Patent Publication Number: US-8971170-B2

Title: Wireless communication apparatus and wireless communication method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of International Application No. PCT/JP2009/070781, filed on Dec. 11, 2009, the entire contents of which are incorporated herein by reference. 
    
    
     FIELD 
     The embodiments discussed herein are directed to a wireless communication apparatus and a wireless communication method. 
     BACKGROUND 
     At the 3rd Generation Partnership Project (3GPP), a standards organization for mobile communication, specifications for Evolved Universal Terrestrial Radio Access (E-UTRA) are currently being drawn up. These specifications are the standard for next-generation mobile communications. In E-UTRA, a single-carrier frequency-division multiple access (SC-FDMA) method will be used as an uplink wireless access method. The SC-FDMA method is a wireless access method for transmitting data values using a physical channel, such as a physical random access channel (PRACH). 
     A wireless communication apparatus that uses the SC-FDMA method performs a discrete Fourier transformation on N data values in the time domain to transform N data values into N discrete Fourier transformation values (hereinafter, referred to as “transformation values”) in the frequency domain. Then, the wireless communication apparatus maps the N transformation values onto subcarriers and transmits, along a physical channel, such as a PRACH, to the outside, data values in the time domain, which is obtained by performing an inverse Fourier transformation process on the mapped transformation values.
     Patent Literature 1: International Publication Pamphlet No. WO 2007/91675   

     However, with the conventional wireless communication apparatus that uses the SC-FDMA method described above, because all of the N discrete Fourier transformation values are calculated using a discrete Fourier transform equation, there is a problem in that the amount of computation becomes enormous when calculating discrete Fourier transformation values. Specifically, if N data values in the time domain are x u,ncs (n) (0≦n&lt;N), the wireless communication apparatus calculates all of the N transformation values X(k) (0≦k&lt;N) by using the discrete Fourier transform equation illustrated below: 
     
       
         
           
             
               
                 
                   
                     X 
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         0 
                       
                       
                         N 
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         
                           X 
                           
                             u 
                             , 
                             
                               n 
                               cs 
                             
                           
                         
                         ⁡ 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       ⁢ 
                       
                         W 
                         N 
                         nk 
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     where, W N  illustrated in Equation (1) is defined by Equation (2) below: 
     
       
         
           
             
               
                 
                   
                     W 
                     M 
                   
                   = 
                   
                     ⅇ 
                     
                       
                         - 
                         j 
                       
                       ⁢ 
                       
                         
                           2 
                           ⁢ 
                           π 
                         
                         N 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     The number of times multiplications of real numbers performed by using Equation (1) above is given by 4N(N−1), which is an enormous number of times. For example, if a wireless transmission device transmits data values using a PRACH, because N=839, the number of times real number multiplications are performed using Equation (1) above is 4×839×(839−1)=2,812,328, which is an enormous number of times. 
     SUMMARY 
     According to an aspect of an embodiment of the invention, a wireless communication apparatus includes a first transformation value calculating unit that calculates three transformation values continuous in a frequency domain from N data values (N is an integer equal to or greater than one) by using a discrete Fourier transform equation that is used to transform the N data values continuous in a time domain into N transformation values continuous in the frequency domain; a phase difference calculating unit that obtains a change in a phase difference, which is a fixed value, from the three transformation values calculated by the first transformation value calculating unit and that calculates, on the basis of the obtained change in the phase difference, the phase difference between a calculated transformation value and a not-yet calculated transformation value; a second transformation value calculating unit that sequentially calculates the not-yet calculated transformation value by multiplying the calculated transformation value by a twiddle factor that uses the phase difference calculated by the phase difference calculating unit as a rotation angle; and a transmitting unit that maps, onto subcarriers, the transformation values calculated by the first transformation value calculating unit and the transformation values calculated by the second transformation value calculating unit, that performs an inverse Fourier transformation process on the mapped transformation values, and that transmits the transformation values subjected to the inverse Fourier transformation process. 
     The object and advantages of the embodiment will be realized and attained by means of the elements and combinations particularly pointed out in the claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the embodiment, as claimed. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram illustrating the configuration of a wireless communication apparatus according to a first embodiment. 
         FIG. 2  is a block diagram illustrating the configuration of a wireless communication apparatus according to a second embodiment. 
         FIG. 3  is a schematic diagram illustrating a process performed by a phase difference calculating unit. 
         FIG. 4  is a schematic diagram illustrating a process performed by a second transformation value calculating unit. 
         FIG. 5  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus according to the second embodiment. 
         FIG. 6  is a block diagram illustrating the configuration of a wireless communication apparatus according to a third embodiment. 
         FIG. 7  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus according to the third embodiment. 
         FIG. 8  is a block diagram illustrating the configuration of a wireless communication apparatus according to a fourth embodiment. 
         FIG. 9  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus according to the fourth embodiment. 
         FIG. 10  is a block diagram illustrating the configuration of a wireless communication apparatus according to a fifth embodiment. 
         FIG. 11  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus according to the fifth embodiment. 
         FIG. 12  is a block diagram illustrating the configuration of a wireless communication apparatus according to a sixth embodiment. 
         FIG. 13  is a schematic diagram illustrating an example of information stored in a transformation value storing unit. 
         FIG. 14  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus according to the sixth embodiment. 
         FIG. 15  is a block diagram illustrating a computer that executes a wireless communication program. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Preferred embodiments of a wireless communication apparatus and a wireless communication method disclosed in the present invention will be described in detail below with reference to the accompanying drawings. 
     [a] First Embodiment 
     First, a wireless communication apparatus according to the first embodiment will be described.  FIG. 1  is a block diagram illustrating the configuration of a wireless communication apparatus  1  according to a first embodiment. As illustrated in  FIG. 1 , the wireless communication apparatus  1  according to the first embodiment includes a first transformation value calculating unit  2 , a phase difference calculating unit  3 , a second transformation value calculating unit  4 , and a transmitting unit  5 . 
     The first transformation value calculating unit  2  calculates three transformation values from N data values continuous in the frequency domain by using a discrete Fourier transform equation to transform N data values (N is an integer equal to or greater than one) continuous in the time domain into N transformation values continuous in the frequency domain. The phase difference calculating unit  3  obtains a change in a phase difference, which is a fixed value, from the three transformation values calculated by the first transformation value calculating unit  2  and calculates, on the basis of the obtained change in the phase difference, the phase differences between a calculated transformation value and a not-yet calculated transformation value. The second transformation value calculating unit  4  sequentially calculates a not-yet calculated transformation value by multiplying the calculated transformation value by a twiddle factor, which uses the phase difference calculated by the phase difference calculating unit  3  as a rotation angle. The transmitting unit  5  maps, onto subcarriers, the transformation values calculated by the first transformation value calculating unit  2  and the transformation values calculated by the second transformation value calculating unit  4 , performs an inverse Fourier transformation process on the mapped transformation values, and transmits the transformation values. 
     In this way, the wireless communication apparatus  1  according to the first embodiment calculates three continuous transformation values from N data values by using a discrete Fourier transform equation to transform the N data values into N transformation values. Then, the wireless communication apparatus  1  obtains the fixed change in the phase difference from the three calculated transformation values and calculates a not-yet calculated transformation value by multiplying a calculated transformation value by a twiddle factor obtained from the change in the phase difference. Specifically, the wireless communication apparatus  1  calculates three continuous transformation values from among the N transformation values by using a discrete Fourier transform equation. In contrast, the wireless communication apparatus  1  calculates the rest of the transformation values, other than the three already-calculated transformation values from among the N transformation values, by multiplying the calculated transformation values by a twiddle factor. Accordingly, the wireless communication apparatus  1  according to the first embodiment can reduce the amount of computation needed to calculate a discrete Fourier transformation values when compared with the conventional method in which all of the N transformation values are calculated by using a discrete Fourier transform equation. 
     [b] Second Embodiment 
     In the following, as a second embodiment, a specific example of the wireless communication apparatus  1  according to the first embodiment will be described. The wireless communication apparatus according to the second embodiment is a wireless communication apparatus, such as a mobile terminal device that uses a single-carrier frequency-division multiple access (SC-FDMA) method as an uplink wireless access method. 
     First, the wireless communication apparatus according to the second embodiment will be described.  FIG. 2  is a block diagram illustrating the configuration of a wireless communication apparatus  10  according to a second embodiment. As illustrated in  FIG. 2 , the wireless communication apparatus  10  according to the second embodiment includes a data value creating unit  11 , a DFT unit  12 , and a data value transmitting unit  13 . 
     The data value creating unit  11  creates N sequences (hereinafter, referred to as “data values”) and outputs the created N data values to the DFT unit  12 . Specifically, the data value creating unit  11  includes a Zadoff-Chu (ZC) sequence creating unit  21  and a cyclic shift (CS) unit  22 . 
     The ZC sequence creating unit  21  creates a ZC sequence of N data values continuous in the time domain. Specifically, if a ZC sequence number is input from a higher layer that controls the wireless communication apparatus  10 , the ZC sequence creating unit  21  creates, in accordance with the input ZC sequence number, a ZC sequence of N data values in the time domain. At this time, the ZC sequence x u (n) (0≦n&lt;N) created by the ZC sequence creating unit  21  is represented by Equation (3) below: 
     
