Abstract:
An equalizer applied in a multiple input multiple output (MIMO) orthogonal frequency division multiplex (OFDM) system for alleviating interference among a plurality of received symbol blocks is disclosed. The equalizer includes: a matched filter for extracting a preliminary equalized signal vector from a received symbol block; a blocking device for generating a preliminary interference signal vector by attenuating a equalized signal vector from the received symbol block; a weighting device, electrically connected to the blocking device, for generating an interference signal vector by adjusting the preliminary interference signal vector; and a subtractor, electrically connected to the weighting device and the matched filter, for generating the equalized signal vector of the received symbol block according to the difference between the interference signal vector and the preliminary equalized signal vector.

Description:
BACKGROUND  
       [0001]     The disclosure relates to an equalizer, and more particularly to an equalizer applied in a MIMO-OFDM system.  
         [0002]     Generally, a key feature of the multiple input multiple output (MIMO) system is respectively arranging a plurality of antennas at a transmitter and a receiver of the MIMO system. Therefore, the MIMO system is capable of transceiving data via a plurality of channels among the plurality of antennas. Take  FIG. 1  as an example,  FIG. 1  is a schematic diagram of a related art MIMO system  10 . The related art MIMO system  10  comprises a transmitter  20  having three antennas  22 ,  24 ,  26 , and a receiver  30  having two antennas  32 ,  34 . The signals T 1 , T 2 , T 3  (i.e., a transmitted signal vector) radiate from the transmitter  20  pass through 3*2 channels  42 ,  44 ,  46 ,  48 ,  52 ,  54  then arrive at the receiver  30 . Assume that the transmitter  20  attempts to transmit two data streams D 1 , D 2  to the receiver  30 . Firstly, the transmitter  20  generates each transmitted signal by integrating the data streams D 1 , D 2  multiplied by different gain values. Next, the transmitter  20  transmits the transmitted signals T 1 , T 2 , T 3  via antennas  22 ,  24 ,  26 , respectively. The operation of generating the transmitted signals T 1 , T 2 , T 3  is represented as the following equations: 
 
 T   1   =D 1* V   1,1   +D 2* V   1,2   Equation (1) 
 
 T   2   =D 1* V   2,1   +D 2* V   2,2   Equation (2) 
 
 T   3   =D 1* V   3,1   +D 2* V   3,2   Equation (3) 
 
         [0003]     In Equations (1), (2), (3), the elements of the three-dimension vector [V 1,1 , V 2,1 , V 3,1 ] T  determines the percentages of the transmitted signals T 1 , T 2 , T 3  corresponding to the data stream D 1 . As a result, the three-dimension vector [V 1,1 , V 2,1 , V 3,1 ] T  is a transmitting vector of the data stream D 1 . In the same manner, the elements of the three-dimension vector [V 1,2 , V 2,2 , V 3,2 ] T  determines the percentages of the transmitted signals T 1 , T 2 , T 3  corresponding to the data stream D 2 . Therefore, the three-dimension vector [V 1,2 , V 2,2 , V 3,2 ] T  is a transmitting vector of the data stream D 1 . In the related art, the MIMO system  10  utilizes a method of Singular Value Decomposition (SVD) to determine the transmitting vectors [V 1,1 , V 2,1 , V 3,1 ] T  and [V 1,2 , V 2,2 , V 3,2 ] T , so as to make the data streams D 1 , D 2  received by the receiver  30  orthogonal to each other. As a result, the receiver  30  is capable of extracting the data streams D 1  and D 2  from a plurality of received signals R 1  and R 2 .  
         [0004]     A popular application of the MIMO system is the MIMO-OFDM system. The transmitter of the MIMO-OFDM system radiates n symbols S 1 (k), S 2 (k), . . . , S n (k) (i.e., a symbol block S(k)) via n antennas, and the receiver of the MIMO-OFDM system receives m symbol R 1 (k), R 2 (k), . . . , R m (k) (i.e., a received symbol block R(k)) via m antennas. According to the related art, each symbol of one symbol block comprises a cyclic prefix for alleviating the interference among a plurality of symbol blocks. The cyclic prefix is actually a copy of the last portion of the symbol appended to the front of the symbol during the guard interval. Since the multipath fading causes tones and delayed replicas of tones to arrive at the receiver with some delay spread (i.e., ISI), the cyclic prefix is utilized to allow the tones to be realigned at the receiver. Thus the tones regain orthogonal to each other with the cyclic prefix. As the phenomenon of ISI grows worse, a longer cyclic prefix is required. Because of increasing the cyclic prefix, the channel capacity is reduced accordingly. In other words, if a high-quality equalizer is adopted in the receiver of the MIMO system to alleviate the ISI, the length of the cyclic prefix can be shortened thereby increasing the channel capacity.  
       SUMMARY  
       [0005]     An equalizer applied in a MIMO-OFDM system for alleviating interference among a plurality of received symbol blocks is disclosed. The equalizer comprises: a matched filter for extracting a preliminary desired signal vector from a received symbol block; a blocking device for generating a preliminary interference signal vector by removing a desired signal vector from the received symbol block; a weighting device, electrically connected to the blocking device, for generating an interference signal vector by adjusting the preliminary interference signal vector; and a subtractor, electrically connected to the weighting device and the matched filter, for generating an equalized signal vector of the received symbol block according to the difference between the interference signal vector and the preliminary desired signal vector.  
         [0006]     An equalizing method applied in a MIMO-OFDM system for alleviating interference among a plurality of received symbol blocks is disclosed. The equalizing method comprises: extracting a preliminary desired signal vector from a received symbol block; generating a preliminary interference signal vector by removing a desired signal vector from the received symbol block; generating an interference signal vector by adjusting the preliminary interference signal vector; and generating an equalized signal vector of the received symbol block according to the difference between the interference signal vector and the preliminary desired signal vector. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0007]      FIG. 1  is a schematic diagram of a MIMO system of the related art.  
         [0008]      FIG. 2  is a schematic diagram of an embodiment of the equalizer applied in a receiver of the MIMO-OFDM system according to the first embodiment.  
         [0009]      FIG. 3  is a schematic diagram of an embodiment of the equalizer applied in a receiver of the MIMO-OFDM system according to the second embodiment. 
     
