Abstract:
A diversity hybrid receiver structure is provided for estimating the sequence of transmitted symbols in a digital communication system. A joint optimizer determines optimal effective channel coefficients for use by an equalizer using a power method, and determines optimal filter coefficients for use by a space-time filter. The space-time filter mitigates co-channel interference and produces an intermediate sequence of signal samples. The equalizer acts on the intermediate sequence of signal samples and corrects for intersymbol interference to estimate the transmitted sequence of symbols. The equalizer uses an efficient block decision-feedback sequence estimation method. An interference detection scheme is also provided.

Description:
RELATED APPLICATIONS 
     U.S. patent application entitled “Minimum Mean-Squared Error Block-Decision Feedback Sequence Estimation in Digital Communication Systems” by Ratnarajah et al., filed on same date, and assigned to the assignee of the present application, discloses and claims subject matter related to that of the present invention and is herein incorporated by reference. 
     FIELD OF THE INVENTION 
     This invention relates to digital communication systems, and more particularly to the estimation of the sequence of transmitted symbols in such systems. 
     BACKGROUND OF THE INVENTION 
     In EDGE (Enhanced Data Rates for GSM Evolution) cellular communication systems a sequence of symbols is transmitted as an 8 Phase Shift Keying (8-PSK) modulated signal. The signal may propagate along several propagation paths to a receiver. If the time delay between the various propagation paths is comparable to the intersymbol period, then the&#39;signal received by the receiver will contain intersymbol interference. The attenuation along each path will vary, as will phase changes due to reflections, so the intersymbol interference will not be merely additive. In addition, transmitted symbols in neighbouring cells in Time Division Multiple Access systems can cause co-channel interference. Finally, the received signal will contain noise, which is assumed to be additive white Gaussian noise. 
     The receiver must estimate the transmitted sequence of symbols s from the received sequence of signal samples x. In a diversity receiver having M antennae, the M spatially distinct received signal samples at any discrete time k can be represented as a vector X k =[x 1 , . . . , x M ]k T . A hybrid receiver considers the contributions of co-channel interference and intersymbol interference separately. The hybrid receiver includes a space-time filter which acts on the M received signal samples x k  to mitigate co-channel interference, and an equalizer which then corrects for intersymbol interference. The output of the equalizer is an estimated sequence of symbols ŝ which ideally is equal to the transmitted sequence of symbols s. 
     If the space-time filter takes L+1 delayed time-taps of the received signal, then the spatially distinct received signal samples x k  can be extended to include temporal distinctions. If ordered sequentially, the received signal samples can be represented as a space-time stacked vector of vectors x k =[x k   T , . . . , x k−L   T]   T  of length M(L+1), or            x   _     k     =     [           x     1   ,   k               ⋮             x     M   ,   k                 x     1   ,     k   -   1                 ⋮             x     M   ,     k   -   1                 ⋮             x     1   ,     k   -   L                 ⋮             x     M   ,     k   -   L               ]                            
     where for each element of the vector the first subscript refers to the antenna at which the signal sample was received, and the second subscript refers to the time-tap. 
     An intermediate signal sample y k  can be defined as an output of the space-time filter such that y k =w T x k  where w is a vector of M(L+1). space-time filter coefficients, w=[w 1, 1 , . . . , w M,1 , . . . , w 1,L+1 , . . . , w M,L+1 ] T . For a sequence of N received signal samples, the space-time stacked vector x k  is extended to form a matrix X=[x k , . . . , x k+N−1 ], or        X   =       [           x     1   ,   k             x     1   ,     k   +   1             ⋯         x     1   ,     k   +   N   -   1                 ⋮       ⋮       ⋯       ⋮             x     M   ,   k             x     M   ,     k   +   1             …         x     M   ,     k   +   N   -   1                   x     1   ,     k   -   1               x     1   ,   k           …         x     1   ,     k   +   N   -   2                 ⋮       ⋮       …       ⋮             x     M   ,     k   -   1               x     M   ,   k           …         x     M   ,     k   +   N   -   2                 ⋮       ⋮       …       ⋮             x     1   ,     k   -   L               x     1   ,     k   +   1   -   L             …         x     1   ,     k   +   N   -   1   -   L                 ⋮       ⋮       …       ⋮             x     M   ,     k   -   L               x     M   ,     k   +   1   -   L             …         x     M   ,     k   +   N   -   1   -   L               ]     ∈     C     M                   (     L   +   1     )     ×   N                                
     and an intermediate sequence of singal samples y of length N is then produced by the space-time filter such that y T w T X. 
     The intermediate sequence of signal samples y can also be expressed as y T =h T S+e T  where h is a vector of effective channel coefficients, S is a matrix of transmitted symbols of the form          S   =       [           s   k           s     k   +   1           …         s     k   +   N   -   1                 s     k   -   1             s   k         …       ⋮           ⋮       ⋮       ⋰       ⋮             s     k   -   v   -   L           …       …         s     k   -   v   -   L   +   N   -   1             ]     ∈     C                    (     v   +   L   +   1     )     ×   N             ,                          
     v+1 is the number of propagation paths being considered for the environment in which the signal propagates, v+L+1 is the number of effective channels which will be considered by the equalizer, and e is a disturbance. The effective channel coefficients are used in the equalizer, as discussed below. From the perspective of the equalizer y is a received sequence of signal samples having passed through v+L+1 effective channels with impulse response coefficients given by h, the effective channels consisting of the propagation paths and the effects of the space-time filter. 
     Combining the two expressions for y, it is seen that the disturbance can be expressed as e T =w T X−h T S. A signal-to-interference-plus-noise ratio SINR can be defined as        SINR   =                  h   _     T                   S          2              e   _          2               SINR   =                  h   _     T                   S          2                    w   _     T                   X     -         h   _     T                   S            2                              
     The filter coefficients w and the effective channel coefficients h are jointly optimized by maximizing the SINR with respect to w and h to produce optimal coefficients w opt  and h opt . Using the technique of separation of variables, h opt  is found to be            h   _     opt     =       arg                     max     h   _                             h   _     H                     S   *                     S   T                     h   _             h   _     H                     S   *                     P   *          S   T                     h   _             ∈     C       (     v   +   L   +   1     )     ×   1                                
     where P=(I−X H (XX H ) −1 X), I is an identity matrix, the superscript H indicates the Hermitian of the matrix or vector to which it refers, and the superscript indicates the complex conjugate of the matrix or vector to which it refers. This is a generalized eigenvalue problem, and h opt  is the eigenvector corresponding to the largest eigenvalue of (S*P*S T ) −1 S*S T . w opt  is then found from 
     
