Patent Publication Number: US-7710340-B2

Title: Reconfigurable payload using non-focused reflector antenna for HIEO and GEO satellites

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   The present application claims the benefit of priority under 35 U.S.C. §119 from U.S. Provisional Patent Application Ser. No. 60/758,674 entitled “RECONFIGURABLE PAYLOAD USING NON-FOCUSED REFLECTOR ANTENNA FOR HIEO AND GEO SATELLITES,” filed on Jan. 13, 2006, the disclosure of which is hereby incorporated by reference in its entirety for all purposes. 

   STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
   Not applicable. 
   FIELD OF THE INVENTION 
   The present invention generally relates to spacecraft payloads and, in particular, relates to reconfigurable payloads for highly inclined elliptical orbit (HIEO) and geostationary orbit (GEO) communication satellites. 
   BACKGROUND OF THE INVENTION 
   Satellites with reconfigurable payloads provide desirable on-orbit mission flexibility. A reconfigurable payload allows a satellite to change the shape and location of its beams in order to change earth coverage regions. These changes may be necessary in order to compensate for spacecraft yaw steering, to back up or replace another satellite in-orbit, or as a result of changing market demands or customer requirements. 
   One approach to providing a reconfigurable payload involves using a Gregorian reflector antenna with an elliptical sub-reflector in order to produce a very broad elliptical beam. By rotating the elliptical sub-reflector, the far-field beam can be rotated to compensate for the yaw rotation of the satellite. This approach suffers from reliability problems because the reconfiguration is mechanical. Moreover, the gain of such an antenna is insufficient for many applications. 
   Another approach to providing a reconfigurable payload uses phased array optics to illuminate a reflector. In this approach, several hundred optical elements are used to provide the required phase delay between elements. Because of the large number of elements, this approach suffers from increased mass and expense. Moreover, this approach is unsuitable for handling large power loads due to the fact that the large number of amplifiers required can not be accommodated on a spacecraft. Other limitations include the difficulty of power dissipation and very high cost. 
   Yet another approach uses a system in which a feed array is located out of the focal plane of a parabolic reflector to de-focus the beam. This approach provides limited or no beam reconfiguration. Further, because the basic reflector geometry is de-optimized, the system suffers from increased scan losses, inferior cross-polar performance, mutual coupling effects and the like. Moreover, the number of optical and other elements required is still undesirably large, and the system requires complex input and output hybrid matrices. 
   Accordingly, there is a need for a flexible, reconfigurable payload with less complexity, more beam configurability, better reliability, and higher performance. The present invention satisfies these needs, and provides other benefits as well. 
   SUMMARY OF THE INVENTION 
   In accordance with the present invention, an antenna system having improved on-orbit beam configurability is provided. The antenna system includes a plurality of feed antennas located in the focal plane of a non-parabolic reflector that illuminate the reflector to form one or more defocused beams. The configurability is provided by changing the relative phase distribution among the feed antennas, which is accomplished at a low-level (i.e., prior to amplification). One or more incoming signals are divided in one or more corresponding dividing networks and are provided to a plurality of variable phase shifters, each of which corresponds to one of the feed antennas. After phase shifting, the signals are amplified by a plurality of fixed-amplitude amplifiers and provided to the feed antennas. 
   According to one embodiment, the present invention is an antenna system for generating and configuring at least one defocused beam. The antenna system includes a reflector having a focal plane and a non-parabolic curvature that forms the at least one defocused beam and a plurality of feed antennas that illuminate the reflector. Each feed antenna is disposed in the focal plane of the reflector. The antenna system further includes at least one incoming signal dividing network that divides at least one incoming signal into a plurality of sub-signals. Each sub-signal corresponds to one of the plurality of feed antennas. The antenna system further includes a plurality of variable phase shifters, each variable phase shifter receiving one of the plurality of sub-signals from the at least one incoming signal dividing network and phase shifting the one of the plurality of sub-signals to generate a corresponding phase-shifted sub-signal. The antenna system further includes a plurality of fixed-amplitude amplifiers, at least one amplifier corresponding to each of the plurality of feed antennas. The at least one amplifier for each feed antenna amplifies the corresponding phase-shifted sub-signal to generate an amplified phase-shifted sub-signal which is provided to the corresponding feed antenna. 
   According to another embodiment, the present invention is a method for generating and configuring at least one defocused beam using an antenna system including a reflector having a non-parabolic curvature and a plurality of feed antennas disposed in a focal plane of the reflector. The method includes the step of dividing at least one incoming signal with at least one incoming signal dividing network into a plurality of sub-signals, each sub-signal corresponding to one of the plurality of feed antennas. The method further includes the step of phase shifting the plurality of sub-signals with a plurality of variable phase shifters, each variable phase shifter receiving one of the plurality of sub-signals from the at least one incoming signal dividing network and phase shifting the one of the plurality of sub-signals to generate a corresponding phase-shifted sub-signal. The method further includes the step of amplifying the plurality of phase-shifted sub-signals with a plurality of fixed-amplitude amplifiers, at least one amplifier corresponding to each of the plurality of feed antennas. The at least one amplifier for each feed antenna amplifies a corresponding phase-shifted sub-signal to generate an amplified phase-shifted sub-signal which is provided to the corresponding feed antenna. The method further includes the step of illuminating the reflector with the plurality of feed antennas to generate the at least one defocused beam. 
