Fourier-transform based linear equalization for MIMO CDMA downlink

Abstract

In the reception of a downlink MIMO CDMA signal, the receiving unit performs a simplified process of linear equalization that eliminates the need for inverting the correlation matrix. The correlation matrix is approximated to a good degree by a circulation matrix that is diagonalized by FFT operations, thus substituting two FFTs and one IFFT having a complexity of O ( L F  ( N   Δ ) 3 + ( N   Δ ) 2 + 2  ( N   Δ ) 2  L F  log 2  L F ) for the direct matrix inversion having a complexity of O(L F 3 ).

1 - 36 . (canceled) 
   
   
       37 . A method comprising:
 estimating a channel correlation matrix R of a received signal vector r(i);   generating a filter matrix w without inverting the channel correlation matrix R;   applying the generated filter matrix w to the received signal vector r(i) to find an estimated chip d(i); and   outputting one of an audio signal or data from the estimated chip d(i).   
   
   
       38 . The method of  claim 37 , wherein generating the filter matrix w without inverting the channel correlation matrix R comprises:
 converting the channel correlation matrix R to a block circulant matrix S; and   obtaining an inverse of the block circulant matrix S via Fourier transform operations.   
   
   
       39 . The method of  claim 38 , wherein converting the channel correlation matrix R to the block circulant matrix S comprises adding corner matrices to the channel correlation matrix R. 
   
   
       40 . The method of  claim 39 , wherein the corner matrices are Hermitian conjugates of one another. 
   
   
       41 . The method of  claim 38 , wherein obtaining the inverse of the block circulant matrix S via Fourier transform operations comprises executing an inverse discrete Fourier transform on only one column of the block circulant matrix S multiplied by a discrete Fourier transform of a chip-level channel impulse vector h. 
   
   
       42 . The method of  claim 38 , wherein obtaining the inverse of the block circulant matrix S via Fourier transform operations comprises executing an inverse discrete Fourier transform on only one column of the block circulant matrix S and multiplying the result by a fast Fourier transform of a chip-level channel impulse vector h. 
   
   
       43 . The method of  claim 38 , wherein obtaining the inverse of the block circulant matrix S via Fourier transform operations comprises executing an inverse discrete Fourier transform on an inverted form of a first column of the block circulant matrix S and applying the result as frequency domain filter taps of the generated filter matrix w. 
   
   
       44 . The method of  claim 43 , further comprising adding a noise floor to the block circulant matrix S as a unit matrix multiplied by a constant. 
   
   
       45 . The method of  claim 38 , wherein obtaining the inverse of the block circulant matrix S via Fourier transform operations comprises increasing filter length of the filter w while performing the Fourier transform operations in the frequency domain and truncating the increased filter length after an inverse Fourier transform operation. 
   
   
       46 . The method of  claim 37 , wherein the received signal vector r(i) is received over M antennas where M is an integer greater than one, and wherein generating the filter matrix w without inverting the channel correlation matrix R comprises:
 converting the channel correlation matrix R to a block circulant matrix S;   cyclically shifting at least a block column of the block circulant matrix S; and   obtaining an inverse of the cyclically shifted block circulant matrix S via Fourier transform operations that are executed separately on each of M dimensions of the received signal.   
   
   
       47 . A storage medium tangibly embodying a program of machine-readable instructions that are executable by a computer processor to perform actions directed toward processing a received signal according to actions comprising:
 estimating a channel correlation matrix R of a received signal vector r(i);
 generating a filter matrix w without inverting the channel correlation matrix R; 
 applying the generated filter matrix w to the received signal vector r(i) to find an estimated chip d(i); and 
 outputting one of an audio signal or data from the estimated chip d(i). 
   
   
   
       48 . The storage medium of  claim 47 , wherein generating the filter matrix w without inverting the channel correlation matrix R comprises:
 converting the channel correlation matrix R to a block circulant matrix S; and   obtaining an inverse of the block circulant matrix S via Fourier transform operations.   
   
   
       49 . The storage medium of  claim 48 , wherein converting the channel correlation matrix R to the block circulant matrix S comprises adding corner matrices to the channel correlation matrix R. 
   
   
       50 . The storage medium of  claim 49 , wherein the corner matrices are Hermitian conjugates of one another. 
   