       
           w   opt   T   =h   opt   T   SX   H ( XX   H ) −1   
       
     
     h opt  and w opt  can be found if the matrices S and X are formed from known training data. Unfortunately the eigenvalue problem is a complex one, and an efficient method of determining h opt  is needed. 
     Once w opt  and h opt  are determined the estimated sequence of symbols ŝ can be determined. The intermediate sequence of signal samples y produced by the space-time filter is found from y T =w T X where X is now the matrix of received sequences of signal samples for user data rather than for training data, having N+v+L columns where N is the number of symbols in the transmitted sequence (which is half a slot in EDGE systems). From the perspective of the equalizer, y=Hs+e where H is a matrix of effective channel coefficients having the form        H   =       [           h   1           h   0         0       …       …       …       0             h   2           h   1           h   0         ⋯       ⋯       ⋯       0             h   3           h   2           h   1         ⋯       …       …       0           ⋮       ⋮       ⋮       ⋰       ⋰       ⋰       ⋮             h     v   +   L             h     v   +   L   -   1             h     v   +   L   -   2           …       …       …       0           0         h     v   +   L             h     v   +   L   -   1           …       …       …       0           ⋮       ⋮       ⋮       …       …       …       ⋮         ]     ∈     C       (     N   +   v   +   L     )     ×   N                                
     and the values of the matrix elements hi are given by h opt , determined earlier during the joint optimization. 
     One method of estimating the transmitted sequence of symbols in the presence of intersymbol interference is the Maximum Likelihood Sequence Estimation (MLSE) method. For each of the possible transmitted symbols, the received signal is compared with the signal that should have been received if it was that symbol that had been transmitted. Based on these comparisons, the MLSE method then selects the symbol which was most likely to have been transmitted. The MLSE method is a very accurate sequence estimation method. However, the complexity of the MLSE method is proportional to the number of possible transmitted symbols raised to the power of the number of effective channels being considered. In EDGE systems there are eight possible transmitted symbols and seven effective paths are considered (v=5, L=1), and the complexity of the MLSE method makes it impractical. 
     A second method of estimating the transmitted symbols is the Zero-Forcing Block Linear Equalizer (ZF-BLE) method. In the ZF-BLE method, the quantity Q is minimized with respect to s, where 
     
