Abstract:
An array of geodesic lens antennas (GLAs) comprises multiple vertical radiating slots, each formed into an annulus, which are individually controlled by feeding rings. One feeding ring is provided for each of the GLA elevation elements, resulting in multiple, parallel waveguide channels that together enable elevation beam steering, thus forming a concentric stack of geodesic lenses. Accordingly, exemplary embodiments of the invention are capable of RF beam formation in azimuth and elevation by using these lenses to form, shape, and steer one or more RF beams. Each GLA in the stack forms an element in the elevation plane with separate amplitude and phase control, providing the degrees of freedom required to independently and simultaneously control azimuth and elevation beam forming and steering.

Description:
BACKGROUND 
     A conventional geodesic lens antenna (GLA) can provide an antenna solution for low cost, and weight restricted applications. A typical geodesic lens antenna has many advantages, including simplicity of design. Due to its ease of construction and design, geodesic apertures are suited for applications that require 360° coverage in azimuth. For certain applications it is desired to perform simultaneous azimuth and elevation beam pointing, while still using a simple, low part count, geodesic lens approach. 
     One drawback of known GLAs is the inability to form antenna beams in two simultaneous dimensions (namely, azimuth and elevation). One conventional approach to solving this shortcoming is to adding azimuthal slots in the vertical dimension. For example, the geodesic slotted cylindrical antenna of Howell, et al., U.S. Pat. No. 6,011,520, (incorporated herein by reference in its entirety) incorporates horizontal radiating slots in the geodesic lens cone to create an elevation illumination profile for elevation beam shaping. This approach does not provide for elevation beam steering by purely electrical means, however. Furthermore, the time of arrival to the horizontal slots varies with frequency and is limited to narrow band operations due to elevation “beam walk” (or “beam wander”) caused by the frequency sensitivity of the horizontal slot approach. 
     Another attempt to solve this and other related problems may be seen in the geodesic cone antenna of B. S. Cramer, “Geodesic Cone Antenna,” Proceedings of the Antenna Applications Symposium (ADA142003), vol. 1, March 1984, incorporated herein by reference in its entirety. However, the proposed design is not capable of elevation steering. 
     Similarly, another antenna design is discussed in Wyman Williams and Chris Burton, “Lightweight agile beam antennas for UAVs,” Proceedings of the 2006 IEEE Conference on Military Communications (MILCOM &#39;06), IEEE Press, Piscataway, N.J., USA, pp. 115-119, incorporated herein by reference in its entirety. This design is also not capable of elevation steering, but does allow a certain amount of beamforming. 
     What is needed is a relatively simple, yet compact, geodesic lens antenna system that is able to provide full electronic azimuth and elevation beam steering. 
     SUMMARY 
     In contrast to the above-described conventional approaches, embodiments of the invention are directed to an array of geodesic lens antenna (GLA) elements configured to provide azimuth and elevation beam steering over a wide range of frequencies and with a wide bandwidth. 
     In one exemplary embodiment, an array of GLAs comprises multiple vertical radiating slots, each formed into an annulus, that are individually controlled by feeding rings. One feeding ring is provided for each of the desired elevation “elements,” resulting in multiple, parallel waveguide channels that enable elevation beam steering. These vertical, radiating slots may thus form a concentric stack of geodesic lenses. 
     Accordingly, exemplary embodiments of the invention are capable of RF beam formation in azimuth and elevation by using lenses above and below a middle geodesic lens to form, shape, and steer the beam. Each GLA in the stack is thus an “element” in the elevation plane with separate amplitude and phase control. This provides the degrees of freedom required to independently (and simultaneously) control azimuth and elevation beam forming and steering. 
     This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other objects, features and advantages of the invention will be apparent from the following description of particular embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. It is understood that the drawings are not necessarily to scale. 
         FIG. 1  is an isometric illustration of an array of three geodesic lens antennas, according to one embodiment of the present invention. 
         FIG. 2A  is an illustration of the feed element network for a three-GLA array, according to one embodiment of the present invention. 
         FIG. 2B  is a bottom view of one embodiment of the feed element connectors. 
