Patent Publication Number: US-8116406-B2

Title: Apparatus and method for generating soft bit metric and M-ary QAM receiving system using the same

Description:
TECHNICAL FIELD 
     The present invention relates to an apparatus and method for generating a soft bit metric and a multi-level (M-ary) Quadrature Amplitude Modulation (QAM) receiving system using the same. More specifically, the invention relates to an apparatus and method for generating a soft bit metric, in which a received symbol signal is converted into soft bit metric information per bit and then transmitted to an iterative decoder such as a Turbo or Low Density Parity Check (LDPC) decoder so as to recover data from the received signal modulated by a higher-order modulation scheme, and an M-ary QAM receiving system using the same. 
     BACKGROUND ART 
     Iterative decoding schemes are used in a receiver in order to perform channel coding using Turbo codes or LDPC codes. However, since an M-ary QAM modulation signal in which one symbol is expressed as some bits is transmitted in symbol unit, it is inevitable that a symbol signal is converted into information in the form of bits for iterative decoding. Such conversion is accomplished by soft decoding, soft metric, Log Likelihood Ratio (LLR), soft demapping and the like. 
     Therefore, as will be described later, in an M-ary QAM receiving system that transmits log 2 M number of bits per symbol by using Gray mapping, the present invention is to convert a received symbol signal into soft bit metric information per bit (I or Q channel) and transmits the converted information to an iterative decoder such as a Turbo or LDPC decoder, as illustrated in  FIG. 2 . 
     As methods for converting a symbol signal into a bit signal, there are generally a Maximum A Posteriori (MAP) scheme and a signal space division scheme. However, since the MAP scheme is very complex in formula operation, it is advanced to a log-MAP that applies algebraic operation to MAP. And, the log-MAP is again enhanced to a Max-Log-MAP algorithm with even lower complexity in design. On the other hand, the signal space division scheme uses geometric space division formulas to divide signal space based on a constellation position of a transmitted signal. So there are many different implementation methods that are based on the signal constellation. 
     In general, a Look-Up Table (LUT) based method using a memory is employed to reduce implementation complexity, but it also has drawbacks in that errors may occur, and especially, when Adaptive Modulation and Coding (AMC) scheme that changes a modulation method is used, various LUTs must be provided depending on a given symbol arrangement and also be updated according to a selected modulation method. 
     Moreover, the conventional MAP exhibiting high-performance involves an exponential calculation, the log-MAP that is logarithmic MAP requires an exponential operation, and the Max-Log-MAP that approximates the log-MAP also has high-complexity in design. In particular, even in case of a scheme using a signal space, an LUT must be configured in accordance with a symbol arrangement. 
     Therefore, the iterative decoding scheme is essential for maintaining an efficient and stable communication quality in receiving a higher-order modulation signal. This iterative decoding scheme is based on binary transmission, and thus, when a higher-order modulation symbol signal is received, the symbol signal should be converted into information in the form of bits so that the receiving system can effectively employ the binary iterative decoding scheme. 
     Especially, the QAM decoding method is known to be the best decoding method that can most effectively use the same bandwidth. However, the QAM transmission is susceptive to the influence of fading or noises and thus requires a high Signal to Noise Ratio (SNR) to ensure stable reception. The iterative decoding scheme is useful to compensate the above shortcomings because it can acquire the high coding gain over channel coding such as Turbo codes or LDPC codes, which becomes a transmission system suitable for wideband transmission. In order to utilize the iterative decoding scheme for the higher-order modulation QAM signal, it is absolutely necessary to generate a soft bit metric that converts a transmitted symbol signal into soft bit information. 
     Consequently, the soft bit metric generation for the conversion of symbol-to-bit information requires a complex operation algorithm, so there is a need to develop a new scheme for reducing implementation complexity of such algorithm and generating soft bit metric information effectively. 
     DISCLOSURE 
     Technical Problem 
     It is, therefore, an object of the present invention to provide an apparatus and method for generating a soft bit metric, in which a received symbol signal is converted into soft bit metric information per bit and then transmitted to an iterative decoder such as a Turbo or LDPC decoder so as to recover data from a received signal modulated using higher-order modulation scheme, and an M-ary QAM receiving system using the same. 
     The other objectives and advantages of the invention will be understood by the following description and will also be appreciated by the embodiments of the invention more clearly. Further, the objectives and advantages of the invention will readily be seen that they can be realized by the means and its combination specified in the claims. 
     Technical Solution 
     In accordance with one aspect of the present invention, there is provided an apparatus for generating a soft bit metric, including: an analog to digital converter for converting an analog symbol signal of a demodulated I or Q channel into a digital signal; a scaler for scaling the converted digital signal based on a reference value used for determining a space between symbols; a positive integer converter for calculating a positive integer of the scaled digital I or Q channel symbol signal; a sign determinator for determining a sign of the scaled digital I or Q channel symbol signal; and a bit information converter for converting the scaled digital I or Q channel symbol signal into soft bit metric information per bit on the basis of the calculated positive integer and the determined sign value. 
     In accordance with another aspect of the present invention, there is provided a method for generating a soft bit metric, including the steps of: scaling a digital signal converted through an A/D converter by using a reference value used for determining a space between symbols; calculating a positive integer of the scaled digital I or Q channel symbol signal and determining a sign thereof; and converting the scaled digital I or Q channel symbol signal into soft bit metric information per bit based on the calculated positive integer and the determined sign value. 
     In accordance with still another aspect of the present invention, there is provided an M-ary QAM receiving system using a soft bit metric generating apparatus, the system including: an I/Q demodulator for recovering a symbol signal of each of an I channel and a Q channel; an I channel soft bit metric generator for converting an I channel symbol signal into soft bit metric information per bit; a Q channel soft bit metric generator for converting a Q channel symbol signal into soft bit metric information per bit; a parallel to serial data converter for performing a parallel to serial conversion on I and Q bit metric information; and an iterative decoder for iteratively decoding the serially converted I and Q bit metric information. 
     ADVANTAGEOUS EFFECTS 
     As mentioned above and will be described below, the present invention can substantially reduce the design complexity by employing the Max-Log-MAP algorithm for symbol-to-bit information conversion in the M-ary QAM signal receiving system using Gray mapping that is typically used for forming a symbol with bits. 
     In particular, according to the present invention, even though the modulation order M may be increased, the calculation courses or routes can be increased as many as the increased number of bits without changing the structure, or the same courses can be used iteratively. 
    