    
     DETAILED DESCRIPTION  
       [0010]     Please refer to  FIG. 2 .  FIG. 2  is a schematic diagram of an embodiment of the equalizer  100  applied in a receiver of the MIMO-OFDM system according to the first embodiment. In the present embodiment, the equalizer  100  is Generalized Sidelobe Canceller (GSC)-based equalizer. As shown in  FIG. 2 , the equalizer  100  comprises a Fourier transform module  110 , a matched filter  120 , a blocking device  140 , a weighting device  160 , and a subtractor  180 . Firstly, the Fourier transform module  110  generates a signal vector z(k) equal to the Fourier transform of the received symbol block r(k). The mathematical module of the received symbol block r(k) and signal vector z(k) are expressed as Equations (4) and (5).  
                   r   ⁡     (   k   )       =       [             r     (   1   )       ⁡     (   k   )               r     (   2   )       ⁡     (   k   )           …           r     (   M   )       ⁡     (   k   )             ]     T       ,     
     ⁢   where     ⁢     
     ⁢               r     (   m   )       ⁡     (   k   )       =       ⁢         ∑     n   =   1     N     ⁢       H   0     (     m   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁢     (   k   )           +       ∑     n   =   1     N     ⁢       H   1     (     m   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁢     (     k   -   1     )           +       v     (   m   )       ⁡     (   k   )                     =       ⁢         ∑     n   =   1     N     ⁢       H     (     m   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁡     (   k   )           +       ∑     n   =   1     N     ⁢       H   1     (     m   ,   n     )       ⁢     F     -   1       ⁢     s   n     ⁢     (     k   -   1     )         +                     ⁢         ∑     n   =   1     N     ⁢       H   2     (     m   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁡     (   k   )           +       v     (   m   )       ⁡     (   k   )                         Equation   ⁢           ⁢     (   4   )               
 
