Abstract:
Provided are a channel estimation method and apparatus in mobile communication system having dispersed pilot. The channel estimation apparatus includes an entire band channel estimation unit and an edge channel estimation unit. The entire band channel estimation unit performs channel estimation on an entire frequency band. The edge channel estimation unit performs channel estimation on an edge region. By separately performing the gating operation of the entire band channel estimation unit and the gating operation of the edge channel estimation unit, a channel frequency response is more accurately calculated even in an edge region.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority under 35 U.S.C. §119 to Korean Patent Application No. 10-2008-0128835, filed on Dec. 17, 2008 and Korean Patent Application No. 10-2009-0082065, filed on Sep. 1, 2009 in the Korean Intellectual Property Office, the disclosures of which are incorporated herein by reference in its entirety. 
     TECHNICAL FIELD 
     The following disclosure relates to a channel estimation apparatus and method in mobile communication system, and in particular, to a channel estimation apparatus and method in mobile communication system, which uses a Single Carrier Frequency Division Multiple Access (SC-FDMA) scheme or an Orthogonal Frequency Division Multiple Access (OFDMA) scheme based on a dispersed pilot. 
     BACKGROUND 
     Many mobile communication technologies are adopting an OFDMA scheme or a SC-FDMA scheme. In IEEE 802.16, 802.20 and Wibro systems that are applied to a portable Internet system, the OFDMA scheme is adopted as the standard. Standardization for a cellular system is made in 3 Generation Partnership Project (3GPP). 3GPP adopted the OFDMA scheme and the SC-FDMA scheme. 
     A communication system using the OFDMA scheme and the SC-FDMA scheme uses a cyclic prefix symbol. At this point, the length of the cyclic prefix symbol is designed longer than that of the impulse response of a channel for overcoming limitations caused by multipath fading. Accordingly, by using a single tap equalizer in a frequency domain, the distortion of an estimated channel is compensated. In this case, the accurate estimation of a channel is required for compensating the distortion of the channel. 
     In a mobile communication system having dispersed pilots, a channel estimation operation is performed using the dispersed pilots, and the channel between a plurality of data sub-carriers is estimated through the channel estimation operation. That is, a Least Square (LS) estimator estimates a channel with a pilot sub-carrier, and channel-estimated values, i.e., channels between the data sub-carriers are estimated in a linear interpolation scheme. In such a method, however, the maximum delay time of a wireless channel is long. In the estimation of a channel having high frequency selectivity, accordingly, channel estimation performance is degraded. For solving this, a channel estimation method in a time domain using a Fast Fourier Transform (FFT) scheme is applied. 
     The channel estimation method in the time domain changes channel-estimated values, in which the LS estimator has estimated channels for a pilot sub-carrier, into a time domain through an Inverse Fast Fourier Transform (IFFT) scheme. Subsequently, an N-point FFT operation is performed through an operation of extracting samples in which the power of a sample in a desired time domain exceeds a specific critical value, i.e., a gating operation. When the N-point FFT operation is completed, channel estimation in a pilot sub-carrier and a channel frequency response in a data sub-carrier position are acquired. 
     In a channel estimation method in a time domain, when the gating operation is completed, performance is improved in portions other than the both end regions (hereinafter referred to as an edge) of an IFFT input, irrespective of a frequency selectivity. However, channel estimation performance is degraded in the edge region of the IFFT input. This provides causes that further deteriorate the channel estimation performance by being added to the Gibbs phenomenon that occurs when a time domain is changed into a frequency domain. 
     SUMMARY 
     In one general aspect, a channel estimation method in a mobile communication system includes: extracting a plurality of samples, in which a power of a sample in a time domain exceeds a first critical value, from a received pilot signal to perform channel estimation of an entire frequency band; extracting a plurality of samples, in which a power of a sample in a time domain exceeds a second critical value, from an edge of an Inverse Fast Fourier Transform (IFFT) input in the received pilot signal to perform channel estimation on the edge of the IFFT input; and estimating a final channel frequency response on the basis of a channel estimation result of the entire frequency band and a channel estimation result for the edge of the IFFT input. 
     In another general aspect, a channel estimation method in a mobile communication system includes: extracting a plurality of samples, in which a power of a sample in a time domain exceeds a first critical value, from a received pilot signal to perform channel estimation of an entire frequency band; setting an edge channel estimation mode; and extracting a plurality of samples, in which a power of a sample in a time domain exceeds a second critical value, from an edge of an Inverse Fast Fourier Transform (IFFT) input in the received pilot signal to perform channel estimation on the edge of the IFFT input, according to the edge channel estimation mode. 
     In another general aspect, a channel estimation apparatus in a mobile communication system includes: an entire band channel estimation unit extracting a plurality of samples, in which a power of a sample in a time domain exceeds a first critical value, from a received pilot signal to perform channel estimation of an entire frequency band; an edge channel estimation unit extracting a plurality of samples, in which a power of a sample in a time domain exceeds a second critical value, from an edge of an Inverse Fast Fourier Transform (IFFT) input in the received pilot signal to perform channel estimation on the edge of the IFFT input; and a channel frequency response output unit estimating a final channel frequency response on the basis of a channel estimation result of the entire frequency band and a channel estimation result for the edge of the IFFT input. 
     Other features and aspects will be apparent from the following detailed description, the drawings, and the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating a channel estimation apparatus according to an exemplary embodiment. 
         FIG. 2  is a block diagram illustrating the configuration of an entire band channel estimation unit in  FIG. 1 , according to an exemplary embodiment. 
         FIG. 3  is a diagram illustrating the channel frequency response of pilot sub-carriers including an edge section in an entire frequency band, according to an exemplary embodiment. 
         FIG. 4  is a block diagram illustrating an entire band channel estimation unit in  FIG. 1 , according to another exemplary embodiment. 
         FIG. 5  is a block diagram illustrating the configuration of an edge channel estimation unit in  FIG. 1 , according to an exemplary embodiment. 
         FIG. 6  is a diagram illustrating an IFFT input corresponding to an edge region that is generated through an IFFT input generator in  FIG. 5 . 
         FIG. 7  is a diagram illustrating the output result of an Ns-point IFFT in  FIG. 5 , the output result of a sample extractor in  FIG. 5  and the output result of a sample extractor in  FIG. 8 . 
         FIG. 8  is a block diagram illustrating an edge channel estimation unit in  FIG. 1 , according to another exemplary embodiment. 
         FIG. 9  is a graph illustrating a block error rate in a case of applying the channel estimation apparatus in  FIG. 1 . 
     