    
     
       DESCRIPTION OF DRAWINGS 
       The above and other objects and features of the present invention will become apparent from the following description of the preferred embodiments given in conjunction with the accompanying drawings, in which: 
         FIG. 1  shows a Gray coded 16-QAM signal constellation which is one of square QAMs where M=16; 
         FIG. 2  is a block diagram illustrating an M-ary QAM receiving system using an apparatus for generating a soft bit metric in accordance with one embodiment of the present invention; 
         FIG. 3  is a diagram describing a soft bit metric generation principle of an 8-PAM constellation diagram for a Gray coded I or Q signal in accordance with the present invention; 
         FIG. 4  is a diagram describing a b 2  bit soft bit metric generation principle of an 8-PAM constellation for a Gray coded I or Q signal in accordance with the present invention; 
         FIG. 5  is a diagram illustrating an apparatus for generating a soft bit metric in accordance with another embodiment of the present invention; 
         FIG. 6  is a detailed diagram of the soft bit metric operation unit of k-th bit in the soft bit metric generating apparatus in accordance with the invention; and 
         FIG. 7  shows a 64-QAM signal constellation to which the present invention can be applied. 
     
    
    
     BEST MODE FOR THE INVENTION 
     The above-mentioned objectives, features, and advantages will be more apparent by the following detailed description associated with the accompanying drawings, and thus, the invention will readily be conceived by those skilled in the art. Further, in the following description, well-known arts will not be described in detail if it seems that they could obscure the invention in unnecessary detail. Hereinafter, preferred embodiments of the present invention will be set forth in detail with reference to the accompanying drawings. 
     A transmitted M-ary QAM signal is configured in a manner that an m-number (m=log 2 M) of bits are collected to form a codeword which consists of one signal symbol to be sent. At this time, bits constituting a symbol are assigned according to the Gray mapping rule. A Gray coded 2-dimensional signal space having an M-number of signal points is divided into I (Inphase) channel having an N-number of signal points and Q (Quadrature) channel having an L-number of signal points, each channel being Gray coded one-dimensional Pulse Amplitude Modulation (PAM) signal space having the same properties. If the numbers of signal points arranged at the I and Q channels are the same, it becomes a square QAM. Otherwise, it becomes a rectangular QAM. 
       FIG. 1  shows a Gray coded 16-QAM signal constellation which is one of square QAMs where M=16. 
     Using the above constellation, therefore, a soft bit metric of QAM can be generated by recognizing the I and Q channels as respective independent PAMs and through the soft bit metric generation for such PAMs. 
       FIG. 2  is a block diagram illustrating an M-ary QAM receiving system using a soft bit metric generating apparatus in accordance with one embodiment of the present invention. 
     As illustrated in  FIG. 2 , the M-ary QAM receiving system using the apparatus for generating a soft bit metric of the invention includes an I/Q demodulator  201  for demodulating symbol information of each of I and Q channels, I and Q channel soft bit metric generators  202  and  203  for converting symbol signals of the I and Q channels provided through the I/Q demodulator  201  into soft bit metric information per bit, and an iterative decoder  205  for iteratively decoding the I and Q channel bit metric signals outputted from the I and Q channel soft bit metric generators  202  and  203  through a parallel to serial data converter  204 . 
