Abstract:
A receiver of an OFDM signal includes a reception unit to receive an OFDM signal formed by a plurality of OFDM symbols respectively including data subcarriers to which data signals are allocated and pilot subcarriers to which cyclically shifted pilot signals are allocated in frequency domain, an estimator to estimate phase errors of the pilot signals to generate first estimated values related to an offset of the OFDM symbol corresponding to each two or more OFDM symbols in the OFDM signal, a weighting adder to perform weighting additions on the first estimated values to obtain one second estimated value related to the offset, a compensator to compensate the offset by using the second estimated value to obtain a compensated OFDM signal, and a decoder to decode the compensated OFDM signal to reproduce the data signals.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from prior Japanese Patent Application No. 2006-247041, filed Sep. 12, 2006, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a method for receiving an OFDM signal, and a receiver. 
     2. Description of the Related Art 
     A transmitter of a radio communication system using an orthogonal frequency division multiplexing (OFDM) technique (OFDM communication system) allocates modulated symbols obtained by applying an orthogonal modulation to an information signal to be transmitted to each subcarrier. The transmitter generates an OFDM signal by applying inverse fast Fourier transform (IFFT) to each subcarrier with modulated symbols allocated thereto, and radio-packetizes the OFDM signal to transmit it. On the other hand, a receiver of the OFDM communication system receives the transmitted OFDM signal to demodulate it. 
     In the receiver, it is necessary to compensate for the carrier offset and clock offset caused by frequency deviations between a crystal oscillator in the transmitter and that of the receiver. The carrier offset is generated in down converting of a received signal in a baseband signal. The clock offset is generated in analog-digital converting the received signal, and results in occurrence of a conversion error in a digital signal. 
     According to IEEE 802.11a, which is one of the conventional wireless LAN standards, a known signal is inserted in a preamble of the head of a wireless packet. A receiver uses the known signal in a received signal to estimate carrier offset and clock offset to compensate the carrier offset and the clock offset in accordance with the obtained estimated value. However, since the known signal is lost due to noise, estimating and compensating the carrier offset and the clock offset in use of the known signal also poses the problem of a residual offset behind the preamble. To solve such a problem, IEEE 802.11a uses a subcarrier (referred to as pilot subcarrier) of a part of data to transmit a pilot signal, and the receiver uses the received pilot signal to estimate and compensate for the residual offset. 
     One example of a method for compensating for clock offset by using the pilot signal is disclosed in JP-A 2004-312372 (KOKAI). Angles of phase rotations caused by the clock offset become smaller the closer the subcarriers are to a center frequency, and larger if the subcarriers are more distant from the center frequency. According to  FIGS. 15  (A) and (B) in JP-A 2004-312372 (KOKAI), white points represent signal reception points when no clock offset is present, and black points represent phase rotations caused by the clock offset. In contrast, the angles of phase rotations caused by the carrier offset are identical in all pilot subcarriers. 
     Since the carrier offset and the clock offset occur simultaneously, phase rotations in which influences from the carrier offset and influence from the clock offset are combined occur. Using this occurrence of the phase rotations achieves estimation and compensation of the clock offset by using the received pilot signals in JP-A 2004-312372 (KOKAI). 
     Meanwhile, a multi input multi output (MIMO) system, using each of a plurality of antennas for a transmitter and a receiver, has received attention in view of its high throughput. Further, a MIMO-OFDM system using both the MIMO and OFDM has been regarded as the most likely next-generation radio communication system. However, transmitting identical pilot signals from a plurality of antennas poses the problem of mutual interference. This interference results in a phenomenon, for instance, in which a strong pilot signal is transmitted in a certain direction, but not in another direction. This phenomenon is called a beam forming influence. 
     In a draft “Joint Proposal: High throughput extension to the 802.11 Standard: PHY” (Document 1) of IEEE 802.11n, which is a next-generation wireless LAN system in which the MIMO-OFDM system is regarded to be adopted as a standard, devising an idea for transmission patterns of the pilot subcarrier transmitted from a plurality of antennas prevents the influence of beam forming. In pilot subcarrier patterns depicted in Table 17-Pilot values for 40 MHz transmission in Document 1, N sts  is the number of all streams transmitted simultaneously (here, read as the number of all transmission antennas), and i sts  following the N sts  is the number of streams to be actually transmitted (here, read as the number of transmission antennas). Next to the i sts , a −21st, a −7th, a +7th, and a +21st pilot subcarriers of transmit signals are transmitted. For instance, if the number of transmission antennas is four, in a 0th OFDN symbol, a 0th transmission antenna transmits a signal with a pattern of (1, 1, 1, −1), a 1st transmission antenna transmits a signal with a pattern of (1, 1, −1, 1), a 2nd transmission antenna transmits a signal with a pattern of (1, −1, 1, 1), and a 3rd transmission antenna transmits a signal of a pattern (−1, 1, 1, 1). 
