IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 64, NO. 3, MARCH 2016 953

Single-Feed Quad-Beam TransmitarrayAntenna Design

Ahmed H. Abdelrahman, Member, IEEE, Payam Nayeri, Member, IEEE, Atef Z. Elsherbeni, Fellow, IEEE,and Fan Yang, Senior Member, IEEE

Abstract—We present a design methodology for single-feedmultibeam transmitarray antennas through case studies of quad-beam designs. Different far-field pattern masks and fitness func-tions are studied for multibeam designs, and the particle swarmoptimization (PSO) technique is implemented for aperture phasesynthesis. A quad-layer configuration of double square loops isused for the transmitarray elements, and a quad-beam transmi-tarray prototype is fabricated and tested. The effects of variousapproximations in unit-cell analysis are also investigated in detail.The Ku-band prototype generates four symmetric beams with 50◦

elevation separation between the beams and gains around 23 dB.

Index Terms—Multibeam, particle swarm optimization (PSO),phase synthesis, transmitarray antenna.

I. INTRODUCTION

P LANAR transmitarray antennas have attracted a grow-ing interest in the area of high-gain antennas due to theirnumerous advantages [1], [2]. They combine the favorable fea-tures of optical lens and array antennas leading to a low-profileaperture and light weight design, which is well appropriatefor long distance communications and space applications [3].One of the main advantages of transmitarray antennas com-pared to dielectric lens is the individual phase control of eachtransmitarray element, which provides flexibility in array phasesynthesis, and hence is suitable for various applications thatrequire radiation pattern control [4]–[6].

Multibeam antennas receive considerable attention in space[7]–[8], radar [9]–[10], SAR [11], millimeter wave [12], andMIMO [13] applications. High-gain antennas with multiplesimultaneous beams are usually implemented using reflec-tors or lenses with feed-horn clusters, or large phased arrays.The main disadvantages of these structures are cost, size, andweight, mainly for space applications. Similar to reflectarrayantennas [14], [15], a transmitarray antenna with a single feed

Manuscript received June 08, 2015; revised October 29, 2015; acceptedDecember 31, 2015. Date of publication January 13, 2016; date of current ver-sion March 01, 2016. This work is supported by NSF Award # ECCS-1413863.

A. H. Abdelrahman is with the Millimeter Wave Circuits and AntennasLaboratory, Electrical and Computer Engineering Department, University ofArizona, Tucson, AZ 85721 USA (e-mail: abdelrahman@email.arizona.edu).

P. Nayeri and A. Z. Elsherbeni are with the Department of ElectricalEngineering and Computer Science, Colorado School of Mines, Golden, CO80401 USA (e-mail: pnayeri@mines.edu; aelsherb@mines.edu).

F. Yang is with the Microwave and Antenna Institute, Department ofElectronic Engineering, Tsinghua University, Beijing 100084, China (e-mail:fan_yang@tsinghua.edu.cn).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TAP.2016.2517660

can achieve multiple simultaneous beams with the added advan-tages of light weight and low-profile aperture [16], [17]. Incomparison to a multibeam reflectarray, the main advantageof a multibeam transmitarray is the inherent ability to avoidfeed blockage, which is typically a concern for simultaneousmultibeam patterns [15].

In this paper, we present a general design methodologyfor multibeam transmitarray antennas using a single sourcefeed, through case studies of several quad-beam designs. Itshould be noted that since all beam are generated with a sin-gle source, they carry the same signal. The particle swarmoptimization (PSO) technique is implemented to synthesize thetransmission phase of the transmitarray elements [18], and var-ious pattern masks and fitness functions are implemented formultibeam designs. A Ku-band quad-beam transmitarray pro-totype is fabricated and tested using quad-layer double squareloop (QLDSL) elements. Effects of oblique incidence andlocal periodicity approximation in the element design are alsoinvestigated in detail to determine their impacts on the ele-ment transmission coefficients and the overall antenna radiationpattern.

