Patent Publication Number: US-2023143739-A1

Title: Antenna array calibration device and method thereof

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This non-provisional application claims priority under 35 U.S.C. § 119(a) on Patent Application No(s). 110141779 filed in Republic of China (Taiwan) on 2021 Nov. 10, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND 
     1. Technical Field 
     The present invention relates to the field of antenna array calibration device and method thereof, and more particularly, to an antenna array calibration device and method thereof capable of using both phase rotation and amplitude attenuation to achieve fast calibration. 
     2. Related Art 
     In modern days, phased array antennas are indispensable technologies in mobile communications, satellite communications systems, and military radar systems. To achieve accurate beam forming, the vector electric field (which includes both the amplitude and phase) of each radiating element of the array antenna must be accurately controlled. However, due to the amplitude and phase of each radio frequency (RF) path cannot in perfect consistency, the initial amplitudes and initial phases of the phase shifters being equivalent to random variables, the existence of the electromagnetic couple between antennas, etc., the amplitude and phase of each radiating antenna present in a random manner. Therefore, how to utilize the electromagnetic theory and power measurement in order to accurately obtain the initial amplitude and phase of each radiation source remains an issue to be studied in the field calibrating phased array antenna systems. 
     Most of the existing literatures and current methods use the Rotating Element Electric Field Vector (REV) method for phase compensation. However, since the Rotating Element Electric Field Vector method must adjust each phase shifter and measure the variation of power total of all antennas in an antenna array at the same time, the measurement session is agonizingly long and seems unrealistic to phased array systems under a changeable operating environment that require intensive calibrations. 
     SUMMARY 
     According to the above, an embodiment of the present invention, an antenna array calibration device, applied to an antenna array comprising a plurality of antennas, the antenna array calibration device comprises: a processor, configured to analyze and calculate whether is a real number solution of a simultaneous equation of amplitudes and phases; and a controller, configured to adjust the antennas from having an initial phase to having a random phase, and adjust the antennas from having an initial amplitude to having a maximum amplitude; wherein the processor calculates a phase difference by subtracting one of the initial phase and the random phase from the other, calculates an amplitude difference by subtracting one of the initial amplitude and the maximum amplitude from the other, and introduces the phase difference, the amplitude difference and a power total of the antenna array into the simultaneous equation of amplitudes and phases; if there is a real number solution for the simultaneous equation of amplitudes and phases, the controller obtains initial amplitudes and initial phases of the antennas to calibrate the phase of the antenna array; and if there is no real number solution for the simultaneous equation of amplitudes and phases, the controller adjusts the antennas to having another random phase different from the random phase, and the processor recalculates the simultaneous equation of amplitudes and phases according to the other random phase in order to obtain a real number solution. 
     According to another embodiment of the present invention, an antenna array calibration method, applied to an antenna array, wherein the antenna array is composed of a plurality of antennas, a plurality of phase shifters and a plurality of active components, each of the antennas is coupled to a corresponding phase shifter among the phase shifters and to a corresponding active component among the active components, and the antenna array calibration method comprises: measuring a power total of the antenna array; controlling the active components to adjust the antennas from having an initial amplitude to having a maximum amplitude; controlling the phase shifters to adjust the antennas from having an initial phase to having a random phase; calculating a phase difference by subtracting one of the initial phase and the random phase from the other, calculating an amplitude by subtracting one of the initial amplitude and the maximum amplitude from the other, introducing the phase difference, the amplitude difference and the power total of the antenna array into a simultaneous equation of amplitudes and phases in order to calculate whether there is a real number solution for the simultaneous equation of amplitudes and phases; if there is a real number solution for the simultaneous equation of amplitudes and phases, obtaining initial amplitudes and initial phases of the antennas to calibrate the phase of the antenna array; and if there is no real number solution for the simultaneous equation of amplitudes and phases, controlling the phase shifters to adjust the antennas to having another random phase different from the random phase, and recalculating the simultaneous equation of amplitudes and phases according to the other random phase in order to obtain a real number solution. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a schematic view of an antenna array calibration device according to an embodiment of the present invention. 
         FIG.  2    is a zoomed-in view of the antenna array calibration device according to an embodiment of the present invention. 
         FIG.  3    is a flow chart of an antenna array calibration method according to an embodiment of the present invention. 
         FIG.  4    is a schematic view of the power circle generated by the simultaneous equation of amplitudes and phases according to the present invention. 
         FIG.  5 A  is a schematic view of an actual initial phase of a 16×16 antenna array. 
         FIG.  5 B  is a schematic view of a calculated initial phase of the 16×16 antenna array of  FIG.  5 A  according to another embodiment of the present invention. 
         FIG.  5 C  is a schematic view of the phase difference between  FIG.  5 A  and  FIG.  5 B . 
         FIG.  5 D  is a schematic view of the phase distribution of the calculated phase of the 16×16 antenna array of  FIG.  5 A  according to another embodiment of the present invention. 
         FIG.  6    is a schematic view of the phase difference between before and after calibration according to another embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     The phased array is based on the linear superposition principle, where the radiation electric field of an antenna array system can be formed by superposing multiple electric fields of each antenna. However, due to the initial phase and the initial amplitude of each radio frequency (RF) path not in consistency as well as the coupling effect between antennas, the difference between the initial electric fields at one end of the antennas is driven large. The objective of the present invention uses mathematical methods to calculate the initial electric field of each antenna of the antenna array, and thereby uses a phase adjustable phase shifter and an amplitude adjustable attenuator to compensate for the difference between the initial electric fields. 