       
           Q=∥y−Hs ∥ Ree   2 , 
       
     
     R ee=ε{ee   H } is the expectation value of the covariance matrix of the disturbance, and the operator ε denotes an expectation value. The solution to this minimization is 
     
       
           ŝ =( H   H   R   ee   −1   H ) −1   H   H   R   ee   −1   y   
       
     
     where ŝ is the estimation of the sequence of transmitted symbols s. However the ZF-BLE method is less than optimum. 
     A hybrid receiver is needed in which the optimization of the coefficients w opt  and h opt  is simplified, and in which the sequence estimation method used in the equalizer does not have the complexity of the MLSE method and which improves performance over the ZF-BLE method. 
     SUMMARY OF THE INVENTION 
     The present invention provides a diversity hybrid receiver in a digital communication system. The receiver includes a joint optimization processor which contains instructions for producing optimal filter coefficients and optimal effective channel coefficients h opt  from sequences of received training signal samples and a sequence of known training symbols. The receiver also includes a space-time filter which contains means for producing an intermediate sequence of signal samples y from a received sequence of signal samples and the optimal filter coefficients. The receiver also includes an equalization processor which contains instructions for producing an estimated sequence of symbols ŝ. These instructions comprise: forming a matrix of optimal effective channel coefficients H from the optimal effective channel coefficients h opt ; determining a lower triangular matrix L from a relationship LL H =H H R ee   −1 H+I where LH is the Hermitian of L, HH is the Hermitian of H, I is an identity matrix, and R ee is a covariance matrix of a disturbance e; calculating a vector z=L −1 H H R ee   −1 y; and determining an estimated sequence of symbols ŝ belonging to a set of discrete possible symbol values such that the square of the magnitude of a difference vector L H ŝ−z is minimized. 
     A diversity hybrid receiver is also provided in which, either with or without the equalization processor described above, there are M antennae, each antenna receiving one sequence of received training signal samples, and L time-taps of each sequence of received training signal samples is produced. The instructions contained in the joint optimization processor comprise: defining a matrix X from the sequences of received training signal samples as        X   =       [           x     1   ,   k             x     1   ,     k   +   1             ⋯         x     1   ,     k   +   p                 ⋮       ⋮       ⋯       ⋮             x     M   ,   k             x     M   ,     k   +   1             …         x     M   ,     k   +   p                   x     1   ,     k   -   1               x     1   ,   k           …         x     1   ,     k   +   p   -   1                 ⋮       ⋮       …       ⋮             x     M   ,     k   -   1               x     M   ,   k           …         x     M   ,     k   +   p   -   1                 ⋮       ⋮       …       ⋮             x     1   ,     k   -   L               x     1   ,     k   +   1   -   L             …         x     1   ,     k   +   p   -   L                 ⋮       ⋮       …       ⋮             x     M   ,     k   -   L               x     M   ,     k   +   1   -   L             …         x     M   ,     k   +   p   -   L               ]     ∈     C     M                   (     L   +   1     )     ×     (     p   +   1     )                                  
     where k indicates the sequential position of a received training signal sample in a sequence of received training signal samples and p+1 indicates the number of received training signal samples in each sequence of received training signal samples; defining a matrix S from the sequence of known training symbols as        S   =       [           s   k           s     k   +   1           …         s     k   +   p                 s     k   -   1             s   k         …       ⋮           ⋮       ⋮       ⋰       ⋮             s     k   -   v   -   L           …       …         s     k   -   v   -   L   +   p             ]     ∈     C                    (     v   +   L   +   1     )     ×   N                                  
     where v+L+1 is the number of effective channels considered by the equalization processor; initializing h opt  to be the first column of a matrix B=(S*P*S T ) −1 S*S T  where P=(I−X H (XX H ) −1 X) and X H  is the Hermitian of X; and carrying out iterative steps a predetermined number of times, the iterative steps comprising calculating a vector q=Bh opt  and calculating a new value for the vector h opt =q/∥q∥. 
     An interference detection method is also provided in which a signal-to-interference-plus-noise ratio SINR is determined by: determining orthogonal weights w opt   ⊥  of the optimal filter coefficients w opt ; determining an interference pulse noise y I  from the expression            y   _     I   T     =       ∑     i   =   1         M                   (     L   +   1     )       -   1                           (       w   _       opt   i     ⊥     )     T                   X                              
     where M(L+l)− 1  is the number of orthogonal weights; determining an estimated desired signal y D  from the expression 
     
