Patent Publication Number: US-10790586-B2

Title: Adjustable stacked phase-mode feed for 2D steering of antenna arrays

Description:
FIELD 
     The present disclosure relates to beam-steering of antenna arrays. In particular, the present disclosure relates to a stacked phase-mode feed network for antenna arrays. 
     BACKGROUND 
     An antenna array is a set of individual radiating elements, connected together to act as a single antenna, with a main beam or lobe. Conventionally, an antenna array may be referred to as a single antenna. Beam steering is the angular positioning of the main beam by controlling the amplitude and/or phase of the individual radiating elements. Beam steering allows the antenna array to transmit in a preferential direction, namely the direction of the main beam, or provide increased reception sensitivity to signals received from the direction of the main beam. In order to obtain a desired radiation pattern for the main beam, different phase modes of the antenna array may be combined. 
     Circuitry for beam steering may comprise individual phase-shifters and/or delay units for each of the individual radiating elements that make up the antenna array. As the target frequency range of an antenna increases, the ideal spacing of radiating elements in the array decreases. The reduced spacing between radiating elements may increase the complexity in implementing the beam steering circuitry and feed network used to connect to the radiating elements, as the beam steering circuitry and feed network generally do not scale with wavelength, unlike antenna structures. 
     SUMMARY 
     In order to achieve a main beam having a greater tilt from the z-axis (i.e., greater radial steering range, or polar angle), it may be necessary to combine higher order phase modes of the antenna array. 
     In various examples, a sparse phase-mode feed network is described. The feed network enables any number of radiating elements in an antenna array to be fed by a smaller number of phase-mode feed probes. In examples disclosed herein, the feed network includes two feed ports and no Butler matrix, to feed any arbitrary number of radiating elements. Two waveguides are stacked, each waveguides serving one of two rings of a concentric antenna array. The disclosed configuration enables forming two consecutive-order phase modes, with the order of the phase modes adjustable by a control signal. 
     In some examples, the present disclosure describes a feed network for a steerable antenna array. The feed network includes a waveguide assembly including first and second radial transverse electromagnetic (TEM) waveguides, and first and second variable phase shifters. The first radial TEM waveguide includes a first plurality of radiating element probes for coupling to a first ring of radiating elements of the antenna array and the second radial TEM waveguide includes a second plurality of radiating element probes for coupling to a second ring of radiating elements of the antenna array. The first variable phase shifter is positioned in the first radial TEM waveguide. The first variable phase shifter is configured to cause additional progressive electrical phase shifts in the first ring of radiating elements, directly proportional to angular position of the radiating elements in the first ring, from 0 to an integer multiple of 2π radians, the integer multiple being controllable. The second variable phase shifter is positioned in the second radial TEM waveguide. The second variable phase shifter is configured to cause additional progressive electrical phase shifts in the second ring of radiating elements, directly proportional to angular position of the radiating elements in the second ring, from 0 to an integer multiple of 2π radians, the integer multiple being controllable. The feed network also includes first and second phase-mode feed probes coupled to the first and second radial TEM waveguides, respectively. The phase-mode feed probes provide respective phase-mode feed ports. When the feed network is coupled to the antenna array, two consecutive-order phase modes are provided at the phase-mode feed ports. The orders of the phase modes are selectable in accordance with at least one phase shift control signal controlling the integer multiple of the first and second variable phase shifters. 
     In any of the above embodiments/aspects, the waveguide assembly may be configured for a concentric circular antenna array. The first radial TEM waveguide may be configured to couple to an inner concentric ring of the antenna array and the second radial TEM waveguide may be configured to coupled to an outer concentric ring of the antenna array. The first and second radial TEM waveguides may be concentrically stacked on each other. 
     In any of the above embodiments/aspects, a lower order of the consecutive-order phase modes may be obtained from the first radial TEM waveguide, and a higher order of the consecutive-order phase modes may be obtained from the second radial TEM waveguide. 
     In any of the above embodiments/aspects, a higher order of the consecutive-order phase modes may be obtained from the first radial TEM waveguide, and a lower order of the consecutive-order phase modes may be obtained from the second radial TEM waveguide. 
     In any of the above embodiments/aspects, the waveguide assembly may be configured for a polygonal antenna array. 
     In any of the above embodiments/aspects, the first and second phase-mode feed probes may be coaxially arranged 
     In any of the above embodiments/aspects, the first and second variable phase shifters may be liquid crystal analog phase shifters. 
     In any of the above embodiments/aspects, separate first and second phase shift control signals may be used to control the integer multiple of the first and second variable phase shifters, respectively. The first variable phase shifter may be controlled to cause phase shifts in the first ring of radiating elements from 0 to K2π radians. The second variable phase shifter may be controlled to cause phase shifts in the second ring of radiating elements from 0 to (K+1) 2π radians, K being an integer. The phase modes provided at the phase-mode feed ports may be K-th and K+1-th order phase modes. 
