Patent Publication Number: US-9903908-B2

Title: Nonlinear distortion detection device and distortion compensation power amplifier

Description:
CROSS REFERENCES TO RELATED APPLICATIONS 
     This application claims priority to Japanese Patent Application No. 2014-033041, filed on Feb. 24, 2014, the contents of (each of) which are hereby incorporated by reference. 
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a nonlinear distortion detection device that detects nonlinear distortion produced by a power amplifier used for a wireless communication device and the like and a distortion compensation power amplifier that is provided with the nonlinear distortion detection device. 
     2. Description of the Related Art 
     In recent years, mobile equipment equipped with a wireless communication function, such as mobile telephones and laptop personal computers, have been increasingly spread. In the wireless communication devices equipped in such equipment, there is a demand for high linearity in order to suppress an increase in adjacent channel leakage power derived from nonlinear input/output properties of a power amplifier. However, since it is difficult to attain higher output and higher efficiency while keeping high linearity, it becomes important to apply a nonlinear distortion compensation technique. 
     As an approach to compensate nonlinear properties of power amplifiers, a predistortion approach has been attracting attention in recent years. A predistortion approach is a method in which properties opposite to the distortion properties produced by a power amplifier are given to an input signal in advance to be inputted to the power amplifier. As a distortion compensation power amplifier using the predistortion approach, there is one described in Japanese Unexamined Patent Application Publication No. 2005-079935, for example. 
     SUMMARY 
     However, in the distortion compensation power amplifier described in Japanese Unexamined Patent Application Publication No. 2005-079935, an amount of operations to obtain a distortion factor representing nonlinear properties of the power amplifier is large, so that there is a problem of causing a larger circuit size or a longer operation time. 
     Thus, one non-limiting and exemplary embodiment provides a nonlinear distortion detection device and a distortion compensation power amplifier that are capable of simplifying operations to obtain a distortion factor representing nonlinear properties of a power amplifier. 
     Additional benefits and advantages of the disclosed embodiments will be apparent from the specification and Figures. The benefits and/or advantages may be individually provided by the various embodiments and features of the specification and drawings disclosure, and need not all be provided in order to obtain one or more of the same. 
     In one general aspect, the techniques disclosed here feature a nonlinear distortion detection device of the present disclosure is a nonlinear distortion detection device that includes a test signal generator that generates a test signal and outputs the test signal to have the power amplifier amplify the test signal, a Fourier transformer that converts the amplified signal to a signal in a frequency domain, and a distortion factor calculator that calculates a distortion factor of the power amplifier based on amplitude information and phase information of the signal in the frequency domain. 
     According to the present disclosure, it is possible to simplify operations to obtain a distortion factor representing nonlinear properties of a power amplifier. 
     These general and specific aspects may be implemented using a system, a method, and a computer program, and any combination of systems, methods, and computer programs. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier in the predistortion approach described in Japanese Unexamined Patent Application Publication No. 2005-079935; 
         FIG. 2  is a block diagram illustrating a schematic configuration of a nonlinear distortion detection device according to First Embodiment; 
         FIG. 3  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Second Embodiment; 
         FIG. 4  is a diagram illustrating a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier according to Second Embodiment; 
         FIG. 5  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Third Embodiment; 
         FIG. 6  is a diagram illustrating a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier according to Third Embodiment; 
         FIG. 7  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Fourth Embodiment; 
         FIG. 8  is a diagram illustrating a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier according to Fourth Embodiment; 
         FIG. 9  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Fifth Embodiment; 
         FIG. 10  is a diagram illustrating a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier according to Fifth Embodiment; 
         FIG. 11  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Sixth Embodiment; 
         FIG. 12  is a diagram illustrating a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier according to Sixth Embodiment; 
         FIGS. 13A through 13E  are diagrams that represent major signals in the distortion compensation power amplifier according to Sixth Embodiment; 
         FIGS. 14A through 14E  are diagrams that represent major signals in the distortion compensation power amplifier according to Sixth Embodiment; and 
         FIG. 15  is a diagram illustrating a flow chart that describes a process to obtain a distortion factor A k  in a modification of the distortion compensation power amplifier according to Sixth Embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Descriptions are given below to embodiments of the present disclosure with reference to the drawings. 
     (Underlying Knowledge Forming Basis of One Embodiment of the Present Disclosure) 
       FIG. 1  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier in the predistortion approach described in Japanese Unexamined Patent Application Publication No. 2005-079935. A distortion compensation power amplifier  49  illustrated in  FIG. 1  is configured with a predistorter  50 , a power amplifier  51 , a distortion factor calculator  52 , a compensation factor calculator  53 , an evaluation function calculator  54 , and a back-off controller  55 . After given distortion of properties opposite to nonlinear distortion of the power amplifier  51 , a signal (input signal) x inputted to the predistorter  50  is outputted as a signal (output signal) y. The output signal y from the predistorter  50  is inputted to the power amplifier  51  to be outputted as a signal (output signal) z after distortion compensation by canceling each other out with the nonlinear distortion properties of the power amplifier  51 . 
     Here, relationship between the output signal z of the power amplifier  51  and the output signal y of the predistorter  50  is represented as Expression (1) using complex power series. 
     
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       ∑ 
                       k 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         A 
                         k 
                       
                       ⁢ 
                       
                         
                            
                           y 
                            
                         
                         
                           k 
                           - 
                           1 
                         
                       
                       ⁢ 
                       y 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           3 
                           , 
                           5 
                           , 
                           … 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Here, A k  is a factor that represents nonlinear distortion properties of the power amplifier  51  and hereinafter referred to as a distortion factor. Similarly, relationship between the input signal x and the output signal y of the predistorter  50  is also represented as Expression (2) using complex power series. 
     
       
         
           
             
               
                 
                   y 
                   = 
                   
                     
                       ∑ 
                       k 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         B 
                         k 
                       
                       ⁢ 
                       
                         
                            
                           x 
                            
                         
                         
                           k 
                           - 
                           1 
                         
                       
                       ⁢ 
                       x 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           3 
                           , 
                           5 
                           , 
                           … 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Here, B k  is a factor that represents inverse distortion properties given in the predistorter  50  and hereinafter referred to as a compensation factor. When Expression (2) is substituted into Expression (1), relationship between input and output of the distortion compensation power amplifier  49  is represented as Expression (3). 
     