     Because the radiation electric field is a complex number, it has two variables: phase and amplitude. The two variables must be solved using two equations to obtain a simultaneous solution of a simultaneous equation of amplitudes and phases. The phase shifter is used to adjust the phase, which can provide a leading phase or a lagged phase. The attenuator is used to adjust the amplitude, which can generate an amplified amplitude or attenuated amplitude. For example, the attenuator can achieve amplification or attenuation according to different attenuation factors. 
     Refer to  FIG.  1    and  FIG.  2   .  FIG.  1    is a schematic view of an antenna array calibration device  100  according to an embodiment of the present invention, and  FIG.  2    is a zoomed-in view of the antenna array calibration device  100  according to an embodiment of the present invention. 
     In an embodiment, as illustrated in  FIG.  1   , the antenna array calibration device  100  is applied to an antenna array  20 . The antenna array  20  comprises a plurality of antennas  22 , and the antenna array calibration device  100  comprises a controller  30  and a processor  40 . 
     In some embodiments, the antennas  22  can be one-dimensionally or two-dimensionally arranged in the antenna array  20 , but the present invention does not limit the dimension of the antennas  22  of the antenna array  20  to be arranged in particular ways. For example, the technical means of the present invention can also be applied to a three-dimensional structure. In some embodiments, the antenna array  20  of the present disclosure can be implemented as a single set or multiple sets in a communication device. The communication device can be a mobile communication device, a mobile computing device, a computer device, a telecommunication device, a base station device, a wireless bridge device, a network equipment, a computer or network peripherals, etc. In some embodiments, the antenna array calibration device  100  can comprise one or more antenna arrays  20 , and the number of antennas  22  assigned to an antenna array  20  depends on actual design requirements. For example, the antenna array  20  shown in  FIG.  1    can be composed of M×N antennas  22 , wherein both M and N are positive integers. In some embodiments, the antenna array  20  can be composed of 256 (16×16) antennas  22 . 
     The controller  30  is configured to adjust each antenna  22  from having an initial phase to having a random phase, and adjust the antennas  22  from having an initial amplitude to having a maximum amplitude. 
     In an embodiment, the antenna array calibration device  100  may comprise a plurality of phase shifters  24  and a plurality of active elements  26 . In some embodiments, each antenna  22  can be coupled to a corresponding one of the phase shifters  24  and a corresponding one of the active elements  26 . For example, the embodiment of  FIG.  1    illustrates that each phase shifter  24  is coupled between a corresponding antenna  22  and active element  26 , while other embodiments may instead arrange each active element  26  to be coupled between a corresponding antenna  22  and phase shifter  24 . In some embodiments, the active elements  26  can be implemented with at least one of digital attenuators, analog attenuators, operational amplifiers and variable gain amplifiers (VGA). In some embodiments, in addition to the phase shifters  24  and the active elements  26 , each antenna  22  can be coupled to one or more elements, such as a driver, a detector, a splitter (beam splitter), a temperature controller, a filter, a converter, a rectifier, a digital-to-analog converter, an another phase shifter, an another active component, a chip, a circuit, or a feedback circuit, etc. The above chip or the above circuit may be, for example, an electronic circuit, an integrated circuit, a microchip, and an active/passive semiconductor component, etc. 
     In an embodiment, each antenna  22  can be used to transmit or receive signals, such as radio frequency (RF) signals. In some embodiments, each antenna  22  can handle a single signal beam or multiple signal beams. In some embodiments, the antenna array  20  can control a phase shifter  24  of each antenna  22  through the controller  30  in order to adjust the phase of each antenna  22 . For example, the controller  30  controls the antennas  22  to adjust from having the initial phase to having a random phase. In some embodiments, the phase variation (i.e. the phase difference) between the random phase and the initial phase can be in any angle, such as 1 degree, 10 degrees, 15 degrees, 45 degrees, or 90 degrees. 
     In an embodiment, the antenna array  20  can control an active element  26  of each antenna  22  through the controller  30  in order to adjust the amplitude of each antenna  22 . For example, the controller  30  adjusts the antennas  22  to from having the initial amplitude to having a maximum amplitude. 
     The processor  40  is configured to analyze and calculate whether there is a real number solution for a simultaneous equation of amplitudes and phases. In some embodiments, the processor  40  may be a device capable of executing coded arithmetic, logic, and/or I/O operating commands. In some embodiments, the processor  40  can comprise an arithmetic logic unit (ALU), a control unit, and/or a register, wherein the above register can be any type of fixed or removable random access memory (RAM), read-only memory (ROM), flash memory, hard disk drive (HDD), solid state drive (SSD), similar elements or a combination of the above elements. In some embodiments, the processor  40  and the controller  30  can be integrated in a same chip or container. In some embodiments, the antenna array calibration device  100  may comprise one or more processors  40 . In some embodiments, the processor  40  is a single-core processor capable of executing one command each time (or executing a single command pipeline), or a multi-core processor capable of executing multiple commands at the same time. In some embodiments, the processor  40  may be one or more integrated circuits. In some embodiments, the processor  40  may be a central processing unit (CPU), other programmable general-purpose or special-purpose microprocessors, a digital signal processor (DSP), a programmable controller, an application specific integrated circuit (ASIC), other similar components or a combination of any of the above components, but the disclosure is not limited to the embodiments. In some embodiments, the processor  40  may comprise an interconnection or transmission function, such as a wireless network function or a local area network function. 
     In some embodiments, the above simultaneous equation of amplitudes and phases can be expressed by the following Equation 1 and Equation 2: 
     