   According to yet another embodiment, the present invention is a method for generating and configuring at least one defocused beam using an antenna system including a reflector having non-parabolic curvature and a plurality of feed antennas disposed in a focal plane of the reflector, the reflector including a single-axis gimbal mechanism. The method includes the step of dividing at least one incoming signal with at least one incoming signal dividing network into a plurality of sub-signals, each sub-signal corresponding to one of the plurality of feed antennas. The method further includes the step of phase shifting the plurality of sub-signals with a plurality of variable phase shifters, each variable phase shifter receiving one of the plurality of sub-signals from the at least one incoming signal dividing network and phase shifting the one of the plurality of sub-signals to generate a corresponding phase-shifted sub-signal. The method further includes the step of amplifying the plurality of phase-shifted sub-signals with a plurality of fixed-amplitude amplifiers, at least one amplifier corresponding to each of the plurality of feed antennas. The at least one amplifier for each feed antenna amplifies a corresponding phase-shifted sub-signal to generate an amplified phase-shifted sub-signal which is provided to the corresponding feed antenna. The method further includes the step of illuminating the reflector with the plurality of feed antennas to generate the at least one defocused beam. The plurality of variable phase shifters phase shift the plurality of sub-signals to compensate for a yawing motion of the antenna system. The single-axis gimbal mechanism of the reflector gimbals the reflector to compensate for a rolling motion of the antenna system. 
   It is to be understood that both the foregoing summary of the invention and the following detailed description are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The accompanying drawings, which are included to provide further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. In the drawings: 
       FIG. 1  depicts an antenna system according to one embodiment of the present invention; 
       FIG. 2  depicts an antenna system according to another embodiment of the present invention; 
       FIGS. 3A to 3C  illustrate feed arrays according to various aspects of the present invention; 
       FIG. 4  illustrates the effect of the curvature of a reflector of an antenna system according to one aspect of the present invention; 
       FIGS. 5A and 5B  illustrate various arrangements of feed arrays according to various aspects of the present invention; 
       FIG. 6  illustrates the geometry of an antenna system according to one aspect of the present invention; 
       FIGS. 7 to 9  depict EIRP contour plots at for an antenna system on a HIEO satellite at various angles of yaw according to various aspects of the present invention; 
       FIGS. 10A and 10B  illustrate an advantage in cross-polar isolation enjoyed by an antenna system according to one aspect of the present invention; 
       FIG. 11  depicts a cross-polar isolation contour plot for an antenna system on a HIEO satellite according to one aspect of the present invention; 
       FIGS. 12 and 13  depict EIRP contour plots for an antenna system on a GEO satellite in various configurations according to various aspects of the present invention; 
       FIGS. 14 and 15  depict cross-polar isolation contour plots for an antenna system on a GEO satellite in various configurations according to various aspects of the present invention; and 
       FIG. 16  is a flowchart depicting a method for generating and configuring at least one defocused beam according to another embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   In the following detailed description, numerous specific details are set forth to provide a full understanding of the present invention. It will be apparent, however, to one ordinarily skilled in the art that the present invention may be practiced without some of these specific details. In other instances, well-known structures and techniques have not been shown in detail to avoid unnecessarily obscuring the present invention. 
     FIG. 1  illustrates an antenna system for generating and configuring at least one defocused beam according to one embodiment of the present invention. Antenna system  100  includes a reflector  110  having a non-parabolic curvature for forming one or more defocused beams. A plurality of feed antennas  120  are disposed in the focal plane  111  of reflector  110 . The feed antennas  120  illuminate reflector  110  to generate the one or more defocused beams in the following manner. 
   An incoming signal  130  is divided by an incoming signal dividing network  140  into a plurality of sub-signals  145 . Each sub signal  145  corresponds to one of the feed antennas  120 . Each sub-signal  145  is received from incoming signal dividing network  140  by a variable phase shifter  150  which phase shifts sub-signal  145  to generate a corresponding phase-shifted sub-signal  155 . A corresponding fixed-amplitude amplifier  160  amplifies each phase-shifted sub-signal  155  to generate an amplified phase-shifted sub-signal  165  which is provided to the corresponding feed antenna  120 . Feed antennas  120  together illuminate reflector  110  with amplified phase-shifted sub-signals  165  to generate the one or more defocused beams. 
