Artificial lens for third-generation automotive radarantenna at millimetre-wave frequencies

F. Gall!ee, G. Landrac and M.M. Ney

Abstract: A focusing system based on low-cost foam printed technology is investigated. The designis based on artificial lenses consisting of stacked parallel-plate waveguides of various lengths. Thefoam technology allows a single block configuration with the primary source. As the dimensions ofthe lens are at least 10l0, full-wave analysis is not appropriate for fast design. A theoretical modelbased on ray tracing, Goudet’s formula and using an array factor is proposed and validated by theexperiment. Simulations and experimental results show that the model is sufficiently accurate forfast design and optimisation. The low-cost technological solution proposed can potentially meetspecifications for collision avoidance radar at millimetre-wave frequencies.

1 Introduction

Research on collision avoidance radar systems has been thefocus of much attention since the beginning of the 1980s[1–4]. The objective of these systems is to detect the presenceof one or several vehicles, and determine their position andvelocity. There is some advantage in using a microwavesignal because of its ability to operate reliably, regardless ofthe atmospheric conditions and atmospheric turbulence.

Third-generation systems (ACC: Automotive CruiseControl) are typically designed for US highway operation(maximum speed 80 km/h). To set the specifications used inthis work, data published in [5] and [6] were applied to avehicle with 130 km/h maximum speed on a Europeanhighway. Regarding the antenna, the following specifica-tions are expected: 25 to 40 dB gain with 51 beamwidth inthe elevation plane; a minimum 7151 angle of view in theazimuth plane with 0.71 resolution and linear polarisation.Furthermore, an operating frequency from 76 to 77 GHzwith 1% bandwidth is considered. This allows both goodspatial resolution and compactness. Finally, sidelobe levelsshould be as low as possible to avoid false alarms.

To achieve both resolution and angle of view, beam-scanning techniques can be considered. This can be achievedeither mechanically [7] or electronically. However, only thelatter technique can be considered for a low-cost solution.Also, electronic continuous beam scanning with phasedarrays cannot be considered because of the relatively highcost of phase shifters at millimetre-wave frequencies. Step-by-step beam scanning, which requires as many sources assteps, may be used for third-generation systems such asACC (77.51 angle of view). Some investigation remains tobe done on the feasibility of using this technique for widerangles of view, such as 7151, as required above.

Another approach is to use monopulse radar techniques[8, 9] that require only two or three beams. By comparing

the signal amplitude (amplitude monopulse) or phase(phase monopulse) received at all antenna terminals, oneis able to determine the angle of arrival of the wave echoedby an obstacle. The field of view of an amplitude monopulsesystem is nearly equal to twice the �3 dB beamwidth.However, the larger the beam, the poorer the spatialresolution (about 1/20 of the total angle of view). For phasemonopulse systems, the maximum phase variation shouldnot exceed 1801. This implies a minimum distance of 8 mmbetween antennas (at 76 GHz) for 7151 angle of view.

Although a phase monopulse system has been used forbistatic radar operation [10], it cannot provide the requiredangle of view. Amplitude monopulse systems seem moreinteresting as, for the same beamwidth, the angle of view istwice as large. However, for 0.51 resolution the total angleof view should be 101. This requires antennas with 51halfpower beamwidth or 30 dB directivity [11].

2 Low-cost technology

Antennas based on a guiding structure have someadvantage in terms of losses at millimetre-wave frequencies.However, they generally require elaborate surface machin-ing, precluding a low-cost solution. Moulding by injectionfollowed by metalisation [12] may provide a low-costsolution in the future. However, the metalisation process isnot yet completely mastered to yield low-loss above a fewgigahertz. Finally, waveguide antennas are not fullycompatible with MMICs or other components in terms ofconnections.

2.1 Primary sourceTo obtain sufficient gain, an alternative solution is to useplanar structures as primary sources associated with afocusing element. It is well-known that the efficiency ofplanar antennas such as patches increases as the permittivityof the substrate decreases. As a result, low-permittivitysubstrates are favoured to implement printed antennas atmillimetre-wave frequencies.