       
         
           
             
               
                 
                   
                     
                       x 
                       u 
                     
                     ⁡ 
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     exp 
                     ⁡ 
                     
                       [ 
                       
                         
                           - 
                           j 
                         
                         ⁢ 
                         
                           
                             π 
                             × 
                             u 
                             × 
                             n 
                             × 
                             
                               ( 
                               
                                 n 
                                 + 
                                 1 
                               
                               ) 
                             
                           
                           N 
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     The CS unit  22  performs a cyclic shift on the N data values in the time domain that are input from the ZC sequence creating unit  21  and outputs the N data values subjected to the cyclic shift to the DFT unit  12 . Specifically, if the amount of cyclic shift (hereinafter, referred to as the “CS amount”) that is the number of data values subjected to the cyclic shift is input from the higher layer, the CS unit  22  performs the cyclic shift such that the sequence of the N data values is shifted in accordance with the input CS amount. Then, the CS unit  22  outputs the N data values subjected to the cyclic shift to the DFT unit  12 . The N data values x u,ncs (n) (0≦n&lt;N) subjected to the cyclic shift by the CS unit  22  is given by Equation (4) below:
 
 x   u,n     cs   ( n )= x   u (( n+n   cs )mod  N )  (4)
 
     The DFT unit  12  transforms the N data values in the time domain that are input from the data value creating unit  11  into N discrete Fourier transformation values (hereinafter, simply referred to as “transformation values”) in the frequency domain. Specifically, the DFT unit  12  includes a first transformation value calculating unit  23 , a phase difference calculating unit  24 , and a second transformation value calculating unit  25 . 
     By using a discrete Fourier transform equation, which is an equation used to transform N data values that are input from the data value creating unit  11  into N transformation values, the first transformation value calculating unit  23  calculates continuous first to third transformation values from among the N data values. Specifically, by using the discrete Fourier transform equation that is Equation (1) described above, the first transformation value calculating unit  23  calculates, from among the N transformation values X(k) (0≦k&lt;N), the first to the third transformation values X(0), X(1), and X(2). 
     The phase difference calculating unit  24  obtains the change in the phase difference from the three transformation values calculated by the first transformation value calculating unit  23  and calculates, on the basis of the obtained change in the phase difference, the phase difference between a calculated transformation value and an arbitrary transformation value that appears among the fourth and the subsequent transformation values that have not been calculated. In the following, a specific example of a process performed by the phase difference calculating unit  24  will be described with reference to  FIG. 3 .  FIG. 3  is a schematic diagram illustrating a process performed by the phase difference calculating unit  24 . 
     First, the phase difference calculating unit  24  calculates the phases of the first to the third transformation values on the basis of the real number component and the imaginary number component of the first to the third transformation values calculated by the first transformation value calculating unit  23 . In the example illustrated in  FIG. 3 , the phase difference calculating unit  24  calculates a phase θ (k) of the first to the third transformation values X(k) on the basis of the real number component Re[X(k)] and the imaginary number component Im[X(k)] of the first to the third transformation values X(k) (0≦k≦2). The phase θ (k) of the first to the third transformation values X(k) (0≦k≦2) is represented by Equation (5) below:
 
θ( k )=arctan( Im[X ( k )]/ Re[X ( k )])  (5)
 
     Subsequently, on the basis of the calculated phases of the first to the third transformation values, the phase difference calculating unit  24  calculates the phase difference between the first transformation value and the second transformation value and the phase difference between the second transformation value and the third transformation value. If θ(0), θ(1), and θ(2) represent the phases of the first to the third transformation values, respectively, a phase difference d(0) between the first transformation value and the second transformation value and a phase difference d(1) between the second transformation value and the third transformation value are represented by Equations (6) and (7) below:
 
 d (0)=θ(1)−θ(0)  (6)
 
 d (1)=θ(2)−θ(1)  (7)
 
     Subsequently, on the basis of the calculated phase difference between the first transformation value and the second transformation value and the calculated phase difference between the second transformation value and the third transformation value, the phase difference calculating unit  24  calculates the change in the phase difference. The change in the phase difference calculated at this time is a fixed value. 
     If d(0) represents the phase difference between the first transformation value and the second transformation value and d(1) represents the phase difference between the second transformation value and the third transformation value, the change in the phase difference a is represented by Equation (8) below:
 
 a=d (1)− d (0)  (8)
 
     Subsequently, on the basis of the calculated change in the phase difference, the phase difference calculating unit  24  calculates the phase difference between a calculated transformation value and an arbitrary transformation value, from among the N transformation values, that appears among the fourth and the subsequent transformation values that have not been calculated. If the change in the phase difference is represented by a, the phase difference d(k−1) between an arbitrary transformation value X(k) (3≦k&lt;N) that appears among the fourth and the subsequent transformation values and the transformation value X(k−1) appearing immediately before the arbitrary transformation value is represented by Equation (9) below. At this time, the transformation value X(k−1) appearing immediately before the arbitrary transformation value is assumed to be the calculated transformation value.
 
 d ( k− 1)= d ( k− 2)+ a   (9)
 
     A description will be given here by referring back to  FIG. 2 . By multiplying a calculated transformation value appearing immediately before an arbitrary transformation value that appears among the fourth and the subsequent transformation values by a twiddle factor, which uses the phase difference calculated by the phase difference calculating unit  24  as a rotation angle, the second transformation value calculating unit  25  sequentially calculates the fourth to the N th  transformation values that have not been calculated. In the following, a process performed by the second transformation value calculating unit  25  will be specifically described with reference to  FIG. 4 .  FIG. 4  is a schematic diagram illustrating a process performed by the second transformation value calculating unit  25 . 
     The N transformation values are usually located on the unit circle in the complex plane. In the example illustrated in  FIG. 4 , from among the N transformation values, the arbitrary transformation value X(k) (3≦k&lt;N) that appears among the fourth and the subsequent transformation values and the calculated transformation value X(k−1) appearing immediately before the arbitrary transformation value X(k) are located on the unit circle in the complex plane. The phase difference Δθ indicates the phase difference between the transformation value X(k) and the transformation value X(k−1). 
     Under the condition illustrated in  FIG. 4 , by multiplying the transformation value X(k−1) by a twiddle factor exp(jΔθ), which uses the phase difference Δθ as the rotation angle, the second transformation value calculating unit  25  calculates the fourth to the N th  transformation values X(k) (3≦k&lt;N) from among the N transformation values. Specifically, the fourth to the N th  transformation values X(k) (3≦k&lt;N) are obtained from Equation (10) below:
 
