Abstract:
Disclosed is a method of detecting signals at a receiver of a communication system with a multiple input multiple output antenna. With the signal detection method, a square of the distance between a received signal vector and a channel status-considered transmission symbol vector is calculated first, and the square of the distance is then classified into first and second components. The first component is minimized to calculate a plurality of first soft symbol estimates. A solution set of the first component is calculated on the basis of the plurality of first soft symbol estimates. The second component is minimized to calculate a plurality of second soft symbol estimates. A solution set of the second component is calculated on the basis of the plurality of second soft symbol estimates. A final solution set is calculated by doing the sum of the first component solution set and the second component solution.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims priority to and the benefit of Korean Patent Application Nos. 10-2008-0120726 and 10-2009-0091963 filed in the Korean Intellectual Property Office on Dec. 1, 2008 and Sep. 28, 2009, the entire contents of which are incorporated herein by reference. 
       BACKGROUND OF THE INVENTION 
       [0002]    (a) Field of the Invention 
         [0003]    The present invention relates to a signal detection method, and a receiver. 
         [0004]    (b) Description of the Related Art 
         [0005]    As wireless communication systems are being developed, speed-related requirements are becoming more and more important. In order to satisfy such requirements, it is needed to use a wide frequency bandwidth, but frequency resources are limited. Accordingly, a multiple input, multiple output (MIMO) antenna technology is used in order to transmit larger amounts of data while using the limited frequency bandwidths. 
         [0006]    Among the multiple input multiple output antenna techniques, there are basically a spatial diversity technique where the transmission reliability is enhanced by obtaining diversity profits corresponding to the square of the number of transceiver antennas, and a spatial multiplexing (SM) technique where different data streams are made through different transmission routes. 
         [0007]    With the double spatial multiplexing technique, mutual interference is liable to occur between different data streams, and hence the receiver detects and decodes signals considering the interference. The optimal way is to calculate the likelihood of the respective data bits considering the detection and the decoding simultaneously, but it is difficult to operate in such a way because it involves excessive complexity regarding the dimension of constellations and the number of antennas. 
         [0008]    Accordingly, an iterative detection decoding (IDD) technique where the likelihood of respective bits is calculated in respective cases of detection and decoding, and the calculated results are repeatedly exchanged so as to calculate the final likelihood of the respective bits, has been introduced. However, such a technique also still involves high complexity so that it is difficult to practically realize the desired system. 
         [0009]    The above information disclosed in this Background section is only for enhancement of understanding of the background of the invention and therefore it may contain information that does not form the prior art that is already known in this country to a person of ordinary skill in the art. 
       SUMMARY OF THE INVENTION 
       [0010]    The present invention has been made in an effort to provide a communication system with a multiple input multiple output antenna having advantages of performing signal detection with low complexity. 
         [0011]    An exemplary embodiment of the present invention provides a method of detecting signals at a receiver of a communication system with a multiple input multiple output antenna. With the signal detection method, a square of the distance between a received signal vector and a channel status-considered transmission symbol vector is calculated, and the square of the distance is classified into first and second components. The first component is minimized to calculate a plurality of first soft symbol estimates. A solution set of the first component is calculated on the basis of the plurality of first soft symbol estimates. The second component is minimized to calculate a plurality of second soft symbol estimates. A solution set of the second component is calculated on the basis of the plurality of second soft symbol estimates. A final solution set is calculated by doing the sum of the first component solution set and the second component solution set. 
         [0012]    The step of calculating the first component solution set may include finding a plurality of first points around the plurality of first soft symbol estimates on a constellation, and calculating the first component solution set by using the plurality of first points. 
         [0013]    The step of finding the plurality of first points may include finding a first closest point by rounding with respect to the plurality of first soft symbol estimates, respectively. 
         [0014]    The step of finding the plurality of first points may further include finding a second closest point by adding 2 to the first closest point or subtracting 2 therefrom. 
         [0015]    The step of calculating the second component solution set may include finding a plurality of second points around the plurality of second soft symbol estimates on the constellation, and calculating the second component solution set by using the plurality of second points. 
         [0016]    The step of finding the plurality of second points may include finding a first closest point by rounding with respect to the plurality of second soft symbol estimates, respectively. 
         [0017]    The step of finding the plurality of second points may further include finding a second closest point by adding 2 to the first closest point or subtracting 2 therefrom. 
         [0018]    The signal detection method may further include calculating a point set on the constellation by doing the sum of the plurality of first points and the plurality of second points, and calculating the likelihood of the respective bits of the signals by using the point set and the final solution set. 
         [0019]    The step of calculating the square of the distance may include QR-decomposing the maximum likelihood resolution. 
         [0020]    The step of calculating the square of the distance may include QR-decomposing the augmented channel matrix. 
         [0021]    Another exemplary embodiment of the present invention provides a method of detecting signals at a receiver of a communication system with a multiple input multiple output antenna. With the signal detection method, a square of the distance between a received signal vector and a channel status-considered transmission symbol vector is first calculated, and the square of the distance is classified into first and second components. The first component is minimized to calculate a plurality of first soft symbol estimates. A solution set of the first component is calculated on the basis of the plurality of first soft symbol estimates. A part of the first component solution set is selected, and a plurality of second soft symbol estimates are calculated by using the selected first component solution set. A solution set of the second component is calculated on the basis of the plurality of second soft symbol estimates. A part of the second component solution set is selected, and a final solution set is calculated by doing the sum of the selected first component solution set and the selected second component solution set. 
