Directional Modulation Design Based on Crossed-Dipole Arrays for Two Signals with Orthogonal Polarisations

Directional Modulation Design Based on Crossed-Dipole Arrays for Two Signals With Orthogonal Polarisations

Bo Zhang, Wei Liu1 and Xiang Lan Communications Research Group, Department of Electronic and Electrical Engineering University of Sheffield, Sheffield S1 4ET, United Kingdom 1 w.liu@sheffield.ac.uk

Abstract—Directional modulation (DM) is a physical layer Recently, the time modulation technique was introduced to security technique based on antenna arrays and so far the DM to form a four-dimensional (4-D) antenna array in [11]. polarisation information has not been considered in its designs. To increase the channel capacity, we consider exploiting the polarisa- However, the polarisation information is not exploited in all tion information and send two different signals simultaneously at the same direction, same frequency, but with different polarisa- aforementioned DM designs, and a single signal is transmitted tions. These two signals can also be considered as one composite through the propagation channel. To increase system capacity, signal using the four dimensional (4-D) modulation scheme across we can exploit the polarisation information of the electromag- the two polarisation diversity channels. In this paper, based on netic signal and send two different signals simultaneously at cross-dipole arrays, we formulate the design to ﬁnd a set of the same direction, same frequency, but different polarisations. common weight coefﬁcients to achieve directional modulation for such a composite signal and examples are provided to verify the This can be achieved by employing polarisation-sensitive ar- effectiveness of the proposed method. rays, such as tripole arrays and crossed-dipole arrays [12–18]. Index Terms— Directional modulation, crossed-dipole ar- These two signals can also be considered as one composite ray, orthogonal polarisations. signal using the four dimensional (4-D) modulation scheme across the two polarisation diversity channels [16, 19, 20]. I.INTRODUCTION In this paper, based on this idea, we proposed a DM design Directional modulation (DM) is a physical layer security using crossed-dipole arrays, which can send two separate

technique which keeps known constellation mappings in a signals (S1 and S2) with orthogonal polarisation states to desired direction or directions, while scrambling them for the the same direction simultaneously. To receive and separate remaining ones [1, 2]. Both reconﬁgurable arrays and phased the two orthogonally polarised signals, at the receiver side, array structures can be used for its design. For reconﬁgurable a crossed-dipole antenna or array is needed, similar to the arrays, their elements are switched for each symbol to make transmitter side [21]. However, the polarisation directions of their constellation points not scrambled in desired directions, the antennas at the receiver side do not need to match those of but distorted in other directions [3]. For phased arrays [4, 5], the transmitted signals, as cross-interference due to a mismatch DM can be implemented by phase shifting the transmitted can be solved easily using some standard signal processing antenna signals properly. In [6], a method named dual beam techniques [16].

arXiv:1801.00418v1 [eess.SP] 1 Jan 2018 DM was introduced, where the I and Q signals are transmitted by different antennas. The bit error rate (BER) performance of The remaining part of this paper is structured as follows. a system based on a two-antenna array was studied using the A review of polarised beamforming based on crossed-dipole DM technique for eight phase shift keying modulation in [7]. arrays is given in Sec. II. Directional modulation designs A more systematic pattern synthesis approach was presented for two signals transmitted to the same direction, but with in [8], followed by an orthogonal vector approach which orthogonal polarisation states are presented in Sec. III. In Sec. produces an artificial orthogonal noise vector from information IV, design examples are provided, with conclusions drawn in to achieve DM in [9], and energy-constrained design in [10]. Sec. V. II.REVIEWOF POLARISED BEAMFORMING z A narrowband linear array for transmit beamforming based on N crossed-dipole antennas is shown in Fig. 1. For each 澳T antenna, there are two orthogonally orientated dipoles, and the 澳 one parallel to the x axis is connected to a complex valued d N 澳 d weight coefficient represented by wn,x, and the one parallel to the y axis is connected to wn,y for n = 0,...,N − 1. The spacing from the first antenna to its subsequent antennas is 澳I x y represented by dn for n = 1,...,N − 1. The elevation angle is denoted by θ ∈ [0, π] and azimuth angle is represented by φ ∈ [0, 2π]. The spatial steering vector of the array, a function Fig. 1. A crossed-dipole linear array. of elevation angle θ and azimuth angle φ, is given by