         FIG. 3  is a cut-away side view of a three-GLA array, according to one embodiment of the present invention. 
         FIG. 4A  is a section view of one embodiments of the feed elements, showing certain mechanical support details. 
         FIG. 4B  is a section view of one aspect of the mechanical support at the base of the antenna, according to one embodiment of the present invention. 
         FIG. 5  is an isometric illustration of a three-GLA array with a surrounding radome, according to another embodiment of the present invention. 
         FIG. 6  is a flowchart of a method of controlling the beam steering in azimuth and elevation using an exemplary embodiment of the present system. 
         FIG. 7  is a representative geometric interpretation for use in calculating the azimuth portion of the beam steering vectors. 
         FIG. 8  is a representative coordinate system for use in calculating the elevation portion of the beam steering vectors. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present system are directed to an array of geodesic lens antenna (GLA) elements arranged in a nested coaxial stack such that each GLA element is individually fed from a plurality of feed elements. By means of adjustments to the feed element amplitude and relative phase in each GLA, azimuthal beam control is achieved. Feed element control in amplitude and phase in each GLA element relative to the other GLA elements enables elevation beam forming and steering. Thus, the presently-disclosed nested plurality of coaxial geodesic lenses provides elevation and azimuth beam forming and steering in a compact, simplified antenna array. 
     One embodiment of the invention is directed to an antenna  100  formed of nested plurality of geodesic lens antenna  110 A- 110 C, wherein each geodesic lens is individually fed by a plurality of feed elements  102  disposed in a ring  130  concentric with the primary axis  101  of each geodesic lens, as depicted in  FIG. 1 . A geodesic parallel plate waveguide can be created by forming a parallel plate waveguide from a pair of matched conformal structures, such as a pair of cylinders or, as here, a pair of conic sections, made from a conductive material. More specifically, by placing a cone of conductive material within another cone of conductive material, a parallel plate waveguide can be formed with each cone representing the opposing plates of the waveguide. The parallel plate waveguide formed thereby has no side walls. The theory of operation and construction of a geodesic cone antenna may be further explored in B. S. Cramer, “Geodesic Cone Antenna,” Proceedings of the Antenna Applications Symposium (ADA142003), vol. 1, March 198, incorporated herein by reference in its entirety. 
     In the concepts, systems, and techniques disclosed herein, a flared section (in one exemplary embodiment, a biconical horn) at the top of the inner cone is employed to further focus the resulting waveguide radiation pattern, thus creating the geodesic lens. As depicted in  FIG. 1 , the top-most flared section  177  is the inner wall of the innermost of the three GLAs, GLA  110 A; the outer wall of GLA  110 A ( 178 ) forms the inner wall of GLA  110 B. (Flared portions  177  and  178  thus form aperture  120 A; the corresponding wall pairs form corresponding apertures  120 B and  120 C.) In like fashion, outer wall  210  (illustrated in  FIG. 2A ) forms the second parallel cone of GLA  110 C.  FIG. 3  further illustrates the use of the biconical horn and nested concentric cone structure of antenna  100 . (In this cut-away view, a cover or radome  310  is shown. One of ordinary skill in the art will appreciate that such RF-transparent, low-loss environmental covers may be used with antenna of various types, without limitation.) 
     Referring to  FIG. 1  again, the plurality of geodesic lenses  110 A- 110 C are stacked vertically so that their primary axes are parallel and coincident, with the lens apertures  120 A- 120 C arrayed linearly along the primary axis  101 . The respective radial feed element arrays  130 A- 130 C are each disposed in a plane perpendicular to the lens axis  101  and offset from one another along that axis. 
     The relatively large number of RF feed elements  102  in the feed element array  130 A- 130 C of each geodesic lens  110 A- 110 C is handled using a tiered (or layered) system of radial feed probe arrays  130 A- 130 C, where each probe is equally spaced radially along the circumference of each geodesic lens antenna  110 A- 110 C but staggered or offset relative to the other GLAs  110 A- 110 C, as illustrated in  FIGS. 1-4 . In this way, each geodesic lens is fed separately by a single set of feed probes all located in the same tier at the near end of the GLA (i.e., the end proximate to the end connectors  106  discussed below and distal from the wave-launching apertures  120 A- 120 C). Each feed tier is located so as to avoid physical or mechanical interference with the other tiers. 
