Beam Broadening for Phased Antenna Arrays using Multi-beam Subarrays

Open Journal of Antennas and Propagation, 2014, 2, 21-28 Published Online June 2014 in SciRes. /journal/ojapr /10.4236/ojapr.2014.22003Improvement in Reflectarray Antenna Bandwidth with Changing the Geometrical ShapeAlireza Bayat, Vahid Soufi NiyarakiDepartment of Communication, Imam Khomeini International University, Qazvin, Iran Email: **************.ir , ********************** Received 13 April 2014; revised 21 May 2014; accepted 13 June 2014Copyright © 2014 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/Abstract The method of this paper is based on change in the geometrical shape of the reflectarray plane which is similar to a concave shape and with this changing, it is tried to make the incident waves orthogonal as much as possible in order to remove the phase error caused by incident wave varia- tion. The other benefit of this work is omitting frequency change error caused by path difference between reflectarray antenna bandwidth. Two types of reflectarray antennas operating at X-band frequency with a linear polarization are considered in this design: concave and flat reflectarray antennas with the diameter of 135 mm. elements which are used in this paper are variable-size patches. The proposed reflectarray antenna (concave) approximately has 25% 3-dB bandwidth which shows an increment in bandwidth about 18% compared to flat reflectarray antenna. KeywordsIncreasing of Reflectarray Antenna Bandwidth, Non-Flat Reflectarray Antenna1. IntroductionReflectarray antennas are the new generation of traditional parabolic reflectors. They are combination of both printed phased arrays and parabolic reflectors [1]. They are light and easy to fabricate and occupy less space than parabolic reflectors. Reflectarrays have the advantage of high gain and low cost; therefore they have been used in development activities [1]-[3]. A reflectarray consists of array of elements to create a focused beam in a desired direction. Usually, there are three different ways to determine printed reflectarrays. The first one is the usage of identical microstrip patches connected to variable-length delay lines [4]. The second is to use variable-size printed elements [5]. The third way is utilization of elements with different angular rotations and is only usable for circular polarization antennas [6] [7].Design and analysis of reflectarray antennas is based on reflection phase versus elements size. In this method it is supposed that the phase response is independent of incident field, this technique is valid for those elements which are located in the center of the reflectarray plane and with a center-fed situation. The technique of ortho-gonal incident field can have suitable estimation for reflectarray antennas with center-fed when an enormous amount of reflection fields reflected from the center region of the antenna. For variable size patches with 40˚ in-cident wave, phase will change about 25˚ beside the orthogonal incident wave. When the incident wave is about 60˚, this variation in phase reaches to 50˚[8]. Therefore, this technique is not suitable for the elements near the edges of the reflectarray and a new technique is needed. The technique which is used in this paper is based on making the ground plane in form of a concave in order to cause the incident waves become orthogonal to the patches and also reducing the frequency change error for increasing the bandwidth.2. Design of the Non-Flat Reflectarray Antenna (Concave)Beside the reflection waves from the reflectarray patches, specular reflection is also considered. Two specular reflections occur from reflectarray plane: reflection from the ground plane and reflection from the resonating patches. Because of the reflection from the resonating patches are negligible, only the reflection from the ground plane of the reflectarray is considered. Specular reflections from the ground plane in the regions near to the cen-ter of the reflectarray are approximately in the direction of reradiated waves but as the becomes bigger, specular reflections more apart from the reradiation waves and it causes increase in side lobes in radiation pattern of the antenna (Figure 1).Figure 2 indicates the new structure of the ground plane which has a concave shape.For the first part of design a suitable degree (α) is required in which the maximum of reflection waves are si-tuated in the main beam direction. In this design, the reflectarray shape is considered as a square in which each side is 135 mm. as can be seen in Figure 3, the ground plane of the reflectarray is divided in two parts: center part and other corner parts in which the center part is a square which has L side and the corner parts with trape-zoid shape which are connected to the four sides of center part.Figure 1. Flat reflectarray antenna.Figure 2. Side view of proposed ground plane.Figure 3. Front view of proposed ground plane.The small side and altitude of the trapezoid are equaled to L. Also trapezoidal planes are located angular with the Z axis in which the angle between the normal (orthogonal) vector of trapezoidal planes and Z axis is α.With considering the ground plane size (135 mm) and with considering f/D to 1, we locate the phase center of the horn antenna in the 135 mm distance from the center of concave plane and examine the directivity according to the variation in α degree. With considering Figure 4, with changing α from 0˚ to 20˚, it can be seen that the maximum directivity is in α = 10˚. Here, the maximum directivity indicates the maximum reflection waves in the main beam direction.2.1. Reflectarray Elements DesignThis part is based on situating dielectric layer on the ground plane and also designing patches on the dielectric. Because the ground plane shape of this antenna is not like the conventional reflectarrays, a suitable solution is needed. For calculation of phase difference for every patches in order to control main beam in (),b b θφ direc-tion, equation ()()0,cos sin sin R i i i i b i b b x y k d x y φφφθ =−− is useable but this equation is valid only for aflat reflectarray planes.The main issue in this design is making all elements of the proposed reflectarray inphase. In flat reflectarray with using previous equation, we can make the elements of the center plane and trapezoidal planes inphase but the major problem is making these elements inphase together. This issue is illustrated in Figure 5.2.2. Novel Formula for Calculating Elements Phase of a Non-Flat ReflectarrayIn this section, a novel formula for making all elements of a non-flat reflectarray plane is presented. First of all, an important point exists in designing patches which is when a constant value ()02π,0,1,2,n n φ==±±⋅⋅⋅ adds to the computing phase, inphase condition of the patches will keep [9]-[11]. Figure 6 verifies this point. In Figure 6, 00,,,b D x k θ are antenna diameter, angle between antenna main beam and Z axis, constant value as shown in Figure 6, propagation constant, respectively.Based on these values, it can be concluded that ()000sin b k D x φθ=+ is constant because all parameters in this formula have a constant value and also these parameters should be choose in order to make 0φ equals2πn in which n is integer as a result ()00sin 2πb k D x n θ+=. As mentioned in previous sentence, with adding this constant (0φ) to()()0,cos sin sin R i i i i b i b b x y k d x y φφφθ =−− , inphase situation of element will keep. If we assume 0b φ=, equations of this examination are presented below:()()000,sin ,2π,0,1,2,R i i i i b x y k d x n nφθφφ =−×+==±±⋅⋅⋅ (1) ()()()()000,sin sin R i i i i b b x y k d x k D x φθθ =−×++ (2)Figure 4. Directivity of the proposed ground plane.Figure 5. The antenna which is designed by conventional formula.Figure 6. The reflectarray coordination and virtual plane.()()()()00,sin sin sin R i i i i b b b x y k d x x D φθθθ =−++ (3)()()()()000,sin R i i i i b x y k d k D x x φθ=++− (4)By substituting ()0sin i b D x x θ +− with i d ′, the Equation (4) will become:()()0,R i i i i x y k d d φ′=+ (5)As can be seen in Figure 6, i d is the elements distance from the horn phase center and i d ′ is the elements distance from the virtual plane in which the orthogonal vector of the virtual plane ids located in the main beam direction of the antenna. It should be noticed that the virtual plane should be parallel with the reradiation wave plane from the patches and also one side of the virtual plane should have connection with end of reflectarray plane (connection point in Figure 6). 2.3. Computation of Reflectarray Element PhaseIn this section, we obtain (calculate) phase of elements which are located on the non-flat reflectarray by using the equation ()()0,R i i i i x y k d d φ′=+. In order to use this technique firstly we should consider a suitable virtual plane. Considering that the maximum of specular reflections in the proposed antenna (Figure 4) is in the Z axis direction, the antenna main beam (caused by resonating patches) is also will design in that direction. As the main beam direction of the antenna of Figure 4 is in the Z axis direction, therefore, orthogonal vector of virtual plane should be paralleled with the Z axis.Concerning Figure 7, we consider the virtual plane in a special height from the ground plane and also in front of it. In order to obtain the phase of each element, it is required to calculate i d , i d ′ parameter for each ele-ment.In this antenna, the variable sized patches are used. For computing elements phase, firstly size of each unit cell should be calculated. Here, size of each element (unit cell) is 2λ and center frequency of this design is 10 GHz as a result of which each side of every unit cell is 15 mm. Dielectric constant which is used in this antenna equals to 2.2 ( 2.2r ε=) and also dielectric height is 1 mm (h = 1 mm). Phase-element of microstrip patches with L side is shown in Figure 8.2.4. Radiation Pattern and Bandwidth of Non-Flat ReflectarrayA horn antenna is used as feed in which the phase center distance from the reflectarray plane is 135 mm. Radia-tion pattern of the antenna are shown in Figure 9 and Figure 10.Figure 7. Reradiation waves for designed reflectarray with pro-posed formula.Figure 8. Reflectarray element phase versus size of the patch.Figure 9. Radiation pattern of non-flat reflectarray antenna.Figure 10. Two dimensional radiation pattern of non-flat reflectarray antenna in E-plane.As can be seen in Figure 10, directivity of antenna in 10 GHz is about 19.2 dB. Figure 11 indicates the an-tenna directivity in the frequency range from 9 GHz to 14 GHz. −3 dB bandwidth obtained from this figure is about 25%.3. Design of a Flat Reflectarray Antenna with the Same Scale of Non-Flat Proposed Reflectarray in Order to Compare Their BandwidthIn this design, ground plane has some condition of ground plane of Figure 2, with the difference in α which here equals to zero. With this value the antenna has the conventional shape as other reflectarrays. In other words, ground plane is a square with 135 mm side. Dielectric constant is same as non-flat reflectarray and also same thickness ( 2.2,1mm r h ε==).Feed for this antenna is same as non-flat reflectarray which is a horn and have phase center distance from the ground plane which is radiation pattern of this antenna in center frequency of 10 GHz is shown in Figure 12. As can be seen in Figure 13, directivity of antenna in 10 GHz is about 21.6 dB. From Figure 10 and Figure 13, it is considerable that the side lobe level of the proposed ground plane is lower than flat one which shows an im-provement in this parameter.Figure 14 shows directivity of this antenna for frequency range from 9 GHz to 11 GHz. −3 dB bandwidth in center frequency is about 6.3%. As can be understood from the results, the non-flat reflectarray has increment in bandwidth about 18%.Another important parameter in antenna is cross-polarization which should be decreased in design. Radiation pattern with cross-polarization for non-flat and flat reflectarray antenna are shown in Figure 15. By considering the Figure 15, an improvement in cross-polarization for non-flat reflectarray exists.4. ConclusionTwo major results obtained in this part, first of all, Equation (5) can be used for calculation of elements phase ofFigure 11. Frequency response of non-flat reflectarray antenna with the diameter of 135 mm.Figure 12. Radiation pattern of flat reflectarray antenna.Figure 13. Two dimensional radiation pattern of flat reflectarray antenna in E-plane.Figure 14. Frequency response of flat reflectarray antenna with the diameter of 135 mm.a non-flat reflectarray. Another important result is improvement in incident angle of horn antenna to elements which are located in the edges of a reflectarray by changing the geometrical of the antenna and also an improve- ment in bandwidth is attainable.Figure 15. Cross polarization for flat and non-flat reflectarray antennas in center frequency of 10 GH. Obtained bandwidth for a non-flat reflectarray (proposed antenna) with 135 mm diameter is about 25% which has improvement about 18% compared to flat reflectarray with same size.References[1]Huang, J. and Encinar, J.A. (2008) Reflectarray Antennas, IEEE/John Wiley & Sons, New York, 2008.[2]Legay, H., Bresciani, D., Girard, E., Chiniard, R., Labiole, E., Vendier, O. and Caille, G. (2009) Recent Developmentson Reflectarray Antennas at Thales Alenia Space. Proceedings of EuCAP, Berlin.[3]Roederer (2009) Reflectarray Antennas. Proceedings of EuCAP, Berlin.[4]Huang, J. (1991) Microstrip Reflectarray. IEEE AP-S/URSI Symposium, London, June 1991, 612-615.[5]Pozar, D.M. and Metzler, T.A. (1993) Analysis of a Reflectarray Antenna Using Microstrip Patches of Variable Size.Electronics Letters, 657-658. /10.1049/el:19930440[6]Huang, J. and Pogorzelski, R.J. (1998) A Ka-Band Microstrip Reflectarray with Elements Having Variable RotationAngles. IEEE Transactions on Antennas Propagation, 46, 650-656. /10.1109/8.668907[7]Sarah, A. and Hany, H. (2013) A Novel Microstrip Rotating Cell for CP-Reflectarray Applications. 2013 IEEE Radioand Wireless Symposium (RWS),20-23 January 2013, 121-123.[8]Roederer, A. (2002) US6411255 “Reflector Antenna Comprising a Plurality of Panels”.[9]Pham, K.T., Nguyen, B.D., Van-Su Tran, Bui, L.-P.P., Linh, M., Yonemoto, N., Kohmura, A. and Futatsumori, S. (2013)Ku Band Aperture-Coupled C-Patch Reflectarray Element Using Phase Shifting Line Technique. 2013 International Conference on Advanced Technologies for Communications (ATC),465-468.[10]Li, L., Chen, Q., Yuan, Q.W., Sawaya, K., Maruyama, T., Furuno, T. and Uebayashi, S. (2011) Frequency SelectiveReflectarray Using Crossed-Dipole Elements with Square Loops for Wireless Communication Applications. IEEE Transactions on Antennas and Propagation,59, 89-99.[11]Targonski, S.D. and Pozar, D.M. (1994) Analysis and Design of a Microstrip Reflectarray Using Patches of VariableSize. Antennas and Propagation Society International Symposium, AP-S. Digest, June 1994, 1820-1823.。