   Amplifiers  160  are fixed-amplitude amplifiers. Accordingly, the configuration of the one or more beams is accomplished with phase-only synthesis, as is discussed in greater detail below. The use of fixed-amplitude amplifiers allows antenna system  100  to operate close to saturation with maximum DC-to-RF conversion efficiency (e.g., about 60% efficiency). According to one embodiment, amplifiers  160  are traveling wave tube amplifiers (“TWTAs”). According to an alternate embodiment, amplifiers  160  may be solid state power amplifiers (“SSPAs”) or any other fixed-amplitude amplifiers. 
   Reflector  110  has a non-parabolic curvature to form one or more defocused beams. According to one embodiment of the present invention, the curvature of reflector  110  is optimized to minimize the number of elements (e.g., amplifiers, feed antennas, etc.) in the feed array and to efficiently combine the individual beamlets (i.e., the signals from each feed antenna  120 ). For example, according to one embodiment, the curvature of reflector  110  is selected so that the resultant beam has a quadratic phase distribution in the aperture plane of reflector  110 . This curvature broadens the one or more defocused beams to about 2 to 3 times the breadth that would be generated by a parabolic reflector, thereby reducing the required number of feed array elements by a factor of 4, as is discussed in greater detail below with respect to  FIG. 4 . 
   According to one embodiment, reflector  110  is a 12 meter mesh reflector. According to other embodiments, reflector  110  may be any other size, and may be any other kind of reflector known to those of skill in the art. According to one embodiment, reflector  110  may include a single-axis gimbal mechanism  105  to provide ground track compensation for the rolling motion of a satellite vehicle on which antenna system  100  is deployed. 
   According to one embodiment, variable phase shifters  150  are 8-bit phase shifters with the ability to adjust the phase of a signal in increments of 1.4°. According to other embodiments, variable phase shifters  150  may be any kind of phase shifter known to those of skill in the art. Post-amplification signal losses are kept low by phase shifting the sub-signals  145  with variable phase shifters  150  prior to amplification. 
   While in the exemplary embodiment illustrated in  FIG. 1 , incoming signal dividing network  140  is illustrated as a 1:3 network (i.e., dividing incoming signal  130  into three sub-signals  145 ), the scope of the present invention is not limited to such an arrangement. Rather, an incoming signal dividing network of the present invention may divide an incoming signal into any number of sub-signals, corresponding to the number of feed antennas, as will be apparent to one of skill in the art. For example, in an embodiment in which the antenna system has 37 feed antennas, an incoming signal dividing network of the present invention will divide an incoming signal into 37 sub-signals. 
   The amplification in antenna system  100  is distributed by providing feed antennas  120  with corresponding amplifiers  160 . This distributed amplification mitigates the risk of multipaction. While in the present exemplary embodiment illustrated in  FIG. 1 , one amplifier  160  corresponds to each feed antenna  120 , the scope of the present invention is not limited to such an arrangement. Rather, as will be apparent to one of skill in the art, an antenna system of the present invention may have more than one amplifier corresponding to each feed antenna, as is illustrated in greater detail with respect to  FIG. 2 . 
   Turning to  FIG. 2 , an antenna system according to another embodiment of the present invention is illustrated. Antenna system  200  includes a reflector  210  having a non-parabolic curvature for forming one or more defocused beams. A plurality of feed antennas  220  are disposed in the focal plane  211  of reflector  210 . The feed antennas  220  illuminate reflector  210  to generate the one or more defocused beams in the following manner. 
   An incoming signal  230  is divided by an incoming signal dividing network  240  into a plurality of sub-signals  245 . Each sub signal  245  corresponds to one of the feed antennas  220 . Each sub-signal  245  is received from incoming signal dividing network  240  by a variable phase shifter  250  which phase shifts sub-signal  245  to generate a corresponding phase-shifted sub-signal  255 . A corresponding pre-amp dividing network  270  divides each phase-shifted sub-signal  255  to generate a plurality of divided phase-shifted sub-signals  275 . Each divided phase-shifted sub-signal  275  is provided to a corresponding fixed-amplitude amplifier  260 . Each amplifier  260  amplifies the corresponding divided phase-shifted sub-signal  275  to generate an amplified divided phase-shifted sub-signal  265 . Corresponding to each pre-amp dividing network  270  is a combining network  280 , which receives the amplified divided phase-shifted sub-signals  265  from each amplifier in a group of amplifiers corresponding to one feed antenna  220  and combines them to generate a corresponding amplified phase-shifted sub-signal  285 , which is provided to the corresponding feed antenna  220 . Feed antennas  220  together illuminate reflector  210  with amplified phase-shifted sub-signals  285  to the generate the one or more defocused beams. 
   According to one aspect of the present invention, the RF power of an antenna system of the present invention depends upon the number of feed antennas provided and the number of amplifiers associated with each feed antenna. Accordingly, Table 1, below, illustrates various arrangements in which the number of feed antennas and the number of amplifiers associated with each feed antenna are varied to provide a different levels of RF power. For the purposes of the present exemplary embodiment of Table 1, each amplifier is assumed to be a 230 W TWTA. 
   