       
         
           
             
               
                 
                                    
                   
                     
                       
                         
                           ( 
                           
                             
                               X 
                               n 
                             
                             + 
                             
                               
                                 
                                   P 
                                   α 
                                 
                               
                               
                                 1 
                                 - 
                                 α 
                               
                             
                           
                           ) 
                         
                         2 
                       
                       + 
                       
                         Y 
                         n 
                         2 
                       
                     
                     = 
                     
                       
                         ( 
                         
                           
                             
                               P 
                               0 
                             
                           
                           
                             1 
                             - 
                             α 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   1 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     
                       
                         ( 
                         
                           
                             X 
                             n 
                           
                           + 
                           
                             
                               
                                 
                                   P 
                                   α 
                                 
                               
                               ⁢ 
                               
                                 ( 
                                 
                                   
                                     cos 
                                     ⁢ 
                                     ψ 
                                   
                                   - 
                                   α 
                                 
                                 ) 
                               
                             
                             
                               
                                 α 
                                 2 
                               
                               - 
                               
                                 2 
                                 ⁢ 
                                 α 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 ψ 
                               
                               + 
                               1 
                             
                           
                         
                         ) 
                       
                       2 
                     
                     + 
                     
                       
                         ( 
                         
                           
                             y 
                             n 
                           
                           + 
                           
                             
                               
                                 
                                   P 
                                   α 
                                 
                               
                               ⁢ 
                               sin 
                               ⁢ 
                               ψ 
                             
                             
                               