−jωd1 sin θ sin φ/c −jωdN−1 sin θ sin φ/c T ss(θ, φ) = [1, e , . . . , e ] , and w is the complex valued weight vector

(1) T w = [w0,x, . . . , wN−1,x, w0,y, . . . , wN−1,y] . (7) where {·}T is the transpose operation, and c is the speed of propagation. For a uniform linear array (ULA) with a half- wavelength spacing (dn − dn−1 = λ/2), the spatial steering III.DIRECTIONAL MODULATION DESIGN vector can be simplified to In traditional crossed-dipole array design, the weight coeffi- s (θ, φ) = [1, e−jπ sin θ sin φ, . . . , e−jπ(N−1) sin θ sin φ]T . (2) s cients are designed for one single beam response and therefore Moreover, the spatial-polarisation coherent vector of the signal can only cater for one transmitted DM signal. To increase is given by [21, 22] the transmission capacity, in this section, we design a set of " # common weight coefficients for two signals (S1 and S2) with − sin φ cos γ + cos φ cos θ sin γejη sp(θ, φ, γ, η) = orthogonal polarisation states transmitted to the same direction cos φ cos γ + sin φ cos θ sin γejη simultaneously. Based on the parameter representations in Sec. " # (3) spx(θ, φ, γ, η) II, we have s(θ, φ, γ , η ), s(θ, φ, γ , η ), p(θ, φ, γ , η ), and = , 1 1 2 2 1 1 spy(θ, φ, γ, η) p(θ, φ, γ2, η2) to represent steering vectors for S1 and S2, and where γ ∈ [0, π/2] is the auxiliary polarisation angle and η ∈ beam responses for S1 and S2, respectively. [−π, π) represents the polarisation phase difference. For M-ary signaling, such as multiple phase shift keying For convenience, we split the array structure into two sub- (MPSK), each of S1 and S2 can create M constellation points arrays: one is parallel to the x-axis and the other to the y-axis. (M symbols), leading to M desired responses. Then, for S1 2 Then, the steering vectors of the two sub-arrays are given by and S2 transmitted simultaneously, there are M different symbols and M 2 sets of response pairs, represented by a sx(θ, φ, γ, η) =spx(θ, φ, γ, η)ss(θ, φ), 2 (4) 1 × 2 vector pm(θ, φ, γ, η) for m = 0,...,M − 1, and sy(θ, φ, γ, η) =spy(θ, φ, γ, η)ss(θ, φ). each response pm(θ, φ, γ, η) corresponds to a weight vec- T The beam response of the array can be given by [23] tor wm = [w0,x,m, . . . , wN−1,x,m, w0,y,m, . . . , wN−1,y,m] . Here, we assume r points are sampled in the mainlobe and H p(θ, φ, γ, η) = w s(θ, φ, γ, η), (5) R − r points in the sidelobe range; then the responses for where {·}H represents the Hermitian transpose, s(θ, φ, γ, η), two signals in the mainlobe direction pML,m and the sidelobe a 2N × 1 vector representing the overall steering vector of the range pSL,m are given by array, is given by pSL,m = [pm(θ0, φ, γ1, η1), . . . , pm(θR−r−1, φ, γ1, η1) T s(θ, φ, γ, η) =[sx(θ, φ, γ, η), sy(θ, φ, γ, η)] , pm(θ0, φ, γ2, η2), . . . , pm(θR−r−1, φ, γ2, η2)], T sx(θ, φ, γ, η) =[s0,x(θ, φ, γ, η), . . . , sN−1,x(θ, φ, γ, η)] , pML,m = [pm(θR−r, φ, γ1, η1), . . . , pm(θR−1, φ, γ1, η1) T sy(θ, φ, γ, η) =[s0,y(θ, φ, γ, η), . . . , sN−1,y(θ, φ, γ, η)] , pm(θR−r, φ, γ2, η2), . . . , pm(θR−1, φ, γ2, η2)]. (6) (8) Here we have implicitly assumed that all the responses are considered with a fixed φ. Moreover, we put all the 2(R − r) 0 S (symbol 0000) steering vectors of both S1 and S2 at the sidelobe region into Re S (symbol 00) -10 1 S (symbol 00) an 2N × 2(R − r) matrix SSL, and the 2r steering vectors 2 at the mainlobe direction into an 2N × 2r matrix, denoted by -20

