Patent Publication Number: US-9906389-B2

Title: Receiver, receiving method, and non-transitory computer readable medium

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a national stage application of International Application No. PCT/JP2015/000904 entitled “RECEIVER, RECEIVING METHOD, AND NON-TRANSITORY COMPUTER READABLE MEDIUM” filed on Feb. 24, 2015, which claims the benefit of the priority of Japanese Patent Application No. 2014-134112, filed on Jun. 30, 2014, the disclosures of each of which are hereby incorporated by reference in their entirety. 
     TECHNICAL FIELD 
     The present invention relates to receivers, receiving methods, and non-transitory computer readable media, and relates to, for example, an OFDM receiver, an OFDM receiving method, and a non-transitory computer readable medium storing an OFDM receiving program. 
     BACKGROUND ART 
     Over recent years, in various types of radio communication systems, an OFDM (Orthogonal Frequency Division Multiplexing) technique has been employed. The OFDM technique can increase a symbol length by parallel transmission using a plurality of carrier waves, and therefore it is possible to equalize received signals using a simple receiver configuration even in a multipath communication line having frequency selectivity. 
     In general, in the OFDM technique, a CP (Cyclic Prefix) is provided between OFDM symbols in order to handle a delay in a multipath communication line.  FIG. 10  is a schematic diagram illustrating CP addition processing on a transmitting side. On the transmitting side, an OFDM symbol  601  is generated by IFFT (Inverse Fast Fourier Transform). Then, on the transmitting side, an end  602  of the OFDM symbol  601  is copied to generate a CP  603 , and the generated CP  603  is added right in front of the OFDM symbol  601 . 
     Usually, a CP length is designed taking into account a spread of delay between multipath communication lines. However, if the spread of delay exceeds the CP length, anterior and posterior OFDM symbols in the time direction interfere with each other, which causes OFDM ISI (Inter Symbol Interference) and ICI (Inter Carrier Interference) in which subcarriers in the frequency direction interfere with each other, which results in receiving characteristic degradation. 
     The ISI is an interference that is caused by the fact that OFDM symbols disposed before and behind an OFDM symbol subjected to FFT (Fast Fourier Transform) on a receiving side exceed a CP length and then leak into an FFT window. On the other hand, the ICI is an interference between subcarriers that is caused by the fact that a communication path matrix is not diagonalized in FFT because a communication path matrix becomes a non-circulant matrix because a spread of delay exceeds a CP length. 
     As techniques to solve the above-described problem, receivers disclosed in PTL 1, PTL 2, PTL 3, and NPL 1 are known. For example, in NPL 1, under the environment where there is a spread of delay exceeding a card interval corresponding to a CP length, an ISI replica and an ICI replica are generated using a signal after decoding, and then the ISI replica and the ICI replica are subtracted from a received signal. 
       FIG. 11  is a diagram illustrating an example of conventional receivers. Specifically,  FIG. 11  is a simplified block diagram to illustrate the receiver disclosed in NPL 1. The receiver disclosed in NPL 1 of  FIG. 11  includes an ISI elimination unit  701 , an ICI elimination unit  702 , an optimum detection filtering unit  703 , a decoding unit  704 , a symbol replica generating unit  705 , an ISI replica generating unit  706 , and an ICI replica generating unit  707 . Hereinafter, configurations of the ICI replica generating unit  707  and the ICI elimination unit  702  that relate to ICI reduction processing will be described. 
     The ICI replica generating unit  707  generates an ICI replica using a symbol replica generated in the symbol replica generating unit  705  and a channel estimation value of an impulse response from a transmission path between a transmitter and a receiver. Specifically, the ICI replica generating unit  707  calculates an ICI channel matrix by performing matrix multiplication for a non-circulant matrix of a communication path matrix generated from the channel estimation value and a Fourier transform matrix. Next, ICI replica is generated by multiplying the ICI channel matrix and a symbol replica vector together. The ICI replica generating unit  707  outputs the ICI replica to the ICI elimination unit  702 . 
     The ICI elimination unit  702  subtracts the ICI replica from a received signal obtained by eliminating the ISI in the ISI elimination unit  701 . The ICI elimination unit  702  outputs the received signal having been subtracted to the optimum detection filtering unit  703 . The optimum detection filtering unit  703  executes FFT processing and channel equalization at the same time. 
     As described above, in ICI elimination processing of the receiver disclosed in NPL 1, an ICI replica is calculated for each subcarrier on a frequency axis, and the ICI replica is subtracted from a received signal. 
     CITATION LIST 
     Patent Literature 
     
         
         [PTL 1] Japanese Patent Application Laid-open Publication No. 2010-178273 
         [PTL 2] International Publication No. WO2007/032497 
         [PTL 3] Japanese Patent Application Laid-open Publication No. 2005-79911 
       
    
     Non Patent Literature 
     
         
         [NPL 1] S. Suyama, H. Suzuki, K. Fukawa, “A MIMO-OFDM Receiver Employing the Low-Complexity Turbo Equalization in Multipath Environments with Delay Difference Greater than the Guard Interval,” IEICE Trans. Commun., vol. E88-B, no. 1, January 2005. 
       
    
     SUMMARY OF INVENTION 
     Technical Problem 
     In the technique disclosed in NPL 1, it is necessary to matrix-multiply a communication path matrix of a non-circulant matrix and a Fourier transform matrix together in the ICI replica generating unit  707 ; consequently, the complexity of a receiver increases due to a lot of complex multiplication calculations. Specifically, according to the technique disclosed in NPL 1, if an FFT point number is represented by N, a rough estimation of the number of complex multiplication calculations necessary for ICI reduction is expressed in formula (1), and the number of complex multiplication calculations increases substantially as the FFT point number increases.
 
O(N 3 +N 2 )  (1)
 
     Because a signal dynamic range of an ICI channel matrix is large, there is fear that characteristics are degraded due to a quantization bit limitation of digital signal processing. 
     The object of the present invention is to provide a receiver, a receiving method, and a receiving program that reduce the number of calculations in Fourier transform for a radio received signal and reduce receiving characteristic degradation due to a delay equal to or larger than a CP length. 
     Solution to Problem 
     A receiver according to an exemplary aspect of the present invention includes an adding means for compensating for a symbol lost within a Fourier transform window to received signals received through a plurality of paths; and a Fourier transform means for performing, in a range of the Fourier transform window, Fourier transform on a received signal with a lost symbol added in the addition means. 
     A receiving method according to an exemplary aspect of the present invention includes an adding step for compensating for a symbol lost within a Fourier transform window to received signals received through a plurality of paths; and a Fourier transform step for performing, in a range of the Fourier transform window, Fourier transform on a received signal with a lost symbol added in the addition step. 
     A non-transitory computer readable medium according to an exemplary aspect of the present invention, the receiving program comprising: an adding step for compensating for a symbol lost within a Fourier transform window to received signals received through a plurality of paths; and a Fourier transform step for performing, in a range of the Fourier transform window, Fourier transform on a received signal with a lost symbol added in the addition step, and outputting a signal after transform. 