         [0022]    The step of calculating the first component solution set may include finding a plurality of first points around the plurality of first soft symbol estimates on a constellation, and calculating the first component solution set by using the plurality of first points, while the step of calculating the second component solution set includes finding a plurality of second points around the plurality of second soft symbol estimates on the constellation, and calculating the second component solution set by using the plurality of second points. 
         [0023]    The signal detection method may further include selecting the first point corresponding to the selected first component solution set, selecting the second point corresponding to the selected second component solution set, calculating a point set on the constellation by doing the sum of the selected first point and the selected second point, and calculating the likelihood of the respective bits of the signals by using the point set and the final solution set. 
         [0024]    The step of selecting a part of the first component solution set may include listing elements of the first component solution set in a sequence of from the smallest to the largest and selecting the listed elements sequentially from the smallest, and the step of selecting a part of the second component solution set may include listing elements of the second component solution set in a sequence of from the smallest to the largest and selecting the listed elements sequentially from the smallest. 
         [0025]    The number of the first points and the number of the second points may be 2 or less, respectively. 
         [0026]    The step of finding the plurality of first points may include finding a first closest point by rounding with respect to the plurality of first soft symbol estimates, and finding a second closest point by adding 2 to the first closest point or subtracting 2 therefrom. 
         [0027]    The step of finding the plurality of second points may include finding a first closest point by rounding with respect to the plurality of second soft symbol estimates, respectively, and finding a second closest point by adding 2 to the first closest point or subtracting 2 therefrom. 
         [0028]    Another exemplary embodiment of the present invention provides a receiver for a communication system with a multiple input multiple output antenna. The receiver includes a plurality of receiver antennas for receiving signals, a detector for producing the likelihood of the respective bits of the signals from the receiver antenna and detecting signals, and a decoder for decoding the signals detected from the detector. The likelihood is produced by classifying a square of the distance between a received signal vector and a channel status-considered transmission symbol vector into first and second components, and using a plurality of first soft symbol estimates obtained through minimizing the first component, a plurality of second soft symbol estimates obtained through minimizing the second component, first points around the plurality of first soft symbol estimates on a constellation, and second points around the plurality of second soft symbol estimates on the constellation. 
         [0029]    The plurality of first points may include a first closest point calculated by rounding with respect to the plurality of first soft symbol estimates, respectively. 
         [0030]    The plurality of first points may include a second closest point found by adding 2 to the first closest point or subtracting 2 therefrom. 
         [0031]    With the present invention, a receiver for a communication system with a multiple input multiple output antenna can detect signals, and decode the detected signals at a low complexity. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0032]      FIG. 1  illustrates a wireless communication system according to an exemplary embodiment of the present invention. 
           [0033]      FIG. 2  is a flowchart of a signal detection method according to an exemplary embodiment of the present invention. 
           [0034]      FIG. 3  is a flowchart of a signal detection method according to another exemplary embodiment of the present invention. 
           [0035]      FIG. 4  illustrates a way of listing a solution set with a signal detection method according to another exemplary embodiment of the present invention. 
           [0036]      FIG. 5  illustrates elements of the solution set listed according to the way of  FIG. 4  with a signal detection method according to another exemplary embodiment of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       [0037]    In the following detailed description, only certain exemplary embodiments of the present invention have been shown and described, simply by way of illustration. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. Accordingly, the drawings and description are to be regarded as illustrative in nature and not restrictive. Like reference numerals designate like elements throughout the specification. 
         [0038]    In addition, unless explicitly described to the contrary, the word “comprise” and variations such as “comprises” or “comprising” will be understood to imply the inclusion of stated elements but not the exclusion of any other elements throughout the specification. The terms “-er,” “-or”, and “module” described in the specification mean units for processing at least one function or operation, which can be implemented by hardware components, software components, or combinations thereof. 
         [0039]    In this specification, the mobile station (MS) may refer to a terminal, a mobile terminal (MT), a subscriber station (SS), a portable subscriber station (PSS), user equipment (UE), or an access terminal (AT), and may have the functions of some or all of those referred to. 
         [0040]    In this specification, the base station (BS) may refer to an access point (AP), a radio access station (RAS), a node B (Node B), an evolved node B (eNodeB), a base transceiver station (BTS), or a mobile multihop relay (MMR)-BS, and have the functions of some or all of those referred to. 
         [0041]    A signal detection method and receiver method according to an exemplary embodiment of the present invention will now be described in detail with reference to the accompanying drawings. 
         [0042]      FIG. 1  illustrates a wireless communication system according to an exemplary embodiment of the present invention. 
         [0043]    As shown in  FIG. 1 , the wireless communication system includes a transmitter  100  and a receiver  200 . 
         [0044]    The transmitter  100  includes a plurality of transmitter antennas  110 . The transmitter  100  conducts scrambling, encoding, and modulating with respect to the transmission data, and broadcasts them to the air through the transmitter antennas  110 . 
         [0045]    The receiver  200  includes a plurality of receiver antennas  210 , a detector  220 , and a decoder  230 . The data received through the respective receiver antennas  210  are signal-detected at the detector  220 , and the detected signals are decoded at the decoder  230 . 
         [0046]    The signal detection made at the detector  220  is to produce the likelihood of the bits of the received signals. 
         [0047]    The received signal vector y can be expressed by Equation 1. 
         [0000]        y=Hs+n    (Equation 1) 
         [0048]    In Equation 1, H represents a channel matrix, s represents a transmission symbol vector, and n represents an additive white noise vector. The likelihood L D (x k |y) produced by the detector  220  is expressed by Equation 2. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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         [0049]    In Equation 2, the prior information 
         [0000]    
       
