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 analog of the information-theoretic inequality I(X;S)lesI((X,H);S) in terms of diversity. It provides a lower bound on the performance of noncoherent codes when used in coherent scenarios. This leads in turn to a code design decomposition result splitting coherent code design into two complexity reduced subtasks. Moreover, a geometrical criterion for high-performance space-time code design is derived.