Patent Publication Number: US-8121234-B2

Title: Multi-dimensional detector for receiver of MIMO system

Description:
TECHNICAL FIELD 
     The present invention relates to a multi-dimensional detector for a receiver of a Multiple Input Multiple Output (MIMO) system, and a method thereof; and, more particularly, to a multi-dimensional detector for a receiver of an MIMO system and a method thereof, which uses multiple dimensions of a received signal when each of symbols is demodulated at a receiver of an orthogonal frequency division multiplexing (OFDM) MIMO system in order to improve performance while reducing hardware complexity. 
     This work was supported by the IT R&amp;D program of MIC/IITA [2006-S-002-02, “IMT-Advanced Radio Transmission Technology with Low Mobility”]. 
     BACKGROUND ART 
     Current wireless communication system requires transmission of a high-volume and high-quality multimedia data through limited frequency. As a method for transmitting high-volume data using limited frequency, a Multiple Input and Multiple Output (MIMO) system was introduced. The MIMO system forms a plurality of independent fading channels using multiple antennas at receiving and transmitting ends and transmits different signals through each of multiple transmission antennas, thereby significantly increasing a data transmission rate. Accordingly, the MIMO system can transmit a great deal of data without expansion of a frequency. 
     However, the MIMO system has a shortcoming that the MIMO system is weak to inter-symbol interference (ISI) and frequency selective fading. In order to overcome the shortcoming, an Orthogonal Frequency Division Multiplexing (OFDM) scheme was used. OFDM scheme is the most proper modulation scheme for transmitting data at a high speed. The OFDM scheme transmits one data sequence through a subcarrier having a low data transmission rate. 
     A channel environment for wireless communication has multiple paths due to obstacles such as a building. In a wireless channel environment having multi-paths, delay spread occurs due to the multiple paths. If delay spray time is longer than a symbol transmission interval, inter-symbol interference (ISI) is caused. In this case, frequency selective fading occurs in a frequency domain. In case of using a single carrier, an equalizer is used to remove the ISI. However, complexity of the equalizer increases as a data transmission rate increases. 
     The shortcomings of the MIMO system can be attenuated using an Orthogonal Frequency Division Multiplexing (OFDM) technology. In order to overcome the shortcomings of the MIMO system while maintaining the advantages of the MIMO system, an OFDM technology was applied to an MIMO system having N transmission antennas and M reception antennas. That is, an MIMO-OFDM system was introduced. 
       FIGS. 1A and 1B  are block diagrams schematically illustrating an MIMO OFDM system.  FIG. 1A  is a block diagram of a transmitting part in the MIMO-OFDM system, and  FIG. 1B  is a block diagram of a receiving part in the MIMO-OFDM system. 
     Referring to  FIG. 1A , the transmitting part includes a serial-to-parallel (S/P) converter  101 , a plurality of encoders  102 , a plurality of Quadrature Amplitude Modulation (QAM) mappers  103 , a plurality of inverse fast Fourier transform (IFFT) units  104 , a plurality of cyclic prefix (CP) adders  105 , and digital-to-analog converter (DAC) and radio frequency (RF) units  106 . The S/P converter  101  divides transmission data into a plurality of data sequences before encoding the transmission data. The encoders  102  encode the data sequences, respectively. After encoding, the QAM mappers  103  modulate the encoded data sequences based on a predetermined modulation scheme such as Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), 16 QAM, and 64 QAM. The IFFT units  104  transform the modulated symbols into time domain signals, respectively. The CP adders  105  insert a CP code for a guard interval into the time domain signals. Then, the DAC &amp; RF unit  106  converts the CP inserted digital signals to analog signals and convert the analog signals to RF signals. The RF signals are transmitted through an antenna. 
     Referring to  FIG. 1B , the receiving part includes a plurality of analog-to-digital converter (ADC) and radio frequency (RF) units  107 , a plurality of CP removers  108 , a plurality of Fast Fourier Transform (FFT) units  109 , an MIMO receiver, a plurality of decoders  111 , and a P/S converter  112 . The ADC &amp; RF units  107  convert RF signals to analog signals and convert the analog signals to digital signals. The CP removers  108  remove CP codes which were inserted for a guard interval and transfer the CP code removed signals to the FFT units  109 . The FFT units  109  perform FFT on the input parallel signals which are the CP removed signals. The MIMO receiver  110  estimates transmission data symbols which are generated by FFT. The MIMO receiver  110  calculates a log likelihood ratio (LLR) from the estimated symbols. The decoders  111  decode data sequences transferred from the MIMO receiver  110  and estimate the transmission data, respectively. The P/S converters  112  convert parallel data modulated by each decoder  111  into serial data. 
     The MIMO receiver  110  generally uses a decision feedback equalizer (DFE), zero forcing (ZF), minimum mean square error estimation (MMSE), and bell labs layered space-time (BLAST). As described above, the MIMO receiver has a problem of low performance although the MIMO receiver has a comparative simple structure compared to maximum likelihood detection (MLD). 
     DISCLOSURE 
     Technical Problem 
     An embodiment of the present invention is directed to providing a multi-dimensional detector for a receiver of a multiple input multiple output (MIMO) system and a method thereof, which uses multiple dimensions of a received signal when each of symbols is demodulated at a receiver of an Orthogonal Frequency Division Multiplexing (OFDM) MIMO system in order to improve performance while reducing hardware complexity. 
     Other objects and advantages of the present invention can be understood by the following description, and become apparent with references to the embodiments of the present invention. Also, it is obvious to those skilled in the art of the present invention that the objects and advantages of the present invention can be realized by the unit as claimed and combinations thereof. 
     Technical Solution 
     In accordance with an aspect of the present invention, there is provided a multi-dimensional detector for a receiver of a Multiple Input Multiple Output (MIMO) system, including: a first symbol detecting unit for calculating symbol distance values using an upper triangular matrix (R) obtained from QR decomposition to detect an m th  symbol; a symbol deciding unit for deciding a symbol having a minimum distance value among the calculated symbol distance values from the first symbol detecting unit; and a second symbol detecting unit for calculating symbol distance values using an updated received signal y and the upper triangular matrix R to detect a (m−1) th  symbol. 
     The multi-dimensional detector may further include a column removing and y updating unit for removing an m th  column of an upper triangular matrix R from the decided m th  symbol, and updating the received signal y, and providing the column removed upper triangular matrix R and the updated received signal y to the second symbol detecting unit. 
     The multi-dimensional detector may further include: a first log likelihood ratio calculating unit for calculating a first log likelihood ratio using the symbol distance values outputted from the first symbol detecting unit; and a second log likelihood ratio calculating unit for calculating a second log likelihood ratio using the symbol distance values outputted from the second symbol detecting unit. 
     In accordance with another aspect of the present invention, there is provide a multiple detecting method for a receiver of a multiple input multiple output. (MIMO) system, including: calculating symbol distance values using an upper triangular matrix R obtained from QR decomposition to detect an m th  symbol; deciding a symbol having a minimum distance value among the calculated symbol distance values; and calculating symbol distance values using an updated received signal y and the upper triangular matrix R to detect a (m−1) th  symbol. 
     In accordance with still another embodiment of the present invention, there is provided a receiver of a Multiple Input Multiple Output (MIMO) system, including: a QR decomposing unit for decomposing a received signal to an unitary matrix Q and an upper triangular matrix R; and a multi-dimensional detecting unit for deciding an m th  symbol and a (m−1) th  symbol through multi-dimensional detection for the output of the QR decomposing unit, wherein the multi-dimensional detecting unit includes: a first symbol detecting unit for calculating symbol distance values using an upper triangular matrix (R) obtained from QR decomposition to detect an m th  symbol; a symbol deciding unit for deciding a symbol having a minimum distance value among the calculated symbol distance values from the first symbol detecting unit; and a second symbol detecting unit for calculating symbol distance values using an updated received signal y and the upper triangular matrix R to detect a (m−1) th  symbol. 
     Advantageous Effects 
     A multi-dimensional detector for a receiver of an MIMO system and a method thereof according to the present invention uses multiple dimensions of a received signal when each of symbols is demodulated at a receiver of an OFDM MIMO system. Therefore, performance can be improved while reducing hardware complexity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIGS. 1A and 1B  are schematic block diagrams illustrating an Orthogonal Frequency Division Multiplexing (OFDM) Multiple Input Multiple Output (MIMO) system. 
         FIG. 2  is a block diagram illustrating a transmitter of an OFDM MIMO system to which the present invention is applied. 
         FIG. 3  is a block diagram illustrating a receiver of an OFDM MIMO system to which the present invention is applied. 
         FIG. 4  is a block diagram illustrating a multi-dimensional detector in accordance with an embodiment of the present invention. 
         FIG. 5  is a block diagram illustrating an 8 th  symbol detector in accordance with an embodiment of the present invention. 
         FIG. 6  is a block diagram illustrating a symbol hard decision unit and a symbol distance calculator in accordance with an embodiment of the present invention. 
         FIG. 7  is a block diagram illustrating a hard decision unit in accordance with an embodiment of the present invention. 
         FIGS. 8A and 8B  illustrate a symbol structure having a typical lattice point. 
     