         
           
             
               
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         [0000]    is calculated by using the likelihood of the respective bits received through feedback from the decoder  230 . When no information from the decoder  230  exists, the value of zero which is obtained by substituting 0.5 for the numerator and denominator is used with respect to the respective bits. As very high complexity is required to correctly compute the L E (x k |y) part of Equation 2, such a part is approximated and expressed by Equation 3. 
         [0000]    
       
         
           
             
               
                 
                   
                     
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         [0050]    In Equation 3, x is a vector of the +1 or −1 bits obtained from the transmission symbol vector s. Therefore, with the case of the binary phase shift keying (BPSK), x and s are the same vector. However, in case other constellations are used, x and s are not identical. The respective elements of the vector x have the value of +1 or −1, but the elements of the vector s are given by one point on the constellation. Furthermore, the set X k,+1  being a vector set where the k-th element of the vector x is +1 and other elements thereof involve all possible cases is defined by Equation 4. 
         [0000]        X   k,+1   ={x|x   k =+1 }, X   k,−1   ={x|x   k =−1}  (Equation 4) 
         [0051]    Furthermore, the vector x [k]  is defined by a vector where the k-th element x k  of the vector x is removed, and similarly, L A,[k] expresses a vector of L A  values concerning all the elements of the vector x except for the element x k . The highest complexity is required in computing the given L E (x k |y) to calculate ∥y−Hs∥ 2  with respect to all the vectors x (i.e., s corresponding thereto) belonging to the set X k,+1 . 
         [0052]    A signal detection method, that is, a likelihood calculation method according to an exemplary embodiment of the present invention, will now be described with respect to  FIG. 2  and  FIG. 3 . 
         [0053]      FIG. 2  is a flowchart illustrating a signal detection method according to an exemplary embodiment of the present invention. 
         [0054]    Referring to  FIG. 2 , with a signal detection method according to an exemplary embodiment of the present invention, the maximum likelihood (ML) resolution or the augmented channel matrix {tilde over (H)} is QR-decomposed so as to express ∥y−Rs∥ 2  at the step S 210 . 
         [0055]    The ML resolution is obtained in the following way. 
         [0056]    Assuming that the number of transmitter antennas  110  is four and the data transmission rate is 2, spatio-temporal codes like Equation 5 are considered. 
         [0000]    
       
         
           
             
               
                 
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         [0057]    In case the number of receiver antennas  210  is assumed to be n r , the received signal r is written by Equation 6. 
         [0000]        r=Ĥ+n    (Equation 6) 
         [0058]    In Equation 6, 
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                         4 
                       
                       ″ 
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           1 
                           , 
                           4 
                         
                         ′ 
                       
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           1 
                           , 
                           3 
                         
                         ″ 
                       
                     
                   
                   
                     
                       h 
                       
                         1 
                         , 
                         3 
                       
                       ′ 
                     
                   
                 
                 
                   
                     ⋮ 
                   
                   
                     ⋮ 
                   
                   
                     ⋮ 
                   
                   
                     ⋮ 
                   
                   
                     ⋮ 
                   
                   
                     ⋮ 
                   
                   
                     ⋮ 
                   
                   
                     ⋮ 
                   
                 
                 
                   
                     
                       h 
                       
                         
                           n 
                           r 
                         
                         , 
                         2 
                       
                       ′ 
                     
                   
                   
                     
                       h 
                       
                         
                           n 
                           r 
                         
                         , 
                         2 
                       
                       ″ 
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           
                             n 
                             r 
                           
                           , 
                           1 
                         
                         ′ 
                       
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           
                             n 
                             r 
                           
                           , 
                           1 
                         
                         ″ 
                       
                     
                   
                   
                     
                       h 
                       
                         
                           n 
                           r 
                         
                         , 
                         2 
                       
                       ′ 
                     
                   
                   
                     
                       h 
                       
                         
                           n 
                           r 
                         
                         , 
                         2 
                       
                       ″ 
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           
                             n 
                             r 
                           
                           , 
                           3 
                         
                         ′ 
                       
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           
                             n 
                             r 
                           
                           , 
                           3 
                         
                         ″ 
                       
                     
                   
                 
                 
                   
                     
                       h 
                       
                         
                           n 
                           r 
                         
                         , 
                         2 
                       
                       ″ 
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           
                             n 
                             r 
                           