     That is, the M-ary QAM receiving system of the invention is a receiver, in which a received signal is demodulated in the I/Q demodulator  201 . More specifically, an output of the I/Q demodulator  201  for recovering symbol information of each of the I and Q channels is inputted to each of the I and Q channel PAM signal soft bit metric generators  202  and  203 , to generate I and Q channels soft bit metrics, as will be described with reference to  FIG. 5  later. The I and Q bit metric signals are then inputted to the iterative decoder  205  via the parallel to serial data converter  204 . As expressed above, each of the I and Q channels soft bit metric generators  202  and  203  is the PAM soft bit metric generator having the same structure. 
     In a preferred embodiment of the invention, the number of signal points on a PAM signal space is N, and symbol data of a codeword in which each signal point is composed of K bits is mapped to one point on the constellation of a one-dimensional signal space. At this time, when bit values are assigned to each symbol by employing the Gray mapping rule, the left/right signal spaces have an axisymmetry relationship with respect to boundary values of bits constituting codewords. 
       FIG. 3  is diagram for explaining a soft bit metric generation principle of an 8-PAM constellation diagram for a Gray coded I or Q signal in accordance with the present invention, wherein the Gray coded 8-PAM signal constellation and groups by bits are commonly used in the I and Q channels. 
     In  FIG. 3 , when seen on the PAM signal space, the arrangement of each bit value among bits constituting a symbol is bilaterally symmetric with respect to the origin 0. 
     For instance, in G 1 (b 1 ) and G 2 (b 1 ) groups, bit b 1  values assigned to each signal point are symmetric with respect to the origin 0; and bit b 2  values arranged to each symbol, i.e., G 1 (b 2 ) and G 2 (b 2 ) are symmetric to G 3 (b 2 ) and G 4 (b 2 ) with respect to the 0 point, and G 1 (b 2 ) and G 2 (b 2 ), and G 3 (b 2 ) and G 4 (b 2 ) are symmetric with respect to −4 d and +4 d, respectively. This is the same as shifting the signal space of b 1  in the left-hand side signal space by −4 d, and the signal space in the right-hand side signal space by +4 d with respect to the 2-PAM signal space of  FIG. 3(   a ) or the origin of the b 0  signal space. Therefore, it can be seen that the signal space of each group is either identical or axisymmetric to the arrangement of bit values in the 2-PAM signal space, and a coordinate transfer relationship exists between signal spaces. 
     A received Gray coded N-PAM signal may be expressed as:
 
 z=α·s+n   Eq. (1)
 
wherein s denotes a transmitted N-PAM symbol, α denotes a channel gain, and n denotes an Additive White Gaussian Noise (AWGN) in which average is 0 and variance is σ 2 . If α is probably stable (constant), the received signal z becomes a signal that is received through an AWGN channel.
 
     When a PAM signal that is one of I and Q channels is received over the AWGN channel, if an LLR test is conducted, it may be represented by: 
                       LLR   I     ⁡     (     b   k     )       =       ln   ⁢           ⁢       ∑     A   ∈     {       s   :     b   k       =   1     }         ⁢     exp   (     -         (     z   -   A     )     2       2   ⁢     σ   2           )         -     ln   ⁢       ∑     B   ∈     {       s   :     b   k       =     -   1       }         ⁢     exp   (     -         (     z   -   B     )     2       2   ⁢     σ   2           )                   Eq   .           ⁢     (   2   )                 
wherein b k  denotes a k-th bit value of a received signal symbol, z denotes a received signal, A denotes a +reference signal value, B denotes a −reference signal, and σ 2  denotes a variance of AWGN noise.
 