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       ∑ 
                       k 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         C 
                         k 
                       
                       ⁢ 
                       
                         
                            
                           x 
                            
                         
                         
                           k 
                           - 
                           1 
                         
                       
                       ⁢ 
                       x 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           3 
                           , 
                           5 
                           , 
                           … 
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     Here, a factor C k  is represented as Expression (4) using the factors A k  and B k . 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           C 
                           1 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             A 
                             1 
                           
                           ⁢ 
                           
                             B 
                             1 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           C 
                           3 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               A 
                               1 
                             
                             ⁢ 
                             
                               B 
                               3 
                             
                           
                           + 
                           
                             
                               A 
                               3 
                             
                             ⁢ 
                             
                               
                                  
                                 
                                   B 
                                   1 
                                 
                                  
                               
                               2 
                             
                             ⁢ 
                             
                               B 
                               1 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           C 
                           5 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             
                               A 
                               1 
                             
                             ⁢ 
                             
                               B 
                               5 
                             
                           
                           + 
                           
                             
                               ( 
                               
                                 
                                   2 
                                   ⁢ 
                                   
                                     
                                        
                                       
                                         B 
                                         1 
                                       
                                        
                                     
                                     2 
                                   
                                   ⁢ 
                                   
                                     B 
                                     3 
                                   
                                 
                                 + 
                                 
                                   
                                     B 
                                     1 
                                     2 
                                   
                                   ⁢ 
                                   
                                     B 
                                     3 
                                     * 
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               A 
                               3 
                             
                           
                           + 
                           
                             
                               
                                  
                                 
                                   B 
                                   1 
                                 
                                  
                               
                               4 
                             
                             ⁢ 
                             
                               B 
                               1 
                             
                             ⁢ 
                             
                               A 
                               5 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         ⋮ 
                         ⁢ 
                           
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     The distortion factor calculator  52  obtains the factor A k  by solving a simultaneous equation represented as Expression (5). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             z 
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             z 
                             ⁡ 
                             
                               ( 
                               L 
                               ) 
                             
                           
                         
                       
                     
                     ] 
                   
                   = 
                   
                     D 
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               A 
                               1 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               A 
                               K 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Here, a matrix D is represented Expression (6). 
     
       
         
           
             
               
                 
                   D 
                   = 
                   
                     [ 
                     
                       
                         
                           
                             y 
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             
                               
                                  
                                 
                                   y 
                                   ⁡ 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                  
                               
                               
                                 K 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               y 
                               ⁡ 
                               
                                 ( 
                                 1 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           ⋮ 
                         
                         
                           ⋱ 
                         
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             y 
                             ⁡ 
                             
                               ( 
                               L 
                               ) 
                             
                           
                         
                         
                           … 
                         
                         
                           
                             
                               
                                  
                                 
                                   y 
                                   ⁡ 
                                   
                                     ( 
                                     L 
                                     ) 
                                   
                                 
                                  
                               
                               
                                 K 
                                 - 
                                 1 
                               
                             
                             ⁢ 
                             
                               y 
                               ⁡ 
                               
                                 ( 
                                 L 
                                 ) 
                               
                             
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Next, the compensation factor calculator  53  calculates B k  based on Expression (7). Expression (7) is obtained by making C 3 , C 5 , . . . to be zero in Expression (4). 
     
       
         
           
             
               
                 
                   
                     
                       B 
                       1 
                     
                     = 
                     
                       B 
                       1 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       B 
                       3 
                     
                     = 
                     
                       
                         - 
                         
                           
                              
                             
                               B 
                               1 
                             
                              
                           
                           2 
                         
                       
                       ⁢ 
                       
                         B 
                         1 
                       
                       ⁢ 
                       
                         
                           A 
                           3 
                         
                         
                           A 
                           1 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       B 
                       5 
                     
                     = 
                     
                       
                         
                           - 
                           
                             
                                
                               
                                 B 
                                 1 
                               
                                
                             
                             4 
                           
                         
                         ⁢ 
                         
                           B 
                           1 
                         
                         ⁢ 
                         
                           
                             A 
                             5 
                           
                           
                             A 
                             1 
                           
                         
                       
                       - 
                       
                         
                           ( 
                           
                             
                               2 
                               ⁢ 
                               
                                 
                                    
                                   
                                     B 
                                     1 
                                   
                                    
                                 
                                 2 
                               
                               ⁢ 
                               
                                 B 
                                 3 
                               
                             
                             + 
                             
                               
                                 B 
                                 1 
                                 2 
                               
                               ⁢ 
                               
                                 B 
                                 3 
                                 * 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           
                             A 
                             3 
                           
                           
                             A 
                             1 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   ⋮ 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     The evaluation function calculator  54  and the back-off controller  55  determine B 1  in such a manner that an adjacent channel leakage power ratio becomes not more than a predetermined threshold. The predistorter  50  carries out distortion compensation based on Expression (2) from B k  (k=3, 5, . . . ) that is obtained in the compensation factor calculator  53  and B 1  that is obtained in the back-off controller  55  to output the output signal y to the power amplifier  51 . 
     The technique described in Japanese Unexamined Patent Application Publication No. 2005-079935 has following problems. That is, in order to obtain the distortion factor A k  of the power amplifier  51 , the simultaneous equation in Expression (5) or an inverse matrix of the matrix D represented by Expression (6) has to be solved. When solving as a simultaneous equation, a method such as elimination is used. When solving as an inverse matrix, whether or not there is an inverse matrix has to be determined by calculating a determinant of the matrix D to calculate each component of the inverse matrix. When seeking for a greater distortion compensation effect, the dimension of the matrix D has to be increased and the amount of operations rapidly increases. As a result, the circuit size becomes larger or the operation time becomes longer. 
     In addition, when operating by incorporating the output signal z of the power amplifier  51  in Expression (5), the output signal z is converted to a digital signal using ADC, where a number of significant bits of ADC has to be secured sufficiently for accurate conversion including distortion components at lower signal levels compared with the dominant wave components. However, the increase in number of significant bits is directly linked to an increase in circuit size and power consumption, so that the number of significant bits is forced to be suppressed particularly when the sampling rate is very high speed. In other words, when it is not possible to sufficiently secure a number of bits of ADC, the distortion factor A k  is not obtained accurately due to the influence of a quantization error. 
     Descriptions are given below to a nonlinear distortion detection device and a distortion compensation power amplifier that are capable of simplifying operations to obtain a distortion factor of a power amplifier and also obtaining a distortion factor accurately even when it is not possible to secure a number of bits of ADC sufficiently. 
     First Embodiment 
       FIG. 2  is a block diagram illustrating a schematic configuration of a nonlinear distortion detection device according to First Embodiment. In  FIG. 2 , a nonlinear distortion detection device  1  according to First Embodiment detects nonlinear distortion produced by a power amplifier  11  and is provided with a test signal generator  10 , a Fourier transformer  12 , and a distortion factor calculator  13 . The test signal generator  10  generates a test signal xt to obtain a distortion factor A k  for output to the power amplifier  11 . The Fourier transformer  12  applies Fourier transform to an output signal z of the power amplifier  11  for conversion to a signal in the frequency domain. The distortion factor calculator  13  calculates the distortion factor A k  of the power amplifier  11  based on amplitude information and phase information of the output signal obtained from the Fourier transformer  12 . The power amplifier  11  outputs a signal z obtained by inputting the test signal xt generated by the test signal generator  10  for amplification (output signal). 
     The test signal generator  10  described above outputs two-tone signal illustrated in Expression (8) as the test signal xt.
 
 xt=a (cos ω 1   t +cos ω 2   t )  (8)
 
     Here, a is an amplitude of the test signal xt. 
     The output signal z of the power amplifier  11  is represented by Expression (9). 
     
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       ∑ 
                       k 
                     
                     ⁢ 
                     
                       
                         A 
                         k 
                       
                       ⁢ 
                       
                         
                            
                           xt 
                            
                         
                         
                           k 
                           - 
                           1 
                         
                       
                       ⁢ 
                       
                         xt 
                         ( 
                         
                           
                             k 
                             = 
                             1 
                           
                           , 
                           3 
                           , 
                           5 
                           , 
                           … 
                         
                         ⁢ 
                         
                             
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     When Expression (8) is substituted into Expression (9), the output signal z is represented by Expression (10). 
     
