Most space-time coding schemes can be classified either as non-coherent (decoding is performed without forming an explicit channel estimate) or coherent (decoding is performed conditioned upon a channel estimate as if it were the actual channel realisation). In this thesis, we consider a correlated quasi-static Rayleigh flat fading channel with additive white Gaussian noise. We prove that optimal non-coherent decoding can always be decomposed into a channel estimation step followed by a coherent decoding step. Surprisingly, the required estimators of this coherent approach do not in general minimise the mean square error between the estimated and actual channel realisation. We investigate the characteristics of these estimators and discuss their optimality.