    
    
     BEST MODE FOR THE INVENTION 
     The advantages, features and aspects of the invention will become apparent from the following description of the embodiments with reference to the accompanying drawings, which is set forth hereinafter. 
       FIG. 2  is a block diagram illustrating a transmitter of an MIMO-OFDM system to which the present invention is applied. 
     Referring to  FIG. 2 , the transmitter includes a serial to parallel converter, a plurality of encoders  201 , a plurality of Inverse Fast Fourier Transform (IFFT) units  203 , a plurality of cyclic prefix (CP) adders  204 , and a plurality of digital-to-analog converter (DAC) &amp; radio frequency (RF) units  205 . The transmitter receives data from a transmission antenna. The S/P converter converts the received data to parallel data sequences and outputs the parallel data sequences to the g encoders  201  where g is an integer number. Each of the g encoders  201  is connected to q QAM mappers  202 , respectively. Each of the QAM mappers  202  may have a different channel coding rate and modulation scheme. 
     The QAM mappers  202  are sequentially connected to the IFFT units  203 , the CP adders  204 , and the DAC &amp; RF units  205 , respectively. Since the operations of the QAM mappers  202 , the IFFT units  203 , the CP adders  204 , and the DAC and RF units  205  are identical to the constituent elements shown in  FIG. 1A , the detailed descriptions: on them will be omitted herein. 
       FIG. 3  is a block diagram illustrating a receiver of an OFDM MIMO system where the present invention applied to. 
     Referring to  FIG. 3 , the receiver includes a plurality of analog digital converter (ADC) &amp; radio frequency (RF) units  301 , a plurality of cyclic prefix (CP) removers  302 , a plurality of Fast Fourier Transform (FFT) units  303 , an MIMO receiver and decoder  304 , and a parallel-to-serial (P/S) converter. The ADC &amp; RF units  301  convert a radio frequency (RF) signal to an analog signal and convert the analog signal to a digital signal. The CP removers  302  remove a cyclic prefix (CP) code which is inserted for a guard interval. The FFT units  303  perform FFT on the CP removed parallel signal. 
     The MIMO receiver and decoder  304  are a multi-dimensional receiver and decoder that demodulate the received symbols from the FFT units  303 . 
     If it is assumed that the receiver includes M transmission antennas and N receipt antennas, a received signal vector z can be expressed as Eq. 1 in a sub carrier after FFT.
 
 z=Hs+n   Eq. 1
 
     In Eq. 1, the received signal vector Z can be expressed as 
               z   =     [           z   1               z   2             ⋮             z   N           ]       ,         
a channel H can be expressed as
 
               H   =     [           h     1   ,   1             h     1   ,   2           …         h     1   ,   M                 h     2   ,   1             h     2   ,   2           …         h     2   ,   M               ⋮       ⋮       ⋱       ⋮             h     N   ,   1             h     N   ,   2           …         h     N   ,   M             ]       ,         
and a transmission symbol s can be expressed as
 
     
       
         
           
             S 
             = 
             
               
                 [ 
                 
                   
                     
                       
                         S 
                         1 
                       
                     
                   
                   
                     
                       
                         S 
                         2 
                       
                     
                   
                   
                     
                       ⋮ 
                     
                   
                   
                     
                       
                         S 
                         M 
                       
                     
                   
                 
                 ] 
               
               . 
             
