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.