 X ( k )= X ( k− 1)exp[ jΔθ]   (10)
 
     The phase difference Δθ in Equation (10) above is the phase difference d(k−1), which is calculated by the phase difference calculating unit  24 . Accordingly, if the phase difference Δθ in Equation (10) above is substituted for the phase difference d(k−1) in Equation (9), Equation (10) above is represented by Equation (11) below:
 
 X ( k )= X ( k− 1)×exp[ j×d ( k− 1)]  (11)
 
     Specifically, when calculating the fourth transformation value X(3) from among the N transformation values, the second transformation value calculating unit  25  multiplies the third transformation value X(2), which is immediately before the fourth transformation value X(3), by a twiddle factor, which uses the phase difference d(2) calculated by the phase difference calculating unit  24  as the rotation angle. More specifically, by using Equation (11) above, the second transformation value calculating unit  25  performs the calculation below: 
     
       
         
           
             
               
                 
                   
                     
                       X 
                       ⁡ 
                       
                         ( 
                         3 
                         ) 
                       
                     
                     = 
                     
                       
                         X 
                         ⁡ 
                         
                           ( 
                           2 
                           ) 
                         
                       
                       × 
                       
                         exp 
                         ⁡ 
                         
                           [ 
                           
                             j 
                             × 
                             
                               d 
                               ⁡ 
                               
                                 ( 
                                 2 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   
                     = 
                     
                       
                         X 
                         ⁡ 
                         
                           ( 
                           2 
                           ) 
                         
                       
                       × 
                       
                         exp 
                         ⁡ 
                         
                           [ 
                           
                             j 
                             × 
                             
                               { 
                               
                                 
                                   d 
                                   ⁡ 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                 + 
                                 a 
                               
                               } 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
             
               
           
         
       
     
     Furthermore, when calculating the fifth transformation value X(4) from among the N transformation values, the second transformation value calculating unit  25  multiplies the fourth transformation value X(3), which is immediately before the fifth transformation value X(4), by a twiddle factor, which uses the phase difference d(3) calculated by the phase difference calculating unit  24  as the rotation angle. Specifically, by using Equation (11) above, the second transformation value calculating unit  25  performs the calculation below: 
     
       
         
           
             
               
                 
                   
                     
                       X 
                       ⁡ 
                       
                         ( 
                         4 
                         ) 
                       
                     
                     = 
                     
                       
                         X 
                         ⁡ 
                         
                           ( 
                           3 
                           ) 
                         
                       
                       × 
                       
                         exp 
                         ⁡ 
                         
                           [ 
                           
                             j 
                             × 
                             
                               d 
                               ⁡ 
                               
                                 ( 
                                 3 
                                 ) 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   
                     = 
                     
                       
                         X 
                         ⁡ 
                         
                           ( 
                           3 
                           ) 
                         
                       
                       × 
                       
                         exp 
                         ⁡ 
                         
                           [ 
                           
                             j 
                             × 
                             
                               { 
                               
                                 
                                   d 
                                   ⁡ 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   a 
                                 
                               
                               } 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
             
               
           
         
       
