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

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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. REVIEW OF 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 2 [0; π] and azimuth angle is represented by φ 2 [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 −j!d1 sin θ sin φ/c −j!dN−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 2 [0; π=2] is the auxiliary polarisation angle and η 2 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 jjpSL;m − wmSSLjj2 2 (10) H -20 subject to wmSML = pML;m; -30 where jj · jj2 denotes the l2 norm.
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