An optically controlled phased array antenna based on single sideband polarizationmodulationYamei Zhang, Huan Wu, Dan Zhu, and Shilong Pan* Key Laboratory of Radar Imaging and Microwave Photonics (Nanjing Univ. Aeronaut. Astronaut.), Ministry of Education, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China*pans@Abstract: A novel optically controlled phased array antenna consisting asimple optical beamforming network and an N element linear patch antennaarray is proposed and demonstrated. The optical beamforming network isrealized by N independent phase shifters using a shared optical singlesideband (OSSB) polarization modulator together with N polarizationcontrollers (PCs), N polarization beam splitters (PBSs) andN photodetectors (PDs). An experiment is carried out. A 4-element linearpatch antenna array operating at 14 GHz and a 1 × 4 optical beamformingnetwork (OBFN) is employed to realize the phased array antenna.The radiation patterns of the phased array antenna at −30°, 0° and 30°are achieved.©2014 Optical Society of AmericaOCIS codes: (050.5080) Phase shift; (280.5110) Phased-array radar; (060.5625) Radiofrequency photonics.References and links1. R. Tang and R. W. Burns, “Array technology,” Proc. IEEE 80(1), 173–182 (1992).2. N. A. Riza, Selected Papers on Photonic Control Systems for Phased Array Antennas (SPIE, 1997).3. J. P. Yao, “Microwave photonics,” J. Lightwave Technol. 27(3), 314–335 (2009).4. D. Dolfi, F. Michel-Gabriel, S. Bann, and J. P. Huignard, “Two-dimensional optical architecture for time-delaybeam forming in a phased-array antenna,” Opt. Lett. 16(4), 255–257 (1991).5. N. A. Riza, “Liquid crystal-based optical control of phased array antennas,” J. Lightwave Technol. 10(12), 1974–1984 (1992).6. N. A. Riza, “Acousto-optic liquid-crystal analog beam former for phased-array antennas,” Appl. Opt. 33(17),3712–3724 (1994).7. W. Ng, A. A. Walston, G. L. Tangonan, J. J. Lee, I. L. Ncwberg, and N. Bernstein, “The first demonstration ofan optically steered microwave phased array antenna using true-time-delay,” J. Lightwave Technol. 9(9), 1124–1131 (1991).8. A. Meijerink, C. G. H. Roeloffzen, R. Meijerink, L. M. Zhuang, D. A. I. Marpaung, M. J. Bentum, M. Burla, J.Verpoorte, P. Jorna, A. Hulzinga, and V. Etten, “Novel ring resonator-based integrated photonic beamfomer for broadband phased array receive antennas—part I: design and performance analysis,” J. Lightwave Technol.28(1), 3–18 (2010).9. J. L. Corral, J. Mart, S. Regidor, J. M. Foster, R. Laming, and M. J. Cole, “Continuously variable true time-delayoptical feeder for phased-array antenna employing chirped fiber gratings,” IEEE Trans. Microwave Theory Technol. 45(8), 1531–1536 (1997).10. N. A. Riza, “Analog vector modulation-based widely tunable frequency photonic beamformer for phased arrayantennas,” IEEE Trans. Microwave Theory Technol. 45(8), 1508–1512 (1997).11. L. A. Bui, A. Mitchell, K. Ghorbani, T. Chio, S. Mansoori, and E. R. Lopez, “Wide-band photonically phasedarray antenna using vector sum phase shifting approach,” IEEE Trans. Antennas Propag. 53(11), 3589–3596 (2005).12. N. A. Riza, S. A. Khan, and M. A. Arain, “Flexible beamforming for optically controlled phased array antennas,”Opt. Commun. 227(4-6), 301–310 (2003).13. X. K. Yi, T. X. H. Huang, and R. A. Minasian, “Photonic beamforming based on programmable phase shifterswith amplitude and phase control,” IEEE Photonics Technol. Lett. 23(18), 1286–1288 (2011).14. S. L. Pan and Y. M. Zhang, “Tunable and wideband microwave photonic phase shifter based on a single-sideband polarization modulator and a polarizer,” Opt. Lett. 37(21), 4483–4485 (2012).#203399 - $15.00 USD Received 19 Dec 2013; revised 31 Jan 2014; accepted 1 Feb 2014; published 10 Feb 2014 (C) 2014 OSA24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.003761 | OPTICS EXPRESS 376115. E. Carpentieri, U. F. D’Elia, E. De Stefano, L. Di Guida, and R. Vitiello, “Millimeter-wave phased-arrayantennas,” in IEEE Radar Conference (RADAR'08) (2008), pp. 1–5.16. Y. M. Zhang and S. L. Pan, “Generation of phase-coded microwave signals using a polarization-modulator-basedphotonic microwave phase shifter,” Opt. Lett. 38(5), 766–768 (2013).1. IntroductionPhased array antenna plays an important role in multifunctional radars and high-throughput wireless communications [1]. In the phased array antenna, beamforming network is one of the key components. Thanks to the inherent advantages brought by the photonic technology, such as small size, low weight, large bandwidth, low transmission loss, high tunability, and immunity to electromagnetic interference [2,3], it is of great interests to implement the beamforming network in the optical domain. Previously, a lot of efforts have been devoted to the development of the optical beamforming network (OBFN) [4–13]. Although optical true-time delay can realize squint-free beamformer [7–9], beamforming networks based on phase shifters are still widely used if the fractional bandwidth is not large. In 1997 and 2005, Riza [10] and Bui et al. [11] proposed OBFNs based on vector-sum phase shifting, respectively. In [11], the optical RF signal to be phase shifted is split into two paths with different fiber lengths by a variable directional coupler. By controlling the coupling ratio of the variable directional coupler, the combined signal after photodetection has different phase shifts. The key limitation associated with this approach is that N independent sets of laser source, modulator and vector-sum module are required for N antenna elements, which is complex and costly. Besides, flexible beamforming technologies based on programmable photonic processor comprising a 2-D array of liquid crystal on silicon (LCoS) pixels are also proposed by Riza [12] and Yi et al. [13], respectively. The methods are flexible since the photonic processor can manipulate the amplitude and phase of different optical spectral components independently. However, the state-of-the-art photonic processor is still complex, lossy and costly. In addition, the number of the output ports of the photonic processor is small (typically ≤4), so the antenna elements in the phased array antenna are limited.In this paper, a novel phased array antenna based on a simple OBFN is proposed and demonstrated. A polarization modulator (PolM) incorporated with an optical bandpass filter (OBPF) is used to perform optical single sideband (OSSB) polarization modulation. A 1 × N optical coupler is followed to split the OSSB polarization-modulated signal into N paths. In each path, a polarization controller (PC) and a polarization beam splitter (PBS) are inserted to realize a phase shifter [14], in which the phase shift is adjusted by the PC. The signals are then converted back to the electrical domain by photodetectors (PDs). A 1 × N OBFN is thus achieved. By incorporated the OBFN with an N -element linear patch antenna array, a phased array antenna is implemented. An experiment is carried out. A phased array antenna based on the OBFN is experimentally realized. The radiation patterns of the phased array antenna are measured.2. PrincipleFigure 1 illustrates the schematic diagram of the principle of a general beamforming network using phase shifters. As can be seen, N antennas incorporated with N phase shifters forms a phased array antenna. In the phased array antenna, the adjacent antennas are separated by a distance of d . When the beam direction is steered to an angle of θ, we havesin R d θΔ=⋅ (1) where ΔR is the minimum distance from the wave front to the antenna elements. As the signals radiated from the N antennas have the same phase shifts at the wave front, the phase difference between the adjacent antennas is expressed as2/R φπλΔ=⋅Δ (2) #203399 - $15.00 USD Received 19 Dec 2013; revised 31 Jan 2014; accepted 1 Feb 2014; published 10 Feb 2014(C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.003761 | OPTICS EXPRESS 3762where λ is the wavelength of the radiated microwave signal. Substituting (2) to (1), we obtain 11sin sin 2R d d λφθπ−−Δ⋅Δ==⋅ (3) As can be seen from (3), the beam pointing angle θ is a function of the phase difference Δφ which can be adjust by the phase shifters.Fig. 1. The schematic diagram of beam forming using phase shifters.Fig. 2. The schematic diagram of the proposed phased array antenna. LD: laser diode; PC:polarization controller; OBPF: optical bandpass filter; PolM: polarization modulator; PBS:polarization beam splitter; PD: photodetector.Figure 2 shows the schematic diagram of the proposed phased array antenna. The keycomponents for the phased array antenna are the N OSSB-polarization-modulation-basedmicrowave photonic phase shifters, which are implemented by a shared laser source, a sharedPolM, a shared OBPF, a 1 × N optical coupler, N PCs, N PBSs and N PDs. When a microwave signal is applied to the PolM, two double-sideband (DSB) modulated signals with complementary phase modulations along the two orthogonal axes are generated. The DC bias of the PolM is controlled to introduce a phase difference of 90° between the two principal axes of the PolM. The OBPF is followed by the PolM to remove the sidebands in one side (for example, the left sidebands), so an OSSB polarization-modulated signal is generated. For this OSSB polarization-modulated signal, assume that the optical carrier along one principal axis has a phase of 0°, the phases of the optical carrier along the other principal axis and the right sidebands along the two principal axes are 90°, 90°, 0°, respectively, i.e. the combined optical carrier and sideband are circularly polarized with opposite handedness. This OSSB polarization-modulated signal is split into N paths by the 1 × N coupler and each path includes one PC, one PBS and one PD. The PC together with the PBS is served as a polarizer. When the polarization direction of the polarizer is aligned with one principal axis of the PolM, the phase of the generated microwave signal at the PD is −90°, and if the polarizer is rotated to select the optical signal along the other polarization axis, this phase is changed to 90°. For other polarization directions, the phase shift is 2α + 90° [14], where α is the angle between the polarization direction of the polarizer and one principal axis of the PolM. As a result, the #203399 - $15.00 USD Received 19 Dec 2013; revised 31 Jan 2014; accepted 1 Feb 2014; published 10 Feb 2014(C) 2014 OSA 24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.003761 | OPTICS EXPRESS 3763phase shift can be independently and continuously tuned from −180 ° to 180° by adjusting the setting of the PC before the PBS in each path. Because both the combined optical carrier and sideband are circularly polarized, the optical carrier and the sideband after the polarizer have unchanged magnitudes, resulting in an invariable amplitude of the microwave signal when tuning the phase. The generated N microwave signals with independently-controlled phase shifts are then radiated by an N-element linear patch antenna array. By carefully adjusting the PC in each path, the far-field radiation with desired pattern can be achieved. Because the laser source, PolM and OBPF are shared by all phase shifters, the system is simple and compact. The flat power response of the phase shifters makes the system free of phase-amplitude coupling effect which is a serious problem in conventional electrical beamforming networks. In addition, the bandwidth of the phase shifter is broad, limited only by the bandwidth of the PolM and the PDs [14], so the proposed phased array antenna is suitable for frequency-agile system. The fiber-based PC and PBS array in the proposed scheme can also be replaced by 2-D spatial light modulators and free-space PBSs [2]. Therefore, the proposed system can be potentially altered to have large number of antennas. This kind of optically controlled phased array antenna would be attractive for communications, automotive systems, tracking radar and satellite links at millimeter-wave band [15], in which the frequency is too high for the electronic technology to achieve high performance and the fractional bandwidth is relatively small.Fig. 3. Photos of the proposed phased array antenna in an anechoic chamber.3. Experimental demonstrationA proof-of-concept experiment is carried out based on the configuration shown in Fig. 2. Photos of the experiment setup are illustrated in Fig. 3. The key parameters of the devices used in the experiment are as follows. The wavelength of the LD is 1561.9 nm and its power is 10 dBm. The 3-dB bandwidth and the half-wave voltage of the PolM (Versawave Inc.) are 40 GHz and 3.5 V, respectively. The OBPF has a 3-dB bandwidth of 50 GHz. The OSSB polarization-modulated signal is split by a 1 × 4 coupler. The PDs have a bandwidth of 20 GHz and a responsivity of 0.8 A/W. The 4-element linear patch antenna array has a 10-dB bandwidth of 500 MHz and a center frequency of 14 GHz. The antenna elements are separated by a distance of 100 mm, which is close to half of the operating RF signal wavelength. The RF signal introduced to the PolM has a frequency of 14 GHz and a power of 15 dBm. The radiation patterns are measured in an anechoic chamber.From [14], the phase shifter, comprising of a LD, a PolM, an OBPF, a PC, a PBS and a PD, has flat phase responses over a large working bandwidth of 10-40 GHz. By controlling the polarization states of the PC, the phase of the RF signal can be tuned from −180° to 180°, which indicates that the OBFN based on the phase shifters can operate in a wide frequency range. To investigate the feasibility of the proposed phased array antenna, radiation patterns #203399 - $15.00 USD Received 19 Dec 2013; revised 31 Jan 2014; accepted 1 Feb 2014; published 10 Feb 2014 (C) 2014 OSA24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.003761 | OPTICS EXPRESS 3764with different pointing angles are measured. As can be calculated from (3), phase shifts of [0°, 84°, 168°, −106°], [0°, 0°, 0°, 0°] and [0°, −84°, −168°, 106°] are required to obtain the radiation patterns with pointing angles of −30°, 0°, and 30°, respectively. These phase shifts are achieved by carefully adjusting the PCs with the assistance of a vector network analyzer(VNA, Aglient N5230A). Figure 4 shows the simulated and the experimentally measured radiation patterns of the phased array antenna based on the OBFN. As can be seen, all themain lobes of the measured radiation patterns are steered to the desired angles, which agreevery well with the simulated radiation patterns. The 3-dB bandwidth of the main lobes at −30°, 0°, and 30° are 30° (−45° to −15°), 26° (−13° to 13°) and 30° (15° to 45°), respectively. The small difference of the side lobes is caused by the uneven powers emitted from the4 antennas. For practical system, the PCs should be replaced by electronically-controlled PCs.In that case, the radiation pattern of the phased array antenna can be switched at a high speed as the PC can be replaced by a PolM [16].Fig. 4. The simulated and experimentally measured radiation patterns of the phased arrayantenna based on the OBFN when the angle of the beam is (a) −30°, (b) 0°, and (c) 30°. Theblack dashed and the red solid curves are the simulated and experimental results, respectively.4. ConclusionA novel optically controlled phased array antenna using OSSB polarization modulation based OBFN was proposed and demonstrated. Experimental results demonstrated that the OBFN can be used to steer the main lobe of the radiation pattern of the phased array antenna to anydesired directions by simply adjusting the PC in each path. Good agreement between thetheoretical results and the experimental results are confirmed. The proposed phased array antenna is suitable for the frequency-agile system and can be possibly swept at a high speed, which may find potential applications in radars and satellite communications. AcknowledgmentsThis work was supported in part by the National Natural Science Foundation of China (61107063, 61201048), the Jiangsu Provincial Funds for Distinguished Young Scientists (BK2012031, BK2012381), the Fundamental Research Funds for the Central Universities, the Foundation of Graduate Innovation Center in Nanjing University of Aeronautics and Astronautics (kfjj130113), the China Postdoctoral Science Special Foundation (2013T60533), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.#203399 - $15.00 USD Received 19 Dec 2013; revised 31 Jan 2014; accepted 1 Feb 2014; published 10 Feb 2014 (C) 2014 OSA24 February 2014 | Vol. 22, No. 4 | DOI:10.1364/OE.22.003761 | OPTICS EXPRESS 3765。

