Patent Publication Number: US-8976066-B2

Title: Beam-forming antenna with amplitude-controlled antenna elements

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application is a continuation of U.S. patent application Ser. No. 12/981,326, filed Dec. 29, 2010, now, U.S. Pat. No. 8,456,360, which is a continuation-in-part of U.S. patent application Ser. No. 12/253,790, filed Oct. 17, 2008, now U.S. Pat. No. 7,864,112, which is a continuation of U.S. patent application Ser. No. 11/201,680, filed Aug. 11, 2005, now U.S. Pat. No. 7,456,787, all titled BEAM-FORMING ANTENNA WITH AMPLITUDE-CONTROLLED ANTENNA ELEMENTS, the disclosures of which are hereby incorporated by reference as if set forth in full herein. 
    
    
     FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not Applicable 
     BACKGROUND 
     This invention relates generally to the field of directional antennas for transmitting and/or receiving electromagnetic radiation, particularly (but not exclusively) microwave and millimeter wavelength radiation. More specifically, the invention relates to a composite beam-forming antenna comprising an array of antenna elements, wherein the shape of the transmitted or received beam is determined by controllably varying the effective oscillation amplitude of individual antenna elements. In the context of this invention, the term “beam shape” encompasses the beam direction, which is defined as the angular location of the power peak of the transmitted/received beam with respect to at least one given axis, the beamwidth of the power peak, and the side lobe distribution of the beam power curve. 
     Beam-forming antennas that allow for the transmission and/or reception of a highly directional electromagnetic signal are well-known in the art, as exemplified by U.S. Pat. No. 6,750,827; U.S. Pat. No. 6,211,836; U.S. Pat. No. 5,815,124; and U.S. Pat. No. 5,959,589. These exemplary prior art antennas operate by the evanescent coupling of electromagnetic waves out of an elongate (typically rod-like) dielectric waveguide to a rotating cylinder or drum, and then radiating the coupled electromagnetic energy in directions determined by surface features of the drum. By defining rows of features, wherein the features of each row have a different period, and by rotating the drum around an axis that is parallel to that of the waveguide, the radiation can be directed in a plane over an angular range determined by the different periods. This type of antenna requires a motor and a transmission and control mechanism to rotate the drum in a controllable manner, thereby adding to the weight, size, cost, and complexity of the antenna system. 
     Other approaches to the problem of directing electromagnetic radiation in selected directions include gimbal-mounted parabolic reflectors, which are relatively massive and slow, and phased array antennas, which are very expensive, as they require a plurality of individual antenna elements, each equipped with a costly phase shifter. 
     There has therefore been a need for a directional beam antenna that can provide effective and precise directional transmission as well as reception, and that is relatively simple and inexpensive to manufacture. 
     SUMMARY OF THE INVENTION 
     Broadly, the present invention is a reconfigurable, directional antenna, operable for both transmission and reception of electromagnetic radiation (particularly microwave and millimeter wavelength radiation), that comprises a transmission line that is electromagnetically coupled to an array of individually controllable antenna elements, each of which is oscillated by the transmitted or received signal with a controllable amplitude. 
     More specifically, for each beam-forming axis, the antenna elements are arranged in a linear array and are spaced from each other by a distance that is no greater than one-third the wavelength, in the surrounding medium, of the transmitted or received radiation. The oscillation amplitude of each of the individual antenna elements is controlled by an amplitude controlling device that may be a switch, a gain-controlled amplifier, a gain-controlled attenuator, or any functionally equivalent device known in the art. The amplitude controlling devices, in turn, are controlled by a computer that receives as its input the desired beamshape, and that is programmed to operate the amplitude controlling devices in accordance with a set of stored amplitude values derived empirically, by numerical simulations, for a set of desired beamshapes. 
