On finite dimensional approximation in MIMO

We consider measures of richness in multipath wireless channels. We examine bounds on the dimensionality of spatially constrained wireless signals. We show that the continuous system-model bounds on dimensionality rely on an implicit model for noise. We consider dimensionality bounds where the noise model is made an explicit parameter. We show that the dimensionality of a spatially constrained field may be considered as a parameter for a virtual antenna model. We propose a simple antenna model which incorporates spatial dimensionality and relate this to the current point-like model used in MIMO channel models.