     Advantageous Effects of Invention 
     According to the present invention, it is possible to reduce the number of calculations in Fourier transform for a radio received signal and reduce receiving characteristic degradation due to a delay equal to or larger than a CP length. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a block diagram illustrating a configuration of a receiver in accordance with a first exemplary embodiment of the present invention. 
         FIG. 2  is a block diagram illustrating a configuration of an extended CP replica generating unit in accordance with the first exemplary embodiment of the present invention. 
         FIG. 3  is a schematic diagram illustrating OFDM symbol replica processing in the first exemplary embodiment of the present invention. 
         FIG. 4  is a flowchart illustrating receiving process in accordance with the first exemplary embodiment of the present invention. 
         FIG. 5  is a flowchart illustrating extended CP replica generation processing in accordance with the first exemplary embodiment of the present invention. 
         FIG. 6A  is a schematic diagram illustrating an example of signals received through multipaths in the first exemplary embodiment of the present invention. 
         FIG. 6B  is a schematic diagram illustrating an example of OFDM symbols of the signals received through the multipaths in the first exemplary embodiment of the present invention. 
         FIG. 6C  is a schematic diagram illustrating an example of channel estimation values of the signals received through the multipaths in the first exemplary embodiment of the present invention. 
         FIG. 6D  is a schematic diagram illustrating an example of CP interval-outside channel estimation values selected by a CP interval-outside selection unit  111  in the first exemplary embodiment of the present invention. 
         FIG. 6E  is a schematic diagram illustrating an example of signals after being subjected to convolution multiplication by a channel convolution multiplying unit  202  in the first exemplary embodiment of the present invention. 
         FIG. 6F  is a schematic diagram illustrating an example of extended CP replica signals selected by an extended replica CP selection unit  203  in the first exemplary embodiment of the present invention. 
         FIG. 6G  is a schematic diagram illustrating an example of signals shifted by an extended CP replica shift unit  204  in the first exemplary embodiment of the present invention. 
         FIG. 6H  is a diagram illustrating an example of signals obtained by compensating for a defective component in received OFDM symbols within an FFT window, in the first exemplary embodiment of the present invention. 
         FIG. 7  is a block diagram illustrating a configuration of an extended CP replica generating unit in accordance with a second exemplary embodiment of the present invention. 
         FIG. 8A  is a schematic diagram illustrating an example of signals received through multipaths in the second exemplary embodiment of the present invention. 
         FIG. 8B  is a schematic diagram illustrating an example of OFDM symbols of the signals received through the multipaths in the second exemplary embodiment of the present invention. 
         FIG. 8C  is a schematic diagram illustrating an example of channel estimation values of the signals received through the multipaths in the second exemplary embodiment of the present invention. 
         FIG. 8D  is a schematic diagram illustrating an example of CP interval-outside channel estimation values selected by a CP interval-outside selection unit  111  in the second exemplary embodiment of the present invention. 
         FIG. 8E  is a schematic diagram illustrating an example of signals after being subjected to convolution multiplication by a channel multiplication unit  401  in the second exemplary embodiment of the present invention. 
         FIG. 8F  is a schematic diagram illustrating an example of signals selected as extended CP replicas in the second exemplary embodiment of the present invention. 
         FIG. 8G  is a schematic diagram illustrating an example of signals shifted by an extended CP replica shift unit  403  in the second exemplary embodiment of the present invention. 
         FIG. 8H  is a diagram illustrating an example of signals to which respective path components are added in the second exemplary embodiment of the present invention. 
         FIG. 8I  is a diagram illustrating an example of signals obtained by compensating for a defective component in received OFDM symbols within an FFT window, in the second exemplary embodiment of the present invention. 
         FIG. 9  is a block diagram illustrating a configuration of a receiver in accordance with a third exemplary embodiment of the present invention. 
         FIG. 10  is a schematic diagram illustrating CP addition processing in a transmission side. 
         FIG. 11  is a diagram illustrating an example of a conventional receiver. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     A First Exemplary Embodiment of the Present Invention 
     In a first exemplary embodiment of the present invention, under the environment where a spread of delay in a multipath communication line exceeds a CP length, demodulation is performed reducing an influence of ISI and ICI. As an example, in the first exemplary embodiment of the present invention, a case will be described in which OFDM is used as a transmission scheme and two receiving antennas are used. 
       FIG. 1  is a block diagram illustrating a configuration of a receiver in accordance with the first exemplary embodiment of the present invention. In  FIG. 1 , a receiver  10  includes a radio receiving unit  100 , an ISI elimination unit  101 , an extended CP addition unit  102 , an FFT window timing determination unit  103 , FFTs  104 - 1  and  104 - 2 , an equalization filtering unit  105 , a demodulation unit  106 , a decoding unit  107 , a symbol replica generating unit  108 , an IFFT  109 , an ISI replica generating unit  110 , a CP interval-outside selection unit  111 , an extended CP replica generating unit  112 , and a channel estimation unit  113 . 
     The radio receiving unit  100  performs, on received signal received through the antenna, respective processings for conversion to a baseband (base frequency band) frequency, lowpass filtering, AGC (Auto Gain Control), and A/D (Analog-to-Digital) conversion. The radio receiving unit  100  outputs received signals after the processing to the ISI elimination unit  101 . 
     The ISI elimination unit  101  eliminates ISI from the received signals using an ISI replica output from the ISI replica generating unit  110 . Specifically, the ISI elimination unit  101  subtracts the ISI replica from the received signals and outputs received signals after the subtraction to the extended CP addition unit  102 . 
     The extended CP addition unit  102  compensates for a symbol lost within a Fourier transform window to received signals received through a plurality of paths. Specifically, the extended CP addition unit  102  compensates for a symbol lost within a Fourier transform window to received signals after ISI elimination using an extended CP replica output from the extended CP replica generating unit  112 . Specifically, the extended CP addition unit  102  adds the extended CP replica to the received signals after ISI elimination and outputs resultant signals to the FFTs  104 - 1  and  104 - 2 . At a first equalization, since an ISI replica and an extended CP replica are not generated, an ISI replica and an extended CP replica may be initialized and set at zero. 
     The FFT window timing determination unit  103  determines a timing for FFT processing referring to the received signal to which the extended CP is added in the extended CP addition unit  102 . The FFT window timing determination unit  103  outputs the information on the determined timing for FFT processing, to the FFTs  104 - 1  and  104 - 2 , the ISI replica generating unit  110 , the CP interval-outside selection unit  111 , and the extended CP replica generating unit  112 . The timing for FFT processing can be determined by an autocorrelation technique using a CP of an OFDM symbol in the received signals or by a cross-correlation technique using a known reference signal. 
     The FFTs  104 - 1  and  104 - 2  perform the fast Fourier transform on the received signal after the extended CP added output from the extended CP addition unit  102  at the timing within the FFT window that is output from the FFT window timing determination unit  103 . Specifically, the FFTs  104 - 1  and  104 - 2  perform the fast Fourier transform processing in which a head timing of the FFT window is set at a starting position for each receiving antenna. The FFTs  104 - 1  and  104 - 2  output the received signals after the transform to the equalization filtering unit  105 . DFT (Discrete Fourier Transform) may be used instead of the FFT. 