                                 α 
                                 2 
                               
                               - 
                               
                                 2 
                                 ⁢ 
                                 α 
                                 ⁢ 
                                 cos 
                                 ⁢ 
                                 ψ 
                               
                               + 
                               1 
                             
                           
                         
                         ) 
                       
                       2 
                     
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             P 
                             Φ 
                           
                         
                         
                           
                             α 
                             2 
                           
                           - 
                           
                             2 
                             ⁢ 
                             α 
                             ⁢ 
                             cos 
                             ⁢ 
                             ψ 
                           
                           + 
                           1 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
               
                 
                   Equation 
                   ⁢ 
                       
                   2 
                 
               
             
           
         
       
     
     wherein the parameter P α  in Equation 1 and Equation 2 denotes the power total (in linear coordinates) of the nth antenna  22  of the antenna array  20  with the amplitude being adjusted by α (e.g. amplified or attenuated by α), the parameter P 0  denotes the power total of the antenna array  20  under an initial state, and the parameter P Φ  denotes the power total of the nth antenna of the antenna array  20  with the phase being adjusted by ψ. 
     The variables X n  and Y n  in Equation 1 and Equation 2 are unknown variables that need to be calculated, and can be expressed by the following Equation 3 and Equation 4: 
       X n =|E n |cos ψ n   Equation 3
 
