Nonlinear hierarchical space-time block codes: construction and regular MTCM design

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.