     The equalization filtering unit  105  equalizes the received signals after the FFT output from the FFTs  104 - 1  and  104 - 2 . Specifically, the equalization filtering unit  105  causes synthesis of the signals after the FFT for each receiving antenna according to an equalization weight and obtains equalized signals after the receiving antenna synthesis. The equalization filtering unit  105  outputs the equalized signal after the receiving antenna synthesis to the demodulation unit  106 . As the equalization weight, an equalization weight by which a received signal power to noise power ratio (SNR) is maximized may be used, for example. As a calculation method for the equalization weight, any of various types of methods described in prior art documents is applicable. 
     The demodulation unit  106  converts the equalized signal after the receiving antenna synthesis into soft decision information for each bit. The demodulation unit  106  outputs the soft decision information to the decoding unit  107 . 
     The decoding unit  107  performs error correction decoding on the soft decision information output from the demodulation unit  106 . The decoding unit  107  outputs the soft decision information after the error correction with enhanced reliability to the symbol replica generating unit  108 . The convolution decoding or the turbo decoding is used for the error correction decoding, for example. The decoding unit  107  may output binary information, which is hard decision information, instead of the soft decision information. In this case, it is preferable for the decoding unit  107  to preform, together with the error correction decoding, a binary decision on the soft decision information using a predetermined threshold. 
     The symbol replica generating unit  108  converts the soft decision information after the decoding output from the decoding unit  107  into a soft symbol replica. The symbol replica generating unit  108  outputs the soft symbol replica to the IFFT  109 . 
     For the soft symbol replica, QPSK (Quadrature Phase Shift Keying), 16QAM (16 Quadrature Amplitude Modulation), or 64QAM (64 Quadrature Amplitude Modulation) is used, for example. As a method for converting the soft decision information into the soft symbol replica, various types of methods described in prior art documents are applicable. The symbol replica generating unit  108  outputs a hard symbol replica to the IFFT  109  instead of the soft symbol replica if the binary information, which is the hard decision information, is inputted from the decoding unit  107 . 
     The IFFT  109  generates an OFDM symbol replica by performing the inverse fast Fourier transform processing on the soft symbol replica (or the hard symbol replica) output from the symbol replica generating unit  108 . The IFFT  109  outputs the OFDM symbol replica to the ISI replica generating unit  110  and the extended CP replica generating unit  112 . IDFT (Inverse Discrete Fourier Transform) may be used instead of IFFT. 
     The ISI replica generating unit  110  generates an ISI replica using the OFDM symbol replica output from the IFFT  109 , the FFT window timing output from the FFT window timing determination unit  103 , and a channel estimation value of an impulse response of a communication path between a transmitter and a receiver. Specifically, the ISI replica generating unit  110  convolution-multiplies the OFDM symbol replica and the channel estimation value together, and generates the ISI replica based on the FFT window timing. The ISI replica generating unit  110  outputs the ISI replica to the ISI elimination unit  101 . As to a method for generating the ISI replica, the ISI replica can be generated by the method disclosed in NPL 1, for example. 
     The CP interval-outside selection unit  111  selects a channel estimation value outside an interval corresponding to the CP length of a head within the FFT window from among channel estimation values output from the channel estimation unit  113  based on the FFT window timing output from the FFT window timing determination unit  103 . The CP interval-outside selection unit  111  outputs the selected channel estimation value, that is, the channel estimation value outside an interval corresponding to the CP length of a head within the FFT window, to the extended CP replica generating unit  112 . 
     The extended CP replica generating unit  112  generates an extended CP replica by using the OFDM symbol replica output from the IFFT  109  and the CP interval-outside channel estimation value output from the CP interval-outside selection unit  111  based on the FFT window timing output from the FFT window timing determination unit  103 . The extended CP replica generating unit  112  outputs the extended CP replica to the extended CP addition unit  102 . 
     The extended CP replica is a signal corresponding to a defective component of a self-OFDM symbol in an FFT window by multipaths. Adding the extended CP replica to a received signal makes a communication path matrix a circulant matrix, and makes it possible to reduce ICI that occurs after the FFT. A detailed configuration of the extended CP replica generating unit  112  will be described below with reference to  FIG. 2 . 
     The channel estimation unit  113  calculates a channel estimation value using a reference signal in received signals and a reference signal replica. The channel estimation unit  113  outputs the channel estimation value to the ISI replica generating unit  110  and the CP interval-outside selection unit  111 . The channel estimation value can be calculated by the cross-correlation processing of a known reference signal replica and a receiving reference signal, for example. As the reference signal replica, a replica corresponding to a reference signal generated in the symbol replica generating unit may be used. The reference signal is a reference signal that is Fourier-transformed in each of the FFTs  104 - 1  and  104 - 2 . 
     As mentioned above, in the first exemplary embodiment of the present invention, an extended CP replica is generated as a signal corresponding to a defective component of a self-OFDM symbol within an FFT window by multipath, and the extended CP replica is added to a received signal. 
     Next, detailed configurations to generate the extended CP replica will be described.  FIG. 2  is a block diagram illustrating a configuration of the extended CP replica generating unit in accordance with the first exemplary embodiment of the present invention. The configuration of the extended CP replica generating unit  112  illustrated in  FIG. 2  is an example suitable for a case in which a path head timing, indicating a head of OFDM symbols before adding CP in every path, is located later than an FFT window timing. In  FIG. 2 , the extended CP replica generating unit  112  includes an end elimination unit  201 , a channel convolution multiplying unit  202 , an extended CP replica selection unit  203 , and an extended CP replica shift unit  204 . 
     The end elimination unit  201  eliminates an end interval corresponding to a CP length in the OFDM symbol replica output from the IFFT  109  in  FIG. 1 . The end elimination unit  201  outputs the OFDM symbol replica with the end interval eliminated to the channel convolution multiplying unit  202 . 
       FIG. 3  illustrates the processing for the OFDM symbol replica in the end elimination unit  201 .  FIG. 3  is a schematic diagram illustrating the OFDM symbol replica processing in the first exemplary embodiment of the present invention. The end elimination unit  201  eliminates an end interval corresponding to a CP length in an OFDM symbol replica  301  output from the IFFT  109  and generates an OFDM symbol replica  302  with the end eliminated. 
     Returning to  FIG. 2 , the configuration of the extended CP replica generating unit will be described. The channel convolution multiplying unit  202  convolution-multiplies the OFDM symbol replica with the end eliminated in the end elimination unit  201  by a CP interval-outside channel estimation value output from the CP interval-outside selection unit  111 . The channel convolution multiplying unit  202  outputs a signal after convolution-multiplying to the extended CP replica selection unit  203 . 