                           , 
                           2 
                         
                         ′ 
                       
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           
                             n 
                             r 
                           
                           , 
                           1 
                         
                         ″ 
                       
                     
                   
                   
                     
                       h 
                       
                         
                           n 
                           r 
                         
                         , 
                         1 
                       
                       ′ 
                     
                   
                   
                     
                       h 
                       
                         
                           n 
                           r 
                         
                         , 
                         2 
                       
                       ″ 
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           
                             n 
                             r 
                           
                           , 
                           2 
                         
                         ′ 
                       
                     
                   
                   
                     
                       - 
                       
                         h 
                         
                           
                             n 
                             r 
                           
                           , 
                           3 
                         
                         ″ 
                       
                     
                   
                   
                     
                       h 
                       
                         
                           n 
                           r 
                         
                         , 
                         3 
                       
                       ′ 
                     
                   
                 
               
               ] 
             
           
         
       
     
         [0059]    Furthermore, ( )′ and ( )″ represent the real number and the imaginary number parts of the complex number values, and r i   j  represents the received signal at the t-th time slot in the j-th receiver antenna  210 , while h j,i  represents the channel gain ranged from the i-th transmitter antenna to the j-th receiver antenna. And, n i   j  represents the white noise at the t-th slot in the j-th receiver antenna. 
         [0060]    Assuming that the respective transmission symbols g k  are generated from the constellation given as the M 2- quadrature amplitude modulation (QAM), the symbol s k  is generated from the constellation given as the M-pulse amplitude modulation (referred to hereinafter as the “PAM”), which is indicated by C as with Equation 7. 
         [0000]        s   k εC:={−M+ 1 ,−M+ 3 , . . . , − 1 , 1 , . . . , M− 3 ,M− 1 } 
         [0061]    In this case, the maximum ML resolution s ML  is obtained through Equation 8. 
         [0000]    
       
         
           
             
               
                 
                   
                     s 
                     ML 
                   
                   = 
                   
                     arg 
                      
                     
                       
                         min 
                         
                           s 
                           ∈ 
                           
                             C 
                             8 
                           
                         
                       
                        
                       
                         
                           
                              
                             
                               r 
                               - 
                               
                                 
                                   H 
                                   ^ 
                                 
                                  
                                 s 
                               
                             
                              
                           
                           2 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     8 
                   
                   ) 
                 
               
             
           
         
       
     
         [0062]    When the QR decomposition is made with respect to the channel matrix Ĥ, Equation 8 is re-written as Equation 9. 
         [0000]    
       
         
           
             
               
                 
                   
                     s 
                     ML 
                   
                   = 
                   
                     arg 
                      
                     
                       
                         min 
                         
                           s 
                           ∈ 
                           
                             C 
                             8 
                           
                         
                       
                        
                       
                         
                            
                           
                             
                               y 
                               ^ 
                             
                             - 
                             
                               
                                 R 
                                 ^ 
                               
                                
                               s 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     9 
                   
                   ) 
                 
               
             
           
         
       
     
         [0063]    Meanwhile, the augmented channel matrix like Equation 10 is considered, and QR-decomposed. 
         [0000]    
       
         
           
             
               
                 
                   
                     H 
                     ~ 
                   
                   := 
                   
                     
                       [ 
                       
                         
                           
                             
                               H 
                               ^ 
                             
                           
                         
                         
                           
                             
                               
                                 1 
                                 
                                   γ 
                                 
                               
                                
                               
                                 I 
                                 
                                   8 
                                   × 
                                   8 
                                 
                               
                             
                           
                         
                       
                       ] 
                     
                     = 
                     
                       
                         
                           Q 
                           ~ 
                         
                          
                         
                           R 
                           ~ 
                         
                       
                       = 
                       
                         
                           [ 
                           
                             
                               
                                 
                                   
                                     Q 
                                     ~ 
                                   
                                   1 
                                 
                               
                             
                             
                               
                                 
                                   
                                     Q 
                                     ~ 
                                   
                                   2 
                                 
                               
                             
                           
                           ] 
                         
                          
                         
                           R 
                           ~ 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     10 
                   
                   ) 
                 
               
             
           
         
       
     
         [0064]    In Equation 10, {tilde over (Q)} is a unit matrix having a dimension of (4n R +8)×8, and {tilde over (R)} is an upper-triangle matrix having a dimension of 8×8. Furthermore, {tilde over (Q)} 1  is a part matrix of {tilde over (Q)} having a dimension of 4n R ×8, and {tilde over (Q)} 2  is a part matrix of {tilde over (Q)} having a dimension of 8×8. In this case, the signal detection is made as with Equation 11. 
         [0000]    
       
         
           
             
               
                 
                   
                     s 
                     ~ 
                   
                   = 
                   
                     arg 
                      
                     
                       
                         min 
                         
                           s 
                           ∈ 
                           
                             C 
                             8 
                           
                         
                       
                        
                       
                         
                            
                           
                             
                               y 
                               ~ 
                             
                             - 
                             
                               
                                 R 
                                 ~ 
                               
                                
                               s 
                             
                           
                            
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     11 
                   
                   ) 
                 
               
             
           
         
       
     