基于非均匀特异媒质的赋形天线设计摘要：在PCB板表面蚀刻不同尺寸的微带单元结构，构建非均匀特异媒质层，并将其放置在天线辐射单元前方，利用非均匀特异媒质层对电磁波不同的反射系数，实现对天线辐射波束的赋形。

设计了由不同尺寸正方形贴片组成的非均匀特异媒质层，并放置于工作频率为5.8 GHz的矩形贴片天线前方。

仿真和测试表明：该非均匀特异媒质层能够在基本保持贴片天线工作频点和回波损耗曲线不变条件下，通过调整与贴片天线距离，实现辐射波束由笔形波束向宽角波束和马鞍形波束的赋形转换。

为赋形天线设计提供了一种有效的新方法。

关键词：特异媒质；宽角赋形天线；马鞍形赋形天线；回波损耗中图分类号：TN820.1?34 文献标识码：A 文章编号：1004?373X（2014）11?0096?05Abstract：The non?uniform metamaterial layers are built by engraving microstrip units with different size on the surface of PCBs. Through placing a proposed metamaterial layer in front an antenna and making use of the spatial varying reflection coefficient of the non?uniform metamaterial layer for theelectromagnetic wave，the radiation pattern of the antenna can be shaped. In this paper，a proposed layer consisted of square patches with different size is designed and then placed in frontof a rectangular patch antenna working at a frequency of 5.8 GHz. Both simulation and measurement show that thenon?uniform metamaterial layer is able to realize the conversion of the antenna’s radiation pattern from a pencil? shaped beam to a wide beam pattern or a saddle?shaped beam，through adjusting the distance between the patch antenna and the metamaterial layer，while the antenna’s working frequency and return loss curve almost remain unchanged. The research result provided a new method for the design of the shaped beam antenna.Keywords：metamaterial；wide shaped beam antenna；saddle?shaped antenna；return loss0 引言随着无线通信、雷达和遥感遥测等科技的发展，对天线的性能要求越来越高，许多应用领域要求对天线波束进行赋形，即赋形天线[1]。

