Geometrical relations between space time block code designs and complexity reduction

In this work, the geometric relation between space time block code design for the coherent channel and its noncoherent counterpart is exploited to get an analogue of the information theoretic inequality I(X;S) I((X;H);S) in terms of diversity. It provides a lower bound on the performance of non-coherent codes when used in coherent scenarios. This leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced sub tasks. Moreover a geometrical criterion for high performance space time code design is derived.