Hindawi International Journal of Antennas and Propagation Volume 2019, Article ID 9784252, 13 pages https://doi.org/10.1155/2019/9784252 Research Article On the Implementation of a Dynamic Direction Modulation System with Vector Modulators Edith Annette Cabrera-Hernández ,1 Josep Parron,1 and Alan Tennant2 1 Department of Telecommunication and System Engineering, Escola d’Enginyeria, Universitat Autònoma de Barcelona (UAB), Campus de la UAB, Q Building, Carrer de les Sitges, Bellaterra, Cerdanyola del Vallès, 08193 Barcelona, Spain 2 Department of Electronic & Electrical Engineering, Portobello Centre, The University of Sheffield, Pitt Street, Sheffield (S1 4ET), UK Correspondence should be addressed to Edith Annette Cabrera-Hernández; edithannette.cabrera@uab.cat Received 26 November 2018; Revised 18 February 2019; Accepted 20 February 2019; Published 2 May 2019 Academic Editor: Shiwen Yang Copyright © 2019 Edith Annette Cabrera-Hernández et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Dynamic directional modulation (DDM) has already proven to be an efficient technique to achieve physical layer security in wireless communications. System architectures based on vector modulators provide a flexible framework to implement synthesis methods that allow us to obtain increased security and/or independent multichannel transmissions. However, the implementation of DDM with vector modulators requires an accurate calibration (amplitude and phase) of every component in the RF path. In this contribution, we study the sensitivity of the response of a DDM system based on commercial vector modulators showing how to correct the nonideal behavior of all the components thanks to the flexibility provided by the vector modulator. 1. Introduction know the direction of the legitimate receiver. A DM transmit- ter projects digitally modulated information signals into a Over the past few decades, wireless communication systems prespecified secure spatial direction in free space, while have expanded at an exponential rate, fueled by consumer simultaneously the constellation formats of the same sig- demand and aided by increasing levels of technological nals are distorted in all other directions [3]. In the case advancement in terms of scalability, flexibility, and low that the distortion is dynamically updated (usually at the reduced cost. However, wireless systems are more susceptible symbol rate) the DM is referred as dynamic (DDM) and to interception than their wired counterparts due, partially, provides better performance in terms of security than to the absence of physical boundaries in the transmission static DM (SDM) [4]. medium. An attractive solution to improve the security of The hardware architectures of a DDM system with wireless transmission is to apply encryption at the physical phased arrays mainly differ in the array feeding network layer level to limit the amount of information that an illegit- implementation and we can distinguish: Fourier beam- imate receiver can extract from the transmission medium [1]. forming lens [5], radio frequency (RF) switch arrays [6–8], The use of phased arrays to project nulls in the directions reconfigurable attenuators and/or phase shifters [9–11], and of illegitimate receivers [2] can be considered an antecedent vector modulators [3, 12, 13]. In this work, we will consider to current physical layer security techniques. This method the option of vector modulators (Figure 1) since it is very is simple and efficient but is limited by the need to know in flexible and allows us to easily implement DM synthesis advance the locations of illegitimate eavesdroppers that will methods [3] to obtain increased security and/or independent tend to obfuscate their position. multichannel transmissions [12, 13]. Phased arrays can be also used to generate directional The performance of a DDM system is usually assessed in modulation (DM) [3–13]. This is an attractive option to terms of the bit error rate (BER) increase of the received sig- achieve physical layer security since it is only necessary to nal in other directions than the prespecified secure direction 2 International Journal of Antennas and Propagation Vector 𝜆/2 dipole array modulators VV_1 Va_m1 1:5 power 𝜆/2 divider VV_2 Va_m2 𝜆/2 + VV_3 Va_m3 𝜆/2 − Vinput VV_4 Va_m4 𝜆/2 𝜃 VV_5 Va_m5 