constellation point, we take the real part of (1) and derive the real modulated signal as(2)Rest=ReAcos⁡γkejwctsin⁡γkejηkejwct=Acos⁡γkcos⁡wct+0∗sin⁡wctsin⁡γkcos⁡ηkcos⁡wct-sin⁡γksin⁡ηksin⁡wct.As we can see, two components of the polarized signal are both divided into I and Q parts, which will be separately transmitted in the SEDPM scheme.


## 3. Principle of the SEDPM Scheme

### 3.1. Signal Transmission

We consider a dual-polarized antenna array as shown in Figure1 in the x-y coordinate system; N, W, E, and S are used to mark the four elements. N1 and N2 are two orthogonal polarized components of the dual-polarized antenna N, where N1 is parallel to the x axis and N2 is vertical to the x axis. In addition, the same is to W1, W2, E1, E2, S1, and S2. According to [12], inverse-excitations are taken to drive the copolarization antennas N1 and S1 (N2 and S2), then the radiation pattern can be expressed as(3)f1θ=sin⁡πdλcos⁡θ,where λ denotes the wavelength, θ denotes the azimuth angle and d=λ/2 denotes the distance between antenna elements in the same axis. Similarly, the radiation pattern of W-E can be written as(4)f2θ=sin⁡πdλsin⁡θ.Figure 1
Signal transmission design.The beam pattern off1θ, f2θ and the normalized synthesized pattern fθ=f12θ+f22θ are shown in Figure 2.Figure 2
Beam gain of the dual-polarized array.In order to improve the spectrum efficiency and security performance, we replace thecos⁡γkcos⁡wct in (5) by(5)cos⁡γkbm2cos⁡wct+cmcos⁡γk2sin⁡wct,where bm∈-1,1 and cm∈-1,1. By selecting different values of bm and cm, we can realize QPSK in polarization 1 like the manner in [12]. In addition, both two components of the polarized signal are divided into two parts, which will be transmitted by designed beams separately. The excitation signals for each antenna are shown in Table 1, where S^1,S^2,S^3,S^4 are phase inverse ones of S1,S2,S3,S4 and S1=cos⁡γk/2cos⁡wct  S2=sin⁡γkcos⁡ηkcos⁡wct, S3=-sin⁡γksin⁡ηksin⁡wct, and S4=cos⁡γk/2sin⁡wct [12].Table 1
Excitation signals of each antenna.
Antenna Polarization 1 excitation signal Antenna Polarization 2 excitation signal N1 b m S 1 N 2 S 3 W1 c m S 4 W 2 S 2 S1 b m S ^ 1 S 2 S ^ 3 E1 c m S ^ 4 E 2 S ^ 2


### 3.2. Signal Demodulation

At the receiver side, the signal demodulation can be divided into two steps: the demodulation of the QPSK signal in polarization 1 and the demodulation of PM signal. We assume that there is no depolarization effect; then, the received signal can be expressed as(6)y=F1F2=Af1θbmcos⁡γkcos⁡wct+f2θcmcos⁡γksin⁡wct2+n1sin⁡γkf1θcos⁡ηkcos⁡wct-f2θsin⁡ηksin⁡wct+n2=Afθcos⁡γkcos⁡wct-φ12+n1f^θsin⁡γkcos⁡wct+φ2+n2where(7)fθ=f12θ+f22θf^θ=f1θcos⁡ηk2+f2θsin⁡ηk2,and φ2=arctan⁡f2θ/f1θtan⁡ηk and φ1=arctan⁡cmf2θ/bmf1θ.Considering the data of polarization 1, it is found that, by changingbm and cm, QPSK signals can be obtained as shown in Figure 3 and Table 2 shows the received vectors of the QPSK in polarization 1 (QPSKP) with the bm and cm created by the four sets of values ((1,1),(-1,1),(1,-1),(-1,-1)). For QPSKP, the Euclidean distance between the two constellation points is associated with f1θ and f2θ, unlike the traditional QPSK signal which only depends on fθ. In the desired direction, the constellation structure of QPSKP is the same as that of QPSK, while it scrambles when the receiver is off the desired azimuth angle. Thus, the constellation structure received by users in different azimuth angle is changing along with the array gain of dual beams, and this is the key technology for secure transmission, which is similar to the dual-beam directional modulation (DM) technology in [12].Table 2
QPSK modulation in polarization 1.
bm c m QPSK in polarization 1 1 1 f θ cos ⁡ γ k ∠ f 2 θ f 1 θ  1 - 1 f θ cos ⁡ γ k ∠ - f 2 θ f 1 θ  - 1 1 f θ cos ⁡ γ k ∠ f 2 θ - f 1 θ  - 1 - 1 f θ cos ⁡ γ k ∠ - f 2 θ - f 1 θFigure 3
QPSKP constellation structure.
(a)
Traditional QPSK (b)
QPSK in polarization 1On the other hand, in the desired direction, (6) can be rewritten as(8)y=F1F2=Af1θcos⁡γkcos⁡wct-φ1+n1f1θsin⁡γkcos⁡wct+φ2+n2,where f1θ=f2θ. It is easy to find that the maximum amplitude of F1 is unaffected by bm and cm. Therefore, during every symbol period, the receiver can obtain the polarization parameters by(9)γkR=arctan⁡absmax⁡F2max⁡F1,ηkR=ΞF2where Ξ• is the phase acquisition operation.With polarization parameters, PS of the transmitted signal can be gotten and inverse mapping can be conducted to recover the useful information.Obviously, the transmitted signal’s PS is also affected by the array gain of dual beams and only in the desired directions (45∘,135∘) where f1θ=f2θ that γkR=γk,ηkR=ηk. While in other directions, polarization constellation structure is distorted. In this way, the secure transmission performance is also enhanced by PM. In addition, the combination of M1-th order PM and M2-th DM would result in a (M1×M2)-th order modulation scheme, which significantly improves the spectrum efficiency.