A first approach is to use foam (imide polymethacrylic)material as substrate. Constitutive parameters are near tothose of air (m0, er¼ 1.07) with a relatively low loss factor(tan d¼ 10�3 at 76 GHz). Metalisation is carried out byinserting a thin film of polypropylene (er¼ 2.2, 50mm

The authors are with the Laboratory of Electronics and Systems forTelecommunications (LEST), CS 83818, 29238/3, Brest Cedex , France

r IEE, 2003

IEE Proceedings online no. 20030745

doi:10.1049/ip-map:20030745

Paper first received 28th June 2002 and in revised form 21st May 2003. Onlinepublishing date: 17 October 2003

470 IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 6, December 2003

thickness) between copper foils (17mm thickness and4� 107 S/m conductivity) and the foam substrate. Gluingaction is obtained by pressing stacked layers at hightemperature (1601C). The required thickness of the foamsubstrate is obtained by adjusting the pressure action.Antenna motives are obtained by standard etchingtechniques. As very thin substrates are required at highfrequencies (typically 0.2 mm thickness at 76 GHz) imple-mentation with foam may produce insufficient rigidity and/or errors owing to manufacturing tolerances.

The second approach to obtain an equivalent permittivitysubstrate close to that of air is to use membrane technology:a polymer thin film (Diclad 38mm thickness, er¼ 2.2) issandwiched between a copper base sheet and a copper foil.Hot temperature pressing is used to glue the thin Diclad.Both antenna motives and the cavity underneath themembrane are obtained by a standard low-cost etchingprocess [13]. The cavity is closed by a ground base(packaging) ensuring electrical contact without vias.

2.2 Focusing systemsIn the Ku band, low-cost reflectors for satellite commu-nications are commonly realised by pressing at hightemperature a metallic grid (mesh dimension less than 1/10 of a wavelength) on a machined mould. A mix ofpolyester and glass fibre coats the grid. Although this low-cost technique is well suited to mass production, somedifficulty arises owing to mechanical tolerances. Machiningand polishing processes may be used but do not providelow-cost solutions. Present processes are oriented towardsmoulding techniques followed by surface metalisation.However, the problem of obtaining accurate positioningof primary sources is still to be solved. Accurate milling(10mm precision) can be used to shape reflector surfaces ona block of foam. Metalisation of the surfaces is simplyobtained by spraying [14]. This solution allows accuratepositioning of printed primary sources, but machining is nota low-cost process.

Finally, other solutions consist in using lenses as focusingelements. For instance, teflon lenses [15, 16] have beenproposed. However, material cost and variability ofpermittivity values, even from the same manufacturer, arestill drawbacks. Taking into account low-cost and compact-ness criteria, a system based on artificial lenses is proposedin this paper. It has the advantage of being less sensitive tomanufacturing tolerances. In addition, both the primarysource and the focusing system can be implemented on thesame block of foam, which facilitates their relativepositioning.

3 Artificial lens

3.1 StructureOriginally, artificial lenses were composed of parallelmetallic plates separated by air and fixed on a frame [17].To obtain a more compact structure that is easy to realise,one can use foam technology. The basic element, which isan air-filled parallel-plate waveguide, is realised using thesame process as for printed antenna (Fig. 1). After aligningand staking the various elements, the lens is made in onesingle block in which air is replaced by foam material(Fig. 2). Characterisation of a stacked foam (5 mm thick-ness) and polypropylene structure yields a relative permit-tivity of 1.1 and a loss factor of 2� 10�3 in the 75–110 GHzfrequency range.