     The extended CP replica selection unit  203  selects a signal outside an interval of the FFT window from the signal convolution-multiplied in the channel convolution multiplying unit  202  using an FFT window timing from the FFT window timing determination unit  103  in  FIG. 1 . The extended CP replica selection unit  203  outputs the selected signal outside the interval of the FFT window to the extended CP replica shift unit  204 . 
     The extended CP replica shift unit  204  generates an extended CP replica by shifting, to a head timing in the FFT window, a signal after the CP interval-outside channel estimation value convolution-multiplication that is located outside the interval behind the FFT window in the signal after the CP interval-outside channel estimation value convolution-multiplication that is located outside the FFT window interval. The extended CP replica shift unit  204  outputs the extended CP replica to the extended CP addition unit  102 . 
     Since the transmitting technique based on OFDM is a block transmitting technique based on FFT, the end signal and the head signal of the OFDM are continuous. So the extended CP replica shift unit  204  cyclic-shifts a signal after the CP interval-outside channel estimation value convolution-multiplication in the same OFDM symbol so that a received signal after adding the extended CP replica may not be lost within the FFT window. 
     Next, processing steps for the receiver of the first exemplary embodiment will be described.  FIG. 4  is a flowchart illustrating receiving process in accordance with the first exemplary embodiment of the present invention. Specifically,  FIG. 4  is a flowchart illustrating an operation example of ISI elimination, extended CP addition, and demodulation in the receiver of the first exemplary embodiment. The flowchart of  FIG. 4  includes steps A 01  to A 13 . 
     The FFT window timing determination unit  103  determines an FFT window timing referring to received signals, and the processing moves to step A 02  (step A 01 ). 
     The FFTs  104 - 1  and  104 - 2  perform FFT processing on the received signals based on the FFT window timing, and the processing moves to step A 03  (step A 02 ). 
     The equalization filtering unit  105  performs a receiving antenna synthesis by multiplying the received signals FFT-processed and equalization weights together, and the processing moves to step A 04  (step A 03 ). 
     The demodulation unit  106  generates soft decision information for each bit from the equalized signal subjected to equalization weight multiplication processing, and the processing moves to step A 05  (step A 04 ). 
     The decoding unit  107  generates soft decision information after the error correction by performing error correction decoding processing on the soft decision information, and the processing moves to step A 06  (step A 05 ). 
     In step A 06 , it is determined whether the number of repetition processing from step A 01  to step A 13  exceeds a predetermined number of times, and the processing moves to step A 07  if the repeat count does not exceed the predetermined number of times. If the repeat count has exceeded the predetermined number of times, the processing is completed. When a CRC (Cyclic Redundancy Check) is added to a transmitting signal, the hard decision results of the soft decision information after decoding are subjected to a cyclic redundancy check. If the CRC result is no good, the processing moves to step A 07 , and the processing may be terminated if the CRC result is OK. 
     The symbol replica generating unit  108  generates a soft symbol replica from the soft decision information after the error correction, and the processing moves to step A 08  (step A 07 ). 
     The IFFT  109  generates an OFDM symbol replica by performing IFFT processing on the soft symbol replica, and the processing moves to step A 09  (step A 08 ). 
     The ISI replica generating unit  110  generates an ISI replica from the soft symbol replica and a channel estimation value based on the FFT window timing, and the processing moves to step A 10  (step A 09 ). 
     The CP interval-outside selection unit  111  selects a channel estimation value outside the CP interval of the head within the FFT window from among channel estimation values, and the processing moves to step A 11  (step A 10 ). If the channel estimation value is updated for each repetition processing, the CP interval-outside channel estimation value may be updated by performing step A 10  for each repetition processing. On the other hand, if the channel estimation value is not updated for each repetition processing, it is acceptable to perform step A 10  at a first equalization processing and move to step A 11  skipping step A 10  after the first repetition. 
     The extended CP replica generating unit  112  generates an extended CP replica from the soft symbol replica and the CP interval-outside channel estimation value based on the FFT window timing, and the processing moves to step A 12  (step A 11 ). 
     The ISI elimination unit  101  subtracts the ISI replica from the received signal, and the processing moves to step A 13  (step A 12 ). 
     The extended CP addition unit  102  adds the extended CP replica to the received signal, and the processing moves to step A 01  (step A 13 ). 
     Next, a detailed operation of the extended CP replica generation processing will be described.  FIG. 5  is a flowchart illustrating the extended CP replica generation processing in accordance with the first exemplary embodiment of the present invention. Specifically,  FIG. 5  is a flowchart illustrating a detailed operation example of the extended CP replica generation processing (step A 11 ) in  FIG. 4 . The flowchart in  FIG. 5  includes steps B 01  to B 04 . 
     The end elimination unit  201  eliminates an end interval corresponding to the CP length in the OFDM symbol replica, and the processing moves to step B 02  (step B 01 ). 
     The channel convolution multiplying unit  202  convolution-multiplies the OFDM symbol replica with the end eliminated and a CP interval-outside channel estimation value together, and the processing moves to step B 03  (step S 02 ). 
     The extended CP replica selection unit  203  selects an interval-outside component of the FFT window in a signal after CP interval-outside channel estimation value convolution multiplication, and the processing moves to step B 04  (step B 03 ). 
     The extended CP replica shift unit  204  generates an extended CP replica by shifting a signal after selection of the interval-outside component of the FFT window and (step B 04 ). 
     Next, using  FIG. 6A  to  FIG. 6H , the signal processing according to the first exemplary embodiment will be described.  FIG. 6A  to  FIG. 6H  illustrate a series of processing details to generate an extended CP replica from an OFDM symbol replica in the CP interval-outside selection unit  111  and the extended CP replica generating unit  112  included in the receiver described in  FIG. 1 . Specifically,  FIG. 6A  to  FIG. 6H  illustrate images of signal processing results in a case where a path head timing indicating a head of an OFDM symbol before CP addition is located later than an FFT window timing. 
       FIG. 6A  is a schematic diagram illustrating an example of the signals received through multipath.  FIG. 6B  is a schematic diagram illustrating an example of OFDM symbols of the signals received through multipath.  FIG. 6C  is a schematic diagram illustrating an example of channel estimation values of the signals received through multipath.  FIG. 6D  is a schematic diagram illustrating an example of CP interval-outside channel estimation values selected by the CP interval-outside selection unit  111 .  FIG. 6E  is a schematic diagram illustrating an example of the signals convolution-multiplied by the channel convolution multiplying unit  202 .  FIG. 6F  is a schematic diagram illustrating an example of the extended CP replica signals selected by the extended replica CP selection unit  203 .  FIG. 6G  is a schematic diagram illustrating an example of the signals shifted by the extended CP replica shift unit  204 .  FIG. 6H  is a diagram illustrating an example of the signals obtained by compensating for defective components in received OFDM symbols within an FFT window. 
     In  FIG. 6A , paths P 0 , P 1 , P 2 , and P 3  represent signals that are received at different timings due to delay difference resulting from different communication paths. In  FIG. 6A , the vertical axis represents a gain and the horizontal axis represents a time difference of the signals received through each path. Each path is expressed as a timing at a head of each CP and a gain. 