SML, where -30

-40 SSL = [s(θ0, φ, γ1, η1),..., s(θR−r−1, φ, γ1, η1) Beam pattern (dB) -50 s(θ0, φ, γ2, η2),..., s(θR−r−1, φ, γ2, η2)], (9) -60 SML = [s(θR−r, φ, γ1, η1),..., s(θR−1, φ, γ1, η1) -90 -60 -30 0 30 60 90 θ (degree) s(θR−r, φ, γ2, η2),..., s(θR−1, φ, γ2, η2)]. (a) Then, for the m-th symbol, its corresponding weight coefﬁ- 0 cients can be solved by S (symbol 0001) Re S (symbol 00) H -10 1 S (symbol 01) min ||pSL,m − wmSSL||2 2 (10) H -20 subject to wmSML = pML,m, -30 where || · ||2 denotes the l2 norm. The objective function in -40

(10) ensures a minimum difference between the desired and Beam pattern (dB) designed responses for two signals in the sidelobe, and the -50 constraint keeps a desired constellation value of two signals to -60 -90 -60 -30 0 30 60 90 the mainlobe. To ensure that the constellation is scrambled in θ (degree) the sidelobe regions, the phase of the desired response for two (b) signals pSL,m at different sidelobe directions can be randomly 0 S (symbol 0011) generated. Re S (symbol 00) -10 1 S (symbol 11) The problem in (10) can be solved by the method of 2 Lagrange multipliers, and the optimum value for the weight -20 H -30 vector wm is given in (11), where R = SSLSSL. −1 H H −1 −1 -40

wm =R (SSLpSL,m − SML((SMLR SML) Beam pattern (dB) (11) H −1 H H -50 (SMLR SSLpSL,m − pML,m))). -60 As these two signals S1 and S2 are modulated to generate -90 -60 -30 0 30 60 90 θ (degree) a 4-D modulated signal SRe in the far-ﬁeld, to separate the corresponding components from the received composite signal, (c) at the receiver side, we need a crossed-dipole antenna array 0 S (symbol 0010) Re S (symbol 00) in the same way as given in [16]. -10 1 S (symbol 10) 2 IV. DESIGNEXAMPLES -20 In this section, we provide design examples based on a -30 9λ aperture ULA with a half wavelength spacing between -40 Beam pattern (dB) adjacent antennas to show the performance of the proposed -50 formulations. The polarisation characteristics are deﬁned by -60 (γ , η ) = (0◦, 0◦) S -90 -60 -30 0 30 60 90 1 1 for 1 for a horizontal polarisation, and θ (degree) ◦ ◦ (γ2, η2) = (90 , 0 ) for S2 for a vertical polarisation. For (d) each of S1 and S2, the desired response is a value of one (magnitude) with 90◦ phase shift at the mainlobe (QPSK), i.e., Fig. 2. Resultant beam responses based on the design (10) for symbols (a) ‘00,00’, (b)‘00,01’, (c)‘00,11’, (d)‘00,10’. symbols ‘00’, ‘01’, ‘11’, ‘10’ correspond to 45◦, 135◦, −45◦ and −135◦, respectively, and a value of 0.1 (magnitude) with random phase shifts over the sidelobe regions. Therefore, for S S 180 signals 1 and 2 transmitted simultaneously, we can construct