     Here, a pilot subcarrier, for example, a −21st subcarrier is considered. The −21st pilot subcarrier simultaneously transmits signals with patterns of (1, 1, 1, −1) from four transmission antennas. This pattern differs from that of a signal transmitted through another pilot subcarrier. Especially, when the number of transmission antennas is four, a pattern of a signal transmitted from a certain pilot subcarrier is orthogonal to a pattern of a signal transmitted from another pilot subcarrier. Therefore, even if the receiver is present in a null direction of a transmission beam formed of a −7th, a +7th and a +21st pilot subcarrier, a possibility that a transmission beam formed of a −21st pilot subcarrier reaches the receiver becomes high. 
     In general, a signal transmitted from a transmitter generates reflection diffraction by a feature. If reflection diffraction is generated, the receiver receives the signal transmitted from one transmitter as a plurality of signals via a plurality of paths, so that the envelope of the received signal varies depending on the place and time (referred to as fading). If fading has occurred, even if the transmission beam formed of a pilot subcarrier (in an example given above, −21st pilot subcarrier) is directed in the direction of the receiver, the influence of fading lowers the received power of the −21st, −7th, +7th and +21st pilot subcarriers sometimes. As a result, in the forgoing situation in which the receiver is located in the null direction of the transmission beam formed of the −7th, +7th and +21st pilot subcarriers, there is a possibility that the electric power of the +21st pilot subcarrier received will be lowered. Thereby, the receiving performance of the receiver greatly drops. 
     As explained above, the combination between the offset compensation technique disclosed in JP-A 2004-312372 (KOKAI) and the pilot subcarrier pattern described in Document 1 cannot receive the pilot signals to compensate for the offset, and deteriorates the reception performance sometimes. 
     BRIEF SUMMARY OF THE INVENTION 
     An object of the present invention is to enable estimation and compensating an offset of the OFDM symbol which is hardly influenced by fading in receiving an OFDM signal. 
     One aspect of the present invention provides a receiver of an OFDM signal comprising: a reception unit to receive an OFDM signal formed by a plurality of OFDM symbols respectively including data subcarriers to which data signals are allocated and pilot subcarriers to which cyclically shifted pilot signals are allocated in frequency domain; an estimator to estimate phase errors of the pilot signals to generate first estimated values related to an offset of an OFDM symbol corresponding to each two or more OFDM symbols in the OFDM signal; a weighting adder to perform weighting additions on the first estimated values to obtain one second estimated value related to the offset; a compensator to compensate the offset by using the second estimated value to obtain a compensated OFDM signal; and a decoder to decode the compensated OFDM signal to reproduce the data signals. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
         FIG. 1  is an exemplary block diagram depicting a radio communication system according to an embodiment; 
         FIG. 2  is an exemplary view depicting examples of wireless packets transmitted from reception antennas in  FIG. 1 ; 
         FIG. 3  is an exemplary block diagram depicting a main part of a receiver in  FIG. 1 ; 
         FIG. 4  is an exemplary view depicting pilot signals transmitted at each time from transmission antennas in  FIG. 1 ; 
         FIG. 5  is an exemplary view for explaining operations of a residual offset estimator in  FIG. 3 ; 
         FIG. 6  is an exemplary block diagram depicting an example of the residual offset estimator; and 
         FIG. 7  is an exemplary block diagram depicting another example of the residual offset estimator. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring now to  FIG. 1 , in a MIMO-OFDM communication system presumed in one embodiment of the present invention, a transmitter  100  having two transmission antennas  101   a  and  101   b  makes transmissions toward a receiver  200  having two reception antennas  201   a  and  202   b . Haa represents a channel response from the transmission antenna  101   a  to the reception antenna  201   a , Hab represents a channel response from the transmission antenna  101   a  to the reception antenna  202   b , Hba represents a channel response from the transmission antenna  101   b  to the reception antenna  201   a , and Hbb represents a channel response from the transmission antenna  101   b  to the reception antenna  202   b , respectively. 
     In general, in a multipath channel (multipath propagation path), values in channel responses differ from one another for each subcarrier of an OFDM signal. Here, for purpose of simplification, it is presumed that the channel responses have identical values for each subcarrier. 