         [0011]     In Equation (4), M denotes the number of receiving antennas, N denotes the number of transmitting antennas, F −1  denotes a Q×Q IFFT matrix, where Q denotes the number of subcarriers, s n  denotes the transmitted signal corresponding to the n-th antenna placed on the transmitter, r (m)  denotes the received symbol of the m-th transmitting antenna, v (m)  denotes the channel noise at the m-th receiving antenna, and H 0   (m,n) , H 1 , and H 2  are respectively defined as:  
           H     (     m   ,   n     )       =     [             h     (     m   ,   n     )       ⁡     (   0   )           0           h     (     m   ,   n     )       ⁡     (   L   )           …           h     (     m   ,   n     )       ⁡     (   1   )               ⋮           h     (     m   ,   n     )       ⁡     (   0   )           0       …       ⋮               h     (     m   ,   n     )       ⁡     (   L   )           …       ⋰       …       ⋮           ⋮       ⋰       …       ⋰       0           0       …           h     (   m   )       ⁡     (   L   )           …           h     (   m   )       ⁡     (   0   )             ]       ,     
     ⁢       H   1     (     m   ,   n     )       =     [         0       …           h     (     m   ,   n     )       ⁡     (   L   )           …           h     (     m   ,   n     )       ⁡     (     G   +   1     )               ⋮       ⋰       0       ⋰       ⋮           0       …       ⋰       …           h     (     m   ,   n     )       ⁡     (   L   )               ⋮       ⋮       ⋮       ⋰       ⋮           0       …       0       …           h     (   m   )       ⁡     (   0   )             ]       ,     
     ⁢   and       
           H   2     (     m   ,   n     )       =     [         0       …           h     (     m   ,   n     )       ⁡     (   L   )           …           h     (     m   ,   n     )       ⁡     (     G   +   1     )           0           ⋮       ⋰       ⋰       ⋮       ⋮       ⋰           0       …       …       …           h     (     m   ,   n     )       ⁡     (   L   )           ⋰           ⋮       ⋮       ⋮       ⋮       ⋮       ⋰           0       …       …       0       0       0         ]       ,       
 
         [0012]     where h (m,n)  denotes the channel impulse response between the m-th receiving antenna and n-th transmitting antenna with order L, and G denotes the length of the cyclic prefix appended in front of a symbol. In Equation (4), the fact that H 0 =H+H 2  is used. It is noted that H 1  and H 2  respectively represent the effects of inter-symbol interference (ISI) and Inter-Carrier Interference (ICI). The frequency-domain counterpart of r(k) can be immediately obtained as  
                   z   ⁡     (   k   )       =       [             z       (   1   )     ⁢   T       ⁡     (   k   )               z       (   2   )     ⁢   T       ⁡     (   k   )           …           z       (   M   )     ⁢   T       ⁡     (   k   )             ]     T       ,     
     ⁢   where     ⁢     
     ⁢               z     (   m   )       ⁡     (   k   )       =       ⁢       Fr     (   m   )       ⁡     (   k   )                   =       ⁢         ∑     n   =   1     N     ⁢       FH   0     (     m   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁡     (   k   )           +                     ⁢         ∑     n   =   1     N     ⁢       FH   1     (     m   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁡     (     k   -   1     )           +       Fv     (   m   )       ⁡     (   k   )                     =       ⁢         ∑     n   =   1     N     ⁢       FH     (     m   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁡     (   k   )           +                     ⁢         ∑     n   =   1     N     ⁢       FH   1     (     m   ,   n     )       ⁢     F     -   1       ⁢     s   n     ⁢     (     k   -   1     )         -                     ⁢         ∑     n   =   1     N     ⁢       FH   2     (     m   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁡     (   k   )           +       Fv     (   m   )       ⁡     (   k   )                     =       ⁢         ∑     n   =   1     N     ⁢       D     (     m   ,   n     )       ⁢       s   n     ⁡     (   k   )           +                     ⁢         ∑     n   =   1     N     ⁢       FH   1     (     m   ,   n     )       ⁢     F     -   1       ⁢     s   n     ⁢     (     k   -   1     )         -                     ⁢             ∑     n   -   1       N     ⁢       FH   2     (     m   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁡     (   k   )           +       Fv     (   m   )       ⁡     (   k   )         ,             ⁢     
     ⁢   where   ⁢     
     ⁢       D     (     m   ,           ⁢   n     )       =       FH     (     m   ,           ⁢   n     )       ⁢     F     -   1                   Equation   ⁢           ⁢     (   5   )               
 