     In any of the above embodiments/aspects, the feed network may include a fixed spiral phase shifter in the first radial TEM waveguide. The fixed spiral phase shifter may be configured to cause additional progressive electrical phase shifts in the first ring of the antenna array from 0 to 2π radians. The first and second variable phase shifters may be controlled by a common phase shift control signal. 
     In any of the above embodiments/aspects, the waveguide assembly may be configured for an antenna array having circularly polarized radiating elements. The first and second variable phase shifters may be controlled by a common phase shift control signal. 
     In some aspects, the present disclosure describes an apparatus for beam steering a steerable antenna array. The apparatus includes any of the above embodiments of the feed network and a beam steering circuitry. The beam steering circuitry is coupled to the phase-mode feed ports of the feed network. The beam steering circuitry is configured to combine the two consecutive-order phase modes to generate a main beam of the steerable antenna array. The beam steering circuitry controls the polar angle and azimuth angle of the main beam to direct the main beam in a selected direction. 
     In any of the above embodiments/aspects, the beam steering circuitry may include a monitoring and control sub-circuit configured to monitor signal strength of at least one of the phase modes and provide feedback for the phase shift control signal. 
     In some aspects, the present disclosure describes a steerable antenna array system. The system includes a plurality of radiating elements arranged in a planar antenna array. The system also includes any of the above embodiments of the feed network and any of the above embodiments of the beam steering circuitry. 
     In any of the above embodiments/aspects, the planar antenna array may be a circular antenna array, and the radiating elements may be arranged in concentric rings. 
     In any of the above embodiments/aspects, the planar antenna array may be a polygonal antenna array, and the radiating elements may be arranged in concentric polygons. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Reference will now be made, by way of example, to the accompanying drawings which show example embodiments of the present application, and in which: 
         FIG. 1  is a schematic diagram illustrating an example system for beam steering of a planar circular antenna array. 
         FIG. 2  schematically illustrates the incorporation of a variable phase shifter into one waveguide in the waveguide assembly of the feed network shown in  FIG. 1 ; 
         FIG. 3  is a schematic diagram illustrating an example liquid-crystal analog implementation of a variable phase shifter; 
         FIG. 4  is a schematic diagram illustrating a stacked waveguide assembly, showing incorporation of variable phase shifters into each waveguide; 
         FIG. 5  is a schematic diagram illustrating a stacked waveguide assembly, showing incorporation of variable phase shifters and a fixed phase shifter into the waveguides; 
         FIG. 6  is a schematic diagram illustrating orientation of circularly polarized radiating element, to achieve a first-order phase mode increment; 
         FIG. 7  is a schematic diagram of an example beam steering circuitry suitable for use in the system of  FIG. 1 ; 
         FIG. 8  illustrates an example hybrid splitter/combiner suitable for use in the beam steering circuitry of  FIG. 7 ; 
         FIG. 9  shows simulations of the radiation pattern of an example main beam, in an example configuration of the stacked waveguide assembly; and 
         FIG. 10  shows simulations of the radiation pattern of an example main beam, in another example configuration of the stacked waveguide assembly. 
     
    
    
     Similar reference numerals may have been used in different figures to denote similar components. 
     DESCRIPTION OF EXAMPLE EMBODIMENTS 
     The present disclosure describes a sparse phase-mode feed network that does not require a full N-port network to feed N radiating elements in an antenna array. In examples described below, two feed probes are used to feed two stacked waveguides. The phase-modes at the two phase-mode ports are two consecutive order phase-modes (generally referred to as P K  and P K+1 ), which may be selected using a control signal to control K. The example configurations disclosed herein may enable simple planar construction, without use of a Butler matrix. Because a Butler matrix is not required, space savings and reduction of feed losses may be achieved. The disclosed feed network may interface with any suitable beam steering circuitry, such as any beam steering circuitry designed for circular antenna arrays. 
     Examples described below may be suitable for use with a planar circular antenna array with two concentric rings of radiating elements. An example of an antenna array with concentric rings of radiating elements is described by Tiezhu Yuan, Hongqiang Wang, Yuliang Qin, and Yongqiang Cheng in “Electromagnetic Vortex Imaging Using Uniform Concentric Circular Arrays”  IEEE Antennas and Wireless Propagation Letters , Vol. 15, pp. 1024-1027, 2016, incorporated herein by reference in its entirety. 
     Spatial combining of the fields generated by the concentric radiating elements, fed by two consecutive phase-modes, result in a 2D steerable beam with a desired tilt from the z-axis. A variable ratio combiner (VRC) may also be implemented in the beam steering circuitry, as discussed further below. 