       Y n =|E n | sin ψ n   Equation 4
 
     wherein the parameter E n  and ϕ n  in Equation 3 and Equation 4 are the initial amplitude and the initial phase of the nth antenna  22  in the antenna array  20 , respectively. 
     In an embodiment, as illustrated in  FIG.  2   , the processor  40  may calculate a phase difference according to the adjustment from the initial phase to the random phase (e.g. the phase shifting angle ψ shown in  FIG.  2   ). For example, the phase difference may be calculated by subtracting one of the initial phase and the random phase from the other. In addition, the processor  40  may calculate the above-mentioned amplitude difference according to the adjustment from the initial amplitude to the maximum amplitude. For example, the amplitude difference may be calculated by subtracting one of the initial amplitude and the maximum amplitude from the other. The processor  40  introduces the above-mentioned phase difference, the above-mentioned amplitude difference and the power total of the antenna array  20  into the above-mentioned simultaneous equation of amplitudes and phases, to obtain a real number solution. 
     If there is a real number solution in the above-mentioned simultaneous equation of amplitudes and phases, meaning that the initial amplitude E n  and the initial phase ψ n  of each antenna  22  can be generated. The controller  30  can calibrate the phase of the antenna array  20  according to the calculation of the above-mentioned initial amplitude and the above-mentioned initial phase of each antenna  22 , and perform phase compensation to make the main beam A of the antenna array  20  (see  FIG.  1    and  FIG.  6   ) reach a predetermined target angle, such as the calibrated angle θ shown in  FIG.  1   . 
     If there is no real number solution in the above-mentioned simultaneous equation of amplitudes and phases, the controller  30  will again control the antennas  22  to adjust to having another random phase that is different from the above-mentioned random phase, and the processor  40  recalculates the above simultaneous equation of amplitudes and phases to obtain a real number solution according to the above-mentioned another random phase. In some embodiments, for example, the phase difference between two consecutive random phases can be fixed to 1 degree, 10 degrees, 15 degrees, 45 degrees, or 90 degrees. In some embodiments, the present invention requires can obtain the real number solution by merely using the controller  30  to adjust the phase variation for one time and adjust the amplitude variation for one time to obtain the initial phase and the initial amplitude of an antenna  22 . For example, to solve the above simultaneous equation of amplitudes and phases using the antenna array  20  composed of 256 (16×16) antennas  22  implemented in the present invention, it requires merely 512 (256×2) phase modulations and power measurements. That is, it takes only 512 phase modulations to complete the phase calibration of the antenna array  20 . 
     Refer to  FIG.  3   ,  FIG.  3    is a flow chart of an antenna array calibration method according to an embodiment of the present invention. 
     In an embodiment, as illustrated in Step S 1  of  FIG.  3   , a processor  40  measures the power total of an antenna array  20 . 
     In Step S 3 , a controller  30  controls the active elements  26  to adjust the antennas  22  from having an initial amplitude to having a maximum amplitude. 
     In Step S 5 , the controller  30  controls the phase shifters  24  to adjust the antennas  22  from having an initial phase to having a random phase. 
     In Step S 7 , the processor  40  calculates a phase difference by subtracting one of the above-mentioned initial phase and the above-mentioned random phase from the other, and the processor  40  calculates an amplitude difference by subtracting one of the above-mentioned initial amplitude and the above-mentioned maximum amplitude from the other. The processor  40  introduces the above-mentioned phase difference, the above-mentioned amplitude difference and the power total of the antenna array  20  into the above-mentioned simultaneous equation of amplitudes and phases. In Step S 9 , the processor  40  determines whether there is a real number solution in the above-mentioned simultaneous equation of amplitudes and phases. 
     In Step S 11 , if there is a real number solution in the above-mentioned simultaneous equation of amplitudes and phases, the processor  40  will obtain the above-mentioned initial amplitude and initial phase of the antenna array  20 , and the controller  30  will perform phase compensation to calibrate the antenna array  20  according to the above-mentioned initial amplitude and the above-mentioned initial phase. 
     In Step S 13 , if there is no real number solution in the above-mentioned simultaneous equation of amplitudes and phases, the controller  30  will again control the phase shifters  24  to adjust the antennas  22  of the antenna array  20  from having the random phase to having another random phase, and the processor  40  will recalculate the above-mentioned simultaneous equation of amplitudes and phases until a real number solution is generated. 
     Refer to  FIG.  4   ,  FIG.  4    is a schematic view of the power circle generated by the simultaneous equation of amplitudes and phases according to the present invention. 
     In an embodiment, as illustrated in  FIG.  4   , because the above-mentioned initial phase and the above-mentioned initial amplitude of the antennas  22  cannot be estimated (a random distribution), in the linear coordinate system of the variable X n  as the X-axis and variable Y n  as the Y-axis according to the above-mentioned simultaneous equation of amplitudes and phases, a first power circle  42  can be obtained after an amplitude adjustment (amplification or attenuation) α by the Equation 1, and a second power circle  44 , a third power circle  46  and a fourth power circle  48  can be obtained after phase shifting angle ψ 1 , ψ 2 , and ψ 3  respectively by the Equation 2. 