3.2 Plate separation distanceTo obtain focalisation, the TE1 mode, whose electric field istransverse and parallel to the plates, is required. For

maximum efficiency, the maximum energy provided by theprimary source should be transferred to the TE1 mode. Anycoupling to the TEM fundamental mode should be avoided.Consequently, the primary source polarisation should alsobe transverse and parallel to the conducting plates. Single-mode operation requires a frequency signal below TE2-mode cut-off frequency. For the medium used here, the cut-off frequency of the TEn mode is given by

fcn ¼n

2dffiffiffiffiffiffiffiffiffiffiffiffiere0m0

p ð1Þ

where d and er are the distance between the parallel platesand the relative permittivity of the medium, respectively.For 76 GHz operation, one can deduce from (1) thecondition:

1:9 mmodo3:8 mm ð2Þfor TE1 single-mode operation. Also, it is easy to show thatnegligible dispersion occurs for d42.2 mm while dielectriclosses are near minimum for d42.4 mm (20 dB/m, tand¼ 10�3 at 76 GHz). Note that metallic losses are negligible(2 dB/m for sc¼ 4� 107 S/m). From the above discussion,the value d¼ 2.4 mm is chosen for a constant index lensprofile at 76 GHz. A similar analysis yields an optimumvalue of d¼ 5.6 mm at 32 GHz. The equivalent refractiveindex is given by the ratio between the free-spacewavelength l0 and the guided wavelength lg in theparallel-plate waveguide:

n ¼ l0

lg¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 � fc

f

� �2s

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1 � l0

2dffiffiffiffier

p� �2

sð3Þ

foamsubstrate

polypropylene film

copper foil

Fig. 1 Artificial lens basic element: parallel-plate waveguiderealised by foam technology

stacked foamsubstrates

printed primarysource with feed

artificial lens

printed parallel-platewaveguides

Fig. 2 Sketch of artificial lens with primary source in planartechnology

IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 6, December 2003 471

For instance, the above values of d for a constant index lensyield n¼ 0.655 (d¼ 2.4 mm) and n¼ 0.6325 (d¼ 5.6 mm)for 76 GHz and 32 GHz operation, respectively. Note that,unlike dielectric lenses, the equivalent refractive index issmaller than one. This is because phase velocity in parallel-plate waveguides is larger than that in free space. Anartificial lens with variable refractive index is easily obtainedby varying the distance d.

3.3 Lens profile geometryThe analysis of the artificial lens can be carried out usingray tracing theory. Hence, it is possible to determine theprofile geometry of a unifocal or bifocal lens given the lensdiameter and focal length [18]. It is determined by enforcingequality between all optical path lengths. This ensuresin-phase signals at the output of all parallel-plate wave-guides constituting the artificial lens.

As for classical dielectric lenses, it is possible to realiseunifocal (Figs. 3a and 3c) or bifocal (Figs. 3b and 3d) lenses.Adjusting the plate length modifies the phase shift betweenwaveguides and the distance d gives an additional degree offreedom compared to classical lenses. By adjusting theequivalent refractive index, one can realise unifocal lenses

with two parallel faces (Fig. 3c) or bifocal lenses with oneplane face (Fig. 3d).

3.4 Lens for wide angle of viewWhen the primary source is no longer at the focal point, aphase error occurs that degrades the radiation pattern [18].One solution is to use a bifocal lens instead. Indeed, the zerophase error point is located on a single point on the lens axisin the case of a unifocal lens, while there are two such pointslocated symmetrically on that axis for a bifocal lens. Forinstance, consider the case of a 151 beam steering angle forwhich one can compute the phase error at points located onthe lens axis. Within a 74 l0 distance from the focal point,the unifocal lens yields 7501 phase error, while it is below31 for a bifocal lens (optimised for 7101 beam steeringangle).

Note that for d¼ 2.4 mm and 76 GHz operatingfrequency (or 5.6 mm and 32 GHz), it is not possible torealise a unifocal lens with one planar face and to maintaina ratio focal length to diameter (F/D) less than unity. Thisrequirement is necessary to minimize spillover from theprimary source. However, by giving a proper shape to theexternal face, it is possible to design a unifocal artificial lenswith both F/Do1 and an optimal d value for minimumloss.

3.5 Radiation patternComputation of the radiation pattern is a two-stepprocedure. First, the field produced by the primary sourceat the level of the lens input is computed. Then, theradiation pattern of the lens fed by the primary source iscomputed. The procedure implies that coupling between theprimary source and the lens can be neglected.

