Abstract:
The present invention describes a channel equalizer and a method for channel equalization in a receiver in a multi-user communication system. The method comprises the steps of receiving a signal with at least two antennas to produce at least two antenna input streams, measuring the temporal of each antenna input stream and the spatial correlation between the antenna input streams, determining a user-independent pre-equalization filter from the temporal and spatial correlation, filtering the antenna input streams with the pre-equalization filter, and finally inputting the filtered signal to a user-dependent receiver configured to detect the received data symbols of a given user.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a 35 U.S.C. §371 National Phase Entry Application from PCT/EP2009/066138 filed Dec. 1, 2009, and designating the United States. 
     TECHNICAL FIELD 
     The present invention relates to a channel equalization method used in a multi-user communication system. While the invention particularly relates to a WCDMA communication system, it should be noted that it could be applicable to other communication systems, including LTE, WiMAX, WiFi, UWB, GSM, etc. The invention is low complexity user-independent spatial and temporal minimum mean square error (MMSE) pre-equalization. 
     BACKGROUND 
     In any wireless communication system, the transmitted signal is distorted due to the dynamic properties of the wireless channel. These dynamics leads to a frequency selective channel. Therefore, at the receiver side, some kind of equalization scheme can be applied in order to compensate for dynamics of the wireless channel. An ideal compensation would cancel the effects of the radio channel and make the resulting equalized channel completely frequency-flat. However, such a scheme would in most, cases lead to unwanted noise amplification which limits the performance. The equalization scheme should also suppress interference by decorrelation of the receiver antennas. Equalization schemes must therefore provide a trade-off between interference suppression, noise amplification and making the equalized channel frequency-flat. 
     In third generation cellular systems (including both WCDMA and CDMA2000), direct sequence code division multiple access (DS-CDMA) is adopted as multiple access scheme. CDMA is a spread spectrum technique that uses specially designed spreading sequences to spread symbol-level data to higher bandwidth chip-level sequences. One notable advantage of CDMA is its ability to exploit the multipath diversity of the wireless channel by combining the different propagation delays of the received signal. This is possible when the spreading sequences are selected in such a way that their autocorrelation function is (or at least approximately is) zero for time shifts different from zero. The most commonly used receiver for CDMA over multipath channels is the Rake receiver ( 2 ,  2 A,  2 B). The Rake receiver is so named because its structure resembles a garden rake, where each rake finger collects the energy corresponding to a certain propagation delay ( 5 A-B,  5 C-D,  5 E-F and  5 G-H). 
       FIG. 1A  illustrates a CDMA multi-user receiver with N receive antennas that employs Rake receivers for each of the M users. The N antenna branches are coupled to an RF front-end (RX) which encompasses circuitry for transforming the received signals to baseband. Hence, the RF front-end outputs N antenna input streams, which are used as inputs to M user-specific Rake receivers ( 2 A,  2 B).  FIG. 2A  illustrates the conventional Rake receiver that is employed for each user in the multi-user receiver of  FIG. 1A . Each of the N input streams are fed to a Rake receiver and assigned to one or multiple Rake fingers ( 5 A-H). The Rake fingers are allocated by the path searcher ( 4 A), which analyzes a power delay profile of the received signal and assigns a finger to each multipath component with an energy level above a certain threshold. The main function of each finger is to despread its multipath component from chip-level back to symbol-level. After despreading, the symbol-level outputs of the Rake fingers are combined by a maximal ratio combiner (MRC). The MRC ( 6 A) is an optimum combiner which weights the symbol-level output symbols in proportion to the signal power of each finger. In the MRC, a weight estimation unit (WEU) extracts a pilot sequence from the despread signal of each finger to determine the MRC weight. 
     The conventional Rake receiver is optimal for demodulating a COMA signal in the presence of white noise. However, in presence of multi-user interference (MUI), normally encountered in cellular systems, the noise may be colored and the RAKE receiver is no longer optimal and may even be very far from the optimal receiver. A better solution in this case would be to employ an MMSE-optimized Rake or Generalized Rake (G-Rake) receiver for each user. An example of a MMSE-Rake/G-Rake receiver for N receive antennas is illustrated in  FIG. 2B . 
     The MMSE-Rake and G-Rake receivers ( 3 ,  3 A,  3 B) have a similar structure to that of the conventional Rake receiver ( 2 ,  2 A,  2 B). There are, however, some details that differentiate them from the conventional Rake receiver. First, the number of Rake fingers, determined by the path searcher ( 4 B), may be larger than the number of multipath components indicated on the power delay profile. Second, the weight estimation unit (WEU- 2 ) needs to take ail fingers into account when the weights used for MRC ( 6 B) are computed. Hence, the weight estimation unit (WEU- 2 ) of an MMSE-optimized Rake or G-Rake is considerably more computationally intensive than for the conventional Rake receiver. 
     The MMSE-optimized Rake receiver offers improved performance over a conventional Rake receiver at the cost of a more computationally intensive implementation. Hence, in a receiver node with limited computational capabilities one may only afford to use MMSE-Rake or G-Rake receivers for a few prioritized users, while remaining users have to accept the lower level of service offered by the conventional Rake receiver. 
     SUMMARY 
     According to the present invention, the problem of providing a computationally simple yet MMSE-optimized receiver is solved by user-independent temporal and spatial pre-equalization of the antenna input streams. Unlike the G-Rake and MMSE-Rake solutions ( 3 ,  3 A,  3 B), the computational complexity of the proposed method in relation to a conventional Rake receiver does not increase with the number of users. 
     The present invention describes a method for channel equalization in a receiver in a multi-user communication system. The method comprises the steps of:
         receiving ( 601 ) a signal with at least one antenna to produce at least one antenna input stream,   measuring ( 602 ) the temporal correlation of the at least one antenna input stream and, moreover, measuring ( 602 ) the spatial correlation between the antenna input streams when at least two antenna input streams are provided,   determining ( 603 ) a user-independent pre-equalization filter ( 7 ) from the temporal correlation when at least one antenna input stream is provided or determining a user independent pre-equalization filter from the temporal correlation and the spatial correlation when at least two antenna input streams are provided,   filtering ( 604 ) the at least one antenna input stream with the user independent pre-equalization filter ( 7 ),   inputting ( 605 ) the at least one filtered stream to at least one user-dependent receiver ( 2 A,  2 B).       