   
       51 . The storage medium of  claim 48 , wherein obtaining the inverse of the block circulant matrix S via Fourier transform operations comprises executing an inverse discrete Fourier transform on only one column of the block circulant matrix S multiplied by a discrete Fourier transform of a chip-level channel impulse vector h. 
   
   
       52 . The storage medium of  claim 48 , wherein obtaining the inverse of the block circulant matrix S via Fourier transform operations comprises executing an inverse discrete Fourier transform on only one column of the block circulant matrix S and multiplying the result by a fast Fourier transform of a chip-level channel impulse vector h. 
   
   
       53 . The storage medium of  claim 48 , wherein obtaining the inverse of the block circulant matrix S via Fourier transform operations comprises executing an inverse discrete Fourier transform on an inverted form of a first column of the block circulant matrix S and applying the result as frequency domain filter taps of the generated filter matrix w. 
   
   
       54 . The storage medium of  claim 43 , the actions further comprising adding a noise floor to the block circulant matrix S as a unit matrix multiplied by a constant. 
   
   
       55 . The storage medium of  claim 48 , wherein obtaining the inverse of the block circulant matrix S via Fourier transform operations comprises increasing filter length of the filter w while performing the Fourier transform operations in the frequency domain and truncating the increased filter length after an inverse Fourier transform operation. 
   
   
       56 . The storage medium of  claim 47 , wherein the received signal vector r(i) is received over M antennas where M is an integer greater than one, and wherein generating the filter matrix w without inverting the channel correlation matrix R comprises:
 converting the channel correlation matrix R to a block circulant matrix S;   cyclically shifting at least a block column of the block circulant matrix S; and   obtaining an inverse of the cyclically shifted block circulant matrix S via Fourier transform operations that are executed separately on each of M dimensions of the received signal.   
   
   
       57 . A device comprising:
 a channel estimator configured to estimate a channel correlation matrix R of a received signal vector r(i);   an equalizer configured to generate a filter matrix w without inverting the channel correlation matrix R, and for applying the generated filter matrix w to the received signal vector r(i) to output an estimated chip d(i)   
   
   
       58 . The device of  claim 57 , wherein the channel estimator is configured to generate the filter matrix w without inverting the channel correlation matrix R by:
 converting the channel correlation matrix R to a block circulant matrix S; and   obtaining an inverse of the block circulant matrix S via Fourier transform operations.   
   
   
       59 . The device of  claim 58 , wherein the channel estimator is configured to convert the channel correlation matrix R to the block circulant matrix S by adding corner matrices to the channel correlation matrix R. 
   
   
       60 . The device of  claim 59 , wherein the corner matrices are Hermitian conjugates of one another. 
   
   
       61 . The device of  claim 38 , wherein the channel estimator is configured to obtain the inverse of the block circulant matrix S via Fourier transform operations by executing an inverse discrete Fourier transform on only one column of the block circulant matrix S multiplied by a discrete Fourier transform of a chip-level channel impulse vector h. 
   
   
       62 . The device of  claim 58 , wherein the channel estimator is configured to obtain the inverse of the block circulant matrix S via Fourier transform operations by executing an inverse discrete Fourier transform on only one column of the block circulant matrix S and multiplying the result by a fast Fourier transform of a chip-level channel impulse vector h. 
   
   
       63 . The method of  claim 58 , wherein the channel estimator is configured to obtain the inverse of the block circulant matrix S via Fourier transform operations by executing an inverse discrete Fourier transform on an inverted form of a first column of the block circulant matrix S and applying the result as frequency domain filter taps of the generated filter matrix w. 
   
   
       64 . The device of  claim 63 , wherein the channel estimator is further configured to add a noise floor to the block circulant matrix S as a unit matrix multiplied by a constant. 
   
   
       65 . The device of  claim 58 , wherein the channel estimator is configured to obtain the inverse of the block circulant matrix S via Fourier transform operations by increasing filter length of the filter w while performing the Fourier transform operations in the frequency domain and truncating the increased filter length after an inverse Fourier transform operation. 
   
   
       66 . The device of  claim 57 , wherein the received signal vector r(i) is received over M antennas where M is an integer greater than one, and wherein the channel estimator is configured to generate the filter matrix w without inverting the channel correlation matrix R by:
 converting the channel correlation matrix R to a block circulant matrix S;   cyclically shifting at least a block column of the block circulant matrix S; and   separately executing on each of M dimensions of the received signal the Fourier transform operations so as to obtain the inverse of the cyclically shifted block circulant matrix S.