Computing filter coefficients for an equalizer in a communication receiver

1. A method for computing equalizer filter coefficients in a communications receiver, the method including:

determining, using a processor in a computer, a channel estimation vector f, from at least one channel estimation input;

determining equalizer filter coefficients on a basis of a real matrix T generated from said channel estimation vector f, vector f comprising a vector of dimension N, N comprising an odd number, and T comprising an N×N matrix;

generating the matrix T by solving a matrix Gc 0 =i 0 for each real and imaginary term in c 0 , wherein G is a channel estimation matrix, c 0 comprises an inverse of a middle column of the matrix G, and i 0 comprises an identity matrix's middle column;

performing a matrix inversion on the matrix T in order to determine a middle column of T −1 ;

forming a vector v from a middle column of a matrix T −1 and a constant;

determining c 0 H on a basis of v; and

determining filter coefficients w 0 using a relationship w 0 =c 0 H H H where H H comprises a Hermitian transpose of a channel response matrix H,

wherein, the elements of c 0 H are determined on a basis of v according to the following:

c 0 H (( N+ 1)/2) to be equal to v (( N+ 1)/2);

for elements 1 to (N−1)/2 of c 0 H , c 0 H (x) equals v(x)−(0+i(v(N+1−x)); and

for elements (N+1)/2 to N of c 0 H , c 0 H (x) equals v(N+1−x)+(0+i(v(x)),

wherein v and c 0 H comprise elements 1 to N, and notations v(x) and c 0 H (x) denote an x-th element in vectors v and c 0 H respectively,

wherein rows and columns of the matrix T and columns of vector f, are numbered from 1 to N, a notation T(x, y) denotes an entry in the matrix T in its x-th row and v-th column, a notation f(y) denotes an entry in vector f in its v-th column; R[z] denotes a real part of a number z; and I(z) denotes an imaginary part of the number z, and

wherein the elements of the matrix T are generated as follows:

T (( N+ 1)/2, ( N+ 1)/2)= R[f (1)/2];

for row (N+1)/2, column numbers from 1 to (N−1)/2:

T (( N+ 1)/2, ( N+ 1)/2−column number)= R[f (col−1)] and

T (( N+ 1)/2, ( N+ 1)/2+column number)= I[f (col+1)]; and

for row number 1 to (N−1)/2 and for the middle column:

T (row number, ( N+ 1)/2)= R[f (( N+ 1)/2] ; and

T ( N+ 1−row number, ( N+ 1)/2)= I[f (( N+ 1)/2)];

for column numbers 1 to (N−1)/2:

T (row number, column number)= R[f (column number)]+ R[f ( N+ 1−column number)]; and

T ( N+ 1−row number, N+ 1−column number)= R[f (column number)]− R[f ( N+ 1−column number)];

for column numbers from ((N+1)/2+1) to N:

T (row number, column number)= I[f (column number)]− I[f ( N+ 1−column number)]; and

T ( N+ 1−row number, N+ 1−column number)= I[f (column number)]+ I[f ( N+ 1−col)]; and

for f vector column numbers from N down to 2:

f (col)= f (col−1);

R[f (1)]= T (( N+ 1)/2, ( N+ 1)/2−row); and

i I[f(1)=− T (( N+ 1)/2, ( N+ 1)/2+row)).

2. A method as claimed in claim 1 , further comprising directly forming the matrix T from said vector f.

3. A method as claimed in claim 2 , further comprising:

conducting a matrix inversion on the matrix T using a Cholesky decomposition to obtain a lower triangular matrix L, and

performing forward and backward substitution on the matrix L.

4. A method of processing a received signal in a communications receiver, said method comprising:

computing one or more equalizer filter coefficients using a method as claimed in claim 2 ; and

equalizing said received signal using the computed equalizer filter coefficients.

5. A method as claimed in claim 1 , further comprising:

conducting a matrix inversion on the matrix T using a Cholesky decomposition to obtain a lower triangular matrix L, and

performing a forward and a backward substitution on L.

6. A method of processing a received signal in a communications receiver, said method comprising:

computing one or more equalizer filter coefficients using a method as claimed in claim 1 ; and

equalizing said received signal using the computed equalizer filter coefficients.

7. An equalizer for use in a communication receiver, the equalizer comprising:

a first input for receiving a input data for equalization,

a second input for receiving channel estimation data relating to the input data;

a signal processing path configured to perform a signal processing method of claim 6 on said input data to generate an equalized output data; and

at least one output unit for outputting said equalized output data.

8. An equalizer for use in a communications receiver, said equalizer being configured to implement a method according to claim 1 .

9. An equalizer as claimed in claim 8 , wherein the equalizer includes one or more of the following signal processing blocks:

a channel matrix calculation block configured to compute vectors h and f based on a basis of a received channel estimation;

a real matrix calculation block configured to form the matrix T;

a matrix decomposition block for performing a matrix decomposition on the matrix T;

a forward and backward substitution block configured to compute values of elements in a middle column of the matrix T −1 ;

a middle column calculation block configured to determine element values in a middle column of the matrix G −1 (c 0 );

a filter coefficient generation block configured to compute filter coefficients w 0 =c 0 H H H ; and

a finite impulse response filter.

10. A communications receiver including an equalizer according to claim 8 .