Patent Publication Number: US-6218985-B1

Title: Array synthesis method

Description:
LICENSING INFORMATION 
     The invention described below is assigned to the United States Government and is available for licensing commercially. Technical and licensing inquiries may be directed to Harvey Fendelman, Patent Counsel, Space and Naval Warfare Systems Center San Diego, Code D0012 Rm 103, 53510 Silvergate Avenue, San Diego, Calif. 92152; telephone no. (619)553-3001; fax no. (619)553-3821. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates generally to steered beam antenna arrays. More specifically, but without limitation thereto, the present invention relates to a method for selecting amplitudes and phases of a drive signal input to elements of a multiple element antenna to approximate a radiation pattern having a desired beamwidth, sidelobe level and gain. 
     Multiple element antennas, or antenna arrays, are used in many commercial and military systems. An example of such an antenna array used on surface ships is a circular array of 64 dipoles, where each dipole is inside a cavity. The power distribution and phase shift of the transmit signal input to each antenna element is typically controlled by phase shifters, switches, and a waveguide. The parameters of beamwidth, sidelobe level and gain are currently improved by increasing the size of the array. The larger array size has the disadvantage of consuming valuable space on the uppermost areas of the ship. Previous methods for optimizing performance of an antenna array calculate the amplitude and phase drive current at each antenna element to generate a desired beam pattern. These methods typically place the largest amplitudes in the center of the array and the smallest amplitudes at the ends of the array. A disadvantage of these methods is that a large array diameter is required to achieve stringent beamwidth, sidelobe level, and gain parameters. 
     A need therefore continues to exist for a method for meeting goals of beamwidth, sidelobe level, and gain parameters of an antenna array while decreasing the size of the array. 
     SUMMARY OF THE INVENTION 
     The method of the present invention is directed to overcoming the problems described above and may provide further related advantages. No embodiment of the present invention described herein shall preclude other embodiments or advantages that may exist or become obvious to those skilled in the art. 
     The method for steering a beam of an antenna array of the present invention minimizes a least squares approximation of an error function of a desired radiation pattern relative to an antenna array pattern calculated from a known radiation pattern for each antenna element. 
     An advantage of the method of the present invention is that a higher gain and narrower beamwidth may be obtained with a reduced array aperture. 
     Another advantage is that beam steering of an antenna array may be conveniently and rapidly implemented. 
     Yet another advantage is that the beam pattern may be preserved during transmissions of different frequencies by changing amplitude weights and phase shift angles for each antenna element in real time. 
     The features and advantages summarized above in addition to other aspects of the present invention will become more apparent from the description, presented in conjunction with the following drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram of a configuration for practicing the method of the present invention with an antenna array having 64 antenna elements. 
     FIG. 2 is a diagram of a waveguide for FIG.  1 . 
     FIG. 3 is a diagram of a 1:4 power splitter for FIG.  1 . 
     FIG. 4 is a diagram of a phase shifter for FIG.  1 . 
     FIG. 5 is a diagram of a single-pole-16-throw switch for FIG.  1 . 
     FIG. 6 is a diagram of a single-pole-eight-throw switch and an antenna element for FIG.  1 . 
     FIGS. 7,  7 A, and  7 B, show a flow chart of a computer program for practicing the present invention. 
    