Control/modulation Figure 1: Transmission system demonstrator block diagram. V−a_1n V−a_2n V−a_3n V±a_nn V−a_Nn Z0 Z0 Z0 Z0 Z0 + V0 − Figure 2: Geometry for obtaining the active element pattern of the element n of the array of N antennas. [3–10] without considering how sensitive this BER is to small Z11_n Z22_n variations in the response of the components used. However, Iv_n −Ia_mn the implementation of DDM with vector modulators + + requires an accurate calibration (amplitude and phase) of + Vv_n − Z21v_mn·Iv_n Va_mn every component in the RF path; otherwise, the transmitted − − constellations in the secure direction could be distorted as it was shown in a preliminary study in [14]. Figure 3: Equivalent circuit for Z parameters of the vector This contribution is aimed at studying the sensitivity of modulator (unilateral assumption). the response of a DDM system based on commercial vector modulators and showing how to correct the nonideal behav- ior of its components thanks to the flexibility provided by the vector modulator. The paper is organized as follows. Section array of 5 half wavelength long dipole antennas in a side by 2 describes the system architecture and some concepts side arrangement; the spacing between dipoles is λ/2 (λ is related to the generation of DDM. Section 3 derives the the free space wavelength). The operating frequency of the theoretical expressions for the S21 parameter of the vector RF source of the system is set arbitrarily to 2.45 GHz. A full modulators for transmitting DDM considering real RF com- model of the system has been created using the electromag- ponents. Section 4 evaluates the quality of the transmitted netic simulation software FEKO [15]. signal in the secure direction when commercial RF compo- The array radiation pattern used to transmit symbol m in nents are used and discusses the trade-off between power a given direction θ can be expressed as and security. Finally, the main conclusions of the work are summarized in Section 5. 5 Sm θ = 〠 Bmn · AEPn θ , 1 n=1 2. DDM System Description Figure 1 shows the scheme of the DDM transmission system where AEPn (θ) is the active element pattern of antenna n under consideration. It is composed of a 5-way power [16] and Bmn is the weight of AEPn (θ) when transmitting divider, followed by 5 vector modulators (VM) that feed an symbol m. By varying the control inputs of the vector International Journal of Antennas and Propagation 3 Vv_1 1 N 2 S21_m1 Va_m1 Vector_modulator_s21_m1 Dipole 1 Vv_2 Dipole 2 1 1 Va_m2 N 2 S21_m2 2 3 N Vector_modulator_s21_m2 4 5 Vv_3 Dipole 3 6 Power_divider 1 Va_m3 Vinput N S21_m3 2 Vv_4 Vector_modulator_s21_m3 Dipole 4 N 1 Va_m4 S21_m4 2 Vector_modulator_s21_m4 Dipole 5 Vv_5 1 Va_m5 N S21_m5 2 Vector_modulator_s21_m5 Figure 4: FEKO model of the transmission system demonstrator. modulators, the parameter S21 of each vector modulator can According to [16], AEPn θ can be obtained by feeding be adjusted to set the desired Bmn , thus allowing for tailored element n of the array with all the other array elements termi- radiation patterns. As such, equation (1) is familiar as a clas- nated in matched loads Z 0 , as shown in Figure 2. sic form describing the array radiation pattern. With this scheme, the matrix that contains the input The required weights for a DM system (Bmn _DM) can voltage of antenna p when antenna n is fed with a source of be obtained using the orthogonal vector approach 1 V can be written as described in [3]: first, we design the weights for a non- 1 DM (conventional) array (Bmn _nonDM), and next, we add Va pn = U + Sa , 2 2 orthogonal noise (W mn ) to the former weights (Bmn DM = Bmn nonDM + W mn ) in such a way as the constella- where [Sa ] is the S parameter matrix of the array and [U] is tion at the desired secure direction remains invariant. When the identity matrix of order N. W mn are dynamically updated (usually at the symbol rate), With the AEP of each antenna, we obtain the weights we are using DDM. Bmn _DM by applying the procedure described in the previ- The directional modulation power efficiency (PEDM) is ous section. Then, by using the superposition principle, defined as the ratio of the power used in the non-DM the matrix that contains the input voltage in antenna n array to the power used in the DM array [3]. It describes when transmitting