Performance of Rotated Lattice Constellations in Fading Channels

We study the error probability performance of rotated lattice constellations in frequency-flat block-fading channels. In particular, we use the sphere lower bound on the underlying infinite lattice as a performance benchmark. We show that the sphere lower bound has full diversity. We observe that optimally rotated lattices with largest known minimum product distance perform very close to the lower bound, while the ensemble of random rotations is shown to lack diversity and perform far from it. We furthermore use the bound in the multiple-antenna case, and we observe that the Golden code, the optimal full-rate full-diversity 2times2 space-time block code, is also very close to the lower bound