    
    
     DETAILED DESCRIPTION OF EMBODIMENTS 
     Hereinafter, exemplary embodiments will be described in detail with reference to the accompanying drawings. Throughout the drawings and the detailed description, unless otherwise described, the same drawing reference numerals will be understood to refer to the same elements, features, and structures. The relative size and depiction of these elements may be exaggerated for clarity, illustration, and convenience. The following detailed description is provided to assist the reader in gaining a comprehensive understanding of the methods, apparatuses, and/or systems described herein. Accordingly, various changes, modifications, and equivalents of the methods, apparatuses, and/or systems described herein will be suggested to those of ordinary skill in the art. Also, descriptions of well-known functions and constructions may be omitted for increased clarity and conciseness. 
       FIG. 1  is a block diagram illustrating a channel estimation apparatus according to an exemplary embodiment. 
     Referring to  FIG. 1 , a channel estimation apparatus according to an exemplary embodiment includes an LS channel estimation unit  100 , an entire band channel estimation unit  200 , an edge channel estimation unit  300 , an edge channel estimation mode selection unit  400 , and a channel frequency response output unit  500 . Moreover, although not shown, the channel estimation apparatus may further include a plurality of reception antennas. 
     The plurality of reception antennas  1  to Prx output a pilot reception signal {Y k   Prx } k=0   M-1  in response to a pilot transmission signal transmitted from a plurality of transmission antennas  1  to Ptx. Herein, { } k=0   M-1  means a set that is composed of an M number of elements, and Y k   Prx  means a reception signal in a kth pilot sub-carrier that is received through the Prx-th reception antenna. Accordingly, {Y k   Prx } k=0   M-1  means a set of M pilot sub-carriers. 
     The LS channel estimation unit  100  receives the pilot reception signal {Y k   Prx } k=0   M-1  from the reception antennas  1  to Prx to estimate a channel according to an LS technique. That is, the LS channel estimation unit  100  divides the pilot reception signal {Y k   Prx } k=0   M-1  by a reference signal {X k   Ptx } k=0   M-1  corresponding to the kth pilot sub-carrier of the Ptx-th transmission antenna to calculate the channel frequency responses {Ĥ k   (Prx,Ptx) } k=0   M-1  the pilot sub-carriers. 
     The channel frequency responses {Ĥ k   (Prx,Ptx) } k=0   M-1  of the calculated M pilot sub-carriers are provided to the entire band channel estimation unit  200  and the edge channel estimation unit  300 . Herein, {Ĥ k   (Prx,Ptx) } k=0   M-1  means the least square estimation value of a pilot channel frequency response between the Prx-th reception antenna and the Ptx-th transmission antenna in the kth pilot sub-carrier. 
     The entire band channel estimation unit  200  always operates. However, the edge channel estimation unit  300  operates according to the switching operation of the edge channel estimation mode selection unit  400 . 
     In the case of a sub-carrier that is modulated through 64 Quadrature Amplitude Modulation (QAM) and 16 QAM requiring high channel estimation performance due to a high Signal to Noise Ratio (SNR), the edge channel estimation mode selection unit  400  drives the edge channel estimation unit  300 . Moreover, the channel estimation mode selection unit  400  sets parameters necessary for the edge channel estimation unit  300 . 
     Hereinafter, the entire band channel estimation unit  200  will be described in detail. 
       FIG. 2  is a block diagram illustrating the configuration of the entire band channel estimation unit in  FIG. 1 , according to an exemplary embodiment.  FIG. 3  is a diagram illustrating the channel frequency responses of pilot sub-carriers including an edge section in an entire frequency band, according to an exemplary embodiment. Herein, an upper figure in  FIG. 3  illustrates the channel frequency responses of the pilot sub-carriers that are inputted to the entire band channel estimation unit  200  in  FIG. 2 , and a lower figure in  FIG. 3  illustrates the channel frequency responses of the pilot sub-carriers in an entire frequency band that is inputted to the entire band channel estimation unit  200  in  FIG. 2 . 
     Referring to  FIGS. 2 and 3 , an entire band channel estimation unit  210  according to an exemplary embodiment includes an IFFT input generator  211 , an N-point IFFT  212 , a sample extractor  213 , and an N-point FFT  214 . 
     The IFFT input generator  211  sets the exponent size of 2, greater than the number of sub-carriers of an entire frequency band, as an IFFT size ‘N’, and inputs the channel frequency responses of the pilot sub-carriers to a sub-carrier position that is assigned in actual transmission. Subsequently, the IFFT input generator  211  inserts ‘0’ into another sub-carrier position and another guar band. Therefore, an IFFT input for entire band channel estimation is generated. 
     The N-point IFFT  212  performs an IFFT operation on the IFFT input to calculate the time domain response of the pilot signal. The time domain response of the pilot signal is repeated by a pilot sub-carrier interval K in a frequency domain and is thereby emerged. 
     The sample extractor  213  extracts a plurality of samples from a time domain response that is at the first stage in a repeated time domain response, on the basis of multipath delay. At this point, an operation of extracting samples, in which the power of each sample exceeds a predetermined critical value (where α is a real number more than 0), is referred to as a gating operation. ‘0’ is inserted into the positions of other time domain samples that are not extracted by the sample extractor  213 , and the inserted ‘0’ and an output including a plurality of samples are provided to the N-point FFT  214 . 