         [0065]    In Equation 11, {tilde over (y)}={tilde over (Q)} T r. 
         [0066]    Meanwhile, it is required in calculating the likelihood ratio L E (x k |y) to obtain the results of Equation 9 and Equation 11, and a plurality of points therearound on the constellation. A method of obtaining the plurality of points will now be described. 
         [0067]    The matrixes {circumflex over (R)} and {tilde over (R)} are calculated by using the Gram-Schmidt method, and each are indicated in the same form as with Equation 12. 
         [0000]    
       
         
           
             
               
                 
                   R 
                   = 
                   
                     [ 
                     
                       
                         
                           
                             α 
                             1 
                           
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             β 
                             1 
                           
                         
                         
                           
                             β 
                             2 
                           
                         
                         
                           
                             β 
                             3 
                           
                         
                         
                           
                             β 
                             4 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           
                             α 
                             1 
                           
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             - 
                             
                               β 
                               2 
                             
                           
                         
                         
                           
                             β 
                             1 
                           
                         
                         
                           
                             - 
                             
                               β 
                               4 
                             
                           
                         
                         
                           
                             β 
                             3 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             α 
                             1 
                           
                         
                         
                           0 
                         
                         
                           
                             - 
                             
                               β 
                               3 
                             
                           
                         
                         
                           
                             
                               β 
                               ~ 
                             
                             4 
                           
                         
                         
                           
                             β 
                             1 
                           
                         
                         
                           
                             - 
                             
                               β 
                               2 
                             
                           
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             α 
                             1 
                           
                         
                         
                           
                             - 
                             
                               β 
                               4 
                             
                           
                         
                         
                           
                             - 
                             
                               β 
                               3 
                             
                           
                         
                         
                           
                             β 
                             2 
                           
                         
                         
                           
                             β 
                             1 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             α 
                             2 
                           
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             α 
                             2 
                           
                         
                         
                           0 
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             α 
                             2 
                           
                         
                         
                           0 
                         
                       
                       
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           0 
                         
                         
                           
                             α 
                             2 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     12 
                   
                   ) 
                 
               
             
           
         
       
     
         [0068]    In Equation 12, 
         [0000]    
       
         
           
             
               
                 α 
                 1 
               
               = 
               
                  
                 
                   h 
                   1 
                 
                  
               
             
             , 
             
               
 
             
              
             
               
                 β 
                 1 
               
               = 
               
                 
                   1 
                   
                     α 
                     1 
                   
                 
                  
                 
                   h 
                   1 
                   T 
                 
                  
                 
                   h 
                   5 
                 
               
             
             , 
             
               
 
             
              
             
               
                 β 
                 2 
               
               = 
               
                 
                   1 
                   
                     α 
                     1 
                   
                 
                  
                 
                   h 
                   1 
                   T 
                 
                  
                 
                   h 
                   G 
                 
               
             
             , 
             
               
 
             
              
             
               
                 β 
                 3 
               
               = 
               
                 
                   1 
                   
                     α 
                     1 
                   
                 
                  
                 
                   h 
                   1 
                   T 
                 
                  
                 
                   h 
                   7 
                 
               
             
             , 
             
               
 
             
              
             
               
                 β 
                 4 
               
               = 
               
                 
                   1 
                   
                     α 
                     1 
                   
                 
                  
                 
                   h 
                   1 
                   T 
                 
                  
                 
                   h 
                   8 
                 
               
             
           
         
       
       
         
           
             
               α 
               2 
             
             = 
             
               
                 
                   
                      
                     
                       h 
                       5 
                     
                      
                   
                   2 
                 
                 - 
                 
                   β 
                   1 
                   2 
                 
                 - 
                 
                   β 
                   2 
                   2 
                 
                 - 
                 
                   β 
                   3 
                   2 
                 
                 - 
                 
                   β 
                   4 
                   2 
                 
               
             
           
         
       
     
         [0069]    In Equation 12, if h j  represents the j-th column of Ĥ, R represents {circumflex over (R)}, while if h j  represents the j-th column of {tilde over (H)}, R represents {tilde over (R)}. 
         [0070]    Furthermore, {circumflex over (Q)} and {tilde over (Q)} may be expressed in the same form as with Equation 13. 
         [0000]      Q=[q 1 , q 2 , q 3 , q 4 , q 5 , q 6 , q 7 , q 8 ]  (Equation 13) 
         [0071]    In Equation 13, the respective columns q j  are given in the following way. 
         [0000]    
       
         
           
             
               
                 q 
                 j 
               
               = 
               
                 
                   1 
                   
                     α 
                     1 
                   
                 
                  
                 
                   h 
                   j 
                 
               
             
             , 
             
               j 
               = 
               1 
             
             , 
             2 
             , 
             3 
             , 
             4 
           
         
       
       
         
           
             
               q 
               j 
             
             = 
             
               
                 1 
                 
                   α 
                   2 
                 
               
                
               
                 ( 
                 
                   
                     h 
                     j 
                   
                   - 
                   
                     
                       ∑ 
                       
                         k 
                         = 
                         1 
                       
                       4 
                     
                      
                     
                       
                         R 
                         
                           k 
                           , 
                           j 
                         
                       
                        
