Method for calculating filter coefficients for an equaliser in a communication receiver using hermitian optimisation
View Patent ↗A method for calculating filter coefficients for an equalizer in a communication receiver, the method including the steps of calculating ( 22 ) channel response matrices G and H from channel estimation inputs; performing ( 24 ) a Cholesky decomposition of the channel response matrix G into a lower triangular matrix L and an upper triangular matrix U; performing ( 26 ) forward substitution on the lower triangular matrix L to calculate a column vector d; performing ( 28 ) backward substitution on the column vector d and the Hermitian transpose L H of the lower triangular matrix L to calculate a middle column c 0 of the inverse G −4 of the channel response matrix G; and calculating ( 30 ) the filter coefficients from the middle column c 0 of the inverse channel response matrix G −1 and the Hermitian transpose H H of the response matrix H.
1. A method for computing filter coefficients for an equaliser in a communication receiver, the method including the steps of:
calculating channel response matrices G and H from channel estimation inputs;
performing a Cholesky decomposition of the channel response matrix G into a lower triangular matrix L and an upper triangular matrix U;
performing forward substitution on the lower triangular matrix L to calculate a column vector d;
performing backward substitution on the column vector d and a Hermitian transpose L H of the lower triangular matrix L to calculate a middle column c 0 of an inverse G −1 of the channel response matrix G; and
calculating the filter coefficients from the middle column c 0 of the inverse channel response matrix G −1 and a Hermitian transpose H H of the channel response matrix H.
2. A method according to claim 1 , wherein a vector ĉ 0 of only half of the elements of the middle column c 0 of the inverse channel response matrix G −1 are calculated during the backward substitution step.
3. A method according to claim 2 , wherein the step of calculating the filter coefficients includes the step of obtaining the filter middle column c 0 from the vector ĉ 0 .
4. A method according to any one of the preceding claims, wherein the forward substitution step includes performing computations to solve the system of equation
Ld
=
ⅇ
(
N
+
1
)
/
2
=
[
ⅇ
1
,
ⅇ
2
,
…
,
ⅇ
N
]
T
where
ⅇ
i
=
{
1
i
=
(
N
+
1
)
/
2
0
otherwise
to obtain the column vector d.
5. A method according to claim 3 , wherein the backward substitution step includes performing computations to solve the system of equation
{circumflex over (L)} H ĉ 0 ={circumflex over (d)}
where
{circumflex over (L)} H [i,j]=L H [i+ ( N− 1)/2, j+ ( N− 1)/2]∀0 ≦i,j≦ ( N− 1)/2 (4)
where ĉ 0 is half of the middle column c 0 of the inverse channel response matrix G −1 , and {circumflex over (d)}=d[(N−1)/2, . . . , N−1].
6. A method according to claim 5 , wherein the middle column c 0 is obtained from the vector ĉ 0 by performing computations to solve the equation
c 0 [( N− 1)/2 +k]=ĉ 0 [k], c 0 [k]=c 0 [N− 1 −k]*, k= 0, . . . , ( N− 1)/2.
7. An equaliser for use in a communications device, the equaliser including:
one or more processing blocks for carrying out a method for calculating filter coefficients according to claim 1 ; and
a filter for using the calculated filter coefficients to equalise input signals received by the equaliser.