     The N-point FFT  214  performs an FFT operation on the output of the sample extractor  213  to calculate a channel frequency response {{tilde over (H)} k   (Prx,Ptx) } k=0   M-1  for the pilot sub-carrier and the data sub-carrier. 
       FIG. 4  is a block diagram illustrating the entire band channel estimation unit in  FIG. 1 , according to another exemplary embodiment. 
     Referring to  FIGS. 3 and 4 , an entire band channel estimation unit  220  according to another exemplary embodiment includes an IFFT input generator  221 , an Ms-point IFFT  222 , a sample extractor  223 , an N-point FFT  224 , and a rate converter  225 . 
     The entire band channel estimation unit  220  in  FIG. 3  collects the channel frequency responses of the pilot sub-carriers to perform an IFFT operation on the collected responses. That is, the IFFT input generator  221  sets the exponent size of 2 greater than ‘M’ as an IFFT size ‘Ms’, and inserts two guard bands into the left and right of the channel frequency responses of the pilot sub-carriers to generate an IFFT input. At this point, the size of the guard band is “(Ms−M)/2”. Herein, ‘M’ is the number of pilot sub-carriers, and ‘Ms’ is the size of IFFT for selecting only a pilot sub-carrier to estimate a channel. 
     The Ms-point IFFT  222  performs an IFFT operation on the generated IFFT input to calculate the time domain response of the pilot signal. Only one time domain response is emerged regardless of a pilot sub-carrier interval ‘K’. 
     The sample extractor  223  extracts a plurality of samples from the time domain response on the basis of multipath delay. At this point, the sample extractor  223  extracts only samples in which the power of each sample exceeds a predetermined critical value (where β is a real number more than 0). ‘0’ is inserted into the positions of other time domain samples that are not extracted by the sample extractor  213 . Moreover, because a channel for the sub-carrier of an entire frequency band is required, ‘0’ is additionally inserted into the positions of the other time domain samples for performing an N-point FFT operation. 
     The N-point FFT  224  performs an FFT operation on the output of the sample extractor  223 . 
     When the pilot sub-carrier interval ‘K’ is the exponent of 2, the rate converter  225  is not required. When the pilot sub-carrier interval ‘K’ is not the exponent of 2, because channel estimation between the pilot sub-carriers is performed “N/Ms” times, the rate converter  225  extracts a channel equal to the pilot sub-carrier interval ‘K’ to calculate a channel frequency response {{tilde over (H)} k   (Prx,Ptx) } k=0   KM-1  for an entire band sub-carrier by using an extracted result. 
     Hereinafter, the edge channel estimation unit  300  will be described in detail. 
       FIG. 5  is a block diagram illustrating the configuration of the edge channel estimation unit in  FIG. 1 , according to an exemplary embodiment.  FIG. 6  is a diagram illustrating an IFFT input corresponding to an edge region that is generated through the IFFT input generator in  FIG. 5 .  FIG. 7  is a diagram illustrating the output result of the Ns-point IFFT  312  in  FIG. 5 , the output result of the sample extractor  313  in  FIG. 5  and the output result of the sample extractor  323  in  FIG. 8 . That is, the output result of the Ns-point IFFT  312  is illustrated in the upper portion of  FIG. 5 , the input of a K*Ns-point Discrete Fourier Transform (DFT) is illustrated in the left of the lower portion of  FIG. 5 , and an Nss-point input is illustrated in the right of the lower portion of  FIG. 5 . Moreover, for convenience,  FIG. 6  illustrates only an IFFT input for a left edge region LR that is generated through the IFFT input generator among an edge region including the left edge region LR and a right edge region RR. 
     Referring to  FIGS. 5 and 6 , an edge channel estimation unit  310  according to an exemplary embodiment performs channel estimation of a time domain based on DFT. That is, the edge channel estimation unit  310  performs edge channel estimation on a left edge region LR adjacent to a left guard band, i.e., the channel frequency responses {Ĥ k   (Prx,Ptx) } k=0   M-1  of an M L  number of pilot sub-carriers and a right edge region RR adjacent to a right guard band, i.e., the channel frequency responses {Ĥ k   (Prx,Ptx) } k=0   M     L     −1  of an M U  number of pilot sub-carriers, among the channel frequency responses {Ĥ k   (Prx,Ptx) } k=M−M     U     −1   M-1  of an M number of pilot sub-carriers that are transferred from the LS channel estimation unit  100  (see  FIG. 1 ), respectively. Herein, ‘M L ’ and ‘M U ’ may be variably set according to a system designer. As an example, six and seven pilot sub-carriers may be set, respectively. For example, in the case of an edge region in which a sub-carrier interval is 15 KHz, a pilot sub-carrier interval is ‘6’ and a bandwidth is about 600 KHz, six pilot sub-carriers among an M number of pilot sub-carriers are assigned to a left edge region adjacent to the left guard band, and seven pilot sub-carriers among the M pilot sub-carriers are assigned to a right edge region adjacent to the right guard band. 
     In this embodiment, as illustrated in the upper portion of  FIG. 6 , the following description will be made on the assumption of that four pilot sub-carriers are assigned to a left edge region LR adjacent to a left guard band and a right edge region RR adjacent to a right guard band. 
     Specifically, the edge channel estimation unit  310  includes an IFFT input generator  311 , an Ns-point IFFT  312 , a sample estimator  313 , a (K*Ns)-point DFT  314 , and a guard band remover  315 . 
     The IFFT input generator  311  sets the exponent value of 2 greater than ‘M L ’ and ‘M U ’ as an IFFT size ‘Ns’, and generates an IFFT input {{tilde over (G)} L,k   (Prx,Ptx) } k=0   N     S     −1  for a left edge region LR and an IFFT input {{tilde over (G)} U,k   (Prx,Ptx) } k=0   N     S     −1  for a right edge region RR, as expressed in Equation (1). 
     