       
           y   D   T =( w   opt ) T   X ; and 
       
     
     determining the SINR as the ratio of the square of the magnitude of the interference pulse noise to the square of the magnitude of the estimated desired signal. 
     The methods provide an efficient means for determining the optimal filter coefficients and the optimal effective channel coefficients used by the space-time filter and the equalizer respectively. Furthermore, the accuracy of the sequence estimation is improved. 
    
    
     Other aspects and features of the present invention will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments of the invention in conjunction with the accompanying figures. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will now be described in greater detail with reference to the accompanying diagrams, in which: 
     FIG. 1 is a block diagram illustrating an example diversity hybrid receiver; 
     FIG. 2 is a flow chart showing the joint optimization method of the invention; 
     FIG. 3 is a flow chart showing,the equalization method of the invention; and 
     FIG. 4 is a flow chart showing the interference detection method of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Referring to FIG. 1, a hybrid diversity receiver is shown. The receiver comprises a space-time filter  40 , an equalizer  42 , and a joint optimizer  44 . The diversity receiver shown has two antennae  46  and  48 , though in general there may be M antennae. A transmitted sequence of N symbols s (not shown), each symbol having one of a set of discrete possible values, is transmitted along at least one propagation path to the receiver. The antenna  46  receives a first received sequence of signal samples x 1    50 , and the antenna  48  receives a second received sequence of signal samples x 2    52 , each received sequence of signal samples containing N signal samples. The received sequence of signal samples  50  is spatially distinct from the received sequence of signal samples  52 . The space-time filter  40  takes time-taps of each received sequence of signal samples using delay blocks  54 . The space-time filter  40  shown in FIG. 1 takes one time-tap of each received sequence of signal samples though in general there may be L time-taps taken of each received sequence of signal samples, and there will be M×L delay blocks. Collectively, the received sequences of signal samples and their respective time-taps can be represented as a matrix of received signal samples X given generally by        X   =       [           x     1   ,   k             x     1   ,     k   +   1             ⋯         x     1   ,     k   +   N   -   1                 ⋮       ⋮       ⋯       ⋮             x     M   ,   k             x     M   ,     k   +   1             …         x     M   ,     k   +   N   -   1                   x     1   ,     k   -   1               x     1   ,   k           …         x     1   ,     k   +   N   -   2                 ⋮       ⋮       …       ⋮             x     M   ,     k   -   1               x     M   ,   k           …         x     M   ,     k   +   N   -   2                 ⋮       ⋮       …       ⋮             x     1   ,     k   -   L               x     1   ,     k   +   1   -   L             …         x     1   ,     k   +   N   -   1   -   L                 ⋮       ⋮       …       ⋮             x     M   ,     k   -   L               x     M   ,     k   +   1   -   L             …         x     M   ,     k   +   N   -   1   -   L               ]     ∈     C     M                   (     L   +   1     )     ×   N                                
     where in the example of FIG. 1 there are two antennae so M=2, and there is one time-tap so L=1. Each signal sample and time-tap of a signal sample is multiplied by a filter coefficient w and passed to a summer  78 . In the example of FIG. 1 there are four filter coefficients (w 11    70 , w 12    72 , w 21    74 , and w 22    76 ) though there will in general be M(L+1) filter coefficients. The filter coefficients can be represented as a vector w. The space-time filter  40  determines an intermediate sequence of signal samples y at an output  56  of the summer  78  using a relationship y T =w T X. The intermediate sequence of signal samples y is passed to the equalizer  42  containing an equalization processor (not shown). The equalization processor produces an estimated sequence of symbols ŝ at an output  58  from a relationship y=Hs+e where H is a matrix of effective channel coefficients given by          H   =       [           h   1           h   0         0       …       …       …       0             h   2           h   1           h   0         ⋯       ⋯       ⋯       0             h   3           h   2           h   1         ⋯       …       …       0           ⋮       ⋮       ⋮       ⋰       ⋰       ⋰       ⋮             h     v   +   L             h     v   +   L   -   1             h     v   +   L   -   2           …       …       …       0           0         h     v   +   L             h     v   +   L   -   1           …       …       …       0           ⋮       ⋮       ⋮       …       …       …       ⋮         ]     ∈     C       (     N   +   v   +   L     )     ×   N           ,                          