     As will be more readily appreciated from the detailed description that follows, the present invention provides an antenna that can transmit and/or receive electromagnetic radiation in a beam having a shape and, in particular, a direction that can be controllably selected and varied. Thus, the present invention provides the beam-shaping control of a phased array antenna, but does so by using amplitude controlling devices that are inherently less costly and more stable than the phase shifters employed in phased array antennas. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic view of a beam-forming antenna in accordance with the present invention, in which the antenna is configured for transmission; 
         FIG. 2  is a schematic view of a beam-forming antenna in accordance with the present invention, in which the antenna is configured for reception; 
         FIG. 3  is a schematic view of a beam-forming antenna in accordance with the present invention, in which the antenna is configured for both transmission and reception; 
         FIG. 4  is a schematic diagram of a beam-forming antenna in accordance with the present invention, in which the spacing distances between adjacent antenna elements are unequal; 
         FIG. 5  is a schematic diagram of a plurality of beam-forming antennas in accordance with the present invention, wherein the antennas are arranged in a single plane, in parallel rows, to provide beam-shaping in three dimensions; 
         FIG. 6   a  is a first exemplary far-field beam shape produced by a beam-forming antenna in accordance with the present invention, wherein a denotes the azimuth angle; and  FIG. 6   b  is a graph of the RF power distribution for the array of antenna elements that results in the beam shape of  FIG. 6   a;    
         FIG. 7   a  is a second exemplary far-field beam shape produced by a beam-forming antenna in accordance with the present invention, wherein a denotes the azimuth angle; and  FIG. 7   b  is a graph of the RF power distribution for the array antenna elements that results in the beam shape of  FIG. 7   a;    
         FIG. 8   a  is a third exemplary far-field beam shape produced by a beam-forming antenna in accordance with the present invention, wherein a denotes the azimuth angle; and  FIG. 8   b  is a graph of the RF power distribution for the array of antenna elements that results in the beam shape of  FIG. 8   a;    
         FIG. 9   a  is a fourth exemplary far-field beam shape produced by a beam-forming antenna in accordance with the present invention, wherein a denotes the azimuth angle; and  FIG. 9   b  is a graph of the RF power distribution for the array of antenna elements that results in the beam shape of  FIG. 9   a;    
         FIG. 10   a  is a fifth exemplary far-field beam shape produced by a beam-forming antenna in accordance with the present invention, wherein a denotes the azimuth angle; and  FIG. 10   b  is a graph of the RF power distribution for the array of antenna elements that results in the beam shape of  FIG. 10   a;    
         FIG. 11   a  is a sixth exemplary far-field beam shape produced by a beam-forming antenna in accordance with the present invention, wherein a denotes the azimuth angle; and  FIG. 11   b  is a graph of the RF power distribution for the array of antenna elements that results in the beam shape of  FIG. 11   a;    
         FIGS. 12-14  are graphs of exemplary far-field power distributions produced in three dimensions by a 2-dimensional beam-forming antenna in accordance with the present invention, wherein α represents azimuth and β represents elevation, and wherein the power contours on the graph are measured in dB; 
         FIG. 15  is a semi-diagrammatic view of a beam-forming antenna in accordance with the present invention; 
         FIGS. 16   a - b  show exemplary far-field beam shapes produced by a beam-forming antenna in accordance with the present invention; 
         FIG. 17  is a graph of pixel spacings for a beam-forming antenna in accordance with one embodiment of the present invention; 
         FIGS. 18   a - b  show exemplary far-field beam shapes produced by a beam-forming antenna having the pixel spacing of  FIG. 18 ; 
         FIG. 19  is a graph of pixel spacings for a beam-forming antenna in accordance with another embodiment of the present invention; 
         FIGS. 20   a - b  show exemplary far-field beam shapes produced by a beam-forming antenna having the pixel spacing of  FIG. 19 ; 
         FIG. 21  is a semi-diagrammatic view of a beam-forming antenna in accordance with still another embodiment of the present invention; 
         FIG. 22  is a graph of pixel locations for the beam-forming antenna of  FIG. 21 ; 
         FIG. 23  shows an exemplary far-field beam shapes produced by the beam-forming antenna of  FIG. 21 ; 
         FIG. 24  is a semi-diagrammatic view of a beam-forming antenna in accordance with a further embodiment of the present invention; 
         FIG. 25  is a graph of pixel locations for the beam-forming antenna of  FIG. 24 ; 
         FIG. 26  shows an exemplary far-field beam shapes produced by the beam-forming antenna of  FIG. 24 ; 
         FIG. 27  is a semi-diagrammatic view of one embodiment of a surface-array beam-forming antenna in accordance with an aspect of the present invention; 
         FIG. 28  shows an exemplary far-field beam shape produced by the beam-forming antenna of  FIG. 27 ; 
         FIG. 29  is a semi-diagrammatic view of another embodiment of a surface-array beam-forming antenna in accordance with the present invention; 
         FIG. 30  shows an exemplary far-field beam shape produced by the beam-forming antenna of  FIG. 29 ; 
         FIG. 31  is a semi-diagrammatic view of still another embodiment of a surface-array beam-forming antenna in accordance with the present invention; and 
         FIG. 32  shows an exemplary far-field beam shape produced by the beam-forming antenna of  FIG. 31 . 