       
         
           
             
               
                 
                   
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     Herein, ‘0’ is not inserted into left and right guard bands other than the channel frequency responses of an M L  or M U  number of pilot sub-carriers, and as illustrated in the lower portion of  FIG. 6 , the values V 1  and V 2  of both ends are expanded (i.e., repeated). This is for preventing the frequency response of both ends from reaching ‘0’. 
     The Ns-point IFFT  312  performs an IFFT operation on the IFFT input {{tilde over (G)} L,k   (Prx,Ptx) } k=0   N     S     −1  of a left edge region LR and the IFFT input {{tilde over (G)} U,k   (Prx,Ptx) } k=0   N     S     −1  of a right edge region RR that are generated through the IFFT input generator  311 . Consequently, the time domain response {g L,n   (Prx,Ptx) } n=0   N     S     −1  of a pilot signal for the left edge region LR and the time domain response {g U,k   (Prx,Ptx) } k=0   N     S     −1  of a pilot signal for the right edge region RR are calculated. 
     The sample extractor  313  extracts a plurality of samples on the basis of multipath delay and provides the extracted samples to the (K*Ns)-point DFT  314 . 
     Referring to  FIG. 7 , the sample extractor  313  extracts only samples in which the power of each sample exceeds a predetermined critical value (where E is a real number more than 0), and generates a DFT input as expressed in the following Equation. Herein, the size of DFT  314  is K*Ns. 
                 g   ~       L   ,   n       (     Prx   ,   Ptx     )       =     {                 g     L   ,   n       (     Prx   ,   Ptx     )       ,                    g     L   ,   n       (     Prx   ,   Ptx     )            2     ≥     ɛ   ⁢           ⁢   and   ⁢           ⁢   n     &lt;     W   1                   g     L   ,     n   -     (       K   ·     N   S       -     N   S       )           (     Prx   ,   Ptx     )       ,                          g     L   ,     n   -     (       K   ·     N   S       -     N   S       )           (     Prx   ,   Ptx     )            2     ≥                 ɛ   ⁢           ⁢   and   ⁢           ⁢     (     n   -     K   ·     N   S         )       ≥                 -     W   2       ,     n   =   0     ,   1   ,   …   ⁢           ,       K   ·     N   S       -   1                       0   ,         otherwise         ⁢     
     ⁢       g   ~       U   ,   n       (     Prx   ,   Ptx     )         =     {             g     U   ,   n       (     Prx   ,   Ptx     )       ,                    g     U   ,   n       (     Prx   ,   Ptx     )            2     ≥     ɛ   ⁢           ⁢   and   ⁢           ⁢   n     &lt;     W   1                   g     U   ,     n   -     (       K   ·     N   S       -     N   S       )           (     Prx   ,   Ptx     )       ,                          g     U   ,     n   -     (       K   ·     N   S       -     N   S       )           (     Prx   ,   Ptx     )            2     ≥                 ɛ   ⁢           ⁢   and   ⁢           ⁢     (     n   -     K   ·     N   S         )       ≥                 -     W   2       ,     n   =   0     ,   1   ,   …   ⁢           ,       K   ·     N   S       -   1                       0   ,         otherwise                     
where W1 is a gating parameter in a positive region, W2 is a gating parameter in a negative region. W1 and W2 are determined on the basis of multipath delay. As an example, when ε is ‘0’, all the samples of all time domains are selected, whereupon an interpolation operation is performed through DFT.
 