基于编码超表面的太赫兹宽频段雷达散射截面缩减的研究∗闫昕;梁兰菊;张雅婷;丁欣;姚建铨【期刊名称】《物理学报》【年(卷),期】2015(0)15【摘要】In this paper, we propose a flexible, non-directional lowering scattering 1 bit coding metasurface which can signifi-cantly reduce the radar cross section (RCS) within an ultra wide terahertz (THz) frequency band. The total thickness of the coding metasurface is only 40.4 µm. The 1 bit coding metasurface is composed of“0”and“1”elements. Andthe“0”and“1”elements of metasurface are realized separately by a substrate without any metallic covering and that with a square metallic ring covering, the reflection phase difference of the two elements is about 180 degree in a wide THz frequency range. The theoretical, analytical, and simulation results show that the coding metasurfaces simply manipu-late electromagnetic waves by coding the“0”and“1”elements in different sequences. Specific coding sequences result in the far-field scattering patterns varying from single beam to two, three, and numerous beams in THz frequencies. The metasurface with the numerous scattering waves can disperse the reflection into a variety of directions for non-periodic coding sequence way, and in each direction the energy is small based on the energy conservation principle. Full-wave simulation results show that the reflectivity less than−10 dB for coding metasurface can be achieved in awide frequency range from 1–1.4 THz at normal incidence, and the RCS reduction as compared with a bare metallic plate with the same size is essentially more than 10 dB, in agreement with the bandwidth of reflectivity being less than −10 dB; the maximum reduction can be up to 19 dB. The wideband RCS reduction results are consistent with the bandwidth of 180 degrees phase difference between the twoelements“0”and“1”. This wideba nd characteristic of RCS reduction can be kept up as the coding metasurface is wrapped around a metallic cylinder with a diameter of 4 mm. The presented method opens a new way to control THz waves by coding metasurface, so it is of great application values in stealth, imaging, and broadband communications of THz frequencies.%本文设计了一种柔性,非定向低散射的1bit编码超表面,实现了太赫兹宽频带雷达散射截面的缩减.这种设计基于对“0”和“1”两种基本单元进行编码,其反射相位差在很宽的频段范围内接近180◦,为一种非周期的排列方式,该电磁超表面使入射的电磁波发生漫反射,从而实现雷达散射截面的缩减.全波仿真结果表明,在垂直入射条件下,编码超表面的镜像反射率低于−10 dB的带宽频段范围为1.0—1.4 THz,该带宽内超表面相对同尺寸金属板可将雷达散射截面所减量达到10 dB以上,最大缩减量达到19 dB.把柔性编码表面弯曲在直径为4 mm的金属圆柱面上,雷达散射截面的所减量高于10 dB以上的带宽频段范围为0.9—1.2 THz,仍然可实现宽频带缩减特性.总之,编码超表面为调控太赫兹波提供一种新的途径,将在雷达隐身、成像、宽带通信等方面具有重要的意义.【总页数】8页(P1-8)【作者】闫昕;梁兰菊;张雅婷;丁欣;姚建铨【作者单位】天津大学精密仪器与光电子工程学院，天津 300072; 枣庄学院光电工程学院，枣庄 277160;天津大学精密仪器与光电子工程学院，天津 300072; 枣庄学院光电工程学院，枣庄 277160;天津大学精密仪器与光电子工程学院，天津300072;天津大学精密仪器与光电子工程学院，天津 300072;天津大学精密仪器与光电子工程学院，天津 300072【正文语种】中文【相关文献】1.电磁超表面在微波和太赫兹波段雷达散射截面缩减中的应用研究进展 [J], 闫昕;梁兰菊;张雅婷;丁欣;姚建铨2.太赫兹超表面RCS缩减特性研究 [J], 梁兰菊;车凯琪;刘凤收;王亚茹;李院平3.基于微波倍频源太赫兹频段雷达散射截面测量 [J], 吴洋;白杨;殷红成;张良聪4.基于十字形结构的相位梯度超表面设计与雷达散射截面缩减验证∗ [J], 吴晨骏;程用志;王文颖;何博;龚荣洲5.基于编码超表面的双向太赫兹多波束调控器件 [J], 沈仕远;王元圣;池瑶佳;马新迎;杨青慧;陈智;文岐业因版权原因，仅展示原文概要，查看原文内容请购买。

２０２１年１月１０日第５卷第１期现代信息科技Modern Information TechnologyJan.2021 Vol.5 No.1682021.1基于平面近场的有源相控阵系统G ／T 值测量方法吴瑞荣，邹永庆，龙永刚，李景峰，吴贻伟（中国电子科技集团公司第三十八研究所，安徽 合肥 230088）摘 要：文章提出了一种基于平面近场的有源相控阵天线系统G /T 值测量方法，通过分别测量接收系统的有源增益和有源噪声功率，进而测量出G /T 值。

该方法在暗室平面近场进行，实现简单，受环境影响小，重复度高，解决了大型阵列天线G /T 值测量困难的问题。

给出了测量原理和测试误差分析，并通过对Ka 频段接收相控阵的G /T 值实测，与理论计算结果一致，且多次测量的抖动在0.25 dB 内。

关键词：G /T 值测量；有源相控阵天线；平面近场中图分类号：TN82文献标识码：A文章编号：2096-4706（2021）01-0068-03G ／T Ｖａｌｕｅ　Ｍｅａｓｕｒｅｍｅｎｔ　Ｍｅｔｈｏｄ　ｏｆ　Ａｃｔｉｖｅ　Ｐｈａｓｅｄ　Ａｒｒａｙ　Ｓｙｓｔｅｍ　Ｂａｓｅｄ　ｏｎＰｌａｎａｒ　Ｎｅａｒ　ＦｉｅｌｄWU Ruirong ，ZOU Yongqing ，LONG Yonggang ，LI Jingfeng ，WU Yiwei（The 38th Research Institute of China Electronics Technology Group Corporation ，Hefei 230088，China ）Abstract ：In this paper ，a method of measuring G /T value of active phased array antenna system based on planar near field isproposed. By measuring the active gain and active noise power of the receiving system respectively ，the G /T value can be measured. The method is implemented in the near field of the dark chamber plane ，which is simple to realize ，small affected by the environment and high repetition. It solves the difficult problem of measuring the G /T value of large array antenna. The measurement principle and error analysis are given in this paper. The measurement principle and error analysis are given. The measured G /T value of Ka band receiving phased array is consistent with the theoretical calculation ，and the jitter of multiple measurements is within 0.25 dB.Keywords ：G /T value measurement ；active phased array antenna ；planar near field收稿日期：2020-11-290 引 言有源相控阵天线因其具备波束指向、形状等灵活可变的高弹性，在测控通信、微波成像等多个领域广泛应用，随着芯片和微波集成技术发展，毫米波大型相控阵列得到长足应用。