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       
                         ( 
                         
                           
                             aA 
                             1 
                           
                           + 
                           
                             
                               9 
                               4 
                             
                             ⁢ 
                             
                               a 
                               3 
                             
                             ⁢ 
                             
                               A 
                               3 
                             
                           
                           + 
                           
                             
                               25 
                               4 
                             
                             ⁢ 
                             
                               a 
                               5 
                             
                             ⁢ 
                             
                               A 
                               5 
                             
                           
                           + 
                           … 
                         
                         ⁢ 
                         
                             
                         
                         ) 
                       
                       ⁢ 
                       
                         ( 
                         
                           
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ω 
                               1 
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ω 
                               2 
                             
                             ⁢ 
                             t 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             
                               3 
                               4 
                             
                             ⁢ 
                             
                               a 
                               3 
                             
                             ⁢ 
                             
                               A 
                               3 
                             
                           
                           + 
                           
                             
                               25 
                               8 
                             
                             ⁢ 
                             
                               a 
                               5 
                             
                             ⁢ 
                             
                               A 
                               5 
                             
                           
                           + 
                           … 
                         
                         ⁢ 
                         
                             
                         
                         ) 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                       ω 
                                       1 
                                     
                                   
                                   - 
                                   
                                     ω 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                       ω 
                                       2 
                                     
                                   
                                   - 
                                   
                                     ω 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             t 
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           
                             
                               5 
                               8 
                             
                             ⁢ 
                             
                               a 
                               5 
                             
                             ⁢ 
                             
                               A 
                               5 
                             
                           
                           + 
                           … 
                         
                         ⁢ 
                         
                             
                         
                         ) 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     3 
                                     ⁢ 
                                     
                                       ω 
                                       1 
                                     
                                   
                                   - 
                                   
                                     2 
                                     ⁢ 
                                     
                                       ω 
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     3 
                                     ⁢ 
                                     
                                       ω 
                                       2 
                                     
                                   
                                   - 
                                   
                                     2 
                                     ⁢ 
                                     
                                       ω 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             t 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   ⋮ 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     From Expression (10), it is found that the output signal z includes, in addition to frequency components (ω 1 , ω 2 ) included in the test signal xt, distortion components (2ω 1 -ω 2 , 2ω 2 -ω 1 , 3ω 1 -2ω 2 , 3ω 2 -2ω 1 , . . . ) produced by nonlinearity of the power amplifier  11 . 
     When a Fourier coefficient for Fourier transform of the output signal z of Expression (10) is Z k , Z k  is represented by Expression (11). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           
                             Z 
                             1 
                           
                         
                       
                       
                         
                           
                             Z 
                             3 
                           
                         
                       
                       
                         
                           
                             Z 
                             5 
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                     
                     ] 
                   
                   = 
                   
                     E 
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               A 
                               1 
                             
                           
                         
                         
                           
                             
                               A 
                               3 
                             
                           
                         
                         
                           
                             
                               A 
                               5 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Here, Z 1  is a Fourier coefficient corresponding to the frequencies at ω 1 , ω 2 , Z 3  is a Fourier coefficient corresponding to the frequencies at 2ω 1 -ω 2 , 2ω 2 -ω 1 , and Z 5  is a Fourier coefficient corresponding to the frequencies at 3ω 1 -2ω 2 , 3ω 2 -2ω 1 . A matrix E is represented by Expression (12). 
     
       
         
           
             
               
                 
                   E 
                   = 
                   
                     [ 
                     
                       
                         
                           a 
                         
                         
                           
                             
                               9 
                               4 
                             
                             ⁢ 
                             
                               a 
                               3 
                             
                           
                         
                         
                           
                             
                               25 
                               4 
                             
                             ⁢ 
                             
                               a 
                               5 
                             
                           
                         
                         
                           
                               
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             
                               3 
                               4 
                             
                             ⁢ 
                             
                               a 
                               3 
                             
                           
                         
                         
                           
                             
                               25 
                               8 
                             
                             ⁢ 
                             
                               a 
                               5 
                             
                           
                         
                         
                           … 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             
                               5 
                               8 
                             
                             ⁢ 
                             
                               a 
                               5 
                             
                           
                         
                         
                           
                               
                           
                         
                       
                       
                         
                           
                               
                           
                         
                         
                           ⋮ 
                         
                         
                           
                               
                           
                         
                         
                           
                               
