Spatially Modulated Metamaterial Array for Transmit (SMMArT) and Slow-Leaky-Wave Antennas

Transcription

1 Spatially Modulated Metamaterial Array for Trasmit (SMMArT) ad Slow-Leaky-Wave Ateas Alessadro Saladrio, Patrick M. McCormick, Mario D. Balcazar, ad Shao D. Blut Radar Systems Lab (RSL), Uiversity of Kasas Lawrece, KS, USA Abstract Waveform diversity (WD) has the potetial to profoudly impact radar operatio through ew advatageous uses of desig degrees-of-freedom as log as the waveform ad sigal processig structure ca be appropriately married to the physical electromagetic (EM) ad system operatio. Withi this cotext, the EM behavior of the recetly itroduced Spatially Modulated Metamaterial Array for Trasmit (SMMArT) cocept, itself a realizatio of a special class of MIMO radar deoted as spatial modulatio, is aalyzed by meas of full-wave fiite-elemets simulatios. Radiatio patters uder various forms of excitatio are calculated. A parametric study of a slotted Clarricoats-Waldro waveguide (CWW) is preseted that idetifies the practical feasibility of desig costraits that must be cosidered i order to suppress udesired itermodal couplig. Keywords Slow Waves; Slotted Waveguides; Leaky Wave Ateas; Metamaterials; MIMO Radar; Spatial Modulatio. I. INTRODUCTION To achieve may of the promised advaces of waveform diversity (WD) [1-3] i practical radar systems ecessitates a holistic perspective i which all aspects of the radar operatio are cosidered, from the physical electromagetic iterface to the waveforms ad sigal processig [4,5]. The particular WD topic of multiple-iput multiple-output (MIMO) radar has received sigificat attetio over the last decade [6], alog with cotroversy over realism ad practical applicatio to existig modalities [7,8]. The physical realizatio of MIMO radar requires cosideratio of the fudametal costraits imposed by the uderlyig physics of electromagetic radiatio i additio to the sigal processig attributes ad waveform characteristics. Therefore, mergig electromagetic theory, sigal processig, ad radio frequecy (RF) system egieerig is ecessary. Fast-time spatial modulatio represets a special-case of MIMO that mimics the actuatio of the huma eye by geeratig a coheret trasmit beam that moves about a ceter look directio durig each pulse [9,10], thereby couplig the space ad rage dimesios which icreases the degrees the freedom available for receive processig [11]. Beig based o FM waveforms that maitai a coheret beam, spatial modulatio is less susceptible tha geeral MIMO to mutual couplig effects [12-14] ad avoids the problem of emittig ito the ivisible space [15,16]. I fact, spatial modulatio actually subsumes the frequecy diverse array (FDA) cocept [17-20] by permittig arbitrary beam-steerig i fast-time. Recetly, a particular implemetatio of this emissio scheme, deoted as the Spatially Modulated Metamaterial Array for Trasmit (SMMArT) [21], was coceived by ispiratio from slow-light optics [22,23]. The SMMArT implemetatio eables fast-time spatial modulatio without requirig the hardware complexity of separate arbitrary waveform geeratio capability at every atea elemet/subarray. I its simplest istatiatio the SMMArT structure comprises a serially-fed slotted waveguide possessig a metamaterial dielectric core (to provide slow group velocity) ad drive by a sigle waveform geerator, yet it ca realize spatial modulatio i oe dimesio ad readily emulate the FDA [17-20] whe drive by a liear FM (LFM) waveform [21]. It is evisioed that more sophisticated versios will provide 2D spatial modulatio [16] as well as fast-time polarizatio modulatio [24]. Here a computatioal electromagetic study of SMMArT is preseted alog with evaluatio of the far-field emissio geerated whe the SMMArT structure is drive by a arbitrary FM waveform. II. SMMART PRINCIPLE OF OPERATION The SMMArT architecture is a geeralizatio of the wellkow slotted waveguide frequecy scaed array (e.g. [25-27]) to icorporate FM pulse compressio, a cocept that was first proposed by Mile i 1964 [28]. The specific attributes of SMMArT are 1) use of a metamaterial dielectric core to achieve slow group velocity ad 2) leveragig the structure of ew FM waveform implemetatio/optimizatio methods (e.g. [29-33]). Collectively, these factors establish a desig space that ecompasses both the electromagetic operatio of the slotted waveguide array ad the waveform structure to facilitate their joit optimizatio for the far-field emissio. Figure 1. Schematic of a serially-fed array of ateas represeted by their imput impedaces Z i. SMMArT is based o a costraied series travelig-wave (o-resoat) feed architecture, as schematically illustrated i Figure 1. I terms of beam-steerig mechaism, SMMArT departs from covetioal frequecy-scaed leaky-wave ateas [34] by virtue of relyig o a slow-group-velocity