     
    
    
     DETAILED DESCRIPTION 
       FIGS. 1 ,  2 , and  3  respectively illustrate three configurations of a beam-forming antenna in accordance with a broad concept of the present invention. As will be described in more detail below, the beam-forming antenna in accordance with the present invention comprises at least one linear array of individual antenna elements, each of which is electromagnetically coupled to a transmission line through an amplitude controlling device, wherein the antenna elements are spaced from each other by a spacing distance that is less than or equal to one-third the wavelength, in the surrounding medium, of the electromagnetic radiation transmitted and/or received by the antenna. As shown in  FIGS. 1 ,  2 , and  3 , the spacing distances between each adjacent pair of antenna elements may advantageously be equal, but as discussed below with respect to  FIG. 4 , these spacing distances need not be equal. 
     More specifically,  FIG. 1  illustrates a beam-forming antenna  100  configured for transmitting a shaped beam of electromagnetic radiation in one direction (i.e., along one linear axis). The antenna  100  comprises a linear array of individual antenna elements  102 , each of which is coupled (by means such as a wire, a cable, or a waveguide, or by evanescent coupling) to a transmission line  104 , of any suitable type known in the art, that receives an electromagnetic signal from a signal source  106 . The phase velocity of the electromagnetic signal in the transmission line  104  is less than the phase velocity in the medium (e.g., atmospheric air) in which the antenna  100  is located. Each of the antenna elements  102  is coupled to the transmission line  104  through an amplitude controlling device  108 , so that the signal from the transmission line  104  is coupled to each of the antenna elements  102  through an amplitude controlling device  108  operatively associated with that antenna element  102 . 
       FIG. 2  illustrates a beam-forming antenna  200  configured for receiving electromagnetic radiation preferentially from one direction. The antenna  200  comprises a linear array of individual antenna elements  202 , each of which is coupled to a transmission line  204  that feeds the electromagnetic signal to a signal receiver  206 . Each of the antenna elements  202  is coupled to the transmission line  204  through an amplitude controlling device  208 , so that the signal from each of the antenna elements  202  is coupled to the transmission line  204  through an amplitude controlling device  208  operatively associated with that antenna element  202 . The antenna  200  is, in all other respects, similar to the antenna  100  of  FIG. 1 . 
       FIG. 3  illustrates a beam-forming antenna  300  configured for both receiving a beam of electromagnetic radiation preferentially from one direction, and transmitting a shaped beam of electromagnetic radiation in a preferred direction. The antenna  300  comprises a linear array of individual antenna elements  302 , each of which is coupled to a transmission line  304  that, in turn, is coupled to a transceiver  306 . Each of the antenna elements  302  is coupled to the transmission line  304  through an amplitude controlling device  308 , so that signal coupling between each antenna element  302  and the transmission line  304  is through an amplitude controlling device  308  operatively associated with that antenna element  302 . The antenna  300  is, in all other respects, similar to the antennas  100  and  200  of  FIGS. 1 and 2 , respectively. 
     The amplitude controlling devices  108 ,  208 ,  308 , of the antennas  100 ,  200 ,  300 , respectively, may be switches, gain-controlled amplifiers, gain-controlled attenuators, or any suitable, functionally equivalent devices that may suggest themselves to those skilled in the pertinent arts. The electromagnetic signal transmitted and/or received by each antenna element  102 ,  202 ,  302  creates an oscillating signal within the antenna element, wherein the amplitude of the oscillating signal is controlled by the amplitude controlling device  108 ,  208 ,  308  operatively associated with that antenna element. The operation of the amplitude controlling devices, in turn, is controlled by a suitably programmed computer (not shown), as will be discussed below. 
       FIG. 4  illustrates a beam-forming antenna  400 , in accordance with the present invention, comprising a linear array of antenna elements  402  coupled to a transmission line  404  through an amplitude controlling device  408 , as described above. In this variant of the invention, however, each adjacent pair of antenna elements  402  is separated by a spacing distance a 1  . . . a N , wherein the spacing distances may be different from each other, as long as all are less than or equal to one-third the wavelength of the electromagnetic signal in the surrounding medium, as mentioned above. The spacing distances may, in fact, be arbitrarily distributed, as long as this maximum distance criterion is met. 