           
         
       
     
     The channel H can be expressed as H=QR after QR decomposition. Here, R denotes an upper triangular matrix. Since the MIMO system includes N antennas for receiving a signal and M antennas for transmitting a signal, the upper triangular matrix R can be expressed as follow. 
     
       
         
           
             R 
             = 
             
               
                 
                   Q 
                   H 
                 
                 ⁢ 
                 H 
               
               = 
               
                 [ 
                 
                   
                     
                       
                         r 
                         
                           1 
                           , 
                           1 
                         
                       
                     
                     
                       
                         r 
                         
                           1 
                           , 
                           2 
                         
                       
                     
                     
                       … 
                     
                     
                       
                         r 
                         
                           1 
                           , 
                           M 
                         
                       
                     
                   
                   
                     
                       0 
                     
                     
                       
                         r 
                         
                           2 
                           , 
                           2 
                         
                       
                     
                     
                       … 
                     
                     
                       
                         r 
                         
                           2 
                           , 
                           M 
                         
                       
                     
                   
                   
                     
                       ⋮ 
                     
                     
                       ⋮ 
                     
                     
                       ⋱ 
                     
                     
                       ⋮ 
                     
                   
                   
                     
                       0 
                     
                     
                       0 
                     
                     
                       … 
                     
                     
                       
                         r 
                         
                           M 
                           , 
                           M 
                         
                       
                     
                   
                   
                     
                       0 
                     
                     
                       0 
                     
                     
                       … 
                     
                     
                       0 
                     
                   
                   
                     
                       ⋮ 
                     
                     
                       ⋮ 
                     
                     
                       ⋱ 
                     
                     
                       ⋮ 
                     
                   
                   
                     
                       0 
                     
                     
                       0 
                     
                     
                       … 
                     
                     
                       
                         0 
                         
                           N 
                           , 
                           M 
                         
                       
                     
                   
                 
                 ] 
               
             
           
         
       
     
     Q denotes a Unitary matrix (Q H Q=I). Since the channel matrix H is N×M, the unitary matrix Q is N×N and the upper triangular matrix R is N×M. The unitary matrix Q can be expressed as follow. 
     
       
         
           
             Q 
             = 
             
               
                 [ 
                 
                   
                     
                       
                         q 
                         
                           1 
                           , 
                           1 
                         
                       
                     
                     
                       
                         q 
                         
                           1 
                           , 
                           2 
                         
                       
                     
                     
                       
                         q 
                         
                           1 
                           , 
                           3 
                         
                       
                     
                     
                       
                         q 
                         
                           1 
                           , 
                           4 
                         
                       
                     
                     
                       … 
                     
                     
                       
                         q 
                         
                           1 
                           , 
                           N 
                         
                       
                     
                   
                   
                     
                       
                         q 
                         
                           2 
                           , 
                           1 
                         
                       
                     
                     
                       
                         q 
                         
                           2 
                           , 
                           2 
                         
                       
                     
                     
                       
                         q 
                         
                           2 
                           , 
                           3 
                         
                       
                     
                     
                       
                         q 
                         
                           2 
                           , 
                           4 
                         
                       
                     
                     
                       … 
                     
                     
                       
                         q 
                         
                           2 
                           , 
                           N 
                         
                       
                     
                   
                   
                     
                       
                         q 
                         
                           3 
                           , 
                           1 
                         
                       
                     
                     
                       
                         q 
                         
                           3 
                           , 
                           2 
                         
                       
                     
                     
                       
                         q 
                         
                           3 
                           , 
                           3 
                         
                       
                     
                     
                       
                         q 
                         
                           3 
                           , 
                           4 
                         
                       
                     
                     
                       … 
                     
                     
                       
                         q 
                         
                           3 
                           , 
                           N 
                         
                       
                     
                   
                   
                     
                       
                         q 
                         
                           4 
                           , 
                           1 
                         
                       
                     
                     
                       
                         q 
                         
                           4 
                           , 
                           2 
                         
                       
                     
                     
                       
                         q 
                         
                           4 
                           , 
                           3 
                         
                       
                     
                     
                       
                         q 
                         
                           4 
                           , 
                           4 
                         
                       
                     
                     
                       … 
                     
                     
                       
                         q 
                         
                           4 
                           , 
                           N 
                         
                       
                     
                   
                   
                     
                       ⋮ 
                     
                     
                       ⋮ 
                     
                     
                       ⋮ 
                     
                     
                       ⋮ 
                     
                     
                       ⋱ 
                     
                     
                       ⋮ 
                     
                   
                   
                     
                       
                         q 
                         
                           N 
                           , 
                           1 
                         
                       
                     
                     
                       
                         q 
                         
                           N 
                           , 
                           2 
                         
                       
                     
                     
                       
                         q 
                         
                           N 
                           , 
                           3 
                         
                       
                     
                     
                       
                         q 
                         
                           N 
                           , 
                           4 
                         
                       
                     
                     
                       … 
                     
                     
                       
                         q 
                         
                           N 
                           , 
                           N 
                         
                       
                     
                   
                 
                 ] 
               
               . 
             
           
         
       
     
     After QR decomposition, a received signal can be expressed as Eq. 2. 
     
       
         
           
             
               
                 
                   y 
                   = 
                   
                     
                       
                         [ 
                         
                           
                             
                               
                                 y 
                                 1 
                               
                             
                           
                           
                             
                               
                                 y 
                                 2 
                               
                             
                           
                           
                             
                               ⋮ 
                             
                           
                           
                             
                               
                                 y 
                                 N 
                               
                             
                           
                         
                         ] 
                       
                       ⁢ 
                       
                         Q 
                         H 
                       
                       ⁢ 
                       z 
                     
                     = 
                     
                       
                         Rs 
                         + 
                         
                           n 
                           ′ 
                         
                       
                       = 
                       
                         
                           
                             [ 
                             
                               
                                 
                                   
                                     r 
                                     
                                       1 
                                       , 
                                       1 
                                     
                                   
                                 
                                 
                                   
                                     r 
                                     
                                       1 
                                       , 
                                       2 
                                     
                                   
                                 
                                 
                                   … 
                                 
                                 
                                   
                                     r 
                                     
                                       1 
                                       , 
                                       M 
                                     
                                   
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   
                                     r 
                                     22 
                                   
                                 
                                 
                                   … 
                                 
                                 
                                   