    
     DESCRIPTION OF THE INVENTION 
     The following description is presented solely for the purpose of disclosing how the present invention may be made and used. The scope of the invention is defined by the claims. 
     FIG. 1 is a block diagram of an example of an array synthesizer  10  suitable for practicing the method of the present invention to generate a radiation pattern having a desired beamwidth, sidelobe level and gain for a 64-element antenna array. A transmit signal  104  is generated by a transmit signal source  100  according to well known techniques. A waveguide  200  inputs transmit signal  104  and generates eight amplitude levels  106  that are input respectively to eight 1:4 power splitters  300 . Each of power splitters  300  divides corresponding amplitude level  106  to produce a total of 32 splitter outputs  108 . Each of 32 splitter outputs  108  is connected to one of 32 phase shifters  400 . Each of 32 phase shifters  400  generates a phase-shifted output  114  from power splitter outputs  108  to one of 32 single-pole, 16-throw switches  500 . Each of 32 single-pole, 16-throw switches  500  connects one of phase-shifted outputs  114  to one of 64 single-pole, eight-throw switches  602 . Each of single-pole, eight-throw switches  602  selects one of phase-shifted outputs  114  to connect to one of 64 antenna elements  606 . 
     FIG. 2 is a diagram of waveguide  200  in FIG.  1 . Waveguide  200  divides transmit signal  104  into eight relative amplitude weights  106  having values A 1 -A 8  respectively. Exemplary values for amplitude weights A 1 -A 8  are: A 1 =1.0000, A 2 =0.9429, A 3 =0.7028, A 4 =0.5086, A 5 =0.3574, A 6 =0.2825, A 7 =0.2587, and A 8 =0.2512. 
     FIG. 3 is a diagram of one of eight power splitters  300 . Each of power splitters  300  divides an amplitude weight from one of amplitude weights A 1 -A 8  output from waveguide  200  into four splitter outputs Ai shown collectively as  108 . Power splitters  300  may be, for example, commercially available power splitters or well known voltage dividers. In this example, a 1:4 power splitter is used. 
     FIG. 4 is a diagram of one of 32 phase shifters  400 . Each of phase shifters  400  is controlled by a digital input  410  that selects a phase shift angle equal to the product of 22.5 degrees multiplied by an integer from 0 to 15. Such digitally controlled phase shifters are readily available commercially. 
     FIG. 5 is a diagram of one of 32 single-pole-16-throw (SP16T) switches  500 . Each of SP16T switches  500  connects one of phase shifted outputs  114  to one of  16  switched outputs  110 . In this example, each SP16T switch  500  is made of a single-pole, four-throw (SP4T) switch  502  cascaded with four additional SP4T switches  504 . SP4T switches  502  and  504  are each controlled by two-line digital inputs  506 - 514  that select one of four switched outputs  110  for each SP4T switch  504 . 
     FIG. 6 is a diagram of one of 64 single-pole-eight-throw (SP8T) switches  602 . Each of single-pole-eight-throw (SP8T) switches  602  is controlled by a digital input  604  that selects one of switched outputs  110  to connect to each antenna drive output  112 . Each antenna drive output  112  is connected to a corresponding n th  antenna element  606  of the 64-element antenna array. 
     The array synthesis method of the present invention minimizes an error function of the desired beam pattern of the antenna array versus a calculated beam pattern of the antenna array from a sum of known electric fields of the antenna elements. The electric field of the antenna array is substantially equal to the sum of the electric fields of the antenna elements if each antenna element is isolated from the others by at least 20 dB. If the magnitude and phase of the electric field generated from each antenna element are known for a given transmit signal input to each antenna element, the electric field of the antenna array may be calculated for any transmit signal input to each antenna element by summing the weighted values of the known electric fields of the antenna elements. 
     An illustrative example is an antenna array in which the n th  antenna element has an axis pointed toward an azimuth φ n  in the horizontal plane, a normalized electric field given by e n (φ n ) per amp of input current, and a location given by (x n ,y n ,z n ). An active sector of the antenna array, i.e., those antenna elements of the antenna array that are being driven, begins with the n1 th  element and ends at the n2 th  element. The resultant electric field of the antenna array as a function of azimuth φ may then be expressed as:                E        (   Φ   )       =       ∑     n   =   n1     n2                       B   n            e   n          (     Φ   -     Φ   n       )            exp        (     2      π                 j                 f          {         x   n          cos        (   Φ   )         +       y   n          sin        (   Φ   )           }     /   c       )                   (   1   )                         
     where: 
     B n ≡complex current input to the n th  antenna element; 
     j≡{square root over (−1)}; 
     f≡transmit signal frequency; and 
     c≡speed of light. 
     The desired beam pattern F(φ) of the antenna array may be selected for M values of φ, for example, M=360 for values of φ for 0° to 359° in one degree increments. The desired steered beam pattern F(φ m ), i.e. the desired electric field of the antenna array at azimuth m, has a dimension of 1×M. For an active sector of N elements of the antenna array where N=n2−n1+1, a beamforming matrix Z may be defined having dimensions N×M as follows: 
     