       FIG. 1  schematically illustrates components of an example system for beam steering of a steerable antenna array. The system  100  may be used for both transmission and reception. The system  100  includes a circular antenna array (not shown) and a feed network  102 . Although other antenna array arrangements may be suitable, in examples described herein the antenna array has a set of N radiating elements (not shown) arranged in a planar circular array of two concentric rings. Generally, the antenna array may have any arrangement of radiating elements (e.g., in a circular or polygonal configuration), provided the radiating elements are arranged such that they give rise to the phase modes (e.g., radiating elements are arranged concentrically along the perimeter of a polygon). The individual radiating elements are arranged at a spacing of approximately half the wavelength A at which the antenna array is designed to operate. Each of the individual radiating elements is connected to a respective radiating element probe  104  of a radial waveguide transition assembly  130 . Each radiating element probe  104  provides the transmission or reception signal to or from the respective radiating element. 
     In the example shown, the waveguide transition assembly  130  includes two stacked radial transverse electromagnetic (TEM) waveguides  106   a ,  106   b  (generally referred to as radial TEM waveguide  106 ), with the radiating element probes  104  arranged in a circular pattern in each radial TEM waveguide  106 , corresponding to the concentric arrangement of the radiating elements in the antenna array. The construction of the radial TEM waveguide  106  may be similar to that described in U.S. Pat. No. 9,413,067, filed Apr. 25, 2013; U.S. Pat. No. 9,768,503, filed Jun. 3, 2014; U.S. Pat. No. 10,148,009, filed Nov. 23, 2015; and U.S. Pat. No. 10,283,862, filed Oct. 17, 2016; all of which are hereby incorporated by reference in their entireties, with appropriate modifications as described herein. It should be noted that although the TEM waveguides  106  are stacked on each other, the radiating element probes  104  may be coupled to radiating elements that are in the same or different plane. In this example, the TEM waveguides  106  are stacked with the upper radial TEM waveguide  106   a  being smaller than the lower radial TEM waveguide  106   b . In other examples, the upper radial TEM waveguide  106   a  may be larger than the lower radial TEM waveguide  106   b . Generally, the upper and lower radial TEM waveguides  106   a ,  106   b  may be referred to as first and second radial TEM waveguides  106   a ,  106   b . For ease of understanding, the following discussion will refer to upper and lower radial TEM waveguides  106   a ,  106   b , however it should be understood that the “upper” and “lower” are not intended to be limiting. 
     In this example, there are two feed probes  108   a ,  108   b  (generally referred to as feed probe  108 ) coupled to phase-mode feed ports  110  of the feed network  102 . Notably, a Butler matrix is not required, which may result in space saving and/or reduction of feed losses due to the Butler matrix. The number of phase-mode feed probes  108  is always two regardless of the number N of radiating elements. In the examples disclosed herein, the two feed probes  108  are provided in a coaxial configuration (also referred to as a triaxial configuration), however other arrangements of the feed probes  108  may also be suitable, for example configurations having more conductor layers and/or having rings, caps or other structures attached for impedance matching and/or tuning purposes. 
     In  FIG. 1 , the feed probes  108  are shown separated from the waveguide assembly  130 , for clarity, however when implemented the feed probes  108  are connected to the waveguide assembly  130 . For example, as shown in  FIG. 1 , the inner feed probe  108   a  may be connected to the upper radial TEM waveguide  106   a , and the outer probe  108   b  may be connected to the lower radial TEM waveguide  106   b . It should be noted that, as shown in  FIG. 1 , the outer probe  108   b  is not necessarily provided by the outermost conductor of the coaxial feed probes  108 . Similarly, the inner probe  108   a  is not necessarily provided by the innermost conductor of the coaxial feed probes  108 . In this particular example, the innermost coaxial cylinder of the coaxial feed probes  108  protrudes into the upper radial TEM waveguide  106   a  (e.g., about half-way or ⅛ wavelength into the waveguide  106   a ) and interfaces with the K-th phase-mode signal. The inner surface of the middle cylinder of the coaxial feed probes  108  provides the return path for the currents of the K-th phase-mode interface from the inner surface of the bottom disk of the upper radial TEM waveguide  106   a . The outer surface of the middle cylinder of the coaxial feed probes  108  forms the interface for the K+1-th phase-mode signal in the lower radial TEM waveguide  106   b  and connects to the top metal disk of the lower radial TEM waveguide  106   b . Similarly, the inner surface of the outermost cylinder of the coaxial feed probes  108  connects to the bottom disk of the lower radial TEM waveguide  106   b  and provides the return path for the currents of the K+1-th phase-mode interface. All three coaxial conductors of the coaxial feed probes  108  are separated by dielectric materials and their bottom ends can terminate in the same plane at or below the bottom conductor disk of the lower radial TEM waveguide  106   b.    
