A Tight Upper Bound on the PEP of a Space-Time Coded System

For a space-time coded system subject to flat Rayleigh fading, we formulate the pairwise error probability (PEP) in a unified expression, which accounts for the cases of perfect channel-state information, imperfect channel estimation, and unknown channel. The unified PEP expression is then bounded by an exponential-type inequality leading to a tight upper bound on the PEP. The bound indicates that to design a good code set, we not only need to maximize the geometric mean of the nonzero eigenvalues of the code difference matrix, but also minimize their harmonic mean.