doi:10.3969/j.issn.1003-3114.2023.05.021引用格式:高克,张海洋,王保云.基于动态超表面天线的雷达通信一体化设计[J].无线电通信技术,2023,49(5):946-952.[GAO Ke,ZHANG Haiyang,WANG Baoyun.Beamforming Design for Dual-functional Radar-communication Systems with Dynamic Metasurface Antennas[J].Radio Communications Technology,2023,49(5):946-952.]基于动态超表面天线的雷达通信一体化设计高㊀克,张海洋,王保云(南京邮电大学通信与信息工程学院,江苏南京210003)摘㊀要:雷达通信一体化(Dual-Functional Radar-Communication,DFRC)利用相同的硬件平台㊁频谱资源同时实现雷达感知和无线通信双功能,是当前无线通信领域研究的热点技术㊂针对动态超表面天线(Dynamic Metasurface Antenna,DMA)辅助的雷达通信一体化系统,研究了最优波束成形设计问题㊂最优波束成形设计是一个非凸优化问题,很难直接求解㊂设计全数字天线架构下的最优波束,将动态超表面天线雷达波束设计转换为拟合最优编码矩阵问题㊂转换后的波束设计问题仍为非凸,为此将其分解为两个子问题交替最小化,其中两个子问题分别采用黎曼共轭梯度和半正定松弛算法求解㊂数值仿真表明,满足通信质量约束的情况下,动态超表面天线架构的DFRC 雷达波束性能接近于无频谱共享时的纯雷达波束性能㊂关键词:雷达通信一体化;动态超表面天线;交替最小化;黎曼共轭梯度;半正定松弛中图分类号:TN929.5㊀㊀㊀文献标志码:A㊀㊀㊀开放科学(资源服务)标识码(OSID):文章编号:1003-3114(2023)05-0946-07Beamforming Design for Dual-functional Radar-communicationSystems with Dynamic Metasurface AntennasGAO Ke,ZHANG Haiyang,WANG Baoyun(Communication and Information Engineering,Nanjing University of Posts and Telecommunications,Nanjing 210003,China)Abstract :Dual-Functional Radar-Communication (DFRC)uses same hardware platform and spectrum re-sources to realize dualfunctions of radar detection and wireless communication simultaneously,which is a hot topic in the field of wireless communications.Forthe Dynamic Metasurface Antennas (DMA)-assisted DFRC system,an optimal beamforming design problem is studied.The optimalbeamforming design is a non-convex optimization problem that is difficult to solve directly.In this paper,an optimal beam with a digitalantenna architecture is designed first,and then the dynamic metamaterial antenna radar beam design is converted into a fitting optimalcoding matrix problem.Though the resulting design problem is still non-convex.it can be decom-posed into two sub-problems and then been solved alternately.In particular,the two sub-problems are solved by riemannian conjugate gradient and semidefinite relaxation algo-rithms,respectively.Finally,numerical results show that the performance of our proposed beamforming design for DMA-assisted DFRC system is close to that of the radar only beamforming without communication requirement.Keywords :DFRC;DMA;alternate minimization;riemannian conjugate gradient;semidefinite relaxation收稿日期:2023-05-050　引言随着5G 时代的到来,无线设备数量和种类均呈现出了爆发性增长,全球通信产业对无线频谱的需求日益迫切㊂有很多场景需要感知与通信联合设计,例如:自动驾驶㊁智慧城市和智能家居等[1]㊂与此同时,随着无线通信速率需求的不断提高,载波频率被推向了传统上分配给雷达系统的毫米波频率频段[2]㊂未来后5G 及6G 时代,为提高频谱效率以及降低雷达与通信系统之间的电磁干扰问题,雷达通信一体化(Dual-Functional Radar-Communication,DFRC)系统成为了一个有前途的热门研究领域㊂在雷达通信一体化系统中,雷达与通信系统之间共享相同的硬件平台和频谱资源,同时实现通信和雷达感知的双功能㊂在雷达通信一体化系统中,由于雷达和通信具有不同的需求且共享相同的资源,因此需要精心设计传输波束以平衡二者的性能㊂为了在保证通信用户服务质量的同时提高雷达的性能,文献[3]研究了发射波束成形优化设计㊂针对全数字天线架构,文献[4]考虑波束之间的相互干扰因素,设计了性能更优的雷达波束㊂考虑到全数字天线功耗大㊁成本高的问题,目前对雷达通信一体化系统研究比较广泛的是基于相移器的混合波束天线架构[5-10],其中文献[5-6]研究了设计模拟和数字预编码矩阵,使其与最优通信预编码矩阵和最优雷达波束预编码矩阵之间误差的加权总和最小;文献[7-8]研究主要集中在雷达波束与理想波束差距小于一定阈值作为约束条件,最大化用户通信质量;文献[9-10]研究了在保证用户通信质量前提下,最优化雷达波束性能,其雷达的波束性能直接由雷达接收机的信干扰加噪声比(Signal to Interference plus Noise Ratio, SINR)决定㊂智能超表面是当前无线通信领域的另外一个研究热点,其可用于增强无线通信盲区覆盖㊁物理层辅助安全通信㊁大规模D2D(Device-to-Device)通信㊁物联网中无线携能通信以及室内覆盖等领域[11]㊂然而,智能超表面除了用来做被动的反射外,还可以用来实现低功耗的主动收发天线㊂动态超表面天线(Dynamic Metasurface Antennas,DMA)是一种典型的基于超表面天线的收发天线㊂在基于DMA的收发器中,每个超表面天线单元是由低功耗的超表面组成,且每个天线单元的幅频特性可以动态实时调控[12]㊂DMA天线架构可以被视为混合模拟数字天线架构,即它不需要额外的专用模拟相移器网络,仅利用自身的信号处理功能便可实现模拟预编码[13]㊂此外,DMA可以包含大量可调谐的超表面天线元件,并且其天线单元之间的距离可以是亚波长,DMA需要的物理面积可以更小,有助于设备的小型化[14]㊂1㊀系统模型和问题描述1.1㊀系统模型雷达通信一体化系统场景示意图如图1所示,一个雷达通信一体化基站拥有N T根天线,为K个单天线用户提供通信服务并探测区域内目标㊂基站使用的动态超表面天线架构,其由数字预编码矩阵㊁L T条射频链路和模拟预编码矩阵组成㊂图1㊀雷达通信一体化系统场景示意图Fig.1㊀Schematic diagram of DFRC基带信号表示为sɪKˑ1,s i~(0,1),iɪ{1, 2, ,K}为第i个用户接收到的信息符号㊂发射信号可以表示为:y=UF DMA F BB s,(1)式中:F DMAɪN TˑL T为DMA天线模拟预编码矩阵, F BBɪN DMAˑK为数字预编码矩阵,DMA微带内的信号传播公式为:u i,j=e-ρi,j(αi+jβi),∀i,j,其中αi为波导衰减系数,βi为波数,ρi,j表示第i微带中第l个单元的位置,其中U((i-1)L+l,(i-1)L+l)=u i,l,L为每条微带上单元的个数[13]㊂功率约束条件为 UF DMA F BB 2FɤP max,P max为基带最大分配功率㊂F DMA矩阵满足以下形式[15]:F DMA=t10 00t2 0︙︙︙00 t L Téëêêêêêùûúúúúú,(2)式中:t iɪN TN DMAˑ1,非零相q i,l=j+e jφi,l2,{φi,lɪ[0,2π]}ɪF DMA,∀i,l㊂雷达在θ角方向的传输功率波束图可以表示为:P(θ;R)=a H(θ)Ra(θ),(3)式中:RɪN TˑN T为传输波束的协方差矩阵,R= UF DMA F BB ss H F H BB F H DMA U-H=UF DMA F BB F H BB F H DMA U H㊂对于N个天线单元的均匀线性天线阵列,其导向矢量为:a(θ)=1N[1,e j2πλdsin(θ), ,e j2πλd(N-1)sin(θ)]T,(4)式中:λ为信号波长,d=λ/2为天线单元间距㊂雷达在θ1和θ2两角之间的波束互相关可以表示为:P c(θ1,θ2;R)=a H(θ1)Ra T(θ2)㊂(5)由式(3)和式(5)可以看出,雷达的传输功率波束图和波束互相关都是由传输波束的协方差矩阵R决定㊂通过波束方向误差和波束互相关两部分的加权和组成一个损失函数,用损失函数评估雷达性能㊂第一部分可以用接收到的波束与理想波束之间的均方差来评估:L r,1(R,α)=1LðL l=1|αd(θl)-P(θl;R)|2,(6)式中:α为比例因子,d(θl)为θl方向理想接收波束㊂第二部分用波束互相关均方差来评估:L r,2(R)=2P2-PðP-1p=1㊀ðP q=p+1|P c(θ-p,θ-q);R|2㊂(7)㊀㊀将以上两部分加权和后,雷达波束图的损失函数表示为:L r(R,α)=L r,1(R,α)+ωL r,2(R)㊂(8)在本文雷达通信一体化系统中,假设通信用户是单天线的,则第k个用户接收信号为:y k=h H k UF DMA F BB,k s k+ðK iʂk h H k UF DMA F BB,i s i+n k,(9)式中:h kɪN Tˑ1为基站与第k个用户之间的下行通道,n k~(0,σ2k)为第k个用户加性高斯白噪声(Additive White Gaussian Noise,AWGN)㊂第k个用户接收信号的SINR可以表示为:γk=|h H k UF DMA F BB,k|2σ2k+ðK iʂk|h H k UF DMA F BB,i|2㊂(10)1.2㊀问题描述雷达通信一体化系统需要权衡通信和雷达之间的性能㊂基于动态超表面天线的雷达通信一体化系统,在保证每个通信用户的SINR高于给定阈值前提下的式(10),使雷达传输波束的性能达到最优的式(8)㊂另外,加上预编码矩阵有功率限制和模拟预编码矩阵相位限制的式(2),雷达通信一体化系统传输波束成形设计问题可以表示为:㊀min FBB,F DMA L r(R,α)㊀㊀㊀㊀㊀㊀㊀㊀㊀㊀s.t.㊀ UF DMA F BB 2FɤP max,F DMA(i,l)=j+e jφi,l2,φi,lɪ[0,2π],|h H k UF DMA F BB,k|2σ2k+ðK iʂk|h H k UF DMA F BB,i|2ȡΓ,(11)式中:Γ为给定用户的SINR阈值㊂式(11)涉及到数字预编码矩阵和模拟预编码矩阵的联合设计,并且问题本身也是非凸的,很难求解㊂当天线架构为全数字天线架构时,该问题对应的问题容易求解,并且在用户SINR满足一定阈值时,其最优预编码矩阵获得的波束与理想波束十分相似㊂因此可以先求出全数字天线最优预编码矩阵,然后将动态超表面天线的模拟预编码矩阵和数字预编码矩阵拟合全数字天线的最优预编码矩阵,由此得到动态超表面天线的模拟与数字最优预编码矩阵㊂2㊀雷达通信一体化波束成形设计2.1㊀基于全数字天线架构先设计基于全数字天线架构的雷达通信一体化系统预编码矩阵W,使其在满足功率约束和用户SINR高于一定阈值前提下,雷达波束性能达到最优㊂其问题表示为:㊀㊀㊀min R L r(R,α)s.t.㊀R=WW HɪS+MW 2FɤP max|h H k w k|2σ2k+ðK iʂk|h H k w i|2ȡΓ,(12)式中:w i为W的第i列,W=(w1,w2 ,w K)㊂将第三个约束化简后的问题为:min R,RkL r(R,α)s.t.㊀R=WW HɪS+MW 2FɤP maxRkɪS+M,rank(R k)=1,k=1,2, ,K(1-Γ-1)h H k R k h kȡh H k Rh k+σ2k,(13)式中:R k=w k w H k,R=ðK k=1R k㊂由于其中的约束条件rank(R k)=1,k=1,2, , K是非凸的,可以先将其松弛掉,松弛后的问题是凸问题:min R,RkL r(R,α)s.t.㊀R=WW HɪS+MW 2FɤP maxRkɪS+M,k=1,2, ,K(1-Γ-1)h H k R k h kȡh H k Rh k+σ2kW=(w1,w2, ,w K),R k=w k w H k㊂(14)可以用Matlab中CVX工具箱求得最优解:R^, R^k,k=1,2, ,K㊂如果式(14)全局最优解满足R^kɪS+M,k=1,2, ,K 秩为1,那么求解式(13)中使用的松弛就是紧的,即松弛后问题的解也是原非凸问题的解㊂定理1㊀式(13)存在最优解R ~,R ~k ,k =1,2, ,K ,满足rank(R ~k )=1,k =1,2, ,K ㊂证明㊀R ^,R ^i ,i =1,2, ,K 为式(14)的全局最优解,将R ^,R ^i,i =1,2, ,K 做以下变换:R ~=R ^,w ~i =(h H i R ^i h i )-1/2R ^i h i ,R ~i =w ~i w ~H i ,R ~,R ~i ,i =1,2, ,K 为半正定矩阵且秩为一㊂因为R ~=R^,并且式(13)和式(14)的最终问题是相同的,所以R ~是式(13)全局最优解㊂现在只要证明R ~,R ~i ,i =1,2, ,K 为式(13)的可行解,则R ~,R ~i ,i =1,2, ,K 为式(13)的全局最优解㊂由于h H kR ~k h k =h H kw ~k w ~H k h k =h H k R ^k h k ,将其带入到(1-Γ-1)h H k R ~k h k=(1-Γ-1)h H k R ^k h k ȡh H k R ^k h k +σ2k =h H k R ~k h k +σ2k 满足式(13)的限制条件㊂所以R ~,R ~i ,i =1,2, ,K 为原问题的全局最优解㊂由定理1可知将式(14)最优解做以下变换:R ~=R ^,w ~k =(h H k R ^k h k )-1/2R ^k h k ,R ~k=w ~k w ~H k ,R ~k ɪS +M ,k=1,2, ,K 且秩为1,并且R ~仍为原问题的解㊂由此可以求解得到全数字天线最优预编码矩阵的列向量w k ,全数字天线架构的最优预编码矩阵W 也就可以求出㊂2.2㊀基于动态超表面天线架构在上节求解得到了全数字天线最优预编码矩阵,本节设计动态超表面天线架构预编码矩阵,使雷达通信一体化系统在满足功率约束㊁模拟预编码矩阵相位约束和通信用户信干扰加噪声比高于一定阈值前提下,最优拟合全数字天线预编码矩阵,其问题表示为:min F BB ,F DMAUF DMA F BB -W ~2Fs.t.