Patent Publication Number: US-7583729-B2

Title: Adaptive equalizer and related method thereof

Description:
BACKGROUND 
     The invention relates to an adaptive equalizer and related method thereof, and more particularly, to an adaptive equalizer and related method capable of utilizing a weighted signal for controlling the adjustment weight of the equalization coefficients. 
     In communication systems, utilization of digital communication increases with each passing day. In order to raise the performance of the transmission device, it is important to overcome the non-ideal properties of the transmission channel. Common communication systems adopt equalizers in the front ends of receivers to decrease the effects of these non-ideal properties. The equalizer reduces the channel noise and other interference of the received data, so as to decode the received data more precisely. As a result, the transmission quality is guaranteed. Take the adaptive equalizer as an example, the adaptive equalizer utilizes a plurality of equalization coefficients to equalize a received signal, and adjusts the equalization coefficients according to the received signal and a reference signal. The reference signal may be a training sequence or a bit stream corresponding to a computing result of a slicer decoder or a Viterbi detector. The slicer decoder determines the received signal to be “0” or “1” by comparing the equalized signal with a slicing threshold. The Viterbi detector determines the received signal to be “0” or “1” by considering the relationship of a series of received data. Hence, the accuracy of the Viterbi detector is higher than the slicer decoder. 
     Please refer to  FIG. 1 .  FIG. 1  is functional block diagram of a related art adaptive equalizer  10 . The adaptive equalizer  10  comprises an equalization unit  12 , a reference signal generator  14 , and a coefficient adapting circuit  15 . The coefficient adapting circuit  15  includes an error computing unit  16  and a coefficient computing unit  18 . Firstly, the equalization unit  12  utilizes a plurality of equalization coefficients C 0 (0), C 1 (0), . . . , C N (0) to process a received signal y, and then generates an equalized signal y eq  accordingly. The operation of the equalization unit  12  will be detailed in the following paragraph. Secondly, the reference signal generator  14  generates a desired signal ŷ by utilizing a training sequence, or by utilizing the bit stream d outputted by a slicer decoder or a Viterbi detector. Thirdly, the error computing unit  16  subtracts a desired signal ŷ from the equalized signal y eq  to generate an error signal e. Finally, the coefficient computing unit  18  utilizes the received signal y and the error signal e to perform a Least Mean Square (LMS) operation to update the plurality of equalization coefficients to be C 0 (1), C 1 (1) . . . , C N (1). The equalization coefficients as C 0 , C 1 , . . . , C N  will approach proper values by repeating the operation mentioned above several times. The operation of the related art coefficient computing unit  18  is represented in the following equation:
 
 C   j ( k )= C   j ( k− 1)−τ· e ( k )· y ( k−j )  Equation (1)
 
     In Equation (1), τ denotes a coefficient adjustment factor, which can be a predetermined value or an adjustable value relating to the channel environment. When the variation of the channel environment is very high, τ can be determined to be a greater number, which causes the equalization coefficients C 0 , C 1 , . . . , C N  to be adjusted substantially and to enter a stable state (i.e. are convergent) quickly. On the contrary, if τ is set to be a smaller number, the equalization unit  12  will take more time to let the equalization coefficients C 0 , C 1 , . . . , C N  enter the stable state. In addition, if τ is set to be a smaller number, the probability of the equalization coefficients C 0 , C 1 , . . . , C N  not being convergent is reduced. Hence, the system error rate is reduced at the same time. As the equalization coefficients C 0 , C 1 , . . . , C N  are updated several times, the error signal e approaches zero. As a result, the equalization coefficients C 0 , C 1 , . . . , C N  enter the stable state. Until the channel environment changes, the error signal e increases, then the adaptive equalizer  10  adjusts the equalization coefficients C 0 , C 1 , . . . , C N  utilized by the equalization unit  12  in the same manner. 
     Please refer to  FIG. 2 .  FIG. 2  is schematic diagram of the equalization unit  12  shown in  FIG. 1 . The equalization unit  12  comprises a plurality of delay units  22 ,  24 ,  26 , a plurality of multipliers  32 ,  34 ,  36 ,  38  with adjustable coefficients C 0 (k), C 1 (k), . . . , C N (k), and a plurality of adders  42 ,  44 ,  46 . The delay time of the delay units  22 ,  24 ,  26  relate to the sampling time of the received signal y. The delay units  22 ,  24 ,  26  output a plurality of received signals y(k), y(k−1) . . . y(k−N) (i.e., delayed signals), respectively, corresponding to different sampling times. The multipliers  32 ,  34 ,  36 ,  38  respectively multiply the adjustable equalization coefficients C 0 (k), C 1 (k), . . . , C N (k) by the corresponding delay signals y(k), y(k−1) . . . y(k−N). The sum of the multiplication result is the equalized signal y eq . The operation of the equalization unit  12  is shown in the following equation:
 