     e is a disturbance, and v+L+1 is the number of effective channels being considered by the equalizer. The effective channel coefficients can be represented as a vector h. 
     The filter coefficients w and the effective channel coefficients h are generally not known by the space-time filter  40  or the equalizer  42 . However optimal filter coefficients w opt  and optimal effective channel coefficients h opt  can be determined by the joint optimizer  44  and passed to the space-time filter  40  and the equalizer  42  to inputs  64  and  66  respectively. A sequence of p+1 known training symbols, transmitted temporally proximate to the transmitted sequence of symbols s, is received by the M antennae as M sequences of received training signal samples and passed to an input  60  of the joint optimizer  44 . The joint optimizer  44  determines w opt  and h opt  by processing the sequence of known training symbols  62  with the M sequences of received training signal samples. L time-taps are produced of each sequence of received training signal samples. The matrix of received signal samples corresponding to training symbols, X, takes the form        X   =       [           x     1   ,   k             x     1   ,     k   +   1             ⋯         x     1   ,     k   +   p                 ⋮       ⋮       ⋯       ⋮             x     M   ,   k             x     M   ,     k   +   1             …         x     M   ,     k   +   p                   x     1   ,     k   -   1               x     1   ,   k           …         x     1   ,     k   +   p   -   1                 ⋮       ⋮       …       ⋮             x     M   ,     k   -   1               x     M   ,   k           …         x     M   ,     k   +   p   -   1                 ⋮       ⋮       …       ⋮             x     1   ,     k   -   L               x     1   ,     k   +   1   -   L             …         x     1   ,     k   +   p   -   L                 ⋮       ⋮       …       ⋮             x     M   ,     k   -   L               x     M   ,     k   +   1   -   L             …         x     M   ,     k   +   p   -   L               ]     ∈     C     M                   (     L   +   1     )     ×     (     p   +   1     )                                  
     and a matrix of known training symbols S is formed as        S   =       [           s   k           s     k   +   1           …         s     k   +   p                 s     k   -   1             s   k         …       ⋮           ⋮       ⋮       ⋰       ⋮             s     k   -   v   -   L           …       …         s     k   -   v   -   L   +   p             ]     ∈     C                    (     v   +   L   +   1     )     ×   N                                  
     The solution to the joint maximization of a signal-to-interference-plus-noise ratio        SINR   =                  h   _     T                   S          2                    w   _     T                   X     -         h   _     T                   S            2                              
     indicates that h opt  is an eigenvector corresponding to the largest eigenvalue of a matrix, B=(S*P*S T ) −1 S*S T  where P=(I−X H (XX H ) −1 X), I is an identity matrix, and X H  is the Hermitian of X. Referring to FIG. 2, the method by which a joint optimization processor in the joint optimizer  44  determines w opt  and h opt  is shown. A power method is used to determine the eigenvector of B corresponding the largest eigenvalue. At step  100  the value of h opt  is initialized as the first column of the matrix. B and an integer n is initialized as n=1. A vector q is calculated from q=Bh opt  at step  102 . A new value for h opt  is calculated at step  104  from            h   _     opt     =       q   _            q   _                                   
     At step  106  the value of n is compared with a predetermined integer n max . If n is not equal to n max  then at step  108  the value of n is increased by one. The algorithm returns to step  102 , creating an iterative loop that exits when n reaches n max . When n reaches n max  at step  106 , h opt  has the correct value, being an eigenvector corresponding to the largest eigenvalue of B. In fact, a value of n max =2 is sufficient to obtain the required eigenvector. Once h opt  has been found, w opt  is determined at step  112  from 
     