     When the phase-mode feed ports  110  are coupled to the phase-mode feed probes  108 , each of the phase-mode feed ports  110  may correspond to the antenna array transmitting, or receiving, signals according to a respective one of two consecutive-order phase modes P K  and P K+1 , discussed further below. Although  FIG. 1  shows the outer feed probe  108   b , when connected to the lower radial TEM waveguide  106   b , providing the K+1-th phase mode and the inner feed probe  108   a , when connected to the upper radial TEM waveguide  106   a , providing the K-th phase mode, this may be reversed, as discussed further below. 
     The phase-mode feed ports  110  are coupled to a beam steering circuitry  120 , which provides a steered main beam M at a main port  122 . Examples of suitable beam steering circuitries are described in the above-referenced U.S. patent applications. 
     The beam steering circuitry  120  may combine signals from the two phase-mode feed ports  110  to obtain a desired main beam M directed at a desired direction. For example, the two consecutive-order phase modes of the antenna array may be combined to achieve a desired tilt, or polar angle, of the main beam M. It has been found that combination of phase modes that differ by one results in a main beam M that may be more easily steered circumferentially using simple phase control. The beam steering circuitry  120  may control the radial (i.e., polar angle) and circumferential (i.e., azimuth angle) directions of the main beam M in order to enable scanning of the antenna array in desired directions. A phase shift control signal  155  is used to control phase shift of the radiating elements of the antenna array so as to create the requisite phase-modes. The phase shift control signal  155  is used to control a variable phase shifter (not shown in  FIG. 1 ) in each of the radial TEM waveguides  106 , discussed further below. The variable phase shifter is shown as a spiral in various figures for the purpose of illustration only. Further, the variable phase shifter may be incorporated into the waveguide assembly  130  and may not be visible externally. The phase shift control signal  155  may be outputted to the variable phase shifter from the beam steering circuitry  120  or from a separate circuitry. The main beam M, provided at the main port  122  of the beam steering circuitry  120 , is provided to a radio transceiver  140  for use in transmission/reception. An auxiliary output, such as auxiliary signals A 1  and/or A 2  (see  FIG. 7 ), may also be provided for purposes such as interference mitigation or direction-finding. 
     An example configuration of the radial TEM waveguide  106  is now described. The upper and lower radial TEM waveguides  106   a ,  106   b  may be similar in construction and the following description may be similarly applicable to both the upper and lower radial TEM waveguides  106   a ,  106   b . In an example, the upper and lower radial TEM waveguides  106   a ,  106   b  differ in radii by half of wavelength A in the dielectric material used in their construction. This λ/2 difference in radii between the upper and lower radial TEM waveguides  106   a ,  106   b  was found to achieve a main beam M with reduced side lobes. However, other dimensions may also be suitable. 
     The example configuration described here may be suitable for use with a planar circular antenna array. In an example, each radial TEM waveguide  106  includes substantially parallel conductive circular disks separated by about ¼ wavelength λ in dielectric. The total thickness of the stacked waveguide assembly  130  is then less than or equal to about half wavelength λ in air. The N radiating element probes  104  are about ¼ wavelength λ from a circumferential vertical conductive wall joining the top and bottom circular disks in each radial TEM waveguide  106 . In the example shown, each radial TEM waveguide  106  has the same number of probes  104  (corresponding to the configuration of radiating elements in the antenna array). In the lower radial TEM waveguide  106   b , the probes  104  are spaced slightly wider than half-wavelength, and in the upper radial TEM waveguide  106   a , the probes  104  are spaced slightly closer than half-wavelength; the average spacing of all the probes  104  is about half-wavelength. In other examples, there may be different numbers of probes  104  for the two TEM waveguides  106 , and the spacing of the probes  104  may be different. In this example, the radial spacing between the probes  104  of the upper and lower TEM waveguides  106  is about half-wavelength, but this may also be varied. The N outer radiating element probes  104  have their outer conductors connected to the top disk and their inner conductors protruding about ⅛ wavelength λ into the space between the disks, but not touching the bottom disk. The other ends of the N radiating element probes  104  inner conductors are connected to the radiating elements via matched-impedance element-feed planar or non-planar networks. This planar construction may enable easier incorporation into the antenna array and feed network. 
     Example dimensions and properties of the above example configuration are now described. In some examples, λ=1.876 mm. The example dielectric used in the coaxial probes and between the disks has the following properties: ε r =7.1, DuPont 9K7 LTCC material, f=60 GHz. In each TEM waveguide  106 , the separation between parallel metal disks=0.53 mm (i.e., 0.2824λ or approximately λ/4). The probe height between the top pair of the parallel metal circular disks (defining the upper radial TEM waveguide  106   a )=0.234 mm (i.e., approximately λ/8). The innermost conductor of the coaxial probes has a diameter of 115 μm (about 0.0617λ). The central conductor has an outer diameter of 200 μm (or about λ/10). The diameters of the inner and central conductors in the coaxial feed probe assembly  108  should have the same ratio as the diameters of the central and outer conductors. Thus, the outermost conductor has an outer diameter of 348 μm, or about 0.16 to 0.1854λ (not accounting for the thickness of the metal). In some examples, cylindrical coaxial structures may be added to the coaxial conductors of each of the central feed probes  108  in order to optimize their impedance matches to their respective radial TEM waveguides  106 . The characteristic impedances of the concentric inner and outer coaxial probes in this example are 12.06 Ohms. 