symbol m is the extra power (W mn ) injected into the array to obtain the directional modulation. In Section 4, it will be shown 1 that decreasing PEDM increases the distortion in nondesired Va mn = U + Sa · Bmn DM , 3 2 directions, thus improving the privacy of the communica- tion. Therefore, there exists a compromise between security and the matrix that contains the input current in antenna and PEDM. n when transmitting symbol m becomes 3. Generation of the Radiation Patterns with the 1 Ia mn = U − Sa · Bmn DM 4 Vector Modulators 2Z 0 This section is devoted to derive the expressions for the S21 By combining (3) and (4), we can easily obtain the parameters of the vector modulators that will allow us to input impedance (Z L mn ) and the corresponding reflection generate DDM with the scheme of Figure 1. coefficient (ΓL mn ). It must be noted that, even when each 4 International Journal of Antennas and Propagation 0.8 0.7 X: 70 X: 110 0.6 Y: 0.5167 Y: 0.5167 Magnitude (V) 0.5 0.4 X: 60 X: 120 Y: 0.4176 Y: 0.4176 0.3 0.2 40 50 60 70 80 90 100 110 120 130 140 𝜃 AEP1 AEP4 AEP2 AEP5 AEP3 (a) 150 100 50 X: 70 X: 110 Y: 15.02 Y: 15.02 Phase (deg) 0 −50 X: 120 X: 60 Y: −100 Y:−100 −100 −150 40 50 60 70 80 90 100 110 120 130 140 𝜃 AEP1 AEP4 AEP2 AEP5 AEP3 (b) Figure 5: Active element pattern (H-plane) for an array of 5 λ/2 dipole antennas spaced λ/2. (a) Magnitude. (b) Phase. antenna is designed to be well matched (with all the other Hence, it can be easily derived that elements terminated in matched loads), ΓL mn changes with the element and transmitted symbol due to mutual Bmn DM 2 = 6 coupling between the antennas. V a mn 1 + ΓL mn It is also noted that for each element and symbol we also have Our goal now becomes setting the S21 parameter for each vector modulator n and symbol m (S21 mn ) that gen- erates the desired V a mn and I a mn at the antenna input. Bmn DM − Va mn = Z0Ia mn 5 We are going to operate under the (realistic) assumptions International Journal of Antennas and Propagation 5 PEDM = 12% 3 2.5 2 Magnitude (V) 1.5 1 0.5 0 0 20 40 60 80 100 120 140 160 180 𝜃 (a) PEDM = 50% 3 2.5 2 Magnitude (V) 1.5 1 0.5 0 0 20 40 60 80 100 120 140 160 180 𝜃 (b) Figure 6: Magnitude of radiation patterns that transmit the same symbol at 60° for two different values of PEDM (ideal power divider and vector modulator). that the vector modulator is a unilateral network (S12 = 0), S21 mn and S11 and S22 do no not change with the symbol to Z 21 mn = 2Z 0 8 1 − S11 n 1 − S22 n transmit. The equivalent circuit for Z parameters of the vector From Figure 3, it is straight forward that modulator is depicted in Figure 3. The Z parameters are related to the S parameters through the following equations that assume S12 = 0 [17]: Va mn − Z 21 mn · I v n = −Z 22 n · I a mn 9 1 + Sii n Z ii n = Z 0 , i = 1, 2, 7 by substituting (7) and (8) into (9), and after a few mathe- 1 − Sii n matical manipulations, we obtain 6 International Journal of Antennas and Propagation PEDM = 50% 2 1.8 1.6 Magnitude (V) 1.4 1.2 1 0.8 0.6 0.4 0.2 0 40 45 50 55 60 65 70 75 80 𝜃 (a) PEDM = 50% 2 1.8 1.6 1.4 Magnitude (V) 1.2 1 0.8 0.6 0.4 0.2 0 40 45 50 55 60 65 70 75 80 𝜃 (b) Figure 7: Magnitude of radiation patterns that transmit a 16-QAM constellation at 60° (PEDM = 50%) using (12) to compute S21 mn in the vector modulators. (a) Ideal components. (b) Real components. 1 − S22 n ΓL mn V a mn Bmn DM S21 mn = 1 + S11 n , 10 S21 mn = 12 1 + ΓL mn Vv n 2V v n where V v n is the input voltage for each vector modulator (which does not depend on the transmitted symbol). Finally, 4. Performance Assessment of a DDM recalling (6), we obtain System with Real Components 1 − S22 n ΓL mn Bmn DM Figure 4 shows the FEKO model of the DDM system based S21 mn = 1 + S11 n 11 2 Vv n on vector modulators of Figure 1. The dipole array is evalu- ated through full electromagnetic simulation to include And for perfectly matched vector modulators (Sii n = 0, mutual coupling effects between antennas. Each component i = 1, 2), (11) becomes of the array feeding network is characterized by its respective International Journal of Antennas and Propagation 7 PEDM = 50%, 𝜃 = 60°, SNR = 25.7 dB 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1 −0.5 0 0.5 1 (a) PEDM = 12%, 𝜃 = 60°, SNR = 17.2 dB 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1 −0.5 0 0.5 1 (b) Figure 8: DDM 16-QAM modulation transmitted at the secure direction 60° using real components and (12) to compute S21 mn in the vector modulators. (a) PEDM = 50%. (b) PEDM = 12%. S parameters. Then, once we compute S21 mn , using either antenna array) since their effects can be easily embedded (11) or (12), we can obtain the radiation patterns for inside the components. transmitting every symbol with very low computational In a previous step, the AEP of each dipole has been requirements. In the first approach, we are not going to con- evaluated (Figure 5) and used to obtain the array weights sider the transmission lines that connect the main compo- Bmn that will generate the desired radiation patterns for nents of our system (power divider, vector modulators, and each symbol m. 8 International Journal of Antennas and Propagation PEDM = 50%, 𝜃 = 60º, SNR = 310.3 dB 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1 −0.5 0 0.5 1 (a) PEDM = 12%, 𝜃 = 60º, SNR = 305.8 dB 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1 −0.5 0 0.5 1 (b) Figure 9: DDM 16-QAM modulation transmitted at the secure direction 60° using real components and (11) to compute S21 mn in the vector modulators. (a) PEDM = 50%. (b) PEDM = 12%. As a starting point, we use (12) to evaluate S21 mn . (2) Ideal vector modulators: both ports perfectly We assume matched and S12 = 0 (1) Ideal power divider: all ports perfectly matched, Figure 6 shows simulated radiation patterns that can be balanced power division (amplitude and phase), and used to transmit the same symbol in the secure direction of isolated output ports 60° for two different values of PEDM. In the case of ideal International Journal of Antennas and Propagation 9 PEDM = 50%, 𝜃 = 60°, SNR = 29.3 dB 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4 –0.6 –0.8 –1 –1 –0.5 0 0.5 1 (a) PEDM = 12%, 𝜃 = 60°, SNR = 20.5 dB 1 0.8 0.6 0.4 0.2 0 –0.2 –0.4 – 0.6 –0.8 –1 –1 –0.5 0 0.5 1 (b) Figure 10: DDM 16-QAM modulation transmitted at the secure direction 60° using real components, coaxial cables and (12) to compute S21 mn in the vector modulators; AEP measurement did not consider coaxial cables. (a) PEDM = 50%. (b) PEDM = 12%. components, any constellation can be (theoretically) pro- Next, we introduce the characteristics of real components duced in a desired observation angle without issue. into the system. The power divider outputs will be assigned a In Figure 6, it is also important to highlight the trade-off nominal amplitude balance of ±1.2 dB [18] and a phase var- between transmitted power and security: as PEDM decreases iation of ±3°. We also assume the vector modulators of [19] (W mn power increases), we have a narrower secure beam which show a measured S12 parameter always below -70 dB width around 60° and the distortion of symbols in undesired and input and output return losses around 9 and 10 dB, directions becomes larger. respectively. 10 International Journal of Antennas and Propagation PEDM = 50%, 𝜃 = 60°, SNR = 34.1 dB 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1 −0.5 0 0.5 1 (a) PEDM = 12%, 𝜃 = 60°, SNR = 26.1 dB 1 0.8 0.6 0.4 0.2 0 −0.2 −0.4 −0.6 −0.8 −1 −1 −0.5 0 0.5 1 (b) Figure 11: DDM 16-QAM modulation transmitted at the secure direction 60° using real components, coaxial cables and (11) to compute S21 mn in the vector modulators; AEP measurement did not consider coaxial cables. (a) PEDM = 50%. (b) PEDM = 12%. At first sight, one could think that, for these vector mod- that the radiation patterns not only have less amplitude but ulators, the unilateral assumption is reasonably well satisfied also are slightly distorted. and the input and output are fairly well matched, so the use As a result, the constellation generated at the desired of (12) to compute S21 mn should be enough to generate sim- secure direction of 60° exhibits additional noise on the trans- ilar radiation patterns to those that would be obtained with mitted symbol (Figure 8). This behavior is due to the finite ideal components (Figure 7(a)). However, Figure 7(b) shows output return loss of the vector modulators (S22 n ) and the International Journal of Antennas and Propagation 11 0.8 0.7 Magnitude (V) 0.6 X: 70 X: 110 Y: 0.4629 Y: 0.4593 0.5 0.4 X: 60 Y: 0.3705 X: 120 0.3 Y: 0.3716 0.2 40 50 60 70 80 90 100 110 120 130 140 𝜃 