       FIG. 5  illustrates a two-dimensional beam-forming antenna  500  that provides beam-shaping in three dimensions, the beam&#39;s direction being typically described by an azimuth angle and an elevation angle. The antenna  500  comprises a plurality of linear arrays  510  of individual antenna elements  512 , wherein the arrays  510  are arranged in parallel and are coplanar. Each array  510  is coupled with a transmission line  514 , and the transmission lines  514  are connected in parallel to a master transmission line  516  so as to form a parallel transmission line network. Each antenna element  512  is coupled to its respective transmission line  514  through an amplitude controlling device  518 . The phase of the signal fed to each of the transmission lines  514  is determined by the location on the master transmission line  516  at which each transmission line is coupled to the master transmission line  516 . Thus, as shown in  FIG. 5 , in one specific example, a first phase value is provided by coupling the transmission lines  514  to the master transmission line  516  at a first set of coupling points  520 , while in a second specific example, a second phase value may be provided by coupling the transmission lines  514  to the master transmission line  516  at a second set of coupling points  520 ′ (shown at the ends of phantom lines). Each linear array  510  is constructed in accordance with one of the configurations described above with respect to  FIGS. 1-4 . As an additional structural criterion, in the two-dimensional configuration, the distance between adjacent arrays  510  is less than or equal to one-half the wavelength, in the surrounding medium, of the electromagnetic signal transmitted and/or received by the antenna  500 . 
       FIGS. 6   a ,  6   b  through  11   a ,  11   b  graphically illustrate exemplary beam shapes produced by an antenna constructed in accordance with the present invention. In general, as mentioned above, the amplitude controlling devices, be they switches, gain-controlled amplifiers, gain-controlled attenuators, or any functionally equivalent device, are controlled by a suitably-programmed computer (not shown). The computer operates each amplitude controlling device to provide a specific signal oscillation amplitude in each antenna element, whereby the oscillation amplitudes that are distributed across the element antenna array produce the desired beam shape (i.e., power peak direction, beam width, and side lobe distribution). 
     One specific way of providing computer-controlled operation of the amplitude controlling devices is to derive empirically, by numerical simulation, sets of amplitude values for the antenna element array that correspond to the values of the beam shape parameters for each desired beam shape. A look-up table with these sets of amplitude values and beam shape parameter values is then created and stored in the memory of the computer. The computer is programmed to receive an input corresponding to the desired beam shape parameter values, and then to generate input signals that represent these values. The computer then looks up the corresponding set of amplitude values. An output signal (or set of output signals) representing the amplitude values is then fed to the amplitude controlling devices to produce an amplitude distribution along the array that produces the desired beam shape. 
     A first exemplary beam shape is shown in  FIG. 6   a , having a peak P 1  at about −50° in the azimuth, with a moderate beam width and a side lobe distribution having a relatively gradual drop-off. The empirically-derived oscillation amplitude distribution (expressed as the RF power for each antenna element i) that produces the beam shape of  FIG. 6   a  is shown in  FIG. 6   b.    
     A second exemplary beam shape is shown in  FIG. 7   a , having a peak P 2  at about −20° in the azimuth, with a narrow beam width and a side lobe distribution having a relatively steep drop-off. The empirically-derived oscillation amplitude distribution that produces the beam shape of  FIG. 7   a  is shown in  FIG. 7   b.    
     A third exemplary beam shape is shown in  FIG. 8   a , having a peak P 3  at about 0° in the azimuth, with a narrow beam width and a side lobe distribution having a relatively steep drop-off. The empirically-derived oscillation amplitude distribution that produces the beam shape of  FIG. 8   a  is shown in  FIG. 8   b.    
     A fourth exemplary beam shape is shown in  FIG. 9   a , having a peak P 4  at about +10° in the azimuth, with a moderate beam width and a side lobe distribution having a relatively steep drop-off. The empirically-derived oscillation amplitude distribution that produces the beam shape of  FIG. 9   a  is shown in  FIG. 9   b.    
     A fifth exemplary beam shape is shown in  FIG. 10   a , having a peak P 5  at about +30° in the azimuth, with a moderate beam width and a side lobe distribution having a relatively steep drop-off. The empirically-derived oscillation amplitude distribution that produces the beam shape of  FIG. 10   a  is shown in  FIG. 10   b.    