     Moreover, the method concerns the cases wherein:
         the multi-user communication system is a CDMA communication system and the user-dependent receiver is a Rake receiver ( 2 A,  2 B).   the filtering is divided into two processes respectively corresponding to temporal pre-equalization ( 9 ) and spatial pre-equalization ( 10 ),   the temporal pre-equalization and the spatial pre-equalization are performed subsequently,   the temporal pre-equalization is performed on each antenna input stream separately,   the user-independent pre-equalization filtering is performed fully or partially in frequency domain ( FIGS. 3B ,  4 B and  5 ).       

     The present invention also describes a receiver node in a multi-user communication system. The receiver node comprising:
         at least one antenna ( 1 A,  1 B) for receiving at least one antenna input stream,   a correlation estimation unit (CEU) for measuring the temporal correlation of the at least one antenna input stream or the temporal and spatial correlation of at least two antenna input streams,   a user-independent pre-equalization filter ( 7 ) to compensate for said temporal correlation or said temporal and spatial correlation,   at least one user-dependent receiver ( 2 A,  2 B) configured to detect the received data symbols of a given user.       

     Moreover, the receiver node concerns the cases wherein:
         the multi-user communication system is a CDMA multi-user communication system and the user-dependent receiver is a Rake receiver ( 2 A,  2 B),   the pre-equalization filter is divided into two stages respectively corresponding to temporal pre-equalization ( 9 ,  11 ) and spatial pre-equalization ( 10 ,  12 ),   the temporal pre-equalization filter and the spatial pre-equalization filter are arranged in series,   the temporal pre-equalization filtering is performed separately on each antenna input stream (not shown),   the user-independent pre-equalization filtering is performed fully or partially in frequency domain ( FIG. 3B ,  FIG. 4B  and  FIG. 5 ).       

