Distance spectrum of space-time block codes: a union bound point of view

Space-time block codes (STBC) have attracted great interest due to their simple structure and ability to exploit the diversity possible in a multiple input multiple output (MIMO) system. A currently popular approach to STBC code design is to find code sets which optimize the worst pairwise error probability (PEP). The worst case PEP is a good performance criterion, but does not guarantee the best overall probability of decoding error. Several works have emphasized the consideration of the overall distance spectrum of the code set; however designing code sets which achieve the optimal symbol error rate (SER) has proven challenging due to the computational complexity associated with determining the exact SER. This paper proposes a single performance index based on union bound analysis on SER at high signal-to-noise ratio (SNR). This union bound approach is extended to the low SNR scenario, where the exact PEP is used in the union bound calculation. Search results are reported and properties of the resultant code sets analyzed.