                                     r 
                                     
                                       2 
                                       , 
                                       M 
                                     
                                   
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   ⋮ 
                                 
                                 
                                   ⋱ 
                                 
                                 
                                   ⋮ 
                                 
                               
                               
                                 
                                   0 
                                 
                                 
                                   … 
                                 
                                 
                                   0 
                                 
                                 
                                   
                                     r 
                                     
                                       N 
                                       , 
                                       M 
                                     
                                   
                                 
                               
                             
                             ] 
                           
                           ⁡ 
                           
                             [ 
                             
                               
                                 
                                   
                                     s 
                                     1 
                                   
                                 
                               
                               
                                 
                                   
                                     s 
                                     2 
                                   
                                 
                               
                               
                                 
                                   ⋮ 
                                 
                               
                               
                                 
                                   
                                     s 
                                     M 
                                   
                                 
                               
                             
                             ] 
                           
                         
                         + 
                         
                           [ 
                           
                             
                               
                                 
                                   n 
                                   1 
                                   ′ 
                                 
                               
                             
                             
                               
                                 
                                   n 
                                   2 
                                   ′ 
                                 
                               
                             
                             
                               
                                 ⋮ 
                               
                             
                             
                               
                                 
                                   n 
                                   N 
                                   ′ 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
           
         
       
     
     Eq. 2 can be simplified as follow. 
     
       
         
           
             y 
             = 
             
               
                 
                   [ 
                   
                     
                       
                         
                           y 
                           1 
                         
                       
                     
                     
                       
                         
                           y 
                           2 
                         
                       
                     
                     
                       
                         ⋮ 
                       
                     
                     
                       
                         
                           y 
                           N 
                         
                       
                     
                   
                   ] 
                 
                 ⁢ 
                 
                   Q 
                   H 
                 
                 ⁢ 
                 z 
               
               = 
               
                 
                   Rs 
                   + 
                   
                     n 
                     ′ 
                   
                 
                 = 
                 
                   
                     
                       [ 
                       
                         
                           
                             
                               r 
                               
                                 1 
                                 , 
                                 1 
                               
                             
                           
                           
                             
                               r 
                               
                                 1 
                                 , 
                                 2 
                               
                             
                           
                           
                             … 
                           
                           
                             
                               r 
                               
                                 1 
                                 , 
                                 M 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             
                               r 
                               22 
                             
                           
                           
                             … 
                           
                           
                             
                               r 
                               
                                 2 
                                 , 
                                 M 
                               
                             
                           
                         
                         
                           
                             0 
                           
                           
                             ⋮ 
                           
                           
                             ⋱ 
                           
                           
                             ⋮ 
                           
                         
                         
                           
                             0 
                           
                           
                             … 
                           
                           
                             0 
                           
                           
                             
                               r 
                               
                                 M 
                                 , 
                                 M 
                               
                             
                           
                         
                       
                       ] 
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             
                               s 
                               1 
                             
                           
                         
                         
                           
                             
                               s 
                               2 
                             
                           
                         
                         
                           
                             ⋮ 
                           
                         
                         
                           
                             
                               s 
                               M 
                             
                           
                         
                       
                       ] 
                     
                   
                   + 
                   
                     [ 
                     
                       
                         
                           
                             n 
                             1 
                             ′ 
                           
                         
                       
                       
                         
                           
                             n 
                             2 
                             ′ 
                           
                         
                       
                       
                         
                           ⋮ 
                         
                       
                       
                         
                           
                             n 
                             M 
                             ′ 
                           
                         
                       
                     
                     ] 
                   
                 
               
             
           
         
       