II. DESIGN OF SINGLE-FEED MULTIBEAMTRANSMITARRAY ANTENNAS

A. Design Methodologies

In transmitarray antennas, the element amplitudes are fixedby the properties of the feed and the element locations.However, the elements of a transmitarray antenna have the flex-ibility to achieve any value of phase shift. Utilizing this directcontrol of phase shift for every element, the phase distribu-tion on the array aperture can be synthesized to achieve anydesired pattern shape, such as multibeam patterns. Accordingly,the design procedure of the proposed transmitarray antennastarts with synthesis of the transmission phase distribution ofthe array aperture using PSO technique. Once the requiredtransmission phase is determined for each element, the corre-sponding element dimension is obtained using the transmis-sion phase versus element dimension curve, which is usuallyobtained from the unit-cell full EM wave analysis.

Two different synthesis approaches are available for single-feed multibeam space-fed arrays, i.e., direct analytical solutionsor optimization methods. While analytical solutions are typ-ically simple to implement, recent studies [14] have shownthat the performance of these methods is not satisfactory inmany cases. Optimization methods on the other hand have the

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954 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 64, NO. 3, MARCH 2016

Fig. 1. Quad-layer unit-cell configuration of a double square loop element.(a) Top view. (b) Side view.

potential to find a solution to the synthesis problem; however,they typically require long computational time to converge [15].

In this study, we use the PSO global search method to syn-thesize the aperture phase distribution of transmitarray antennasfor multibeam performance. Far-field pattern masks are definedbased on the design requirements, and different fitness func-tions are studied to achieve optimal beam performance andsidelobe level. Pattern computation is conducted efficientlyusing an in-house code, which is based on the array theoryformulation with spectral transformations for computationalspeedup [19].

B. Design of Single-Feed Quad-Beam Transmitarray Antennasat Ku-Band

To demonstrate the feasibility of the proposed design tech-nique for single-feed multibeam transmitarray antennas, westudy a symmetric quad-beam system. The elevation separa-tion between the four beams is designed to be 50◦, such thatthe four beams are pointing at ϑ1,2,3,4 = 25◦, ϕ1 = 0◦, ϕ2 =90◦, ϕ3 = 180◦, and ϕ4 = 270◦. The transmitarray is designedfor the center operating frequency of 13.5 GHz.

A linearly polarized corrugated conical horn with a gainequal to 16.3 dB at 13.5 GHz is used as the feed antenna. Thephase center of the horn is placed at a distance of 275 mm fromthe transmitarray antenna aperture. For the simulation model,the radiation pattern of this feed is approximated with a cosq (θ)model with q = 9.25.

The array has a circular aperture with a diameter of 311 mmconsisting of 648 elements. The elements are QLDSL asdescribed in [20]. The element configuration and design param-eters are shown in Fig. 1.

The unit-cell simulations were carried out using CSTMicrowave Studio software [21]. The optimum dimensions ofthe separation between the two loops (S) and the loop width(W) were determined through parametric analysis aiming toachieve an optimal linear slope of the transmission phase, undernormal incidence excitation. These dimensions were deter-mined to be S = 0.2 L1 and W = 4.2 mm, and phase tuningis achieved by varying the length L1 from 6.6 to 10.4 mm.L1 is the only variable parameter, S and L2 are dependentparameters of L1. The four-layers of the unit-cell are identical.The elements are printed on a Taconic TLX-8 dielectric sub-strate with permittivity �r = 2.574 and thickness T = 0.5 mm.The periodicity of the unit-cell element is P = 11.1 mm, and

Fig. 2. Transmission coefficient of the QLDSL element with normal incidenceat 13.5 GHz.

the separation between layers is equal to H = 5 mm, whichcan achieve a 360◦ transmission phase range with transmissionmagnitudes better than −1.2 dB at 13.5 GHz [2], as shown inFig. 2.