     
     The second transformation value calculating unit  25  sequentially performs the calculation described above until it calculates the N th  transformation value X(N−1). By doing so, the second transformation value calculating unit  25  sequentially calculates the fourth to the N th  transformation values from among the N transformation values. 
     A description will be given here by referring back to  FIG. 2 . The data value transmitting unit  13  maps, onto subcarriers, the transformation values calculated by the first transformation value calculating unit  23  and the transformation values calculated by the second transformation value calculating unit  25 ; performs an inverse Fourier transformation process on the mapped transformation value; and transmits them. The data value transmitting unit  13  includes a sub-carrier mapping unit  26 , an IFFT unit  27 , a cyclic prefix (CP) inserting unit  28 , a filter processing unit  29 , and a wireless processing unit  30 . 
     The sub-carrier mapping unit  26  maps, onto subcarriers, the transformation values calculated by the first transformation value calculating unit  23  and the transformation values calculated by the second transformation value calculating unit  25 . By performing an inverse Fourier transformation process on the transformation values mapped by the sub-carrier mapping unit  26 , the IFFT unit  27  transforms the transformation values in the frequency domain into data values in the time domain. 
     The CP inserting unit  28  defines the end of the data values received from the IFFT unit  27  as the CP and inserts the CP into the top of the data values. The filter processing unit  29  performs a filter process for smoothing the boundary between the data values that are input from the CP inserting unit  28  and outputs the data value subjected to the filter process to the wireless processing unit  30 . The wireless processing unit  30  performs, on the data values input from the filter processing unit  29 , a wireless process, such as digital to analog (D/A) conversion or up conversion, and transmits a signal subjected to the wireless process to the outside. 
     The data value creating unit  11 , the DFT unit  12 , and the data value transmitting unit  13  are electronic circuits. The ZC sequence creating unit  21  and the CS unit  22  are electronic circuits. The first transformation value calculating unit  23 , the phase difference calculating unit  24 , and the second transformation value calculating unit  25  are electronic circuits. The sub-carrier mapping unit  26 , the IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30  are electronic circuits. Examples of the electronic circuits include an integrated circuit, such as an application specific integrated circuit (ASIC) or a field programmable gate array (FPGA), a central processing unit (CPU), or a micro processing unit (MPU). 
     In the following, a wireless communication process performed by the wireless communication apparatus  10  according to the second embodiment will be described.  FIG. 5  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus  10  according to the second embodiment. As illustrated in  FIG. 5 , in the wireless communication apparatus  10  according to the second embodiment, the ZC sequence creating unit  21  in the data value creating unit  11  creates a ZC sequence that corresponds to N data values (Step S 11 ). The CS unit  22  performs a cyclic shift on the N data values that are input from the ZC sequence creating unit  21  (Step S 12 ). Then, the CS unit  22  outputs the N data values subjected to the cyclic shift to the DFT unit  12 . 
     By using a discrete Fourier transform equation that is an equation used to transform the N data values that are input from the data value creating unit  11  to N transformation values, the first transformation value calculating unit  23  in the DFT unit  12  calculates the first to the third transformation values from among the N transformation values (Step S 13 ). 
     On the basis of the real number component and the imaginary number component of the first to the third transformation values calculated by the first transformation value calculating unit  23 , the phase difference calculating unit  24  calculates the phases of the first to the third transformation values (Step S 14 ). Subsequently, on the basis of the calculated phases of the first to the third transformation values, the phase difference calculating unit  24  calculates the phase difference between the first transformation value and the second transformation value and the phase difference between the second transformation value and the third transformation value (Step S 15 ). Then, on the basis of the calculated phase difference between the first transformation value and the second transformation value and the calculated phase difference between the second transformation value and the third transformation value, the phase difference calculating unit  24  calculates the change in the phase difference (Step S 16 ). Then, on the basis of the calculated change in the phase difference, the phase difference calculating unit  24  calculates the phase difference between, from among the N transformation values, an arbitrary transformation value that appears among the fourth and the subsequent transformation values and a calculated transformation value appearing immediately before the arbitrary transformation value (Step S 17 ). 
     By multiplying the calculated transformation value by a twiddle factor, which uses the phase difference calculated by the phase difference calculating unit  24  as a rotation angle, the second transformation value calculating unit  25  sequentially calculates, from among the N transformation values, the fourth to the N th  transformation value that have not been calculated (Step S 18 ). 
     Then, the sub-carrier mapping unit  26  in the data value transmitting unit  13  maps, onto subcarriers, the first to the third transformation values calculated by the first transformation value calculating unit  23  and the fourth to the N th  transformation values calculated by the second transformation value calculating unit  25  (Step S 19 ). The IFFT unit  27  transforms the transformation values in the frequency domain to data values in the time domain by performing an inverse Fourier transformation process on the transformation values mapped onto the subcarriers (Step S 20 ). The CP inserting unit  28  defines the end of the data values that are input from the IFFT unit  27  as a CP and inserts the CP into the top of the data values (Step S 21 ). The filter processing unit  29  performs a filter process for smoothing the boundary between the data values that are input from the CP inserting unit  28  and outputs the data value subjected to the filter process to the wireless processing unit  30  (Step S 22 ). The wireless processing unit  30  performs, on the data values that are input from the filter processing unit  29 , the wireless process, such as digital to analog conversion or up conversion, and transmits a signal subjected to the wireless process to the outside (Step S 23 ). 
     As described above, by using a discrete Fourier transform equation to transform N data values to N transformation values, the wireless communication apparatus  10  according to the second embodiment calculates the first to the third transformation values from the N data values. Then, the wireless communication apparatus  10  obtains a fixed change in the phase difference from the calculated first to the third transformation values and sequentially calculates the fourth to the N th  transformation values by multiplying a calculated transformation value appearing immediately before an arbitrary transformation value that appears among the fourth and the subsequent transformation values by a twiddle factor that is obtained from the change in the phase difference. Specifically, the wireless communication apparatus  10  calculates, from among the N transformation values, the first to the third transformation values by using a discrete Fourier transform equation, whereas, it calculates, from among the N transformation values, the fourth to the N th  transformation values by multiplying the calculated transformation value by a twiddle factor. Accordingly, the wireless communication apparatus  10  according to the second embodiment can reduce the amount of computation needed to calculate discrete Fourier transformation values when compared with the conventional method in which all of the N transformation values are calculated by using a discrete Fourier transform equation. 
     Specifically, the number of times complex multiplications are needed to calculate the first to the third transformation values from among N transformation values by using a discrete Fourier transform equation is 2N times. Furthermore, the number of times complex multiplications are needed to calculate the fourth to the N th  transformation values from among the N transformation values by multiplying the calculated transformation value by a twiddle factor is (N−3) times. If a complex multiplication is performed once, the number of times real number multiplications are performed is four. Accordingly, when calculating the N transformation values, the wireless communication apparatus  10  according to the second embodiment performs the real number multiplication for 4{2N+(N−3)=12(N−1) times. 
     In contrast, in the conventional method for calculating all of the N transformation values by using a discrete Fourier transform equation, when calculating the N transformation values, the number of times real number multiplications are performed is 4N(N−1) times. Accordingly, when compared with the conventional method for calculating all of the N transformation values by using a discrete Fourier transform equation, the wireless communication apparatus according to the second embodiment can reduce the number of times real number multiplications are performed to 12(N−1)/{4N(N−1)}=3/N. For example, if the wireless communication apparatus  10  transmits data values using a PRACH, because N=839, when compared with the conventional method, the wireless communication apparatus  10  can reduce the number of times real number multiplications are performed to 3/839=0.004. 
     [c] Third Embodiment 
     In the second embodiment described above, a description has been given of a case of performing the cyclic shift on N data values in the time domain and calculating N transformation values in the frequency domain from the N data values subjected to the cyclic shift. However, the cyclic shift may also be performed in the process for calculating the N transformation values in the frequency domain. Accordingly, in a third embodiment, a description will be given of a case of performing the cyclic shift in a process for calculating the N transformation values in the frequency domain. 
     First, the configuration of a wireless communication apparatus  40  according to the third embodiment will be described.  FIG. 6  is a block diagram illustrating the configuration of the wireless communication apparatus  40  according to a third embodiment. As illustrated in  FIG. 6 , the wireless communication apparatus  40  according to the third embodiment includes a data value creating unit  41 , a DFT unit  42 , and a data value transmitting unit  43 . The data value creating unit  41  includes a ZC sequence creating unit  21 . The ZC sequence creating unit  21  corresponds to the ZC sequence creating unit  21  illustrated in  FIG. 2 . 
     The DFT unit  42  transforms N data values in the time domain, which are input from the data value creating unit  41 , into N transformation values in the frequency domain. The DFT unit  42  includes a first transformation value calculating unit  51 , a CS unit  52 , a phase difference calculating unit  53 , and a second transformation value calculating unit  54 . 
     Similarly to the first transformation value calculating unit  23  illustrated in  FIG. 2 , by using a discrete Fourier transform equation that is an equation used to transform the N data values that are input from the data value creating unit  41  to the N transformation values, the first transformation value calculating unit  51  calculates the first to the third transformation values from among the N transformation values. However, unlike the first transformation value calculating unit  23 , the first transformation value calculating unit  51  calculates the first to third transformation values X′(0), X′(1), and X′(2) from among N transformation values X′(k) (0≦k&lt;N) by using the discrete Fourier transform equation (12) below: 
     
       
         
           
             
               
                 
                   
                     
                       X 
                       ′ 
                     
                     ⁡ 
                     
                       ( 
                       k 
                       ) 
                     
                   
                   = 
                   
                     
                       ∑ 
                       
                         n 
                         = 
                         0 
                       
                       
                         N 
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         
                           X 
                           u 
                         
                         ⁡ 
                         
                           ( 
                           n 
                           ) 
                         
                       
                       ⁢ 
                       
                         W 
                         N 
                         nk 
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The symbol x u (n) in Equation (12) is Zadoff-Chu sequence x u (n) (0≦n&lt;N) indicated by Equation (3) above. 
     The CS unit  52  performs a cyclic shift on the first to the third transformation values calculated by the first transformation value calculating unit  51 . Specifically, if a CS amount is input from a higher layer, the CS unit  52  performs the cyclic shift by shifting the sequence of the first to the third transformation values in accordance with the CS amount. The first to the third transformation values X(k) (0≦k≦2) subjected to the cyclic shift by the CS unit  52  are represented by Equation (13) below: 
                     X   ⁡     (   k   )       =         X   ′     ⁡     (   k   )       ×     exp   ⁡     [     j   ×   2   ⁢   π   ×       n   cs     N     ×   k     ]                 (   13   )               
where n cs  represents the CS amount.
 
