On performance limits of space-time codes: a sphere-packing bound approach

A sphere-packing bound (SPB) on average word-error probability (WEP) is derived to determine the performance limits of space-time codes on Rayleigh block-fading channels under delay and maximum energy constraints. Two other explicit bounds, a looser bound and a tight approximate bound, are also derived to provide more intuition on how the system parameters affect the performance limits. Moreover, it is shown that as the block length grows to infinity, the SPB converges to the outage probability, and the asymptotic behavior of performance limits is determined by the outage probability.