     Since Eq. (2) needs logarithmic calculation, it has an increased implementation complexity. Therefore, by applying the following approximated equation, Eq. (3), to Eq. (2) above, Eq. (4) is obtained as follows: 
     
       
         
           
             
               
                 
                   
                     
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     The above-described Eq. (4) is widely known as the Max-Log-MAP algorithm, but max(·) or min(·) therein becomes a factor in increasing complexity due to an increase in a modulation order N since the number of cases is considered. Therefore, the following equation may be obtained by summarizing the results as discussed above: 
                     LLR   ⁡     (     b   k     )       =       G       z   ^     ,   k       ·     m   k     ·       d       ma   ⁢           ⁢   x     ,   k       2     ·     (         d       m   ⁢           ⁢   i   ⁢           ⁢   n     ,   k       2     -            z   ^     k            )               Eq   .           ⁢     (   5   )                 
wherein {circumflex over (z)} k  denotes a correction value for a k-th bit group in a received symbol area by a moving distance of the coordinate axis, G {circumflex over (z)},k  denotes a sign value sign ({circumflex over (z)} k ) of a corrected symbol value {circumflex over (z)} k , m k  indicates whether the k-th bit arrangement in the group coincides with 2-PAM (coincidence: +1, non-coincidence: −1), d min,k  denotes a closest distance value to a bit boundary value in a corresponding bit group to which the received signal belongs, and d max,k  denotes a farthest distance value from a bit boundary value in a group area of the received symbol.
 
     Also, d min,k  and d max,k  satisfy the following: d max,k =d min,k +2 d. 
     For instance, applying an example of the calculation of d max,k  and d min,k  used in Eq. (5) to a bit b 1 , in the signal space of  FIG. 3(   b ), 
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     In the soft bit metric calculation procedure using Eq. (5), if the received signal belongs to S 1  0≦z≦2 d) among the areas in  FIG. 3(   b ) for the bit b 1 , the soft bit metric can be calculated from Eq. (6) blow by using the parameters employed in Eq. (5): 
     
       
         
           
             
               
                 
                   
                     
                       
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                       1 
                     
                   
                   , 
                   
                     
                       
                         d 
                         
                           
                             m 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             i 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             n 
                           
                           , 
                           1 
                         
                       
                       2 
                     
                     = 
                     d 
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         d 
                         
                           
                             m 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             ax 
                           
                           , 
                           1 
                         
                       
                       2 
                     
                     = 
                     
                       2 
                       ⁢ 
                       d 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     6 
                     ) 
                   
                 
               
             
           
         
       
     
     Therefore, the soft bit metric LLR in this example is determined as follows: 
     
       
         
           
             
               
                 
                   
                     
                       LLR 
                       I 
                     
                     ⁡ 
                     
                       ( 
                       
                         b 
                         1 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           - 
                           1 
                         
                         · 
                         
                           - 
                           1 
                         
                         · 
                         2 
                       
                       ⁢ 
                       
                         d 
                         ⁡ 
                         
                           [ 
                           
                             d 
                             - 
                             
                                
                               
                                 z 
                                 - 
                                 
                                   4 
                                   ⁢ 
                                   d 
                                 
                               
                                
                             
                           
                           ] 
                         
                       
                     
                     = 
                     
                       
                         - 
                         2 
                       
                       ⁢ 
                       
                         d 
                         ⁡ 
                         
                           ( 
                           
                             
                               3 
                               ⁢ 
                               d 
                             
                             - 
                             z 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
           
         
       