                       
                         q 
                         k 
                       
                     
                   
                 
                 ) 
               
             
           
         
       
     
         [0072]    In Equation 13, R k,j  represent the (k, j)th elements of the matrix R. 
         [0073]    Equation 9 and Equation 11 can be expressed by Equation 14, Equation 15, and Equation 16 while using Equation 12 and Equation 13. 
         [0000]      ∥ y−Rs∥   2   =A+B    (Equation 14) 
         [0074]    (Equation 15) 
         [0000]    
       
         
           
             
               
                 
                   
                      
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           5 
                         
                         8 
                       
                        
                       
                         
                           ( 
                           
                             
                               y 
                               k 
                             
                             - 
                             
                               
                                 α 
                                 2 
                               
                                
                               
                                 s 
                                 k 
                               
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     ℬ 
                     = 
                     
                       
                         ∑ 
                         
                           k 
                           = 
                           1 
                         
                         4 
                       
                        
                       
                         
                           
                             ( 
                             
                               
                                 y 
                                 k 
                               
                               - 
                               
                                 
                                   α 
                                   1 
                                 
                                  
                                 
                                   s 
                                   k 
                                 
                               
                               - 
                               
                                 
                                   ∑ 
                                   
                                     j 
                                     = 
                                     5 
                                   
                                   8 
                                 
                                  
                                 
                                   
                                     R 
                                     
                                       k 
                                       , 
                                       j 
                                     
                                   
                                    
                                   
                                     s 
                                     j 
                                   
                                 
                               
                             
                             ) 
                           
                           2 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     16 
                   
                   ) 
                 
               
             
           
         
       
     
         [0075]    Equation 15 being the first term of Equation 14 is minimized so as to obtain soft symbol estimates ŝ k  where k is 5, 6, 7, and 8 as with Equation 17, at the step S 220 . 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         s 
                         ^ 
                       
                       k 
                     
                     = 
                     
                       
                         y 
                         k 
                       
                       
                         α 
                         2 
                       
                     
                   
                   , 
                   
                     k 
                     = 
                     5 
                   
                   , 
                   6 
                   , 
                   7 
                   , 
                   8. 
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     17 
                   
                   ) 
                 
               
             
           
         
       
     
         [0076]    Thereafter, the constellation point closest to such values and the surrounding constellation points therearound are found. That is, M A  numbers of surrounding points with respect to the respective ŝ k  and a set S A  with total (M A ) 4  numbers of points are obtained. Furthermore, a set Φ A  of A values is calculated at step S 230 . 
         [0077]    As Equation 15 is formed with a sum of four independent terms, the four terms can be each considered in a separate manner. That is, a rounding like method is used to find the closest point with respect to the respective ŝ k  where k is 5, 6, 7, and 8, and the second closest point is obtained by adding or subtracting 2 to or from the closest point in case the constellation is given by Equation 7. 
         [0078]    In this way, with the present invention, M A  numbers of surrounding points are calculated with respect to the respective ŝ k . The ik-th closest point to the point ŝ k  is expressed by {tilde over (s)} k   (i     k     )  where k is 5, 6, 7, and 8. A set with the total (M A ) 4  numbers of points is represented by S A  as with Equation 18. 
         [0000]        S   A ={({tilde over (s)} 5   (i     5     )   ,{tilde over (s)}   6   (i     6     )   ,{tilde over (s)}   7   (i     7     )   ,{tilde over (s)}   (i     8     ) ): i   5   ,i   6   ,i   7   ,i   8 =1, . . . ,  M   A }. (Equation 18) 
         [0079]    A set of A values where the respective points of Equation 18 are computed by applying them to Equation 15 is represented by Φ A  as with Equation 19. 
         [0000]      Φ A   ={A   i5,i6,i7,i8   :i   5   ,i   6   ,i   7   ,i   8 =1, . . . ,  M   A }  (Equation 19) 
         [0080]    The complexity usually becomes (M A ) 4  in order to calculate Φ A  with (M A ) 4  numbers of elements. However, with the present invention, as A is a sum of four independent terms, the respective (y k −α 2 s k ) 2  are computed by M A , and the computed values are combined with each other by (M A ) 4 . Therefore, the complexity becomes 4M A . 
         [0081]    Then, Equation 16 being the second term of Equation 14 is minimized so as to calculate soft symbol estimates ŝ k  where k is 1, 2, 3, and 4 as with Equation 20, at the step S 240 . 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           s 
                           ^ 
                         
                         k 
                       
                        
                       
                         ( 
                         
                           
                             s 
                             ~ 
                           
                           A 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         
                           y 
                           k 
                         
                         - 
                         
                           
                             R 
                             
                               k 
                               , 
                               5 
                             
                           
                            
                           
                             
                               s 
                               ~ 
                             
                             5 
                             
                               ( 
                               
                                 i 
                                 5 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           
                             R 
                             
                               k 
                               , 
                               6 
                             
                           
                            
                           
                             
                               s 
                               ~ 
                             
                             6 
                             
                               ( 
                               
                                 i 
                                 6 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           
                             R 
                             
                               k 
                               , 
                               7 
                             
                           
                            
                           
                             