     
     The MIMO receiver according to the present embodiment includes a QR decomposition unit, a multi-dimensional detector (MDD), an inverse matrix and weight calculator, an interference remover, and a weight zero forcing (WZF) unit. 
     The QR decomposition unit calculates the unitary matrix Q, the upper triangular matrix R, and a vector size (norm) from the received signal vector z during a long training field (LTF) period. The QR decomposition unit stores the calculated unitary matrix Q and the upper triangular matrix R, vector sizes (norm) for each element of the unitary matrix Q. Here, the norm i  is equivalent to ∥q i ∥ 2 . 
     A signal field detector performs detection for a signal field from an output vector of the QR decomposing unit in a SIG interval. The inverse matrix and weight calculator calculates an inverse matrix of the upper triangular matrix R during first two symbol intervals among symbols for receiving data symbols using the calculated upper triangular matrix R and the vector size (1/√{square root over (norm)}. The multi-dimensional detector MDD calculates a log likelihood ratio (LLR) through multiple detections using the output vector y and the upper triangular matrix value of the QR decomposition. The calculated LLR value is inputted to a channel decoder, and used to demodulate the signal. 
     The interference remover receives the data stream demodulated by the channel decoder, generates symbols corresponding to a data stream demodulated through symbol mapping, and removes interference from the output vector, which is the QR decomposition result, using the generated symbol. The WZF unit performs zero-forcing using the interference removed output vector and the inverse matrix of the upper triangular matrix R. The channel decoder receives the LLR value outputted from the WZF unit and uses the LLR value to demodulate signals. 
       FIG. 4  is a block diagram illustrating a multi-dimensional detector for deciding 7 th  and 8 th  symbols in accordance with an embodiment of the present invention. 
     Referring to  FIG. 4 , The multi-dimensional detector according to the present embodiment includes an 8 th  symbol detector, a symbol decider  402 , an LLR calculator  403 , a column remover and updater  404 , a 7 th  symbol detector  405 , and an LLR calculator  406 . The 8 th  symbol detector  401  calculates distances for a symbol in order to detect the 8 th  symbol using an upper triangular matrix R value of an R memory and the upper triangular matrix value R of the QR decomposition unit symbols which is inputted when an mdd_ene enable signal is in an On state. The described above operation of the 8 th  symbol detector  401  will be described in detail with reference to  FIG. 5 . The LLR calculator  403  calculates a log likelihood ratio (LLR) value using the calculated symbol distances for detecting the 8 th  symbol. 
     The symbol decider  402  decides an 8 th  symbol having a minimum distance among the calculated symbol distances calculated by the 8 th  symbol detector  401 . The column remover and updating unit  404  removes an 8 th  column of the upper triangular matrix R from the determined 8 th  symbol from the symbol determiner  402  and updates a signal y. 
     The 7 th  symbol detector  405  calculates symbol distances for detecting a 7 th  symbol using the updated signal y through the same operations performed for detecting the 8 th  symbol. The LLR calculator  406  calculates a log likelihood ratio (LLR) using the calculated distances by the 7 th  symbol detector  405 . 
       FIG. 5  is a block diagram illustrating an 8 th  symbol detector  401  in accordance with an embodiment of the present invention. 
     Referring to  FIG. 5 , the 8 th  symbol detector  401  includes a symbol generator, a 7 th  symbol hard decision and 8 th  symbol distance calculator  502 , a 6 th  symbol hard decision and 7 th  symbol distance calculator  503 , a 1 st  symbol hard decision and 2 nd  symbol distance calculator  504 , a 1 st  symbol distance calculator  505 , a Y register  506 , a distance accumulator and buffer  507 . The symbol generator  501  generates symbols having lattice points. For example, the symbol generator  501  generates a symbol having 16 lattice points in case of 16 QAM. Therefore, there are 16 distances for a symbol. 
     The 7 th  symbol hard decision and 8 th  symbol distance calculator  502  performs hard decision for a 7 th  symbol for symbols generated from the symbol generator  501  and calculates distance values of a 8 th  symbol in order to detect a 8 th  symbol using an output vector of QR decomposition and an upper triangular matrix R value of a R memory when an enable signal mdd_ene is in an on state. Then, the 7 th  symbol hard decision and 8 th  symbol distance calculator  502  stores the updated signal y to the y register  506  while removing the 8 th  column of the upper triangular matrix R. 
     The 6 th  symbol hard decision and 7 th  symbol distance calculator  503  performs hard decision for a 6 th  symbol generated from the symbol generator  501  and calculates distance values of the 7 th  symbol using the updated y value of the y register  506  and the upper triangular matrix R value of the R memory in order to detect the 8 th  symbol. The distance value accumulator and buffer  507  accumulates the distance values of the 8 th  symbol and the distance values of the 7 th  symbol and stores the accumulated distance values in a register. 
     The 5 th  symbol hard decision and 6 th  symbol distance calculator performs hard decision for a 5 th  symbol generated by the symbol generator  501  using the updated y value of the y register  506  in order to detect the 8 th  symbol and the upper triangular matrix R value in the R memory and calculates distance values of a 6 th  symbol. 
     Then, distances for a 5 th  symbol, distances for a 4 th  symbol, distances for a 3 rd  symbol, distances  504  for a 2 nd  symbol, and distances  505  for a 1 st  symbol are sequentially calculated through the same operations as described above. 
     The distance value accumulator and buffer  507  accumulates distance values of each symbol for detecting the calculated 8 th  symbol and stores the accumulated distance value in a register. The values, stored in the distance value accumulator and buffer  507 , are transferred to the LLR calculator and the symbol decider. 
     A 7 th  symbol detector for detecting a 7 th  symbol has the similar structure of the 8 th  symbol detector shown in  FIG. 5 . However, the 7 th  symbol detector receives a signal y with a 8 th  column of an upper triangular matrix R removed and calculates distance values for detecting a 7 th  symbol. 
     The operations for deciding the 8 th  symbol and the 7 th  symbol will be described as cycle. 
     In {tilde over (y)} 1,8,8,x , a 1 st  subscript denotes cycle, a 2 nd  subscript denotes a symbol number to estimate, and a 3 rd  subscript denotes a number of a signal y vector, and x denotes the number of symbols generated from the symbol generator. 
     For example, the x may be smaller than 4 for QPSK, the x may be smaller than 16 for 16 QAM, and smaller than 64 for 64 QAM. In E 8,8,x , a 1 st  subscript denotes a symbol number to estimate, a 2 nd  subscript denotes the number of vector elements for calculating a distance, and a 3 rd  subscript denotes the number of symbols generated from the symbol generator. In {tilde over (S)} 8,7,x , a 1 st  subscript denotes the number of symbols generated from the symbol generator, a 2 nd  subscript denotes the number of vector elements for hard decision, and a 3 rd  subscript denotes the number of symbols generated from the symbol generator. In one cycle, C denotes constant of Eq. 3. 
     
       
         
           
             
               
                 
                   
                     
                       y 
                       i 
                     
                     = 
                     
                       C 
                       * 
                       
                         y 
                         i 
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       where 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       C 
                     
                     = 
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   
                                     
                                       Q 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       4 
                                       ⁢ 
                                       _POW 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     = 
                                     
                                       0.5 
                                       
                                         1 
                                         / 
                                         
                                           2 
                                         
                                       
                                     
                                   
                                   , 
                                 
                               
                               
                                 
                                   for 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   QPSK 
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       Q 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       16 
                                       ⁢ 
                                       _POW 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     = 
                                     
                                       0.5 
                                       
                                         2 
                                         / 
                                         
                                           10 
                                         
                                       
                                     
                                   
                                   , 
                                 
                               
                               
                                 
                                   for 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   16 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   QAM 
                                 
                               
                             
                             
                               
                                 
                                   
                                     
                                       Q 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       64 
                                       ⁢ 
                                       _POW 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       2 
                                     
                                     = 
                                     
                                       0.5 
                                       
                                         4 
                                         / 
                                         
                                           42 
                                         
                                       
                                     
                                   
                                   , 
                                 
                               
                               
                                 
                                   for 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   64 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   QAM 
                                 
                               
                             
                           
                           ⁢ 
                           
                             
 
                           
                           ⁢ 
                           
                             s 
                             i 
                           
                         
                         = 
                         
                           { 
                           
                             
                               
                                 
                                   
                                     
                                       
                                         ( 
                                         
                                           
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                                         ) 
                                       
                                       + 
                                       
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                                         ⁡ 
                                         
                                           ( 
                                           
                                             
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                                             , 
                                             
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                                           ) 
                                         
                                       
                                     
                                     , 
                                   
                                 
                                 
                                   
                                     for 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     QPSK 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         ( 
                                         
                                           
                                             - 
                                             
                                               3 
                                               4 
                                             
                                           
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                                           ) 
                                         
                                       
                                     
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                                     for 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     16 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     QAM 
                                   
                                 
                               
                               
                                 
                                   
                                     