       
           w   opt   T   =h   opt   T   SX   H ( XX   H ) −1   
       
     
     The estimated sequence of transmitted symbols ŝ can now be determined by the equalization processor using a Minimum Mean-Squared Error Block Decision-Feedback Sequence Estimation (MMSE-BDFSE) method. If the transmitted sequence of symbols s is presumed to have a distribution described by a mean μ and a covariance matrix R ss , and recalling that y=Hs+e, then a solution for ŝ can be found by minimizing the expectation value of ∥ŝ−s∥ 2 . The well known solution is 
     
       
           ŝ =μ+( H   H   R   ee   −1   H+R   ss   −1 ) −1   H   H   R   ee   −1 ( y−H μ) 
       
     
     where R ee  is the covariance matrix of the disturbance e and H H  is the Hermitian of the matrix H. For an 8-PSK communication system, such as an EDGE system, μ=0 and R ss =I, and so 
       ŝ =( H   H   R   ee   −1   H+I ) −1   H   H   R   ee   −1   y   
     Referring to FIG. 3, the space-time filter  40  determines the intermediate sequence of signal samples y at step  14  from the expression y T =w opt   T X, where X is now the matrix of received signal samples and w opt  has been determined by the joint optimization processor. The intermediate sequence of signal samples y is passed to the equalizer  42 . The equalizer receives the optimal effective channel coefficients h opt  at step  16 . At step  22  the equalization processor determines a product of triangular matrices LL H  by performing a Cholesky decomposition, such that 
     
       
         
           LL 
           H 
           =H 
           H 
           R 
           ee 
           −1 
           H+I 
         
       
     
     Substituting LL H  into the solution for ŝ, and multiplying both sides of the equation by L H , it can be readily seen that 
     
       
         
           L 
           H 
           ŝ=L 
           −1 
           H 
           H 
           R 
           ee 
           −1 
           y 
         
       
     
     Although ŝ could be calculated from this expression, the resulting values would lie on a continuum and would generally not match the discrete possible values of the transmitted symbols. However, if a vector z is defined as 
     
       
         
           z=L 
           −1 
           H 
           H 
           R 
           ee 
           −1 
           y 
         