                               s 
                               ~ 
                             
                             7 
                             
                               ( 
                               
                                 i 
                                 7 
                               
                               ) 
                             
                           
                         
                         - 
                         
                           
                             R 
                             
                               k 
                               , 
                               8 
                             
                           
                            
                           
                             
                               s 
                               ~ 
                             
                             8 
                             
                               ( 
                               
                                 i 
                                 8 
                               
                               ) 
                             
                           
                         
                       
                       
                         R 
                         
                           k 
                           , 
                           k 
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                       
                   
                    
                   
                     k 
                     = 
                     1 
                   
                   , 
                   2 
                   , 
                   3 
                   , 
                   4. 
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     20 
                   
                   ) 
                 
               
             
           
         
       
     
         [0082]    In Equation 20, {tilde over (s)} A =({tilde over (s)} 5   (i     5     ) ,{tilde over (s)} 6   (i     6     ) ,{tilde over (s)} 7   (i     7     ) ,{tilde over (s)} 8   (i     8     ) ). 
         [0083]    Now, M B  numbers of surrounding points are calculated with respect to the respective ŝ k  , and a set S B  with total (M B ) 4  numbers of points is obtained. Furthermore, the solution set of B values Φ B  is calculated at the step S 250 . 
         [0084]    The values of S B  and Φ B  can be calculated in the same way as with the calculation of the values S A  and Φ A . First, assuming that {tilde over (s)} k   (i     k     ) ({tilde over (s)} A ) where k is 1, 2, 3, and 4 indicate the constellation points i k -th closest to the points obtained by way of Equation 20 being the points ŝ k ({tilde over (s)} A ) where k is 1, 2, 3, and 4, M B  numbers of close points are calculated with respect to the respective ŝ k ({tilde over (s)} A ) where k is 1, 2, 3, and 4. These points can be calculated in the same way as with the above-calculated {tilde over (s)} k   (i     k     )  where k is 5, 6, 7, and 8. A set with the calculated total (M B ) 4  numbers of points is indicated by S B ({tilde over (s)} A ), and expressed by Equation 21, while the solution set Φ B ({tilde over (s)} A ) of the B values calculated by applying the respective points to Equation 16 is expressed by Equation 21 and Equation 22. 
         [0000]        S   B ( {tilde over (s)}   A )={( {tilde over (s)}   1   (i     1     ) ( {tilde over (s)}   A ), {tilde over (s)}   2   (i     2     ) ( {tilde over (s)}   A ), {tilde over (s)}   3   (i     3     ) ( {tilde over (s)}   A ), {tilde over (s)}   4   (i     4     ) ( {tilde over (s)}   A )): i   1   ,i   2   ,i   3   ,i   4 =1, . . . ,  M   B }.   (Equation 21) 
         [0000]      Φ B ({tilde over (s)} A )={ B   i     1     ,i     2     ,i     3     ,i     4   ( {tilde over (s)}   A ): i   1   ,i   2   ,i   3   ,i   4 =1, . . . ,  M   B }  (Equation 22) 
         [0085]    The final point set S of constellations is calculated by doing the sum of S A  and the point set S B ({tilde over (s)} A ) as with Equation 23, and the solution set Φ A  and the solution set Φ B ({tilde over (s)} A ) are put together so as to calculate the final solution set Φ of metric values as with Equation 24, at the step S 260 . 
         [0000]        S ={( {tilde over (s)}   1 ( {tilde over (s)}   A ), {tilde over (s)}   2 ( {tilde over (s)}   A ), {tilde over (s)}   3 ( {tilde over (s)}   A ), {tilde over (s)}   4 ( {tilde over (s)}   A ), {tilde over (s)}   5   (i     5     )   ,{tilde over (s)}   6   (i     6     )   ,{tilde over (s)}   7   (i     7     )   ,{tilde over (s)}   8   (i     8     ) ): i   5   ,i   6   ,i   7   ,i   8 =1, . . . ,  M   A }  (Equation 23) 
         [0000]      Φ={ A   i     6     ,i     7     ,i     8     ,i     9     +{tilde over (B)}:i   5   ,i   6   ,i   7   ,i   8 =1, . . . ,  M   A }  (Equation 24) 
         [0086]    Finally, the likelihood L E (x k |y) with respect to the respective bits is calculated by using them at the step S 270 . 
         [0087]    Previously, total (M A  M B ) 4  numbers of constellation points and metric values ∥y−Rs∥ 2  corresponding thereto were calculated. When an intersection of the point set S and X k,+1 , X k,+1  of Equation 4 is calculated by using them, the likelihood L E (x k |y) with respect to the respective bits can be calculated by using Equation 3. 