     By using the first to the third transformation values subjected to the cyclic shift by the CS unit  52 , the phase difference calculating unit  53  calculates, from among the N transformation values, the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent transformation values and a transformation value appearing immediately before the arbitrary transformation value. The specific process performed by the phase difference calculating unit  53  is the same as that performed by the phase difference calculating unit  24  according to the second embodiment. 
     By multiplying the transformation values that appears among the third and the subsequent transformation values by a twiddle factor, which uses the phase difference calculated by the phase difference calculating unit  53  as a rotation angle, the second transformation value calculating unit  54  calculates the fourth to the N th  transformation values from among the N transformation values. The specific process performed by the second transformation value calculating unit  54  is the same as that performed by the second transformation value calculating unit  25  according to the second embodiment. 
     The data value transmitting unit  43  maps, onto subcarriers, the transformation value subjected to the cyclic shift by the CS unit  52  and the transformation values calculated by the second transformation value calculating unit  54  and transmits, to the outside, the data values obtained by performing an inverse Fourier transformation process on the mapped transformation values. The data value transmitting unit  43  includes a sub-carrier mapping unit  55 , the IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30 . 
     The IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30  correspond to the IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30 , respectively, illustrated in  FIG. 2 . The sub-carrier mapping unit  55  maps, onto subcarriers, the transformation values subjected to the cyclic shift by the CS unit  52  and the transformation values calculated by the second transformation value calculating unit  54 . 
     The data value creating unit  41 , the DFT unit  42 , and the data value transmitting unit  43  are electronic circuits. The first transformation value calculating unit  51 , the CS unit  52 , the phase difference calculating unit  53 , and the second transformation value calculating unit  54  are electronic circuits. The sub-carrier mapping unit  55  is an electronic circuit. Examples of the electronic circuits include an integrated circuit, such as an ASIC or an FPGA, a CPU, and a MPU. 
     In the following, the wireless communication process performed by the wireless communication apparatus  40  according to the third embodiment will be described.  FIG. 7  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus  40  according to the third embodiment. Because Steps S 31 , S 35  to S 38 , and S 40  to S 43  correspond to Steps S 11 , S 15  to S 18 , and S 20  to S 23  described in the second embodiment, respectively, a simplified description thereof will be given. As illustrated in  FIG. 7 , with the wireless communication apparatus  40  according to the third embodiment, the ZC sequence creating unit  21  in the data value creating unit  41  creates a Zadoff-Chu sequence that corresponds to N data values (Step S 31 ). 
     By using a discrete Fourier transform equation that is an equation used to transform the N data values received from the data value creating unit  41  to the N transformation values, the first transformation value calculating unit  51  in the DFT unit  42  calculates the first to the third transformation values from among the N transformation values (Step S 32 ). The CS unit  52  performs the cyclic shift on the first to the third transformation values calculated by the first transformation value calculating unit  51  (Step S 33 ). 
     The phase difference calculating unit  53  calculates the phases of the first to the third transformation value on the basis of the real number component and the imaginary number component of the first to the third transformation values subjected to the cyclic shift performed by the CS unit  52  (Step S 34 ). Then, the phase difference calculating unit  53  calculates the phase difference between the first transformation value and the second transformation value and the phase difference between the second transformation value and the third transformation value (Step S 35 ) and calculates the change in the phase difference (Step S 36 ). Subsequently, the phase difference calculating unit  53  calculates, from among the N transformation values, the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent transformation values and a calculated transformation value appearing immediately before the arbitrary transformation value (Step S 37 ). 
     By multiplying a calculated transformation value by a twiddle factor, which uses the phase difference calculated by the phase difference calculating unit  53  as a rotation angle, the second transformation value calculating unit  54  sequentially calculates the fourth to the N th  transformation values that have not been calculated from among the N transformation values (Step S 38 ). 
     Then, the sub-carrier mapping unit  55  in the data value transmitting unit  43  maps, onto subcarriers, the first to the third transformation values subjected to the cyclic shift by the CS unit  52  and the fourth to the N th  transformation value calculated by the second transformation value calculating unit  54  (Step S 39 ). Subsequently, the IFFT unit  27  transforms the transformation values in the frequency domain to the data values in the time domain by using an inverse Fourier transformation process (Step S 40 ) and the CP inserting unit  28  inserts the CP into the top of the data values (Step S 41 ). Then, the filter processing unit  29  performs the filter process (Step S 42 ) and the wireless processing unit  30  transmits a signal subjected to the wireless process to the outside (Step S 43 ). 
     As described above, the wireless communication apparatus  40  according to the third embodiment performs a cyclic shift on the first to the third transformation values in the frequency domain calculated by using a discrete Fourier transform equation. Then, the wireless communication apparatus  40  obtains a fixed change in the phase difference from the first to the third transformation values subjected to the cyclic shift and multiplies a calculated transformation value, which appears immediately before an arbitrary transformation value that appears among the fourth and the subsequent transformation values, by a twiddle factor that is obtained from the change in the phase difference, and thereby the wireless communication apparatus  40  sequentially calculates the fourth to the N th  transformation values. In other words, the wireless communication apparatus  40  performs a cyclic shift on the first to the third transformation values in the frequency domain during a process of calculating the N transformation values in the frequency domain. The number of times the cyclic shifts are performed is three. Accordingly, the wireless communication apparatus  40  according to the third embodiment can reduce the number of cyclic shifts from N times to 3 times when compared with a case in which N transformation values in the frequency domain are calculated from the N data values subjected to the cyclic shift. 
     [d] Fourth Embodiment 
     In the second embodiment, an example case has been described in which the fourth to the N th  transformation values are sequentially calculated by multiplying a calculated transformation value by a twiddle factor, which uses, as a rotation angle, the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent transformation values from among the N transformation values and the calculated transformation value appearing immediately before the arbitrary transformation value. However, the fourth to the N th  transformation values may also be calculated by multiplying one of the calculated first to third transformation values by a twiddle factor that uses, as a rotation angle, the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and one of the calculated first to third transformation values. Accordingly, in a fourth embodiment, a description will be given of a case in which the fourth to the N th  transformation values are calculated by multiplying one of the calculated first to third transformation values by a twiddle factor that uses, as a rotation angle, the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and the one of the calculated first to third transformation values. 
     First, the configuration of a wireless communication apparatus  60  according to the fourth embodiment will be described.  FIG. 8  is a block diagram illustrating the configuration of the wireless communication apparatus  60  according to a fourth embodiment. As illustrated in  FIG. 8 , the wireless communication apparatus  60  according to the fourth embodiment includes the data value creating unit  11 , a DFT unit  62 , and the data value transmitting unit  13 . The data value creating unit  11  and the data value transmitting unit  13  correspond to the data value creating unit  11  and the data value transmitting unit  13  illustrated in  FIG. 2 , respectively. 
     The DFT unit  62  transforms N data values in the time domain that are input from the data value creating unit  11  into N transformation values in the frequency domain. The DFT unit  62  includes the first transformation value calculating unit  23 , a phase difference calculating unit  63 , and a second transformation value calculating unit  64 . The first transformation value calculating unit  23  corresponds to the first transformation value calculating unit  23  illustrated in  FIG. 2 . 
     By using the transformation values calculated by the first transformation value calculating unit  23 , the phase difference calculating unit  63  calculates the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and one of the calculated first to the third transformation values. In this case, as an example, a description will be given of a case in which the phase difference is calculated between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and a calculated third transformation value. A process for calculating the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and a calculated first or second transformation value is the same as the process for calculating the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and a calculated third transformation value. 
     Specifically, first, on the basis of the real number component and the imaginary number component of the first to the third transformation values calculated by the first transformation value calculating unit  23 , the phase difference calculating unit  63  calculates the phases of the first to the third transformation values. Then, on the basis of the calculated phases of the first to the third transformation values, the phase difference calculating unit  63  calculates the phase difference between the first transformation value and the second transformation value and the phase difference between the second transformation value and the third transformation value. Subsequently, on the basis of the calculated phase difference between the first transformation value and the second transformation value and the calculated phase difference between the second transformation value and the third transformation value, the phase difference calculating unit  63  calculates the change in the phase difference. The processes performed up to this step are the same as those performed by the phase difference calculating unit  24  according to the second embodiment. 
     Subsequently, on the basis of the change in the calculated phase difference, the phase difference calculating unit  63  calculates the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and a third transformation value that is calculated by the first transformation value calculating unit  23 . If a represents the change in the phase difference, the phase difference f(k) between an arbitrary transformation value X(k) (3≦k&lt;N) that appears among the fourth and the subsequent N transformation values and the third transformation value X(2) is represented by Equation (14) below: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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     By multiplying one of the first to the third transformation values that are calculated by the first transformation value calculating unit  23  by a twiddle factor that uses the phase difference calculated by the phase difference calculating unit  63  as a rotation angle, the second transformation value calculating unit  64  calculates the fourth to the N th  transformation values that have not been calculated. In this case, as an example, a description will be given of a case in which the phase difference calculating unit  63  calculates the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and the calculated third transformation value. 
     Specifically, by multiplying the third transformation value X(2) by a twiddle factor exp{j×f(k)} that uses the phase difference f(k), which is indicated by Equation (14), as a rotation angle, the second transformation value calculating unit  64  calculates the fourth to the Nth transformation values X(k) (3≦k&lt;N) from among the N transformation values. In other words, the fourth to the N th  transformation values X(k) (3≦k&lt;N) are obtained using Equation (15) below:
 