3.5.1 Primary source field computation: Forsources such as dipoles or horns, analytical expressionscan be used to determine near or far-field values. For othermore complex structures such as planar sources, numericalmethods may be used. For the total structure far fieldcomputation, the procedure can be substantially acceleratedby determining far fields in both E and H planes only andthen, from these values, computing far fields everywhere bythe approach described in [19].

3.5.2 Primary source-lens system radiation pat-tern in H-plane: For the H-plane, the lens can be seen asan array whose elements are open-ended parallel-platewaveguides. Assuming that the aperture field is the TE1-mode, Goudet’s formula can be used to compute the farfield of each element. Finally, with the assumption thatcoupling between elements can be neglected, the classicalarray factor can be used to compute the whole systemradiation pattern. This very simple and fast procedure turnsout to yield good accuracy for the main lobe computation.Note that a fullwave analysis of the whole structure wouldinvolve excessive computer costs as the dimensions exceedten wavelengths.

By adding losses produced by reflections at variousinterfaces and the dielectric (foam), the total losses (metalliclosses can be neglected as discussed earlier) amounts to1 dB. This corresponds to 80% maximum efficiency.

3.6 Model validationTo validate the simplified model presented above, measure-ments were carried out at 76 GHz in an anechoic chamber.The primary source was a W-band pyramidal hornimplemented in metalised foam technology with a measuredgain of 13.2 dB (Fig. 4). Note that there is only 0.3 dB

d

c

b

a

d

d

focalpoint

focalpoint 1

focalpoint 2

focalpoint 1

focalpoint 2

focalpoint

d1

d2

d2

d

d

d1

Fig. 3 Various types of artificial lensesa Unifocal lens with constant equivalent refractive index and one planefaceb Bifocal lens with constant equivalent refractive indexc Unifocal lens with variable equivalent refractive index and two planefacesd Bifocal lens with variable equivalent refractive index and one planeface

472 IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 6, December 2003

difference in gain compared to an entirely machinedcommercial horn. Measurements showed that good agree-ment is obtained with the analytical field expressions for thehorn, in both E- and H-planes.

3.7 H-plane focused lensFigure 5 shows the H-plane radiation pattern of the abovepyramidal horn associated with an H-plane focusedunifocal lens with constant refractive index (lens no. 1 inTable 1). A 6 dB gain increase in that plane (in the E-planethe aperture is not equiphase) can be observed, yielding atotal system gain of 19.2 dB. The same figure shows acomparison with the analytical model for the horn–lenssystem. Very good agreement can be observed for the mainlobe. However, discrepancies arise at the sidelobe levelwhich is underestimated by the model. This is explained bythe fact that plate edge diffractions are not accounted for,and there is some spillover resulting from the primarysource.

Figures 6a and 6b shows the simulated radiation patternsof lens no. 1 and 2, respectively. As mentioned in Table 1,these lenses are illuminated by a pyramidal horn at 76 GHz.One can observe that the unifocal lens (no. 1) producessidelobe whose level increases with steering angle (�13 dBmax. for 201). The sidelobe asymmetry is produced by thecoma error [20], while main beam widening and levelling ofsidelobe level comes from the phase quadratic error. As

predicted, the bifocal lens produces lower sidelobe levels(Fig. 6b), which are below �20 dB for 201 beam steeringangle. In addition, the main beam width remains within 51.

3.8 Alternative bifocal lens configurationsAs mentioned earlier, a constant equivalent index lens has aconstant distance d between plates. Consequently, it isnecessary to use non-planar surfaces at both ends to obtaina bifocal lens. The advantage of this configuration is itspractical implementation: all motives can be printed on thesame foam substrate and then cut to be stacked.Unfortunately, it was found that conforming the endsurfaces of the lens results in higher sidelobe levels for anglesgreater than 701. This is explained by the presence ofsignificant interaction between plates that is enhanced bythe curved configuration.