## 3.1. Signal Transmission

We consider a dual-polarized antenna array as shown in Figure1 in the x-y coordinate system; N, W, E, and S are used to mark the four elements. N1 and N2 are two orthogonal polarized components of the dual-polarized antenna N, where N1 is parallel to the x axis and N2 is vertical to the x axis. In addition, the same is to W1, W2, E1, E2, S1, and S2. According to [12], inverse-excitations are taken to drive the copolarization antennas N1 and S1 (N2 and S2), then the radiation pattern can be expressed as(3)f1θ=sin⁡πdλcos⁡θ,where λ denotes the wavelength, θ denotes the azimuth angle and d=λ/2 denotes the distance between antenna elements in the same axis. Similarly, the radiation pattern of W-E can be written as(4)f2θ=sin⁡πdλsin⁡θ.Figure 1
Signal transmission design.The beam pattern off1θ, f2θ and the normalized synthesized pattern fθ=f12θ+f22θ are shown in Figure 2.Figure 2
Beam gain of the dual-polarized array.In order to improve the spectrum efficiency and security performance, we replace thecos⁡γkcos⁡wct in (5) by(5)cos⁡γkbm2cos⁡wct+cmcos⁡γk2sin⁡wct,where bm∈-1,1 and cm∈-1,1. By selecting different values of bm and cm, we can realize QPSK in polarization 1 like the manner in [12]. In addition, both two components of the polarized signal are divided into two parts, which will be transmitted by designed beams separately. The excitation signals for each antenna are shown in Table 1, where S^1,S^2,S^3,S^4 are phase inverse ones of S1,S2,S3,S4 and S1=cos⁡γk/2cos⁡wct  S2=sin⁡γkcos⁡ηkcos⁡wct, S3=-sin⁡γksin⁡ηksin⁡wct, and S4=cos⁡γk/2sin⁡wct [12].Table 1
Excitation signals of each antenna.
Antenna Polarization 1 excitation signal Antenna Polarization 2 excitation signal N1 b m S 1 N 2 S 3 W1 c m S 4 W 2 S 2 S1 b m S ^ 1 S 2 S ^ 3 E1 c m S ^ 4 E 2 S ^ 2