       
     
     and a difference vector Δ is defined as 
     
       
         Δ= L   H   ŝ−z   
       
     
     then the equalization processor can determine ŝ by minimizing the square of the magnitude of the difference vector Δ with respect to the vector of discrete possible values. At step  28  the vector z is calculated. 
     If the vectors and matrix are expanded, the square of the magnitude of this difference vector is seen to be                       Δ                  2       =                     [           l   11           l   12         ⋯         l     1      N               0         l   22         ⋯         l     2      N               ⋮       ⋮       ⋰       ⋮           0       0       ⋯         l   NN           ]          [             s   ^     1                 s   ^     2             ⋮               s   ^     N           ]       -     [           z   1               z   2             ⋮             z   N           ]                 2                            
     and then                               Δ   _                    2       =                                  l   NN            s   ^     N       -     z   N                 2     +                     l       N   -   1     ,     N   -   1                s   ^       N   -   1         +       l       N   -   1     ,   N              s   ^     N       -     z     N   -   1                   2     +   …   +                                                ∑     j   =   i     N                       l   ij            s   ^     j         -     z   i                 2     +   …   +                     ∑     j   =   1     N                       l     1      j              s   ^     j         -     z   1                 2                                    
     For convenience, the terms in the above series will be referred to as Δ N , Δ N−1 , . . . Δ 1 . At step  34  the terms in the expression for ∥Δμ 2  are minimized iteratively with respect to each possible discrete value of a transmitted symbol. The only unknown in the first term Δ N  is the value of the N-th estimated symbol ŝ N . The term Δ N  is minimized by substituting in turn each possible value of the transmitted symbol into ŝ N . The value which results in the lowest value of Δ N  is assigned to ŝ N . The next term, Δ N−1 , is minimized in the same way to find ŝ N−1 , using the value of ŝ N  found when minimizing the previous term. This process is repeated for each term until a value is found for each symbol ŝ in the estimated sequence of symbols ŝ. The actual transmitted sequence of symbols s is then presumed to be the complete estimated sequence of symbols ŝ. 
     The above method minimizes the square of the magnitude of the difference vector with respect to the possible transmitted symbols one at a time. If a symbol is inaccurately estimated early in the method, the error will propagate through the estimation of the remaining symbols. The risk of this type of error can be reduced by grouping the vector and matrix elements in the expression ∥Δ∥ 2  into blocks. A term in the expression for ∥Δ∥ 2  can then be minimized with respect to several symbols simultaneously, yielding more accurate estimations. For example, if blocks of two elements are used, the matrix expression for ∥Δ∥ 2  becomes                         Δ   _                    2       =                     [           L   11           L   12         ⋯         L     1      Q               0         L   22         ⋯         L     2      Q               ⋮       ⋮       ⋰       ⋮           0       0       ⋯         L   QQ           ]          [               s   ^     _     1                   s   ^     _     2             ⋮                 s   ^     _     Q           ]       -     [             z   _     1                 z   _     2             ⋮               z   _     Q           ]                 2                            
     and then                               Δ   _                    2       =                                  L   QQ              s   ^     _     Q       -       z   _     Q                 2     +                     L       Q   -   1     ,     Q   -   1                  s   ^     _       Q   -   1         +       L       Q   -   1     ,   Q                s   ^     _     Q       -       z   _       Q   -   1                   2     +   …   +                                                ∑     j   =   i     Q                       L   ij              s   ^     _     j         -       z   _     i                 2     +   …   +                     ∑     j   =   1     Q                       l     1      j                s   ^     _     j         -       z   _     1                 2                                    
     where Q=N/2, ŝ 1 =(ŝ 1 , ŝ2), . . . ŝ Q (ŝ N− 1, ŝ N ) z 1 =(z 1 , z 2 ), . . . z Q =(z N−1 , z N ), and            L   11     =     [           l   11           l   12             0         l   22           ]       ,       …                   L   QQ       =     [           l       N   -   1     ,     N   -   1               l       N   -   1     ,   N               0         l     N   ,   N             ]                              
     The first term, Δ Q  is minimized with respect to ŝ Q  by substituting each combination of two possible transmitted symbols into ŝ N−1  and ŝ N . The two values which result in the lowest value of Δ Q  are assigned to ŝ N−1  and ŝ N . The remaining terms are minimized in the same way, using the values of ŝ previously determined. The transmitted sequence of symbols s is then presumed to be the complete estimated sequence of symbols ŝ. Larger block sizes can yield more accurate estimations of the transmitted sequence. However since the number of combinations of symbol values which must be considered in minimizing each term is equal to the number of possible symbol values raised to the power of the size of the blocks, processing capabilities will limit the blocks to reasonable sizes (normally 3 or 4 for an 8-PSK communication system). 
     An alternate method by which the equalization processor can determine the estimated sequence of symbols is the Zero-Forcing Block Decision-Feedback Sequence Estimation (ZF-BDFSE) method. In the ZF-BDFSE method, no assumption regarding the statistical properties of the transmitted symbols is made. As in the ZF-BLE method the quantity 
     