     As illustrated in  FIG. 2 , the configuration of wireless packets transmitted from the transmission antennas  101   a  and  101   b  in  FIG. 1  is the same as that proposed in IEEE 802.11n, described in Document 1. In  FIG. 2 , an STF represents a short training field, an LTF represents a long training field, and an SIG represents a signal field. “L-” means legacy, and fields with “L-” represent ones compliant to the wireless LAN standard (IEEE 802.11a or IEEE 802.11g). “HT-” is a short for high throughput, and the fields with the “HT-” represent ones peculiar to the next-generation wireless LAN standard. 
     After receiving L-STFs to detect wireless packets, the receiver applies automatic gain control (AGC) by using a variable gain amplifier (VGA) to the received signal then performs gain control so that the amplitude of the received signal is within an input dynamic range of an analog to digital converter (ADC) in the next stage of the VGA. Since packet detection and the AGC function are well-known techniques, their detailed descriptions will be skipped. 
     Next, the receiver  200  estimates frequency offset to perform compensation (coarse adjustment) of the frequency offset on the basis of the estimation, and further, detects the boundary between the L-STF and L-LTF in the use of a timing synchronizing function. Subsequently, the receiver  200  performs channel estimation and fine adjustment of the frequency offset by using the L-LTF. The coarse adjustment and the fine adjustment for the frequency offset are well-known techniques, thus explanations about such will be omitted. 
     If the offset estimation is performed in a state that it is buried in noise, even after compensating the L-STF and the L-LTF, the estimation results in generation of a residual offset. In the case of temporal variations of an offset value, it is impossible for the L-STF and the L-LTF to compensate for the variations. 
       FIG. 3  illustrates the configuration following the synchronous processing unit of the receiver  200 . The L-SIG and the HT-SIG in  FIG. 2  are output from both the reception antennas  201   a  and  201   b . The signals output from the reception antennas  201   a  and  201   b  are transmitted to fast Fourier transform (FFT) units  202   a  and  202   b  to be applied with FFT. The signals after being applied with FFT are input to an interference removing unit  203 . 
     Here, the signals in the sections from the L-STF to the HT-SIG in  FIG. 2  (namely, sections from L-STF, L-LTF, L-SIG, and HT-SIG) are the same in the wireless packets respectively transmitted from the two antennas  101   a  and  101   b , and the signals are transmitted in the cyclic shift system. In this system, the other antenna transmits the signal that is the signal which has been transmitted from one antenna and has been temporally and cyclically shifted. In other words, in the section between the L-STF to the HT-SIG, the two transmission antennas  101  and  101   b  transmit a common signal, but the transmission timings differ from each other due to the cyclic shift. If the number of the kinds of the transmission signals at this moment is defined as “stream number”, the number of the signal streams from the L-STF to the HT-SIG is one. After the HT-STF and the HT-STF, two transmission antennas  201  and  21   b  respectively transmit independent signals, therefore the number of streams become two. 
     Like this, in the section from the L-STF to the HT-SIG, the transmitting signals from the transmission antenna  101   a  being cyclically shifted and being transmitted from another transmission antenna  101   b , the transmitting signals from the transmission antenna  101   a  and that from the transmission antenna  101   b  are the signals of basically single streams. Therefore, the interference removing unit  203  operates as a maximum ratio combining unit in the section from the L-STF to the HT-SIG, and the interference removing unit  203  combines the signals received by the reception antennas  201   a  and the  201   b  to form a single output signal. 
     After phase-compensating by either a phase compensator  205   a  or a phase compensator  205   b , the output signal from the interference removing unit  203  is input to a decoder  207  through a parallel-serial (P-S) converter  206  to a decoder  207 . At this moment, the signal input to the phase compensator  205   a  or  205   b  is of the single stream, and phase compensation can be achieved by a well-known technique, such as that described in JP-A 2004-312372 (KOKAI), thus no explanation will be given of this here. 
     The L-SIG and the HT-SIG describe additional information on modulation systems of data sections (MIMO DATA), on data lengths, on the number of the transmission antennas, etc., and the receiver  200  decodes the L-SIG and the HT-SIG to enable the additional information to be understood. 
     Subsequently, in the HT-STF section, AGC to receive the HT-LTF and the MIMO DATA is implemented. After this, in the HT-LTF section, the receiver  200  estimates channel responses (channel estimation) from the transmission antennas  101   a  and  101   b  to the reception antennas  201   a  and  201   b . Well known techniques can be used for AGC and the channel estimation, thus their descriptions will be omitted. 
     Using the values of the channel responses estimated in the manner given above may express a received signal RXa output from the reception antenna  202  and a received signal RXb output from the reception antenna  202   b  during the reception of the MIMO DTA in the following equation. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       RXa 
                       RXb 
                     