     Feed element arrays (not visible) are each incorporated into support flanges  140 A- 140 C, which provide both mechanical support for geodesic lenses  110 A- 110 C and the necessary structure for feed-throughs  104  that connect feed elements  102  to end connectors  106  (not visible here). 
       FIG. 2A  is an expanded view of the feed element network for the three-GLA array depicted in  FIG. 1 , according to one embodiment of the present invention. In this view, a representative feed element  102  is shown penetrating outer wall  210  of GLA  110 C. Feed element (or probe)  102  is connected to end connector  106  by one or more feed throughs  104  and waveguide sections  103 . In this exemplary embodiment, outermost GLA  110 C is fed from feed element array  130 C (referring to  FIG. 1 ); the waveguide connection to corresponding end connectors  106  for each feed element  102  passes through support flange  140 C, then  140 B and finally through support flange  140 A. The connection to the corresponding end connector  106  for a feed element of GLA  110 A (the innermost GLA) has a shorter path, requiring only one waveguide section  103  and one feed through  104  before terminating at end connector  106 . 
       FIG. 2B  is a bottom view of one embodiment of the feed element end connectors  106 , showing the bottom of support flange  140 A. 
     Feed element  102  may be, in some exemplary embodiments, a conventional quarter-wavelength feed probe. Alternatively, other feed probe configurations as known and used by those of ordinary skill in the antenna arts may be used. 
     The feed elements  102  are fed (via end connectors  106 , feed throughs  104 , and waveguide sections  103 , as discussed above) by a network of phase shifters and power dividers that can provide the necessary phase and amplitude control to each element of each GLA. Conventional feed probes for use in geodesic antennas are well known to those of ordinary skill in the antenna arts; see, for example and not by way of limitation, Patent Cooperation Treaty (PCT) Published Application No. WO 99/43046, “GEODESIC SLOTTED CYLINDRICAL ANTENNA,” published on Aug. 26, 1999, incorporated herein by reference in its entirety. In general, the types of radiating structures that may be used are any type that can provide the proper impedance match within the waveguide cavity. A simple monopole is the most simple approach, but more complex forms may be used without limitation as long as the element has a broad “azimuth” pattern gain, in order to support propagation to the other side of the geodesic cone. 
     It is to be noted that feed element arrays  130 A- 130 C do not necessarily (or even desirably) have the same number of feed elements or probes  102 . This fact arises from the nature of the concentric rings or tiers on which each feed element arrays  130  is mounted: since the GLAs are concentric, the upper, outermost feed element array  130 C has a larger circumference than the lowermost, bottom feed element array  130 A. Since it is desirable to maintain the same radial spacing between feed elements  102  in every tier, the number of feed elements can vary from tier to tier. Accordingly, there is not as much radial space available to mount feed elements  102  on feed element array  130 A versus feed element array  130 C. In some embodiments, therefore, feed element array  130 A may have relatively fewer elements  102  than feed element array  130 B. Likewise, feed element array  130 B may have relatively fewer elements  102  than feed element array  130 C. 
     Feed element arrays  130 A- 130 C are operably connected to a conventional feed network that may comprise, inter alia, a plurality of adjustable phase shifters and gain elements. Working in combination with a conventional beam steering computer (BSC), the phase and amplitude of the signal fed into each feed element may be varied to effect azimuthal control of the number, shape, and directionality of the RF beams produced in each geodesic lens antenna. The beams, each formed in separate GLA, combine to form a composite beam that is controlled in elevation by the relative phasing of each beam, as discussed in further detail below. 
     In one exemplary embodiment, each geodesic lens antenna may be separately constructed from a conductive material, such as but not limited to a metal or a metal-containing polymer. In one particular embodiment, the geodesic lens antenna may be constructed from aluminum according to conventional methods of antenna fabrication well known in the art. 