Three different design models are investigated for quad-beamtransmitarray antennas. First, we consider two different patternmasks: a constant sidelobe level of −30 dB (Design 1), and atapered mask with −25 dB SLL at the first sidelobe to −40 dBat ϑ = 90◦ (Design 2). A two term fitness function is defined,which evaluates the radiation performance of the array in termsof the peak gain for each beam and sidelobe level in the entireangular space based on the mask requirements as described in[15]. The fitness function to be minimized is

Cost =W1∑

(u,v)/∈mainbeamand |F (u,v)|>MU (u,v)

∑(|F (u, v)| −MU (u, v))2

+W2∑

(u,v)∈mainbeamand |F (u,v)|

ABDELRAHMAN et al.: SINGLE-FEED QUAD-BEAM TRANSMITARRAY ANTENNA DESIGN 955

TABLE ICOMPARISON OF THREE DIFFERENT DESIGN MODELS FOR SINGLE-FEED

QUAD-BEAM TRANSMITARRAY ANTENNAS

Fig. 3. (a) Synthesized phase distribution. (b) Radiation pattern mask.(c) Simulated radiation patterns for the quad-beam transmitarray antenna at13.5 GHz.

space, and thus was selected for fabrication. The synthesizedphase distribution on the aperture, the pattern mask, and theradiation patterns for this design are given in Fig. 3.

III. PROTOTYPE FABRICATION AND MEASUREMENTS

The optimized quad-beam prototype is fabricated using acommercial PCB etching process. The mask and photographof one layer of the fabricated array with 648 QLDSL elementsare shown in Fig. 4. The fabricated prototype is tested using theNSI planar near-field measurement system at the University ofMississippi. An image of the test setup is shown in Fig. 5.

The far-field radiation patterns for y-polarized feed-horn aredepicted in Fig. 6, which show a good quad-beam performance.The four beams are located at elevation angle θ1,2,3,4 = 25◦,

Fig. 4. One layer of the fabricated quad-beam transmitarray prototype.(a) Mask. (b) Photograph.

Fig. 5. Measurement setup of the quad-beam transmitarray antenna in the NSIplanar near-field system.

Fig. 6. Far-field patterns. (a) xz-plane. (b) yz-plane. (c) 3-D pattern.

except a 1◦ shift in one beam, and azimuth angles φ1 =0◦,φ2 = 90◦,φ3 = 180◦, and φ4 = 270◦ as desired. The mea-sured gain of the two beams along the yz-plane are the sameand equal to 23.8 dB, and those along the xz-plane are equal to22.3 dB and 22.6 dB. Note that the simulated gain is 24.77 dBfor each beam. The sidelobe and cross polarized levels are lessthan −14 dB and −30 dB, respectively.

956 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 64, NO. 3, MARCH 2016

Fig. 7. Transmission coefficients of the QLDSL element versus element dimen-sion L1. (a) Magnitude of elements along x-axis. (b) Phase of elements alongx-axis. (c) Magnitude of elements along y-axis. (b) Phase of elements alongy-axis.

The gain reduction of 1.5 and 1.2 dB observed for the twobeams along the xz-plane in comparison with the other twobeams along the yz-plane is primarily attributed to polarizationeffects [3]. Additionally, the higher sidelobe levels observedin the measured results are attributed to fabrication toler-ances, and approximation errors in the unit-cell analysis, whichinclude normal incidence and local periodicity approximations.Detailed investigations on these sources of error are conductedand presented in the following sections.

IV. EFFECTS OF VARIOUS APPROXIMATIONS

A. Oblique Incidence Effects on the Element Performance

In this section, we study the transmission performance of thephasing elements under oblique incidence excitation. The aimof this study is to investigate the potential errors due to normalincidence approximation in the element design. Fig. 7 depictsthe variations in the transmission magnitude and phase of theQLDSL element at different oblique incidence angles and fory-polarized incidence wave. The parameters θ and ϕ are theelevation and azimuth angles of the incident wave, respectively.

The results shown here indicate that despite some minor dif-ferences, the transmission magnitude and phase of the elementsdo not differ significantly with the normal incidence case forelevation angles up to 30◦. It should be noted, however, thatfor the case of L1 = 9.4 mm, when placed along the x-axis(ϕ = 0◦), the element does exhibit a resonance for obliqueexcitation angles that significantly degrades its performance.However, the fabricated prototype only has four elements withthis dimension, which are not along the x-axis, and are close tothe aperture edge, thus they also exhibit a weaker taper. In sum-mary, the errors arising from the normal incident approximationare relatively small, and the discrepancies between measuredand simulated results are not attributed to this approximation.