2 trasmissio lie i order to perform itra-pulse ad iter-pulse radiatio-patter modulatio. Per Figure 1, cosider a idealized model i which the shut impedeces distributed alog the trasmissio-lie are the radiatio resistaces of a set of idetical isotropic radiators located at the Cartesia positios r =(0,0,z ). The curret desity over the radiatig elemets ca be writte as J ( z, t) I( t) ( z z). (1) We assume a voltage waveform at the geerator with amplitude V 0 (t) ad phase φ(t) such that V ( t) ( ) j () t V0 t e. (2) The amplitudes I (t) are related to the iput voltage waveform of (2) as 1 z I () t V0 t e Z v g z j t v p where v g ad v p are the group velocity ad phase velocity, respectively. Figure 2. Spatial ad temporal distributio of a pulse i a waveguide with group velocity v g=c (left colum) ad i a waveguide with v g=c/10 (right colum). All distaces are ormalized with respect to the vacuum wavelegth λ. The temporal traces are evaluated over the blue lies, ad the spatial traces are evaluated over the red lies. (3) The radiated far-field i spherical coordiates ca be obtaied from Jefimeko s equatios [35] applied to (1) ad (3) as r z cos z j t 1 c r vp N 1 1 r z E r,, t V0 t e. r 1 Z c vg (4) I geeral, (4) ca be applied to ay serially-fed array, where the distictive feature of the SMMArT array is a low-groupvelocity trasmissio lie, i.e. v g << c. The low-group-velocity trasmissio lie employed i SMMArT serves the purpose of compressig the spatial extet of the waveform alog the trasmissio lie feedig the radiatig elemets. Neglectig group velocity dispersio effects, the spatial extet of a pulse of duratio τ propagatig i a trasmissio lie is approximately d = v g τ. I a trasmissio lie operatig i the fudametal TEM mode i air where v g c, a pulse havig a temporal duratio of τ = 100 s would have a spatial extet of d = 30 km, thereby far exceedig the dimesios of ay practical array. As a result, essetially the same portio of the waveform would ecouter all radiatig elemets simultaeously ad the beam would be static, with the directio determied by the feed system delays aloe. However, a low group-velocity (v g << c) feed-lie would make the pulse much shorter i space. This cocept is illustrated i Figure 2 which compares the spatial ad temporal extet of a pulse propagatig i a trasmissio lie with high ad low group-velocity. As apparet from the spatial traces (bottom row), the waveform spatial extet is sigificatly compressed i the latter. I a low group-velocity waveguide differet portios of the waveform ecouter the radiatig elemets at a give time, thereby allowig for far-field emissio desig to be accomplished through joit desig of the waveform ad the serial feed system. Figure 3a illustrates a far-field emissio geerated by a 20 elemet slotted SMMArT havig the dispersio relatio discussed i the ext sectio (Figure 8) ad excited with a upchirped LFM waveform of 100 MHz badwidth cetered at 10 GHz ad pulse duratio 1 µs. I this case the fast-time spatial modulatio realizes a liear beamsteerig durig the pulse such as could be accomplished usig FDA [17-20]. The correspodig delay/agle ambiguity fuctio [36] for the same cofiguratio is show i Figure 3b. Figure 4 shows the time-domai ad frequecy domai radiatio patter of a SMMArT (with dispersio relatio of Figure 8) havig 30 radiatig elemets with iter-elemet separatio of 15mm. This array is excited with a radom polyphase-coded frequecy-modulated (PCFM) waveform [29,30] cetered at 10 GHz with 200 MHz badwidth, pulse duratio of 1 µs, ad power spectrum show i Figure 5. Note that the mai lobe of the spectral radiatio patter show i Figure 4b mirrors exactly the group velocity distributio of the SMMArT feed lie. Figure 6 illustrates the delay/agle ambiguity fuctio for this emissio. Such a mode may have utility i trackig applicatios by mimickig the fixatioal movemet of the huma eye [9,10] to modify the delay/agle ambiguity fuctio i a adaptive/cogitive maer.