     
       
         
             
             
             
             
             
           
             
                 
               TABLE 1 
             
             
                 
                 
             
             
                 
               # of Feeds 
               # Amps/Feed 
               RF Power 
               DC Power 
             
             
                 
                 
             
           
          
             
                 
             
          
         
         
             
             
             
             
             
          
             
                 
               32 
               1 
               7,360 
               12,475 
             
             
                 
               16 
               2 
               7,360 
               12,475 
             
             
                 
               37 
               1 
               8,510 
               14,424 
             
             
                 
               20 
               2 
               9,200 
               15,593 
             
             
                 
               48 
               1 
               1,1040 
               18,712 
             
             
                 
                 
             
          
         
       
     
   
   In the exemplary embodiment illustrated in  FIG. 2 , each feed antenna  220  has two corresponding fixed-amplitude amplifiers  260 . The scope of the present invention, however, is not limited to such an arrangement. Rather, as will be apparent to one of skill in the art, the present invention has application to antenna systems in which any number of amplifiers corresponds to each feed antenna, including arrangements in which different numbers of amplifiers correspond to different feed antennas. 
   For example,  FIG. 3A  illustrates a feed array  310  according to one aspect of the present invention in which one feed antenna  316  corresponds to two fixed-amplitude amplifiers  306  and  307 , while other feed antennas  315  and  317  each correspond to one fixed-amplitude amplifier  305  and  308 , respectively. If each amplifier  305 ,  306 ,  307  and  308  have the same amplitude, feed antenna  316  will provide a beamlet with twice the amplitude of feed antennas  315  and  317 . 
     FIG. 3B  illustrates a feed array  320  according to another aspect of the present invention, in which fixed-amplitude amplifiers do not correspond to particular feed antennas. An incoming signal  321  is divided by an incoming signal dividing network  322  into a plurality of sub-signals  323 . Each sub signal  323  corresponds to one of the feed antennas  349  and  350 . Each sub-signal  323  is received from incoming signal dividing network  322  by a variable phase shifter  324  which phase shifts sub-signal  323  to generate a corresponding phase-shifted sub-signal  325 . A redundancy ring with a plurality of fixed-amplitude amplifiers  326  amplifies phase-shifted sub-signals  325  and passes the amplified phase-shifted sub-signals  327  to couplers  328  and  329 . In the present exemplary embodiment, each coupler  328  is a 2:1 coupler, while coupler  329  is a 32:1 coupler. Accordingly, feed antenna  350  will provide a beamlet with 16 times the amplitude of any of feed antennas  349 . 
     FIG. 3C  illustrates a feed array  360  according to another aspect of the present invention, in which multiple incoming signals are provided to generate multiple beams. Each incoming signal  361  is divided by a corresponding incoming signal dividing network  362  to generate a corresponding plurality of sub-signals  363 . Each sub signal  363  generated by a single incoming signal dividing network corresponds to one of the feed antennas  377 . Each sub signal  363  is received from one of the incoming signal dividing networks  362  by a variable attenuator  364  and a variable phase shifter  365  which adjust the amplitude of sub-signal  363 , and phase shift sub-signal  363 , respectively, to generate a corresponding phase-shifted sub-signal  366 . Corresponding to each incoming signal dividing network  362  is a combining network  367  which combines one phase-shifted sub-signal  366  corresponding to each incoming signal dividing network  362  to generate a combined phase-shifted sub-signal  368  corresponding to one of the feed antennas  377 . The combined phase-shifted sub-signals  368  are received from combining networks  367  by an input hybrid matrix  369 , which generates hybrid phase-shifted sub-signals  370 . Each hybrid phase-shifted sub-signal  370  corresponds to one of the feed antennas  377 . Each hybrid phase-shifted sub-signal  370  passes through redundancy input switch matrix  371  and is provided to a corresponding fixed-amplitude amplifier  372  which amplifies the corresponding hybrid phase-shifted sub-signal  370  to generate an amplified hybrid phase-shifted sub-signal  373 . Amplified hybrid phase-shifted sub-signals  373  then pass through redundancy output switch matrix  374  and are received by an output hybrid matrix  375 , which generates amplified phase-shifted sub-signals  376 , which are provided to corresponding feed antennas  377 . Feed antennas  377  together illuminate a non-focused reflector (not illustrated) to generate a plurality of defocused beams. 