     The proposed pre-equalization is user-independent and the processing is done on all receiver antennas but only once, independent of the number of users. Thus, in a multi-user receiver, which demodulates and detects a large number of users, the computational complexity per user will be very low on average. The pre-equalization can be performed in one stage or divided into two stages corresponding to temporal and spatial pre-equalization, respectively. By dividing the pre-equalization info two separate stages, the computational complexity is further reduced. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  shows a multi-user receiver where each user is detected with a conventional Rake, an MMSE-optimized Rake or a G-Rake receiver, 
         FIG. 2   a  shows a conventional Rake receiver, 
         FIG. 2   b  shows an MMSE-optimized Rake receiver, 
         FIG. 3   a  shows a first embodiment of the present invention, 
         FIG. 3   b  shows an alternative of the first embodiment, 
         FIG. 4   a  shows a second embodiment of the present invention, 
         FIG. 4   b  shows an alternative of the second embodiment, 
         FIG. 5  shows a third embodiment of the present invention, 
         FIG. 6  shows a flowchart of the channel equalization method of the present invention, and 
         FIG. 7  shows a flowchart of the overlap-add FFT method. 
     
    
    
     DETAILED DESCRIPTION 
     Three embodiments of the present invention are described in detail below with reference to  FIGS. 3-5 . Common elements in all embodiments are N receive antennas ( 1 A,  1 B), RF front-end circuitry (RX) for each antenna to transform the received signal to baseband, a correlation estimation unit (CEU) for measuring the spatial and temporal correlation, a spatial and temporal pre-equalization filter ( 7 ) and M user-specific receivers ( 2 A,  2 B). It should be noted that the scope of the present invention is not limited to the particular embodiments described herein, but only limited by the appended claims. 
     In the description below, the temporal filtering is performed in the frequency domain. Several methods exist to generate the frequency domain representation of a time domain signal. In  FIGS. 3B ,  4 B and  5 , the time to frequency domain conversion is illustrated with a fast Fourier transform (FFT) module and the frequency to time domain conversion with an inverse fast Fourier transform (IFFT) module. In  FIG. 7 , a more detailed description illustrates how the overlap-add method for FFT and IFFT works. Here, short non-overlapping segments of samples in the time domain are extracted ( 701 ) and padded with zeros ( 702 ) to compensate for the time domain convolution. By means of an FFT, the time-domain blocks are converted to frequency domain ( 703 ). Temporal filtering ( 704 ) is now done as an element wise multiplication for each frequency index. The filtered blocks are converted back to the time domain with an IFFT ( 705 ), and the time domain signal is obtained by overlapping the filtered segments and adding them together. 
     It should be noted that it is well-known to a person skilled in the art that frequency domain filtering may be equivalent performed in the time domain. Hence, the present invention is not restricted to frequency domain filtering and may equivalent be implemented in time domain as illustrated in  FIGS. 3A and 4A . The advantage of using frequency domain filtering is that the convolution operation of a time domain filter becomes a simple element-wise multiplication. In the following, each block of frequency domain samples is enumerated with block index k. 
     A vector with Nr received signals in the frequency domain, for frequency m and frequency domain block number k, can be modeled as
 
 V ( m,k )= H ( m,k ) Z ( m,k )+η( m,k ),  (1)
 
where η(m,k) is a vector with additive noise and interference, Z(m,k) is transmitted signal from one user, and
 
                     H   ⁡     (     m   ,   k     )       =     [             h   0     ⁡     (     m   ,   k     )                   h   1     ⁡     (     m   ,   k     )               M               h       N   r     -   1       ⁡     (     m   ,   k     )             ]             (   2   )               
is the radio channel matrix.
 