3 Figure 5. Power spectrum of radom PCFM waveform Figure 3. a) Far-field of a 20 elemet SMMArT that is fed with a upchirped LFM waveform with 100MHz badwidth cetered at 10GHz ad pulse duratio 1µs ad b) the correspodig delay-agle ambiguity fuctio [36]. Figure 6. Delay-agle ambiguity fuctio for SMMArT drive by a radom polyphase-coded FM waveform The radiatio patters displayed i Figure 3 ad 4 are calculated uder ideal sigle-mode operatio of the slow-wave trasmissio lie. I practice such coditios are difficult to achieve because of itermodal couplig i the proposed slowwave trasmissio lie. I Sectios III ad IV a physical realizatio of such a trasmissio lie is preseted, alog with a discussio of the measures to be take i order to approach ideal sigle-mode operatio. III. SLOW GROUP VELOCITY CLARRICOATS-WALDRON WAVEGUIDE I this sectio we describe a physical realizatio of the low group velocity feed lie that serves as the foudatio of SMMArT. This system relies o a slotted waveguide of the Clarricoats-Waldro type [22,23]. The Clarricoats-Waldro waveguide (CWW) features two essetial elemets: (i) a hollow metallic waveguide that is (ii) coaxially loaded with a high permittivity rod. A example layout for X-bad operatio is show i Figure 7. Figure 4. a) Time-domai ad b) frequecy domai radiatio patter of a 30 elemets SMMArT, excited with a radom polyphase-coded frequecymodulated (PCFM) waveform cetered at 10 GHz with 200 MHz badwidth ad pulse duratio of 1 µs.

4 Figure 7. Layout of a slotted rectagular Clarricoats-Waldro waveguide for operatio aroud 10GHz. This ihomogeeous waveguide system is uique i that it supports backward modes (i.e. with atiparallel phase ad group velocity), i spite of the fact that the structure is uiform i the propagatio directio. The dispersio relatio associated with the structure of Figure 7, which is desiged to operate aroud 10GHz, is show i Figure 8. The egative slope brach of the dispersio curve (show i red) is idicative of a backward-wave mode. The blue brach o the other had idicates a forward-wave mode. Notice that for frequecies i the 10GHz 11GHz iterval, two degeerate forward-wave ad backward-wave modes are allowed. Iterestigly, aroud 10GHz, where the two braches coalesce, the dispersio curve flattes out, idicatig a vaishig group velocity. Figure 8. Dispersio relatio for a Clarricoats-Waldro waveguide. The red brach ad the blue brach idicate the backward-wave ad forward-wave modes, respectively. I the frequecy rage from 10GHz to 11GHz the two modes coexist, while for frequecies above 11GHz oly the forward-wave mode is supported. The dashed black lie idicates the light-lie. The electric ad magetic field distributios of the fudametal backward mode at 10 GHz are show i Figure 9. The reversal of the magetic lies of force aroud the two covective regios visible i Figure cause the Poytig vector to chage sig ad become egative for positios exteral to the gree lie show i Figure 9, where the Poytig vector vaishes. This power flow reversal results i the low-group velocity regime observed i the dispersio curve of Figure 8. Figure 9. Modal field distributio ad effective idices of the forward-wave mode (top) ad of the backward-wave mode (bottom). The red ad blue arrows idicate the electric ad the magetic fields, respectively. The gree lie deotes the regio of zero Poytig vector. IV. ELECTROMAGNETIC PROPERTIES OF A SLOTTED CLARRICOATS-WALDRON WAVEGUIDE To use a CWW for the physical realizatio of SMMArT, a mechaism must be itroduced to allow the appropriate guided mode to radiate eergy ito free space. As i covetioal slotted waveguide arrays (SWA), slits opeed o either the broad wall or the arrow wall of the metallic eclosure of the CWW will allow radiatio to leak out of the waveguide mode, with a radiatio patter determied, to first order perturbatio, by the modal phase at the slit locatios. Oe essetial