     The radiating element probes  104  may have inner and outer diameters of 115 μm (about 0.0617λ) and 200 μm (or about λ/10), respectively, or other dimensions that facilitate matching of the element impedances to that of the radial TEM waveguides  106 . In the upper radial TEM waveguide  106   a , the element probes  104  may be placed uniformly around a circle of a radius that is about λ/4 smaller than that required to space them at λ/2 intervals around its circumference, i.e. 1.9196 mm. The vertical conductive wall connecting the top and bottom metal disks of the upper radial TEM waveguide  106   a  may have a radius of 2.3886 mm, which would place it λ/4 farther from center than the element probes  104 . The element probes  104  in the lower radial TEM waveguide  106   b  may be evenly spaced at a radius about λ/4 larger than the outer wall of the upper waveguide  106   a , or about 2.8576 mm, and the outer vertical wall connecting the top and bottom disks of the lower radial TEM waveguide  106   b  may have a radius about λ/4 larger than that of the circle of its element probes  104 , or about 3.3266 mm. 
     As also demonstrated in other disclosures noted above, the radiating elements themselves may be built into the top metallic disks of the TEM waveguides  106 , such as crossed slots, omitting the element probes  104  entirely. 
       FIG. 2  schematically represents a variable phase shifter  150  incorporated into one radial TEM waveguide  106 , in this example the lower radial TEM waveguide  106   b . It should be understood that another variable phase shifter  150 , of similar or identical construction (e.g., smaller dimensions or same dimensions), may be similarly incorporated into the upper radial TEM waveguide  106   a . The variable phase shifter  150  is positioned in the radial TEM waveguide  106   b  such that the TEM wave propagating radially between the radiating element probes  104  and the corresponding phase-mode feed probe  108   b  experiences an electrical phase shift ranging linearly from 0 to K2π radians (corresponding to radial propagation distance of Kλ) with the azimuthal angular direction of propagation inside the radial TEM waveguide  106   b . The variable phase shifter  150  thus causes additional phase shift at the radiating elements, from a phase shift of 0 to a phase shift of an integer multiple of 2π radians, denoted K2π, where K is a selectable integer value corresponding to the order of the phase mode and K is controlled by the phase shift control signal  155 , where the phase shift progresses for one complete physical angular cycle around the plane of the TEM waveguide  106   b . The phase shifter  150  causes a phase shift in the radiating elements that progresses linearly from 0 to K2π radians. That is, the phase shifter  150  causes a phase shift in the radiating elements that is directly proportional to the angular position of the radiating elements in the circle. Generally, for N evenly-spaced radiating elements, the variable phase shifter  150  causes an additional phase shift at the m-th radiating element that is equal to (mK2π)/N radians. Where the radiating elements are arranged in a circular arrangement in a planar circular antenna array, the radiating element at a first position has an additional phase shift of (K2π)/N radians, and the phase shift linearly increases in a circular direction (as represented as a spiral shown in  FIG. 2 ) such that the radiating element at the Nth position (which is adjacent to the first position) has an additional phase shift of K2π radians. In some examples, the phase shift control signal  155  may be provided as an adjustable voltage signal proportional to K. The phase shift control signal  155  may be provided by the beam steering circuitry  120  or by a separate circuitry. 
       FIG. 3  is a schematic diagram illustrating an example liquid-crystal analog implementation of the variable phase shifter  150 . The example variable phase shifter  150  shown in  FIG. 3  may be incorporated into the dielectric between the two disks of the radial TEM waveguide  106 , for example. In this example, the variable phase shifter  150  has a circular configuration, to cause phase shift in a planar circular antenna array. The variable phase shifter  150  may be configured similarly to the liquid-crystal analog phase shifter described in U.S. patent application Ser. No. 14/603,908 filed Jan. 23, 2015, incorporated herein by reference in its entirety. In the example of  FIG. 3 , the spiral phase shifter  150  has a torus-shaped liquid crystal compartment  152 . The liquid crystal compartment  152  may be similar to that described by Kuangda Wang and Ke Wu in “Liquid Crystal Enabled Substrate Integrated Waveguide Variable Phase Shifter for Millimeter-Wave Applications at 60 GHz and Beyond”,  Proceedings of IEEE International Microwave Symposium IMS,  2015, incorporated herein by reference in its entirety. 