B. Variations in Dimensions of Neighbor Elements

In multibeam space-fed arrays, the aperture phase distri-bution is considerably different than traditional single-beam

Fig. 8. Large unit-cell analysis.

designs. For the latter, the elements exhibit a smooth phasevariation between their neighboring elements and phase wraps(element dimension jumping from a maximum to minimum orvice versa) are only observed at the edge of the Fresnel zones.As such, local periodicity is generally considered to be a reason-able approximation. For multibeam designs, however, the phasedistribution on the aperture is quite complex and significant dif-ferences between each element and its surrounding neighborelements are observed (see Fig. 4). Accordingly, the approxi-mations in the traditional unit-cell analysis, which consider allelements to be identical, could lead to noticeable error in thetransmission coefficient values.

In order to investigate the accuracy of the unit-cell elementapproximations, a large unit-cell consisting of nine neighborelements is studied, which is known as the surrounded ele-ment approach [22]. Three different cases, as shown in Fig. 8,are simulated using CST Microwave Studio software [21]. Thedimensions L1 of the center element for the three cases are7.2, 7.75, and 8.85 mm, respectively. The dimensions of theother neighbor elements are selected according to their actualdimensions in the designed quad-beam transmitarray prototype.

The transmission coefficients of the three cases are com-pared with those of the conventional unit-cell element in Fig. 9.Due to the asymmetry of the large unit-cell, the transmis-sion coefficients for both perpendicular (TE) and parallel (TM)polarizations are considered [3]. It can be seen that Case 1) andCase 2) both show large phase error and magnitude loss whencompared with the conventional unit-cell element. Case 3) onthe other hand shows almost no significant change in the trans-mission coefficient values. This is due to the fact that thedimensional difference between the elements in this case issmall compared to the other two cases. This study shows thatthe local periodicity approximation appears to be the primaryreason for the transmission coefficient errors of the elements.

ABDELRAHMAN et al.: SINGLE-FEED QUAD-BEAM TRANSMITARRAY ANTENNA DESIGN 957

Fig. 9. Transmission coefficients of the large unit-cell compared with theconventional unit-cell. (a) Magnitude. (b) Phase.

Fig. 10. Average radiation patterns of 20 trials for different standard deviationsof the random phase error distribution.

Fig. 11. Average radiation patterns of 20 trials for different standard deviationsof the random magnitude loss distribution.

C. Impact of Element Phase Error and Magnitude Loss onAntenna Radiation Pattern

The potential sources of error were investigated in the previ-ous two sections and it was shown that approximation of localperiodicity led to significant inaccuracies in the transmissioncoefficients values of the elements. Here, we study the effectof both transmission phase error and loss of the elements onthe radiation pattern of the quad-beam transmitarray prototype.For phase error analysis, a random phase is added to the actualphase of each element using a normal distribution with meanvalue of 0◦. The standard deviation for this normal distribu-tion ranges from 0◦ to 60◦. For each standard deviation value,the average normalized radiation pattern of 20 trials is demon-strated in Fig. 10. In the same way, the effects of elementloss is analyzed, by adding a random loss to the actual mag-nitude of each element using a normal distribution with meanvalue of 0 dB and with different standard deviation values thatrange from 0 to −15 dB. Because the magnitude loss leads to areduction in the transmission magnitude, the random magnitudelosses must be negative values. Similar to the phase error anal-ysis, for each standard deviation value, the average normalizedradiation pattern of 20 trials is presented in Fig. 11.

The results given in Figs. 10 and 11 reveal that while bothphase error and magnitude loss of the transmitarray elements

have little effect on the direction of the main beams, they signif-icantly increase the sidelobe levels. In particular, the sidelobesin the area between the four beams increases by 20 dB witha 40◦ mean random phase error. Moreover, when analyzingeach of the 20 trials individually, we noticed that a very smallbeam-shift could occur due to the local periodicity approxima-tion. Based on the studies presented in Sections IV-A and IV-B,the authors believe that the primary reasons for the discrepan-cies between measured and simulated gain values are attributedto phase and magnitude errors of the elements arising from thelocal periodicity approximation, as well as fabrication errors.