     When angles are adjusted to different angles (e.g. ψ 1 , ψ 2 , ψ 3 ) and the power total obtained by modulating the phase is less than the power total obtained by modulating the attenuation, improper phase shifting angles (e.g. ψ 1 ) will result in real number solution not existed, e.g., the first power circle  42  and the second power circle  44  have no intersection point (no real number solution). Appropriate phase shifting angles (e.g. ψ 2 , ψ 3 ), however, will result in a real number solution existed, e.g., the first power circle  42  intersects with and the third power circle  46  and the fourth power circle  48  and therefore have two intersection points, in which intersection points indicate that there is a real number solution. Therefore, the present invention provides to change the phase shift angle ψ of the antennas  22  according to any random phase (see  FIG.  2   ), which is to change the center point of the power circle converted by Equation 2, in order to obtain a real number solution. In some embodiments, the present invention may continuously generate random phases to generate different power circles until a real number solution is generated. 
     Refer to  FIG.  5 A ,  FIG.  5 B ,  FIG.  5 C  and  FIG.  5 D .  FIG.  5 A  to  FIG.  5 D  are the phase values of each antenna of a 16×16 antenna array.  FIG.  5 A  is a schematic view of an actual initial phase of a 16×16 antenna array.  FIG.  5 B  is a schematic view of a calculated initial phase of the 16×16 antenna array of  FIG.  5 A  according to another embodiment of the present invention.  FIG.  5 C  is a schematic view of the phase difference between  FIG.  5 A  and  FIG.  5 B .  FIG.  5 D  is a schematic view of the phase distribution of the calculated phase of the 16×16 antenna array of  FIG.  5 A  according to another embodiment of the present invention. 
     In an embodiment, as illustrated in  FIG.  5 A , there is an antenna array  20  as an example. The above-mentioned antenna array  20  is composed of 256 (16×16) antennas  22 . Because each antenna  22  has a different initial phase, it is expressed in different gray scales, for example, both a first antenna  52  and a second antenna  54  have a random initial phase of 0 degrees as the same gray scale. 
     Regarding the Rotating Element Electric Field Vector (REV) method, since the power total of the antenna array  20  and the cosine variation of the phase of the phase shifters  24  of the antennas  22  is in consistency, it can be used to adjust the phase of the phase shifter  24  of each antenna  22  sequentially, in order to obtain the cosine curve of the power total difference, and calculate the initial phase and initial amplitude of each antenna  22  as a basis for calibration. Take a 5-bit digital phase shifter as an example, it requires changing the phase of each antenna  32  times and measuring the power total of the antenna array  32  times by using the Rotating Element Electric Field Vector (REV) method. As to the antenna array  20  composed of 256 (16×16) antennas  22 , it requires performing phase modulation and power measurements 8192 (256×32) times. 
     In an embodiment, as illustrated in  FIG.  5 B , according to the present invention implemented in an antenna array  20  composed of 256 (16×16) antennas  22 , it only requires to calculate at least 512 (256×2) times about phase modulations and power measurements by using the above-mentioned simultaneous equation of amplitudes and phases. This fast calibration not only greatly reduces the time-consuming of calibration of the antenna array  20 , but improves its performance. For example, the initial phase calculated by the first antenna  52  according to another embodiment of the present invention is close to 0 degrees, and the initial phase calculated by the second antenna  54  according to another embodiment of the present invention is close to 359 degrees. 
     In an embodiment, as illustrated in  FIG.  5 C , the actual initial phase shown in  FIG.  5 A  and the initial phase calculated according to another embodiment of the present invention shown in  FIG.  5 B  have a phase error. For example, the phase error obtained by the first antenna  52  is close to 0 degrees, and the phase error obtained by the second antenna  54  is close to −1 degree. 
     In an embodiment, as illustrated in  FIG.  5 D , according to the result of the simultaneous equation of amplitudes and phases calculated by the processor  40 , the controller  30  adjusts the phase shifter  24  of each antenna  22  for calibration. For example, with the aid of the phase distribution of the antenna array  20  after calibration in  FIG.  5 D , the main beam A (see  FIG.  1    and  FIG.  6   ) of the antenna array  20  can reach a predetermined target angle (such as 41.05 degrees), wherein the phase of the first antenna  52  after calibration according to another embodiment of the present invention is close to 60 degrees, and the phase of the second antenna  54  after calibration according to another embodiment of the present invention is close to 60 degrees. 
     Refer to  FIG.  6   ,  FIG.  6    is a schematic view of the phase difference between before and after calibration according to another embodiment of the present invention. 
     In an embodiment, as illustrated in  FIG.  6   , the X-axis is the beam angle of the antenna array  20 , and the Y-axis is the size of the array factor in dB. In an embodiment, the beam before calibration  62  of the antenna array  20  composed of 256 (16×16) antennas  22  which shown in  FIG.  5 A  to  FIG.  5 D  is shown by the dotted line in  FIG.  6   . In order to make the main beam A reach a predetermined target angle (such as 41.05 degrees), the controller  30  adjusts the angle of the phase shifter  24  of each antenna  22 , and adjusts the attenuator  26  of each antenna  22  at the same time according to the condition that is the side lobe level −30 dB. The beam after calibration  64  of the antenna array  20  is shown by the solid line in  FIG.  6   , and the corrected beam  64  can have a maximum side lobe  66 , which is a specification below −30 dB. The above-mentioned side lobe setting to −30 dB is for illustrative purposes only, rather than limiting the scope of the present invention. 
     The present invention can adjust the phase difference, amplitude difference of each antenna in any antenna array, and the power total of the antenna array for the antenna array to obtain a real number solution by the simultaneous equation of amplitudes and phases, which is the initial amplitude and initial phase of each antenna. It can be used to quickly calibrate the antenna array. If it cannot obtain a real number solution by the simultaneous equation of amplitudes and phases, the present invention can re-adjust the phase of each antenna in the antenna array again to another random angle until it is a real number solution by the simultaneous equation of amplitudes and phases. As a result, the efficiency of the calibrating antenna can be greatly improved. In other words, the present invention can properly calibrate the antenna array with lower operation complexity.