AEP1 AEP4 AEP2 AEP5 AEP3 (a) 150 100 X: 70 X: 110 Y: 65.21 Y: 69.87 50 Phase (deg) 0 −50 X: 60 X: 120 Y: −63.99 Y: −64.21 −100 −150 40 50 60 70 80 90 100 110 120 130 140 𝜃 AEP1 AEP4 AEP2 AEP5 AEP3 (b) Figure 12: Active element pattern (H-plane) for an array of 5 λ/2 dipole antennas spaced λ/2 with coaxial cables. (a) Magnitude. (b) Phase. variation of the input reflection coefficient with the antenna Another important result that can be derived from and symbol to transmit (ΓL mn ). In Figure 8, we have associ- Figure 8 is that SNR decreases significantly with PEDM. A ated a signal-to-noise ratio (SNR) to the transmitted symbols low scenario PEDM would be required in the case of a highly that represents the threshold of quality that can be achieved secure transmission or in the case of simultaneous multi- in the transmission without additional calibration. Although channel transmissions to different observation angles as in SNR is still quite high for PEDM = 50%, it must be noted that [13]. Therefore, these applications demand an accurate mea- the effects of real coaxial cables have not been considered surement of the components of the system and the use of (11) here, so the case under consideration is quite favorable. to obtain S21 mn . Indeed, Figure 9 shows that, in this case, we 12 International Journal of Antennas and Propagation can transmit the desired constellations without noise regard- Data Availability less of the value of PEDM used. Finally, we add 5 commercial coaxial cables [20] in the The FEKO model and data used to support the findings of system to connect antennas and vector modulators, which this study are available from the corresponding author present attenuation of 1 1 dB ± 0 1 dB and phase variation upon request. of ±3°, and input and output return losses (Sii ) ranged from 20 to 40 dB. Conflicts of Interest Figure 10 shows the transmitted constellation for the secure direction of 60° when we use (12) to compute S21 mn , The authors declare there is no conflict of interest regarding real components and coaxial cables which were not included the publication of this article. in the AEP measurement. It is noticed that an improvement of over 3 dB in SNR with respect to Figure 8 is obtained. This Acknowledgments result may seem counterintuitive since the addition of coaxial cables increases amplitude and phase variations. However, it This work was supported by the Universitat Autònoma de makes sense if we consider that ΓL mn for the array with coax- Barcelona, the Spanish Ministry of Economy and Competi- ial cables is not as sensitive to the symbol to be transmitted tiveness, and FEDER funds through Project TEC2015- due to the additional losses. Conversely, as observed in 69229-R. Figure 10, we also see a reduction of 6 dB in the constellation amplitude which is significantly larger than the 1.1 dB intro- References duced by coaxial cables. Keeping the same scenario and using (11) instead of (12) [1] A. Mukherjee, S. A. A. Fakoorian, J. Huang, and A. L. to compute S21 mn , we obtain some improvements Swindlehurst, “Principles of physical layer security in mul- (Figure 11). Now, the constellation amplitude has only been tiuser wireless networks: a survey,” IEEE Communications Surveys & Tutorials, vol. 16, no. 3, pp. 1550–1573, 2014. reduced by 1 dB, as expected. Nevertheless, although SNR has improved 5-6 dB with respect to Figure 10, we still have [2] S. A. Schelkunoff, “A mathematical theory of linear arrays,” Bell System Technical Journal, vol. 22, no. 1, pp. 80–107, 1943. noisy symbols. The only way to obtain the results of Figure 9 is by using the AEP of each element of the array with [3] Y. Ding and V. F. Fusco, “A vector approach for the analysis and synthesis of directional modulation transmitters,” IEEE coaxial cables (Figure 12) in the computations. Notice in Transactions on Antennas and Propagation, vol. 62, no. 1, Figure 12 the additional attenuation of 1 dB and the slightly pp. 361–370, 2014. loss of symmetry with respect to Figure 5. [4] Y. Ding and V. F. Fusco, “Establishing metrics for assessing the performance of directional modulation systems,” IEEE 5. Conclusions Transactions on Antennas and Propagation, vol. 62, no. 5, pp. 2745–2755, 2014. In this work, a FEKO model of a DDM system based on a [5] Y. Ding, Y. Zhang, and V. Fusco, “Fourier