135 16 different symbols. Moreover, without loss of generality, we ◦ ◦ 90 assume the mainlobe direction is θML = 0 for φ = 90 ◦ ◦ ◦ 45 and the sidelobe regions are θSL ∈ [5 , 90 ] for φ = ±90 , 0 sampled every 1◦, representing two signals are transmitted -45 Phase angle through the y − z plane. -90 S (symbol 00) 1 With the above parameters and design formulations in (10), -135 S (symbol 00) 2 the composite beam patterns for symbols ‘00,00’, ‘00,01’, -180 -90 -60 -30 0 30 60 90 ‘00,11’ and ‘00,10’ are shown in Figs. 2(a), 2(b), 2(c) and θ (degree) 2(d), where all main beams are exactly pointed to 0◦ (3.01dB √ (a) or 2 magnitude) with a reasonable sidelobe level, and its 180 corresponding components for S1 and S2 coincide in the 135 mainlobe direction with 0dB mainlobe level, representing that 90 a value of one for magnitude of desired signals S1 and S2 45 has been satisﬁed. The phase patterns for these symbols are 0 displayed in Figs. 3(a), 3(b), 3(c), 3(d). We can see that the -45 Phase angle -90 phases of S1 and S2 in the desired direction match the standard S (symbol 00) 1 -135 S (symbol 01) QPSK constellation, while for the rest of the θ angles, phases 2 -180 are random, demonstrating that directional modulation has -90 -60 -30 0 30 60 90 θ (degree) been achieved effectively. The beam and phase patterns for

(b) other symbols are not shown as they have the same features as the aforementioned ﬁgures. 180

135 V. CONCLUSIONS 90

45 A crossed-dipole antenna array for directional modulation 0 has been proposed for the ﬁrst time, and a set of common -45