differece exists betwee a CWW ad a covetioal waveguide, which facilitates ew iterestig possibilities to cotrol the radiatio patters, but also makes the desig or radiatig slits more challegig i the case of CWW. This characteristic is the coexistece, at the same frequecy, of two differet field cofiguratios associated with the same mode, as ca be see from the dispersio relatio show i Figure 8. We will improperly refer to these field cofiguratios of the fudametal mode as modes. Assumig that the CWW is excited with the fast backward-wave mode (red brach of the dispersio curve), a set of radiatig slits with sub-wavelegth separatio would ted to radiate, depedig o the frequecy of operatio, i the agular sector from broadside towards backfire. This iterestig ad useful feature caot occur i a simple straight sectio of SWA without itroducig gratig lobes, or without the use of complex delay lies. Oe difficulty arises because the fast backward-wave mode ad the slow forward-wave mode (blue brach of the dispersio curve) are ot orthogoal i terms of polarizatio or field distributio. For this reaso ay structural perturbatio of the waveguide ca, ad i fact will, lead to a power exchage betwee the two modes, which prevets the atea from radiatig uder the desired sigle backward mode regime.

5 We have coducted a parametric study usig a commercial fiite elemet solver to determie a slit cofiguratio that suppresses, or at least mitigates, the udesired couplig betwee forward ad backward CWW modes. We have oly cosidered horizotal slits o the arrow metallic wall of the waveguide. The two mai geometrical parameters that affect itermodal couplig are slit legth ad axial positio. To gauge the effect of slit legth we simulated a CWW with a sigle slit of varyig legth. Two represetative electric field distributios are show i Figure 10 for a CWW operatig at 10GHz ad excited with the backward mode. The mode is lauched ito the waveguide at the port idicated by the red arrow. Figure 10a shows the optimum cofiguratio with a slit of legth 5mm. I this case, less tha 10% of the icidet power is trasferred from the backward mode to the forward mode. It is evidet that the istataeous electric field distributio alog the waveguide maitais its spatial periodicity before ad after the slit, idicatig egligible reflectio ad mode coversio. The opposite situatio is show i Figure 10b for a slit legth of 9mm, where a early complete power trasfer to the forward mode is observed, as is clear from the differet periodicity of the istataeous electric field distributio. Figure 11. Near-field ad radiatio patter of a slotted CWW with te 5mm slits o the arrow wall separated by 17mm. Figure 10. Electric field distributio i CWW Waveguide with a) a 5mm ad b) 9mm slit o the arrow wall. The other parameter that plays a fudametal role i this power trasfer effect betwee backward ad forward modes is the slit separatio, which should be tued so as to iduce a destructive iterferece amog the forward wave cotributios geerated at each slit. Figure 11 shows the ear-field ad radiatio patter at 10GHz of a array of te 5mm-wide slits havig a optimum separatio betwee slits of 17mm. The directive beam observed i the far-field is cosistet with the backward radiatio expected from the backward CWW mode, i.e. the red-brach of the dispersio of Figure 8. For compariso, i Figure 12 the ear-field distributio ad far-field radiatio patter are show for a slit separatio of 15mm. The couplig with the forward mode i this case produces the broadside lobe evidet i the radiatio patter. The parametric aalysis preseted here shows that the issues related to the presece of two simultaeous modes ca be addressed by careful desig of the radiatig elemets to provide destructive iterferece for the uwated mode. Figure 12. Near-field ad radiatio patter of a slotted CWW with te 5mm slits o the arrow wall separated by 15mm.