       FIG. 6B  illustrates the relation between received OFDM symbols having passed through a multipath communication line composed of the paths P 0 , P 1 , P 2 , and P 3  and path head timings of the respective paths. As with  FIG. 6A , in each of  FIG. 6B  to  FIG. 6H , the horizontal axis represents a time difference of the signals received through each path. In each of  FIG. 6B  to  FIG. 6H , a reference t 0  represents a timing of the head of a symbol except a CP through the path P 0 . In a similar way, t 1  represents a timing of the head of a symbol except a CP through the path P 1 , t 2  represents a timing of the head of a symbol except a CP through the path P 2 , and t 3  represents a timing of the head of a symbol except a CP through the path P 3 . The tail end of the symbol including a CP generating source through the path P 0  is represented by t e . 
     In  FIG. 6C  and  FIG. 6D , the vertical axis represents a gain and the horizontal axis represents a time difference of the signals received through each path. Each channel estimation value is expressed as a timing of the head of a symbol through each path and a gain. As illustrated in  FIG. 6C , an FFT window ranges from t 0  to t e . The FFTs  104 - 1  and  104 - 2  perform Fourier transform on symbols of a plurality of paths by the FFT window unit. 
     In the present invention, the processing is performed before Fourier transform, of cyclic-shifting an own symbol replica and adding the resulting replica to the signal, for a signal of a path whose timing differs from a reference for a processing timing equal to or larger than a CP length. Specifically, in the invention of the first exemplary embodiment, the processing is performed before Fourier transform, of cyclic-shifting an own symbol replica and adding the resulting replica to the signal, for a received signal of a path with a delay more than the CP length. 
     The CP interval-outside selection unit  111  selects channel estimation values composed of the paths P 2  and P 3  departing from the CP interval of the head within the FFT window from among channel estimation values composed of the paths P 0 , P 1 , P 2 , and P 3 . That is to say, in  FIG. 6C , the paths P 0  and P 1  included in the paths P 0 , P 1 , P 2 , and P 3 , which are located at the timing ranging from a head timing t 0  of the symbol through the first head path P 0  to t c  that is a timing behind t 0  by the CP length, are paths each of which has a delay equal to or smaller than the CP length. On the other hand, the paths that are positioned at timings behind t c  are paths each of which has a delay larger than the CP length. 
     Since the FFT window ranges from t 0  to t e , the CP interval-outside selection unit  111  selects paths positioned at the timing period from t c  to t e  as paths each of which has a delay larger than the CP length. In  FIG. 6C , the paths P 2  and P 3  are the paths that are positioned at the timing period from t c  to t e , that is, the paths each of which has a delay larger than the CP length. Consequently, the CP interval-outside selection unit  111  selects the channel estimation values of the paths P 2  and P 3  as CP interval-outside channel estimation values.  FIG. 6D  illustrates an example of the selected CP interval-outside channel estimation values. 
     The channel convolution multiplying unit  202  convolution-multiplies an OFDM symbol replica with an end corresponding to the CP length eliminated and a CP interval-outside channel estimation value, and generates a signal after the CP interval-outside channel estimation value convolution-multiplication. A signal corresponding to a path received with a delay longer than the CP length is generated by multiplying the OFDM symbol replica by the CP interval-outside channel estimation value.  FIG. 6E  is a diagram illustrating signals after convolution-multiplying an OFDM symbol replica by a CP interval-outside channel estimation value, that is, signals after CP interval-outside channel estimation value convolution-multiplication. 
     In the first exemplary embodiment, a portion that cannot be compensated for using a CP due to a delay is made up for in OFDM symbols of the signals received through multipath. That is to say, the extended CP replica selection unit  203  selects an interval-outside component of an FFT window from among the signals after CP interval-outside channel estimation value convolution-multiplication, and generates a signal after extended CP replica selection. It is described using  FIG. 6E  to select the signals that are positioned behind t e  of the tail end of the FFT window.  FIG. 6F  is a diagram illustrating an example of signals after the selection. 
     The extended CP replica shift unit  204  shifts an interval-outside component behind the FFT window to the head within the FFT window and generates an extended CP replica.  FIG. 6G  is a diagram illustrating an example of extended CP replica signals after the shift. That is to say, the extended CP replica signal is cyclic-shifted within the FFT window. Specifically, in  FIG. 6G , the extended CP replica signals of the paths P 2  and P 3  are shifted to a timing of t 0 . The extended CP addition unit  102  adds the cyclic-shifted extended CP replica signal to the received OFDM symbol. The results from the addition are illustrated in  FIG. 6H . 
       FIG. 6H  is a diagram illustrating an example of the signals in which a defective component has been compensated for in a received OFDM symbol within the FFT window. As illustrated in  FIG. 6H , it is possible to compensate for defective symbols within the FFT window due to a delay larger than the CP length arising, by adding the cyclic-shifted extended CP replica signals to the paths P 2  and P 3 . That is to say, in  FIG. 6H , a defective symbol is compensated for in the path P 2  during the timing period from t 0  to t 2 —the CP length. In the same manner, in  FIG. 6H , a defective symbol is compensated for in the path P 3  during the timing period from t 0  to t 3 —the CP length. 
     Although it has been described as an example that the channel convolution multiplying unit  202  in the extended CP replica generating unit  112  described in  FIG. 2  is configured to multiply a CP interval-outside channel estimation value by the entire interval of an OFDM symbol replica with its end eliminated, only a signal interval after extended CP replica selection required for each path may be multiplied by the CP interval-outside channel estimation value. 
     That is to say, the signal after extended CP replica selection illustrated in  FIG. 6F  may directly be obtained without selecting the extended CP replica by convolution-multiplying a part of an OFDM symbol replica with its end eliminated illustrated in  FIG. 3  and the CP interval-outside channel estimation value illustrated in  FIG. 6D  together. In this case, the output of the channel convolution multiplying unit  202  is output to the extended CP replica shift unit  204 , and the extended CP replica shift unit  204  receives a signal with an extended CP replica selected from the channel convolution multiplying unit  202  and shifts the signal to the head within the FFT window. This makes it possible to suppress the number of multiplications in the channel convolution multiplying unit to the minimum, as compared to a case in which the entire interval of an OFDM symbol replica with its end eliminated is convolution-multiplied. 
     As described above, the receiver in accordance with the first exemplary embodiment of the present invention generates an extended CP replica as a signal corresponding to a defective component of an self-OFDM symbol within an FFT window through the multipath and adds the extended CP replica to a received signal, which makes a communication path matrix a circulant matrix and makes it possible to reduce ISI and ICI that occur after FFT under an environment where a spread of delay of the communication path exceeds a CP length. The receiver in accordance with the first exemplary embodiment of the present invention can reduce the number of complex multiplications in ICI reduction processing and reduce an influence of the characteristic degradation due to a quantization bit limitation of digital signal processing. 