     A multi-antenna formulation of the MMSE combining coefficients equals 
                             W   MMSE     ⁡     (     m   ,   k     )       =       ⁢     [             W     MMSE   ,   0       ⁡     (     m   ,   k     )                   W     MMSE   ,   1       ⁡     (     m   ,   k     )                                   W     MMSE   ,       N   r     -   1         ⁡     (     m   ,   k     )             ]                 =       ⁢         (       R   ^     ⁡     (     m   ,   k     )       )       -   1       ⁢       H   ^     ⁡     (     m   ,   k     )                     =       ⁢       (     [             R     0   ,   0       ⁡     (     m   ,   k     )           Λ           R     0   ,       N   r     -   1         ⁡     (     m   ,   k     )                   R     1   ,   0       ⁡     (     m   ,   k     )                                       M       O                           R         N   r     -   1     ,   0       ⁡     (     m   ,   k     )                           R         N   r     -   1     ,       N   r     -   1         ⁡     (     m   ,   k     )             ]     )       -   1                       ⁢       [               h   ^     0     ⁡     (     m   ,   k     )                     h   ^     1     ⁡     (     m   ,   k     )               M                 h   ^         N   r     -   1       ⁡     (     m   ,   k     )             ]     ,                   (   3   )               
where Ĥ(m, k) is an estimated channel matrix for a specific user and
 
     
       
         
           
             
               
                 
                   
                     
                       
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     Is the estimated multi-antenna periodogram (a.k.a. power density spectrum) for frequency index m. The multi-antenna periodogram can be estimated as a moving average 
                         R   ^     ⁡     (     m   ,   k     )       =       ∑     l   =   0     k     ⁢           ⁢       α   ⁡     (   l   )       ·     V   ⁡     (     m   ,   l     )       ·       V     *   T       ⁡     (     m   ,   l     )             ,           (   5   )               
where α(l),l=0,1K,k, are suitable scaling coefficients, e.g. α(l)=1/(k+1). Alternatively this multi-antenna periodogram matrix is estimated in a recursive manner,
 
 {circumflex over (R)} ( m,k )=(1−α Spec ) {circumflex over (R)} ( m,k− 1)+α Spec   V ( m,k )· V*   T ( m,k ),  (6)
 
where α Spec  is a suitable forgetting factor, e.g. α Spec =0.01. Several possible ways of combining these moving average and recursive estimators are possible.
 
     The frequency domain MMSE combining can now be formulated as
 
 Z   MMSE ( m )=( W   MMSE ( m ))* T   V ( m ).  (7)
 
     A single antenna frequency domain MMSE combining can be formulated as 
                         Z   MMSE     ⁡     (   m   )       =         (       W   MMSE     ⁡     (   m   )       )     *     ⁢     V   ⁡     (   m   )           ,     
     ⁢   where           (   8   )                   W   MMSE     ⁡     (   m   )       =         H   ^     ⁡     (   m   )           R   ^     ⁡     (   m   )                 (   9   )               
is an MMSE frequency domain filter coefficient, Ĥ(m) is estimated frequency domain channel net response, and {circumflex over (R)}(m) is estimated periodogram of received signal.
 
     First Embodiment 
     In the first embodiment of the invention, both the temporal and spatial pre-equalization can be done within a single stage ( 7 ,  8 ) as illustrated in  FIG. 3 . Denote received frequency domain samples from all antennas ( 1 A,  1 B) by 
                       V   ⁡     (     m   ,   k     )       =     [             V   0     ⁡     (     m   ,   k     )                   V   1     ⁡     (     m   ,   k     )               M               V       N   r     -   1       ⁡     (     m   ,   k     )             ]       ,           (   10   )               
for frequency index m, which is based upon a time interval (or block) of received samples. This block is enumerated by k. Frequency domain spatial and temporal pre-equalization ( 8 ) is done as an element-wise multiplication with W pre (m,k). We have
 
