On the performance of space-time codes

This paper provides an overview of the results in a recent journal submission by the same authors. The first part of that paper studies the pairwise error probability of codewords (PEP) of a space-time code over a quasistatic channel, using an approach that allows both known and unknown channel cases to be considered simultaneously. A closed-form expression for the PEP is provided, and given a constraint on the sum of the squares of the singular values of the difference signal matrix, it is shown that the PEP is minimized by choosing signals with equal singular values. A useful sequence of simple upper and lower bounds that converge to the PEP is also provided. An example space-time code is introduced and shown using this sequence of bounds to outperform the corresponding orthogonal-design-based space-time (ODST) code at all values of SNR. Exact expressions, based on the PEP, are given for the asymptotic coding and diversity gain. It is shown that the diversity gain remains unchanged if the PEP is replaced by either the codeword error probability (CEP) or else the message symbol error probability (SEP). Signal-design implications of the above results are also discussed. The second part deals with ODST codes. It is shown that ODST codes represent an instance of orthogonal signaling. This observation is used to derive a closed-form expression for the pairwise error probability of message symbols (PEP-ms) of these codes, as well as an expression for coding gain based on PEP-ms, that is exact in the case of BPSK signaling.