     The spaces between individual geodesic lens antenna elements in an array may be left unfilled. In an alternate embodiment, any of a number of conventional dielectric materials may be used to fill one or more of the GLA cavities to slow wave propagation as needed for a particular frequency of operation, bandwidth requirement, or other operational parameters. Accordingly, the concepts, systems, and techniques are not limited to any particular dielectric fill or encapsulation of the geodesic lenses that form the GLA array. 
     In one exemplary embodiment built and tested, a geodesic lens operating in C band was demonstrated. However, as will be appreciated by those of ordinary skill in the antenna arts, variations on a design may be scaled in operating frequency through the relatively simple expedient of scaling the geometry of the propagation and feed structures through conventional means. Accordingly, the concepts, systems, and techniques herein disclosed are not limited to any particular frequency band of operation. 
       FIG. 3  is a cut-away side view of the three-GLA array  100  of  FIG. 1 , according to one embodiment of the present invention. 
       FIG. 4A  is a sectional view of one embodiment of the feed elements  470  and mechanical attachments of the support flanges  430 A- 430 C, showing certain mechanical support details according to one embodiment of the present invention. Here, fasteners  410  are employed to attach an outer housing  420  (which may be, in some embodiments, a radome or other environmental housing) to each of support flanges  430 A,  430 B, and  430 C. Fastener  440  may be used to attach antenna assembly  400  (shown in partial view) to base  450 . Fasteners  460  may be used to attach the inner edge of support flanges  430 B and  430 C to the inner wall of each GLA. Fasteners  410 ,  440 , and  460  may be bolts, stud/nut combinations, or any other fastener system commonly used in the antenna arts, without limitation. Furthermore, such attachment may also be made using adhesives, welding, brazing, or any other attachment method known in the art. 
     In one exemplary embodiment, individual feed elements (or probes)  470  project about 0.375 inches into the waveguide, although it must be emphasized that the figures described herein are not necessarily to scale. 
       FIG. 4B  shows certain details of a feed probe penetration  450  constructed according to one embodiment of the present invention. Probe  450  penetrates outer wall  455  of GLA  401 , here shown as the outermost (or bottom) GLA in the assembly  400  of  FIG. 4A . Probe  450  extends into cavity  457  formed by outer wall  455  and inner wall  460 . Probe  450  is attached to outer wall  455  (which may be integrally formed with support flange  430 A, as shown) by conventional means, such as (but not limited to) a sub-miniature “Version A” (SMA) connector  470 . Connector  470  is attached to waveguide section  103 . As discussed above with respect to  FIG. 2A , waveguide section  103  may be routed and/or connected via conventional means through one or more feed throughs  104  before terminating in end connector  106 . 
     End connector  106  may be any conventional waveguide connector known and used in the antenna art, without limitation. In one exemplary embodiment, end connector  106  is an SMA connector. However, although an SMA is described, those skilled in the art will realize that connectors  470  and/or  106 , waveguides  103 , and feed throughs  104  adapted for frequency bands of operation, mechanical configurations, and other common architectural requirements other than those typically suited for SMA connectors can be used. Accordingly, the concepts, systems, and techniques described herein are not limited to any particular type of connector, waveguide, and feed through, or to any particular frequency or bandwidth. The present system is equally useable across a wide range of operating frequencies and bandwidth, limited only by the achievable manufacturing tolerances of the materials selected by the ordinary practitioner. 
     Individual geodesic lens antenna elements may be constructed separately and then attached together with due care being paid to the alignment and avoidance of mechanical interference between the feed array elements. One of ordinary skill in the art will readily appreciate the mechanical assembly and adjustment requirements typically associated with such assemblies; integration is therefore readily achievable without undue experimentation. 
       FIG. 5  is an isometric illustration of a three-GLA array  500  with a surrounding radome  510 , according to another embodiment of the present invention. Although a radome is described, those skilled in the art will realize that environmental protection and/or structural housings other than a conventional radome may be used. Accordingly, the concepts, systems, and techniques described herein are not limited to any particular type of external housing or structural support scheme. 
