Method for decoding a spatially multiplexed data signal using a maximum likelihood detection

1. A method for decoding a received signal Y corresponding to a data signal transmitted in a MIMO communication system through a channel represented by a channel matrix H, said data signal comprising a set of data symbols x transmitted in at least one layer, each layer carrying at least one data symbol belonging to a signal constellation, wherein said method comprises, for one of said at least one layer, called a current layer n:

a detection step that determines the maximum likelihood for at least one data symbol of said data signal, wherein said detection step comprises:

selecting one candidate value for the data symbol of the current layer n, and

determining, with a processor, the Euclidian distance between the received signal Y and the data signal transmitted using said candidate value multiplied by said channel matrix H, weighted by the inverse of a noise covariance matrix C such as ∥Y−Σ i H i x i ∥ C −1 2 , expressed as:

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wherein:

H k is a vector representing the channel associated to a layer k, with kε{i, j, n}, i, j, nε[0, N−1], i, j, n being integers, possibly equal and N being the number of layers of said data signal;

x k is the constellation symbol of the layer k;

α k R =α k I =α k =∥H k ∥ 2 C −1 ,

β i≠n R = H i H C −1 Y− 0.5Σ j≠i,n H i H C −1 H j x j ,

β i≠n I = H i H C −1 Y− 0.5Σ j≠i,n H i H C −1 H j x j ,

β n R = H n H C −1 Y−Σ j≠n H n H C −1 H j x j ,

β n I = H n H C −1 Y−Σ j≠n H n H C −1 H j x j ,

wherein the terms depending on α k are computed by adding to each of them a predetermined constant depending on the size of the constellation of the layer k, called a constellation dependent constant.

2. The method for decoding according to claim 1 , wherein said constellation dependent constant is equal to (1+max( x) 2 )/2, where max( x) corresponds to the maximum real part of the candidate values of said constellation of the layer k.

3. The method for decoding according to claim 1 , wherein the terms depending on βk are computed by adding the constant 2.M.βk to each of them, where M is an integer.

4. The method for decoding according to claim 1 , wherein the method comprises, for all constellation symbols x i and x j different from the constellation symbol x n of the current layer n, an exhaustive search using a maximum likelihood technique for setting values of the constellation symbols x i and x j .

5. The method for decoding according to claim 1 , wherein the method comprises, for constellation symbols x i at of at least one layer i different from the current layer n, a search in a predetermined region of the constellation symbols x i .

6. The method for decoding according to claim 1 , wherein said current layer n is the layer with the highest constellation order.

7. The method for decoding according to claim 1 , wherein when said signal comprises a set of data symbols transmitted in one layer, i=j=n=0 and

α k =α 0 =∥H 0 ∥ 2 C −1 , β i≠n R = H 0 H C −1 Y and β i≠n I = H 0 H C −1 Y.

8. The method for decoding according to claim 1 , wherein when said signal comprises a set of data symbols transmitted in two layers, i=j, et i, nε[0,1]

α k =∥H k ∥ 2 C −1 , β i≠n R = H i H C −1 Y, β n R = H n H C −1 Y− H n H C −1 H i x i , β i≠n I = H i H C −1 Y

and

β n I = H n H C −1 Y− H n H C −1 H i x i .

9. The method for decoding according to claim 7 , wherein when the terms depending on βk are computed by adding the constant 2.M.βk to each of them, where M is an integer and considering that H n H C −1 H i x i = H n H C −1 H i x i − H n H C −1 H i x i and H n H C −1 H i x i = H n H C −1 H i x i + H n H C −1 H i x i ,

β i≠n R H i H C −1 Y=M. H n H C −1 H i +M. H n H C −1 H i

and

β i≠n I H i H C −1 Y−M. H n H C −1 H i +M. H n H C −1 H i .

10. The method for decoding according to claim 1 , wherein it comprises a subsequent step of decoding, for example a turbo-decoding.

11. The method for decoding according to claim 1 , wherein when the noise is a white Gaussian noise, the noise covariance matrix C is equal to σ 2 I, where I is the identity matrix and σ 2 is the variance of said white Gaussian noise.

12. The method for decoding according to claim 1 , wherein said step of selecting one candidate value for the data symbol of the current layer n implements a hard-symbol slicing.