                     ] 
                   
                   = 
                   
                     
                       [ 
                       
                         
                           
                             Haa 
                           
                           
                             Hba 
                           
                         
                         
                           
                             Hab 
                           
                           
                             Hbb 
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         TXa 
                         TXb 
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Wherein, TXa and TXb represent transmitting signals from the transmission antennas  101   a  and  101   b , respectively. 
     The interference removing unit  203  multiplies an inverse matrix of a matrix formed of transfer functions Haa, Hab, Hba, and Hbb of the received signals Rxa and Rxb to demodulate the transmitting signals TXa and TXb. The demodulated signals are expressed by TXa′ and TXb′. 
     In the data section (MIMO DATA), as indicated at the position of n=0 in  FIG. 2 , the pilot subcarriers, indicated by thick arrows, are multiplexed. In a 20 MHz mode of IEEE 802.11n, for example, the −21st, −7th, +7th, and +21st subcarriers are used as the pilot subcarriers. The receiver  200  uses the signals of the pilot subcarriers in the received signals to compensate for the carrier offset and the clock offset of an offset of the OFDM symbol. 
     The demodulated signals TXa′ and TXb′ output from the interference removing unit  203  are input to the residual offset estimator  204 , and the phase compensators  205   a  and  205   b . The signals of the pilot subcarriers in the demodulated signals TXa′ and TXb′ are input to the residual offset estimator  204  then the residual offset components, i.e., the phase below-mentioned phase errors of the received pilot signals are estimated. After removing the interference, the signals of the data subcarriers in the demodulated signals TXa′ and TXb′ are input to the phase compensators  205   a  and  205   b  to be compensated for the carrier offset and clock offset, and decoded through the decoder  207 . In  FIG. 3 , the phase compensators  205   a  and  205   b  are arranged behind the interference removing unit  203 , though a single phase compensator may be arranged in front of the interference removing unit  203 . 
     In IEEE 802.11n described in Document 1, the pilot signals are cyclically transmitted.  FIG. 4  schematically illustrates the pilot signals in the case that the transmitter  100  has two transmission antennas. In the MIMO DATA, as shown in  FIG. 4 , at the time of n=0, the transmission antenna  101   a  transmits a pilot signal (1, 1, −1, −1) though the pilot subcarriers (−21st, −7th, +7th, and +21st subcarriers), and the transmission antenna  101   b  transmits the pilot signal (1, −1, −1, 1) through the same pilot subcarriers. 
     Here, if it is presumed that “m” is the number of two pilot subcarriers, “M” is the total number of pilot subcarriers (in this example, M=4), “k” and “1” refer to the number of space streams, and P k,m  and P l,m  are a certain two pilot signals, the pilot signals in  FIG. 4  are expressed by the following equation. 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         m 
                         = 
                         1 
                       
                       M 
                     
                     ⁢ 
                     
                       
                         p 
                         
                           k 
                           , 
                           m 
                         
                       
                       ⁢ 
                       
                         p 
                         
                           1 
                           , 
                           m 
                         
                       
                     
                   
                   = 
                   
                     αδ 
                     
                       k 
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     Here, δ is a delta function, and only 50 represents “1”, and represents “0” except in the case given above. For example, if “k”=“0 (zero)” and “l”=“1 (one)”, the equation (2) is expressed by the following equation. 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       
                         m 
                         = 
                         1 
                       