     A plurality of electrodes  158  are positioned radially around the liquid crystal compartment  152  and are connected by identical resistors  153 . The variable phase shifter  150  has a first end  154  connected to ground, and a second end  156  that receives the phase shift control signal  155  (which may be in the form of a control voltage). The variable phase shifter  150  generates an electric field that causes the progressive phase shift in the radiating elements. It should be noted that the number of electrodes  158  does not necessarily correspond to the number of radiating elements in the antenna array. However, it may be useful for the number of electrodes  158  to be at least equal to the number of radiating elements, to ensure that the phase shift caused in the radiating elements progresses linearly from 0 to K2π, which effects a K-th order phase mode. Other configurations for the variable phase shifter  150  may be used. For example, where the antenna array has a non-circular arrangement of radiating elements, the variable phase shifter  150  may correspondingly be non-circular in shape. It should be noted that the variable phase shifter  150  is positioned in the radial TEM waveguide  106  to occupy the annular region between the phase-mode feed probes  108  and the radiating element probes  104 . 
       FIG. 4  illustrates the stacked waveguide assembly  130 , with a respective variable phase shifter  150  incorporated into each radial TEM waveguide  106 . For clarity,  FIG. 4  illustrates the upper and lower TEM waveguides  106   a ,  106   b  and the feed probes  108  in an exploded view. In this example, the upper radial TEM waveguide  106   a  is provided with a first variable phase shifter  150   a , which causes a linear phase shift around the radial TEM waveguide  106   a  from 0 to K2π, giving rise to the K-th order phase mode. The lower radial TEM waveguide  106   b  is provided with a second variable phase shifter  150   b , which causes a linear phase shift around the radial TEM waveguide  106   a  from 0 to (K+1)2π, giving rise to the K+1-th order phase mode. As will be discussed further below, the order of the phase modes may be reversed, such that the K-th order phase mode arises from the lower radial TEM waveguide  106   b  and the K+1-th order phase mode arises from the upper radial TEM waveguide  106   a . The variable phase shifters  150   a ,  150   b  may be controlled by a common phase shift control signal  155 , with appropriate circuitry being used to split and modify the phase shift control signal  155  into separate signals proportional to K and K+1, for example. Alternatively, two separate phase shift control signals  155  may be used, with the two phase shift control signals  155  being separately proportional to K and K+1. 
     Alternatively, a common phase shift control signal  155 , proportional K, may be used to directly control both variable phase shifters  150   a ,  150   b  with the addition of a fixed spiral phase shifter, as schematically illustrated in  FIG. 5  in an exploded view. The configuration shown in  FIG. 5  may be similar to that of  FIG. 4 . However, both the first and second variable phase shifters  150   a ,  150   b  may be controlled by a common phase shift control signal  155  such that both the first and second variable phase shifters  150   a ,  150   b  give rise to a linear phase shift from 0 to K2π. One of the radial TEM waveguides  106  (the lower radial TEM waveguide  106   b  in this example) may be provided with a fixed spiral phase shifter  160  that causes a linear phase shift from 0 to 27 around the radial TEM waveguide  106   b , such that the total linear phase shift around the radial TEM waveguide  106   b  is 0 to (K+1)2π. Thus, the configuration illustrated in  FIG. 5  may achieve the same output at the phase-mode feed ports  110  as the configuration in  FIG. 4 , however the configuration illustrated in  FIG. 5  enables a single common phase shift control signal  155  to be used to directly control both the first and second variable phase shifters  150   a ,  150   b . It should be understood that the fixed spiral phase shifter  160  may be provided for the upper radial TEM waveguide  106   a  instead, in order to obtain the K+1-th order phase mode from the upper radial TEM waveguide  106   a . The fixed spiral phase shifter  160  may be implemented in a manner similar to that shown in  FIG. 3 , but without variable control. 
     It should be understood that the fixed spiral phase shifter  160  may be provided for the upper radial TEM waveguide  106   a  instead, such that the K+1-th order phase mode arises from the upper radial TEM waveguide  106   a.    
     Alternatively, instead of using the fixed spiral phase shifter  160 , a first-order phase mode increment may be achieved by appropriate orientation of the radiating elements, in the case where the radiating elements are circularly polarized.  FIG. 6  is a schematic diagram illustrating example orientation of circularly polarized radiating elements in a circular antenna array. In this example, the antenna array  170  includes radiating elements arranged in an inner ring  172  and a concentric outer ring  174 . The radiating elements of the inner ring  172  are coupled to the upper radial TEM waveguide  106   a  (not shown in  FIG. 6 ) and the radiating elements of the outer ring  174  are coupled to the lower radial TEM waveguide  106   b  (not shown in  FIG. 6 ). As shown in  FIG. 6 , the polarization references of the radiating elements in the inner ring  172  are aligned in the same direction, and the polarization references of the radiating elements in the outer ring  174  are aligned in radial directions. Thus, a first-order phase mode increment is effected in the outer ring  174 , due to the orientation of the circularly polarized radiating elements in the outer ring  174 , and the fixed spiral phase shifter  160  is not needed. Using the arrangement shown in  FIG. 6 , a single common phase shift control signal  155  (proportional to K) to be used to directly control both the first and second variable phase shifters  150   a ,  150   b , the first and second variable phase shifters  150   a ,  150   b  may be essentially identical and controlled to provide the same phase shift, and a fixed spiral phase shifter  160  is not required. 