     The determination of the relative phase of the signals applied at each feed element in a single GLA is well-known and relies on determining the geodesic length L  700  (referring to  FIG. 7 ) from each feed element in the illumination sector  701  of the antenna. The combination of multiple geodesic lens antennas that enables elevation control requires additional calculations in order to set the relative phase and amplitude for each feed element in for each GLA to effect elevation beam steering. 
     Geodesic length L  700  is the length of each geodesic ray that intersects at a point in space where the outer-most two rays are conscribed by the desired illumination sector  701  (e.g., 60°, 90°, 120°, etc.) in the radiating slot (aperture) of each GLA (each GLA total sector is 360°). Each feed element  702  defines a ray within the illumination sector that extends from the feed probe to a common point in space  703 . Each ray crosses the edge of the illumination sector at a point i  704  on the GLA; the length of L  700  and the locations of each point i is readily calculated according to well-known solid geometry techniques commonly use for a single, conventional geodesic lens antenna. 
     Following is an example for the elevation portion of the phase calculation. For each point i  800  (referring to  FIG. 8 ) on each GLA in an array of GLAs, a calculation of a second length, L′  804  representing the inner product (or projection) between a vector representing each point i  805  and the desired elevation pointing vector  806  is performed. The vector from the origin to each point i  800  must be represented in (x, y, z) coordinates  802  (i.e., Cartesian coordinates) centered on a point along the common central axis of all three GLAs located in the plane of the aperture slot of bottom-most (i.e., outer-most) GLA. A similar vector is formed for the desired pointing vector  806 . For the coordinate system shown in  FIG. 8 , the radius of each GLA  803  is used to calculate the x and y components of the element i. The z component is the vertical distance from the coordinate system origin and the element i. 
     The sum of L  700  and L′  804  for each element is the total geodesic length for each feed element L total . The phase command value for each element corresponding to each i is then 
             ϕ   =       L   total     *       2   ⁢   π     λ             
where λ (lambda) is the wavelength of the center frequency of interest.
 
     The process  600  by which the relative phase and amplitude for the signal at each feed element may therefore be summarized as shown in  FIG. 6 . In step  610 , receive a pointing vector to the desired point in space P to which to steer the GLA array. In step  620 , for each feed element in each GLA, compute L and vector i. In step  630 , convert the pointing vector into Cartesian (x, y, z) coordinates, if necessary. Some embodiments may require different coordinate conversions, or none at all, depending on the means by which data is transferred and handled in the beam steering computer. 
     In step  640 , compute the vector inner product (dot product) of vector i and the pointing vector to determine scalar L′. Finally, step  650 , calculate the commanded phase value for the element using L total =L+L′ and the equation above. The process then iterates for each feed element in each GLA according to loops  601  and  602 , respectively. 
     The method described in this embodiment and the sample coordinate system may be used for calculation of the phase portion of the complex vector. Amplitude calculations depend on well-known methods where simultaneous equations are solved to achieve multiple spatial angle characteristics such and nulling, multiple main beams, sidelobe control, etc. Such calculations and computations are well-within the skill of one of ordinary skill in the art and need not be further disclosed herein. 
     The order in which the steps of the present method are performed is purely illustrative in nature. In fact, the steps can be performed in any order or in parallel, unless otherwise indicated by the present disclosure. 
     Geodesic lens arrays may be used with or integrated into or onto other radiating structures, such as but without limitation reflector antenna systems (e.g., Cassegrain, offset-fed, reflector array, or annular reflector systems), vehicles, spacecraft, airframes, ships, and the like. When mounted on or in such structures, a radome or other RF-transparent covering may cover the antenna. Such coverings may be conformed to the exterior dimensions of the mounting location (i.e., conformal antenna) or may be protected by armor of the like as necessary for the specific application. Accordingly, embodiments of the present concepts, systems, and techniques are not to be limited to any particular mounting or lack thereof but encompass all applications for which the present geodesic lens antenna array may be desirous. 
     While particular embodiments of the present invention have been shown and described, it will be apparent to those skilled in the art that various changes and modifications in form and details may be made therein without departing from the spirit and scope of the invention as defined by the following claims. Accordingly, the appended claims encompass within their scope all such changes and modifications.