                       M 
                     
                     ⁢ 
                     
                       
                         p 
                         
                           0 
                           , 
                           m 
                         
                       
                       ⁢ 
                       
                         p 
                         
                           1 
                           , 
                           m 
                         
                       
                     
                   
                   = 
                   
                     
                       αδ 
                       
                         - 
                         1 
                       
                     
                     = 
                     0 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     The equation (3) represents the inner product of the pilot signal (1, 1, −1, −1) transmitted from the transmission antenna  101   a  and the pilot signal (1, −1, −1, 1) transmitted from the transmission antenna  101   b , so that it clearly becomes equal to “0”. That is, the equation (2) expresses that the pilot signals respectively transmitted through the two streams from the transmission antennas  101   a  and  102   b  at the time t=0 cross at a right angle to each other on the frequency axis. 
     On the other hand, an the time n=1, the pilot signals are transmitted through the pilot subcarriers of which the frequencies are shifted to the right sides in  FIG. 4  in comparison to the case of the time n=0. More specifically, the pilot signal which has been transmitted by the −21st subcarrier at the time n=0 is transmitted by the −7th pilot subcarrier at time n=1. In a similar way, the pilot signal which has been transmitted by the −7th pilot subcarrier at time n=0 is transmitted by the +7th pilot subcarrier at time n=1. 
     Here, the pilot signals P k,m (n) to be transmitted through the m-th pilot subcarrier of the k-th space stream of the n-th OFDM symbol are expressed by the following equation by using P k,m  (or P l,m ) 
     
       
         
           
               
             
               
                 
                   
                     
                       
                         
                           
                             
                               P 
                               
                                 k 
                                 , 
                                 m 
                               
                             
                             ⁡ 
                             
                               ( 
                               n 
                               ) 
                             
                           
                           = 
                           
                             p 
                             
                               k 
                               , 
                               
                                 
                                   ( 
                                   
                                     n 
                                     + 
                                     m 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   mod 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 N 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             p 
                             
                               k 
                               , 
                               
                                 
                                   ( 
                                   
                                     n 
                                     + 
                                     m 
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   mod 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 4 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     4 
                     ) 
                   
                 
               
             
           
         
       
     
     wherein, (n+m) mod N represents the residue when (n+m) is divided by N (in this example, N=4), i.e., mod is a modulo operator. For instance, in the equation (4), in the case of n=0 and N=4, (n+m) mod N become “m” and the right side of the equation (4) becomes P k,m . If n=1, the right side becomes P k,m+1 , and the pilot signal P k,m  results in a cyclic shift by one cycle toward the right. 
     Next, the operations of the residual offset estimator  204  will be described by referring to  FIG. 5 . White circles in  FIG. 5  indicate each input signal to the residual offset estimator  204  corresponding to a certain pilot subcarrier. Arrows are vectors indicating the channel estimated values of Haa and Hba. 
     At the time n=0, after the −21st subcarriers have transmitted “1” from both the transmission antennas  101   a  and  101   b , the reception antenna  201   a  receives the pilot signal r( 0 )=(Haa+Hba)exp(2πjθ). The exp(2πjθ) expresses a phase rotation due to residual carrier offset and clock offset. For the purpose of simplification, noise components are not depicted. 
     On the other hand, at the HT-LTF just before the MIMO DATA, the channel estimated value corresponding to the pilot subcarrier is known, and the pilot signal pattern shown in  FIG. 4  is also known. Therefore, a replica pilot signal r′( 0 )=Haa+Hba of the pilot signal with no offset may be generated. 
     Next, the residual offset estimator  204  estimates the phase difference between the actually received pilot signal r( 0 ) and the replica r′( 0 ) generated from the channel estimated value as the residual offset (phase error of pilot signal). The estimator  204  performs this estimation by performing, for instance, division between the pilot signals r( 0 ) and r′( 0 ), or complex multiplication between the pilot signals r( 0 ) and r′( 0 ). It is supposed that the estimated value of the phase difference is θ′( 0 ). In the case of complex multiplication, the estimated value θ′( 0 ) is expressed by the following equation. 
     
