Space-weighted communication path estimation

1. A method of estimating a communication path formed of a plurality of channels, associated with a plurality of antennae, the method necessitating an estimate of the impulse response C 1 , C 2 , . . . , C n of said channels, comprising the steps of:

acquiring a space statistic of the communication path,

establishing a corrected impulse response (C′ 1 , C′ 2 , . . . , C′ n ) at least by weighting said impulse response estimates (C 1 , C 2 , . . . , C n ) by means of said space statistic and an estimate of the additive noise (N 01 , N 02 , . . . , N 0n ) of said channels.

2. A method according to claim 1 , wherein said space statistic corresponds to an estimate of the correlation of said communication channels taken two by two.

3. A method according to claim 2 , wherein said estimate of the correlation of the communication channels takes the form of a space correlation matrix (G) in which the element (g ij ) in the ith row and the jth column is obtained by smoothing the product (C h i C j ) of the Hermitian transposition of the estimated impulse response (C i ) of the ith channel and the estimated impulse response (C j ) of the jth channel.

4. A method according to claim 3 , wherein if a signal S received by a channel corresponds to a transmitted training sequence the estimate of the additive noise (N 0 ) of that channel is obtained by normalizing the energy of the vector (S−AC 1 ) where A is the measurement matrix associated with said training sequence.

5. A method according to claim 4 , wherein said normalization is followed by an averaging step.

6. A method according to any of claims 3 to 5 , wherein if a noise matrix (N) is formed from the estimated additive noise (N 01 , N 02 , . . . , N 0n ) of the channels and a space-weighting matrix (G′) is defined on the basis of said spatial correlation matrix (G) and said noise matrix G′=G(G+N) −1 ′ said corrected impulse responses (C′ 1 , C′ 2 , . . . , C′ n ) are obtained from the following expression:

(

⁢

C

1

′

⁢

⁢

t

C

2

′t

⋮

C

n

′

⁢

⁢

t

⁢

)

=

G

′

(

⁢

C

1

t

C

2

t

⋮

C

n

t

⁢

)

7. A method according to claim 6 wherein, if the signal (S) received by a channel corresponds to a transmitted training sequence, the method includes the following steps before establishing said corrected impulse response (C′ 1 ) of that channel:

acquiring a time statistic of the transmission channel,

establishing the estimate (Xp) of the impulse response (C 1 ) of said channel, in which the estimate (X p ) is weighted by said time statistic of the channel by means of said received signal (S).

8. A method according to claim 7 , wherein said time statistic corresponds to an estimate of the covariance of said impulse response.

9. A method according to claim 8 , comprising the steps of:

smoothing said impulse response and orthonormalizing by means of a transformation matrix W to obtain said estimate of the covariance which then takes the form of a matrix L′,

seeking eigenvectors (v i ′) and eigenvalues (λ i ′) associated with that matrix L′,

estimating an instantaneous impulse response of the channel from said received signal (S) and applying that transformation matrix W to form a vector X′, so establishing said weighted estimate (Xp):

X

p

=

∑

(

λ

i

′

-

N

0

λ

i

′

⁢

(

v

i

′

⁢

⁢

h

·

X

′

)

)

⁢

Wv

i

′

⁢

⁢

h

where N 0 is a positive real number representing the additive noise of said channel.

10. A method according to claim 9 , wherein said additive noise (N 0 ) is made equal to the smallest of said eigenvalues (λ i ′).

11. A method according to claim 9 wherein each eigenvalue of a subset of said eigenvalues (λ 1 ′) having a contribution less than a predetermined threshold is forced to the value of said additive noise (N 0 ).

12. A method according to claim 8 , wherein said estimate of the covariance takes the form of a matrix R and said weighted estimate (Xp) is established as follows:

Xp =( A t A+N 0 R −1 ) −1 A t .S

where A is the measurement matrix associated with said training sequence and N 0 is a positive real number representing the additive noise of said channel.

13. A method according to claim 12 , comprising a step of orthonormalizing said matrix R by means of a transformation matrix W to obtain a new matrix R′, the weighted estimate then taking the following new form:

Xp=W t ( I+N 0 R′ −1 ) −1 W t A′ t .S

where the matrix A′ is equal to product of the transformation matrix W and said measurement matrix A and I represents the identity matrix.

14. A method according to claim 13 , wherein the expression (I+N 0 R′ −1 ) −1 is calculated by means of the matrix inversion lemma.