 y   eq ( k )= C   0   ·y ( k )+ C   1   ·y ( k− 1)+ . . .  C   N   ·y ( k−N )  Equation (2)
 
     In practice, the error rates of certain received data, and more particularly the received data with level transition, are higher than other received data. However, the related art adaptive equalizers do not address the problem mentioned above. Therefore, if the error rates of the certain received data mentioned above are reduced, the averaged error rates of the communication systems are improved significantly. 
     SUMMARY 
     It is therefore an objective of the claimed invention to provide an adaptive equalizer and the related method to solve the problem mentioned above. 
     According to the claimed invention, an adaptive equalizer is disclosed. The weighted adaptive equalizer comprises: a reference signal generator for generating a reference signal according to a first reference source; an equalization unit for processing a received signal according to a plurality of equalization coefficients to generate an equalized signal; a weighted signal generator for generating a weighted signal according to a second reference source; and a coefficient adapting circuit for adjusting the plurality of equalization coefficients according to the reference signal, the equalized signal, the weighted signal, and the received signal. 
     According to the claimed invention, an adaptive equalizer is disclosed. The adaptive equalizer comprises: a reference signal generator for generating a reference signal according to a first reference source; an equalization unit for generating an equalized signal by processing a received signal according to a plurality of equalization coefficients; and a coefficient adapting circuit for adjusting the plurality of equalization coefficients according to a projection vector, the reference signal, the equalized signal, and the received signal. 
     According to the claimed invention, an adaptive equalizing method is disclosed. The adaptive equalizing method comprising: generating a reference signal according to a first reference source; generating an equalized signal by processing a received signal according to a plurality of equalization coefficients; generating a weighted signal according to a second reference source; and adjusting the plurality of equalization coefficients according to the reference signal, the equalized signal, the weighted signal, and the received signal. 
     According to the claimed invention, an adaptive equalizing method is disclosed. The adaptive equalizing method comprises: generating a reference signal according to a first reference source; generating an equalized signal by processing a received signal according to a plurality of equalization coefficients; and adjusting the plurality of equalization coefficients according to a projection vector, the reference signal, the equalized signal, and the received signal. 
     The present invention utilizes the weighted signal generator to generate a weighted signal relating to the expected error rate of the received signals, and then the adjustment weight of the equalization coefficients is adjusted according to the weighted signal. In addition, a projecting unit of the adaptive equalizer filters the noises, which induces higher error rates, according to the present invention. Hence, the adaptive equalizer adjusts the equalization coefficients in accordance with the noises that induce higher error rates. As a result, the averaged error rate is reduced significantly according to the present invention. 
     These and other objectives of the present invention will no doubt become obvious to those of ordinary skill in the art after reading the following detailed description of the preferred embodiment that is illustrated in the various figures and drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a functional block diagram of a related art adaptive equalizer. 
         FIG. 2  is schematic diagram of the equalization unit shown in  FIG. 1 . 
         FIG. 3  is a functional block diagram of the weighted adaptive equalizer according to a first embodiment of the present invention. 
         FIG. 4  is a functional block diagram of the weighted adaptive equalizer according to the second embodiment of the present invention. 
         FIG. 5  is functional block diagram of a weighted adaptive equalizer according to a third embodiment of the present invention. 
         FIG. 6  is a functional block diagram of the weighted adaptive equalizer according to the fourth embodiment of the present invention. 
         FIG. 7  is a functional block diagram of the weighted adaptive equalizer according to the fifth embodiment of the present invention. 
         FIG. 8  is a functional block diagram of the third adaptive equalizer according to the sixth embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     Please refer to  FIG. 3 .  FIG. 3  is a functional block diagram of the weighted adaptive equalizer  50  according to a first embodiment of the present invention. As shown in  FIG. 3 , the weighted adaptive equalizer  50  is electrically connected to a Viterbi detector  51 , which is utilized to generate a bit stream d by processing the equalized signal y eq  outputted from the weighted adaptive equalizer  50 . The weighted adaptive equalizer  50  comprises an equalization unit  52 , a reference signal generator  54 , a weighted signal generator  56 , and a coefficient adapting circuit  58 . The coefficient adapting circuit  58  comprises an error computing unit  62  and a coefficient computing unit  64 . The equalization unit  52  utilizes the plurality of equalization coefficients C 0 , C 1  . . . , C N  to equalize a received signal y to generate an equalized signal y eq . The received signal y may be a base-band signal of the wireless communication system and a disc read-back signal. 
     The reference signal generator  54  utilizes the first reference source to generate a desired signal ŷ. In the present embodiment, the first reference source may be a bit stream d outputted from the Viterbi detector  51  or another signal utilized by the communication system, such as an output signal of a related art slicer decoder, which generates the output signal according to the received signal y, or the equalized signal y eq  corresponding to the received signal y. Please note that owing to the operation of generating the desired signal ŷ being well known to people skilled in the art, the description of the operation of the reference signal generator  54  is omitted for the sake of brevity. In other words, any method and apparatus applied in the related art adaptive equalizers generating the desired signal ŷ can be applied to the reference signal generator  54  according to the present invention. Assume the bit stream d is utilized as the first reference source according to the present embodiment. Owing to the bit stream d outputted by the Viterbi detector  51  being determined to be a correct decoded data, the signal derived from the bit stream d is determined to be the desired signal ŷ of the received signal y. As the channel model is (1,2,2,1), the desired signal ŷ is generated with the bit stream d according to the following equation:
 
