TABLE OF CONTENTS Physical channel models have been described in Section 6.3. Yet, for system design and simulations, analytical models might be preferred, as they can reproduce the essential characteristics of a variety of channels without being too complicated.
A first possibility is to model the space-time channel without considering the antenna geometries, i.e. describing the multipath channel in both the temporal (or Doppler frequency) domain and the spatial domain. In [LoBF01], [LoFK02], the classical Wide-Sense-Stationary Uncorrelated Scattering (WSSUS) channel formalism is extended to the spatial dimension. Applying a space-time analogy, the signal in the spatial domain is described through replacing time and frequency by spatial location and spatial frequency, respectively. Generalised impulse response and transfer function can then be defined over delay, time and space. Given knowledge of these, discrete sampling filter models are derived [LoFK02] that can be implemented in channel emulators with space-time variable gain multipliers. These multipliers have random properties similar to those of small-scale fading, and Gaussian amplitude resulting from the sum of many multipath components. Integrating this space-time channel model with array geometries finally yields a model of the MIMO channel matrix.
As an alternative, analytical models presented below aim at describing directly the MIMO channel matrix, rather than describing the spatial channel apart from array geometry. In most cases, these models are built upon correlation properties or a decomposition into steering-/eigenvectors, in combination with an iid random matrix with unity-variance, circularly symmetric complex Gaussian entries (in order to obtain different fading...