       
         
           
               
             
               
                 
                   
                     
                       
                         
                           
                             
                               θ 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               0 
                               ) 
                             
                           
                           = 
                           
                             
                               arg 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   r 
                                   ⁡ 
                                   
                                     ( 
                                     0 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     r 
                                     * 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     0 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           θ 
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
           
         
       
     
     As mentioned above, the transmission beams generated by the −21st, −7th, +7th, and 21st pilot subcarriers are headed to various directions. Therefore, even if there is a pilot subcarrier headed in the direction of the receiver  200 , the reception level may be deeply dropped due to the influence of the fading caused by the reflectors or scatterings near the receiver  200 , the received power may be small, as in the case of the time n=0 in  FIG. 4 , and there is the possibility that the reception signal has been buried in noise at the point close to the origin. In such a case, the receiver  200  cannot receive any of the +21st, −7th, +7th, and +21st pilot subcarriers, which results in a deterioration of reception performance of the receiver  200 . 
     In contrast, at the time n=1, the transmission antenna  101   a  is transmitting “−1” and the transmission antenna  101   b  is transmitting “1”, and the reception antenna  201   a  receives a pilot signal r( 1 )=(−Haa+Hba)*exp(2πj2θ) As is clear from  FIG. 5 , the electric power of the received signal varies in comparison to that of the pilot signal r( 0 ). In this case, the received power of the pilot signal r( 1 ) increases in comparison to the pilot signal r( 0 ). In an actual communication environment, of signals transmitted from a plurality of antennas, final propagation path of the signals transmitted from plurality of antennas are frequently modeled by the product of the influence on a transmission path on a transmission side and the influence on a transmission path on a reception side. Therefore, even in an environment in which the transmitted beam received signal strongly achieves due to the influence of the transmission path on the transmission side, the signal level is reduced due to the influence from the transmission path on the reception side. However, this modeling is complicated, so the radio communication system in this embodiment uses a equation simulating only the influence from the transmission path on the transmission side. 
     Next, an estimated value θ′( 1 ) of the phase difference between the pilot signals r( 1 ) and r′( 1 ) is calculated. Using complex multiplication, the estimated value θ′( 1 ) of the phase difference is expressed by the following equation. 
     
       
         
           
               
             
               
                 
                   
                     
                       
                         
                           
                             
                               θ 
                               ′ 
                             
                             ⁡ 
                             
                               ( 
                               1 
                               ) 
                             
                           
                           = 
                           
                             
                               arg 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   r 
                                   ⁡ 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                                 ⁢ 
                                 
                                   
                                     r 
                                     * 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     1 
                                     ) 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             2 
                             ⁢ 
                             θ 
                           
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     6 
                     ) 
                   
                 
               
             
           
         
       
     
     In this case, due to being deviated twice as compared with the estimate time at n=0, there is a relation of θ′( 1 )=2θ′( 0 ) if the influence of noise is disregarded. 
     It is possible to estimate and correct the carrier offset and clock offset as disclosed in US 2005-0281240 A1 by using either of the estimated value θ′( 0 ) of the phase difference at the time n=0, or the estimated value θ′( 1 ) of the phase difference at the time n=1. However, in the embodiment, the characteristics of the communication system are improved by estimating and correcting the carrier offset and clock offset in use of the estimated values θ′( 0 ) and θ′( 1 ) which can be obtained at both time n=0 and n=1. 
     The signals respectively transmitted from the transmission antennas  101   a  and  101   b  through the −21st pilot subcarriers have the same amplitude and also same phase at the time n=0, but they have an inverse phase at the time n=1. Therefore, the transmitting beam formed by the pilot subcarrier at the time n=0, and the transmitting beam formed by the pilot subcarrier at the time n=1 differ from each other. Accordingly, using the estimated values θ′ ( 0 ) and θ′ ( 1 ) obtained at both the times n=0 and n=1 enables obtaining diversity effect because there is a possibility for the one of the estimated values θ′( 0 ) and θ′( 1 ) to increase in received power even when other is buried in noise. 
     To combine the estimated values θ′( 0 ) and θ′( 1 ) of the phase difference obtained at both the times n=0 and n=1, the receiver  200  may apply weighting addition in accordance with, for instance, the following equation.
 