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     It is possible to obtain the distortion factor A k  by solving Expression (11), and it is found that the matrix E is an upper triangular matrix from Expression (12). An upper triangular matrix is a square matrix having all components lower left from a diagonal component to be zero. When the dimension of the matrix is n, it is understood that a general inverse matrix operation requires an amount of calculation of O(n 3 ) whereas an inverse matrix operation of an upper triangular matrix is done with an amount of calculation of O(n 2 ). In other words, related techniques require a general operation of an inverse matrix as Expression (6) whereas the present disclosure is done with an operation of an inverse matrix of the upper triangular matrix as Expression (12) and thus it is possible to reduce the amount of calculation. 
     In such a manner, with the nonlinear distortion detection device  1  according to First Embodiment, a distortion factor representing nonlinear properties of a power amplifier is obtained by an inverse matrix operation of an upper triangular matrix using a signal after Fourier transform, so that it is possible to attain simplification of the operation to obtain the distortion factor A k  compared with related techniques. 
     Second Embodiment 
     Next, descriptions are given to an embodiment when the nonlinear distortion detection device  1  in First Embodiment is applied to a distortion compensation power amplifier with reference to the drawings. 
       FIG. 3  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Second Embodiment. In  FIG. 3 , identical reference characters are given to components in common with  FIG. 2  described above. A distortion compensation power amplifier  2  illustrated in  FIG. 3  is provided with a test signal generator  10 , a predistorter  14 , a digital-to-analog converter (DAC)  15 , a frequency converter  16 , a power amplifier  11 , a frequency converter  17 , an analog-to-digital converter (ADC)  18 , a Fourier transformer  12 , a distortion factor calculator  13 , and a compensation factor calculator  19 . 
     The test signal generator  10  generates a test signal xt to obtain a distortion factor A k  for output to the predistorter  14 . The predistorter  14  directly outputs the test signal xt to obtain the distortion factor A k , and carries out distortion compensation to the input signal x in accordance with Expression (2) for output to the DAC  15  to communicate after obtaining the distortion factor A k . The DAC  15  converts the signal outputted from the predistorter  14  to an analog signal. The frequency converter  16  upconverts the signal outputted from the DAC  15  from the baseband to a carrier frequency. For example, when the signal outputted from the DAC  15  is represented by complex signals of I and Q, the frequency converter  16  is configured as a quadrature modulator. 
     The power amplifier  11  amplifies the signal outputted from the frequency converter  16  to predetermined power. The input/output properties of the power amplifier  11  are represented by Expression (1). The frequency converter  17  downconverts the frequency of the signal z outputted from the power amplifier  11  from the carrier frequency to the baseband. For example, when the signal inputted to the ADC  18  is represented by complex signals of I and Q, the frequency converter  17  is configured as a quadrature demodulator. The ADC  18  incorporates the signal downconverted by the frequency converter  17  at a predetermined sampling frequency for conversion to a digital signal. The Fourier transformer  12  carries out Fourier transform to the signal outputted from the ADC  18  for conversion to a signal in the frequency domain. The distortion factor calculator  13  calculates a distortion factor A k  of the power amplifier  11  using the signal outputted from the Fourier transformer  12 . The compensation factor calculator  19  calculates a compensation factor B k  from the distortion factor A k  in accordance with Expression (7). The distortion factor calculator  13  calculates the distortion factor A k  by solving Expression (11). Since the matrix E in Expression (11) is an upper triangular matrix as described above, it is possible to simplify the operations to obtain the distortion factor A k  compared with distortion compensation power amplifiers in the past. 
       FIG. 4  is a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier  2  according to Second Embodiment. In  FIG. 4 , firstly the test signal generator  10  outputs a test signal xt (step S 100 ). The test signal xt is inputted through the predistorter  14 , the DAC  15 , the frequency converter  16 , the power amplifier  11 , the frequency converter  17 , and the ADC  18  to the Fourier transformer  12 . At this time, the signal inputted to the Fourier transformer  12  includes, in addition to the original test signal xt, distortion components produced by nonlinearity of the power amplifier  11 . 
     The Fourier transformer  12  carries out Fourier transform to convert the signal outputted from the ADC  18  to a signal in the frequency domain and obtains a Fourier coefficient corresponding to Z k  in Expression (11) (step S 200 ). After the Fourier transformer  12  obtains the Fourier coefficient corresponding to Z k , the distortion factor calculator  13  solves Expression (11) to obtain the distortion factor A k  from Z k . Then, the compensation factor calculator  19  obtains a compensation factor B k  from the distortion factor A k  based on Expression (7) (step S 300 ). 
     After obtaining the compensation factor B k , the compensation factor calculator  19  outputs it to the predistorter  14 . Then, the predistorter  14  gives distortion of inverse properties to the input signal based on the compensation factor B k  for output to the power amplifier  11 . Then, the distortion compensated signal is sent from the power amplifier  11 . 
     In such a manner, with the distortion compensation power amplifier  2  according to Second Embodiment, the distortion factor representing nonlinear properties of a power amplifier is obtained by an inverse matrix operation of an upper triangular matrix using a signal after Fourier transform, so that it is possible to simplify operations of the distortion factor A k  compared with related techniques. Then, it is possible to carry out distortion compensation the power amplifier using the compensation factor B k  obtained from the distortion factor A k . 
     Third Embodiment 
       FIG. 5  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Third Embodiment. In  FIG. 5 , identical reference characters are given to components in common with  FIGS. 2 and 3  described above. A distortion compensation power amplifier  3  illustrated in  FIG. 5  differs from the distortion compensation power amplifier  2  according to Second Embodiment illustrated in  FIG. 3  in that a timing adjuster  20  is provided. In the distortion compensation power amplifier  2  according to Second Embodiment, a case is assumed where the time of inputting the test signal xt outputted from the test signal generator  10  through the power amplifier  11  to the Fourier transformer  12  is sufficiently short. In other words, a case is assumed where the signal inputted to the Fourier transformer  12  is represented by Expression (10). However, the signal inputted to the Fourier transformer  12  is sometimes actually delayed due to the response time of the circuit and the like and a timing offset in the timing to carry out Fourier transform may occur. When Fourier transform is applied while a timing offset occurs, phase rotation occurs in a Fourier coefficient Z k  and it is not possible to correctly obtain the distortion factor A k . With that, in the distortion compensation power amplifier  3  according to Third Embodiment, the timing to carry out Fourier transform in the Fourier transformer  12  is adjusted to appropriate timing by the timing adjuster  20 . 
     Descriptions are given below to behaviors of the timing adjuster  20 . 
     The timing adjuster  20  determines timing to carry out Fourier transform based on an amplitude value of the signal inputted to the Fourier transformer  12 . Specifically, the timing of the maximum amplitude value of the signal is detected and the timing to carry out Fourier transform is determined based on that. The test signal xt is configured with two-tone signal and is a periodic function having a period determined by the frequencies of the two waves. The timing adjuster  20  detects the timing when the amplitude value of the signal becomes maximum by observing one or more periods of the period of the test signal xt. 
     Although the signal inputted to the Fourier transformer  12  through the power amplifier  11  is affected by nonlinear distortion of the power amplifier  11 , the distortion components are at low levels compared with the components of the original test signal xt, so that the distortion components do not greatly affect behaviors of the timing adjuster  20 . Since the signal sampled by the ADC  18  is inputted to the timing adjuster  20 , the timing to carry out Fourier transform is adjustable in each sampling period of the ADC  18 . 
       FIG. 6  is a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier  3  according to Third Embodiment. In  FIG. 6 , same reference characters are given to steps of behaviors same as the flow chart in  FIG. 4  described above to omit the descriptions. In step S 110 , the timing adjuster  20  adjusts timing to carry out Fourier transform. Then, in step S 200 , the Fourier transformer  12  carries out Fourier transform based on the timing adjusted by the timing adjuster  20 . 
     In such a manner, the distortion compensation power amplifier  3  according to Third Embodiment is provided with the timing adjuster  20  and appropriately adjusts timing to carry out Fourier transform, so that it is possible to accurately obtain the distortion factor A k . 
     Fourth Embodiment 
       FIG. 7  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Fourth Embodiment. In  FIG. 7 , identical reference characters are given to components in common with  FIGS. 2 and 3  described above. A distortion compensation power amplifier  4  illustrated in  FIG. 7  is capable of correctly obtaining a distortion factor A k  even when there is a timing offset in the timing to carry outs Fourier transform similar to the distortion compensation power amplifier  3  according to Third Embodiment. In particular, a difference from the distortion compensation power amplifier  2  according to Second Embodiment illustrated in  FIG. 3  is that a phase adjuster  21  is provided. By adjusting a phase of a test signal xt in the phase adjuster  21 , the influence of a timing offset in the timing to carry out Fourier transform is cancelled. 
     Descriptions are given below to a behavioral principle of the phase adjuster  21 . For simplification, Expression (10) is rewritten to be represented by Expression (13). Expression (13) represents a case where there is no timing offset in timing to carry out Fourier transform to. 
     
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       
                         Z 
                         1 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ω 
                               1 
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               ω 
                               2 
                             
                             ⁢ 
                             t 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         Z 
                         3 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                       ω 
                                       1 
                                     
                                   
                                   - 
                                   
                                     ω 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     
                                       ω 
                                       2 
                                     
                                   
                                   - 
                                   
                                     ω 
                                     1 
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             t 
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         Z 
                         5 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     3 
                                     ⁢ 
                                     
                                       ω 
                                       1 
                                     
                                   
                                   - 
                                   
                                     2 
                                     ⁢ 
                                     
                                       ω 
                                       2 
                                     
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             t 
                           
                           + 
                           
                             
                               cos 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     3 
                                     ⁢ 
                                     
                                       ω 
                                       2 
                                     
                                   
                                   - 
                                   
                                     2 
                                     ⁢ 
                                     
                                       ω 
                                       1 
                                     
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             t 
                           
                         
                         } 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   ⋮ 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     When a timing offset Δt occurs in the timing to carry out Fourier transform, z is represented by Expression (14). 
     