         [0013]     In Equation (5), F denotes a Q×Q FFT matrix, and D (m,n)  is a Q×Q signal signature matrix. The signal vector z(k) also can be expressed as:  
                       z   ⁡     (   k   )       =       ⁢         ∑     n   =   1     N     ⁢     [             D     (     1   ,   n     )       ⁢       s   n     ⁡     (   k   )                 ⋮               D     (     M   ,   n     )       ⁢       s   n     ⁡     (   k   )               ]       +                     ⁢         ∑     n   =   1     N     ⁢     [             FH   1     (     1   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁡     (     k   -   1     )                 ⋮               FH   1     (     M   ,   n     )       ⁢     F     -   1       ⁢       s   n     ⁡     (     k   -   1     )               ]       -                     ⁢         ∑     n   ⁢           =           ⁢   1               ⁢   N       ⁢     [             FH             ⁢   2       (     1   ,   n     )       ⁢           ⁢     F     -   1       ⁢           ⁢     s   n     ⁢           ⁢     (   k   )               ⋮               FH             ⁢   2       (     M   ,   n     )       ⁢           ⁢     F     -   1       ⁢           ⁢     s   n     ⁢           ⁢     (   k   )             ]       +     n   ⁢           ⁢     (   k   )                     =       ⁢       Ds   ⁡     (   k   )       +       F   M     ⁢     H   1     ⁢     F   N     -   1       ⁢     s   ⁡     (     k   -   1     )         -                     ⁢         F   M     ⁢     H   2     ⁢     F   N     -   1       ⁢     s   ⁡     (   k   )         +     n   ⁡     (   k   )                       =       ⁢       Ds   ⁡     (   k   )       +       H     ISI   ,   1       ⁢     s   ⁡     (     k   -   1     )         -       H     ISI   ,   2       ⁢     s   ⁡     (   k   )         +     n   ⁡     (   k   )           ,           ⁢     
     ⁢   where   ⁢     
     ⁢         H   i     =     [           H   i     (     1   ,   1     )           …         H   i     (     1   ,   N     )               ⋮       ⋰       ⋮             H   i     (     M   ,   1     )           …         H   i     (     M   ,   N     )             ]       ,     
     ⁢     1   ≤   i   ≤   2               Equation   ⁢           ⁢     (   6   )               
 
 It should be noted that F M =I M           F with {circle around (×)} being the Kronecker product and I i  being the i×i identity matrix and F N =I N           F. As can be seen from the Equations (4) and (6), the value L increases as the phenomenon of ISI grows worse. Since the receiver of the MIMO-OFDM system adopts the equalizer  100  to prevent the ISI, it is not necessary to ensure the length of the appended cyclic prefix is longer than the channel length (i.e., G&gt;L). If the equalizer  100  is adopted, it is not even necessary to append a cyclic prefix in the guard interval. 
 
         [0014]     The matched filter  120  extracts a preliminary desired signal vector ŷ(k) from the signal vector z(k) with a matrix D. The matrix D is determined for alleviating the effect of multipath fading suffered by the received symbol blocks. In other words, the matched filter  120  is designed for filtering a desired signal vector very similar to the transmitted signal vector s(k). The operation of the matched filter  120  is represented in the following equation:  
                       y   ^     ⁡     (   k   )       =       ⁢       D   H     ·     z   ⁡     (   k   )                     =       ⁢         D   H     ⁢     Ds   ⁡     (   k   )         +       D   H     ⁢     H     ISI   ,   1       ⁢   s   ⁢     (     k   -   1     )       -                     ⁢         D   H     ⁢     H     ISI   ,   2       ⁢     s   ⁡     (   k   )         +       D   H     ⁢     n   ⁡     (   k   )                         Equation   ⁢           ⁢     (   7   )               
 
         [0015]     In Equation (7), D denotes an MQ×NQ matrix. Since the operation of the matched filter  120  for determining the matrix D is well known, the detailed description is omitted for the sake of brevity. Next, the blocking device  140  extracts a preliminary interference signal vector b(k) by attenuating the desired signal vector from the signal vector z(k). The operation of the blocking device  140  is shown in the following equation:  
                     b   ⁡     (   k   )       =       ⁢       B   H     ·     z   ⁡     (   k   )                     =       ⁢         B   H     ⁢     Ds   ⁡     (   k   )         +       B   H     ⁢     H     ISI   ,   1       ⁢     s   ⁡     (     k   -   1     )         -                     ⁢         B   H     ⁢     H     ISI   ,   2       ⁢     s   ⁡     (   k   )         +       B   H     ⁢     n   ⁡     (   k   )                         Equation   ⁢           ⁢     (   8   )               
 