Phase angle weight coefficients has been designed for two signals S1 and -90 S (symbol 00) S2 with orthogonal polarisation states transmitted to the same 1 -135 S (symbol 11) 2 direction, based on a fixed given array geometry. As these -180 -90 -60 -30 0 30 60 90 two signals are modulated to generate a 4-D modulated signal θ (degree) SRe in the far-field, to receive and separate the corresponding (c) components from the resultant SRe, at the receiver side, a 180 crossed-dipole antenna array is needed. As shown in the 135 provided design examples, for both S1 and S2, a mainlobe 90 and standard phase pattern have been achieved in the desired 45 direction with low sidelobe level and scrambled phases in other 0 directions. -45 Phase angle -90 S (symbol 00) EFERENCE 1 R -135 S (symbol 10) 2 -180 [1] A. Babakhani, D. B. Rutledge, and A. Hajimiri. Trans- -90 -60 -30 0 30 60 90 θ (degree) mitter architectures based on near-field direct antenna modulation. IEEE Journal of Solid-State Circuits, (d) 43(12):2674–2692, December 2008. Fig. 3. Resultant phase responses based on the design (10) for symbols (a) [2] A. Babakhani, D. B. Rutledge, and A. Hajimiri. Near- ‘00,00’, (b)‘00,01’, (c)‘00,11’, (d)‘00,10’. field direct antenna modulation. IEEE Microwave Mag- azine, 10(1):36–46, February 2009. [3] M. P. Daly and J. T. Bernhard. Beamsteering in pattern Quaternion-Capon beamformer using crossed-dipole ar- reconfigurable arrays using directional modulation. IEEE rays. In Proc. IEEE International Symposium on Mi- Transactions on Antennas and Propagation, 58(7):2259– crowave, Antenna, Propagation, and EMC Technologies 2265, March 2010. for Wireless Communications (MAPE), pages 34–37, [4] M. P. Daly and J. T. Bernhard. Directional modulation Beijing, China, November 2011. technique for phased arrays. IEEE Transactions on [16] W. Liu. Antenna array signal processing for a quaternion- Antennas and Propagation, 57(9):2633–2640, September valued wireless communication system. In Proc. the 2009. Benjamin Franklin Symposium on Microwave and An- [5] B. Zhang, W. Liu, and X. Gou. Compressive sensing tenna Sub-systems (BenMAS), Philadelphia, US, Septem- based sparse antenna array design for directional modula- ber 2014. tion. IET Microwaves, Antennas Propagation, 11(5):634– [17] M. B. Hawes and W. Liu. Design of fixed beamformers 641, April 2017. based on vector-sensor arrays. International Journal [6] T. Hong, M. Z. Song, and Y. Liu. Dual-beam directional of Antennas and Propagation, 2015:181937.1–181937.9, modulation technique for physical-layer secure commu- March 2015. nication. IEEE Antennas and Wireless Propagation [18] J. J. Xiao and A. Nehorai. Optimal polarized beampattern Letters, 10:1417–1420, December 2011. synthesis using a vector antenna array. IEEE Trans- [7] H. Z. Shi and A. Tennant. Enhancing the security of actions on Signal Processing, 57(2):576–587, February communication via directly modulated antenna arrays. 2009. IET Microwaves, Antennas & Propagation, 7(8):606– [19] O. M. Isaeva and V. A. Sarytchev. Quaternion presen- 611, June 2013. tations polarization state. In Proc. 2nd IEEE Topical [8] Y. Ding and V. Fusco. Directional modulation transmitter Symposium of Combined Optical-Microwave Earth and radiation pattern considerations. IET Microwaves, Anten- Atmosphere Sensing, pages 195–196, Atlanta, US, April nas & Propagation, 7(15):1201–1206, December 2013. 1995. [9] Y. Ding and V. Fusco. A vector approach for the [20] L. H. Zetterberg and H. Brandstrom. Codes for com- analysis and synthesis of directional modulation transmit- bined phase and amplitude modulated signals in a four- ters. IEEE Transactions on Antennas and Propagation, dimensional space. IEEE Transactions on Communica- 62(1):361–370, January 2014. tions, 25(29):943–950, September 1977. [10] Y. Ding and V. Fusco. Constraining directional mod- [21] X. Lan and W. Liu. Fully quaternion-valued adaptive ulation transmitter radiation patterns. IET Microwaves, beamforming based on crossed-dipole arrays. Electron- Antennas & Propagation, 8(15):1408–1415, September ics, 6(2):34, April 2017. 2014. [22] X. R. Zhang, W. Liu, Y. G. Xu, and Z. W. Liu. [11] Q. J. Zhu, S. W. Yang, R. L. Yao, and Z. P. Nie. Di- Quaternion-valued robust adaptive beamformer for elec- rectional modulation based on 4-D antenna arrays. IEEE tromagnetic vector-sensor arrays with worst-case con- Transactions on Antennas and Propagation, 62(2):621– straint. Signal Processing, 104:274–283, April 2014. 628, February 2014. [23] M. B. Hawes, W. Liu, and L. Mihaylova. Compressive [12] R. T. Compton. On the performance of a polarization sensing based design of sparse tripole arrays. Sensors, sensitive adaptive array. IEEE Transactions on Antennas 15(12):31056–31068, December 2015. and Propagation, 29(5):718–725, September 1981. [13] A. Nehorai and E. Paldi. Digital Signal Processing Handbook, chapter Electromagnetic vector-sensor array processing, pages 65.1–65.26. CRC Press, 1998. [14] S. Miron, N. Le Bihan, and J. I. Mars. Quaternion- MUSIC for vector-sensor array processing. IEEE Trans- actions on Signal Processing, 54(4):1218–1229, April 2006. [15] X. M. Gou, Y. G. Xu, Z. W. Liu, and X. F. Gong.