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       
                         Z 
                         1 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     1 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     ω 
                                     1 
                                   
                                   ⁢ 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         Z 
                         3 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             cos 
                             ⁢ 
                             
                               { 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           1 
                                         
                                       
                                       - 
                                       
                                         ω 
                                         2 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           1 
                                         
                                       
                                       - 
                                       
                                         ω 
                                         2 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                               
                               } 
                             
                           
                           + 
                           
                             cos 
                             ⁢ 
                             
                               { 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           2 
                                         
                                       
                                       - 
                                       
                                         ω 
                                         1 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           2 
                                         
                                       
                                       - 
                                       
                                         ω 
                                         1 
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                               
                               } 
                             
                           
                         
                         ] 
                       
                     
                     + 
                     
                       
                         Z 
                         5 
                       
                       ⁡ 
                       
                         [ 
                         
                           
                             cos 
                             ⁢ 
                             
                               { 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         3 
                                         ⁢ 
                                         
                                           ω 
                                           1 
                                         
                                       
                                       - 
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           2 
                                         
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         3 
                                         ⁢ 
                                         
                                           ω 
                                           1 
                                         
                                       
                                       - 
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           2 
                                         
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                               
                               } 
                             
                           
                           + 
                           
                             cos 
                             ⁢ 
                             
                               { 
                               
                                 
                                   
                                     ( 
                                     
                                       
                                         3 
                                         ⁢ 
                                         
                                           ω 
                                           2 
                                         
                                       
                                       - 
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           1 
                                         
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     ( 
                                     
                                       
                                         3 
                                         ⁢ 
                                         
                                           ω 
                                           2 
                                         
                                       
                                       - 
                                       
                                         2 
                                         ⁢ 
                                         
                                           ω 
                                           1 
                                         
                                       
                                     
                                     ) 
                                   
                                   ⁢ 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                               
                               } 
                             
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   ⋮ 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     From Expression (14), it is found that different phase rotation occurs for each frequency component. For example, phase rotation of ω 1 Δt occurs with a ω 1  component, and phase rotation of (2ω 1 -ω 2 )Δt occurs with a (2ω 1 -ω 2 ) component. Here, in order to cancel the timing offset Δt, phase rotation is given to the original test signal. When the phase rotation given to the ω 1  component is θ 1  and the phase rotation given to the ω 2  component is θ 2 , Expression (14) is represented as Expression (15). 
     
       
         
           
             
               
                 
                   z 
                   = 
                   
                     
                       
                         Z 
                         1 
                       
                       ⁢ 
                       
                         { 
                         
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     1 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     ω 
                                     1 
                                   
                                   ⁢ 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   θ 
                                   1 
                                 
                               
                               ) 
                             
                           
                           + 
                           
                             cos 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   
                                     ω 
                                     2 
                                   
                                   ⁢ 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   t 
                                 
                                 + 
                                 
                                   θ 
                                   2 
                                 
                               
                               ) 
                             
                           
                         
                         } 
                       
                     
                     + 
                     
                       
                         
                           Z 
                           3 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               cos 
                               ⁢ 
                               
                                 { 
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                             ω 
                                             1 
                                           
                                         
                                         - 
                                         
                                           ω 
                                           2 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                             ω 
                                             1 
                                           
                                         
                                         - 
                                         
                                           ω 
                                           2 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     
                                       θ 
                                       1 
                                     
                                   
                                   - 
                                   
                                     θ 
                                     2 
                                   
                                 
                                 } 
                               
                             
                             + 
                             
                               cos 
                               ⁢ 
                               
                                 { 
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                             ω 
                                             2 
                                           
                                         
                                         - 
                                         
                                           ω 
                                           1 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         
                                           2 
                                           ⁢ 
                                           
                                             ω 
                                             2 
                                           
                                         
                                         - 
                                         
                                           ω 
                                           1 
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     2 
                                     ⁢ 
                                     
                                       θ 
                                       2 
                                     
                                   
                                   - 
                                   
                                     θ 
                                     1 
                                   
                                 
                                 } 
                               
                             
                           
                           ] 
                         
                       
                       ⁢ 
                       
                         
                           Z 
                           3 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               cos 
                               ⁢ 
                               
                                 { 
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           3 
                                           ⁢ 
                                           
                                             ω 
                                             1 
                                           
                                         
                                         - 
                                         
                                           2 
                                           ⁢ 
                                           
                                             ω 
                                             2 
                                           
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         
                                           3 
                                           ⁢ 
                                           
                                             ω 
                                             1 
                                           
                                         
                                         - 
                                         
                                           2 
                                           ⁢ 
                                           
                                             ω 
                                             2 
                                           
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     3 
                                     ⁢ 
                                     
                                       θ 
                                       1 
                                     
                                   
                                   - 
                                   
                                     2 
                                     ⁢ 
                                     
                                       θ 
                                       2 
                                     
                                   
                                 
                                 } 
                               
                             
                             + 
                             
                               cos 
                               ⁢ 
                               
                                 { 
                                 
                                   
                                     
                                       ( 
                                       
                                         
                                           3 
                                           ⁢ 
                                           
                                             ω 
                                             2 
                                           
                                         
                                         - 
                                         
                                           2 
                                           ⁢ 
                                           
                                             ω 
                                             1 
                                           
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     
                                       ( 
                                       
                                         
                                           3 
                                           ⁢ 
                                           
                                             ω 
                                             2 
                                           
                                         
                                         - 
                                         
                                           2 
                                           ⁢ 
                                           
                                             ω 
                                             1 
                                           
                                         
                                       
                                       ) 
                                     
                                     ⁢ 
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     t 
                                   
                                   + 
                                   
                                     3 
                                     ⁢ 
                                     
                                       θ 
                                       2 
                                     
                                   
                                   - 
                                   
                                     2 
                                     ⁢ 
                                     
                                       θ 
                                       1 
                                     
                                   
                                 
                                 } 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                       
                   
                   ⁢ 
                   ⋮ 
                 
               
               
                 
                     
                 
               
             
           
         
       
     
     From Expression (13), it is found that the ω 1  component and the ω 2  component are in a same phase when there is no timing offset. Utilizing this, the phase adjuster  21  detects the timing offset Δt from a phase difference between the ω 1  component and the ω 2  component. When the phase difference between the ω 1  component and the ω 2  component is Δθ, Δθ is represented by Expression (16). The phase of the ω 1  component and the phase of the ω 2  component are obtained from the Fourier transformer  12 . 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           Δ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                         
                         = 
                           
                         ⁢ 
                         
                           
                             ( 
                             
                               Phase 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               of 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ω 
                                 1 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               component 
                             
                             ) 
                           
                           - 
                           
                             ( 
                             
                               Phase 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               of 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 ω 
                                 2 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               component 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                         ⁢ 
                         
                           
                             
                               ω 
                               1 
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                           - 
                           
                             
                               ω 
                               2 
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                             
                           ⁢ 
                           
                             
                               ( 
                               
                                 
                                   ω 
                                   1 
                                 
                                 - 
                                 
                                   ω 
                                   2 
                                 
                               
                               ) 
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                         
                         ⁢ 
                         
                             
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     By deforming Expression (16), Expression (17) is obtained. 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     t 
                   
                   = 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       θ 
                     
                     
                       
                         ω 
                         1 
                       
                       - 
                       
                         ω 
                         
                           2 
                           ⁢ 
                           
                               
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Using the timing offset Δt obtained by Expression (17), θ 1  and θ 2  are given in Expression (18). 
     