       
         
           Q=∥y−Hs∥ 
           Ree 
           2 
         
       
     
     is minimized, yielding the solution 
     
       
           ŝ =( H   H   R   ee   −1   H ) −1   H   H   R   ee   −1   y   
       
     
     However as with the MMSE-BDFSE method the equalization processor implementing the ZF-BDFSE method simplifies the calculations by determining a lower triangular matrix L, defined in this method by 
     
       
         
           LL 
           H 
           =H 
           H 
           R 
           ee 
           −1 
           H 
         
       
     
     The equalization processor then minimizes the difference vector, as is done when using,the MMSE-BDFSE method. Although this alternative has the advantage of not requiring any assumptions about the statistical properties of the transmitted sequence of symbols, it has a disadvantage in that a solution for L does not always exist. A matrix L can only be found if the effective channel correlation matrix H H R ee   −1 H is positive definite. To avoid this risk noise can be added to the matrix H, but this results in performance degradation. 
     Referring to FIG. 4, the hybrid receiver may also implement an interference detection method. Once the joint optimization processor has determined w opt  as described above, an interference detection processor determines a set of orthogonal weights w ⊥   opt  for w ⊥   opt  at step  120 . An interference pulse noise y I  is then calculated at step  122  from an expression            y   _     I   T     =       ∑     i   =   1         M        (     L   +   1     )       -   1                           (       w   _       opt   i     ⊥     )     T        X                              
     where M(L+1) is the number of filter coefficients (and hence M(L+1)−1 is the number of orthogonal weights for w opt , a vector of dimension M(L+1)), and X is the matrix of received signal samples corresponding to training symbols. An estimated desired signal y D  is calculated at step  124  from an expression 
     
       
           y   D    T =(i w opt ) T   X   
       
     
     An estimated signal-to-interference-plus-noise ratio SINR is calculated at step  126  as          SIN                 R     =                        y   _     I                    2                          y   _     D                    2                                
     If at step  128  the value of SINR calculated by the interference detection processor is larger than a threshold, then the optimal filter coefficients w opt  are passed to the space-time filter, and the estimated sequence of symbols ŝ is determined by the space-time filter and the equalizer as described above. Otherwise, the space-time filter can be bypassed at step  130 . In such an event, the equalizer alone is used to determine the estimated sequence of symbols ŝ. The related U.S. patent application entitled “Minimum Mean-Squared Error Block-Decision Feedback Sequence Estimation in Digital Communication Systems” by Ratnarajah et al., incorporated by reference herein, discloses a sequence estimation method when multiple antennae are present. If space-time filter is bypassed at step  130  in the present invention, the equalizer preferably implements the method disclosed in that related application, although this need not be the case. 
     The invention is not confined to EDGE communication systems, nor even to 8-PSK communication systems, but can be applied in any digital communication system. However the MMSE-BDFSE method of implementing the equalizer requires that the transmitted symbols have a mean of 0 and a covariance matrix given by an identity matrix. 
     What has been described is merely illustrative of the application of the principles of the invention. Other arrangements and methods can be implemented by those skilled in the art without departing from the spirit and scope of the present invention.