θ′= arg ( r (0) r *(0)+ r (1) r *(1))/3  (7)
 
     If the level of the received signal is high, the pilot signals r( 0 )r*( 0 ) and r( 1 )r*( 1 ) being also large, by applying maximum ratio combining to the estimated value θ′( 1 ) obtained at the time n=0 and to the estimated value θ′( 1 ) obtained at the time n=1 in the equation (7), the final estimated value θ′ is defined. Maximum ratio combining is, as known well, a method for applying weighting addition to a plurality of signals by using weighting functions in response to the level of each signal. It is acceptable to define the final estimated value by use of weighting addition other than that using maximum ratio combining. It is also possible to select the estimated value at the time point when the reception level is high in the estimated values θ′( 0 ) and θ′( 1 ) without applying such maximum ratio combining. 
     Hereinafter, the residual offset estimator  204  will be described in detail with reference to  FIG. 6 . According to an example of the residual offset estimator shown in  FIG. 6 , estimated value calculators  301   a  to  301   d  calculate according to the formula (6). Here, four subcarriers of the −21st, −7th, +7th, and +21st being used as the pilot subcarriers, the estimated value calculators  301   a  to  301   d  are disposed in response to each pilot subcarrier, but one estimator may be used in a time division manner for the calculators  301   a  to  301   d.    
     The estimated values respectively obtained by the calculators  301   a  to  301   d  are applied weighting addition corresponding to N OFDM symbols through adders  302   a  to  302   d . Here, two estimated values obtained at the times n=0 and n=1 are added after multiplied weights (N=2). To further enhance estimate precision, four estimated values obtained from the adders  302   a  to  302   d  are added, to produce final estimated values. It is also acceptable not to apply weighting addition to all estimated values in this manner, but to select only values of which the reception level has been high among the four estimated values through selector switches  305   a  to  305   d  controlled by a controller  304  to obtain the final estimated values. 
     In finally estimating and compensating by using both estimated values at the times n=0, and n=1, processing for estimation and compensation delays by one OFDM symbol. However, regarding the offset in the data section (MIMO DATA), which is the residual part that was not removed in the preamble, the processing delay to an extent of one OFDM symbol does not pose a practical problem. 
     On the other hand, it is possible to use the method of using the estimated values from the time n=0 to n=3 to do the pilot pattern may come back by four OFDM symbols as shown in  FIG. 4 . However, if all the patterns at the time n=2 are reversed, the patterns becomes as those at the time n=0, and if the patterns at the time n=4 are reversed, the patterns becomes the same as those at the time n=1, so that weighting addition by at least two OFDM symbols is enough. 
     In contrast, as shown in table 17 in Document 1, if the total number of transmission antennas is three or four, it is preferable to estimate the residual offset by using the estimated values by four OFDM symbols, because the cycle rounds by 4OFDM symbol. 
     According to an example of the residual offset estimator  204  depicted in  FIG. 7 , the estimated value calculators  401   a  to  401   d  calculate, for example, the equations (5) and (6) in response to the four OFDM symbols of an i-th, (i+1)-th, (i+2)-th, and (i+3)-th. Here, since the estimated value calculators  401   a  to  401   d  are disposed in response to the i-th, (i+1)-th, (i+2)-th, and (i+3)-th of four OFDM symbols, it is acceptable to use one estimator in a time division manner for the estimated value calculators  401   a  to  401   d.    
     The estimated values respectively obtained by the estimated value calculators  401   a  to  401   d  are applied with weighting addition processing by M OFDM symbols by means of the adders  402   a  to  402   d . Here, after multiplying the weight for each of the estimated value θ′( 0 ) and the estimated value θ′( 0 ) obtained at the times n=0 and n=1, respectively, they are added to each other (M=2). To enhance the estimate precision, the adder  403  adds the four estimated values obtained from the adders  402   a  to  402   d , and produces the final estimated values. It is also preferable not to apply weighting addition to all estimated values in the manner given above, but to select only the values of which the reception levels are high among four estimated values by means of the switches  405   a  to  405   d  controlled by the controller  404 , to obtain the final estimated values. 
     A method for estimating the carrier offset and clock offset in the use of the phase differences obtained by a plurality of pilot subcarriers will be set forth below. It is presumed that the estimated values of the phase differences to be obtained by the −21st, −7th, +7th, and +21st pilot subcarriers are defined θ −21 , θ −7 , θ +7 , and θ +21 , respectively. Each estimated value θ −21 , θ −7 , θ +7 , and θ +21  is calculated in a manner described above. Here, as mentioned above, the carrier offset does not vary due to the subcarriers, and the clock offset has a different value depending on the subcarriers, so that the next equations are established.
 