㊀ UF DMA F BB 2F ɤP maxq i ,l =j +ej φi ,l2,φi ,l ɪ[0,2π]}{ɪF DMA ,∀i ,l|h H kUF DMA F BB,k|2σ2k+ðKi ʂk|h H kUF DMA F BB,i|2ȡΓ㊂(15)由于此问题不是凸问题,故将问题分解成设计两个子问题相互迭代来求解,两个子问题分别设计数字和模拟预编码矩阵㊂然而,数字和模拟预编码矩阵的设计问题都是非凸问题㊂为此,本文分别采用半正定松弛(Semidefinite Relaxation,SDR )技术[16-17]和黎曼共轭梯度(Riemannian Conjugate Gra-dient,RCG)算法[18]分别设计最优数字和模拟预编码矩阵㊂2.2.1设计模拟预编码矩阵当固定数字预编码矩阵F BB 设计最优模拟预编码矩阵时,限制条件只有模拟预编码矩阵的相位限制㊂其问题为:min FDMAUF DMA F BB -W ~2Fs.t.㊀q i ,l =j +ej φi ,l2,φi ,l ɪ[0,2π]}{ɪF DMA ,∀i ,l ㊂(16)由于问题是矩阵形式,不方便求解,所以将矩阵向量化:min FDMAUF DMA F BB -W ~2F =min F DMA(F T BB U )vec(F DMA )-w 2F ,式中:w =vec(W ~)㊂因为vec(F DMA )中的元素除了相位限制元素,其他为零元素㊂由于零元素的具体位置是已知的,所以可以先将零元素剔除掉㊂令q 为vec(F DMA )去除零元素后的向量,A 为(F T BB U )去除掉与vec(F DMA )零元素相对应的列向量㊂此时的问题转换为:㊀min F DMA(F T BB U )vec(F DMA )-w 2F =min q(Aq -w )H (Aq -w )=min qq H A H Aq -2q H A H w +w H w ㊂(17)由于模拟预编码矩阵的非零元素q i ,l 可以描述为圆心点为0,12e j π2(),半径为12的复平面圆上:q i ,l -12e j π2=12,定义向量b 为:b k =2q k -e j π2,所以q =12b +e j π21(),|b k |=1㊂最终可以将问题转换为关于向量b 的问题:min bq H A H Aq -2q H A H w +w H w =min b 14b +e j π21()H A H A b +e j π21()-b +e j π21()H A H w +w H w s.t.㊀|b k |=1ɪb ,(18)这时搜索空间为N T 个复数圆上,是一个N T的黎曼子流形,可以通过RCG 求得最优解b opt ㊂其中该问题的黎曼梯度为Δf (bt +1k)=AH㊃12A b t +1k +e j π21()-w ()㊂由于F DMA 非零位置是已知的,所以将最优解bopt扩展成矩阵形式,可以得到最优模拟预编码矩阵F opt DMA ㊂2.2.2设计模拟预编码矩阵当固定模拟预编码矩阵F DMA 时,限制条件为预编码矩阵功率约束和通信SINR 阈值约束,其问题为:㊀㊀㊀㊀min F BBUF DMA F BB -W ~ 2F㊀㊀㊀㊀s.t.㊀ UF DMA F BB 2FɤP maxh H k UF DMA F BB,k2σ2k+ðKi ʂk|h H kUF DMA F BB,i |2ȡΓ㊂(19)由于式(19)中第二个限制条件F BB 是按列展开的,所以将问题中的矩阵F BB 和W ~也按列展开:ðKk =1UF DMA F BB,k-W ~k 2F =ðK k =1F H BB,k F H DMA U H UF DMA F BB,k -2F H BB,k F H DMA U H W ~k +W ~Hk W ~k ㊂(20)展开后的问题并不容易求解,引入辅助变量t 2=1,可以化解成二次约束二次规划问题(Quadrati-cally Constrained Quadratic Programs,QCQP):v -k =F BB,kt(),Q k =F H DMA U H UF DMA ,-F H DMA U HW ~k ㊀㊀-W ~H k UF DMA ,W ~H k W ~k(),F H BB,k F H DMA U H U F DMA F BB,k -2F H BB,k F H DMA U H W ~k +W ~H k W ~k=v -H k Q v -k ㊂但此时,由于式(20)中第二个限制条件是非凸的,所以该问题也是非凸的㊂引用SDR 技术将问题进行化简,令V k =v -k v -H k ,rank(V k )=1,可以将问题简化为SDR 的标准形式:min V k ðKk =1tr(Q k V k )s.t.㊀ðKk =1trF H DMA U HUF DMA ,00,()V k ()ɤP max ,∀k ,trH k ,00,0()V k ()Γ-ðKi ʂktrH k ,00,()V i ()ȡσ2k ,tr0K ∗K ,00,1()V k ()=1,V k ȡ0,rank(V k )=1,H k =F H DMA U H h k h Hk UF DMA ㊂(21)由于约束项rank(V k )=1是非凸的,先将其松弛掉,之后的问题是凸问题,可以用Matlab 中CVX 工具箱求最优解V opt k ㊂如果该问题可解或有界,则ðKk =1[rank(V opt k )]ɤK +1,又因为每个用户的SINR 阈值限制,最优解满足:rank (V opt k )ȡ1,所以其最优解满足rank(V opt k )=1㊂由此证得rank(V k )=1的松弛是紧的,V opt k是原问题的最优解㊂F opt BB,k 是V optk的最大特征向量乘以最大特征值的平方根,因此,可以得到最优数字预编码矩阵F opt BB ㊂3　仿真分析本节采用数值仿真验证DMA 雷达通信一体化设计算法的性能,并且与全数字天线架构㊁基于相移器的混合波束天线架构和理想雷达波束进行对比㊂考虑雷达通信一体化基站的天线为均匀线性天线阵列,总发射功率为1W 和天线数量为24,其为用户提供通信服务并探测区域内目标㊂在探测区域内设置了方向为-40㊁0ʎ和40ʎ的3个理想目标,其波束表达式为:d (θ)=1,θ0-Δ2ɤθɤθ0+Δ20,㊀㊀otherwise{,(22)式中:Δ为理想波束的宽度,设置为2ʎ㊂当系统设计的DMA 射频链路为12个,信噪比设置为20dB 时,不同天线架构随角度变化的波速比较如图2所示㊂不同天线架构在满足用户需求前提下,使雷达波束达到最优的仿真,图中K =0㊁FD㊁DMA 和BP 线分别为理想目标波束㊁全数字天线架构波束㊁DMA 天线架构波束和基于相移器架构波束㊂可以看出,全数字天线的雷达波束图基本与理想的波束重合,DMA 天线架构和基于相移器架构也很好地还原了最优波束图,并且从中很容易查找出在-40ʎ㊁0ʎ和40ʎ方向有目标,因为这3个方向的波束峰值明显高于其他方向㊂图3是在4个通信用户SINR 的阈值从6dB 调整到14dB,不同天线架构随角度变化的波束比较㊂图2与图3对比可知,在通信用户阈值提高的情况下,DMA 架构和基于相移器的混合架构的目标雷达波束图峰值有明显的变差㊂图4是在6个通信用户信SINR 的阈值为6dB 情况下,不同天线架构随角度变化的波束比较㊂图2与图4对比可知,服务通信用户增加,目标雷达波束图峰值会变差㊂图5是在4个通信用户信SINR 的阈值为6dB,功率约束调整为2W 情况下,不同天线架构随角度变化的波束比较㊂图2与图5对比可知,增加发射功率,图5中目标雷达波束图峰值接近图2中目标峰值的2倍㊂图2㊀不同天线架构随角度变化的波束比较Fig.2㊀Comparison of beams varying by angle fordifferent antennaarchitectures图3㊀调整用户SINR 后的波束比较Fig.3㊀Beam comparison after adjusting theuser sSINR图4㊀调整用户个数后的波束比较Fig.4㊀Beam comparison after adjusting the number ofusers图5㊀调整功率约束后的波束比较Fig.5㊀Beam comparison after adjusting power constraints图6展示了基于DMA 的雷达一体化系统在不同发射功率情况下,用户SINR 阈值约束和雷达波束性能之间的权衡㊂可以看出,在发射功率一定时,随着用户SINR 阈值的增加,DMA 天线预编码矩阵与全数字天线预编码矩阵之间的均方差也在增加,并且发射功率为2W 时的均方差明显大于功率为1W 的设计㊂这是因为当通信质量要求增加时,为满足用户质量需要消耗更多的功率,而生成雷达波束的功率会变少,雷达波束性能也会变差㊂因此,降低通信质量要求,可以提高雷达波束性能㊂图6㊀用户SINR 阈值与雷达波束均方差之间关系Fig.6㊀Relationship between the user s SINR threshold andthe mean square deviation of the radarbeam4　结束语本文研究了基于动态超表面天线的雷达通信一体化系统,设计了相应的最优波束成形策略㊂采用了数字预编码矩阵与模拟预编码矩阵设计联合交替优化设计,分别应用半正定松弛和黎曼共轭梯度算法求解㊂数值仿真结果表明,所提算法设计的动态超表面天线架构的雷达通信一体化系统,在满足通信用户性能的前提下,其雷达性能接近理想雷达波束㊂动态超表面天线架构与基于相移器的混合波束天线架构整体性能相似,其雷达通信一体化系统中雷达与通信性能之间存在负相关,雷达性能随着通信性能的提高而降低㊂参考文献[1]㊀刘凡,袁伟杰,原进宏,等.雷达通信频谱共享及一体化:综述与展望[J].雷达学报,2020,10(3):467-484. 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[8]㊀CHENG Z,HE Z,LIAO B.Hybrid Beamforming for Multi-carrier Dual-function Radar-communication System[J].IEEE Transactions on Cognitive Communications and Net-working,2021,7(3):1002-1015.[9]㊀CHEN C Y,VAIDYANATHAN P.MIMO Radar Wave-form Optimization with Prior Information of the ExtendedTarget and Clutter[J].IEEE Transactions on Signal Pro-cessing,2009,57(9):3533-3544.[10]DAI Y,HAN K,WEI G,et al.Hybrid Beamforming forDFRC System Based on SINR Performance Metric[C]ʊ2021IEEE/CIC International Conference on Communicationsin China(ICCC Workshops).Xiamen,IEEE,2021:82-87.[11]LAN G,IMANI M F,DEL HOUGNE P,et al.WirelessSensing Using Dynamic Metasurface Antennas:Challengesand Opportunities[J].IEEE Communications Magazine,2020,58(6):66-71.[12]SMITH D R,YURDUSEVEN O,MANCERA L P,et al.Analysis of a Waveguide-fed Metasurface Antenna[J].Physical Review Applied,2017,8(5):054048. [13]ZHANG H,SHLEZINGER N,GUIDI F,et al.Beam Focu-sing for Near-field Multiuser MIMO Communications[J].IEEE Transactions on Wireless Communications,2022,21(9):7476-7490.[14]SHLEZINGER N,ALEXANDROPOULOS G C,IMANI M F,et al.Dynamic Metasurface Antennas for6G ExtremeMassive MIMO Communications[J].IEEE WirelessCommunications,2021,28(2):106-113. [15]SHLEZINGER N,DICKER O,ELDAR Y C,et al.Dynam-ic Metasurface Antennas for Uplink Massive MIMO Sys-tems[J].IEEE Transactions on Communications,2019,67(10):6829-6843.[16]LUO Z Q,MA W K,SO A M C,et al.Semidefinite Relax-ation of Quadratic Optimization Problems[J].IEEE Sig-nal Processing Magazine,2010,27(3):20-34. [17]ZHANG S.Quadratic Maximization and Semidefinite Re-lax-ation[J].Mathematical Programming,2000,87:453-465.[18]YU X,SHEN J C,ZHANG J,et al.Alternating Minimiza-tion Algorithms for Hybrid Precoding in Millimeter WaveMIMO Systems[J].IEEE Journal of Selected Topics inSignal Processing,2016,10(3):485-500.作者简介:㊀㊀高㊀克㊀男,(1994 ),硕士研究生㊂主要研究方向:雷达通信信号处理㊂张海洋㊀男,(1987 ),博士研究生㊂主要研究方向:无线通信信号处理㊁面向6G近场无线通信㊂王保云㊀男,(1967 ),博士,教授㊂主要研究方向:香农信息论㊁无线通信中的博弈与协作㊁无线通信中的信号处理技术㊁视频信息的分析与理解㊂。

