Probability of Full-Diversity for Simple Coded and Rotated Multidimensional Constellation Systems

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Executive Summary

The case of rotation, in use together with coding in a channel with B fading blocks, is analyzed in terms of diversity properties of the coded systems with multi-dimensional rotated constellations (coded-rotated system) output. First closed-form expression obtained is related to the diversity performance of un-rotated generic coding structures with given minimum distance, d, block length, and number of fading blocks. Afterwards, another closed-form expression is derived for distinguishing the effect of rotation applied on the given coding structures. This latter expression yields a strict lower bound on the probability of attaining full diversity for any coded-rotated system and gives one a tool to evaluate the improvement with respect to systems involving only coding and also systems with only rotation.

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