     It should be understood that a similar arrangement may be used where the polarization references of the radiating elements progress in the opposite direction, to effect a first-order phase mode decrement. Further, the radial alignment of the polarization references may be switched between the inner and outer rings  172 ,  174 . That is, the polarization references of the radiating elements in the outer ring  174  may be aligned in the same direction and the polarization references of the radiating elements in the inner ring  172  may be radially aligned. 
     Thus,  FIGS. 4, 5 and 6  show alternative approaches to achieving two consecutive-order phase modes at the phase-mode feed ports  110 . The approach that is implemented may be selected based on factors such as cost, size and/or antenna characteristics. For example, the configuration shown in  FIG. 6  may be limited to only antennas having circularly polarized radiating elements. The configuration shown in  FIG. 4  may require the use of two separate phase shift control signals  155 , however may provide greater flexibility in selecting which TEM waveguide  160  effects the higher-order phase mode. The basic main beam steering effect that is produced is not dependent on which of the arrangements of  FIG. 4, 5 or 6  is used. Whether the higher-order phase mode results from the upper radial TEM waveguide  106   a  or the lower radial TEM waveguide  106   b  may be selected depending on the desired beam shape, as discussed further below. 
       FIG. 7  shows an example of the beam steering circuitry  120 , suitable for use with an example feed network  102  as described herein. The beam steering circuitry  120  controls the polar angle φ s  and azimuth angle θ s  of the main beam M. In  FIG. 7 , the feed network  102  for a circular antenna array is represented as a star shape inside concentric rings of circular patches representing the radiating elements of the antenna array. The spiral shapes inside the star shape represents the variable phase shifters. In this example, two variable phase shifters are shown, however any of the configurations described above, for example as discussed with reference to  FIGS. 4, 5 and 6 , may be used with the beam steering circuitry  120  of  FIG. 7 . 
     In  FIG. 7 , the P K+1  and P K  signals are coupled to the beam steering circuitry  120 , and are combined in a selected proportion of amplitude and phase, according to the circuitry shown. The example circuitry includes two variable-ratio couplers (VRCs)  202  that set the polar angle φ s  by varying the electrical phase of its internal opposed phase shifters by ±Φ 5 . The VRCs  202  each includes two hybrid splitters/combiners that are coupled to each other via two phase shifters that provide equal but opposite amounts of phase shifts. 
       FIG. 8  illustrates an example hybrid splitter/combiner suitable for use in the VRCs  202 . The hybrid splitter/combiner may be a 180° hybrid. The relationship between the ports of the hybrid  136  is as shown in  FIG. 8 . 
     Referring back to  FIG. 7 , the P K+1  signal is coupled to a phase shifter  204  that sets the azimuth angle θ s . The output of the beam steering circuitry  120  is the main beam M, as well as an auxiliary signal A 1 , which may be used for other purposes, including interference mitigation, direction finding and/or feedback control, for example. In the example shown, signals M and A 1  are formed from the phase-mode signals as follows:
 
 M =(− j /√{square root over (2)})[ P   K  cos ϕ s   −P   K+1   e   jθ     s    sin ϕ s ]
 
 A   1 =(− j /√{square root over (2)})[ P   K  sin ϕ s   +P   K+1   e   jθ     s    cos ϕ s ]
 
     The example circuitry in  FIG. 7  provides for both azimuthal and radial steering of the main beam. The polar angle is controlled by controlling how the amplitudes of the phase-mode signals are combined, and the azimuth angle is controlled by controlling how the phases of the phase-mode signals are combined. The phase shift control signal  155  controls the amount of phase shift caused by the variable phase shifters of the feed network  102 , which in turn determines the two consecutive-order (i.e., K and K+1) of the phase modes coupled to the beam steering circuitry  120 . Using the phase shift control signal  155 , different values of K can be selected to access higher orders of phase modes. By combining higher orders of phase modes, hence greater axial tilt in the radial direction (i.e., greater values of polar angle φ s ) can be achieved in the main beam M. The azimuthal steering direction θ s  can be varied independently over the full physical range of 2π (corresponding to electrical phase-shift range of 2π) by the phase shifter  204  for any radial tilt direction, including different values of K. The value of K may be selected by iteratively selecting different values of K (e.g., starting from 0 and incrementing by 1 each iteration) and monitoring signals from the beam steering circuitry  120  to select a desired value of K. For example, a monitoring and control sub-circuit  206  may be part of the beam steering circuitry  120 . The monitoring and control sub-circuit  206  may include circuitry and/or a processor to monitor the signal strength of one or both of the phase modes, and search for the value of K that achieves a maximum signal. This search for a suitable value of K may be performed by monitoring the phase modes before they are combined into the main beam M, for example using feedback as indicated in  FIG. 7 . After the appropriate value of K has been selected, the phase shift control signal  155  may control the variable phase shifters of the feed network  102 , to obtain the desired consecutive-order phase modes. The steering of the main beam M may be carried out using suitable beam steering techniques. 
