Abstract
A typical analytical model mathematically expresses the Multiple-Input Multiple-Output (MIMO) channel matrix as a function of a random Gaussian-fading matrix and various channel correlations or steering vectors, without specifying any value for these parameters. Because the correlations depend on the actual antenna configuration used, these models cannot be generalized easily to other configurations, unless new correlation coefficients are extracted from experimental results or physical models. Yet, analytical models are particularly useful while analyzing, mathematically, the impact of correlations on any performance parameter, as the relationship is then explicit. However, the link between system performance and antenna configuration can only be established if the relationship between antenna configuration and correlations in the environment under study is known. As in the case of single-antenna channels, the Rayleigh fading assumption is often used by MIMO system designers, mostly because it is realistic in environments that are rich in scatterers. It corresponds to modeling the narrowband transmission between a transmit and a receive antenna as the sum of a large number of contributions with random and statistically independent phases, directions of departure, and directions of arrival [Par00].
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