   Turning to  FIG. 4 , the curvature of a reflector of an antenna system according to various embodiments of the present invention is illustrated in greater detail.  FIG. 4  illustrates a feed array  430  illuminating three different reflectors  410 ,  411  and  412 . Feed array  430  is disposed in the focal plane (not shown) of all three reflectors  410 ,  411  and  412 , although the angles in  FIG. 4  have been exaggerated for clarity. Reflector  411  is a parabolic reflector. Accordingly, the corresponding wavefront  421  in the aperture plane of reflector  411  has a uniform phase. Reflector  410  has been “opened up” with respect to parabolic reflector  411  (i.e., the curvature of reflector  410  is less than that of reflector  411 ) such that the corresponding wavefront  420  in the aperture plane of reflector  410  has a quadratic phase distribution. A quadratic phase distribution significantly broadens the one or more beams formed by reflector  410 , reducing the number of feed elements required to perform the necessary beam configurations by a factor of 4. Similarly, reflector  412  has been “closed in” with respect to parabolic reflector  411  (i.e., the curvature of reflector  411  is greater than that of reflector  411 ) such that the corresponding wavefront  422  in the aperture plane of reflector  412  has a quadratic phase distribution. 
   While the non-parabolic reflectors  410  and  412  in  FIG. 4  have been illustrated as possessing a curvature for generating a quadratic phase distribution in a wavefront at their respective aperture planes, the scope of the present invention is not limited to such an arrangement. Rather, the present invention has application to reflectors with any non-parabolic curvature to generate one or more de-focused beams. 
   While due to the constraints imposed by schematic diagrams the feed arrays in the foregoing exemplary embodiments have been illustrated as including feed antennas arranged in a linear fashion, the scope of the present invention is not limited to such an arrangement. Rather, as will be apparent to one of skill in the art, the present invention has application to antenna systems in which the feed arrays include feed antennas in any arrangement. For example, as illustrated in greater detail with respect to  FIGS. 5A and 5B , below, a feed array of the present invention may be arranged as a two-dimensional array. 
     FIG. 5A  illustrates the arrangement of a feed array  500  suitable for use in a HIEO satellite according to one aspect of the present invention. Feed array  500  includes 37 feed antennas  501 , each of which has the same amplitude of 238 W. The uniform distribution of amplitude between the large number of feed antennas  501  provides the extensive on-orbit configurability need to compensate for the continual yawing of a HIEO satellite.  FIG. 5B , by way of contrast, illustrates a feed array  510  including 7 feed antennas  511  and  512 . Inner feed antenna  512  has a much larger amplitude (i.e., 5,328 W) than the outer feed antennas  511  (i.e., 380 W). The amplitudes of feed antennas  511  and  512  are, as in  FIG. 5A , fixed amplitudes. This distribution of power among the feed antennas, in which the outer feed antennas  512  have about a −11.5 dB taper relative to central feed antenna  511 , is suitable for use in a GEO satellite, in which the required on-orbit configurability is not as extensive as in a HIEO satellite. 
   Turning to  FIG. 6 , the geometry of an antenna system according to one embodiment of the present invention is illustrated. Antenna system  600  includes non-parabolic reflector  610  and feed array  620  disposed in the focal plane  630  of reflector  610 . Reflector  610  has a diameter D. Focal plane  630  is located a focal distance F from reflector  610 . Feed array  620  is offset a height h from the edge of reflector  610 . According to one embodiment, to minimize scan loss, reflector  610  has a diameter D of 12.0 m and a focal distance F of 8.4 m, providing a moderate F/D ratio of about 0.7. 
   An antenna system of the present invention utilizes phase-only synthesis to configure (e.g., steer, shape, rotate, etc.) the one or more beams that it generates. For example, according to one experimental embodiment of the present invention, an antenna system of the present invention was mathematically modeled to illustrate the capability of phase-only synthesis to provide yaw compensation for a HIEO satellite with 50° of inclination and 12 hours of coverage over the continental United States (“CONUS”). The antenna system of the present exemplary embodiment included 37 feed antennas with 0.24 m apertures and equal amplitudes of 238 W illuminating a 12.0 m non-parabolic reflector with a left-handed circularly polarized (“LHCP”) signal in the S-Band (i.e. 2320.0 to 2332.5 MHz). 
     FIGS. 7 to 9  illustrate the Effective isotropically-radiated power (“EIRP”) contour plots for this exemplary embodiment at each of 0°, 90° and 180° of yaw when the satellite is at apogee (i.e., 08:00 hr). As can be seen with reference to  FIG. 7 , the antenna system is able to generate a beam providing an EIRP of well over 60 dB for the CONUS 700 at 0° yaw. When the satellite on which the antenna system is yawed by 90°, the antenna system is able to compensate by reshaping the beam using phase-only synthesis, as can be seen with reference to  FIG. 8 , in which the CONUS 800 at 90° yaw is still provided with an EIRP of well over 60 dB. Even as the satellite yaws to 180°, the antenna system is able to compensate using phase-only synthesis, as can be seen with reference to  FIG. 9 , in which the CONUS 900 at 180° yaw is still provided with an EIRP of well over 60 dB. The phase-only synthesis allows the beam to cover the CONUS more efficiently, since less spill-over energy is expended outside of the desired coverage area. 
   Table 2, below, illustrates the phase delays introduced by the variable phase shifters (i.e., phase-only synthesis) at apogee for each of the 37 feed antennas in the antenna of the present exemplary embodiment at each of 0°, 45°, 90°, 135° and 180° of yaw. 
   