 ŷ ( k )=1 ·d ( k )+2 ·d ( k− 1)+2 ·d ( k− 2)+1 ·d ( k− 3)  Equation (3)
 
     Please note that there may be a difference between the input timings of reference signal and the received signal y. As a result, a delayed unit can be adopted for alleviating the difference between the input timings. 
     The weighted signal generator  56  utilizes a second reference source to generate a weighted signal w, and drives the coefficient adapting circuit  58  according to the weighted signal w. In the present embodiment, the second reference source may be the bit stream d outputted by the Viterbi detector  51  or other signals utilized by the communication system, such as the received signal y, the output signal of the slicer decoder, which generates the output signal according to the received signal y, the desired signal ŷ, and the equalized signal y eq . The operation of generating the weighted signal w will be detailed in the following paragraph with the input signal being the bit stream d or other signals utilized by the communication system. 
     Assume the bit stream d outputted by the Viterbi detector  51  is utilized as the second reference source. If the bit stream d corresponds to a specific bit stream, the weighted signal generator  56  generates a weighted signal w corresponding to a specific value. For example, when the specific bit stream has a level transition, the weighted signal generator  56  generates the weighted signal w equal to “1”; otherwise, the weighted signal generator  56  generates the weighted signal w equal to “0” according to the present embodiment. Hence, the coefficient adapting circuit  58  is capable of generating proper equalization coefficients according to the weighted signal w. The operation of the weighted signal generator  56  mentioned above is shown in the following equation: 
     
       
         
           
             
               
                 
                   
                     w 
                     ⁡ 
                     
                       ( 
                       k 
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                   = 
                   
                     { 
                     
                       
                         
                           
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                                   d 
                                   
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                             = 
                             
                               
                                 [ 
                                 
                                   00 
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                                   X 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   11 
                                 
                                 ] 
                               
                               ⁢ 
                               
                                   
                               
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                                 or 
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                                 [ 
                                 
                                   11 
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                                   X 
                                   ⁢ 
                                   
                                       
                                   
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                             0 
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                           else 
                         
                       
                     
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                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     4 
                     ) 
                   
                 
               
             
           
         
       