     A sixth exemplary beam shape is shown in  FIG. 11   a , having a peak P 6  at about +50° in the azimuth, with a relatively broad beam width and a side lobe distribution having a moderate drop-off. The empirically-derived oscillation amplitude distribution that produces the beam shape of  FIG. 11   a  is shown in  FIG. 11   b.    
       FIGS. 12-14  graphically illustrate exemplary far field power distributions produced by a two-dimensional beam-forming antenna, such as the antenna  500  described above and shown schematically in  FIG. 5 . In these graphs, the azimuth is labeled α, and the elevation is labeled β. The power contours are measured in dB. 
       FIG. 15  is a semi-diagrammatic view of a beam-forming antenna  1500  in accordance with an aspect of the present invention. The antenna  1500  may be configured for transmitting electromagnetic radiation in a controlled direction and beam shape, receiving electromagnetic radiation with sensitivity having a controlled direction and shape, or both transmitting and receiving. 
     The antenna  1500  includes an array of individual antenna elements  1502 . Although  FIG. 15  illustrates a small number of antenna elements  1502 , an implementation of the antenna  1500  may include a greater number, for example, hundreds. The antenna elements  1502  are coupled to a transmission line  1504 , illustrated in  FIG. 15  as a dielectric waveguide. The transmission line  1504  evanescently couples an electromagnetic signal  1506  to the antenna elements  1502  when the antenna is transmitting. When the antenna is receiving, the antenna elements  1502  evanescently couple an electromagnetic signal to the transmission line  1504 . 
     Each of the antenna elements  1502  is coupled to the transmission line  1504  through an amplitude controlling switch  1508 . Accordingly, the signal from the transmission line  1504  is coupled to each of the antenna elements  1502  with an amplitude controlled by one of switches  1508 . The switches  1508  are illustrated schematically in  FIG. 15 . In various embodiments, the switches  1508  may be semiconductor switches, optical switches, solid state switches, or other types of switches that may be suitable for this application and that may suggest themselves to those skilled in the pertinent arts. The switches  1508  are digitally controlled so that there are a discrete number of amplitude levels. In many implementations, the switches  1508  are binary switches so that the amplitudes have two levels, nominally 0 and 1. Using binary switches allows for digital control of the amplitude, which may be more economical or cost effective to implement than the analog amplitude control described above. The states of the switches  1508  are generally computer controlled, with each switch set according to a desired beam shape and direction. 
     Each of the antenna elements  1502  is spaced from adjacent antenna elements by a distance a n . The separation between elements may be termed a pitch or pixel spacing. Although the distances are illustrated in  FIG. 15  as equal, in various embodiments the spacings vary with the location of the antenna elements  1502 . As described above for the antennas of  FIGS. 1-4 , the pixel spacing is less than or equal to one-third the wavelength of the electromagnetic radiation transmitted or received by the antenna. 
       FIGS. 16   a  and  16   b  show exemplary far-field beam shapes produced by a beam-forming antenna as illustrated in  FIG. 15  with uniform pixel pitch and binary switches. The particular exemplary antenna for which  FIGS. 16   a  and  16   b  apply has a pixel pitch of approximately one-seventh the wavelength of the electromagnetic radiation, approximately 500 antenna elements, and a transmission line with a refractive index of approximately 1.35.  FIG. 16   a  shows an exemplary beam shape, with an azimuth angle α on the x-axis and a gain in decibels on the y-axis, when the switches are set for a direction of −26°. In addition to the main lobe, there are additional side lobes, some of which are attenuated by only approximately 10 dB relative to the main lobe. These side lobes are due to quantization of switch amplitudes and thus may be termed quantization lobes or Q-lobes. The existence of relatively high magnitude Q-lobes may substantially degrade the performance of the antenna. 
       FIG. 16   b  illustrates exemplary far-field beam shapes for a scan of beam directions for the antenna having one beam shape illustrated in  FIG. 16   a . Sixteen beam directions separated by two degrees are superimposed in  FIG. 16   b . The Q-lobes vary in magnitude with beam direction, and many large lobes are present. 