     
       
         
             
             
             
           
             
                 
               TABLE 2 
             
           
          
             
                 
                 
             
             
                 
               Amplitude 
               Phase (deg) 
             
          
         
         
             
             
             
             
             
             
             
          
             
               Element 
               (dB) 
               Yaw = 0° 
               Yaw = 45° 
               Yaw = 90° 
               Yaw = 135° 
               Yaw = 180° 
             
             
                 
             
          
         
         
             
             
             
             
             
             
             
          
             
               1 
               −15.682 
               38.13 
               −130.61 
               39.97 
               −7.61 
               −139.03 
             
             
               2 
               −15.682 
               −75.79 
               −137.26 
               43.93 
               −10.03 
               −137.31 
             
             
               3 
               −15.682 
               −69.34 
               118.29 
               −2.44 
               45.42 
               128.59 
             
             
               4 
               −15.682 
               137.46 
               60.32 
               −69.82 
               −125.82 
               −78.70 
             
             
               5 
               −15.682 
               31.59 
               −114.74 
               −37.07 
               13.57 
               −68.28 
             
             
               6 
               −15.682 
               1.54 
               −84.21 
               42.36 
               −14.40 
               −75.49 
             
             
               7 
               −15.682 
               −80.41 
               52.74 
               36.52 
               −16.50 
               37.54 
             
             
               8 
               −15.682 
               −99.35 
               53.42 
               −28.23 
               −34.41 
               −44.94 
             
             
               9 
               −15.682 
               −64.66 
               40.92 
               −86.30 
               −106.57 
               55.70 
             
             
               10 
               −15.682 
               57.14 
               −10.03 
               −116.74 
               72.36 
               −16.28 
             
             
               11 
               −15.682 
               6.02 
               −35.24 
               −41.61 
               37.05 
               −9.67 
             
             
               12 
               −15.682 
               −10.99 
               −27.02 
               −34.74 
               4.36 
               −6.83 
             
             
               13 
               −15.682 
               −49.35 
               62.48 
               −14.13 
               −27.34 
               30.36 
             
             
               14 
               −15.682 
               −11.21 
               14.07 
               −82.95 
               −59.50 
               48.92 
             
             
               15 
               −15.682 
               14.71 
               42.09 
               −66.11 
               −86.96 
               49.14 
             
             
               16 
               −15.682 
               −9.48 
               28.60 
               −138.05 
               3.94 
               42.76 
             
             
               17 
               −15.682 
               28.60 
               −9.39 
               −99.45 
               −18.46 
               44.99 
             