     
     The result obtained from Eq. (7) is the same as that obtained by using Eq. (4). 
       FIG. 4  describes a b 2  soft bit metric generation procedure among bits constituting an 8-PAM signal symbol in the same method as the principle for generating the b 1  soft bit metric as discussed with reference to  FIG. 3 . 
     As described above, the present invention relates to the I and Q channel soft bit metric generators  202  and  203  in the M-ary QAM receiving system shown in  FIG. 2 , each of which includes a soft bit metric operation unit [LLR generators (b 0  to b k-1 )  55  depicted in  FIGS. 5 and 6 . 
     The principle of the invention is based on the above-discussed Eq. (5), which is commonly applicable to the I and Q channels. In particular,  FIG. 5  shows an algorithm block for implementing the N-PAM soft bit metric generation. 
       FIG. 5  illustrates a detailed block diagram of the soft bit metric generating apparatus shown in  FIG. 2  in accordance with the present invention. 
     As illustrated in  FIG. 5 , the soft bit metric generating apparatus that can be commonly used for the I and Q channels includes an A/D converter  51 , a scaler  52 , a positive integer converter  53 , a sign determinator  54 , and a soft bit metric operation unit  55 . 
     The A/D converter  51  converts an analog symbol signal of a demodulated I (Inphase) channel or Q (Quadrature) channel into a digital signal. The scaler  52  scales the converted digital signal using a reference value (e.g., d) that is used for determining a signal point position similar to the reference value for determining a space between symbols [(see Eq. (5)]. The positive integer converter  53  calculates a positive integer R of the scaled digital I or Q channel symbol signal Z. The sign determinator  54  determines a sign of the scaled digital I or Q channel symbol signal Z, and the soft bit metric operation unit  55  converts the scaled digital I or Q channel symbol signal Z into soft bit metric information per bit. 
     Here, an output value of the positive integer converter  53  is expressed as R=(r 0 , r 1 , . . . , r K-1 ) 2  where ( . . . ) 2  denotes a binary expression and r k  denotes a value of each digit in the binary expression. Likewise, r 0  denotes a Most Significant Bit (MSB) in the binary expression. Now, the soft bit metric operation procedure of the k-th bit implemented in the soft bit metric operation unit  55  of  FIG. 5  will be explained in more detail with reference to  FIG. 6 . 
       FIG. 6  describes a detailed diagram of the soft bit metric operation unit [LLR generators (b 0  to b k-1 )]  55  for the k-th bit included in the soft bit metric generating apparatus in accordance with the present invention. 
     As shown in  FIG. 6 , the soft bit metric operation unit  55  for the k-th bit of the soft bit metric generating apparatus of the invention includes a coordinate shifting value generator  601 , a coincidence decision unit  602 , a correction value generator  603 , a {circumflex over (z)} k  sign value generator  604 , a {circumflex over (z)} k  absolute value generator  605 , a minimum distance value generator  606 , a maximum distance value generator  607 , a real number subtractor  608 , real number multipliers  609  and  612 , and bit multipliers  610  and  611 . 
     The coordinate shifting value generator  601  calculates a value for the coordinate axis shift (i.e., a coordinate space shifting value) using the positive integer R. That is, it determines, using the positive integer R, a group in the signal space where a received signal is included, and calculates a distance for shifting a bit determining boundary of the group to the origin. The coincidence decision unit  602  compares the K-th bit with the 2-PAM bit by using the positive integer R to decide whether the 2-PAM bit value arrangement is axisymmetric or has the same pattern. The correction value generator  603  generates a new received signal correction symbol value based on the coordinate space shifting value, the scaled digital I or Q channel symbol signal Z, and the positive integer R. The {circumflex over (z)} k  sign value generator  604  generates a sign value of the received signal correction symbol value, and the {circumflex over (z)} k  absolute value generator  605  generates an absolute value of the received signal correction symbol value (i.e., an absolute value of the coordinate shifting value). 
     The minimum distance value generator  606 , using the absolute value of the coordinate shifting value, generates a minimum distance value in a corresponding group for determining a closest distance value to the bit boundary value therein. The maximum distance value generator  607 , using the minimum distance value, generates a maximum distance value in a group area for determining a farthest distance value (the maximum distance value) from the bit boundary value therein. The real number subtractor  608  subtracts the absolute value of the coordinate shifting value from the minimum distance value. The real number multiplier  609  multiplies the result calculated at the real number subtractor  608  by the maximum distance value. The bit multiplier  610  multiplies the results from the coincidence decision unit  602  and the {circumflex over (z)} k  sign value generator  604  in the form of bits. The bit multiplier  611  multiplies the operation result of the bit multiplier  610  by the determined sign value Q in the form of bits. The real number multiplier  612  converts the operation result of the real number multiplier  609  into soft bit metric (LLR) information by multiplying the operation result by the operation result of the bit multiplier  611 . 
     To be short, the soft bit metric operation unit  55  of the invention calculates a soft bit metric per bit with z, R, and Q signals obtained from the scaler  52 , the positive integer converter  53  and the sign determinator  54  shown in  FIG. 5 . 
     The coordinate shifting value (D k ) generator  601  determines a group in a signal space where the received signal, as described in  FIGS. 3 and 4  and will be discussed in Eq. (8) below, is contained, and then calculates a distance for moving a bit boundary of the group to the origin (0 point).
 
