Spatial cross-correlation of multilink propagation channels in amplify-and-forward relay systems

In this contribution, an analytical expression is derived for the correlation matrix of the multiple-input multiple-output (MIMO) propagation channel for the amplify-and-forward relay transmission systems. In order to understand the cross-correlation mechanism, we derive the spatial correlation of two arbitrary channels between the source and the destination via relay stations in terms of the direction-delay spread functions of the links. The results show that the coherent components that exist in the channels between the source and the relay stations and in the channels between the destination and the relay stations lead to the non-zero cross-correlation among the links. Channel measurement results in two indoor environments are used to illustrate the existence of cross-correlation among the channels with the link ends located in different environments. These observations together with the theoretical work indicate that it is possible to use the geometry-based approaches that take into account the properties of the propagation environments to model the spatial correlation matrix of the multi-link MIMO channels.