         [0016]     Since B is an MQ×(M−N)Q matrix, the dimension of the preliminary interference signal vector is (M−N)Q. It should be noted that the columns of the matrix B are selected from a plurality of bases of the null space of the matrix D, thereby the desired signal vector of the received symbol block r(k) is theoretically filtered off. Next, the weighting device  160  generates an interference signal vector w(k) as shown in the following equation:  
                     w   ⁡     (   k   )       =       ⁢       U   H     ·     b   ⁡     (   k   )                     =       ⁢         U   H     ⁢     B   H     ⁢     Ds   ⁡     (   k   )         +       U   H     ⁢     B   H     ⁢     H     ISI   ,   1       ⁢     s   ⁡     (     k   -   1     )         -                     ⁢         U   H     ⁢     B   H     ⁢     H     ISI   ,   2       ⁢     s   ⁡     (   k   )         +       U   H     ⁢     B   H     ⁢     n   ⁡     (   k   )                         Equation   ⁢           ⁢     (   9   )               
 
         [0017]     The weighting device  160  determines the matrix U to minimizing the ISI-plus-noise power outputted form the subtractor  180 . The expected value of the ISI-plus-noise power outputted form the subtractor  180  can be expressed as the following equation: 
 
 E{∥i ( k )− U   H   B   H   z ( k )∥ 2 }, where 
 
 i ( k )= D   H ( H   ISI,1   s ( k )− H   ISI,2   s ( k− 1))+ D   H   n ( k )  Equation (10) 
 
 For minimizing the ISI-plus-noise power, the matrix U is determined to be (B H R in B) −1 B H R in D, in which R in =H ISI,1 H ISI,1   H +H ISI,2 H ISI,2   H +R n  and R n  is the correlation matrix of channel noise n(k), according to the Equation (10). Finally, the subtractor  180  generates the equalized signal vector y(k) according to the difference between the interference signal vector w(k) and the preliminary desired signal vector ŷ(t). 
 
         [0018]     It should be noted that the major computational complexity of the equalizer  100  involves the operation of calculating the inversion of (M−N)Q×(M−N)Q matrix. That is, the operation of the weighting device  160  for calculating the inversion of (M−N)Q×(M−N)Q matrix (B H R in B) to determines the matrix U. Therefore, if the operation of computing the matrix U is simplified, the computational complexity of the equalizer  100  decreases.  
         [0019]     A second embodiment is disclosed to decrease the computational complexity. Please refer to  FIG. 3 .  FIG. 3  is a schematic diagram of an embodiment of the equalizer  200  applied in a receiver of the MIMO-OFDM system according to the second embodiment. The equalizer  200  comprises a Fourier transform module  210 , a matched filter  220 , a blocking device  240 , a simplifying device  260 , a weighting device  280 , and a subtractor  290 . The operations and architectures of the Fourier transform module  210 , the matched filter  220 , the blocking device  240 , and the subtractor  290  are the same with the operations and architectures of the components having the same names shown in the  FIG. 2 . The simplifying device  260  utilizes a matrix T to reduce the dimension of the preliminary interference signal vector b(k). The operation of the simplifying device  260  is represented as the following equation: 
 
 b ′( k )= T   H   ·b ( k ), where T=basis of column space of B H H ISI,1   Equation (11) 
 
         [0020]     Since T is an (M−N)Q×N(L−G) matrix and the dimension of the preliminary interference signal vector b(k) is (M−N)Q×1, the dimension of the simplified preliminary interference signal vector b′(k) is N(L−G)×1. According to the specification of the OFDM system, the value Q is much greater than the values M, N, L, G. As a result, the dimension of the simplified preliminary interference signal vector b′(k) is less than the dimension of the preliminary interference signal vector b(k). Next, the weighting device  280  generates the interference signal vector w(k) as the following equation: 
 
 w ( k )= U   H   b ′( k ), where  U =( T   H   B   H   R   in   BT ) −1   T   H   B   H   R   in   D   Equation (12) 
 
         [0021]     According to the Equation (12), the size of the matrix (T H B H R in B T ) is N(L−G)×N(L−G) less than (M−N)Q×(M−N)Q. Therefore, the operation of calculating an inversion of a matrix is simplified, and the computational complexity of the weighting device  280  is reduced accordingly.  
         [0022]     Please note that each component shown in  FIG. 2  and  FIG. 3  may be a computing circuit or a program module. Compared with the related art, the GSC-based equalizer is capable of alleviating the ISI and ICI. As a result, the length of the cyclic prefix of each symbol can be shortened thereby increasing the channel capacity. In addition, since the simplifying device is utilized in the GSC-based equalizer, the computational complexity of the GSC-based equalizer can be reduced.