Rotated modulations for outage probability minimization: a fading space approach

The outage probability limit is a fundamental lower bound on the word error rate of coded communications systems. It is mainly determined by two parameters: the diversity order and the coding gain. With linear precoding, the maximum achievable coding rate yielding full-diversity can exceed the upper limit given by the standard Singleton bound. However, the effect of precoding on the coding gain is not well understood. This paper analyzes linear precoding from an information theoretical point of view and tries to optimize the coding gain. For discrete constellations, it is shown that constellation expansion together with one optimized precoding parameter is sufficient to approach the best outage achieved by a Gaussian alphabet, thus maximizing the coding gain.