Method for decoding 2x2 spatiotemporal codes, in particular golden type code

A method for decoding 2×2 space-time codes of a vector Y, in particular of the Golden Code type, comprising:

• a filtering of the MMSE-GDFE type is carried out in order to obtain a vector YF=RX+W, with YF the vector Y filtered by means of a filter matrix F (“forward filter”), R a conventional matrix named “backward filter”, X the vector transmitted and W the complex noise matrix;
• a constellation recentring is carried out so that the vector to be determined becomes Z, such that Z=YF−2KMRΓS0=2KMRΓS+W, KM being the normalization constant for the constellation in question, Γ being the Golden Code, and S the vector of the information symbols;
• a step of permutation of the elements of the matrices Z, R and Γ is carried out in order to obtain {tilde over (Z)}, {tilde over (R)} and {tilde over (Γ)} such that {tilde over (R)}HR is a matrix in the form of an X and the complex number “i” is moved from Γ to R;
• a step of lattice basis reduction is carried out such that {tilde over (Z)}=2KM{tilde over (ψ)}{tilde over (Γ)}S′+W with {tilde over (ψ)}={tilde over (R)}.Δα(x1,x2,x3,x4) and S′=π+−1(x1,x2,x3,x4).S, πα(x1,x2,x3,x4) being a basis change matrix, πα(x1,x2,x3,x4) is the matrix associated with Δα(x1, x2, x3, x4) which is a matrix in which the determinant module is equal to 1 and defined such that ΔαHΔα is a matrix in the form of an X;
• and
• the ZF-DFE decoding algorithm is applied, in which among the four elements of {tilde over (Z)} two layers are identified, each layer comprising the two elements of the diagonal or anti-diagonal of {tilde over (Z)};
• the DFE algorithm is applied layer by layer and the ZF algorithm within each of the layers.