     The (K*Ns)-point DFT  314  receives a K*Ns size of DFT input signal from the sample extractor  313  and calculates a pilot channel frequency response {{tilde over (G)} L,k   (Prx,Ptx) } k=0   KN     S     −1  corresponding to a left edge region LR and a pilot channel frequency response {{tilde over (G)} U,k   (Prx,Ptx) } k=0   KN     S     −1  corresponding to a right edge region RR. 
     The guard band remover  315 , as expressed in the following Equation, removes most of a guard band that is inserted by the IFFT input generator  311  to output the channel frequency response of an edge portion. 
     
       
         
           
             
               
                 
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               - 
               1 
             
           
         
       
     
       FIG. 8  is a block diagram illustrating the edge channel estimation unit in  FIG. 1 , according to another exemplary embodiment. 
     Referring to  FIGS. 7 and 8 , an edge channel estimation unit  320  according to another exemplary embodiment is configured based on FFT. The edge channel estimation unit  320  includes an IFFT input generator  321 , an Ns-point IFFT  322 , a sample extractor  323 , an Nss-point FFT  324 , a rate converter  325 , and a guard band remover  326 . Herein, since the IFFT input generator  321  has the same configuration and function as those of the IFFT input generator  311  in  FIG. 4  and the Ns-point IFFT  322  has the same configuration and function as those of the Ns-point IFFT  312  in  FIG. 4 , their detailed description will be omitted. 
     For easily implementing the edge channel estimation unit  320  in  FIG. 8 , the Nss-point FFT  324  instead of the (K*Ns)-point DFT  314  in  FIG. 5  is designed. Subsequently, the rate converter  325  calculates the channel frequency response of a desired portion. Herein, the size ‘Nss’ of the Nss-point FFT  324  is selected as the exponent of 2 greater than K*Ns. 
     The sample extractor  323  extracts a plurality of samples on the basis of multipath delay and provides the extracted samples to the Nss-point FFT  324 . At this point, the sample extractor  323  extracts only samples in which the power of each sample exceeds a specific value £, and generates an input as expressed in the following Equation. 
     
       
         
           
             
               
                 g 
                 ~ 
               
               
                 L 
                 , 
                 n 
               
               
                 ( 
                 
                   Prx 
                   , 
                   Ptx 
                 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           
                             g 
                             
                               L 
                               , 
                               n 
                             
                             
                               ( 
                               
                                 Prx 
                                 , 
                                 Ptx 
                               
                               ) 
                             
                           
                           , 
                         
                       
                       
                         
                           
                             
                                
                               
                                 g 
                                 
                                   L 
                                   , 
                                   n 
                                 
                                 
                                   ( 
                                   
                                     Prx 
                                     , 
                                     Ptx 
                                   
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           ≥ 
                           
                             ɛ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             and 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             n 
                           
                           &lt; 
                           
                             W 
                             1 
                           
                         
                       
                     
                     
                       
                         
                           
                             g 
                             
                               L 
                               , 
                               
                                 n 
                                 - 
                                 
                                   ( 
                                   
                                     
                                       K 
                                       · 
                                       
                                         N 
                                         
                                           S 
                                           S 
                                         
                                       
                                     
                                     - 
                                     
                                       N 
                                       S 
                                     
                                   
                                   ) 
                                 
                               
                             
                             
                               ( 
                               
                                 Prx 
                                 , 
                                 Ptx 
                               
                               ) 
                             
                           
                           , 
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                      
                                     
                                       g 
                                       
                                         L 
                                         , 
                                         
                                           n 
                                           - 
                                           
                                             ( 
                                             
                                               
                                                 N 
                                                 
                                                   S 
                                                   S 
                                                 
                                               
                                               - 
                                               
                                                 N 
                                                 S 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         ( 
                                         
                                           Prx 
                                           , 
                                           Ptx 
                                         
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                 ≥ 
                               
                             
                           
                           
                             
                               
                                 
                                   ɛ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   and 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       n 
                                       - 
                                       
                                         N 
                                         
                                           S 
                                           S 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 ≥ 
                               
                             
                           
                           
                             
                               
                                 
                                   - 
                                   
                                     W 
                                     2 
                                   
                                 
                                 , 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 , 
                                 1 
                                 , 
                                 … 
                                 ⁢ 
                                 
                                     
                                 
                                 , 
                                 
                                   
                                     N 
                                     
                                       S 
                                       S 
                                     
                                   
                                   - 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           0 
                           , 
                         
                       
                       
                         otherwise 
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       g 
                       ~ 
                     
                     
                       U 
                       , 
                       n 
                     
                     
                       ( 
                       
                         Prx 
                         , 
                         Ptx 
                       
                       ) 
                     
                   
                 
                 = 
                 
                   { 
                   
                     
                       
                         
                           
                             g 
                             
                               U 
                               , 
                               n 
                             
                             
                               ( 
                               
                                 Prx 
                                 , 
                                 Ptx 
                               
                               ) 
                             