     
     In Equation (4), X denotes any logic value (i.e., “0” or “1”). In other words, when the weighted signal generator  56  determines the bit stream d is “00011”, “00111”, “11000”, or “11000”, the weighted signal generator  56  determines that the bit stream d has a level transition. As a result, the weighted signal generator  56  generates the weighted signal w equal to “1”. Please note that, the length of the bit stream can be a system predetermined value of any value, and is not limited by the present embodiment. In addition, the weighted signal w is capable of relating to more than 2 values according to the present invention. With the present embodiment, the weighted signal w only relates to “0” or “1”, so the weighted signal generator  56  is utilized as a switch to enable or disable the coefficient adapting circuit  58 . If the coefficient adapting circuit  58  is enabled, the coefficient adapting circuit  58  adjusts the equalization coefficients C 0 , C 1 , . . . , C N ; otherwise, the coefficient adapting circuit  58  does nothing about the equalization coefficients C 0 , C 1 , . . . , C N . 
     In addition, other signals of the communication system can be utilized as the second reference source. Take the equalized signal y eq  as an example to describe to operation the weighted signal generator  56 . When the equalized signal y eq  relates to different values, the weighted signal w is determined to be equal to different values. In the present embodiment, the equalized signal y eq  relates to the following values: “6”, “4”, “2”, “0”, “−2”, “−4”, or “−6” equal to the inner product of the four inputted bits and the vector (1 2 2 1). Before generating the inner product, the inputted bits equal to zero are replaced by “−1”, and the inputted bits equal to one are replaced by “+1”. Therefore, if the inputted bit stream is (1111), the value of the corresponding equalized signal y eq  is “6”; if the inputted bit stream is (1110), the value of the corresponding equalized signal y eq  is “4”; if the inputted bit stream is (0110), the value of the corresponding equalized signal y eq  is “2”; if the inputted bit stream is (1000), the value of the corresponding equalized signal y eq  is “−4”. In summary, as the bit stream has more level transitions, the absolute value of the corresponding equalized signal y eq  is smaller. Owing to the error probability increasing with the number of the level transitions of the bits stream, the weighted signal generator  56  generates the weighted signal w equal to “1” if the equalized signal y eq  is “2”, “0”, or “−2”. On the contrary, the weighted signal generator  56  generates the weighted signal w equal to “0” and transmits the weighted signal w to the coefficient adapting circuit  58  if the equalized signal y eq  is “6”, “4”, “−4”, or “−6”. Therefore the coefficient adapting circuit  58  calculates proper equalization coefficients C 0 , C 1 , . . . , C N  according to the weighted signal. The operation of generating the weighted signal w mentioned above is shown in the following equation: 
     
       
         
           
             
               
                 
                   
                     w 
                     ⁡ 
                     
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                       k 
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                   = 
                   
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                           else 
                         
                       
                     
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                   Equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     5 
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     In the Equation (5), only two predetermined ranges are utilized to determine the value of the equalized signal y eq . The predetermined ranges are {y eq |−3&lt;y eq &lt;3} and {y eq |y eq &lt;−3 or y eq &gt;3}. When more than two predetermined ranges are utilized in the present invention, more than two kinds of weighted signal w relating to different values are generated accordingly. 
     The coefficient adapting circuit  58  utilizes the weighted signal w, the received signal y, the desired signal ŷ, and the equalized signal y eq  to calculate proper equalization coefficients C 0 , C 1 , . . . , C N , and updates the equalization coefficients C 0 , C 1  . . . , C N  utilized by the weighted adaptive equalizer  50 . Hence a more reliable equalized signal y eq  is generated according to the updated equalization coefficients C 0 , C 1 , . . . , C N . In the present embodiment, firstly, the error computing unit  62  calculates the difference between the desired signal ŷ and the equalized signal y eq  to generate an error signal e. Next, the coefficient computing unit  64  utilizes the weighted signal w, the error signal e, and the received signal y to perform a Least Mean Square (LMS) operation to adjust the equalization coefficients C 0 , C 1  . . . , C N . The operation of the coefficient computing unit  64  is shown in the following equation:
 
 C   j ( k )= C   j ( k −1)−τ· e ( k )· w ( k )· y ( k−j )  Equation (6)
 