光纤无线融合的波天线相参合成与定位技术Fiber-optic wireless fusion is a cutting-edge technology that combines the advantages of optical fiber and wireless communication. By integrating these two technologies, it promises to revolutionize the way we transmit and receive data. However, one of the challenges associated with this technology is achieving coherent beamforming and positioning with wave antennas.光纤无线融合是一种结合光纤和无线通信优势的尖端技术。

通过整合这两种技术，它承诺颠覆我们传输和接收数据的方式。

然而，与这项技术相关的挑战之一是实现波束合成和定位与波天线的相参。

Coherent beamforming with wave antennas involves aligning the phases of multiple signals to create a stronger and more focused signal. This is essential for improving the efficiency and reliability of wireless communication systems. In the context of fiber-optic wireless fusion, coherent beamforming is crucial for maximizing the capacity and performance of the hybrid network.使用波天线进行波束合成涉及将多个信号的相位进行对齐，以创建更强大和更集中的信号。

现代电子技术Modern Electronics Technique2023年4月1日第46卷第7期Apr.2023Vol.46No.70引言天线在无线通信系统中主要承担着发射和接收信号的作用[1]，目前已经广泛应用于军工、民用电子和航空航天领域。

相比于单个天线，阵列天线[2]具有较高的增益和更低的副瓣[3]、更窄的波束和更深的零陷等特性[4]。

当天线的窄波束以一定规律在宽空域[5]范围扫描，其中一种就是相控[6]扫描，通过对阵元相位的控制，实现波束扫描机制。

影响阵列天线的性能有如下几个因素：阵列单元数、阵元间距、阵元激励的幅度相位以及阵元的馈电方式等。

按照阵列天线的阵元维数排列进行分类，包括一维、二维和三维阵列天线。

本文建立了一维和二维天线阵列的数学模型，通过改变阵元数、阵元间距以及不同的阵元函数等，得到了不同参数变化对阵列方向图的影响[7]。

1阵列天线简介1.1阵列天线方向图计算原理一维直线阵列天线是指阵列单元[8]都在一条直线上的天线，该直线阵上有N 个阵元，设远场观测点为P (r ,θ,ϕ)，对于直线阵而言，观测点和直线阵属于同一平面，所以ϕ=0。

设坐标原点为参考点，信号的入射方向为(θ,ϕ)，其中入射信号的俯仰角为θ，方位角为ϕ。

此时沿观测点方向的单元向量e r 从球坐标系转化为直角坐标系，则有：e r =(sin θcos ϕ,sin θsin ϕ,cos θ)=(sin θ,0,cos θ)（1）天线阵第n 个阵元的激励为I n =I n e j αn，假设直线阵[9]阵元等间距排列，第二个阵元到坐标参考点的间阵列天线波束合成计算李沙，颜毅华，王威，陈志军（中国科学院国家空间科学中心空间天气学国家重点实验室，北京100190）摘要：阵列天线广泛应用于多目标、多任务雷达系统中。

构建直线阵列、平面阵列天线的数学模型，借助Matlab 对不同模型的阵列天线方向图进行了仿真计算。

分析了一维阵列和二维阵列阵元个数、阵元间距以及阵元位置等因素对方向图的影响。

基于超材料的宽带高增益低雷达散射截面天线刘涛;曹祥玉;高军;杨群;李文强【摘要】Based on the metamaterial concept,a broad bandwidth high-gain and low radar cross section（RCS） patch antenna was designed and fabricated on the thinner substrate with the lower permittivity.The periodically loaded complementary triangular electromagnetic resonator （CTER） on the upper patch and strip-line gaps on the bottom ground plane were etched,respectively.Simulated analysis demonstrates that,dueto the left-handed characteristics of metamaterial,the effective medium parameters of substrate of antenna are affected,the wave propagation direction of antenna is further altered which induces the strongest radiation in horizontal direction instead of the vertical direction of the conventional patch pared with the original antenna,the novel antenna has a wider bandwidth significantly broadened from about 2.9%to about 64.5%,and also a low voltage standing wave ratio;the antenna has the lower RCS reduced above 5dB within the whole operation bandwidthat boresight direction,and the most reduction 22dB isobtained.Experimental data show good agreement between the simulation and measured results.%利用超材料概念,通过在天线贴片和接地面上分别蚀刻周期互补三角形电磁谐振单元（CTER）和条形缝隙图案,在低介电常数薄介质基板上设计并且制作了一种宽带高增益低雷达散射界面（RCS）贴片天线。

Electronically Scanned ArraysRobert J. MaillouxUniversity of Massachusetts, Amherst, MAMORGAN & CLAYPOOL PUBLISHING HOUSE2007ABSTRACTScanning arrays present the radar or communications engineers with the ultimate in antenna flexibility. They also present a multitude of new opportunities and new challenges that need to be addressed.In order to describe the needs for scanned array development,this book is a compact but comprehensive treatment of the scanned array, from the underlying basis for array pattern behavior to the engineering choices leading to successful design.The book describes the scanned array in terms of radiation from apertures and wire antennas and introduces the effects resulting directly from scanning, including beam broadening, impedance mismatch and gain reduction and pattern squint and those effects of array periodicity including grating and quantization lobes and array blindness.The text also presents the engineering tools for improving pattern control and array efficiency including lattice selection, subarray technology and pattern synthesis. Equations and figures quantify the phenomenon being described and provide the reader with the tools to trade-off various performance features. The discussions proceed beyond the introductory material and to the state of the art in modern array design.KEY WORDSAntenna array, phased array, scanning antenna, antenna design.PrefaceThis lecture is an introduction to the most important topics that dictate the behavior of scanning array antennas. It is intended to address the needs of engineers familiar with electromagnetics, microwave technology and antennas or antenna systems.The title of the book, Electronically Scanned Arrays employs the term “electronic scanning” rather than the more commonly used “phased”to emphasize that phase shifters and phase control are only one tool for array control. Of equal importance these days is the need for time delay devices and for active control of the amplitude distribution across the array.Much of this control can be done by analog phase shifters and switches, but future arrays will involve more use of digital and optical control where appropriate.The study of array antennas includes the electromagnetics of radiation and the interaction of various radiating array elements. It requires the understanding of a number of phenomenon peculiar to arrays and not the individual elements. Among these are the grating lobes that resulting directly from periodicity and many phenomenon that results from scanning, like the broadening of the array radiated beam, the reduction of gain, the varying interaction between elements and resulting impedance changes. These and other phenomenon characterize the behavior of scanning arrays.The lecture begins by introducing the basic parameters of arrays and presents methods for calculating in its simplest form, giving some mathematical detail for basic dipole elements in chapter 2 and arriving at the concept of an array element pattern. Chapter 3 introduces only a few basic techniques for pattern synthesis. This is a rich topic, but summarized here by several methods that are arguably by the most important ones.The final chapter treats one of the most fundamental issues of array design, how to group elements together to save on phase shifters, time delay units or digital beamforming ports. These groupings are called subarrays, and seeking optimized methods of forming subarrays is of continuing interest in this environment of increasing bandwidth and increasing array size.I am pleased to acknowledge the support of and many illuminating discussions with my colleagues at the Air Force Research Laboratory electromagnetic Technology Division over the years, and throughout numerous institutional name changes. I think my Air Force colleagues Allan Schell, Jay Schindler, Peter Franchi, Hans Steyskal, John Mcilvenna, Jeff Herd, Boris Tomasic, Livio Poles and David Curtis, and Arje Nachman of the Air Force Office of Scientific Research for the support of some of the fundamental aspects of antenna research.Robert J. MaillouxUniversity of Massachusetts, Amherst, MA。

第19卷 第6期 太赫兹科学与电子信息学报Vo1.19，No.62021年12月 Journal of Terahertz Science and Electronic Information Technology Dec.，2021文章编号：2095-4980(2021)06-1033-05Ku/Ka四波段共馈低剖面赋形天线设计张军，李杼，苏萌(92941部队44分队，辽宁葫芦岛 125003)摘 要：针对传统切换式多馈源的低剖面反射面天线结构复杂，不能多频段同时工作的问题，介绍了一款四波段单馈源低剖面环焦反射面天线及设计方法。

该天线工作在四波段14~14.5 GHz,11.45~12.75 GHz,19.6~21.2 GHz,29.4~31 GHz。

整体天线采用双槽深波纹喇叭单馈源、通过口面场分布和多项式拟合过渡函数的方法构造的赋形副反射面和主反射面。

用电磁仿真软件进行了建模仿真和验证。

实测结果表明，整体天线较传统天线的效率提高12%以上，第一旁瓣<-14 dB，指标满足设计要求。

关键词：赋形面；过渡函数；四波段；口面场分布中图分类号：TN820文献标志码：A doi：10.11805/TKYDA2020115Ku/Ka quad-band common-feed low-profile shaped antenna designZHANG Jun，LI Zhu，SU Meng(Unit 92941 of PLA，Huludao Liaoning 125003，China)Abstract：Traditional multi-band low-profile parabolic antennas bear the disadvantages of complex. All Rights Reserved.structure and the inability to multi-band work simultaneously. A novel design method is introduced in thispaper. The proposed quad-band antenna works on the frequency of 14-14.5 GHz,11.45-12.75 GHz,19.6-21.2 GHz,29.4-31 GHz. The whole antenna adopts a two-slot-depths horn feed, shaped sub-reflector andmain reflector. The reflectors are designed by the aperture field distribution function and polynomialtransition function. The overall antenna structure is optimized with full-wave electromagnetic software.The test result shows the efficiency in the entire frequency band is improved by at least 12%, and the firstside lobe is controlled below -14 dB, which meets the performance requirements. This design has beenapplied to actual equipment successfully.Keywords：shaped reflector；transition function；quad-band；aperture field distribution目前同步轨道卫星通信系统需求日新月异，用途越来越广泛，为了满足复合型多用途指挥战术要求，需要多频段、低剖面、功能齐全的车载卫星通信装备。

专利名称：APPARATUS AND METHOD FOR BEAM SCANNING PHASED ARRAY ANTENNA 发明人：ARUFURETSUDO AARU ROPESU申请号：JP8560487申请日：19870407公开号：JPS62243404A公开日：19871023专利内容由知识产权出版社提供摘要：A scanning system for a phased array antenna for operation at a selected frequency between a first frequency and a second frequency includes the storage of phase shift command signals for each of the phase shifters coupled to radiating elements of the antenna. The memory which stores the phase shift commands is addressed sequentially to provide for a step-wise scanning of a beam of radiant energy at a first frequency of the antenna. The addressing is accomplished by incrementing a count resulting from a counting of clock pulses. Compensation for the stepped positions of the beam for the difference between the selected frequency and the first frequency is accomplished by altering the number of pulses which increment the count of the addressing. The altering is accomplished by the storing of sequences of clock pulses at varying temporal spacings which are used for gating out selected ones of the incrementing pulses.申请人：HAZELTINE CORP更多信息请下载全文后查看。

ｄｏｉ：１０．３９６９／ｊ．ｉｓｓｎ．１００３－３１１４．２０２４．０２．０２１引用格式：于瑞涛，符道临，熊伟，等．基于智能超表面的二维相扫天线［Ｊ］．无线电通信技术，２０２４，５０（２）：３８６－３９１．［ＹＵＲｕｉｔａｏ，ＦＵＤａｏｌｉｎ，ＸＩＯＮＧＷｅｉ，ｅｔａｌ．Ｔｗｏ ｄｉｍｅｎｓｉｏｎａｌＰｈａｓｅ ｓｃａｎＡｎｔｅｎｎａＢａｓｅｄｏｎＲＩＳ［Ｊ］．ＲａｄｉｏＣｏｍｍｕｎｉｃａｔｉｏｎｓＴｅｃｈｎｏｌｏｇｙ，２０２４，５０（２）：３８６－３９１．］基于智能超表面的二维相扫天线于瑞涛１，符道临２，熊　伟１，陈　珲３（１．杭州市钱塘区信息高等研究院，浙江杭州３１００１８；２．江苏赛博空间科学技术有限公司，江苏南京２１１１１３；３．东南大学信息科学与工程学院，江苏南京２１００９６）摘　要：针对传统相控阵天线设计复杂、成本高昂等问题，提出了基于智能超表面（ＲｅｃｏｎｆｉｇｕｒａｂｌｅＩｎｔｅｌｌｉｇｅｎｔＳｕｒｆａｃｅ，ＲＩＳ）的空间馈电二维相扫天线。