                           
                           , 
                         
                       
                       
                         
                           
                             
                                
                               
                                 g 
                                 
                                   U 
                                   , 
                                   n 
                                 
                                 
                                   ( 
                                   
                                     Prx 
                                     , 
                                     Ptx 
                                   
                                   ) 
                                 
                               
                                
                             
                             2 
                           
                           ≥ 
                           
                             ɛ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             and 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             n 
                           
                           &lt; 
                           
                             W 
                             1 
                           
                         
                       
                     
                     
                       
                         
                           
                             g 
                             
                               U 
                               , 
                               
                                 n 
                                 - 
                                 
                                   ( 
                                   
                                     
                                       N 
                                       
                                         S 
                                         S 
                                       
                                     
                                     - 
                                     
                                       N 
                                       S 
                                     
                                   
                                   ) 
                                 
                               
                             
                             
                               ( 
                               
                                 Prx 
                                 , 
                                 Ptx 
                               
                               ) 
                             
                           
                           , 
                         
                       
                       
                         
                           
                             
                               
                                 
                                   
                                      
                                     
                                       g 
                                       
                                         U 
                                         , 
                                         
                                           n 
                                           - 
                                           
                                             ( 
                                             
                                               
                                                 N 
                                                 
                                                   S 
                                                   S 
                                                 
                                               
                                               - 
                                               
                                                 N 
                                                 S 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       
                                         ( 
                                         
                                           Prx 
                                           , 
                                           Ptx 
                                         
                                         ) 
                                       
                                     
                                      
                                   
                                   2 
                                 
                                 ≥ 
                               
                             
                           
                           
                             
                               
                                 
                                   ɛ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   and 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     ( 
                                     
                                       n 
                                       - 
                                       
                                         N 
                                         
                                           S 
                                           S 
                                         
                                       
                                     
                                     ) 
                                   
                                 
                                 ≥ 
                               
                             
                           
                           
                             
                               
                                 
                                   - 
                                   
                                     W 
                                     2 
                                   
                                 
                                 , 
                                 
                                   n 
                                   = 
                                   0 
                                 
                                 , 
                                 1 
                                 , 
                                 … 
                                 ⁢ 
                                 
                                     
                                 
                                 , 
                                 
                                   
                                     N 
                                     
                                       S 
                                       S 
                                     
                                   
                                   - 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           0 
                           , 
                         
                       
                       
                         otherwise 
                       
                     
                   
                 
               
             
           
         
       
     
     The Nss-point FFT  324  receives an FFT input signal, obtained through the sample extractor  323 , to calculate channel frequency responses {{tilde over (G)} L,k   (Prx,Ptx) } k=0   KN     S     −1  and {{tilde over (G)} U,k   (Prx,Ptx) } k=0   KN     S     −1 . 
     Since channel estimation between the pilot sub-carriers is performed “N/Ms” times, the rate converter  225  extracts a channel equal to a pilot sub-carrier interval and calculates a channel frequency response {{tilde over (H)} k   (Prx,Ptx) } k=0   KM-1  for an entire band sub-carrier on the basis of the extracted channel. 
     The rate converter  325  calculates a K*Ns number of channel frequency responses. As an example, the rate converter  325  may be implemented as a linear converter, or may be implemented with a filter including a plurality of taps. For example, in a case where the rate converter  325  is implemented as the linear converter, a channel frequency response is calculated as expressed in the following Equation, when K*Ns:Nss=μ:v. 
     
       
         
           
             
               δ 
               L 
             
             = 
             
               
                 ( 
                 
                   
                     
                       G 
                       ~ 
                     
                     
                       L 
                       , 
                       
                         
                           v 
                           · 
                           i 
                         
                         + 
                         j 
                         + 
                         1 
                       
                     
                     
                       ( 
                       
                         Prx 
                         , 
                         Ptx 
                       
                       ) 
                     
                   
                   - 
                   
                     
                       G 
                       ~ 
                     
                     
                       L 
                       , 
                       
                         
                           v 
                           · 
                           i 
                         
                         + 
                         j 
                       
                     
                     
                       ( 
                       
                         Prx 
                         , 
                         Ptx 
                       
                       ) 
                     
                   
                 
                 ) 
               
               / 
               μ 
             
           
         
       
       
         
           
             
               
                 
                   G 
                   ~ 
                 
                 
                   L 
                   , 
                   
                     
                       μ 
                       · 
                       i 
                     
                     + 
                     j 
                   
                 
                 
                   ( 
                   
                     Prx 
                     , 
                     Ptx 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     δ 
                     L 
                   
                   · 
                   j 
                 
                 + 
                 
                   ( 
                   
                     
                       
                         G 
                         ~ 
                       
                       
                         L 
                         , 
                         
                           
                             v 
                             · 
                             i 
                           
                           + 
                           j 
                         
                       
                       
                         ( 
                         
                           Prx 
                           , 
                           Ptx 
                         
                         ) 
                       
                     
                     - 
                     
                       j 
                       · 
                       
                         δ 
                         L 
                       
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               i 
               = 
               0 
             
             , 
             1 
             , 
             … 
             ⁢ 
             
                 
             
