CLAIMS
1. Method for decoding received symbols by a receiver using Lenstra-Lenstra-Lovasz lattice reduction in a receiver receiving constellation points through a Multi 5 Input Multi Output channel, from a matrix representing the Multi Input Multi Output channel which is decomposed into a unitary matrix Q, an upper triangular matrix R, and an unimodular matrix T, characterized in that the reduced upper triangular matrix R, the unitary matrix Q and the unimodular matrix T satisfy the following formula:
M^QRT"1, where M is an upper triangular matrix M of the Multi Input Multi
10 Output channel, the method is executed in a soft output decision algorithm and the
size of the upper triangular matrix M is equal to the number of antennas Nt minus one
of a source which transmits the constellation points, contribution of assumed
transmitted symbols are subtracted from the received contellation points and a
prefiltering which takes into account the subtraction is performed in order to provide 15 the upper triangular matrix, the prefiltering (S401) F- being performed according to
the following formula:

comprising all zeros entries but in the i -th position having a one, A = H'H + p I, zf
is the i-th component of the transmitted vector of received symbols, H is a channel
20 estimate between the sorce and the receiver, p is the signal to noise ratio, I is the
identity matrix and E; is as an Nt x N, identity matrix from which the i -th row have
been removed,
the method comprises the steps of:
- reducing (S503) the k-th column of the upper triangular matrix R and updating
25 the unimodular matrix T into a new unimodular matrix, k being a variable indicating
the rank of a column within the reduced upper triangular matrix R,
- permuting (S506) the k-th and the k-l-th columns of the reduced upper
triangular matrix R and of the new unimodular matrix T according to a comparison
between the elements of the k-lth and k-th row of the k-th column of the reduced
30 upper triangular matrix R,

- triangularizing (S507) the reduced upper triangular matrix R of which columns are permuted into a new reduced upper triangular matrix and updating the unitary matrix Q into a new unitary matrix.
5 2. Method according to claim 1, characterized in that the method comprises
further step of:
updating the variable indicating the rank of the column,
And the reducing, the permuting, the triangularization are executed iteratively on the new upper triangular matrix R, the new unimodular matrix and the new unitary 10 matrix.
3. Method according to claim 2, characterized in that the new reduced upper
triangular matrix R, the new unitary matrix Q and the new unimodular matrix T
satisfy the following formula ,
15 M=QRT1, where M is the upper triangular matrix M of the Multi Input Multi
Output channel.
4. Method according to any of the claims 1 to 3, characterized in that the method
comprises further step of
20 - calculating a coefficient a = lRk_} k / Rk_, k_, 1 , where L1 is a rounding
operation taking the closest integer on the real and imaginary part independently, Rk_! k is the k-l-th element of the k column of R and Rk_t k_j is the k-l-th element of
the k-l-th column of R„ the reducing of the upper triangular matrix is performed using the following formula VI |Rk^lk |2 +|Rkk |2 wherein 5 is a parameter upper than lA
-k-i,k I >lRk-i,k I +lRk,k 30 and lower than or equal to 1.
6. Method according to claim 5, characterized in that the variable k indicating the rank of the column is updated as: if 61 Rk_, k |2>| R^ k f +1 Rk k |2 then
k«~max(k-l,2), else k-^k + 1.

7. Method according to claim 6, characterized in that the variable k indicating
the rank of the column is updated as: k <-mod(k-l,n-l) + 2 where mod is the
modulo operation. 5
8. Device for decoding received symbols by a receiver using a Lenstra-Lenstra-
Lovasz lattice reduction in a receiver receiving constellation points through a Muiti
Input Multi Output channel, from a matrix representing the Multi Input Multi Output
channel which is decomposed into a unitary matrix Q, an upper triangular matrix R,
10 and an unimodular matrix T, characterized in that the reduced upper triangular matrix R, the unitary matrix Q and the unimodular matrix T satisfy the following formula:
M-QRT"1, where M is an upper triangular matrix M of the Multi Input Multi Output channel, the device executs a soft output decision algorithm and the size of the upper triangular matrix M is equal to the number of antennas Nt minus one of a
15 source which transmits the constellation points, contribution of assumed transmitted
symbols are subtracted from the received contellation points and a prefiltering which
takes into account the subtraction is performed in order to provide the upper triangular matrix, the prefiltering (S401) F- being performed according to the following
formula:
,
20
comprising all zeros entries but in the i -th position having a one, A = H' H + p {l, z-
is the i-th component of the transmitted vector of received symbols, H is a channel estimate between the sorce and the receiver, p is the signal to noise ratio, I is the identity matrix and E; is as an Nt x Nt identity matrix from which the i -th row have
25 been removed,
the device comprises:
- means for reducing the k-th column of the upper triangular matrix R and
updating the unimodular matrix T into a new unimodular matrix, k being a variable
indicating the rank of a column within the reduced upper triangular matrix R,
30 - means for permuting the k-th and the k-l-th columns of the reduced upper
triangular matrix R and of the new unimodular matrix T according to a comparison

between the elements of the k-lth and k-th row of the k-th column of the reduced upper triangular matrix R,
- means for triangularizing the reduced upper triangular matrix R of which columns are permuted into a new reduced upper triangular matrix and updating the unitary matrix Q into a new unitary matrix.
9. Computer program which can be directly loadable into a programmable device, comprising instructions or portions of code for implementing the steps of the method according to any of claims 1 to 7, when said computer program is executed on a programmable device.