## 3.2. Signal Demodulation

At the receiver side, the signal demodulation can be divided into two steps: the demodulation of the QPSK signal in polarization 1 and the demodulation of PM signal. We assume that there is no depolarization effect; then, the received signal can be expressed as(6)y=F1F2=Af1θbmcos⁡γkcos⁡wct+f2θcmcos⁡γksin⁡wct2+n1sin⁡γkf1θcos⁡ηkcos⁡wct-f2θsin⁡ηksin⁡wct+n2=Afθcos⁡γkcos⁡wct-φ12+n1f^θsin⁡γkcos⁡wct+φ2+n2where(7)fθ=f12θ+f22θf^θ=f1θcos⁡ηk2+f2θsin⁡ηk2,and φ2=arctan⁡f2θ/f1θtan⁡ηk and φ1=arctan⁡cmf2θ/bmf1θ.Considering the data of polarization 1, it is found that, by changingbm and cm, QPSK signals can be obtained as shown in Figure 3 and Table 2 shows the received vectors of the QPSK in polarization 1 (QPSKP) with the bm and cm created by the four sets of values ((1,1),(-1,1),(1,-1),(-1,-1)). For QPSKP, the Euclidean distance between the two constellation points is associated with f1θ and f2θ, unlike the traditional QPSK signal which only depends on fθ. In the desired direction, the constellation structure of QPSKP is the same as that of QPSK, while it scrambles when the receiver is off the desired azimuth angle. Thus, the constellation structure received by users in different azimuth angle is changing along with the array gain of dual beams, and this is the key technology for secure transmission, which is similar to the dual-beam directional modulation (DM) technology in [12].Table 2
QPSK modulation in polarization 1.
bm c m QPSK in polarization 1 1 1 f θ cos ⁡ γ k ∠ f 2 θ f 1 θ  1 - 1 f θ cos ⁡ γ k ∠ - f 2 θ f 1 θ  - 1 1 f θ cos ⁡ γ k ∠ f 2 θ - f 1 θ  - 1 - 1 f θ cos ⁡ γ k ∠ - f 2 θ - f 1 θFigure 3
QPSKP constellation structure.
(a)
Traditional QPSK (b)
QPSK in polarization 1On the other hand, in the desired direction, (6) can be rewritten as(8)y=F1F2=Af1θcos⁡γkcos⁡wct-φ1+n1f1θsin⁡γkcos⁡wct+φ2+n2,where f1θ=f2θ. It is easy to find that the maximum amplitude of F1 is unaffected by bm and cm. Therefore, during every symbol period, the receiver can obtain the polarization parameters by(9)γkR=arctan⁡absmax⁡F2max⁡F1,ηkR=ΞF2where Ξ• is the phase acquisition operation.With polarization parameters, PS of the transmitted signal can be gotten and inverse mapping can be conducted to recover the useful information.Obviously, the transmitted signal’s PS is also affected by the array gain of dual beams and only in the desired directions (45∘,135∘) where f1θ=f2θ that γkR=γk,ηkR=ηk. While in other directions, polarization constellation structure is distorted. In this way, the secure transmission performance is also enhanced by PM. In addition, the combination of M1-th order PM and M2-th DM would result in a (M1×M2)-th order modulation scheme, which significantly improves the spectrum efficiency.