             
               18 
               −15.682 
               −60.13 
               −37.00 
               19.13 
               4.09 
               25.88 
             
             
               19 
               −15.682 
               0.00 
               0.00 
               0.00 
               0.00 
               0.00 
             
             
               20 
               −15.682 
               −18.24 
               −29.81 
               −41.21 
               12.48 
               74.54 
             
             
               21 
               −15.682 
               −19.91 
               −15.27 
               −80.82 
               −50.68 
               93.32 
             
             
               22 
               −15.682 
               −48.97 
               −28.49 
               −23.22 
               −72.02 
               100.00 
             
             
               23 
               −15.682 
               −0.76 
               68.98 
               −41.66 
               −105.08 
               112.61 
             
             
               24 
               −15.682 
               −27.90 
               −8.66 
               −11.18 
               −37.42 
               41.82 
             
             
               25 
               −15.682 
               −35.17 
               −16.50 
               −59.59 
               −16.33 
               46.29 
             
             
               26 
               −15.682 
               −45.42 
               −42.80 
               −44.10 
               27.92 
               35.01 
             
             
               27 
               −15.682 
               −49.69 
               −38.70 
               −72.44 
               65.35 
               93.72 
             
             
               28 
               −15.682 
               −48.87 
               −10.91 
               −136.85 
               42.61 
               130.65 
             
             
               29 
               −15.682 
               −38.23 
               47.72 
               0.55 
               −84.06 
               103.51 
             
             
               30 
               −15.682 
               −63.62 
               18.65 
               29.36 
               −3.18 
               −26.05 
             
             
               31 
               −15.682 
               −86.30 
               −68.49 
               35.61 
               57.13 
               −10.98 
             
             
               32 
               −15.682 
               −93.65 
               −84.96 
               −35.66 
               66.45 
               80.58 
             
             
               33 
               −15.682 
               −84.76 
               −109.54 
               −113.40 
               105.76 
               131.26 
             
             
               34 
               −15.682 
               −144.28 
               −2.78 
               21.94 
               −13.95 
               128.96 
             
             
               35 
               −15.682 
               −113.18 
               −5.15 
               44.96 
               45.67 
               −30.04 
             
             
               36 
               −15.682 
               −131.69 
               −78.27 
               1.83 
               122.25 
               14.05 
             
             
               37 
               −15.682 
               −133.00 
               −136.45 
               −65.61 
               83.58 
               84.16 
             
             
                 
             
          
         
       
     
   
   As can be seen with reference to Table 2, the amplitude of each feed antenna was a constant −15.682 dB (supplied by a single 238 W fixed-amplitude amplifier per feed antenna). The beam configuration was accordingly provided solely by the phase shift introduced in each beamlet by the variable phase shifters. 
   Turning to  FIGS. 10A and 10B , an additional performance advantage of an antenna system according to one embodiment of the present invention is illustrated.  FIG. 10B  illustrates the phase distribution of the primary pattern of an antenna system according to one embodiment of the present invention, at each of 0° ( 1030 ), 45° yaw ( 1031 ),  90 ° yaw ( 1032 ) and 135° yaw ( 1033 ).  FIG. 10A  is a graph illustrating the cross-polar isolation of the primary pattern of the same antenna system. Over the angle subtended by the feed array (i.e., from about −25° to about 25°), the difference between cross-polar directivity ( 1020  at 0° yaw,  1021  at 45° yaw,  1022  at 90° yaw, and  1023  at 135° yaw) and the co-polar directivity ( 1010  at 0° yaw,  1011  at 45° yaw,  1012  at 90° yaw, and  1013  at 135° yaw) in the primary pattern is greater than 33 dB. This cross-polar isolation of greater than 33 dB in the primary pattern permits an antenna system of the present invention to enjoy high gain and directivity, regardless of the phase distribution of the feed array. 
   Turning to  FIG. 11 , a cross-polar isolation contour plot for this exemplary embodiment at 0° of yaw when the satellite is at apogee (i.e., 08:00 hr) is illustrated. As can be seen with reference to  FIG. 11 , the antenna system is able to generate a beam providing better than 30 dB cross-polar isolation for the CONUS 1100. 
   According to another experimental embodiment of the present invention, an antenna system of the present invention was mathematically modeled to illustrate the capability of phase-only synthesis to provide on-orbit beam reconfiguration for a GEO satellite with an orbital arc of 94° to 98° west. The antenna system of the present exemplary embodiment included 7 feed antennas with 0.37 m apertures and a fixed power distribution (i.e., a central feed of 24×222 W and 6 outer feeds of 2×190 W) illuminating a 12.0 m non-parabolic shaped reflector with a left-handed circularly polarized (“LHCP”) signal in the S-Band (i.e., 2320.0 to 2332.5 MHz). The primary pattern cross-polar isolation was shown to be better than 40 dB, with a feed efficiency of greater than 85% and a multipaction margin for 9 KW peak power of 6.5 dB. 
     FIGS. 12 and 13  illustrate the EIRP contour plots for this exemplary embodiment at 96° W for a baseline configuration and for a configuration in which an additional 1 dB more EIRP is provided to Canada. As can be seen with reference to  FIG. 12 , the antenna system is able to generate a beam providing an EIRP of well over 64 dB for the CONUS 1200. Turning to  FIG. 13 , through phase-only synthesis, the antenna system is able to reconfigure the beam to provide an additional 1 dB of EIRP to Canada 1310 while still providing over 64 dB for the CONUS 1300. 
     FIG. 14  illustrates a cross-polar isolation contour plot for the baseline configuration of this exemplary embodiment at 96° W. As can be seen with reference to  FIG. 14 , the antenna system is able to generate a beam providing a cross-polar isolation of better than 36 dB for substantially all of the CONUS 1400. Turning to  FIG. 15 , when the antenna system is reconfigured through phase-only synthesis to provide an additional 1 dB of EIRP to Canada 1510, the cross-polar isolation over the CONUS 1500 and substantially all of Canada 1510 remains better than 36 dB. 
   Table 3, below, illustrates the phase delays introduced by the variable phase shifters (i.e., phase-only synthesis) for each of the 7 feed antennas in the antenna system of the present exemplary embodiment in the baseline configuration and to provide an additional 1° of EIRP TO Canada. 
   