 D   0 =0
 
 D   1 =2 (K-1)  
 
 D   2 ={( r   0 ) 2 ×2+1}×2 (K-2)  
 
 D   k ={( r   0   Λr   k-2 ) 2 ×2+1}×2 (K-k)   ,k= 3 ,Λ,K− 1  Eq. (8)
 
where (r 0 , r 1 , . . . , r K-1 ) 2  is a binary expression of R=(r 0 , r 1 , . . . , r K-1 ) 2  outputted from the positive integer converter  603 .
 
     In  FIG. 6 , the coincidence (m k ) decision unit  602 , which compares the K-th bit with the 2-PAM bit to decide whether the 2-PAM bit value arrangement is axisymmetric or has the same pattern, is expressed as follows:
 
 m   0 =0(+1)
 
 m   1 =1(−1)
 
 m   k   =r   k-2 (0 or 1)
 
 k= 2,3 Λ,K− 1  Eq. (9)
 
where, if m k  value is ‘+1’, it means that two bits coincide with each other, and if m k  value is ‘−1’, it means that two bits do not coincide with each other. The correction value ({circumflex over (z)} k ) generator  603  generates, on the basis of the principle described in  FIG. 3  or  4 , a new received signal correction symbol value ({circumflex over (z)} k ) by using the coordinate space shifting value Dk calculated at the coordinate shifting value generator  601 , and z and R that are determined by the scaler  52  and the positive integer converter  53  shown in  FIG. 5 , respectively.
 
     Moreover, the {circumflex over (z)} k  sign value generator  604  generates a sign value G k  of {circumflex over (z)} k  based on the received signal correction symbol value {circumflex over (z)} k  newly generated by the correction value generator  603 , and the {circumflex over (z)} k  absolute value generator  605  generates an absolute value (A k =|{circumflex over (z)} k |) of {circumflex over (z)} k . 
     Using the A k  generated by the {circumflex over (z)} k  absolute value generator  605 , the minimum distance value generator  606  determines a minimum distance value (d min,k /2) closest to the bit boundary value in the corresponding group. 
     Then, using the minimum distance value (d min,k /2) determined by the minimum distance value generator  606 , the maximum distance value generator  607  generates a maximum distance value (d max,k /2) farthest from the bit boundary value in the group area. 
     Meanwhile, the real number subtractor  608  calculates a difference between the minimum distance value (d min,k /2) determined by the minimum distance value generator  606  and the absolute value (A k =|{circumflex over (z)} k |) of the coordinate shifting value {circumflex over (z)} k  determined by the {circumflex over (z)} k  absolute value generator  605 . And, the real number multiplier  607  multiplies the calculation result of the real number subtractor  608  by the maximum distance value (d max,k /2) calculated at the maximum distance value generator  607 . The bit multiplier  610  multiplies the results from the coincidence decision unit  602  and from the correction value generator  603 , and the bit multiplier  611  multiplies the sign value Q k  of the received signal determined by the sign determinator  54  by the result from the bit multiplier  610 . The real number multiplier  612  performs sign conversion on the operation result of the real number multiplier  609  depending on the result provided from the bit multiplier  611 . 
     Now, an operation procedure of the soft bit metric generating apparatus of the invention having the above-described structure will be sequentially described in detail with reference to  FIGS. 5 and 6 . 
     1) A symbol of a received two-dimensional signal is recovered by the I/Q demodulator  201  shown in  FIG. 2 . 
     2) When the recovered symbol signal is inputted to the I and Q channel soft bit metric generators  202  and  203 , respectively, the generators  202  and  203  independently generate bit metrics based on the following algorithm. 
     3) The received PAM symbol signal goes through the A/D converter  51 , and is scaled by the scaler  502  with a reference value used for determining a signal point position. 
     4) A positive integer [R=(r 0 , r 1 , . . . r K-1 ) 2 ] of the output of the above 3) is calculated through the positive integer converter  503 . 
     5) Using the output of the above 4), the coordinate shifting value generator  601  calculates a value for shifting the coordinate axis. 
     6) Based on the output of the above 4), the coincidence decision unit  602  decides whether the 2-PAM bit value arrangement is axisymmetric or has the same pattern. 
     7) With respect to b 0 , the sign value from the {circumflex over (z)} k  sign value generator  604  is taken by using the received symbol value that is the output of the above 3). 
     8) Using the coordinate axis shifting value calculated at the above 5), the correction value generator  603  corrects the received symbol value by shifting the coordinate axis. 
     9) The {circumflex over (z)} k  sign value generator  604  determines a sign value of the corrected symbol value like the following: G k =sign ({circumflex over (z)} k ), and the bit multipliers  610  and  611  determine sign values of G k  and m k . 
     10) Using the output of the above 8), the minimum distance value generator  606  generates a minimum distance value d min,k /2 closest to a bit boundary value in a corresponding group and the maximum distance value generator  607  generates a maximum distance value d max,k /2 farthest from to a bit boundary value in a group area. 
     11) Using the results thus obtained, the real number multiplier  612  calculates a soft bit metric LLR per bit. 
     When received signals exist in a 64-QAM signal space, the operation result using the algorithm suggested by the invention is shown in Table 1 below: 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Soft bit metric operation procedure of 64-QAM signal and its results 
               