 X ( k )= X (2)×exp[ j×f ( k )]  (15)
 
     If the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and the first transformation value or the second transformation value, the second transformation value calculating unit multiplies the first transformation value or the second transformation value by a twiddle factor that uses the phase difference as a rotation angle. 
     The DFT unit  62  described above is an electronic circuit. Furthermore, the phase difference calculating unit  63  and the second transformation value calculating unit  64  are electronic circuits. Examples of the electronic circuit include an integrated circuit, such as an ASIC or a FPGA, a CPU, and a MPU. 
     In the following, a wireless communication process performed by the wireless communication apparatus  60  according to the fourth embodiment will be described.  FIG. 9  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus  60  according to the fourth embodiment. Because the processes performed at Steps S 51  to S 56  and S 59  to S 63  correspond to the processes performed at Steps S 11  to S 16  and S 19  to S 23  in the second embodiment, a simplified description thereof will be given. As illustrated in  FIG. 9 , in the wireless communication apparatus  60  according to the fourth embodiment, the ZC sequence creating unit  21  in the data value creating unit  11  creates a Zadoff-Chu sequence that corresponds to N data values (Step S 51 ) and the CS unit  22  performs a cyclic shift on the N data values (Step S 52 ). 
     By using a discrete Fourier transform equation that is an equation used to transform N data values that are input from the data value creating unit  11  to the N transformation values, the first transformation value calculating unit  23  in the DFT unit  62  calculates the first to the third transformation values from among the N transformation values (Step S 53 ). 
     On the bases of the real number component and the imaginary number component of the first to the third transformation values calculated by the first transformation value calculating unit  23 , the phase difference calculating unit  63  calculates the phases of the first to the third transformation values (Step S 54 ). Then, on the bases of the calculated phases of the first to the third transformation values, the phase difference calculating unit  63  calculates the phase difference between the first transformation value and the second transformation value and the phase difference between the second transformation value and the third transformation value (Step S 55 ). Subsequently, on the basis of the calculated phase difference between the first transformation value and the second transformation value and the phase difference between the second transformation value and the third transformation value, the phase difference calculating unit  63  calculates the change in the phase difference (Step S 56 ). 
     Then, on the basis of the calculated change in the phase difference, the phase difference calculating unit  63  calculates the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and one of the first to the third transformation values calculated by the first transformation value calculating unit  23  (Step S 57 ). For example, the phase difference calculating unit  63  calculates the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and the third transformation value. 
     Then, by multiplying one of the first to the third transformation values by a twiddle factor that uses the phase difference calculated by the phase difference calculating unit  63  as a rotation angle, the second transformation value calculating unit  64  calculates the fourth to the N th  transformation values from among the N transformation values (Step S 58 ). For example, if the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent transformation values and the third transformation value by the phase difference calculating unit  63 , the second transformation value calculating unit  64  multiplies the third transformation value by a twiddle factor that uses the phase difference as a rotation angle in order to calculate the fourth to the N th  transformation values. 
     Subsequently, the sub-carrier mapping unit  26  in the data value transmitting unit  13  maps, onto subcarriers, the first to the third transformation values calculated by the first transformation value calculating unit  23  and the fourth to the N th  transformation values calculated by the second transformation value calculating unit  64  (Step S 59 ). Then, the IFFT unit  27  transforms the transformation value in the frequency domain into the data value in the time domain by using the inverse Fourier transformation process (Step S 60 ) and the CP inserting unit  28  inserts the CP into the top of the data values (Step S 61 ). Then, the filter processing unit  29  performs the filter process (Step S 62 ) and the wireless processing unit  30  transmits a signal subjected to the wireless process to the outside (Step S 63 ). 
     As described above, the wireless communication apparatus  60  according to the fourth embodiment multiplies one of the first to the third transformation values by a twiddle factor that uses, as a rotation angle, the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and the one of the first to the third transformation values, and thereby the wireless communication apparatus  60  calculates the fourth to the N th  transformation values. Accordingly, the wireless communication apparatus  60  according to the fourth embodiment does not need to calculate the fourth to the N th  transformation values in the order they appear, and thus it is possible to calculate the fourth to the N th  transformation values in parallel. Therefore, with the wireless communication apparatus  60  according to the fourth embodiment, the calculation speed of discrete Fourier transformation values can be improved. 
     [e] Fifth Embodiment 
     In the fourth embodiment described above, an example has been described in which N data values in the time domain are subjected to a cyclic shift and N transformation values in the frequency domain are calculated from the N data values subjected to the cyclic shift. However, the cyclic shift may also be performed in the process of calculating the N transformation values in the frequency domain. Accordingly, in a fifth embodiment, an example of performing the cyclic shift in the process of calculating the N transformation values in the frequency domain. 
     First, the configuration of a wireless communication apparatus  70  according to the fifth embodiment will be described.  FIG. 10  is a block diagram illustrating the configuration of the wireless communication apparatus  70  according to a fifth embodiment. As illustrated in  FIG. 10 , the wireless communication apparatus  70  according to the fifth embodiment includes a data value creating unit  71 , a DFT unit  72 , and a data value transmitting unit  73 . The data value creating unit  71  includes a ZC sequence creating unit  21 . The ZC sequence creating unit  21  corresponds to the ZC sequence creating unit  21  illustrated in  FIG. 6 . 
     The DFT unit  72  transforms N data values in the time domain input from the data value creating unit  71  into N transformation values in the frequency domain. The DFT unit  72  includes the first transformation value calculating unit  51 , the CS unit  52 , a phase difference calculating unit  74 , and a second transformation value calculating unit  75 . The first transformation value calculating unit  51  and the CS unit  52  correspond to the first transformation value calculating unit  51  and the CS unit  52  illustrated in  FIG. 6 , respectively. 
     By using the first to the third transformation values subjected to the cyclic shift performed by the CS unit  52 , the phase difference calculating unit  74  calculates the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and one of the first to the third transformation values. The specific processes performed by the phase difference calculating unit  74  are the same as those performed by the phase difference calculating unit  63  according to the fourth embodiment. 
     By multiplying a transformation value that appears among the third and the subsequent N transformation values by a twiddle factor that uses the phase difference calculated by the phase difference calculating unit  74  as a rotation angle, the second transformation value calculating unit  75  calculates, from among the N transformation values, the fourth to N th  transformation values. The specific processes performed by the second transformation value calculating unit  75  are the same as those performed by the second transformation value calculating unit  64  according to the fourth embodiment. 
     The data value transmitting unit  73  maps, onto subcarriers, the transformation value subjected to the cyclic shift by the CS unit  52  and the transformation value calculated by the second transformation value calculating unit  75  and transmits, to the outside, the data value obtained by performing the inverse Fourier transformation process on the mapped transformation value. The data value transmitting unit  73  includes a sub-carrier mapping unit  76 , the IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30 . 
     From among the above units, the IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30  correspond to the IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30  illustrated in  FIG. 6 , respectively. The sub-carrier mapping unit  76  maps, onto subcarriers, the transformation value subjected to the cyclic shift performed by the CS unit  52  and the transformation value calculated by the second transformation value calculating unit  75 . 