     
       
         
             
             
             
             
           
             
                 
               TABLE 3 
             
           
          
             
                 
                 
             
             
                 
               Amplitude 
               Phase (deg) 
                 
             
          
         
         
             
             
             
             
             
          
             
                 
               Element 
               (dB) 
               Baseline 
               +1 dB over Canada 
             
             
                 
                 
             
          
         
         
             
             
             
             
             
          
             
                 
               1 
               −1.551 
               0.0 
               0.0 
             
             
                 
               2 
               −13.006 
               0.0 
               3.77 
             
             
                 
               3 
               −13.006 
               0.0 
               −1.55 
             
             
                 
               4 
               −13.006 
               0.0 
               −1.31 
             
             
                 
               5 
               −13.006 
               0.0 
               −2.23 
             
             
                 
               6 
               −13.006 
               0.0 
               −5.07 
             
             
                 
               7 
               −13.006 
               0.0 
               −9.28 
             
             
                 
                 
             
          
         
       
     
   
   As can be seen with reference to Table 3, the amplitude of each feed antenna was kept constant, and the beam configuration was provided solely by the phase shift introduced in each beamlet by the variable phase shifters. 
     FIG. 16  is a flowchart illustrating a method for generating and configuring at least one defocused beam using an antenna system with a non-parabolic reflector and an array of feed antennas according to one embodiment of the present invention. As is discussed in greater detail above, the array of feed antennas is disposed in the focal plane of the non-parabolic reflector. In step  1610 , an incoming signal is divided into a plurality of sub signals using an incoming signal dividing network. Each sub-signal corresponds to one of the feed antennas in the feed array. In step  1620 , each of the sub-signals is phase-shifted, using a variable phase shifter, to generate a corresponding phase-shifted sub-signal. In step  1630 , each of the phase-shifted sub-signals is amplified by one or more amplifiers to generate an amplified phase-shifted sub-signal. As discussed in greater detail with respect to  FIG. 2 , above, in an embodiment in which more than one amplifier corresponds to each feed antenna, each phase-shifted sub-signal will first be divided by a corresponding pre-amp dividing network to generate a plurality of divided phase-shifted sub-signals, which, after amplification, will be combined in a combining network. In step  1640 , each amplified phase-shifted sub-signal generated in step  1630  is provided to the corresponding feed antenna which, in step  1650 , illuminates the non-parabolic reflector to generate at least one defocused beam. 
   While the present invention has been particularly described with reference to the various figures and embodiments, it should be understood that these are for illustration purposes only and should not be taken as limiting the scope of the invention. There may be many other ways to implement the invention. Many changes and modifications may be made to the invention, by one having ordinary skill in the art, without departing from the spirit and scope the invention.