     Specifically, the receiver in accordance with the first exemplary embodiment of the present invention generates an extended CP replica in a time domain in order to reduce ICI and adds the generated replica to a received signal, which makes a communication path matrix a circulant matrix. This makes it possible to reduce the number of complex multiplications without requiring matrix multiplication with a large number of matrices in ICI reduction processing. If a path number of CP interval-outside channel estimation values is represented by L, and if a sample number of signals after extended CP replica selection through a path I is represented by as Ni (Ni≦N), an estimate of the number of complex multiplications required for the ICI reduction processing in the receiver of the first exemplary embodiment of the present invention is expressed in formula (2). The estimate of the number of complex multiplications required for the ICI reduction processing expressed in formula (2) is smaller as compared to formula (1) expressing an estimate of the number of complex multiplications required for the ICI reduction processing in NPL 1. 
     
       
         
           
             
               
                 
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     It is necessary for the receiver disclosed in NPL 1 to process a leaking-in signal of a subcarrier having large amplitude variations on a frequency axis in the ICI reduction processing. In contrast, since the receiver in accordance with the first exemplary embodiment of the present invention processes an OFDM symbol signal on a time axis in the ICI reduction processing, the signal dynamic range is small. This makes it possible to reduce the influence of the characteristic degradation due to a quantization bit limitation of digital signal processing. 
     A Second Exemplary Embodiment of the Present Invention 
     A second exemplary embodiment of the present invention is based on the first exemplary embodiment of the present invention, and is an embodiment in which the extended CP replica can be generated even though a path head timing, indicating a head of an OFDM symbol before adding CP, is located earlier than an FFT window timing. Specifically, a receiver of the second exemplary embodiment of the present invention differs from that of the first exemplary embodiment as to the processing in the FFT window timing determination unit  103  and the extended CP replica generating unit  112 .  FIG. 7  is a block diagram illustrating a configuration of an extended CP replica generating unit in accordance with the second exemplary embodiment of the present invention. In  FIG. 7 , the extended CP replica generating unit  112  includes an end elimination unit  201 , a channel multiplication unit  401 , an extended CP replica selection unit  402 , an extended CP replica shift unit  403 , and a path addition unit  404 . 
     The end elimination unit  201  eliminates an end interval corresponding to a CP length in the OFDM symbol replica output from the IFFT  109  in  FIG. 1 . The end elimination unit  201  outputs the OFDM symbol replica with the end interval eliminated to the channel multiplication unit  401 . The elimination of the end interval is performed as is the case with the processing of the first exemplary embodiment of the present invention illustrated in  FIG. 3 . 
     The channel multiplication unit  401  multiplies, for each path, the OFDM symbol replica with the end interval eliminated in the end elimination unit  201  by a CP interval-outside channel estimation value output from the CP interval-outside selection unit  111 . The channel multiplication unit  401  outputs a signal after the multiplication to the extended CP replica selection unit  402 . 
     In the second exemplary embodiment of the present invention, the FFT window timing determination unit  103  in  FIG. 1  measures, in addition to an FFT window timing, a path head timing indicating an OFDM symbol head before adding CP and outputs these timings to the extended CP replica selection unit  402 . The path head timing can be obtained by cross-correlation processing of a received signal and a known reference signal replica, for example. 
     The extended CP replica selection unit  402  selects, based on the FFT window timing and the path head timing, a signal after the CP interval-outside channel estimation value multiplication for each path output from the channel multiplication unit  401 . Specifically, the extended CP replica selection unit  402  selects an interval-inside signal of the FFT window and outputs the selected signal to the extended CP replica shift unit  403  from among signals after the CP interval-outside channel estimation value multiplication for each path, with respect to a path having a path head timing positioned earlier than the FFT window timing. 
     On the other hand, with respect to a path having a path head timing positioned later than the FFT window timing, the extended CP replica selection unit  402  selects an interval-outside signal of the FFT window from among signals after the CP interval-outside channel estimation value multiplication for each path and outputs the selected signal to the extended CP replica shift unit  403 , as is the case with the first exemplary embodiment of the present invention. 
     The extended CP replica shift unit  403  shifts, to a head within the FFT window, only a replica of a path with a path head timing positioned later than the FFT window timing included in the signals after the extended CP replica selection for each path selected in the extended CP replica selection unit  402 . The extended CP replica shift unit  403  outputs a shifted replica and an unshifted replica to the path addition unit  404 . 
     The path addition unit  404  adds an extended CP replica signal for each path output from the extended CP replica shift unit  403  between the paths and generates an extended CP replica. The path addition unit  404  outputs the generated extended CP replica to the extended CP addition unit  102 . 
     Next, using  FIG. 8A  to  FIG. 8H , the signal processing of the second exemplary embodiment will be described.  FIG. 8A  to  FIG. 8I  are schematic diagrams illustrating a series of processing details to generate an extended CP replica from an OFDM symbol replica in the second exemplary embodiment of the present invention by the CP interval-outside selection unit  111  and the extended CP replica generating unit  112  of the receiver described in  FIG. 1 .  FIG. 8A  to  FIG. 8I  illustrate images of signal processing results in a case where a path head timing indicating a head of an OFDM symbol before CP addition is located earlier than an FFT window timing. 
       FIG. 8A  is a schematic diagram illustrating an example of the signals received through multipath.  FIG. 8B  is a schematic diagram illustrating an example of OFDM symbols of the signals received through the multipath.  FIG. 8C  is a schematic diagram illustrating an example of channel estimation values of the signals received through the multipath.  FIG. 8D  is a schematic diagram illustrating an example of CP interval-outside channel estimation values selected by the CP interval-outside selection unit  111 .  FIG. 8E  is a schematic diagram illustrating an example of the signals multiplied by the channel multiplication unit  401 .  FIG. 8F  is a schematic diagram illustrating an example of the signals selected as extended CP replicas.  FIG. 8H  is a schematic diagram illustrating an example of a signal shifted by the extended CP replica shift unit  403 .  FIG. 8G  is a diagram illustrating an example of the signals to which respective path components are added.  FIG. 8I  is a diagram illustrating an example of the signals obtained by compensating for defective components in received OFDM symbols within an FFT window. Each signal is expressed as a timing at a head of a CP of each path and a gain. 
     In  FIG. 8A , paths P 0 , P 1 , P 2 , and P 3  represent signals that are received at different timings due to delay differences resulting from different communication paths. In  FIG. 6A , the vertical axis represents a gain and the horizontal axis represents a time difference of the signals received through each path. Each path is expressed as a timing at a head of each CP and a gain. 
       FIG. 8B  illustrates the relation between received OFDM symbols having passed through a multipath communication line composed of the paths P 0 , P 1 , P 2 , and P 3  and path head timings of the respective paths. In  FIG. 8A  to  FIG. 8H , the horizontal axis represents a time difference of the signals received through each path. In  FIG. 8A  to  FIG. 8H , a reference t 0  represents a timing of the head of a symbol through the path P 0 . In addition, t 1  represents a timing of the head of a symbol through the path P 1 , t 2  represents a timing of the head of a symbol through the path P 2 , and t 3  represents a timing of the head of a symbol through the path P 3 . Further, t s  represents the head timing of the symbol including a CP through the path P 2 . Further, t e  represents a timing of the tail end of the symbol except a CP generating source through the path P 2 . Here, t s  represents the head of the FFT window, and t e  represents the end of the FFT window. 