     Configuring the pixel spacings in the antenna of  FIG. 15  to be non-uniform can reduce the magnitude of the Q-lobes.  FIG. 17  is a graph of pixel spacings for an embodiment of a beam-forming antenna in which the antenna elements are arranged linearly between a first end (represented by the left end of the represented curve) and a second end (represented by the right end of the curve). The pixel spacings (spacing distances separating the antenna elements) vary in accordance with a parabolic distribution between the first end and the second end. As shown in  FIG. 17 , the antenna elements at the center of the antenna have a minimum pixel spacing. The pixel spacing increases to a maximum at the first and second ends of the antenna. In other embodiments, the pixel spacing may be a maximum in the center of the antenna and a minimum at the first and second ends. In some embodiments, the pixel spacing may not be symmetrical about the center of the antenna. In all cases, as mentioned above, the spacing distances are all less than or equal to one-third of the wavelength of the electromagnetic wavelength transmitted or received by the antenna. 
       FIGS. 18   a  and  18   b  are exemplary far-field beam shapes produced by an exemplary beam-forming antenna having a parabolic pixel spacing as illustrated in  FIG. 17 . The particular exemplary antenna for which  FIGS. 18   a  and  18   b  apply has an average pixel pitch of approximately one-seventh the wavelength of the electromagnetic radiation, approximately 500 antenna elements, binary switches, and a transmission line with a refractive index of approximately 1.35.  FIG. 18   a  shows an exemplary beam shape, with an azimuth angle α on the x-axis and a gain in decibels on the y-axis, when the switches are set for a direction of −26°. In addition to the main lobe, there are additional side lobes. The magnitudes of the side lobes are greater than 20 dB attenuated relative to the main lobe.  FIG. 18   b  illustrates exemplary far-field beam shapes for a scan of beam directions using the antenna having one beam shape illustrated in  FIG. 18   a . Sixteen beam directions separated by two degrees are superimposed in  FIG. 18   b . With reference to  FIGS. 16   a - b , it is seen that Q-lobe attenuation is improved by more than 10 dB using parabolic pixel spacing relative to using uniform pixel spacing. 
       FIG. 19  is a graph of pixel spacings for another embodiment of a beam-forming antenna in which the antenna elements are arranged linearly between a first end (represented by the left end of the represented curve) and a second end (represented by the right end of the curve). The pixel spacings (spacing distances separating the antenna elements) vary with location according to a sinusoidal distribution between the first end and the second end. As shown in  FIG. 19 , the antenna elements at the center of the antenna have a minimum pixel spacing. The pixel spacing increases to a maximum at the first and second ends of the antenna. In other embodiments, the pixel spacing may be a maximum in the center of the antenna and a minimum at the first and second ends, and, in some embodiments, the pixel spacing may not be symmetrical about the center of the antenna. In all cases, as mentioned above, the spacing distances are all less than or equal to one-third of the wavelength of the electromagnetic wavelength transmitted or received by the antenna. 
       FIGS. 20   a  and  20   b  are exemplary far-field beam shapes produced by an exemplary beam-forming antenna having a raised cosine pixel spacing as illustrated in  FIG. 19 . The particular exemplary antenna for which  FIGS. 20   a  and  20   b  apply has the same general characteristics as the exemplary antenna described for  FIG. 17 .  FIG. 20   a  shows an exemplary beam shape when the switches are set for a direction of −26°. As shown, the magnitudes of the side lobes are greater than 20 dB attenuated relative to the main lobe.  FIG. 20   b  illustrates exemplary far-field beam shapes for a scan of beam directions using the antenna having one beam shape illustrated in  FIG. 20   a . Q-lobe attenuation is improved by more than 10 dB using raised cosine pixel spacing relative to uniform pixel spacing. 
       FIG. 21  is a semi-diagrammatic view of another embodiment of a beam-forming antenna  2100  in accordance with an aspect of the present invention. The antenna  2100 , like the previously-described antennas, may be configured for transmitting electromagnetic radiation in a controlled direction and shape, receiving electromagnetic radiation with sensitivity having a controlled direction and shape, or both transmitting and receiving. In some applications, it may be advantageous, due to costs or other factors, to have an antenna with uniform pixel spacing, but that still provides good attenuation of the Q-lobes. The antenna  2100  is illustrative of such an antenna. 
     The antenna  2100  includes an array of individual antenna elements  2102  that are evanescently coupled to a transmission line  2104 , as in the previously described embodiments, whereby an electromagnetic signal  2106  in the transmission line  2104  is coupled to the antenna elements  2102  when the antenna is transmitting, and from the antenna elements  2102  when the antenna is receiving. Each of the antenna elements  2102  is coupled to the transmission line  2104  through an amplitude controlling switch  2108 . The switches  2108  are digitally controlled and, in many implementations, are binary switches. The states of the switches  2108  are generally computer controlled with each switch set according to a desired beam shape and direction. 