             , 
             
               
                 
                   
                     N 
                     SS 
                   
                   / 
                   v 
                 
                 - 
                 1 
               
               ; 
               
                 j 
                 = 
                 0 
               
             
             , 
             1 
             , 
             … 
             ⁢ 
             
                 
             
             , 
             
               μ 
               - 
               1 
             
           
         
       
       
         
           
             
               δ 
               U 
             
             = 
             
               
                 ( 
                 
                   
                     
                       G 
                       ~ 
                     
                     
                       U 
                       , 
                       
                         
                           v 
                           ⁢ 
                           
                               
                           
                           · 
                           i 
                         
                         + 
                         j 
                         + 
                         1 
                       
                     
                     
                       ( 
                       
                         Prx 
                         , 
                         Ptx 
                       
                       ) 
                     
                   
                   - 
                   
                     
                       G 
                       ~ 
                     
                     
                       U 
                       , 
                       
                         
                           v 
                           · 
                           i 
                         
                         + 
                         j 
                       
                     
                     
                       ( 
                       
                         Prx 
                         , 
                         Ptx 
                       
                       ) 
                     
                   
                 
                 ) 
               
               / 
               μ 
             
           
         
       
       
         
           
             
               
                 
                   G 
                   ~ 
                 
                 
                   U 
                   , 
                   
                     
                       μ 
                       · 
                       i 
                     
                     + 
                     j 
                   
                 
                 
                   ( 
                   
                     Prx 
                     , 
                     Ptx 
                   
                   ) 
                 
               
               = 
               
                 
                   
                     δ 
                     U 
                   
                   · 
                   j 
                 
                 + 
                 
                   ( 
                   
                     
                       
                         G 
                         ~ 
                       
                       
                         U 
                         , 
                         
                           
                             v 
                             · 
                             i 
                           
                           + 
                           j 
                         
                       
                       
                         ( 
                         
                           Prx 
                           , 
                           Ptx 
                         
                         ) 
                       
                     
                     - 
                     
                       j 
                       · 
                       
                         δ 
                         U 
                       
                     
                   
                   ) 
                 
               
             
             , 
             
               
 
             
             ⁢ 
             
               i 
               = 
               0 
             
             , 
             1 
             , 
             … 
             ⁢ 
             
                 
             
             , 
             
               
                 
                   
                     N 
                     SS 
                   
                   / 
                   v 
                 
                 - 
                 1 
               
               ; 
               
                 j 
                 = 
                 0 
               
             
             , 
             1 
             , 
             … 
             ⁢ 
             
                 
             
             , 
             
               μ 
               - 
               1 
             
           
         
       
     
     The guard band remover  325  removes a guard band portion, inserted by the IFFT input generator  321 , from a K*Ns number of channel frequency responses and calculates a K*M L  number of channel frequency responses and a K*M U  number of channel frequency responses as expressed in the following Equation. 
     
       
         
           
             
               
                 
                   H 
                   ~ 
                 
                 
                   L 
                   , 
                   k 
                 
                 
                   ( 
                   
                     Prx 
                     , 
                     Ptx 
                   
                   ) 
                 
               
               = 
               
                 
                   G 
                   ⋒ 
                 
                 
                   L 
                   , 
                   
                     k 
                     + 
                     
                       
                         K 
                         ⁡ 
                         
                           ( 
                           
                             
                               N 
                               S 
                             
                             - 
                             
                               M 
                               L 
                             
                           
                           ) 
                         
                       
                       2 
                     
                   
                 
                 
                   ( 
                   
                     Prx 
                     , 
                     Ptx 
                   
                   ) 
                 
               
             
             , 
             
               k 
               = 
               0 
             
             , 
             1 
             , 
             … 
             ⁢ 
             
                 
             
             , 
             
               
                 K 
                 · 
                 
                   M 
                   L 
                 
               
               - 
               1 
             
           
         
       
       
         
           
             
               
                 
                   H 
                   ~ 
                 
                 
                   U 
                   , 
                   k 
                 
                 
                   ( 
                   
                     Prx 
                     , 
                     Ptx 
                   
                   ) 
                 
               
               = 
               
                 
                   G 
                   ⋒ 
                 
                 
                   U 
                   , 
                   
                     k 
                     + 
                     
                       
                         K 
                         ⁡ 
                         
                           ( 
                           
                             
                               N 
                               S 
                             
                             - 
                             
                               M 
                               L 
                             
                           
                           ) 
                         
                       
                       2 
                     
                   
                 
                 
                   ( 
                   
                     Prx 
                     , 
                     Ptx 
                   
                   ) 
                 
               
             
             , 
             
               k 
               = 
               0 
             
             , 
             1 
             , 
             … 
             ⁢ 
             
                 
             
             , 
             
               
                 K 
                 · 
                 
                   M 
                   U 
                 
               
               - 
               1 
             
           
         
       
     
     Referring again to  FIG. 1 , when an edge channel estimation mode is selected through the edge channel estimation mode selection unit  400 , the channel frequency response output unit  500  outputs a final channel frequency response result on the basis of the band channel frequency response of an entire band from the entire band channel estimation unit  200  and a channel frequency response result from the edge channel estimation unit  300 . 
     The channel frequency response output unit  500  may receive the channel frequency responses of the left and right edge regions LR and RR, which are outputted from the edge channel estimation unit  300 , to output the final channel frequency response result. 
     In this embodiment, however, the channel frequency response output unit  500  may receive only a portion of the channel frequency responses of the left and right edge regions LR and RR to output the final channel frequency response result, as expressed in the following Equation. 
     