                                       
                                         ( 
                                         
                                           
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                                         ) 
                                       
                                       + 
                                       
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                                         ⁡ 
                                         
                                           ( 
                                           
                                             
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                                                 8 
                                               
                                             
                                             , 
                                             
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                                             , 
                                             
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                                                 3 
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                                             , 
                                             
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                                                 1 
                                                 8 
                                               
                                             
                                             , 
                                             
                                               7 
                                               8 
                                             
                                             , 
                                             
                                               5 
                                               8 
                                             
                                             , 
                                             
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                                             , 
                                             
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                                           ) 
                                         
                                       
                                     
                                     , 
                                   
                                 
                                 
                                   
                                     for 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     64 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     QAM 
                                   
                                 
                               
                             
                             ⁢ 
                             
                               
 
                             
                             ⁢ 
                             
                               
                                 
                                   
                                     
                                       y 
                                       i 
                                     
                                     = 
                                       
                                     ⁢ 
                                     
                                       
                                         y 
                                         i 
                                       
                                       - 
                                       
                                         
                                           r 
                                           
                                             k 
                                             ; 
                                             i 
                                           
                                         
                                         * 
                                         
                                           s 
                                           i 
                                         
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   
                                     = 
                                       
                                     ⁢ 
                                     
                                       
                                         y 
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                                       - 
                                       
                                         
                                           r 
                                           
                                             k 
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                                                           - 
                                                           
                                                             1 
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                                                       j 
                                                       ⁡ 
                                                       
                                                         ( 
                                                         
                                                           
                                                             - 
                                                             
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                                                             1 
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                                                         ) 
                                                       
                                                     
                                                   
                                                   , 
                                                 
                                               
                                               
                                                 
                                                   for 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   QPSK 
                                                 
                                               
                                             
                                             
                                               
                                                 
                                                   
                                                     
                                                       ( 
                                                       
                                                         
                                                           - 
                                                           
                                                             3 
                                                             4 
                                                           
                                                         
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                                                             3 
                                                             4 
                                                           
                                                         
                                                         ) 
                                                       
                                                     
                                                   
                                                   , 
                                                 
                                               
                                               
                                                 
                                                   for 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   16 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   QAM 
                                                 
                                               
                                             
                                             
                                               
                                                 
                                                   
                                                     
                                                       
                                                         ( 
                                                         
                                                           
                                                             
                                                             
                                                             
                                                             - 
                                                             
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                                                             8 
                                                             
                                                             
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                                                             8 
                                                             
                                                             
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                                                             1 
                                                             8 
                                                             
                                                             
                                                             , 
                                                             
                                                             7 
                                                             8 
                                                             
                                                             , 
                                                             
                                                             5 
                                                             8 
                                                             
                                                             , 
                                                             
                                                             3 
                                                             8 
                                                             
                                                             , 
                                                             
                                                             1 
                                                             8 
                                                             
                                                             
                                                             
                                                           
                                                         
                                                         ) 
                                                       
                                                       + 
                                                       
                                                         j 
                                                         ⁡ 
                                                         
                                                           ( 
                                                           
                                                             
                                                             
                                                             
                                                             
                                                             - 
                                                             
                                                             7 
                                                             8 
                                                             
                                                             
                                                             , 
                                                             
                                                             - 
                                                             
                                                             5 
                                                             8 
                                                             
                                                             
                                                             , 
                                                             
                                                             - 
                                                             
                                                             3 
                                                             8 
                                                             
                                                             
                                                             , 
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             
                                                             - 
                                                             
                                                             1 
                                                             8 
                                                             
                                                             
                                                             , 
                                                             
                                                             7 
                                                             8 
                                                             
                                                             , 
                                                             
                                                             5 
                                                             8 
                                                             
                                                             , 
                                                             
                                                             3 
                                                             8 
                                                             
                                                             , 
                                                             
                                                             1 
                                                             8 
                                                             
                                                             
                                                             
                                                             
                                                           
                                                           ) 
                                                         
                                                       
                                                     
                                                     ; 
                                                   
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                 
                                               
                                               
                                                 
                                                   for 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   64 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   QAM 
                                                 
                                               
                                             
                                           
                                         
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     At first, a first cycle for detecting an 8 th  symbol is expressed as Eq. 4.
 
 {tilde over (y)}   1,8,8,x   =Cy   8   −r   8,8   s   8,x  
 
 {tilde over (y)}   1,8,7,x   =Cy   7   −r   7,8   s   8,x  
 
. . .
 
 {tilde over (y)}   1,8,1,x   =Cy   1   −r   1,8   s   8,x  
 
 E   8,8,x   =|{tilde over (y)}   1,8,8,x | 2  
 
 {tilde over (s)}   8,7,x =hard decision( {tilde over (y)}   1,8,7,x   /r   7,7 )  Eq. 4
 
     A 2 nd  cycle for detecting an 8 th  symbol can be expressed as Eq. 5.
 
 {tilde over (y)}   2,8,7,x   ={tilde over (y)}   1,8,7,x   −r   7,7   {tilde over (s)}   8,7,x  
 
 {tilde over (y)}   2,8,6,x   ={tilde over (y)}   1,8,6,x   −r   6,7   {tilde over (s)}   8,7,x  
 
. . .
 
 {tilde over (y)}   2,8,1,x   ={tilde over (y)}   1,8,7,x   −r   1,7   {tilde over (s)}   8,7,x  
 
 E   8,7,x   =E   8,8,x   +|{tilde over (y)}   2,8,7,x | 2  
 
 {tilde over (s)}   8,6,x =hard decision( {tilde over (y)}   2,8,6,x   /r   6,6 )  Eq. 5
 
     Then, a 3 rd  cycle for detecting an 8 th  symbol can be expressed as Eq. 6.
 
 {tilde over (y)}   3,8,6,x   ={tilde over (y)}   2,8,6,x   −r   6,6   {tilde over (s)}   8,6,x  
 
 {tilde over (y)}   3,8,5,x   ={tilde over (y)}   2,8,5,x   −r   5,6   {tilde over (s)}   8,6,x  
 
. . .
 