     The data value creating unit  71 , the DFT unit  72 , and the data value transmitting unit  73  described above are electronic circuits. The phase difference calculating unit  74  and the second transformation value calculating unit  75  are electronic circuits. The sub-carrier mapping unit  76  is an electronic circuit. Examples of the electronic circuits include an integrated circuit, such as an ASIC or a FPGA, a CPU, and a MPU. 
     In the following, the wireless communication process performed by the wireless communication apparatus  70  according to the fifth embodiment will be described.  FIG. 11  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus  70  according to the fifth embodiment. Because the processes at Steps S 71 , S 75  to S 78 , and S 80  to S 83  correspond to those at Steps S 51 , S 55  to S 58  and S 60  to S 63  in the fourth embodiment, a simplified description thereof will be given. As illustrated in  FIG. 11 , in the wireless communication apparatus  70  according to the fifth embodiment, the ZC sequence creating unit  21  in the data value creating unit  71  creates the Zadoff-Chu sequence that corresponds to the N data values (Step S 71 ). 
     By using a discrete Fourier transform equation that is an equation used to transform N data values that are input from the data value creating unit  71  into the N transformation values, the first transformation value calculating unit  51  in the DFT unit  72  calculates the first to the third transformation values from among the N transformation values (Step S 72 ). The CS unit  52  performs a cyclic shift on the first to the third transformation values calculated by the first transformation value calculating unit  51  (Step S 73 ). 
     On the basis of the real number component and the imaginary number component of the first to the third transformation values subjected to the cyclic shift by the CS unit  52 , the phase difference calculating unit  74  calculates the phases of the first to the third transformation values (Step S 74 ). Then, the phase difference calculating unit  74  calculates the phase difference between the first transformation value and the second transformation value and the phase difference between the second transformation value and the third transformation value (Step S 75 ) and calculates the change in the phase difference (Step S 76 ). Subsequently, the phase difference calculating unit  74  calculates the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and one of the first to the third transformation values (Step S 77 ). 
     Then, by multiplying one of the first to the third transformation values by a twiddle factor that uses the phase difference calculated by the phase difference calculating unit  74  as a rotation angle, the second transformation value calculating unit  75  calculates the fourth to the N th  transformation values from among the N transformation values (Step S 78 ). 
     Subsequently, the sub-carrier mapping unit  76  in the data value transmitting unit  73  maps, onto subcarriers, the first to the third transformation values subjected to the cyclic shift performed by the CS unit  52  and the fourth to the N th  transformation values calculated by the second transformation value calculating unit  75  (Step S 79 ). Then, the IFFT unit  27  transforms the transformation values in the frequency domain into the data values in the time domain by using the inverse Fourier transformation process (Step S 80 ) and the CP inserting unit  28  inserts the CP to the top of the data values (Step S 81 ). Subsequently, the filter processing unit  29  performs the filter process (Step S 82 ), and the wireless processing unit  30  transmits a signal subjected to the wireless process to the outside (Step S 83 ). 
     As described above, the wireless communication apparatus  70  according to the fifth embodiment performs a cyclic shift on the first to the third transformation values in the frequency domain calculated by the discrete Fourier transform equation. Then, the wireless communication apparatus  70  calculates the fourth to the N th  transformation value by obtaining, from the first to the third transformation values subjected to the cyclic shift, a fixed change in the phase difference and by multiplying one of the first to the third transformation values by a twiddle factor obtained from the change in the phase difference. Specifically, in the process of calculating the N transformation values in the frequency domain, the wireless communication apparatus  70  performs a cyclic shift on the first to the third transformation values in the frequency domain. The number of times cyclic shifts are performed at this stage is three. Accordingly, with the wireless communication apparatus  70  according to the third embodiment, the number of times cyclic shifts are performed can be reduced from N to three when compared with the method for calculating, from the N data values subjected to the cyclic shift, the N transformation values in the frequency domain. 
     [f] Sixth Embodiment 
     In the second to the fifth embodiments, examples have been given of a case in which N data values are created and then the first to the third transformation values from among the N transformation values are calculated by using a discrete Fourier transform equation. However, it may also possible to store, in a predetermined storing unit, the first to the third transformation values calculated by using a discrete Fourier transform equation by associating them with an arbitrary sequence number and to read, in accordance with an input sequence number, the transformation value stored in the storing unit. Accordingly, in a sixth embodiment, an example will be given of a case in which the first to the third transformation values to be calculated by using the discrete Fourier transform equation are stored in a predetermined storing unit by associating them with an arbitrary sequence number and are read in accordance with the input sequence number. 
     First, the configuration of the wireless communication apparatus according to the sixth embodiment will be described.  FIG. 12  is a block diagram illustrating the configuration of a wireless communication apparatus  80  according to a sixth embodiment. As illustrated in  FIG. 12 , the wireless communication apparatus  80  according to the sixth embodiment includes a DFT unit  81  and a data value transmitting unit  82 . 
     The DFT unit  81  transforms the N data values in the time domain into the N transformation values in the frequency domain. The DFT unit  81  includes a transformation value storing unit  83 , a transformation value reading unit  84 , a CS unit  85 , a phase difference calculating unit  86 , and a transformation value calculating unit  87 . 
     From among the N transformation values calculated using a discrete Fourier transform equation that is an equation used to transform the N data values in the time domain into the N transformation values, the transformation value storing unit  83  stores the first to the third transformation values by associating them with an arbitrary sequence number. In the following, as an example, a description will be given of a case in which the transformation value storing unit  83  associates the first to the third transformation values with the ZC sequence number, from among the N transformation values calculated from the ZC sequence using the discrete Fourier transform equation, and stores the associated transformation values. 
       FIG. 13  is a schematic diagram illustrating an example of information stored in the transformation value storing unit  83 . As illustrated in  FIG. 13 , from the ZC sequence x u (n) (0≦n&lt;N), the transformation value storing unit  83  associates, from among the N transformation values X′ (k) (0≦k&lt;N) calculated using Equation (12), the first to the third transformation values X′ (k) (0≦k≦2) with the ZC sequence number u. 
     The transformation value reading unit  84  reads, in accordance with the input sequence number, the first to the third transformation values stored in the transformation value storing unit  83 . Specifically, the transformation value reading unit  84  reads, in accordance with the ZC sequence number u that is input from a higher layer, the first to the third transformation values X′ (k) (0≦k≦2) stored in the transformation value storing unit  83 . 
     The CS unit  85  performs the cyclic shift on the first to the third transformation values that are read by the transformation value reading unit  84 . Specifically, if a CS amount is input from a higher layer, the CS unit  85  performs a cyclic shift by shifting the sequence of the first to the third transformation values in accordance with the input CS amount. At this time, the first to the third transformation values X(k) (0≦k≦2) subjected to the cyclic shift by the CS unit  85  are represented by Equation (13) above. 
     By using the first to the third transformation values subjected to the cyclic shift by the CS unit  85 , the phase difference calculating unit  86  calculates the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and a transformation value appearing immediately before the arbitrary transformation value. The specific process performed by the phase difference calculating unit  86  is the same as that performed by the phase difference calculating unit  24  according to the second embodiment. 