     In the Equation (6), τ denotes the coefficient adjustment factor, which can be a predetermined value or an adjustable value corresponding to the channel environment. If the weighted adaptive equalizer  50  determines that the expected error rate of the received signal is higher than usual, the weighted signal generator  56  generates the weighted signal w with a greater value. As a result, the coefficient computing unit  64  adjusts the equalization coefficients C 0 , C 1 , . . . , C N  significantly. On the contrary, if the weighted adaptive equalizer  50  determines that the expected error rate of the received signal is lower than usual, the weighted signal generator  56  generates the weighted signal w with a lesser value. As a result, the coefficient computing unit  64  adjusts the equalization coefficients C 0 , C 1 , . . . , C N  slightly. Next, the newly calculated equalization coefficients C 0 (k), C 1 (k) . . . C N (k) replace the original equalization coefficients C 0 (k−1), C 1 (k−1) . . . C N (k−1) utilized by the weighted adaptive equalizer  50 . Please note that the weighted signal w not only can be utilized to control the coefficient computing unit  64 , but also can be utilized to control the error computing unit  62  according to the Equation (6). That is the weighted signal w is multiplied by the error signal e firstly, then the multiplication result is transmits to the coefficient computing unit  64  for calculating the proper equalization coefficients C 0 (k), C 1 (k) . . . C N (k). No matter if the utilization of the weighted signal w is controlling the coefficient computing unit  64  or controlling the error computing unit  62 , the calculated equalization coefficients C 0 (k), C 1 (k) . . . C N (k) are the same. As a result, the following embodiment of the present invention utilizes the weighted signal w to control the error computing unit  62 . 
     Please refer to  FIG. 4 .  FIG. 4  is a functional block diagram of the weighted adaptive equalizer  50  according to the second embodiment of the present invention. The difference between the weighted adaptive equalizers shown in  FIG. 4  and  FIG. 3  is the connection of the weighted signal generator  56 . According to the second embodiment, the weighted signal generator  56  is electrically connected to the error computing unit  62 . The error computing unit  62  utilizes the weighted signal w to adjust the difference between the desired signal ŷ and the equalized signal y eq , and transmits the weighted error signal e to the coefficient computing unit  64 . Then the coefficient computing unit  64  performs the LMS operation by utilizing the weighted error signal e for generating and updating the proper equalization coefficients C 0 , C 1  . . . C N . 
     Please refer to  FIG. 5 .  FIG. 5  is functional block diagram of a weighted adaptive equalizer  70  according to a third embodiment of the present invention. With the present embodiment, the weighted adaptive equalizer  70  is electrically connected to a Viterbi detector  71 , which processes the equalized signal y eq  outputted by the weighted adaptive equalizer  70  to generate a bit stream d. As shown in  FIG. 5 , the weighted adaptive equalizer  70  comprises an equalization unit  72 , a reference signal generator  74 , a weighted signal generator  76 , and a coefficient adapting circuit  78 . The coefficient adapting circuit  78  further comprises an error computing unit  82 , a projecting unit  84 , and a coefficient computing unit  86 . Since the architectures and the operations of the equalization unit  72 , the reference signal generator  74 , the weighted signal generator  76 , and the error computing unit  82  are the same as that of the components having the same names shown in  FIG. 3 , the detailed description of the equalization unit  72 , the reference signal generator  74 , the weighted signal generator  76 , and the error computing unit  82  is omitted for the sake of brevity. 
     According to the present embodiment, the difference between the weighted adaptive equalizer  70  and the weighted adaptive equalizer  50  shown in  FIG. 3  is the use of the projecting unit  84 . The projecting unit  84  is utilized to filter certain kinds of noise or interference, which may increase the error probability of the following decoding procedure (i.e., the operation of the Viterbi detector  71 ). Therefore, the weighted adaptive equalizer  70  adjusts equalization coefficients C 0 , C 1  . . . , C N  to alleviate these kinds of interference before the interference enters the Viterbi detector  71 . For example, “6, 4, 0, −4” and “4, 0, −4, −6” are two normal bit streams. When the bit stream equal to “4, 0, −4, −6” is transmitted through a communication channel, and is affected by an interference equal to “2, 4, 4, 2”, the Viterbi detector  71  of the receiver will determine the transmitted bit stream is “6, 4, 0, −4”. Hence the following decoding procedure is disturbed by the interference, and an incorrect decision (i.e., incorrect bit stream d) of the decoding procedure is generated. With the present embodiment, the weighted adaptive equalizer  70  utilizes a projection vector {right arrow over (v)} to express the format of the interference mentioned above. The projecting unit  84  generates a projected received signal y v  equal to the inner product of the projection vector {right arrow over (v)} and the received signal y, and also generates a projected error signal e v  equal to and inner product of the projection vector {right arrow over (v)} and the error signal e. The operations of generating the projected received signal y v  and the projected error signal e v  are shown in the following equations:
 
 e   v ( k )=[ e ( k− 1) e ( k ) e ( k +1) e ( k+ 2)]·[ v   1   v   2   v   3   v   4 ]  Equation (7)
 
 y   v ( k )=[ y ( k− 1) y ( k ) y ( k+ 1) y ( k+ 2)]·[ v   1   v   2   v   3   v   4 ]  Equation (8)
 