6 V. CONCLUSIONS The recetly proposed SMMArT structure, a form of Clarricoats-Waldro waveguide, provides a holistic framework withi which to cosider the atea electromagetics ad the waveform i a joit maer. Here a parametric study of the electromagetic properties of SMMArT was preseted. It has bee show that the challeges arisig because of the coexistece of two modes ca be effectively addressed by careful desig of the radiatig slits. Combied with parametric structures for FM waveforms, this overall cocept is a step towards facilitatig the desig of far-field emissios through joit trasmitter/waveform optimizatio. VI. REFERENCES [1] M. Wicks ad E. Mokole, Priciples of waveform diversity ad desig: The Istitutio of Egieerig ad Techology, [2] U. Pillai, K. Y. Li, I. Selesick, ad B. Himed, Waveform diversity: McGraw-Hill, [3] F. Gii, Waveform desig ad diversity for advaced radar systems: The Istitutio of Egieerig ad Techology, [4] H. Griffiths, S. Blut, L. Cohe, ad L. Savy, "Challege problems i spectrum egieerig ad waveform diversity," i 2013 IEEE Radar Coferece (RadarCo13), 2013, pp [5] S. D. Blut ad E. L. Mokole, "A overview of radar waveform diversity," to appear i IEEE Aerospace & Electroic System Magazie. [6] J. Li ad P. Stoica, MIMO radar sigal processig: Wiley Olie Library, [7] E. Brooker, "MIMO radar demystified ad where it makes sese to use," i 2014 Iteratioal Radar Coferece, 2014, pp [8] F. Daum ad J. Huag, "MIMO radar: Sake oil or good idea?," i 2009 Iteratioal Waveform Diversity ad Desig Coferece, 2009, pp [9] S. D. Blut, P. Mccormick, T. Higgis, ad M. Ragaswamy, "Physical emissio of spatially-modulated radar," IET Radar, Soar & Navigatio, vol. 8, pp , [10] P. McCormick ad S. D. Blut, "Fast-time 2-D spatial modulatio of physical radar emissios," i Radar Symposium (IRS), th Iteratioal, 2015, pp [11] P. M. McCormick, T. Higgis, S. D. Blut, ad M. Ragaswamy, "Adaptive receive processig of spatially modulated physical radar emissios," IEEE Joural of Selected Topics i Sigal Processig, vol. 9, pp , [12] B. Cordill, J. Metcalf, S. A. Segui, D. Chatterjee, ad S. D. Blut, "The impact of mutual couplig o MIMO radar emissios," i Electromagetics i Advaced Applicatios (ICEAA), 2011 Iteratioal Coferece o, 2011, pp [13] G. Babur, P. J. Aubry, ad F. Le Chevalier, "Atea couplig effects for space-time radar waveforms: aalysis ad calibratio," IEEE Trasactios o Ateas ad Propagatio, vol. 62, pp , [14] L. Savy ad M. Lesturgie, "Couplig effects i MIMO phased array," i 2016 IEEE Radar Coferece (RadarCof), 2016, pp [15] G. J. Frazer, Y. I. Abramovich, ad B. A. Johso, "Spatially waveform diverse radar: Perspectives for high frequecy OTHR," i 2007 IEEE Radar Coferece, 2007, pp [16] P. M. McCormick, S. D. Blut, ad J. G. Metcalf, "Joit spectrum/beampatter desig of widebad FM MIMO radar emissios," i 2016 IEEE Radar Coferece (RadarCof), 2016, pp [17] P. Atoik, M. C. Wicks, H. D. Griffiths, ad C. J. Baker, "Frequecy diverse array radars," i 2006 IEEE Coferece o Radar, 2006, p. 3 pp. [18] T. Higgis ad S. D. Blut, "Aalysis of rage-agle coupled beamformig with frequecy-diverse chirps," i 2009 Iteratioal Waveform Diversity ad Desig Coferece, 2009, pp [19] P. F. Sammartio, C. J. Baker, ad H. D. Griffiths, "Frequecy diverse MIMO techiques for radar," IEEE Trasactios o Aerospace ad Electroic Systems, vol. 49, pp , [20] W.