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

The performance criteria of multiple-input multiple-output (MIMO) fading channels, diversity gain and coding gain, demand quite different coding techniques than those for Gaussian channels. This paper proposes a new approach to space-time block code (STBC) construction for coherent systems different from algebraic constructions (unitary, orthogonal) by explicitly manipulating the relationship between codewords rather than properties of the individual codeword. Algebraic constructions may incur performance losses of several decibels, relative to code sets determined by exhaustive search. By characterizing the structure of exhaustively searched code sets, a set of isometries between code words is determined. These isometries, in turn, suggest a greedy code construction method: nonlinear hierarchical codes (NHCs). NHCs of arbitrary block sizes/constellations can be constructed bottom-up by optimizing the coding gain layer-by-layer and reusing the optimized structure. The strong symmetry and layered structure make NHCs ideal constituent codes for regular multiple trellis-coded modulation (RMTCM). New RMTCM design procedures are proposed for various rates/block sizes/constellation sizes. The match between the distance spectrum of NHCs to the regular trellis structure optimizes coding gain directly, and full diversity is naturally maintained given the full rank of the constituent NHCs. Several factors which affect performance are analyzed and exploited to improve the overall performance. Set expansion is used to improve high-rate MTCM designs. In each design, the performance/rate/complexity tradeoffs are gracefully balanced and optimized. With limited growth in complexity, the proposed designs can achieve more than 2 dB gain over current MTCM designs.

Space-time block codes have attracted recent interest due to their ability to take advantage of available diversity to transmit data over a wireless fading channel. Since they were first introduced, several strategies have been proposed for their design. In most cases, these designs were optimized for high SNR through a worst case pairwise error probability analysis and either placed strict constraints on the structure of codewords or were limited to codesets of low cardinality. This work addresses the issue of code design specifically for low SNR environments using union bound-based performance criteria which are SNR dependent. A more accurate union bound-based measure for performance evaluation of codes is developed and a variation of a locally optimum algorithm used to systematically construct good codeword sets is presented. New found codes are compared via simulation with other existing codes and are shown to exhibit improved performance.

A new criterion for performance evaluation of space-time block codes, based on the progressive union bound (PUB) is proposed. The PUB is not analytically tractable, in general, but can be well approximated by a saddlepoint approximation. The improvements provided by this new approach are illustrated by comparison with other bounds. New code sets, offering improved performance at low SNR, can also be found via the new bounds.

Recent designs for space-time block codes (STBCs) have exploited the structure of the codes (unitary, orthogonal) to enable systematic construction. Code sets found by an exhaustive search to optimize cost functions can often achieve performance gains of several dB; however, such searches are not feasible for large block or constellation sizes. By exploiting isometries between codewords, properties of the searched codes are determined which suggest a systematic code construction method. The results are nonlinear hierarchical codes (NHCs), where coding gain is optimized at each layer of the hierarchy and codes of arbitrary block-sizes/constellations can be designed. A fundamental difference between the structured codes (unitary, orthogonal) and NHCs is that in NHCs, the relationship between codewords is manipulated, rather than properties of the individual codeword. The proposed scheme is essentially a generalization of D. Slepian's group codes for the Gaussian channel (see Bell System Tech. J., vol.47, p.575-602, 1968) to the multiple-input multiple-output quasi-static fading channel.

In many wireless communication systems, space-time block codes (STBC) alone are insufficient to provide the needed protection from the effects of a fading channel, and hence are more suitable as an inner code for a serially concatenated system. Serial concatenation introduces memory between STBCs indirectly. A direct approach, multiple trellis coded modulation (MTCM), can match the distance spectrum of constituent codes to the trellis structure and optimize coding gain. Full diversity is naturally maintained given the full rank of the constituent STBCs. Previous MTCM designs of STBC relied heavily on orthogonal codes. In this work, nonlinear hierarchical codes (NHC), with no constraint on the size and structure of each block code, serve as a natural candidate for set partitioning and expansion in MTCM design. Regular MTCM design procedures are proposed to exploit the layered structure of NHC which leads to optimized designs for various rates/block sizes/constellation sizes. Several factors which affect performance are analyzed and exploited to improve the overall performance. Set expansion is used to improve high rate MTCM designs. In each design, the performance/rate/complexity tradeoffs are gracefully balanced and optimized. With limited growth in complexity, the proposed designs can achieve more than 3.5 dB of gain over current MTCM designs.