| Lattice codes find good use as higher dimensional signal constellations. When used with QAM, the constituent 2-D constellations of a lattice code determine important properties of the transmitted signal. Using multidimensional Fourier techniques, this work presents a robust method to efficiently generate the point distribution of all the constituent 2-D constellations of a lattice code. The multidimensional discrete Fourier transform (MDFT) is computed for a periodic extension of the lattice code. The MDFT is used in conjunction with a version of the Projection-Slice theorem, derived for the discrete case, to obtain the point distribution of all the constituent 2-D constellations. The implementation of the MDFT is via a multidimensional generalization of the FFT using the Cooley-Tukey decomposition, well matched to lattice properties. Numerical results show that for signal constellations which are not large, the continuous approximation technique is not accurate, and therefore the exact calculations should be used. |
