Tools for Performance Analysis and Design of Space–Time Block Codes

Space-time block codes (STBCs) have attracted recent interest due to their ability to take advantage of both space and time diversity to reliably transmit data over a wireless fading channel. In many cases, their design is based on asymptotically tight performance criteria, such as the worst-case pairwise error probability (PEP) or the union bound. However, these quantities fail to give an accurate performance picture, especially at low signal-to-noise ratio, because the classical union bound is known to be loose in this case. This paper develops tighter performance criteria for STBCs which yield considerably better bounds. First, the union bound is developed as the average of the exact PEPs. By noting that some of the terms in the bound are redundant, a second bound is obtained by expurgation. Since this still yields a loose bound, a tighter bound, denoted as the progressive union bound (PUB), is obtained. Because the PUB cannot be computed in closed form, in its most general case, and to avoid computing a high-dimensional numerical integration, its saddlepoint approximation is developed. In addition to the significant improvement of the PUB analysis over other bounding methods, it is also shown that codes designed to optimize the PUB can perform better than those obtained by the looser criteria