     The channel estimation unit  113  performs channel estimation on each path illustrated in  FIG. 8B  and outputs a channel estimation value illustrated in  FIG. 8C . 
     The CP interval-outside selection unit  111  selects channel estimation values composed of the paths P 3 , P 0 , and P 1  departing from the CP interval of the head of the FFT window from among channel estimation values of the paths P 0 , P 1 , P 2 , and P 3  in  FIG. 8C .  FIG. 8D  illustrates an example of the selected CP interval-outside channel estimation values. In  FIG. 8C  and  FIG. 8D , the CP interval is an interval having a CP length from the head timing of the FFT window. Since the paths P 0  and P 1  of the channel estimation values have the path head timings positioned ahead of the FFT window timing, they are observed in  FIG. 8C  behind the path P 3  as loop-back components within the FFT window. The channel estimation values of the path P 0  and P 1  are observed at the positions of t 0 ′ and t 1 ′. 
     The channel multiplication unit  401  convolution-multiplies an OFDM symbol replica with the end corresponding to the CP length eliminated and a CP interval-outside channel estimation value together, and generates a signal after the CP interval-outside channel estimation value convolution-multiplication. By multiplying the OFDM symbol replica by the CP interval-outside channel estimation value, a symbol replica is generated that corresponds to a signal of a path received with a delay later than the CP length from the head timing of the FFT window.  FIG. 8E  is a diagram illustrating signals obtained by convolution-multiplying the OFDM symbol replica by the CP interval-outside channel estimation value, that is, signals after CP interval-outside channel estimation value convolution multiplication. 
     In the first exemplary embodiment, a portion is compensated for that cannot be compensated for by a CP due to a delay, in the OFDM symbols of signals received through multipath, whereas in the second exemplary embodiment, in addition, a defective portion in a Fourier transform window is also compensated for in a path in which a head of a symbol is positioned at a timing ahead of the Fourier transform window. 
     The extended CP replica selection unit  402  selects only a component within the FFT window interval, for a path in which a path head timing is positioned ahead of the FFT window timing, from among signals after CP interval-outside channel estimation value multiplication, selects only an interval-outside component of the FFT window for a path in which a path head timing is positioned behind the FFT window timing, and generates a signal after extended CP replica selection.  FIG. 8F  is a diagram illustrating an example of signals after the selection. 
     The extended CP replica shift unit  403  shifts an interval-outside component behind the FFT window to the head within the FFT window. 
     The path addition unit  404  adds each path component after the shift.  FIG. 8G  is a diagram illustrating an example of signals to which each path component is added. 
     The extended CP addition unit  102  adds a cyclic-shifted extended CP replica to a received OFDM symbol. The results of the addition are illustrated in  FIG. 8H . 
       FIG. 8I  is a diagram illustrating an example of the signals obtained by compensating for defective components in the received OFDM symbols within the FFT window. As illustrated in  FIG. 8I , by adding the extended CP replicas looped-back in the FFT window to the paths P 0  and P 1 , and a cyclic-shifted extended CP replica to the path P 3 , it is possible to compensate for a defective symbol within the FFT window due to a delay larger than the CP length arising. That is to say, in  FIG. 8I , in the path P 0 , symbols lost in a timing period from t 0 ′ to t e  are compensated for. In the same manner, in  FIG. 8I , in the path P 1 , symbols lost in a timing period from t 1 ′ to t e  are compensated for. Further, in  FIG. 8I , in the path P 3 , symbols lost in a timing period from t s  to t 3 —the CP length are compensated for. 
     Although the configuration has been described as an example in which the channel multiplication unit  401  multiplies the entire interval of an OFDM symbol replica with its end eliminated and a CP interval-outside channel estimation value together, only a signal interval after the extended CP replica selection required for each path may be multiplied by a CP interval-outside channel estimation value, as is the case with the first exemplary embodiment. 
     That is to say, the signal after extended CP replica selection illustrated in  FIG. 8F  may directly be obtained without selecting the extended CP replica by multiplying a part of the OFDM symbol replica with its end eliminated illustrated in  FIG. 3  and the CP interval-outside channel estimation value illustrated in  FIG. 8D  together. 
     In this case, the output of the channel multiplication unit  401  is output to the extended CP replica shift unit  403 . The extended CP replica shift unit  403  performs shift processing on the signal with the extended CP replica selected. These processes make it possible to suppress the number of multiplications in the channel multiplication unit to the minimum, as compared to a case in which the entire interval of an OFDM symbol replica with its end eliminated is multiplied. 
     As described above, it is possible in the second exemplary embodiment of the present invention to make a communication path matrix a circulant matrix and reduce the ICI after FFT by compensating for a defective component within the FFT window, even though there is a path in which a path head timing is positioned ahead of the FFT window. 
     A Third Exemplary Embodiment of the Present Invention 
     A third exemplary embodiment of the present invention will be described citing as an example a case in which the present exemplary embodiment is applied to a receiver for DFT-Spread OFDM and residual multi-path interference (MPI) is eliminated with eliminating the ISI and adding the extended CP. Hereinafter, in the description of the third exemplary embodiment of the present invention, only differences with the first exemplary embodiment of the present invention will be described. 
       FIG. 9  is a block diagram illustrating a configuration of a receiver in accordance with the third exemplary embodiment of the present invention. In the third exemplary embodiment of the present invention, the demodulation is performed decreasing the impacts of ISI, ICI, and residual MPI under an environment where a spread of delay of a multipath communication line exceeds a CP length. The third exemplary embodiment of the present invention will be described citing as an example a case in which DFT-Spread OFDM is used as a transmission system and two receiving antennas are used. 
     A receiver  50  in accordance with the third exemplary embodiment of the present invention includes, in addition to the configurations described in  FIG. 1 , a residual MPI elimination unit  501 , an IDFT  502 , a DFT  503 , and a residual MPI replica generating unit  504 . The configurations with the exception of the residual MPI elimination unit  501 , the IDFT  502 , the DFT  503 , and the residual MPI replica generating unit  504  are the same as those in the first or the second exemplary embodiment of the present invention. 
     An equalization filtering unit  105  equalizes signals by causing synthesis of the signals after the FFT for each receiving antenna according to an equalization weight. The equalization filtering unit  105  outputs the signals after the equalization to the residual MPI elimination unit  501 . It is favorable for DFT-Spread OFDM to use a minimum mean squared error (MMSE) weight as the equalization weight. 
     The residual MPI elimination unit  501  subtracts a residual MPI replica from the signal after the equalization and eliminates residual MPI from the signal after the equalization. The residual MPI elimination unit  501  outputs a signal after the subtraction to the IDFT  502 . 