In Equation (7) and Equation (8), the projection vector [v 1  v 2  v 3  v 4 ] denotes the format of the interference mentioned above. If the channel module is equal to (1,2,2,1), the projection vector {right arrow over (v)}=[v 1  v 2  v 3  v 4 ] is determined to be [1 2 2 1]. The coefficient computing unit  86  utilizes the weighted signal w, projected received signal y v , and the projected error signal e v  to perform the LMS operation to generate the proper equalization coefficients C 0 (k), C 1 (k), . . . , C N (k) accordingly. As a result, the equalization coefficients C 0 (k−1), C 1 (k−1), . . . , C N (k−1) utilized by the equalization unit  72  are updated accordingly. The operation of the coefficient computing unit  86  are shown in the following Equation:
 
 C   j ( k )= C   j ( k −1)−τ· w ( k )· e   v ( k )· y   v ( k−j )  Equation (9)
 
     Please note that the weighted signal w can also be utilized to control the projecting unit  84  according to Equation (9). 
     Please refer to  FIG. 6 .  FIG. 6  is a functional diagram of the weighted adaptive equalizer  70  according to the fourth embodiment of the present invention. As shown in  FIG. 6 , compared with the weighted adaptive equalizer  70  shown in  FIG. 5 , the difference is the weighted signal generator  76  is electrically connected to the projecting unit  84 . The projecting unit  84  adjusts the projected received signal y v  or the projected error signal e v  according to the weighted signal w, and then transmits the adjusting result of projected received signal y v  and projected error signal e v  to the coefficient computing unit  86 . Next, the coefficient computing unit  86  performs a LMS operation to generate the proper equalization coefficients C 0 (k), C 1 (k), . . . C N (k) for updating the currently utilized equalization coefficients C 0 (k−1), C 1 (k−1), . . . C N (k−1). 
     Please refer to  FIG. 7 .  FIG. 7  is a functional block diagram of the weighted adaptive equalizer  70  according to the fifth embodiment of the present invention. Comparing the weighted adaptive equalizer  70  shown in  FIG. 6  with the weighted adaptive equalizer  70  shown in  FIG. 7 , the weighted adaptive equalizer  70  shown in  FIG. 6  only comprises one projecting unit  84 , but the weighted adaptive equalizer  70  shown in  FIG. 7  comprises a plurality of (e.g. M) projecting units  84   a , . . .  84   b . The operations and architectures of the projecting units  84   a , . . .  84   b  are the same as the operation and architecture of the projecting unit  84  shown in  FIG. 6 . With the present embodiment, the weighted adaptive equalizer  70  is capable of alleviating M kinds of interferences inducing higher error probability of the following decoding procedure by adopting M projection vectors {right arrow over (v)} 1  {right arrow over (v)} 2  {right arrow over (v)} 3  . . . {right arrow over (v)} M . Assume the channel model equal to (1,2,2,2,1), the projection vectors {right arrow over (v)} 1 =[v 1  v 2  v 3  v 4  v 5 ]=[1 2 2 2 1] and {right arrow over (v)} 2 =[v 1  v 2  v 3  v 4  v 5  v 6  v 7 ]=[1 2 1 0 −1 −2 −1] are adopted. The related operation of generating the projected received signal y v  and the projected error signal e v  are shown in the following equation:
 
 e   v,i ( k )=[ e ( k− 1) e ( k ) e ( k+ 1) . . .  e ( k −2 +L   i )]· {right arrow over (v)}   i   Equation (10)
 
 y   v,i ( k )=[ y ( k− 1) y ( k ) y ( k+ 1) . . .  y ( k −2 +L   i )]· {right arrow over (v)}   i   Equation (11)
 