     Like the antenna  1500  described above and illustrated in  FIG. 15 , the antenna elements  2102  are advantageously uniformly spaced (i.e., the antenna has uniform pixel spacing). To address the problem of high-magnitude Q-lobes, the antenna elements  2102  are arranged in a non-linear array, specifically a parabolic arc.  FIG. 22  is a graph of antenna element locations for the beam-forming antenna of  FIG. 21 .  FIG. 22  illustrate the location of antenna elements  2102  with the position in a direction generally parallel to the transmission line  2104  on the x-axis and the direction generally in the direction of the electromagnetic radiation on the y-axis. From a reference position at the center of the antenna elements, the antenna elements are positioned increasingly outward according to a parabolic curve. In other embodiments, the locations of the antenna elements may be increasingly inward towards the edges of the antenna, and, in some embodiments, the locations may not be symmetrical about the center of the antenna. 
       FIG. 23  illustrates exemplary far-field beam shapes for a scan of beam directions for the antenna of  FIG. 21 . The illustrated beam shapes are for an exemplary antenna with binary switches, uniform pixel pitches of approximately one-seventh the wavelength of the electromagnetic radiation, approximately 500 antenna elements, and a transmission line with a refractive index of approximately 1.35. Sixteen beam directions separated by two degrees are superimposed in  FIG. 23 . The Q-lobes vary in magnitude, with all attenuated greater than 20 dB relative to the main lobes. 
       FIG. 24  is a semi-diagrammatic view of another embodiment of a beam-forming antenna  2400  in accordance with an aspect of the present invention. The antenna  2400  is similar to the antenna  2100  shown in  FIG. 21 , and it includes an array of individual antenna elements  2402 , a transmission line  2404 , and switches  2408  arranged as described above for the corresponding components of the antenna  2100  of  FIG. 21 . Like the antenna  2100  of  FIG. 21 , the antenna  2400  employs uniform pixel spacing, and it addresses the Q-lobe problem by arranging the antenna elements in a non-linear array. In this embodiment, the antenna elements  2402  are arranged in a circular arc. 
       FIG. 25  is a graph of antenna element locations for the beam-forming antenna  2400 . From a reference position at the center of the antenna elements, the antenna elements are positioned increasingly outward according to a circular curve. In other embodiments, the locations of the antenna elements be increasingly inward towards the edges of the antenna, and, in some embodiments, the locations may not be symmetrical about the center of the antenna. 
       FIG. 26  illustrates exemplary far-field beam shapes for a scan of beam directions for the antenna of  FIG. 24 . The illustrated beam shapes are for an exemplary antenna with binary switches, uniform pixel pitches of approximately one-seventh the wavelength of the electromagnetic radiation, approximately 500 antenna elements, and a transmission line with a refractive index of approximately 1.35. Sixteen beam directions separated by two degrees are superimposed in  FIG. 26 . The Q-lobes vary in magnitude, with all attenuated greater than 20 dB relative to the main lobes. 
       FIG. 27  is a semi-diagrammatic view of an embodiment of a surface-array beam-forming antenna  2700  in accordance with an aspect of the present invention. The antenna  2700  provides beam-shaping in three dimensions, the beam&#39;s direction being typically described by an azimuth angle and an elevation angle. The antenna  2700  includes a plurality of antenna-element arrays  2710 . Each of the antenna-element arrays  2710 , in some embodiments, may advantageously be similar to or the same as the antenna  1500  of  FIG. 15 . 
     Each antenna-element array  2710  includes antenna elements  2712  and switches  2718  arranged as described above for the corresponding components of the antenna of  FIG. 15 . The antenna-element arrays  2710  are coupled to a transmission line  2714  for supplying or receiving a signal. The transmission line  2714  is coupled to the antenna elements as described above for the antenna of  FIG. 15 . The antenna-element arrays  2710  are arranged in parallel. 
       FIG. 28  illustrates an exemplary far-field beam shape produced by the beam-forming antenna of  FIG. 27 . The illustrated shape is for an exemplary antenna having approximately 45 antenna-element arrays, a spacing between antenna-element arrays of approximately one-half the wavelength of the electromagnetic radiation, approximately 500 antenna elements per antenna-element array, a pixel pitch of approximately one-quarter the wavelength of the electromagnetic radiation, binary switches, and a transmission line with a refractive index of approximately 1.35.  FIG. 28  shows an elevation angle on the x-axis and a gain in decibels on the y-axis. The beam shape is for when the switches are set for an angle of −14°. In addition to a main lobe, there are many side lobes, some of which are attenuated by approximately only 8 dB relative to the main lobe. 