     The residual MPI means an MPI component passing through the equalization filtering unit  105  with the MPI not completely suppressed. The modulation symbol in the OFDM transmission system is mapped on a subcarrier. Consequently, a subcarrier interval is small relative to the frequency selectivity of a communication path, so that the influence of the residual MPI is negligible. In contrast, in the DFT-Spread OFDM transmission system, the modulation symbols are mapped across a plurality of subcarriers, so that the residual MPI arises in a signal after equalization filtering under the influence of the frequency selectivity of a communication path. 
     The IDFT  502  performs IDFT processing on a signal after equalization with the residual MPI eliminated. The IDFT  502  outputs an IDFT-processed signal to the demodulation unit  106 . 
     The demodulation unit  106  converts the IDFT-processed signal into soft decision information for each bit. The demodulation unit  106  outputs the soft decision information to the decoding unit  107 . 
     The symbol replica generating unit  108  converts soft decision information after the decoding into a soft symbol replica. The symbol replica generating unit  108  outputs the symbol replica to the DFT  503 . 
     The DFT  503  performs DFT processing on the symbol replica and performs subcarrier mapping. The DFT  503  outputs the DFT-processed symbol replica to the IFFT  109  and the residual MPI replica generating unit  504 . 
     The residual MPI replica generating unit  504  generates a channel estimation value after equalization using a channel estimation value output from the channel estimation unit  103  and an equalization weight, and further generates a replica corresponding to a residual component of the MPI that is not suppressed in the equalization filtering unit  105  using the channel estimation value after equalization and the symbol replica. The residual MPI replica generating unit  504  outputs the generated replica to the residual MPI elimination unit  501 . As a method for generating the residual MPI replica, any of various types of methods described in prior art documents is applicable. 
     The IFFT  109  performs IFFT processing on the soft symbol replica and generates an OFDM symbol replica. The OFDM symbol replica is output to the ISI replica generating unit  110  and the extended CP replica generating unit  112 . 
     As described above, according to the third exemplary embodiment of the present invention, in the receiver for DFT-Spread OFDM, it is possible to reduce ISI and ICI that arise under an environment where a spread of delay of the communication path exceeds a CP length. In addition, it is possible to eliminate the residual MPI that cannot be eliminated by equalization filters. 
     Although the generation accuracy of the ISI replica and the extended CP replica is generally reduced due to the influence of the residual MPI, applying the residual MPI elimination according to the third exemplary embodiment of the present invention enables the generation accuracy of the ISI replica and the extended CP replica to improve. The improvement of the generation accuracy of the ISI replica and the extended CP replica also enables the generation accuracy of the residual MPI replica to improve. 
     As mentioned above, the receiver according to the third exemplary embodiment of the present invention performs repetition processing for interference cancellation, by which the receiver can eliminate ISI, ICI, and the residual MPI mutually, and can obtain excellent reception characteristics with a small repeat count. 
     Although the first to third exemplary embodiments of the present invention has been described using the configuration, as an example, in which the extended CP addition unit  102  is disposed in a stage following the ISI elimination unit  101 , the extended CP addition unit  102  may be disposed in a stage preceding the ISI elimination unit  101 . 
     Although the first to third exemplary embodiments of the present invention has been described using the receiver, as an example, which is assumed to have a single transmission antenna, those exemplary embodiments are also applicable to an example of a receiver assumed to have two or more transmission antennas. 
     Any of the receivers according to the first to third exemplary embodiments of the present invention is applicable to a base station apparatus, a communication terminal device, a radio relaying apparatus, and a radio router. 
     Although the examples of the OFDM transmission system have been described in the above description, the exemplary embodiments are applicable to any system as long as it is a multipath transmission system using a cyclic prefix. The exemplary embodiments may be applied to a single-carrier radio communication system using a cyclic prefix, particularly to a single carrier frequency division multiplexing system, for example. 
     Each configuration of the receiver according to the present invention can be implemented by software or hardware such as an application specific integrated circuit (ASIC). A part of the processing may be implemented by software, and the other part may be implemented by hardware. When the processing is implemented by software, a computer system including one or a plurality of central processing units (CPUs) such as a microprocessor is made to execute the programs to process functional blocks. These programs are stored using various types of non-transitory computer readable media and can be supplied to a computer. The non-transitory computer readable media include various types of tangible storage media. The examples of the non-transitory computer readable medium include a magnetic recording medium (e.g. a flexible disk, a magnetic tape, and a hard disk drive), a magneto-optical recording medium (e.g. a magneto-optical disk), a CD-ROM (Compact Disc Read Only Memory), a CD-R, a CD-R/W, a DVD-ROM (Digital Versatile Disc Read Only Memory), a DVD-R (DVD Recordable), a DVD-R DL (DVD-R Dual Layer), a DVD-RW (DVD ReWritable), a DVD-RAM, a DVD+R, a DVR+R DL, a DVD+RW, a BD-R (Blu-ray (registered trademark) Disc Recordable), a BD-RE (Blu-ray Disc Rewritable), a BD-ROM, and a semiconductor memory (e.g. a mask ROM, a PROM (Programmable ROM), an EPROM (Erasable PROM), a flash ROM, and a RAM (random access memory). The programs may be supplied to the computer by using various types of transitory computer readable media. The examples of the transitory computer readable medium include electrical signals, optical signals, and electromagnetic waves. The transitory computer readable medium can supply the programs to the computer through a wired communication path such as an electrical wire and an optical fiber, or a wireless communication path. 
     INDUSTRIAL APPLICABILITY 
     The present invention is favorably applicable to any of the receivers and methods for the OFDM-based transmission system. 
     While the invention has been particularly shown and described with reference to exemplary embodiments thereof, the invention is not limited to these embodiments. It will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the claims. 
     This application is based upon and claims the benefit of priority from Japanese patent application No. 2014-134112, filed on Jun. 30, 2014, the disclosure of which is incorporated herein in its entirety by reference. 
     REFERENCE SIGNS LIST 
     
         
         
           
               100  Radio receiving unit 
               101  ISI elimination unit 
               102  Extended CP addition unit 
               103  FFT window timing determination unit 
               104 - 1 ,  104 - 2  FFT 
               105  Equalization filtering unit 
               106  Demodulation unit 
               107  Decoding unit 
               108  Symbol replica generating unit 
               109  IFFT 
               110  ISI replica generating unit 
               111  CP interval-outside channel estimation value selection unit 
               112  Extended CP replica generating unit 
               113  Channel estimation unit 
               201  OFDM symbol replica end elimination unit 
               202  Channel convolution multiplying unit 
               203  Extended CP replica selection unit 
               204  Extended CP replica shift unit 
               301  OFDM symbol replica after IFFT 
               302  OFDM symbol replica after end elimination 
               401  Channel multiplication unit 
               402  Extended CP replica selection unit 
               403  Extended CP replica shift unit 
               404  Path addition unit 
               501  Residual MPI elimination unit 
               502  IDFT 
               503  DFT 
               504  Residual MPI replica generating unit