                           ⁢           Z   pre     ⁡     (     m   ,   k     )       =         W   pre     ⁡     (     m   ,   k     )       ·     V   ⁡     (     m   ,   k     )           ,     
     ⁢           ⁢   where             (   11   )                         W   pre     ⁡     (     m   ,   k     )       =       ⁢         W   SSF     ⁡     (   m   )       ⁢       (     L   ⁡     (     m   ,   k     )       )       -   1                     =       ⁢       W   SSF     ⁡     (     m   ,   k     )                       ⁢         (     [             L     0   ,   0       ⁡     (     m   ,   k     )           0       Λ       0               L     1   ,   0       ⁡     (     m   ,   k     )               L     1   ,   1       ⁡     (     m   ,   k     )                       M           M                   O       0               L         N   r     -   1     ,   0       ⁡     (     m   ,   k     )                                       L         N   r     -   1     ,       N   r     -   1         ⁡     (     m   ,   k     )             ]     )       -   1       ,                   (   12   )               
and where W SSF (m) is a scalar Spectrum Shaping Filter (SSF) e.g. a frequency domain representation of raised cosine filter. Here, L(m,k) is the result of a Cholesky factorization of the multi-antenna periodogram, i.e.
 
 L ( m,k )· L*   T ( m,k )= {circumflex over (R)} ( m,k ).  (13)
 
     Second Embodiment 
     In the second embodiment of the invention, the MMSE pre-equalization can be split into two stages: first a temporal pre-equalization ( 9 ,  11 ) and then a spatial decorrelation ( 10 ,  12 ). See  FIGS. 4   a  and  4   b  for two alternative embodiments of this spatial and temporal pre-equalization. 
     In the first stage, temporal pre-equalization ( 11 ) is done with the frequency domain filter coefficient 
                       W     pre   ,   a       ⁡     (     m   ,   k     )       =       1         R   a     ⁡     (     m   ,   k     )           ⁢       W   SSF     ⁡     (   m   )                 (   14   )               
for antenna number a, where W SSF (m) is a scalar Spectrum Shaping Filter (SSF) e.g. a raised cosine filter, and R a (m,k) is a single antenna periodogram for frequency m and block number k. Note that R a (m,k) is real-valued and positive which simplifies the square root and division calculations.
 
     The periodogram, for antenna number a, can be estimated as a moving average 
                           R   ^     a     ⁡     (     m   ,   k     )       =       ∑     l   =   0     k     ⁢           ⁢       α   ⁡     (   l   )       ·              V   a     ⁡     (     m   ,   l     )            2           ,           (   15   )               
where α(l)l=0,1,K,k, are suitable scaling coefficients, e.g. α(l)=1(k+1). Alternatively this periodogram is estimated in a recursive manner,
 
{circumflex over ( R )} a ( m,k )=(1−α Spec ){circumflex over ( R )} a ( m,k− 1)+α Spec   |V   a ( m,k )| 2 ,  (16)
 
where α Spec  is a suitable forgetting factor, e.g. α Spec =0.01. Several possible ways of combining these moving average and recursive estimators are possible.
 
     Temporal pre-equalization ( 11 ) is done as a scalar frequency domain filtering
 
{tilde over ( Z )} pre,a ( m,k )= W   pre,a ( m,k )· V   a ( m,k )  (17)
 
for each antenna a, frequency index m and block k.
 
     In a second stage, spatial decorrelation ( 12 ) is done on temporal pre-equalized data. The temporally pre-equalized signal vector for time n is denoted by
 
{tilde over ( Z )} pre ( m,k )=[{tilde over ( Z )} pre,0 ( m,k ){tilde over ( Z )} pre,1 ( m,k ) K {tilde over (Z)}   pre,N     r     −1 ( m,k )] T .  (18)
 
     The decorrelation is done in frequency domain at each block k of samples
 
 Z   pre ( m,k )= L   F   −1 ( k ){tilde over ( Z )} pre ( m,k ),  (19)
 
where L F (k) is the Cholesky factorization of a covariance matrix
 
                           R   ^     F     ⁡     (   k   )       =     [             r     0   ,   0       ⁡     (   k   )           …           r     0   ,       N   r     -   1         ⁡     (   k   )               M                   M               r         N   r     -   1     ,   0       ⁡     (   k   )           …           r         N   r     -   1     ,       N   r     -   1         ⁡     (   k   )             ]       ⁢     
     ⁢     such   ⁢           ⁢   that             (   20   )                     L   F     ⁡     (   k   )       ⁢       L   F     *   T       ⁡     (   k   )         =         R   ^     F     ⁡     (   k   )               (   21   )               
and L F (k) is lower triangular. Note that this covariance matrix is frequency independent such that only one Cholesky factorization is needed for each block k.
 