       
         
           
             
               
                 
                   
                     
                       θ 
                       1 
                     
                     = 
                     
                       
                         
                           - 
                           
                             ω 
                             1 
                           
                         
                         ⁢ 
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         t 
                       
                       = 
                       
                         
                           
                             - 
                             
                               ω 
                               1 
                             
                           
                           
                             
                               ω 
                               1 
                             
                             - 
                             
                               ω 
                               
                                 2 
                                 ⁢ 
                                 
                                     
                                 
                               
                             
                           
                         
                         ⁢ 
                         Δθ 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       θ 
                       2 
                     
                     = 
                     
                       
                         
                           - 
                           
                             ω 
                             2 
                           
                         
                         ⁢ 
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         t 
                       
                       = 
                       
                         
                           
                             - 
                             
                               ω 
                               2 
                             
                           
                           
                             
                               ω 
                               1 
                             
                             - 
                             
                               ω 
                               2 
                             
                           
                         
                         ⁢ 
                         Δ 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     It is found that Expression (13) is obtained by substituting Expression (18) into Expression (15). In other words, by giving the phase rotation obtained by Expression (18) to the test signal xt in the phase adjuster  21 , it becomes possible to cancel the timing offset Δt in the timing for Fourier transform. In the distortion compensation power amplifier  4  according to Fourth Embodiment, it is possible to adjust by giving arbitrary phase rotation without restricting adjustment accuracy by the sampling period of the ADC  18  as the distortion compensation power amplifier  3  according to Third Embodiment. 
       FIG. 8  is a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier  4  according to Fourth Embodiment. In  FIG. 8 , same reference characters are given to steps of behaviors same as the flow chart in  FIG. 6  described above to omit the descriptions. In step S 120 , the Fourier transformer  12  carries out Fourier transform in timing determined in advance to obtain phase information of the ω 1  component and phase information of the ω 2  component. Subsequently, in step S 130 , the phase adjuster  21  adjusts the phase of the test signal xt in accordance with the phase information of the ω 2  component and the phase information of the ω 2  component. Subsequently, in step S 200 , the Fourier transformer  12  carries out Fourier transform to obtain the Fourier coefficient Z k . 
     In such a manner, with the distortion compensation power amplifier  4  according to Fourth Embodiment, a timing offset in timing for Fourier transform is cancelled by the phase adjuster  21 , so that it is possible to obtain a distortion factor A k  accurately. 
     Fifth Embodiment 
       FIG. 9  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Fifth Embodiment. A distortion compensation power amplifier  5  according to Fifth Embodiment illustrated in  FIG. 9  is capable of correctly obtaining a distortion factor A k  even when there is a timing offset in timing to carry out Fourier transform similar to the distortion compensation power amplifier  3  according to Third Embodiment and the distortion compensation power amplifier  4  according to Fourth Embodiment. The difference from the distortion compensation power amplifier  2  according to Second Embodiment illustrated in  FIG. 3  is that a timing adjuster  20  and a phase adjuster  21  are provided. The timing adjuster  20  adjusts a timing offset in timing to carry out Fourier transform in each sampling period of an ADC  18 . The phase adjuster  21  cancels timing offset less than the sampling period of the ADC  18  in the timing to carry out Fourier transform. In other words, the timing adjuster  20  carries out rough adjustment and the phase adjuster  21  carries out fine adjustment. 
       FIG. 10  is a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier  5  according to Fifth Embodiment. In  FIG. 10 , same reference characters are given to steps of behaviors same as the flow chart in  FIG. 8  described above to omit the descriptions. In step S 110 , the timing adjuster  20  adjusts a timing offset in timing to carry out Fourier transform in each sampling period of the ADC  18 . Then, in steps S 120  and S 130 , by adjusting a phase of a test signal, the phase adjuster  21  adjusts a timing offset in timing to carry out Fourier transform with accuracy less than the sampling period of the ADC  18 . 
     In such a manner, with the distortion compensation power amplifier  5  according to Fifth Embodiment, after carrying out timing adjustment in the sampling period of the ADC  18 , the timing is finely adjusted with accuracy less than the sampling period of the ADC  18 , so that it is possible to accurately adjust the timing to carry out Fourier transform. 
     Sixth Embodiment 
       FIG. 11  is a block diagram illustrating a schematic configuration of a distortion compensation power amplifier according to Sixth Embodiment. A distortion compensation power amplifier  6  according to Sixth Embodiment illustrated in  FIG. 11  is capable of accurately obtaining a distortion factor A k  even when it is not possible to sufficiently secure a number of bits of the ADC  18 . The difference from the distortion compensation power amplifier  5  according to Fifth Embodiment illustrated in  FIG. 9  described above is that a cancellation signal generator  22 , a DAC  23 , an adder  24 , and an amplitude adjuster  25  are provided. The cancellation signal generator  22  generates two-tone signal same as the test signal xt as a cancellation signal and also adjusts the amplitude, the phase, and the delay of the cancellation signal. The DAC  23  converts the cancellation signal to an analog signal. The adder  24  adds a signal outputted from the DAC  23  and a signal outputted from the frequency converter  17 . The amplitude adjuster  25  adjusts the amplitude of the signal outputted from the adder  24  to fit in the input range of the ADC  18 . 
       FIG. 12  is a flow chart that describes a process to obtain a distortion factor A k  in the distortion compensation power amplifier  6  according to Sixth Embodiment. In  FIG. 12 , same reference characters are given to steps of behaviors same as the flow chart in  FIG. 10  described above to omit the descriptions. Step S 100  through step S 200  are executed in a state where the cancellation signal generator  22  does not output anything. In step S 200 , the Fourier transformer  12  executes Fourier transform to obtain Z 1 , which is a Fourier coefficient of the ω 1  component and the ω 2  component. Subsequently, in step S 210 , the cancellation signal generator  22  outputs a cancellation signal. Subsequently, in step S 220 , while observing an output of the Fourier transformer  12 , the cancellation signal generator  22  adjusts the amplitude, the phase, and the delay of the cancellation signal in such a manner that a component, same as the frequency component included in the cancellation signal, of the signal inputted to the Fourier transformer  12  becomes small. Subsequently, in step S 230 , the amplitude adjuster  25  adjusts the gain in such a manner that the level of the signal inputted to the ADC  18  gets closer to the input range of the ADC. Subsequently, in step S 240 , the Fourier transformer  12  executes Fourier transform to obtain Fourier coefficients Z 3 , Z 5 , . . . . Subsequently, in step S 300 , the compensation factor calculator  19  obtains the distortion factor A k  based onbased on the Z 1  obtained in step S 200 , Z 3 , Z 5 , . . . obtained in step S 240 , and the gain of the amplitude adjuster  25  to obtain a compensation factor B k  from the distortion factor A k  based on Expression (7). Here, when the distortion factor A k  is obtained, the gain of the amplitude adjuster  25  to obtain the Fourier coefficient Z 1  is different from the gain of the amplitude adjuster  25  to obtain the Fourier coefficients Z 3 , Z 5 , . . . , so that the gain difference has to be corrected. When the gain of the amplitude adjuster  25  to obtain the Fourier coefficients Z 3 , Z 5 , . . . in step S 240  relative to the gain of the amplitude adjuster  25  to obtain the Fourier coefficient Z 1  in step S 200  is G, Expression (11) to obtain the distortion factor A k  is rewritten as Expression (19). Since it is possible to correct the gain difference of the amplitude adjuster  25  to obtain the Fourier coefficient by solving Expression (19), it is possible to obtain the distortion factor A k  correctly. 
     