V. CONCLUSION

The feasibility of designing single-feed multibeam transmi-tarray antennas is demonstrated through the design of quad-beam patterns. The PSO method is used to synthesize the aper-ture phase distribution of the transmitarray, and various patternmasks and fitness functions are studied for multibeam designs.A Ku-band single-feed quad-beam transmitarray antenna with50◦ elevation separation between the beams is designed, fabri-cated, and tested at 13.5 GHz by using QLDSL elements. Thearray has a circular aperture with a diameter of 311 mm. Themeasured gains of four beams are 23.8, 23.8, 22.3, and 22.6 dB,respectively. Furthermore, the impact of unit-cell approxima-tions during simulation process is studied, and then the effectsof phase error and magnitude loss of the unit-cell element onthe antenna patterns are demonstrated.

REFERENCES

[1] A. Yu, F. Yang, A. Z. Elsherbeni, and J. Huang, “Transmitarray antennas:An overview,” in Proc. IEEE Antennas Propag. Soc. (APS/URSI) Symp.,Jul. 2011.

[2] A. H. Abdelrahman, F. Yang, and A. Z. Elsherbeni “Transmissionphase limit of multilayer frequency selective surfaces for transmitarraydesigns,” IEEE Trans. Antennas Propag., vol. 62, no. 2, pp. 690–697,Feb. 2014.

[3] A. H. Abdelrahman, A. Z. Elsherbeni, and F. Yang, “Transmitarrayantenna design using cross slot elements with no dielectric substrate,”IEEE Antennas Wireless Propag. Lett., vol. 13, pp. 177–180, Feb. 2014.

[4] P. Nayeri, F. Yang, and A. Z. Elsherbeni, “Design of multifocal transmi-tarray antennas for beamforming applications,” in Proc. IEEE AntennasPropag. Soc. Int. Symp. (AP-S), Jul. 2013, pp. 1672–1673.

[5] A. Clemente, L. Dussopt, R. Sauleau, P. Potier, and P. Pouliguen,“Wideband 400-element electronically reconfigurable transmitarray in X-band,” IEEE Trans. Antennas Propag., vol. 61, no. 10, pp. 5017–5027,Oct. 2013.

[6] J. Y. Lau and S. V. Hum, “A wideband reconfigurable transmitarray ele-ment,” IEEE Trans. Antennas Propag., vol. 60, no. 3, pp. 1303–1311,Mar. 2012.

[7] G. Zheng, S. Chatzinotas, and B. Ottersten, “Generic optimization oflinear precoding in multibeam satellite systems”, IEEE Trans. WirelessCommun., vol. 11, no. 6, pp. 2308–2320, Jun. 2012.

[8] S. A. Hasan, “Highly reliable & wideband digital multi beamforminghorn array antenna with gain adjustment capabilities for space applica-tions,” in Proc. China-Japan Joint Microw. Conf. (CJMW), Apr. 2011.

[9] I. Slomian, P. Kaminski, J. Sorocki, I. Piekarz, K. Wincza, andS. Gruszczynski, “Multi-beam and multi-range antenna array for 24 GHzradar applications,” in Proc. IEEE 20th Int. Conf. Microw. RadarsWireless Commun. (MIKON), Jun. 2014.

[10] B. Schoenlinner and G. M. Rebeiz, “Compact multibeam imagingantenna for automotive radars,” in Proc. IEEE MTT-S Int. Microw. Symp.Dig., Seattle, WA, USA, Jun. 2002, vol. 2, pp. 1373–1376.

[11] G. Wen-jun and L. Xiao-meng, “Amplitude-only optimizing methodof multi-subaperture multi-beam antenna for SAR applications,” inProc. IEEE Int. Conf. Electron. Commun. Control (ICECC), Sep. 2011,pp. 117–120.