 {tilde over (y)}   3,8,1,x   ={tilde over (y)}   2,8,1,x   −r   1,6   {tilde over (s)}   8,6,x  
 
 E   8,6,x   =E   8,7,x   +|{tilde over (y)}   3,8,6,x | 2  
 
 {tilde over (s)}   8,5,x =hard decision( {tilde over (y)}   3,8,5,x   /r   5,5 )  Eq. 6
 
     The same operations are repeated from a 4 th  cycle to a 7 th  cycle. Then, an 8 th  cycle is expressed as Eq. 7.
 
 {tilde over (y)}   8,8,1,x   ={tilde over (y)}   7,8,1,x   −r   1,1   {tilde over (s)}   8,1,x  
 
 E   8,1,x   =E   8,2,x   +|{tilde over (y)}   8,8,1,x | 2   Eq. 7
 
     After calculating distance values of each vector element for detecting the 8 th  symbol through the 8 cycles, a symbol having the minimum value among the calculated distance values is detected as the 8 th  symbol in the 9 th  cycle like Eq. 8.
 
min( D   8,1,x )=&gt; {tilde over (s)}   8   Eq. 8
 
     The LLR of the 8 th  symbol is calculated like Eq. 9 in p=(b 0 b 1 b 2 b 3 ) using the calculated distance values at the 9 th  cycle. In Eq. 9, k denotes a symbol number. For example, k is as 8 in case of a 16 QAM modulation scheme.
 
ρ k   0 =min( E   k,1,0   ,E   k,1,1   ,E   k,1,2   ,E   k,1,3   ,E   k,1,4   ,E   k,1,5   ,E   k,1,6   ,E   k,1,7 )−min( E   k,1,8   ,E   k,1,9   ,E   k,1,10   ,E   k,1,11   ,E   k,1,12   ,E   k,1,13   ,E   k,1,14   ,E   k,1,15 )
 
ρ k   1 =min( E   k,1,0   ,E   k,1,1   ,E   k,1,2   ,E   k,1,3   ,E   k,1,8   ,E   k,1,9   ,E   k,1,10   ,E   k,1,11 )−min( E   k,1,4   ,E   k,1,5   ,E   k,1,6   ,E   k,1,7   ,E   k,1,12   ,E   k,1,13   ,E   k,1,13   ,E   k,1,14   ,E   1,1,15 )
 
ρ k   2 =min( E   k,1,0   ,E   k,1,4   ,E   k,1,8   ,E   k,1,12   ,E   k,1,1   ,E   k,1,5   ,E   k,1,9   ,E   k,1,13 )−min( E   k,1,2   ,E   k,1,6   ,E   k,1,10   ,E   k,1,14   ,E   k,1,3   ,E   k,1,7   ,E   k,1,11   ,E   k,1,15 )
 
ρ k   3 =min( E   k,1,0   ,E   k,1,4   ,E   k,1,8   ,E   k,1,12   ,E   k,1,2   ,E   k,1,6   ,E   k,1,10   ,E   k,1,14 )−min( E   k,1,1   ,E   k,1,5   ,E   k,1,9   ,E   k,1,13   ,E   k,1,3   ,E   k,1,7   ,E   k,1,11   ,E   k,1,15 )  Eq. 9
 
     Then, a 10 th  cycle for detecting a 7 th  symbol is expressed as Eq. 10.
 
 {tilde over (y)}   10,7,7,x   =y   7   −r   7,8   {tilde over (s)}   8,x  
 
 {tilde over (y)}   10,7,6,x   =y   6   −r   6,8   {tilde over (s)}   8,x  
 
. . .
 
 {tilde over (y)}   10,7,1,x   =y   1   −r   1,8   {tilde over (s)}   8,x  
 
 E   7,7,x   =|{tilde over (y)}   10,7,7,x | 2  
 
 {tilde over (s)}   7,6,x =hard decision( {tilde over (y)}   10,7,6,x   /r   6,6 )  Eq. 10
 
     Then, an 11 th  cycle for detecting a 7 th  symbol is expressed as Eq. 11.
 
 {tilde over (y)}   11,7,6,x   ={tilde over (y)}   10,7,6,x   −r   6,6   {tilde over (s)}   7,6,x  
 
 {tilde over (y)}   11,7,5,x   ={tilde over (y)}   10,7,5,x   −r   5,6   {tilde over (s)}   7,6,x  
 
. . .
 
 {tilde over (y)}   11,7,1,x   ={tilde over (y)}   10,7,1,x   −r   1,6   {tilde over (s)}   7,6,x  
 
 E   7,6,x   =E   7,7,x   +|{tilde over (y)}   11,7,6,x | 2  
 
 {tilde over (s)}   7,5,x =hard decision( {tilde over (y)}   11,7,5,x   /r   5,5 )  Eq. 11
 
     The same operations are repeated from a 12 th  cycle to a 15 th  cycle. A 16 th  cycle is expressed like Eq. 12.
 
 {tilde over (y)}   16,7,1,x   ={tilde over (y)}   15,7,1,x   −r   1,1   {tilde over (s)}   7,1,x  
 
 E   7,1,x   =E   7,2,x   +|{tilde over (y)}   16,7,1,x | 2   Eq. 12
 
     In a next 17 th  cycle, an LLR for the 7 th  symbol is calculated like Eq. 13. In Eq. 13, k denotes a symbol number and k is 7 for 16 QAM.
 
ρ k   0 =min( E   k,1,0   ,E   k,1,1   ,E   k,1,2   ,E   k,1,3   ,E   k,1,4   ,E   k,1,5   ,E   k,1,6   ,E   k,1,7 )−min( E   k,1,8   ,E   k,1,9   ,E   k,1,10   ,E   k,1,11   ,E   k,1,12   ,E   k,1,13   ,E   k,1,14   ,E   k,1,15 )
 
ρ k   1 =min( E   k,1,0   ,E   k,1,1   ,E   k,1,2   ,E   k,1,3   ,E   k,1,8   ,E   k,1,9   ,E   k,1,10   ,E   k,1,11 )−min( E   k,1,4   ,E   k,1,5   ,E   k,1,6   ,E   k,1,7   ,E   k,1,12   ,E   k,1,13   ,E   k,1,14   ,E   k,1,15 )
 
ρ k   2 =min( E   k,1,0   ,E   k,1,4   ,E   k,1,8   ,E   k,1,12   ,E   k,1,1   ,E   k,1,5   ,E   k,1,9   ,E   k,1,13 )−min( E   k,1,2   ,E   k,1,6   ,E   k,1,10   ,E   k,1,14   ,E   k,1,3   ,E   k,1,7   ,E   k,1,11   ,E   k,1,15 )
 