       
         
           
             
               
                 H 
                 _ 
               
               k 
               
                 ( 
                 
                   Prx 
                   , 
                   Ptx 
                 
                 ) 
               
             
             = 
             
               { 
               
                 
                   
                     
                       
                         
                           H 
                           ~ 
                         
                         
                           L 
                           , 
                           k 
                         
                         
                           ( 
                           
                             Prx 
                             , 
                             Ptx 
                           
                           ) 
                         
                       
                       , 
                     
                   
                   
                     
                       0 
                       ≤ 
                       k 
                       &lt; 
                       
                         M 
                         L1 
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           H 
                           ~ 
                         
                         k 
                         
                           ( 
                           
                             Prx 
                             , 
                             Ptx 
                           
                           ) 
                         
                       
                       , 
                     
                   
                   
                     
                       
                         M 
                         L1 
                       
                       ≤ 
                       k 
                       &lt; 
                       
                         
                           K 
                           · 
                           M 
                         
                         - 
                         
                           M 
                           U1 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           H 
                           ~ 
                         
                         
                           U 
                           , 
                           
                             k 
                             - 
                             
                               ( 
                               
                                 
                                   K 
                                   · 
                                   M 
                                 
                                 - 
                                 
                                   M 
                                   U 
                                 
                               
                               ) 
                             
                           
                         
                         
                           ( 
                           
                             Prx 
                             , 
                             Ptx 
                           
                           ) 
                         
                       
                       , 
                     
                   
                   
                     
                       
                         
                           K 
                           · 
                           M 
                         
                         - 
                         
                           M 
                           U1 
                         
                       
                       ≤ 
                       k 
                       &lt; 
                       
                         
                           K 
                           · 
                           M 
                         
                         - 
                         1 
                       
                     
                   
                 
               
             
           
         
       
     
     A channel frequency response calculated by the edge channel estimation unit  300 , moreover, is better in performance than a channel frequency response calculated by the entire band channel estimation unit  200 . However, the Gibbs phenomenon may occur in the both end portions of the left edge region LR of an IFFT input and the both end portions of the right edge region RR of the IFFT input. Accordingly, in a case that receives the channel frequency response of each edge region to configure a channel frequency response result, performance may be degraded. For example, as illustrated in  FIG. 6 , when four pilot sub-carriers are assigned to the left edge region LR of the IFFT input, only channel frequency responses for other two pilot sub-carriers V 3  and V 4  other than the both end portions V 1  and V 2  of the left edge region LR may be calculated. 
     When the edge channel estimation mode is not selected through the edge channel estimation mode selection unit  400 , as expressed in the following Equation, the channel frequency response calculated by the entire band channel estimation unit  200  is obtained as a final channel frequency response as-is.
 
   H     k   (Prx,Ptx)   ={tilde over (H)}   k   (Prx,Ptx)   , k= 0, 1, . . . ,  KM− 1
 
       FIG. 9  is a graph illustrating a block error rate in a case of applying the channel estimation apparatus in  FIG. 1 .  FIG. 9  illustrates a block error rate in a case of applying a typical urban  6  path model, in an OFDMA system using a 2048 size of FFT. In  FIG. 9 , among 2048 sub-carriers in a transmission bandwidth, the number of effective sub-carriers is 1200, and among the effective sub-carriers, the number of pilot sub-carriers is 200. In  FIG. 9 , moreover, 24 sub-carriers are assigned to a left edge, the 64 QAM is applied as a modulation scheme, and a coding rate represents a block error rate in a case where it is set to ⅔. 
       FIG. 9  substantially illustrates four graphs G 1  to G 4 . The graph G 1  is one that illustrates a channel estimation result using only entire band channel estimation. The graph G 2  is one that illustrates the channel estimation result of the edge region of the edge channel estimation unit in  FIG. 5 , and the graph G 3  is one that illustrates the channel estimation result of the edge region of the edge channel estimation unit in  FIG. 8 . The graph G 4  is one that illustrates an ideal channel estimation result. 
     In a case where the edge channel estimation mode is not set and only an entire band channel estimation scheme is applied (i.e., a=0.6), as illustrated in the graph G 1 , an error floor occurs in a block error rate and thus performance is not improved even when an SNR increases. 
     However, in a case where a channel estimation operation is performed using the edge channel estimation scheme, as illustrated in the graphs G 2  and G 3 , it can be seen that a 1.2 dB error with respect to the graph G 4  merely occurs. Accordingly, it can be seen that channel estimation performance is improved through the edge channel estimation scheme. 
     A number of exemplary embodiments have been described above. Nevertheless, it will be understood that various modifications may be made. For example, suitable results may be achieved if the described techniques are performed in a different order and/or if components in a described system, architecture, device, or circuit are combined in a different manner and/or replaced or supplemented by other components or their equivalents. Accordingly, other implementations are within the scope of the following claims.