958 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 64, NO. 3, MARCH 2016

[12] M. Ettorre, R. Sauleau, and L. Le Coq, “Multi-beam multi-layer leaky-wave siw pillbox antenna for millimeter-wave applications,” IEEE Trans.Antennas Propag., vol. 59, no. 4, pp. 1093–1100, Apr. 2011.

[13] K. Kagoshima, S. Takeda, and K. Itou, “Array excitation coefficients ofa compact multi-beam antenna for MIMO applications,” in Proc. IEEE-APS Topical Conf. Antennas Propag. Wireless Commun. (APWC), Aug.2014, pp. 195–198.

[14] P. Nayeri, F. Yang, and A. Z. Elsherbeni, “Design and experiment ofa single-feed quad-beam reflectarray antenna,” IEEE Trans. AntennasPropag., vol. 60, no. 2, pp. 1166–1171, Feb. 2012.

[15] P. Nayeri, F. Yang, and A. Z. Elsherbeni, “Design of single-feed reflectar-ray antennas with asymmetric multiple beams using the particle swarmoptimization method,” IEEE Trans. Antennas Propag., vol. 61, no. 9,pp. 4598–4605, Sep. 2013.

[16] A. H. Abdelrahman, P. Nayeri, A. Z. Elsherbeni, and F. Yang, “Design ofsingle-feed multi-beam transmitarray antennas,” in Proc. IEEE AntennasPropag. Soc. Int. Symp., Jul. 2014, pp. 1264–1265.

[17] S. H. Zainud-Deen, S. M. Gaber, H. A. Malhat, and K. H. Awadalla,“Perforated transmitarray-enhanced circularly polarized antennas forhigh-gain multi-beam radiation,” in Proc. IEEE Int. Symp. AntennasPropag. (ISAP), Oct. 2013, pp. 484–487.

[18] D. W. Boeringer and D. H. Werner, “Particle swarm optimization ver-sus genetic algorithms for phased array synthesis,” IEEE Trans. AntennasPropag., vol. 52, no. 3, pp. 771–779, Mar. 2004.

[19] P. Nayeri, A. Z. Elsherbeni, and F. Yang, “Radiation analysis approachesfor reflectarray antennas,” IEEE Antennas Propag. Mag., vol. 55, no. 1,pp. 127–134, Feb. 2013.

[20] A. H. Abdelrahman, P. Nayeri, A. Z. Elsherbeni, and F. Yang, “Analysisand design of wideband quad-layer transmitarray antennas,” IEEE Trans.Antennas Propag., vol. 63, no. 7, pp. 2946–2854, Jul. 2015.

[21] CST Microwave Studio, version 2012.01, Feb. 24, 2012.[22] M-A. Milon, D. Cadoret, R. Gillard, and H. Legay, “Surrounded-element

approach for the simulation of reflectarray radiating cells,” IET Microw.Antennas Propag., vol. 1, no. 2, pp. 289–293, Apr. 2007.

Ahmed H. Abdelrahman (S’13–M’15) receivedthe B.S. degree in electrical engineering and theM.S. degree in electronics and communications fromAin Shams University, Cairo, Egypt, and the Ph.D.degree in engineering sciences from the University ofMississippi, University, MS, USA, in 2001, 2010, and2014, respectively.

He is currently a Postdoctoral Research Associatewith the Department of Electrical and ComputerEngineering, University of Arizona, Tucson, AZ,USA. He also possesses over eight years of expe-

rience in Satellite Communications industry. He worked as a RF DesignEngineer and a Communication System Engineer in building the low earth orbitsatellite Egyptsat-1. His research interests include transmitarray/reflectarrayantennas, mobile antennas, 3-D printed antennas, and thermoacoustic andmillimeter-wave imaging.

Dr. Abdelrahman was the recipient of the several prestigious awards, includ-ing the third place Winner Student Paper Competition Award at the 2013 ACESAnnual Conference, and the Honorable Mention Student Paper Competition atthe 2014 IEEE AP-S International Symposium on Antennas and Propagation.