         [0088]    Meanwhile, the minimum number of constellation points calculated in the above way is 256 (M A =M B =2), and the likelihood L E (x k |y) is calculated with respect to all those points. However, in many cases, for example, in case the signal-to-noise ratio (SNR) is high, or in case the channel status is good, or in case the size of constellation is small (the quadrature phase shift keying QPSK, 16-QAM), the calculating of L E (x k |y) with respect to all the 256 numbers of points makes only the complexity be heightened without improving the performance characteristics. Accordingly, in case the complexity is lowered without deteriorating the performance characteristics with the usage of the constellation points with a size smaller than 256, another method is used, which will now be described with reference to  FIG. 3 . 
         [0089]      FIG. 3  is a flowchart illustrating a signal detection method according to another exemplary embodiment of the present invention. 
         [0090]    Referring to  FIG. 3 , as with the exemplary embodiment of  FIG. 2 , the maximum ML resolution or the augmented channel matrix {tilde over (H)} is QR-decomposed so as to express ∥y−Rs∥ 2  at the step S 310 . Thereafter, as in the exemplary embodiment of  FIG. 2 , the soft symbol estimates ŝ k  where k is 5, 6, 7, and 8 are calculated as with Equation 17, at the step S 320 . 
         [0091]    Thereafter, in case M A  is 2, a set S A  of (M A ) 4  numbers of points and a solution set Φ A  of A values are calculated at the step S 330 . 
         [0092]    Thereafter, ξ A  numbers of elements are selected from the set S A  and the solution set Φ A  at the step S 340 . The value ξ A  may range from 1 to 16. As the set of constellation points given thereby may have a dimensional value range from 1 to 256, such a value is controlled properly depending upon the size of constellation or the channel status so that only the minimum complexity can result without deteriorating the signal detection capacity. It is important here to list the elements of the solution set Φ A  in a sequence of from the smallest to the largest, and select relatively small values. 
         [0093]    As the respective set has sixteen (16) elements, the number of possible listings is given by 1×2×3× . . . ×6=16!. 
         [0094]    It can be easily shown first of all that A 1,1,1,1  is an element with a smallest size among the elements of the solution set Φ A  of Equation 19. Then, four elements {A ,2,1,1,1 , A 1,2,1,1 , A 1,1,2,1 , A 1,1,1,2 } are listed in a dimensional sequence. In this step, it is required to make value size comparison maximally six times. Now, assume that d n , n=1, 2, 3, 4 represents the position of 2 at the n-th smallest element script among the four elements. For example, in case the four elements are listed in a dimensional sequence to be A 1,2,1,1 &lt;A 1,1,1,2 &lt;A 2,1,1,1 &lt;A 1,1,2,1 , it is given that d 1 =2, d 2 =4, d 3 −1, d 4 =3. Furthermore, A[d n     1,    . . . , d n     N   ], N≦4 represents the value of the element where the script i j  located at the position of d n     1,    . . . , d n     S    among the values of the elements A i     5,     i     6,     i     7,     8  of Φ A  has a value of 2. For example, in case it is given that d 1 =2, d 2 =4, d 3 =1, d 4 =3, A[d n     1,    . . . , d n     N   ] have values of A[d 2 ]=A 1,1,1,2 , A[d 4 ]=A 1,1,2,1 , A[d 1 , d 3 ]=A 2,2,1,1 , A[d 1 , d 2 , d 4 ]=A 1,2,2,2 , A[d 1 , d 2 , d 3 , d 4 ]=A 2,2,2,2 ). In this case, A[d 1  is the second smallest element among the elements of the solution set Φ A , and A[d 2 ] is the third smallest element among the elements of the solution set Φ A . Furthermore, A[d 1 , d 3 , d 4 ] is the fourteenth smallest element among the elements of the solution set Φ A , while A[d 2 , d 3 , d 4 ] is the fifteenth smallest element among the elements of the solution set Φ A , and A[d 1 , d 2 , d 3 , d 4 ] is the sixteenth smallest element among the elements of the solution set Φ A , (i.e., the largest element). Therefore, only the remaining ten elements among the sixteen (16) elements of the solution set Φ A  can be listed in a dimensional sequence. The listing can be achieved by making size comparison minimally three times or maximally six times. Such a listing is illustrated in  FIG. 4 , and the listed elements are given in  FIG. 5 . As the complexity thereof is minimally 9 or maximally 12, they have relatively low complexity. 
         [0095]    Thereafter, ŝ k , k=1, 2, 3, 4 is calculated by using the ξ A  numbers of element values selected from S A , at the step S 350 . That is, the ξ A  numbers of elements are substituted at Equation 16 so as to calculate such a value as with Equation 20. 
         [0096]    Furthermore, in case M B  is 2, a set S B  of (M B ) 4  numbers of points and a solution set Φ 8  of B values are calculated at the step S 360 . Thereafter, ξ B  numbers of elements are selected from the set S B  and the solution set Φ 13  at the step S 370 . At this time, the way of selection is the same as that of selecting ξ A  numbers of elements from the S A  and the Φ A . 
         [0097]    Then, ξ A  numbers of elements and ξ B  numbers of elements are put together so as to obtain S, and the solution set Φ A  and the solution set Φ B  corresponding thereto are put together so as to calculate the final solution set Φ at the step S 380 . 
         [0098]    Finally, the likelihood L E (x k |y) with respect to the respective bits is calculated at the step S 390 . 
         [0099]    The above-described exemplary embodiments of the present invention may be realized not only by way of method and apparatus, but also by way of a program conducting the functions corresponding to the structural features according to the embodiments of the present invention or a program-recorded medium. 
         [0100]    While this invention has been described in connection with what is presently considered to be practical exemplary embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.