       
         
           
             
               
                 
                   
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                             Z 
                             1 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
                                           Z 
                                           3 
                                         
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                                         G 
                                       
                                     
                                   
                                   
                                     
                                       
                                         
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                                           5 
                                         
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                               A 
                               1 
                             
                           
                         
                         
                           
                             
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                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
       FIGS. 13A through 13E  are diagrams that represent major signals in the distortion compensation power amplifier  6  according to Sixth Embodiment.  FIG. 13A  is a test signal outputted from the test signal generator  10 . As the test signal, two-tone signal having frequency components of ω 1  and ω 2  are outputted.  FIG. 13B  is a signal outputted from the frequency converter  17 . As an example, a case where frequency components of 2ω 1 -ω 2 , 2ω 2 -ω 1 , 3ω 1 -2ω 2 , and 3ω 2 -2ω 1  are produced due to the nonlinear distortion in the power amplifier  11  is illustrated.  FIG. 13C  is a cancellation signal outputted from the cancellation signal generator  22 . The cancellation signal illustrated in  FIG. 13C  is configured with the frequency components of ω 1  and ω 2  out of the frequency components of the signal outputted from the power amplifier  11 . The amplitude, the phase, and the delay are adjusted in such a manner that it is possible to suppress frequency components same as the cancellation signal out of the frequency components of the signal outputted from the power amplifier  11 . 
       FIG. 13D  is a signal outputted from the adder  24 . In  FIG. 13D , as a result of adding the signal in  FIG. 13B  and the signal in  FIG. 13C , the frequency components of ω 1  and ω 2  are suppressed.  FIG. 13E  is a signal outputted from the amplitude adjuster  25 . In  FIG. 13E , the signal in  FIG. 13D  is amplified to the input range of the ADC  18 . In  FIG. 13E , since the frequency components of ω 1  and ω 2  are suppressed, the frequency components of 2ω 1 -ω 2 , 2ω 2 -ω 1 , 3ω 1 -2ω 2 , and 3ω 2 -2ω 1  are amplified with no distortion and it is possible to obtain the distortion factor without affected by a quantization error of the ADC. 
     In such a manner, with the distortion compensation power amplifier  6  according to Sixth Embodiment, after suppressing frequency components having high signal levels out of the signal outputted from the power amplifier  11 , the signal is amplified to the input range of the ADC  18  and then the distortion factor A k  is obtained, so that it is possible to accurately obtain the distortion factor A k  even when it is not possible to sufficiently secure the number of bits of the ADC. 
     Although a case where two-tone signal are used for a test signal is described in First through Sixth Embodiments described above as examples, three or more tone signals may also be used. 
     In addition, although the descriptions are given that Fourier transform is carried out as a behavior of the Fourier transformer  12  in First through Sixth Embodiments described above, fast Fourier transform (FFT) may also be carried out. Alternatively, it may also be a plurality of band pass filters. It may be as long as it is possible to extract a specific frequency component as a principle. 
     In Third and Fifth Embodiments described above, a period to observe the amplitude value of the signal in the timing adjuster  20  may be one period of the test signal and may also be two or more periods. By observing in two or more periods to detect a maximum value a plurality of times, it is possible to reduce the influence of disturbance, such as a noise, and it is possible to accurately determine timing for Fourier transform. 
     In addition, although the descriptions are given that the timing adjuster  20  detects the timing when the amplitude value of the signal inputted to the Fourier transformer  12  becomes maximum in Third and Fifth Embodiments described above, it may be other methods as long as it is possible to detect timing to be a reference of the test signal, which is a periodic function, and timing to have a minimum amplitude value may also be detected. In addition, timing to have a maximum absolute value of the amplitude value or timing to have a minimum absolute value of the amplitude value may also be detected. Further, when the signal outputted from the ADC  18  is complex signals of I and Q, an absolute value of the complex signal or timing to have a maximum or minimum power value may also be detected. 
     In First through Sixth Embodiments described above, the operation of Expression (2) in the predistorter  14  may also be achieved as a look-up table (LUT) to have an output signal y relative to an input signal x. 
     In Sixth Embodiment described above, although the descriptions are given to a case where the cancellation signal is two-tone signal as an example, tone signals of a greater number may also be used. Here, using  FIGS. 14A through 14E , a case of using four-tone signal as a cancellation signal is described.  FIGS. 14A and 14B  are same as  FIGS. 13A and 13B , respectively.  FIG. 14C  is a cancellation signal outputted from the cancellation signal generator  22 . The cancellation signal illustrated in  FIG. 14C  is configured with frequency components of ω 1 , ω 2 , 2ω 1 -ω 1 , and 2ω 2 -ω 1  out of the frequency components of the signal outputted from the power amplifier  11 . The amplitude, the phase, and the delay are adjusted in such a manner that it is possible to suppress the frequency components same as the cancellation signal out of the frequency components of the signal outputted from the power amplifier  11 . 
       FIG. 14D  is a signal outputted from the adder  24 . In  FIG. 14D , as a result of adding the signal in  FIG. 14B  and the signal in  FIG. 14C , frequency components of ω 1 , ω 2 , 2ω 1 -ω 2 , and 2ω 2 -ω 1  are suppressed.  FIG. 14E  is a signal outputted from the amplitude adjuster  25 . In  FIG. 14E , the signal in  FIG. 14D  is amplified to the input range of the ADC  18 . In  FIG. 14E , the frequency components of ω 1 , ω 2 , 2ω 1 -ω 2 , and 2ω 2 -ω 1  are suppressed, so that frequency components of 3ω 1 -2ω 2  and 3ω 2 -2ω 1  are amplified with no distortion and it is possible to obtain a distortion factor without affected by a quantization error of the ADC  18 . 
     Modification of Sixth Embodiment 
       FIG. 15  is a flow chart that describes a process to obtain a distortion factor A k  in a modification of the distortion compensation power amplifier  6  according to Sixth Embodiment. In the modification of the distortion compensation power amplifier  6  according to Sixth Embodiment, the two-tone cancellation signal illustrated in  FIG. 13C  and the four-tone cancellation signal illustrated in  FIG. 14C  are used. In  FIG. 15 , same reference characters are given to steps of behaviors same as the flow chart in  FIG. 12  described above to omit the descriptions. Steps S 100  through S 230  are same as the flow chart in  FIG. 12 . It should be noted that the Fourier coefficient Z 1  obtained in step S 200  corresponds to a first Fourier coefficient. In step S 230 , the amplitude adjuster  25  outputs the signal illustrated in  FIG. 13E . Subsequently, in step S 250 , the Fourier transformer  12  carries out Fourier transform to obtain Z 3  (corresponding to second Fourier coefficient), which is a Fourier coefficient of the component of 2ω 1 -ω 2  and 2ω 2 -ω 1 . Subsequently, in step S 260 , the cancellation signal generator  22  outputs the four-tone cancellation signal illustrated in  FIG. 14C . Subsequently, in step S 270 , while observing an output of the Fourier transformer  12 , the cancellation signal generator  22  adjusts the amplitude, the phase, and the delay of the cancellation signal in such a manner that a component, same as the frequency component included in the cancellation signal, of the signal inputted to the Fourier transformer  12  becomes small. 
     Subsequently, in step S 280 , the amplitude adjuster  25  adjusts the gain in such a manner that the level of the signal inputted to the ADC  18  gets closer to the input range of the ADC. At this time, the signal outputted from the amplitude adjuster  25  is as  FIG. 14E . Subsequently, in step S 290 , the Fourier transformer  12  executes Fourier transform to obtain Fourier coefficients Z 5 , Z 7 , . . . (third Fourier coefficient and later). Subsequently, in step S 300 , the distortion factor calculator  13  obtains a distortion factor A k  based onbased on Z 1  obtained in step S 200 , Z 3  obtained in step S 250 , Z 5 , Z 7 , . . . obtained in step S 290 , and the gain of the amplitude adjuster  25 . Then, the compensation factor calculator  19  obtains a compensation factor B k  from the distortion factor A k  based on Expression (7). Here, G 2  is the gain of the amplitude adjuster  25  to obtain the Fourier coefficient Z 3  in step S 250  relative to the gain of the amplitude adjuster  25  to obtain the Fourier coefficient Z 1  in step S 200 . In addition, G 3  is the gain of the amplitude adjuster  25  to obtain the Fourier coefficients Z 5 , Z 7 , . . . in step S 290  relative to the gain of the amplitude adjuster  25  to obtain the Fourier coefficient Z 1  in step S 200 . Using G 2  and G 3 , Expression (11) to obtain the distortion factor A k  is rewritten as Expression (20). It is possible to correct the gain difference of the amplitude adjuster  25  to obtain the Fourier coefficient by solving Expression (20), so that it is possible to obtain the distortion factor A k  correctly. 
     