Payam Nayeri (S’09–M’12) received the B.Sc.degree in applied physics from Shahid BeheshtiUniversity, Tehran, Iran, the M.Sc. degree in elec-trical engineering from Iran University of Scienceand Technology, Tehran, Iran, and the Ph.D. degreein electrical engineering from the University ofMississippi, University, MS, USA, in 2004, 2007, and2012, respectively.

From 2008 to 2013, he was with the Centerfor Applied Electromagnetic Systems Research(CAESR), University of Mississippi. Prior to this,

he was a Visiting Researcher at the University of Queensland, Brisbane,QLD, Australia. From August 2012 to December 2013, he was a PostdoctoralResearch Associate and an Instructor with the Department of ElectricalEngineering, University of Mississippi. From January 2014 to June 2015, hewas a Postdoctoral Fellow with the Department of Electrical Engineering andComputer Science, Colorado School of Mines, Golden, CO, USA. He joinedthe Department of Electrical Engineering and Computer Science, Colorado

School of Mines, as an Assistant Professor in July 2015. He has authoredover sixty journal articles and conference papers. His research interests includeantennas, arrays, and RF/microwave devices and systems, with applications indeep space communications, microwave imaging, and remote sensing.

Dr. Nayeri is a member of Sigma Xi, and Phi Kappa Phi. He was the recipientof several prestigious awards, including the IEEE Antennas and PropagationSociety Doctoral Research Award in 2010, the University of MississippiGraduate Achievement Award in Electrical Engineering in 2011, and the BestStudent Paper Award of the 29th International Review of Progress in ACES.

Atef Z. Elsherbeni (S’84–M’86–SM’91–F’07)received the B.Sc. degree (Hons.) in electronicsand communications, the B.Sc. degree (Hons.) inapplied physics, and the M.Eng. degree in electricalengineering, all from Cairo University, Cairo, Egypt,and the Ph.D. degree in electrical engineering fromManitoba University, Winnipeg, MB, Canada, in1976, 1979, 1982, and 1987, respectively.

He joined as Faculty at the University ofMississippi, University, MS, USA, in August 1987,as an Assistant Professor of Electrical Engineering.

He advanced to the rank of Associate Professor in 1991, and to the rank ofProfessor in 1997. He was appointed as an Associate Dean of Engineeringfor Research and Graduate Programs in 2009. He became the DobelmanDistinguished Chair and Professor of Electrical Engineering with ColoradoSchool of Mines, Golden, CO, USA, in August 2013. He was appointedas an Adjunct Professor with the Department of Electrical Engineering andComputer Science, Syracuse University, Syracuse, NY, USA, in 2004. Hespent a sabbatical term in 1996 at the Electrical Engineering Department,University of California at Los Angeles (UCLA), Los Angeles, CA, USA,and was a Visiting Professor at Magdeburg University, Magdeburg, Germany,in 2005 and Tampere University of Technology, Tampere, Finland, in 2007.From 2009 to 2011, he was a Finland Distinguished Professor selected bythe Academy of Finland and TEKES. He is the coauthor of the booksAntenna Analysis and Design Using FEKO Electromagnetic SimulationSoftware, ACES Series on Computational Electromagnetics and Engineering,(SciTech, 2014), Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects (Morgan and Claypool,2013), Scattering Analysis of Periodic Structures Using Finite-Difference Time-Domain Method (Morgan and Claypool, 2012), Multiresolution FrequencyDomain Technique for Electromagnetics (Morgan and Claypool, 2012), TheFinite Difference Time Domain Method for Electromagnetics with MatlabSimulations, (SciTech, 2009), Antenna Design and Visualization Using Matlab(SciTech, 2006), MATLAB Simulations for Radar Systems Design (CRCPress, 2003), Electromagnetic Scattering Using the Iterative MultiregionTechnique (Morgan & Claypool, 2007), Electromagnetics and AntennaOptimization using Taguchi’s Method, (Morgan & Claypool, 2007), ScatteringAnalysis of Periodic Structures Using Finite-Difference Time-Domain Method,(Morgan & Claypool, 2012), Multiresolution Frequency Domain Technique forElectromagnetics, (Morgan and Claypool, 2012), and the main author of thechapters Handheld Antennas and The Finite Difference Time Domain Techniquefor Microstrip Antennas in Handbook of Antennas in Wireless Communications(CRC Press, 2001). He was the advisor/coadvisor for 33 M.S. and 20 Ph.D.students.