       
           Z ( n,m )= e   n (φ m −φ n )exp(2 πjf{x   n  cos(φ m )+ y   n  sin(φ m )}/ c )  (2) 
       
     
     Let Q be the N×N matrix given by:                Q        (     n   ,   k     )       =       ∑     m   =   1     M                       Z        (     n   ,   m     )              Z        (     k   ,   m     )         *   T                   (   3   )                         
     where n and k are row and column indices that range from n1 to n2. The operator *T transforms an A×B input matrix into a B×A output matrix as follows. An A×B transform matrix is defined by taking the complex conjugate of each corresponding element of the A×B input matrix. The A×B transform matrix is then transposed to define the B×A output matrix. 
     An error function I that calculates the mean square error of the desired beam pattern of the antenna array relative to the calculated beam pattern of the antenna array may be calculated as follows:              I   =       ∑     m   =   1     M                     {       [       F        (     Φ   m     )       -       ∑     n   =   n1     n2                       B   n          Z        (     n   ,   m     )             ]          [         F   *          (     Φ   m     )       -       ∑     k   =   n1     n2                       B   k   *            Z        (     k   ,   m     )         *   T             ]       }               (   4   )                         
     The values of B n  that minimize the error function I may then be calculated as follows:                B   n     =       ∑     m   =   1     M                     [       F        (     Φ   m     )              ∑     k   =   n1     n2                         Z        (     k   ,   m     )         *   T              Q        (     k   ,   n     )         -   1             ]               (   5   )                         
     In equation (5) the assumption is made that the geometry of the array and the characteristics of each element are known and that the elements are isolated from each other by at least 20 dB. If the isolation between elements is less than 20 dB, the above equations may still be used as long as the coupling between the antenna elements is known and suitably accounted for. 
     The optimum relative amplitude weight R n  of the input current to the n th  antenna element may be calculated as follows: 
     
       
           R   n   =B   n /max( abs ( B   n ))  (6) 
       
     
     In the example of FIG. 1, eight power levels are used with the relative amplitude weights A 1 -A 8  defined above. Each optimum relative weight R n  in equation (6) is approximated by selecting the closest value of A 1 -A 8  input by corresponding SP8T switch  502  in FIG.  5 . More than eight power levels may be used as well as a different selection of amplitude weights to more closely match the resultant beam pattern to the desired beam pattern. 
     The optimum phase shift angle θ n  for the n th  antenna element may be calculated as follows: 
     
       
         θ n =arctan[ imag ( R   n )/real( R   n )]  (7) 
       
     
     Each optimum phase shift angle θ n  calculated from equation 7 is approximated by selecting the closest multiple of 22.5 degrees output to n th  antenna element  506  from corresponding phase shifter  504  in FIG.  5 . 
     FIG.  7 . is a diagram of a flow chart  70  for a computer program implementing the array synthesis method of the present invention using a computer (not shown) to generate control inputs for phase shifters  400 , SP16T switches  500 , and SP8T switches  602  for antenna elements  606 . 
     At step  702  beamforming matrix Z is calculated from equation (2). Matrix Z is used at step  704  to calculate matrix Q from equation (3). Matrix Q is used in step  706  to calculate the complex transmit signal amplitude B n  for each antenna element to minimize mean square error relative to the desired beam pattern F(φ) from equation (5). In step  708  an amplitude weight R n  for each n th  antenna element is calculated from the transmit signal amplitudes B n  in equation (6). The phase shift angle θ n  is calculated at step  710  from equation (7) using the amplitude weights calculated in step  708 . In step  712  the amplitude weights and phase shift angles calculated in steps  708  and  710  are input to a lookup table. In step  714  the lookup table outputs appropriate bit patterns for driving control inputs  410  of phase shifters  400 , control inputs  506 - 514  of SP16T switches  500 , and control inputs  604  of SP8T switches  602 . The bit patterns may be output from a computer implementing the program flow chart of FIG. 7 to array synthesizer  10  by, for example, a parallel I/O port. 
     Other modifications, variations, and applications of the present invention may be made in accordance with the above teachings other than as specifically described to practice the invention within the scope of the following claims.