该天线通过ＲＩＳ技术对来自馈源的电磁波进行相位操纵，实现了天线高增益和天线波束的可重构。

与传统相控阵天线相比，该天线具有结构简单、成本低廉、剖面极低等特点。

天线原型由一块含有１０２４个单元的超表面阵列、驱动模块及自支撑馈源组成，其中超表面阵列通过现场可编程门阵列（ＦｉｅｌｄＰｒｏｇｒａｍｍａｂｌｅＧａｔｅＡｒｒａｙ，ＦＰＧＡ）来实时控制以满足天线波束快速切换、方向图二维实时重构等需求。

超表面单元两种调控状态在６．５～１０．０ＧＨｚ具有低于０．５ｄＢ的幅度损耗，在７～１０ＧＨｚ频带范围内反射相位差在１８０°±５°以内。

天线原型在７．７、８．０、８．３ＧＨｚ的测试增益为２４．７２、２４．９２、２５．０６ｄＢｉ。

天线±６０°扫描增益滚降低于４ｄＢ。

关键词：智能超表面；相控阵天线；二维扫描中图分类号：ＴＮ８２ 文献标志码：Ａ 开放科学（资源服务）标识码（ＯＳＩＤ）：文章编号：１００３－３１１４（２０２４）０２－０３８６－０６Ｔｗｏ ｄｉｍｅｎｓｉｏｎａｌＰｈａｓｅ ｓｃａｎＡｎｔｅｎｎａＢａｓｅｄｏｎＲＩＳＹＵＲｕｉｔａｏ１，ＦＵＤａｏｌｉｎ２，ＸＩＯＮＧＷｅｉ１，ＣＨＥＮＨｕｉ３（１．ＨｏｎｇｚｈｏｕＱｉａｎｔａｎｇＡｄｖａｎｃｅｄＩｎｓｔｉｔｕｔｅｏｆＩｎｆｏｒｍａｔｉｏｎ，Ｈａｎｇｚｈｏｕ３１００１８，Ｃｈｉｎａ；２．ＪｉａｎｇｓｕＣｙｂｅｒｓｐａｃｅＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙＣｏ．，Ｌｔｄ．，Ｎａｎｊｉｎｇ２１１１１３，Ｃｈｉｎａ；３．ＳｃｈｏｏｌｏｆＩｎｆｏｒｍａｔｉｏｎＳｃｉｅｎｃｅａｎｄＥｎｇｉｎｅｅｒｉｎｇ，ＳｏｕｔｈｅａｓｔＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ２１００９６，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｎｏｒｄｅｒｔｏｓｏｌｖｅｔｈｅｐｒｏｂｌｅｍｓｏｆｃｏｍｐｌｅｘｄｅｓｉｇｎａｎｄｈｉｇｈｃｏｓｔｏｆｔｒａｄｉｔｉｏｎａｌｐｈａｓｅｄａｒｒａｙａｎｔｅｎｎａｓ，ａｓｐａｃｅ ｆｅｄｔｗｏ ｄｉｍｅｎｓｉｏｎａｌｐｈａｓｅ ｓｃａｎａｎｔｅｎｎａｂａｓｅｄｏｎＲｅｃｏｎｆｉｇｕｒａｂｌｅＩｎｔｅｌｌｉｇｅｎｔＳｕｒｆａｃｅ（ＲＩＳ）ｗａｓｐｒｏｐｏｓｅｄ．ＴｈｅａｎｔｅｎｎａｕｓｅｓＲＩＳｔｅｃｈｎｏｌｏｇｙｔｏｍａｎｉｐｕｌａｔｅｔｈｅｅｌｅｃｔｒｏｍａｇｎｅｔｉｃｉｎｃｏｍｉｎｇｗａｖｅｓｆｒｏｍｔｈｅｆｅｅｄ，ｗｈｉｃｈｒｅａｌｉｚｅｓｈｉｇｈｇａｉｎａｎｄｒｅｃｏｎｆｉｇｕｒａｂｉｌｉｔｙｏｆｔｈｅａｎｔｅｎｎａｂｅａｍ．Ｃｏｍｐａｒｅｄｗｉｔｈｔｒａｄｉｔｉｏｎａｌｐｈａｓｅｄａｒｒａｙａｎｔｅｎｎａｓ，ｔｈｉｓａｎｔｅｎｎａｈａｓｔｈｅｃｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆｓｉｍｐｌｅｓｔｒｕｃｔｕｒｅ，ｌｏｗｃｏｓｔａｎｄｌｏｗｐｒｏｆｉｌｅ．Ｔｈｅａｎｔｅｎｎａｐｒｏｔｏｔｙｐｅｃｏｎｓｉｓｔｓｏｆａｍｅｔａｓｕｒｆａｃｅａｒｒａｙｃｏｎｔａｉｎｉｎｇ１０２４ｃｅｌｌｓ，ａｄｒｉｖｅｒｍｏｄｕｌｅａｎｄａｓｅｌｆ ｓｕｐｐｏｒｔｉｎｇｆｅｅｄ，ｉｎｗｈｉｃｈｔｈｅｍｅｔａｓｕｒｆａｃｅａｒｒａｙｉｓｃｏｎｔｒｏｌｌｅｄｉｎｒｅａｌｔｉｍｅｔｈｒｏｕｇｈＦｉｅｌｄＰｒｏｇｒａｍｍａｂｌｅＧａｔｅＡｒｒａｙ（ＦＰＧＡ）ｔｏｍｅｅｔｔｈｅｒｅｑｕｉｒｅｍｅｎｔｏｆｒａｐｉｄａｎｔｅｎｎａｂｅａｍｓｗｉｔｃｈｉｎｇａｎｄｔｗｏ ｄｉｍｅｎｓｉｏｎａｌｒｅａｌ ｔｉｍｅｒｅｃｏｎｓｔｒｕｃｔｉｏｎｏｆｔｈｅｐａｔｔｅｒｎ．Ｔｗｏｃｏｎｔｒｏｌｓｔａｔｅｓｏｆｔｈｅｍｅｔａｓｕｒｆａｃｅｕｎｉｔｈａｖｅａｍｐｌｉｔｕｄｅｌｏｓｓｏｆｌｅｓｓｔｈａｎ０．５ｄＢｆｒｏｍ６．５ＧＨｚｔｏ１０．０ＧＨｚ，ａｎｄｔｈｅｒｅｆｌｅｃｔｅｄｐｈａｓｅｄｉｆｆｅｒｅｎｃｅｉｓｗｉｔｈｉｎ１８０°±５°ｉｎｔｈｅｆｒｅｑｕｅｎｃｙｂａｎｄｒａｎｇｅｆｒｏｍ７ＧＨｚｔｏ１０ＧＨｚ．Ｔｈｅａｎｔｅｎｎａｐｒｏｔｏｔｙｐｅｔｅｓｔｅｄｇａｉｎｓａｒｅ２４．７２ｄＢｉ，２４．９２ｄＢｉａｎｄ２５．０６ｄＢｉｒｅｓｐｅｃｔｉｖｅｌｙａｔ７．７ＧＨｚ，８．０ＧＨｚ，ａｎｄ８．３ＧＨｚ．Ｔｈｅａｎｔｅｎｎａ±６０°ｓｃａｎｌｏｓｓｉｓｄｏｗｎｔｏ４ｄＢ．Ｋｅｙｗｏｒｄｓ：ＲＩＳ；ｐｈａｓｅｄａｒｒａｙａｎｔｅｎｎａｓ；２Ｄｓｃａｎｎｉｎｇ收稿日期：２０２３－１１－１５０　引言面对日益增长的通信、探测等需求，传统线馈型相控阵技术路线存在成本高、设计复杂等缺点，难以满足未来通信／探测低成本、低功耗、智能化等迫切需求。

第 45 卷 第 2 期航天返回与遥感2024 年 4 月SPACECRAFT RECOVERY & REMOTE SENSING83激光通信中光学天线的隔离度研究马业辉 1,2 闫钧华 1,2 张超 1,2,3 刘剑峰 3（1 南京航空航天大学空间光电探测与感知工业和信息化部重点实验室，南京 211106）（2 南京航空航天大学航天学院，南京 211106）（3 北京空间机电研究所，北京 100094）摘　要　伴随激光通信组网和轻量化的需求以及收发一体化模式的普遍应用，实现光学天线发射和接收之间的高效隔离至关重要，为此文章对同轴天线与离轴天线的隔离度进行了研究。

首先采用Code V 光学设计软件分别设计了1 550 nm波段的同轴天线和离轴两反式天线，视场角为±1.5 mrad，接近衍射极限；再根据杂散光散射模型，利用分析软件进行光线追迹，模拟出隔离度；然后分别研究了在同轴天线次镜中心放置遮拦来规避开孔风险，以及在离轴天线中调整离轴量和曲率半径的方法，使同轴和离轴天线的隔离度分别提升至−69 dB和−89 dB。

结果表明，上述方法均能够有效提升光学天线的隔离度。

关键词　激光通信　光学天线　隔离度　杂散光中图分类号：TN929.1；V443+.4 文献标志码：A 文章编号：1009-8518(2024)02-0083-09DOI：10.3969/j.issn.1009-8518.2024.02.008Study on the Isolation of Optical Antennas in Laser Communication MA Yehui1,2 YAN Junhua1,2 ZHANG Chao1,2,3 LIU Jianfeng3（ 1 Key Laboratory of Space Photoelectric Detection and Perception, Ministry of Industry and Information Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China ）（ 2 College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China ）（ 3 Beijing Institute of Space Mechanics & Electricity, Beijing 100094, China ）Abstract　Accompanying the demands for laser communication network integration, lightweighting, and the widespread adoption of transceiver integration, achieving efficient isolation between optical antenna transmission and reception is crucial. This article thus investigates the isolation between coaxial and off-axis antennas. Initially, using Code V optical design software, coaxial antennas and off-axis two-reflective antennas operating in the 1 550 nm band were individually designed with a field of view angle of ±1.5 mrad, approaching the diffraction limit. Subsequently, based on the stray light scattering model, ray tracing was conducted using analysis software to simulate isolation. Methods were then studied to place baffles at the center of coaxial antenna secondary mirrors to mitigate aperture risk, and to adjust off-axis tilt and curvature radii in off-axis antennas. Ultimately, the isolation levels of coaxial and off-axis antennas were respectively increased to −69 dB and −89 dB. The results indicate that the aforementioned methods effectively enhance the isolation of optical antennas.Keywords　laser communication; optical antenna; isolation; stray light收稿日期：2024-01-17引用格式：马业辉, 闫钧华, 张超, 等. 激光通信中光学天线的隔离度研究[J]. 航天返回与遥感, 2024, 45(2): 83-91.MA Yehui, YAN Junhua, ZHANG Chao, et al. Study on the Isolation of Optical Antennas in Laser Communication[J].Spacecraft Recovery & Remote Sensing, 2024, 45(2): 83-91. (in Chinese)0　引言空间激光通信技术因其高信息承载能力、优越的光学增益和强大的干扰与截获防护性能而备受关注，被认为是目前处理高速通信挑战的关键手段[1-6]。