     In the Equation (10) and Equation (11), L i  denotes the dimension of the projection vector {right arrow over (v)} i . The projecting unit  84   a  generates the projected error signal e v,1  and the projected received signal y v,1  according to the projection vector {right arrow over (v)} 1 . In the same manner, the projecting unit  84   b  generates the projected error signal e v,n  and the projected received signal y v,n  according to the projection vector {right arrow over (v)} n . Therefore, the coefficient computing unit  86  adjusts the equalization coefficients C 0 , C 1 , . . . , C N  according to the projected error signal e v,1 , . . . , e v,n  and the projected received signal y v,1 , . . . , y v,n . The operation of adjusting the equalization coefficients C 0 , C 1  . . . , C N  is shown is the following equation:
 
 C   j ( k )= C   j ( k− 1)−τ·(Σ i=1   M   w   i ( k )· e   v,i ( k )· y   v,i ( k−j ))  Equation (12)
 
     In Equation (12), w i (k) denotes a weighted signal relating to the projection vector {right arrow over (v)} i , and each weighted signal w i  is capable of relating to different values according to the corresponding projection vectors {right arrow over (v)} i . If the weighted signals w i  are assigned the same value, the weighted signal generator outputs M same output signals w i  (i.e. all projection vectors {right arrow over (v)} i  share one output signal w). Please note that, the weighted signal w i  can be adjusted by the coefficient computing unit  86  according to the importance of the corresponding projection vectors {right arrow over (v)} i . For example, when the importance of a projection vector {right arrow over (v)} k  is greater than usual (i.e. the projection vectors {right arrow over (v)} k  effects the correction of the decoding procedure significantly), the corresponding weighted signal w k  is greater than other weighted signals w i . 
     Please refer to  FIG. 8 .  FIG. 8  is a functional block diagram of the adaptive equalizer  110  according to the sixth embodiment of the present invention. With the present embodiment, the adaptive equalizer  110  is electrically connected to the Viterbi detector  111  utilized to generate a bit stream d by processing the equalized signal y eq  outputted by the adaptive equalizer  110 . The adaptive equalizer  110  comprises an equalization unit  112 , a reference signal generator  114 , and a coefficient adapting circuit  118 . The coefficient adapting circuit  118  comprises an error computing unit  122 , a projecting unit  124 , and a coefficient computing unit  126 . Since the architectures and operations of the equalization unit  112 , the reference signal generator  114 , the error computing unit  122 , the projecting unit  124 , and the coefficient computing unit  126  are the same as the architectures and operations of the components having the same names shown in  FIG. 7 , the detailed description of the equalization unit  112 , the reference signal generator  114 , the error computing unit  122 , the projecting unit  124 , and the coefficient computing unit  126  is omitted for the sake of brevity. Compared with the weighted adaptive equalizer  70  shown in  FIG. 5 , the adaptive equalizer  110  shown in  FIG. 8  does not include a weighted signal generator to simplify the operation of the adaptive equalizer  110 . The cost of the system is reduced at the same time. Therefore the coefficient computing unit  126  adjusts equalization coefficients C 0 , C 1 , . . . , C N  according to the projected error signal e v  and the projected received signal y v  without a weighted signal. The operation of adjusting the equalization coefficients C 0 , C 1 , . . . , C N  is shown in the following equation:
 
 C   j ( k )= C   j ( k− 1)−τ· e   v ( k )· y   v ( k−j )  Equation (13)
 
     Although only one projecting unit is utilized in the adaptive equalizer  110  shown in  FIG. 8  according to the present invention, the adaptive equalizer  110  is capable of utilizing numerous projecting units as shown in  FIG. 7  according to the present invention. 
     Compared with the related art, the adaptive equalizer utilizes the weighted signal generator to generate a weighted signal relating to the expected error rate of the received signal. As the error rate of a received signal may be higher than other received signals, the generated weighted signal is greater than usual. Next the greater weighted signal is utilized to control the operations of the error computing unit, projecting unit, and coefficient computing unit. In addition, a projecting unit is utilized to filter certain noises inducing higher error rates, in order to calculate proper equalization coefficients in accordance with the noises mentioned above. In summary, the weighted signal generator and the projecting unit assist the adaptive equalizer to decrease the error rate significantly. 
     Those skilled in the art will readily observe that numerous modifications and alterations of the device and method may be made while retaining the teachings of the invention. Accordingly, the above disclosure should be construed as limited only by the metes and bounds of the appended claims.