            
           
           
               
               
               
            
               
                   
                 y 1  = (−7.8d, 3.5d) 
                 y 2  = (−3.5d, 4.5d) 
               
            
           
           
               
               
               
               
               
            
               
                   
                 i = −7.8d 
                 q = 3.5d 
                 i = −3.5d 
                 q = 4.5d 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Steps 
                 b I,0   
                 b I,1   
                 b I,2   
                 b Q,1   
                 b Q,2   
                 b Q,3   
                 b I,0   
                 b I,1   
                 b I,2   
                 b Q,1   
                 b Q,2   
                 b Q,3   
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 1) 
                 |z| 
                 7.8 
                 3.5 
                 3.5 
                 4.5 
               
               
                 2) 
                 R 
                 (111) 2   
                 (012) 2   
                 (011) 2   
                 (100) 2   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 3) 
                 C k   
                 0 
                 4 
                 6 
                 0 
                 4 
                 2 
                 0 
                 4 
                 2 
                 0 
                 4 
                 6 
               
               
                 4) 
                 m k   
                 +1 
                 −1 
                 −1 
                 +1 
                 −1 
                 +1 
                 +1 
                 −1 
                 +1 
                 +1 
                 −1 
                 −1 
               
               
                 5) 
                 Q k   
                 −1 
                 +1 
                 +1 
                 +1 
                 +1 
                 +1 
                 −1 
                 +1 
                 +1 
                 +1 
                 +1 
                 +1 
               
               
                 6) 
                 {circumflex over (Z)} k   
                 7.8 
                 3.8 
                 1.8 
                 3.5 
                 −0.5 
                 1.5 
                 3.5 
                 −0.5 
                 1.5 
                 4.5 
                 0.5 
                 −1.5 
               
               
                 7) 
                 G k   
                 −1 
                 +1 
                 +1 
                 +1 
                 −1 
                 +1 
                 −1 
                 −1 
                 +1 
                 +1 
                 +1 
                 −1 
               
               
                 8) 
                 d min,k   
                 3 
                 1 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 0 
                 2 
                 0 
                 0 
               
               
                 9) 
                 d max,k   
                 4 
                 2 
                 1 
                 2 
                 1 
                 1 
                 2 
                 1 
                 1 
                 3 
                 1 
                 1 
               
               
                 10) 
                 LLR 
                 19.2 
                 5.6 
                 1.8 
                 −5.0 
                 −0.5 
                 −1.5 
                 5.0 
                 −0.5 
                 −1.5 
                 −7.5 
                 0.5 
                 −1.5 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Decision 
                 1 
                 1 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
                 0 
                 0 
                 1 
                 0 
               
               
                   
               
            
           
         
       
     
     The method of the present invention as mentioned above may be implemented by a software program that is stored in a computer-readable storage medium such as CD-ROM, RAM, ROM, floppy disk, hard disk, optical magnetic disk, etc. This process may be readily carried out by those skilled in the art; and therefore, details of thereof are omitted here. 
     The present application contains subject matter related to Korean patent application No. 2005-0119590, and No. 2006-0083170, filed in the Korean Intellectual Property Office on Dec. 8, 2005 and Aug. 30, 2006, the entire contents of which are incorporated herein by reference. 
     While the present invention has been described with respect to certain preferred embodiments, it will be apparent to those skilled in the art that various changes and modifications may be made without departing from the scope of the invention as defined in the following claims.