-Q. Wag, "Overview of frequecy diverse array i radar ad avigatio applicatios," IET Radar, Soar & Navigatio, vol. 10, pp , [21] A. Saladrio, D. J. C. Farfa, P. McCormick, E. D. Symm, ad S. D. Blut, "Spatially Modulated Metamaterial Array for Trasmit (SMMArT)." [22] P. Clarricoats ad R. Waldro, "No-periodic Slow-wave ad Backward-wave Structures," Iteratioal Joural of Electroics, vol. 8, pp , [23] A. Saladrio ad D. N. Christodoulides, "Negative idex Clarricoats- Waldro waveguides for terahertz ad far ifrared applicatios," Opt Express, vol. 18, pp , Feb [24] P. McCormick, J. Jakabosky, S. D. Blut, C. Alle, ad B. Himed, "Joit polarizatio/waveform desig ad adaptive receive processig," i 2015 IEEE Radar Coferece (RadarCo), 2015, pp [25] Y. J. Cheg, W. Hog, ad K. Wu, "Millimeter-wave half mode substrate itegrated waveguide frequecy scaig atea with quadri-polarizatio," IEEE Trasactios o Ateas ad Propagatio, vol. 58, pp , [26] J. H. Choi, J. S. Su, ad T. Itoh, "Frequecy-scaig phased-array feed etwork based o composite right/left-haded trasmissio lies," IEEE Trasactios o Microwave Theory ad Techiques, vol. 61, pp , [27] G. Getile, V. Jovaović, M. J. Pelk, L. Jiag, R. Dekker, P. de Graaf, et al., "Silico-filled rectagular waveguides ad frequecy scaig ateas for mm-wave itegrated systems," IEEE Trasactios o Ateas ad Propagatio, vol. 61, pp , [28] K. Mile, "The combiatio of pulse compressio with frequecy scaig for three-dimesioal radars," Radio ad Electroic Egieer, vol. 28, p. 89, [29] S. D. Blut, M. Cook, J. Jakabosky, J. De Graaf, ad E. Perris, "Polyphase-coded FM (PCFM) radar waveforms, part I: implemetatio," IEEE Trasactios o Aerospace ad Electroic Systems, vol. 50, pp , [30] S. D. Blut, J. Jakabosky, M. Cook, J. Stiles, S. Segui, ad E. Mokole, "Polyphase-coded FM (PCFM) radar waveforms, part II: optimizatio," IEEE Trasactios o Aerospace ad Electroic Systems, vol. 50, pp , [31] J. M. Kurdzo, B. L. Cheog, R. D. Palmer, ad G. Zhag, "Optimized NLFM pulse compressio waveforms for high-sesitivity radar observatios," i 2014 Iteratioal Radar Coferece, 2014, pp [32] J. Jakabosky, S. D. Blut, ad B. Himed, "Waveform desig ad receive processig for orecurret oliear FMCW radar," i 2015 IEEE Radar Coferece (RadarCo), 2015, pp [33] J. Jakabosky, S. D. Blut, ad B. Himed, "Spectral-shaped optimized FM oise radar for pulse agility," i IEEE Radar Cof, [34] A. A. Olier ad D. R. Jackso, "Leaky-wave ateas," Atea Egieerig Hadbook, vol. 4, p. 12, [35] O. D. Jefimeko, Electricity ad magetism: Appleto-Cetury-Crofts, 1966.