13. The method for decoding according to claim 1 , wherein said method implements a soft-bit decision step.

14. The method for decoding according to claim 8 , wherein when said signal comprises a set of data symbols transmitted in N>2 layers, the method comprises S≦N iterations, each iteration processing Q<N layers, while the other (N-Q) layers are included in said covariance matrix C, and delivering transmitted symbols of R≦(Q−1) layers of said Q first layers, called resulting layers, one iteration processing Q layers being different from the resulting layers issued by the previous iterations, Q, R, S being integers able to be different from one iteration to the other.

15. A decoder for decoding a received signal Y corresponding to a data signal transmitted in a MIMO communication system through a channel represented by a channel matrix H, said data signal comprising a set of data symbols x transmitted in at least one layer, each layer carrying at least one data symbol belonging to a signal constellation, wherein said decoder comprises, for one of said at least one layer, called a current layer n:

means for detecting that determines the maximum likelihood for at least one data symbol of said data signal,

wherein said means for detecting comprises:

means for selecting one candidate value for the data symbol of the current layer n,

means for determining the Euclidian distance between the received signal Y and the data signal transmitted using said candidate value multiplied by said channel matrix H, weighted by the inverse of a noise covariance matrix C such as ∥Y−Σ i H i x i ∥ C −1 2 , expressed as:

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wherein:

H k is a vector representing the channel associated to a layer k, with kε{i, j, n}, i, j, nε[0,N−1], i, j, n being integers, possibly equal and N being the number of layers of said data signal;

x k is the constellation symbol of the layer k;

α k R =α k I =α k =∥H k ∥ 2 C −1 ,

β i≠n R = H i H C −1 Y− 0.5Σ j≠i,n H i H C −1 H j x j ,

β i≠n I = H i H C −1 Y− 0.5Σ j≠i,n H i H C −1 H j x j ,

β n R = H n H C −1 Y−Σ j≠n H n H C −1 H j x j ,

β n I = H n H C −1 Y−Σ j≠n H n H C −1 H j x j ,

wherein the terms depending on α k are computed by adding to each of them a predetermined constant depending on the size of the constellation of the layer k, called a constellation dependent constant.

16. A non-transitory computer-readable medium comprising a computer program product stored thereon and executable by a microprocessor, said computer program product comprising program code instructions for implementing a method for decoding a received signal Y corresponding to a data signal transmitted in a MIMO communication system through a channel represented by a channel matrix H, said data signal comprising a set of data symbols x transmitted in at least one layer, each layer carrying at least one data symbol belonging to a signal constellation, wherein said computer program product comprises:

program code instructions for processing for one of said at least one layer, called a current layer n, a detection step that determines the maximum likelihood for at least one data symbol of said data signal,

wherein said detection step comprises:

selecting one candidate value for the data symbol of the current layer n,

determining the Euclidian distance between the received signal Y and the data signal transmitted using said candidate value multiplied by said channel matrix H, weighted by the inverse of a noise covariance matrix C such as ∥Y−Σ i H i x i ∥ C −1 2 , expressed as:

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wherein:

H k is a vector representing the channel associated to a layer k, with kε{i, j, n}, i, j, nε[0,N−1], i, j, n being integers, possibly equal and N being the number of layers of said data signal;

x k is the constellation symbol of the layer k;

α k R =α k I =α k =∥H k ∥ 2 C −1 ,

β i≠n R = H i H C −1 Y− 0.5Σ j≠i,n H i H C −1 H j x j ,

β i≠n I = H i H C −1 Y− 0.5Σ j≠i,n H i H C −1 H j x j ,

β n R = H n H C −1 Y−Σ j≠n H n H C −1 H j x j ,

β n I = H n H C −1 Y−Σ j≠n H n H C −1 H j x j ,

wherein the terms depending on α k are computed by adding to each of them a predetermined constant depending on the size of the constellation of the layer k, called a constellation dependent constant.

17. The method for decoding according to claim 9 , wherein when said signal comprises a set of data symbols transmitted in N>2 layers, the method comprises S≦N iterations, each iteration processing Q<N layers, while the other (N-Q) layers are included in said covariance matrix C, and delivering transmitted symbols of R≦(Q−1) layers of said Q first layers, called resulting layers, one iteration processing Q layers being different from the resulting layers issued by the previous iterations, Q, R, S being integers able to be different from one iteration to the other.