In the case of a variable refractive index lens with planarend surfaces, the configuration can be seen as a planar arrayand, thus, does not exhibit increase of sidelobe levelsbeyond 701. However, the distance between plates is nolonger constant and, consequently, requires that only twomotives (because the lens is symmetrical) can be printed ona foam substrate. This increases the number of processesduring fabrication. In addition, as 100mm is the precisioncurrently obtainable for foam height, a larger relative errormay occur. For practical reasons, a lens with constantrefractive index was realised.

The horn, used as primary source, may be associated toan artificial lens that can focus in both the E- and H-plane(Fig. 7). The lens is easily implemented using foamtechnology. The characteristics of the lens for H-planeradiation is the same as for lens no. 1 (see Table 1). For E-plane radiation, the input face has a circular profile, whereasthe output face has a profile such that equiphase conditions

Fig. 4 W-band pyramidal horn realised using metalised foam withwaveguide feedAperture dimension: 5� 6.8 mm, length: 13 mm, gain: 13.5 dB

Table 1: Artificial lens system characteristics

Lens Type Operatingfrequency[GHz]

Refractiveindex

Width,mm

Focallength,mm

Platedistance,mm

Platelength,mm

Platenumber

Primarysource

No. 1 Unifocal 76GHz Constant 40 40 2.4 0.1–12.7 16 Pyramidal horn

No. 2 Bifocal (optimizedfor 101 steeredbeam)

76GHz Constant 40 40 2.4 1–5.7 18 Pyramidal horn

No. 3 Unifocal 32GHz Constant 100 75 5.6 0–46 18 2�2 patch array

–90 –70 –50 –30 –10 10 30 50 70 90–40

–35

–30

–25

–20

–15

–10

–5

0

dB

horn only(measurement)

horn + lens(measurement)

horn + lens(simulation)

angle, degrees

Fig. 5 H-plane radiation pattern of lens no.1

IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 6, December 2003 473

are realised (Fig. 8). The profile can be seen as a continuousarray in that plane.

Measured radiation patterns are shown in Fig. 9 for bothH- and E-planes. The measured gain of the systemhorn+lens is 21 dB. The sidelobe level is higher than thatpredicted in theory for reasons mentioned before. However,the simple model remains sufficient for H-plane radiationpattern computation for double focused lenses.

–70 –60 –50 –40 –30 –20 –10 100 20 30 5040 60 70

0

–40

–35

–30

–25

–20

–15

–10

–5

dB

angle, degrees

–70 –60 –50 –40 –30 –20 –10 100 20 30 5040 60 70

0

–40

–35

–30

–25

–20

–15

–10

–5dB

angle, degrees

a

b

x=0 mmx=5 mmx=10 mmx=15 mm

x=0 mmx=5 mmx=10 mmx=15 mm

Fig. 6 Simulated H-plane radiation pattern of artificial lenses fordifferent position x of the primary sourcea Unifocal lens no. 1b Bifocal lens no. 2

Fig. 7 Double focused lens with horn primary source (Fig. 4) at76 GHz

H

E

Fig. 8 Sketch of internal view of double focused lens similar to oneillustrated in Fig. 7

horn + lenshorn

–90 –70 –50 –30 –10 10 30 50 70 90

horn + lenshorn

0

5

10

–30

–25

–20

–15

–10

–5

dB 0

5

10

–30

–25

–20

–15

–10

–5

dB

angle, degrees

–90 –70 –50 –30 –10 10 30 50 70 90

angle, degrees

a

b

Fig. 9 Measured radiation pattern of radiating system illustratedin Fig. 7 at 76 GHza H-planeb E-plane

474 IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 6, December 2003

To summarise, measurements at 76 GHz showed that thesimple theoretical approach presented above gives reason-able results and can be used for the efficient design ofradiating systems with artificial lenses near this frequency.