ρ k   3 =min( E   k,1,0   ,E   k,1,4   ,E   k,1,8   ,E   k,1,12   ,E   k,1,2   ,E   k,1,6   ,E   k,1,10   ,E   k,1,14 )−min( E   k,1,1   ,E   k,1,5   ,E   k,1,9   E   k,1,13   ,E   k,1,3   ,E   k,1,7   ,E   k,1,11   ,E   k,1,15 )  Eq. 13
 
     In the symbol hard decision and symbol distance calculation, a multiplier is needed for multiplying symbols generated from the symbol generator with elements of the upper triangular matrix R. If the multiplier is used, computation complexity and hardware complexity will increase. 
     If one of constants introduced in Eq. 3 is multiplied with a received signal according to a modulation scheme, the symbol generator outputs symbols as shown in Eq. 3. In order to overcome the increment of hardware and computation complexity, shifters and adders are used in the present embodiment instead of using the multiplier for multiplying the symbols generated by the symbol generator with the elements of the upper triangular matrix R. 
     If the shifters and the adders are used, hardware complexity may be significantly reduced. For example, according to the present invention, ⅝ is equivalent to 4/8+⅛, and r*(⅝) is equivalent to a sum of a result of shifting r once to right and a result of shifting r three times to right. 
       FIG. 6  is a diagram illustrating a symbol hard decision unit and a symbol distance value: calculator using shifters and adders in accordance with an embodiment of the present invention. 
     That is,  FIG. 6  shows a structure of a 6 th  symbol hard decision and 7 th  symbol distance calculator for detecting an 8 th  symbol in accordance with an embodiment of the present invention. 
     Referring to  FIG. 6 , the symbol generator generates a real symbol and an imaginary symbol according to a modulation scheme such as QPSK, 16 QAM, and 64 QAM. The symbols generated by the symbol generator are used to update a vector of a received signal y by shifting and adding output values of an R memory. 
     The 6 th  symbol hard decision and 7 th  symbol distance calculator according to the present embodiment includes a shifting and adding unit  601 , a multiplexer  602 , an adder  603 , a squaring unit  604 , and a subtractor  605 . The shifting and adding unit  601  shifts an inputted upper triangular matrix R as many as symbols generated by the symbol generator and adds them. One of the outputs of the shifting and adding unit  601  is selected by the multiplexer  602  according to the hard decision result of a 7 th  symbol of a previous cycle. 
     The subtractor  603  subtracts the selected output from the multiplexer  602  from the received signal y updated at a previous cycle, thereby outputting a newly updated received signal y. The outputted received signal y from the subtractor  603  is squared in a calculator  604 , the squared value is accumulated with a distance value of a 8 th  symbol of a previous cycle in an adder  605 , and a distance value of a 7 th  symbol is calculated. 
     Then, the hard decision unit  606  performs hard decision for a 6 th  symbol of an upper triangular matrix R. Remaining elements of the upper triangular matrix R are subtracted from the updated received signal y which is calculated at a previous cycle through the shifter, the adder, the multiplexer, and the subtractor. 
       FIG. 7  is a diagram illustrating a hard decision unit in accordance with an embodiment of the present invention. 
     For example, in {tilde over (s)} 8,7,x =hard decision({tilde over (y)} 1,8,7,x /r 7,7 ) for hard decision for a 7 th  symbol value in order to decide a 8 th  symbol value in 64 QAM, an updated received signal must be divided by an element r 7,7  of an upper triangular matrix R. That is, a division operation is required. The division operation increases hardware complexity. 
     In order to avoid the division operation, a simple comparator is used in the present embodiment instead of using a divider. That is, three bits of b 0 , b 1 , and b 2  are decided in a real part and b 3 , b 4 , and b 5  are decided in an imaginary part using the simple comparator.  FIGS. 8A and 8B  show a symbol structure having lattice points different according to a modulation scheme. 
     That is,  FIG. 8A  shows the symbol structure for BPSK, QPSK, and 16 QAM.  FIG. 8B  shows a symbol structure for 64 QAM. In the present embodiment, a hard-decision symbol is decided for bits b 0  b 1  b 2  b 3  b 4  b 5  b 6  by mapping previously decided bits to a symbol structure having lattice points of  FIGS. 8A and 8B . 
     Table 1 shows scaling factors according to a modulation scheme. 
     
       
         
           
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Modulation scheme 
                 Scaling factor 
               
               
                   
                   
               
             
            
               
                   
                 BPSK 
                 1 
               
               
                   
                 QPSK 
                 ½ 
               
               
                   
                 16 QAM 
                 ¼ 
               
               
                   
                 64 QAM 
                 ⅛ 
               
               
                   
                   
               
            
           
         
       
     
     Referring to  FIG. 7 , a bit b 0  is decided through a comparator  701  for comparing a real part of an updated received signal, a bit b 1  is decided through a comparator  704  for comparing a difference  703  between an absolute value  702  of a real part of an updated received signal and a value of r 7,7 /4. For the imaginary part of the updated received signal, bits b 3 , b 3 ′, b 5  are decided through the same operation as described above. 
     The multi-dimensional detector for a receiver of an MIMO system and the method thereof according to the present embodiment were described under an assumption that the MIMO receiver includes eight antennas for receiving and transmitting signals. However, it is obvious that the multi-dimensional detector for a receiver of an MIMO system and the method thereof according to the present embodiment can be identically applied although the MIMO receiver includes the different number of antennas because the number of antennas is parameter of a vector Z or an upper triangular matrix R. 
     The present application contains subject matter related to Korean Patent Application No. 2007-0133323, filed in the Korean Intellectual Property Office on Dec. 18, 2007, the entire contents of which is incorporated herein by reference. 
     The above described method according to the present invention can be embodied as a program and stored on a computer readable recording medium. The computer readable recording medium is any data storage device that can store data which can be thereafter read by the computer system. The computer readable recording medium includes a read-only memory (ROM), a random-access memory (RAM), a CD-ROM, a floppy disk, a hard disk and an optical magnetic disk. 
     While the present invention has been described with respect to the specific embodiments, it will be apparent to those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the following claims.