       FIG. 9  shows simulations of the radiation pattern of an example main beam M, in an example configuration of the waveguide assembly  130  and using the circuitry of  FIG. 7 , in which the higher-order phase mode (i.e., P K+1 ) is from the lower radial TEM waveguide  106   b  and the lower-order phase mode (i.e., P K ) is from the upper radial TEM waveguide  106   a , and where the difference in radii between the upper and lower radial TEM waveguides  106   a ,  106   b  is λ/2 and the radiating elements fed by both TEM waveguides  166  are in the same plane. The simulations in  FIG. 9  were carried out for K=0, 1, 2 and 3 (shown left-to-right).  FIG. 10  shows simulations of the radiation pattern of an example main beam, in another example configuration of the stacked waveguide assembly  130  and using the circuitry of  FIG. 7 . Similar to the simulations carried out for  FIG. 9 , in the simulations carried out for  FIG. 10 , the difference in radii between the upper and lower radial TEM waveguides  106   a ,  106   b  is λ/2 and K=0, 1, 2 and 3 (shown left-to-right). However, in the simulations of  FIG. 10 , the higher-order phase mode (i.e., P K+1 ) is from the upper radial TEM waveguide  106   a  and the lower-order phase mode (i.e., P K ) is from the lower radial TEM waveguide  106   b , and all the radiating elements of the concentric ring antenna array are in the same plane. 
     It can be seen that the radiation patterns in  FIG. 9  has smaller side lobes than the radiation patterns in  FIG. 10 . On the other hand, the radiation patterns in  FIG. 10  may provide finer control of radial tilt than the radiation patterns in  FIG. 9 . Thus, the appropriate configuration may be selected based on different applications. 
     Examples disclosed herein may enable greater tilt from the z-axis, compared to what is available with arrangements using only phase-modes corresponding to K=0, +1, −1, and may be useful particularly where limited 2D steering is desirable. Further, examples disclosed herein may enable reduction of feed losses and reduction in the number of phase-shifters used. For example, because a Butler matrix is not required, the feed network may be simplified. The number of phase-shifters needing to be controlled is a fixed small number independent of the number of radiating elements in the circular antenna array, unlike many conventional approaches. 
     The disclosed configurations may be implemented with the feed and antenna arrays integrated in a planar structure. An all-planar configuration may facilitate integration with an axially-radiating circular antenna array and two-axis phase-mode-enabled beam-steering subsystem. 
     The disclosed configurations enable any number of radiating elements to be fed, using a fixed number of phase shifters independent of the number of elements, thus enabling realization of a low cost, small size antenna. 
     Although examples provided herein show implementation for a planar circular antenna array, the teachings of this disclosure may be adapted to non-circular antenna arrays, including polygonal (e.g., square) antenna arrays. The teachings of this disclosure may be applicable to filled antenna arrays (e.g., radial slot arrays) as well as partially-filled antenna arrays. For polygonal antenna arrays, the variable phase shifter is again positioned in the annular region between the central coaxial phase-mode feed probes and the radiating element probes, and the phase shift progresses in a linear progression in a circumferential direction around the polygon. Although examples described herein show implementation for an antenna array having two concentric rings of radiating elements, there may be a greater number of rings of concentric elements. For example, one or both of the radial TEM waveguides may feed more than one ring of radiating elements. 
     Examples disclosed herein may be useful for microwave and/or millimeter wave (mmWave) antenna arrays, for example in small-cell, high-capacity networks, such as those found in dense urban environments. For example, electronic devices such as small-cell backhaul, mmWave peer-to-peer radio devices, or mobile satellite communications (satcom) terminals may benefit from the disclosed examples. 
     The present disclosure may be embodied in other specific forms without departing from the subject matter of the claims. The described example embodiments are to be considered in all respects as being only illustrative and not restrictive. Selected features from one or more of the above-described embodiments may be combined to create alternative embodiments not explicitly described, features suitable for such combinations being understood within the scope of this disclosure. 
     All values and sub-ranges within disclosed ranges are also disclosed. Also, although the systems, devices and processes disclosed and shown herein may comprise a specific number of elements/components, the systems, devices and assemblies could be modified to include additional or fewer of such elements/components. For example, although any of the elements/components disclosed may be referenced as being singular, the embodiments disclosed herein could be modified to include a plurality of such elements/components. The subject matter described herein intends to cover and embrace all suitable changes in technology.