Dr. Elsherbeni is a Fellow Member of ACES. He is the Editor-in-Chief for ACES Journal, and a past Associate Editor to the Radio ScienceJournal. He was the Chair of the Engineering and Physics Division of theMississippi Academy of Science and was the Chair of the Educational ActivityCommittee for the IEEE Region 3 Section. He was the General Chair forthe APS-URSI 2014 Symposium. He held the President position of ACESSociety from 2013 to 2015. He was the recipient of the 2013 AppliedComputational Electromagnetics Society (ACES) Technical AchievementsAward, the 2012 University of Mississippi Distinguished Research andCreative Achievement Award, the 2006 and 2011 School of EngineeringSenior Faculty Research Award for Outstanding Performance in research,the 2005 School of Engineering Faculty Service Award for OutstandingPerformance in Service, the 2004 ACES Valued Service Award for OutstandingService as 2003 ACES Symposium Chair, Mississippi Academy of Science2003 Outstanding Contribution to Science Award, the 2002 IEEE Region 3Outstanding Engineering Educator Award, the 2002 School of EngineeringOutstanding Engineering Faculty Member of the Year Award, the 2001 ACESExemplary Service Award for leadership and contributions as an ElectronicPublishing Managing Editor 1999–2001, the 2001 Researcher/Scholar ofthe Year Award in the Department of Electrical Engineering, University ofMississippi, and 1996 Outstanding Engineering Educator of the IEEE MemphisSection.

ABDELRAHMAN et al.: SINGLE-FEED QUAD-BEAM TRANSMITARRAY ANTENNA DESIGN 959

Fan Yang (S’96–M’03–SM’08) received the B.S.and M.S. degrees from Tsinghua University, Beijing,China, and the Ph.D. degree from the University ofCalifornia at Los Angeles (UCLA), Los Angeles, CA,USA, in 1997, 1999, and 2002, respectively.

From 1994 to 1999, he was a Research Assistantwith the State Key Laboratory of Microwave andDigital Communications, Tsinghua University. From1999 to 2002, he was a Graduate Student Researcherwith the Antenna Laboratory, UCLA. From 2002 to2004, he was a Postdoctoral Research Engineer and

Instructor with the Electrical Engineering Department, UCLA. In 2004, hejoined the Department of Electrical Engineering, University of Mississippi,University, MS, USA, as an Assistant Professor, and was promoted toan Associate Professor. In 2011, he joined the Department of ElectronicEngineering, Tsinghua University, Beijing, China, as a Professor, and hasserved as the Director of the Microwave and Antenna Institute since then.He has authored over 200 journal articles and conference papers, five bookchapters, and three books entitled Scattering Analysis of Periodic StructuresUsing Finite-Difference Time-Domain Method (Morgan & Claypool, 2012),Electromagnetic Band Gap Structures in Antenna Engineering (CambridgeUniv. Press, 2009), and Electromagnetics and Antenna Optimization UsingTaguchi’s Method (Morgan & Claypool, 2007). His research interests includeantennas, periodic structures, computational electromagnetics, and appliedelectromagnetic systems.

Dr. Yang served as an Associate Editor of the IEEE TRANSACTIONS ONANTENNAS AND PROPAGATION (2010–2013) and an Associate Editor-in-Chief of Applied Computational Electromagnetics Society (ACES) Journal(2008–2014). He was the Technical Program Committee (TPC) Chair ofthe 2014 IEEE International Symposium on Antennas and Propagation andUSNC-URSI Radio Science Meeting. He was the recipient of several pres-tigious awards and recognitions, including the Young Scientist Award ofthe 2005 URSI General Assembly and the 2007 International Symposiumon Electromagnetic Theory, the 2008 Junior Faculty Research Award of theUniversity of Mississippi, the 2009 inaugural IEEE Donald G. Dudley Jr.Undergraduate Teaching Award, and the 2011 Recipient of Global ExpertsProgram of China.