3.9 Planar primary source at 32GHzIn order to design the system primary source–lens withminimum cost, it is proposed to investigate the feasibility ofusing planar sources at 32 GHz. The artificial lens (no. 3 inTable 1) has H-plane focusing property and consists ofprinted metallic motives. The primary source consists of a2� 2 patch array, as shown in Fig. 10. The feed lines arerealised in TFMS (thin film microstrip) technology on athin film substrate (Diclad, er¼ 2.2, 38mm thickness). Thisfilm is also used for the membrane on which patches areprinted. The cavity under the membrane is 254mm high. Toobtain a 1.5 cm equivalent aperture, patches have 0.6l0

spacing in the H-plane. To decrease patch width whilemaintaining a reasonable input impedance value (E200O),TMFS feed lines connect patches via a notch (Fig. 11). Toobtain some directivity in the E-plane (elevation), elementsare separated by 0.9l0 distance in that plane.

The H-plane radiation pattern of the patch–lens system isshown in Fig. 12. Good agreement is observed betweenmeasurement and theory for the main lobe. As before, thecomputed sidelobe levels are lower than the measured ones.

Sidelobe level could be reduced by aligning the outputside of the plates that require non-constant refractive index

and, therefore, different distances between plates. However,as previously stated, the number of processes for lensfabrication is then substantially increased.

A comparison was made with another focusing system;namely, a parabolic reflector with the above planar primarysource in an offset configuration. The reflector was alsoimplemented in metalised foam technology with a 10 cmaperture diameter equivalent to that of the lens. MeasuredH-plane radiation patterns (Fig. 13) show that mainbeamwidths are nearly identical (about 51). The differenceoccurs in terms of sidelobe levels, which are at most �15 dB

Fig. 10 Planar primary source in membrane technology withTFMS feed lines (32 GHz)

4.02

mm

3.17 mm

0.1 mm

0.97

mm

membrane

TFMS feed

Fig. 11 Notch connection to reduce patch feed input impedance(32 GHz)

–90 –70 –50 –30 –10 10 30 50 70 90–40

–35

–30

–25

–20

–15

–10

–5

0

angle, degrees

dB

simulationmeasurement

Fig. 12 Patch array (Fig. 11) + lens (no. 3) H-plane radiationpattern (32 GHz)

–90 –70 –50 –30 –10 10 30 50 70 90–40

–35

–30

–25

–20

–15

–10

–5

0

dB

lensreflector

angle, degrees

Fig. 13 Measured H-plane radiation pattern (32 GHz) – Com-parison between lens no. 3 and a parabolic reflector201- offset, 5-cm focal length, 10-cm diameter

IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 6, December 2003 475

and �22 dB for the lens and the reflector system,respectively. This shows the potential advantage ofmetalised foam structures. Even better performances canbe achieved by optimising the reflector profile [21].However, one has to mention that the lens system is lesssensitive to fabrication tolerances and does not requireprimary source offset.

4 Conclusions and future work

The feasibility of using an artificial lens as the focusingelement of a low-cost antenna system for collisionavoidance radar was investigated. The relatively largedimensions of these lenses (more than 10l0) precludesfullwave analysis in a reasonable computing time. There-fore, a theoretical model to compute radiation patterns wasproposed, based on Goudet’s formula combined with arraytheory, which requires very little computer resources.Comparison with measurement shows that very goodagreement is obtained as far as main lobe computation isconcerned. However, prediction of sidelobe levels wasfound to be substantially below measured values. Never-theless, the model is sufficient for a rapid design andoptimisation procedure.

Foam technology is proposed to implement the artificiallens used as focusing element. In terms of performance, a 51beamwidth was obtained with 19.3 dB gain using apyramidal horn at 76 GHz. However, as the main beam issteered off broadside, measurements showed that sidelobelevels varied from �15 dB to �20 dB. It is generallyadmitted that �20 dB will be the requirement for third-generation radar systems.

Better adjustment of the primary source to avoidspillover, increasing the number of plates, and using nonuniform amplitude give sufficient degrees of freedom tomeet specifications. Also, a lens with plane output face butvarying refractive index may be considered. Investigation at32 GHz demonstrated the possibility of using a planar arrayas primary source that allows full compatibility in terms ofconnection with components. Extension to 76 GHz shouldnot generate major problems as antenna performance ismainly related to lens design.

5 References

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476 IEE Proc.-Microw. Antennas Propag., Vol. 150, No. 6, December 2003