On random rotations diversity and minimum MSE decoding of lattices

We establish a simple relation between high-diversity multidimensional rotations obtained from totally complex cyclotomic fields and the discrete Fourier transform. The diversity distribution of an Hadamard-like random rotation is derived analytically. It is shown that a random multidimensional rotation exhibits an excellent diversity distribution and can be combined to quadrature amplitude modulation (QAM) constellations to combat channel fading. We also describe a mean-square error (MSE) universal lattice decoder suitable for large dimensions up to 1024. The MSE criterion treats the lattice structure as intersymbol interference. The universal decoder is applied to both Gaussian and Rayleigh fading channels to decode dense lattice sphere packings and rotated cubic constellations, respectively.