Outage Theorems for MIMO Block-Fading Channels

The connection between the average codeword or frame error probability (FEP) of space-time codes and the outage probability over general block-fading multiple-input multiple-output (MIMO) channels is established. Three archetypal problems are considered under general fading distributions in a single framework wherein the receiver has channel state information whereas the transmitter knows a) the fading distribution but not the channel realization b) the channel realization but must follow a short term (per codeword) average power constraint, and c) the channel realization but is constrained only by a long-term average power constraint. Three telescoping sets of space-time codes are defined for a given rate and it is shown that average FEPs arbitrarily close to the respective outage probabilities for each of the three cases a)-c) can be achieved by codes in each set for sufficiently large frame lengths. For the smallest set among the three which contains codes with a spectral norm constraint that is stricter than the average or maximum energy constraints commonly assumed, firm sphere-packing lower bounds on the FEP are obtained, and, consequently, strong converse theorems are proved which assert that the respective outage probabilities also represent the best achievable FEP in the large frame-length limit. Moreover, the set of spectral norm constrained codes are also shown to be large enough to contain universal codes that can communicate reliably over any channel realization for which the mutual information exceeds the information rate of the code