       
         
           
             
               
                 
                   
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                             Z 
                             1 
                           
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       
                                         
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                                           2 
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
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                   ( 
                   20 
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     In the flow chart in  FIG. 12 , after obtaining the Fourier coefficient Z 1  firstly, the cancellation signal is outputted to obtain the Fourier coefficients Z 3 , Z 5 , . . . , whereas in the flow chart in  FIG. 15 , after obtaining the Fourier coefficient Z 1  firstly, a two-tone cancellation signal is outputted to obtain the Fourier coefficient Z 3  and after that a four-tone cancellation signal is further outputted to obtain the Fourier coefficients Z 5 , Z 7 , . . . . In such a manner, by obtaining the Fourier coefficients stepwise, it is possible to reduce the influence of the quantization error of the ADC  18  and accurately obtain the distortion factor A k . 
     Outline of Aspect of Present Disclosure 
     A first nonlinear distortion detection device of the present disclosure is a nonlinear distortion detection device that includes a test signal generator that generates a test signal and outputs the test signal to have the power amplifier amplify the test signal, a Fourier transformer that converts the amplified test signal to a signal in a frequency domain, and a distortion factor calculator that calculates a distortion factor of the power amplifier based on amplitude information and phase information of the signal in the frequency domain. 
     A second nonlinear distortion detection device of the present disclosure is the first nonlinear distortion detection device, wherein the test signal is a two-tone signal. 
     A third nonlinear distortion detection device of the present disclosure is the first or second nonlinear distortion detection device, further including a timing adjuster that adjusts timing in which the Fourier transformer converts the amplified test signal to the signal in the frequency domain, wherein the timing adjuster adjusts timing for the conversion based on an amplitude value of the amplified test signal that is inputted to the Fourier transformer. 
     A fourth nonlinear distortion detection device of the present disclosure is any one of the first through third nonlinear distortion detection devices, further including a phase adjuster that adjusts a phase of the test signal, wherein the phase adjuster gives phase rotation to the test signal based on the phase information. 
     A fifth nonlinear distortion detection device of the present disclosure is any one of the first through fourth nonlinear distortion detection devices, further including a cancellation signal generator that generates a cancellation signal and adjusts an amplitude, a phase, and a delay of the cancellation signal, an adder that adds the adjusted cancellation signal and the amplified test signal output from the power amplifier, an amplitude adjuster that adjusts an amplitude of an output signal of the adder, and an ADC that converts the amplitude adjusted signal output from the amplitude adjuster to a digital signal, wherein the Fourier transformer converts the digital signal output from the ADC to a signal in the frequency domain, and the distortion factor calculator obtains the amplitude information and the phase information as first amplitude and phase information when the cancellation signal is not added with the amplified test signal output from the power amplifier and obtains the amplitude information and the phase information as second amplitude and phase information when the cancellation signal is added with the amplified test signal output from the power amplifier to calculate a distortion factor based on the first amplitude and phase information and the second amplitude and phase information. 
     A sixth nonlinear distortion detection device of the present disclosure is the fifth nonlinear distortion detection device, wherein the cancellation signal is a two-tone signal. 
     A seventh nonlinear distortion detection device of the present disclosure is the fifth nonlinear distortion detection device, wherein the cancellation signal is a four-tone signal. 
     An eighth nonlinear distortion detection device of the present disclosure is the fifth nonlinear distortion detection device, wherein the cancellation signal is a two-tone signal and a four-tone signal, and, after a first Fourier coefficient is obtained, the cancellation signal of the two-tone signal is outputted from the cancellation signal generator and the Fourier transformer obtains a second Fourier coefficient, and then, the cancellation signal of the four-tone signal is further outputted from the cancellation signal generator and the Fourier transformer obtains a third Fourier coefficient and later Fourier coefficient. 
     A distortion compensation power amplifier of the present disclosure is a distortion compensation power amplifier that performs predistortion of a power amplifier. The distortion compensation power amplifier includes a test signal generator that generates a test signal, a power amplifier that amplifies the generated test signal and outputs the amplified test signal, a Fourier transformer that converts the amplified test signal to a signal in a frequency domain, a distortion factor calculator that calculates a distortion factor of the power amplifier based on amplitude information and phase information of the signal in the frequency domain, a compensation factor calculator that calculates a compensation factor to perform predistortion based on the distortion factor, and a predistorter that performs predistortion of an input signal using the compensation factor, wherein the test signal is inputted to the power amplifier when the distortion compensation power amplifier calculates the distortion factor, and a signal predistorted using the compensation factor is inputted to the power amplifier when the distortion compensation power amplifier amplifies the input signal. 
     Although the descriptions have been given above to various embodiments with reference to the drawings, the present disclosure is not limited to such examples, of course. It is obvious that those skilled in the art may conceive of various modifications and alterations within the scope of the appended claims and it is naturally understood that they belong to the technical scope of the present disclosure. 
     It is possible to apply the present disclosure to various wireless communication devices, such as wireless LAN, ZigBee®, and Bluetooth®. Particularly, it is useful for wireless communication devices having an FFT circuit, such as wireless communication devices using an orthogonal frequency division multiplex (OFDM) approach for the modulation/demodulation system and wireless communication devices using a frequency domain equalizer (FDE) approach for the equalizer, for example.