## 4. Performance Evaluation

In this section, security performance is evaluated in terms of symbol error rate (SER) as in [19]. According to the analysis in [11], the SER of DM signals can be calculated by(10)Perror=∑i=1M2QdiN0,where di is the smallest Euclidean distance between the i-th constellation point to the other constellation points and M2 is the modulation order. Thus, for the DM signal in polarization 1 (DMP) during the k-th symbol time, the SER can be calculated as (11)PDMP=QAcos⁡γkf1θ2+f2θ22N0,M2=2;12QAcos⁡γkf1θ2N0+QAcos⁡γkf2θ2N0,M2=4,where N0 is the noise power spectral density and Q• is the complementary Gaussian error function.For PM, the constellation structure is assumed to be the same as in [16, 18, 21]. The PM constellation structures used in our research are shown in Figure 4. M1 equipower constellation points with the equal minimum constellation distance dT are placed symmetric to the g1-axis of the unitary Poincare sphere and each constellation point denotes a unique PS.Figure 4
M 1-th order PM constellation structure [16].
(a)
2PM (b)
4PM (c)
8PM (d)
16PMAs we know, the signal’s PS depends onη and γ; therefore, the SER of SEDPM is composed of two parts: the SER from η expressed as Pη and the SER from γ expressed as Pγ. For the parameter η, the SER can be calculated according to (10), which is similar to the calculation in (11). We omit here and denote the SER of η by Pη. In addition, it is noted that, in any directions, the distance between the received constellation points is not affected by changes in ηkR but γkR and the received signal to noise ratio (RSNR) [18]. For parameter γ, according to (6) and (9), the received power and the spherical constellation distance between the received adjacent points can be respectively calculated as(12)ERk=A2fθcos⁡γkcos⁡wct-φ122+f^θsin⁡γkcos⁡wct+φ22,(13)dijR=arccos⁡cos22γiR+sin22γiRcos⁡OM=2,42γiR-γjRM>4,γiR≠γjRarccos⁡cos22γiR+sin22γiRcos⁡OM>4,γiR=γjRwhere O is the spheric angle between the adjacent polarization constellation points and can be calculated as(14)O=∠PiPHPj=2arcsin⁡sin⁡dT/2sin⁡2γi,where dT is the original spherical constellation distance and PH is the horizontal PS. Affected by changes in γiR, the spherical distance of the received constellation points becomes small. Then the SER can be calculated as(15)Pγ=1M∑i=1MSERi(16)SERi=∑j=1c2∫ψijπ∫0αϑij,ψijfti,φidφidti+∫ϑijψij∫0αϑij,tifti,φidφidti,M>2,where αϑij,ti=arccos⁡(tan⁡ϑij/ti) and fti,φi is the joint probability density function of PSi’s colatitude ti and azimuth φi with additional AWGN noise, which can be expressed as(17)fti,φi=sin⁡ti4πe-ERk1-cos⁡ti/2N01+ERk1+cos⁡ti2N0,where φj and tj are colatitude and azimuth of PSj and the received signal to noise ratio RSNR=ERk/N0. ϑij=dijR/2 denotes the half adjacent constellation spherical distance and ψij denotes the sphere distance between PSi and the endpoints of its decision region (c is the number of endpoints), which can be calculated as(18)ψi1=2γiR,ψi2=π-2γiR,M=4;i∈1,4;k=2ψi1=ψi2=arccos⁡cos⁡2γiR+sin⁡2γiRtan⁡γiR+γi+M/2R1+sec2O/2tan2⁡γiR+γi+M/2Rψi3=2γiR,M⩾8;i∈1,M2;k=3ψi1=ψi2=arccos⁡cosγiR-γi-M/2R1+sin2γiR+γi-M/2Rtan2O/2ψi3=π-2γiR,M⩾8;i∈M2,M;k=3For PM, the SER can be calculated by(19)PPM=1-1-Pη1-Pγ,For SEDPM, the SER can be calculated as(20)PSEDPM=PPMRP+PDMPRDRP+RD.where RP and RD are the symbol rate realized by the PM and DMP during 1 second.


## 5. Numerical Results

In our simulations, XPD is assumed to be infinite and the SER of SEDPM is investigated under the additive white Gaussian noise (AWGN) channel. The signal power of the desired direction (45∘ and 135∘) is used as a standard signal power and the overall power of the transmit signal is set to be the same for SEDPM and DPM.Figure5 shows the SER of SEDPM, directional modulation in polarization 1 (DMP), and directional polarization modulation (DPM) in [12] versus RSNR in the desired direction. The number after DPM and DMP denote the modulation order, and the number after SEDPM represents M1-th order PM combined with M2-th order DMP, which results in the M=M1×M2 order SEDPM. For DMP, the SER is excellent and according to (20), it is found that it has little influence on the output SER of SEDPM while improving the spectrum efficiency. Additionally, by comparing SEDPM2∗4 and SEDPM4∗4, it is found that their SER curves achieve almost the same value as DPM4, while the modulation order is higher. In addition, the SER performance of SEDPM4∗4 is better than SEDPM2∗8 and this is because the SER deteriorates quickly as the modulation order grows high for PM. Moreover, for high order modulation, the SEDPM scheme can also achieve a better performance than DPM. Therefore, higher transmission efficiency can be achieved by the SEDPM scheme.Figure 5
The SER of SEDPM, DPM, and DMP versus RSNR.Figure6 shows the SER versus azimuth angle for DPM4, SEDPM2∗4, and SEDPM4∗4 when RSNR=22dB. It is shown that the SER of SEDPM2∗4 is almost the same as that of DPM4 in the desired directions and deteriorates quickly in other directions, while SEDPM2∗4 has a high modulation order. Moreover, the SER of SEDPM4∗4 is a little worse due to its high modulation order, but its SER deteriorates more quickly out of the main lobe than the other two, which means, in the high modulation order, the performance of the proposed scheme is more outstanding. This characteristic of the proposed scheme is beneficial for the secure wireless communication.Figure 6
The SER of SEDPM, DPM, and DMP versus azimuth angle.


## 6. Conclusion

In this letter, a spectrum efficient secure transmission scheme based on PM is proposed for the wireless communication system. Both the transmission security and the spectrum efficient can be improved. At last, the performance of the proposed scheme is analyzed and compared with the DPM approach.



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