     By multiplying the third and the subsequent transformation value by a twiddle factor that uses the phase difference calculated by the phase difference calculating unit  86  as a rotation angle, the transformation value calculating unit  87  calculates the fourth to the N th  transformation values from among the N transformation values. The specific process performed by the transformation value calculating unit  87  is the same as that performed by the second transformation value calculating unit  25  according to the second embodiment. 
     The data value transmitting unit  82  maps, onto subcarrier, the transformation values subjected to the cyclic shift performed by the CS unit  85  and the transformation values calculated by the transformation value calculating unit  87  and transmits, to the outside, the data value obtained by performing the inverse Fourier transformation process on the mapped transformation values. The data value transmitting unit  82  includes a sub-carrier mapping unit  88 , the IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30 . 
     From among the units described above, the IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30  correspond to the IFFT unit  27 , the CP inserting unit  28 , the filter processing unit  29 , and the wireless processing unit  30  illustrated in  FIG. 2 , respectively. The sub-carrier mapping unit  88  maps, onto subcarriers, the transformation values subjected to the cyclic shift performed by the CS unit  85  and the transformation value calculated by the transformation value calculating unit  87 . 
     The DFT unit  81  and the data value transmitting unit  82  described above are electronic circuits. The transformation value reading unit  84 , the CS unit  85 , the phase difference calculating unit  86 , and the transformation value calculating unit  87  are electronic circuits. The sub-carrier mapping unit  88  is an electronic circuit. Examples of the electronic circuit include an integrated circuit, such as an ASIC or a FPGA, a CPU, or a MPU. 
     The transformation value storing unit  83  is a semiconductor memory device, such as a random access memory (RAM), a read only memory (ROM), and a flash memory, or a storage device, such as a hard disk and an optical disk. 
     In the following, the wireless communication process performed by the wireless communication apparatus  80  according to the sixth embodiment will be described.  FIG. 14  is a flowchart illustrating the flow of a wireless communication process performed by the wireless communication apparatus  80  according to the sixth embodiment. As illustrated in  FIG. 14 , in the wireless communication apparatus  80  according to the sixth embodiment, the transformation value reading unit  84  in the DFT unit  81  reads, in accordance with an input sequence number, the first to the third transformation values stored in the transformation value storing unit  83  (Step S 91 ). The CS unit  85  performs a cyclic shift on the first to the third transformation values that are read by the transformation value reading unit  84  (Step S 92 ). 
     On the basis of the real number component and the imaginary number component of the first to the third transformation values subjected to the cyclic shift by the CS unit  85 , the phase difference calculating unit  86  calculates the phases of the first to the third transformation values (Step S 93 ). Then, the phase difference calculating unit  86  calculates the phase difference between the first transformation value and the second transformation value and the phase difference between the second transformation value and the third transformation value (Step S 94 ) and calculates the change in the phase difference (Step S 95 ). Subsequently, the phase difference calculating unit  86  calculates the phase difference between an arbitrary transformation value that appears among the fourth and the subsequent N transformation values and the calculated transformation value appearing immediately before the arbitrary transformation value (Step S 96 ). 
     By multiplying the calculated transformation value by a twiddle factor that uses the phase difference calculated by the phase difference calculating unit  86  as a rotation angle, the transformation value calculating unit  87  sequentially calculates the fourth to the N th  transformation values that have not been calculated from among the N transformation value (Step S 97 ). 
     Then, the sub-carrier mapping unit  88  in the data value transmitting unit  82  maps, onto subcarriers, the first to the third transformation values subjected to the cyclic shift by the CS unit  85  and the fourth to the N th  transformation values calculated by the transformation value calculating unit  87  (Step S 98 ). Subsequently, the IFFT unit  27  transforms the transformation values in the frequency domain into the data values in the time domain using the inverse Fourier transformation process (Step S 99 ). The CP inserting unit  28  inserts the CP into the top of the data values (Step S 100 ). Then, the filter processing unit  29  performs the filter process (Step S 101 ) and the wireless processing unit  30  transmits a signal subjected to the wireless process to the outside (Step S 102 ). 
     As described above, the wireless communication apparatus  80  according to the sixth embodiment stores in advance, in a predetermined storing unit, the first to the third transformation values that are calculated using the discrete Fourier transform equation by associating them with an arbitrary sequence number and reads, in accordance with the input sequence number, the transformation values stored in the storing unit. Accordingly, the wireless communication apparatus  80  according to the sixth embodiment can reduce the processes for calculating the first to the third transformation values from among the N transformation values by using the discrete Fourier transform equation and further reduce the amount of computation needed to calculate discrete Fourier transformation values. 
     [g] Seventh Embodiment 
     In the above explanation, the embodiments of the present invention have been described; however, the present invention can be implemented with various kinds of embodiments other than the embodiments described above. Therefore, in the following, another embodiment included in the present invention will be described. 
     (1) Wireless Access Method 
     In the second to the sixth embodiments, the wireless communication apparatus disclosed in the present invention is used in a wireless communication apparatus that uses an SC-FDMA method that is an uplink wireless access method; however, the present invention is not limited thereto. For example, the present invention can also be used for another wireless access method other than the SC-FDMA method as long as using a wireless access method that performs a calculation process on discrete Fourier transformation values. 
     (2) Program 
     The various processes described in the above embodiments can be implemented by programs prepared in advance and executed by a computer. Accordingly, in the following, a computer that executes a program having the same function performed by the apparatus in the above embodiment will be described with reference to  FIG. 15 .  FIG. 15  is a block diagram illustrating a computer that executes a wireless communication program. 
     As illustrated in  FIG. 15 , a computer  100  functioning as a wireless communication apparatus includes a ROM  110 , a CPU  120 , and a RAM  130 . The ROM  110 , the CPU  120 , and the RAM  130  are connected via a bus  140 . 
     The ROM  110  stores therein, in advance, a wireless communication program having the same function as that in the embodiments, i.e., as illustrated in  FIG. 15 , a first transformation value calculating program  111 , a phase difference calculating program  112 , a second transformation value calculating program  113 , and a transmitting program  114 . The programs  111  to  114  are not always stored in the ROM  110 . 
     The CPU  120  reads the programs  111  to  114  from the ROM  110  and executes them. As illustrated in  FIG. 15 , the programs  111  to  114  function as a first transformation value calculating process  121 , a phase difference calculating process  122 , a second transformation value calculating process  123 , and a transmitting process  124 , respectively. The processes  121  to  124  correspond to the first transformation value calculating unit  2 , the phase difference calculating unit  3 , the second transformation value calculating unit  4 , and the transmitting unit  5  illustrated in  FIG. 1 , respectively. 
     The communication program described in the embodiment can be implemented by a program prepared in advance and executed by a computer, such as a personal computer or a workstation. The program can be distributed via a network, such as the Internet. Furthermore, the program can be stored in a computer-readable recording medium, such as a hard disc drive, a flexible disk (FD), a compact disc read only memory (CD-ROM), a magneto optical disc (MO), and a digital versatile disc (DVD). Furthermore, the program can also be implemented by a computer reading it from the recording medium. 
     All examples and conditional language recited herein are intended for pedagogical purposes to aid the reader in understanding the invention and the concepts contributed by the inventor to furthering the art, and are to be construed as being without limitation to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although the embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.