θ −12 =−21α+β
 
θ −7 =7α+β
 
θ +7 =+7α+β
 
θ +21 =+21α+β  (8)
 
where, α is a value of clock offset, and β is the value of the carrier offset.
 
     It is possible to estimate α and β in the use of these four equations. Calculating α and β may be performed by using a least-squares error criterion. However, they can be more simply obtained by the following equations: 
     
       
         
           
               
             
               
                 
                   
                     
                       β 
                       = 
                       
                         
                           θ 
                           
                             - 
                             21 
                           
                         
                         + 
                         
                           θ 
                           
                             - 
                             7 
                           
                         
                         + 
                         
                           θ 
                           
                             + 
                             7 
                           
                         
                         + 
                         
                           θ 
                           
                             + 
                             21 
                           
                         
                       
                     
                     ⁢ 
                     
                       
 
                     
                     ⁢ 
                     
                       α 
                       = 
                       
                         
                           β 
                           - 
                           
                             θ 
                             
                               - 
                               7 
                             
                           
                         
                         7 
                       
                     
                   
                 
                 
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
     In the foregoing description, α and β are calculated by calculating the phases from r( 0 )r*( 0 ), but it is also possible to calculate them by using the value of r( 0 )r*( 0 ) itself. This method is described in, for instance, “Maximum likelihood tracking algorithms for MIMO-OFDM,” in Proc. Intern. Conf. Commun., vol. 4, (Paris, France), pp. 2468-2472, June 2004, by C. Oberli, et al., (Document 2), and “Joint weighted least-squares estimation of carrier-frequency offset and timing offset for OFDM systems over multipath fading channels,” IEEE Trans. Vehic. Technol., vol. 54, pp. 211-223, January 2005, by P.-Y. Tsai, et al. (Document 3). The methods in Documents 2 and 3 calculate α and β with use of “phase differences obtained for a plurality of pilot subcarriers”. According to the embodiment, by expanding the calculations performed in Documents 2 and 3 so as to estimate by use of the “phase differences obtained for a plurality of pilot subcarriers at a plurality of time points” method, the methods disclosed in the forgoing Documents 2 and 3 become applicable. 
     Thus, after estimating α and β, next, the method calculates the estimated values θ −21 , θ −7 , θ +7 , and θ +21  (phase differences at each subcarrier) by substituting the α, and β into the equation (9). The phase compensators  205   a  and  205   b  multiply the outputs from each subcarrier by the inverse characteristics of each θ −21 , θ −7 , θ +7 , and θ +21  then compensate the phases. Specifically, the compensators  205   a  and  205   b  compensate the phases so that the points indicated by the black circles come to the points indicated by the white circles in  FIG. 5 . Here, there is also no need to use the estimated values at all of the pilot subcarriers, and it is also possible to select only the estimated values at the time points at which the received electrical power is large to estimate the final α and β. 
     As disclosed in US 2005-0281240 A1, the carrier offset depends on the carrier frequency of the radio communication system, and the clock offset depends on the bandwidth of the radio communication system. In general, the carrier frequency is usually larger than the bandwidth. For instance, in IEEE 802.11a and IEEE 802.11n, the carrier frequencies are 5 GHz, and the bandwidths are 20 MHz, respectively. In this case, the clock offset is smaller by 250 times in comparison to the carrier offset. Thus, the contribution of α is much smaller than that of β. 
     Further, the contribution of β is the same in the phase differences of each subcarrier. Therefore, regarding, for example, the carrier offset, it is possible to individually estimate and compensate at each time point of n=0, or n=1, and, regarding the clock offset, it is possible to estimate by using the estimated values at a plurality of symbols, such as n=0, and n=1. Thereby, as to the carrier offset to significantly rotate phases, the receiver estimates and compensates for every symbol so as to follow the significant rotations. In contrast, as to the clock offset to rotate the phase less, the receiver improves the estimate precision by use of the estimated values obtained at a plurality of symbols to calculate the final estimated values, and compensates the offset by using the estimated values. By compensating in this manner, the reception performance of the receiver may be greatly improved. 
     Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.