Rotman lens power divider and vector modulators has been used to dem- enabled directional modulation transmitter,” International onstrate that the system performance relies heavily on the Journal of Antennas and Propagation, vol. 2015, Article ID precision with which the S21 parameters of the vector modu- 285986, 13 pages, 2015. lators are set. [6] N. Valliappan, A. Lozano, and R. W. Heath, “Antenna subset We have derived an expression for the S21 parameters modulation for secure millimeter-wave wireless communica- that takes into account the weight to be set for each antenna tion,” IEEE Transactions on Communications, vol. 61, no. 8, and symbol (that depends on the AEP of each antenna) and pp. 3231–3245, 2013. nonideal effects of the components such as unbalanced RF [7] Q. Zhu, S. Yang, R. Yao, and Z. Nie, “Directional modulation paths (amplitude and phase) and finite return losses. based on 4-D antenna arrays,” IEEE Transactions on Antennas Simulations show that, when nonideal effects are not and Propagation, vol. 62, no. 2, pp. 621–628, 2014. considered in the computation of S21 , different sets of [8] C. Sun, S. Yang, Y. Chen, J. Guo, S. Qu, and J. Hu, “4-D retro- weights, that should generate the same symbol in a desired directive antenna arrays for secure communication based on observation angle, produce slightly different symbols that improved directional modulation,” IEEE Transactions on Antennas and Propagation, vol. 66, no. 11, pp. 5926–5933, have the appearance of noise. For that reason, we have asso- 2018. ciated a SNR to the transmitted symbols. This SNR decreases [9] M. P. Daly and J. T. Bernhard, “Directional modulation tech- when we decrease PEDM to improve the security of the trans- nique for phased arrays,” IEEE Transactions on Antennas mission in a single direction or to transmit, simultaneously, and Propagation, vol. 57, no. 9, pp. 2633–2640, 2009. to different observation angles. Therefore, for these applica- [10] M. P. Daly, E. L. Daly, and J. T. Bernhard, “Demonstration of tions, the S parameters of the components should be accu- directional modulation using a phased array,” IEEE Transac- rately measured and considered in the computation of S21 . tions on Antennas and Propagation, vol. 58, no. 5, pp. 1545– Also, we have shown that the AEP of every antenna needs 1550, 2010. to be accurately evaluated together with the coaxial cables [11] H. Shi and A. Tennant, “Simultaneous multichannel spatially that feed the array. Small variations in amplitude and phase directive data transmission using direct antenna modulation,” in the AEPs used to obtain the weights may result in a signif- IEEE Transactions on Antennas and Propagation, vol. 62, icant reduction of the amplitude of the transmitted symbols. no. 1, pp. 403–410, 2014. International Journal of Antennas and Propagation 13 [12] Y. Ding and V. Fusco, “A review of directional modulation technology,” International Journal of Microwave and Wireless Technologies, vol. 8, no. 7, pp. 981–993, 2016. [13] S. Mufti, A. Tennant, and J. Parrón, “Dual channel broadcast using phase-only directional modulation system,” in 2018 IEEE International Symposium on Antennas and Propagation (APS-URSI), pp. 2219-2220, Boston, MA, USA, 2018. [14] E. A. Cabrera-Hernández, J. Parrón, and A. Tennant, “Influ- ence of non-ideal components in a dynamic directional mod- ulation system,” in 2018 IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (APWC), pp. 882–885, Cartagena de Indias, Colombia, 2018. [15] FEKO EM, “Simulation software,” https://altairhyperworks .com/product/FEKO. [16] D. M. Pozar, “The active element pattern,” IEEE Transactions on Antennas and Propagation, vol. 42, no. 8, pp. 1176–1178, 1994. [17] D. M. Pozar, Microwave Engineering, John Wiley & Sons, 4th edition, 2011. [18] “5-way power divider and combiner (PS5 series),” February 2019, https://mcli.com/products/power-dividers-combiners/ stripline/5-way-power-divider-and-combiner-ps5-series. [19] “HMC631 datasheet and product info analog devices,” Febru- ary 2019, https://www.analog.com/en/products/rf-microwave/ phase-shifters-vector-modulators/vector-modulators/hmc631 .html#product-overview. [20] “Coaxial cable RG174/U,” February 2019, https://www. ecmstockroom.com/writable/items/pdf_files/rg174.pdf. 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