     To prevent the estimation of the covariance matrix to change too rapidly, filtering between blocks is applied. The covariance matrix can be estimated as a moving average 
                           R   ^     F     ⁡     (   k   )       =       ∑     l   =   0     k     ⁢           ⁢       α   ⁡     (   l   )       ·       ∑     m   =   0         N   fft     -   1       ⁢           ⁢           Z   ~     pre     ⁡     (     m   ,   l     )       ·         Z   ~     pre     *   T       ⁡     (     m   ,   l     )                 ,           (   22   )               
where α(l),l=0,1,K, k, are suitable scaling coefficients, e.g. α(l)=1/(k+1). Alternatively this covariance matrix is estimated in a recursive manner.
 
                         R   ^     F     ⁡     (   k   )       =         (     1   -     α   Spec       )     ⁢         R   ^     F     ⁡     (     k   -   1     )         +       α   Spec     ⁢       ∑     m   =   0         N   fft     -   1       ⁢           ⁢           Z   ~     pre     ⁡     (     m   ,   k     )       ·         Z   ~     pre     *   T       ⁡     (     m   ,   k     )                       (   23   )               
where α Spec  is a suitable forgetting factor, e.g. α Spec =0.01. Several possible ways of combining these moving average and recursive estimators are possible.
 
     Third Embodiment 
     In the third embodiment of the invention, the frequency domain spatial decorrelation as described in the second stage of the previous section is done in the time domain ( 10 ). See  FIG. 5  for an illustration of this spatial and temporal pre-equalization. 
     In a first stage, the temporal pre-equalization ( 11 ) is done as in the previous section, i.e. as an element wise scalar multiplication
 
{tilde over ( Z )} pre,a ( m,k )= W   pre,a ( m,k )· V   a ( m )  (24)
 
for each antenna a, frequency index m and block k, where
 
     
       
         
           
             
               
                 
                   
                     
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                   ( 
                   27 
                   ) 
                 
               
             
           
         
       
     
     In a second stage, a time domain spatial decorrelation ( 10 ) can be done as
 
 z   pre ( n )= L   T   −1 ( k ){tilde over ( z )} pre ( n ),  (28)
 
where L T   −1 (k) is the Cholesky factorization of a covariance matrix
 
                         R   ^     T     ⁡     (   k   )       =     [           r     0   ,   0           …         r     0   ,       N   r     -   1                 M                   M             r         N   r     -   1     ,   0           …         r         N   r     -   1     ,       N   r     -   1               ]             (   29   )               
such that
 
 L   T ( k ) L   T * T ( k )={circumflex over ( R )} T ( k )  (30)
 
and L T (k) is lower triangular.
 
     The covariance matrix can be estimated as a moving average over N SDC  samples 
                           R   ^     T     ⁡     (   k   )       =       ∑     n   =     k   ·     N   SDC               (     k   +   1     )     ·     N   SDC       -   1       ⁢           ⁢       α   ⁡     (   n   )       ⁢           z   ~     pre     ⁡     (   n   )       ·       (         z   ~     pre     ⁡     (   n   )       )       *   T               ,           (   31   )               
where α(n) are suitable scaling coefficients, e.g. α(n)=1/N SDC . Alternatively this co-variance matrix is estimated in a recursive manner,
 
{circumflex over ( R )} T ( k )=(1−α Spec ){circumflex over ( R )} T ( k− 1)+α Spec   {tilde over (z)}   pre ( n )·( {tilde over (z)}   pre ( n ))* T   (32)
 
where α Spec  is a suitable forgetting factor, e.g. α Spec =0.01. Several possible ways of combining these moving average and recursive estimators are possible.