       FIG. 29  is a semi-diagrammatic view of another embodiment of a surface-array beam-forming antenna  2900  in accordance with an aspect of the present invention. The antenna  2900  is similar to the antenna of  FIG. 27  and provides beam-shaping in three dimensions. The antenna  2900  includes a plurality of antenna-element arrays  2910 . The antenna-element arrays  2910  are, in some embodiments, similar to or the same as the antenna elements of  FIG. 27 . 
     To achieve improved Q-lobe suppression or attenuation as compared to the antenna  2700  of  FIG. 27 , the antenna-element arrays  2910  of the antenna  2900  are arranged cylindrically. That is, each of the antenna-element arrays  2910  is positioned perpendicular to a cylindrical surface. This result is shown in  FIG. 30 , which illustrates an exemplary far-field beam shape produced by the beam-forming antenna of  FIG. 28 . The illustrated shape is for an exemplary antenna having approximately 45 antenna-element arrays arranged on a cylinder with a radius of approximately fourteen times the wavelength of the electromagnetic radiation, a spacing between antenna-element arrays of approximately one-half the wavelength of the electromagnetic radiation, approximately 500 antenna elements per antenna-element array, a pixel pitch of approximately one-quarter the wavelength of the electromagnetic radiation, binary switches, and a transmission line with a refractive index of approximately 1.35.  FIG. 30  shows an elevation angle on the x-axis and a gain in decibels on the y-axis. The beam shape is for when the switches are set for an angle of −14°. In addition to a main lobe, there are many side lobes, all which are attenuated by greater than 20 dB relative to the main lobe. By comparison to  FIG. 28 , it is seen that Q-lobe attenuation is improved by more than 12 dB using a cylindrical arrangement of antenna elements relative to using planar arrangement. 
       FIG. 31  is a semi-diagrammatic view of another embodiment of a surface-array beam-forming antenna  3100  in accordance with the present invention. The antenna  3100  is similar to the antenna  2900  of  FIG. 29 . The antenna  3100  includes a plurality of antenna-element arrays  3110 . However, the antenna-element arrays  3110  of the antenna  3100  are arranged conically. That is, each of the antenna-element arrays  3110  is positioned perpendicular to the surface of a cone. 
       FIG. 32  illustrates an exemplary far-field beam shape produced by the beam-forming antenna of  FIG. 31 . The illustrated shape is for a particular exemplary antenna having the same general characteristics as the antenna described above in connection with  FIG. 30 . In this embodiment, however, the particular antenna has a cone angle of 15°.  FIG. 32  shows an elevation angle on the x-axis and a gain in decibels on the y-axis. The beam shape is for when the switches are set for an angle of −14°. In addition to a main lobe, there are many side lobes, all which are attenuated by greater than 20 dB relative to the main lobe. 
     From the foregoing description and examples, it will be appreciated that the present invention provides a beam-forming antenna that offers highly-controllable beam-shaping capabilities, wherein all beam shape parameters (angular location of the beam&#39;s power peak, the beamwidth of the power peak, and side lobe distribution) can be controlled with essentially the same precision as in phased array antennas, but at significantly reduced manufacturing cost, and with significantly enhanced operational stability. 
     While exemplary embodiments of the invention have been described herein, including those embodiments encompassed within what is currently contemplated as the best mode of practicing the invention, it will be apparent to those skilled in the pertinent arts that a number of variations and modifications of the disclosed embodiments may suggest themselves to such skilled practitioners. For example, as noted above, amplitude controlling devices that are functionally equivalent to those specifically described herein may be found to be suitable for practicing the present invention. Furthermore, even within the specifically-enumerated categories of devices, there will be a wide variety of specific types of components that will be suitable. For example, in the category of switches, there is a wide variety of semiconductor switches, optical switches, solid state switches, etc. with various amplitude gradations that may be employed. In addition, a wide variety of transmission lines (e.g., waveguides) and antenna elements (e.g., dipoles) may be employed in the present invention. Furthermore, aspect of described embodiments may be combined, for example, an antenna may have both non-uniformly spaced antenna elements and a curved positioning of the antenna elements. These and other variations and modifications that may suggest themselves are considered to be within the spirit and scope of the invention, as defined in that claims that follow.