Dispersion of infinite constellations in MIMO fading channels

In this work we extend the setting of communication without power constraint, proposed by Poltyrev, to a t × r multiple-input multiple-output (MIMO) fast fading channels with channel state information (radio ) at the receiver. The optimal codewords density, or actually the optimal normalized log density (NLD), is considered. Poltyrev´s capacity for this channel is the highest achievable NLD, at possibly large number of channel uses, that guarantees a vanishing error probability. For a given finite number of channel uses n and a fixed error probability e, there is a gap between the highest achievable NLD and Poltyrev´s capacity. As in other channels, this gap asymptotically vanishes as the square root of V over n, multiplied by the inverse Q-function of the allowed error probability ϵ, where V is the channel dispersion. Currently our results are valid for t ≤ r.