Physical channel models described in Chapter 2 are mostly used for simulating system performance. However, they do not allow for the explicit design of space-time coding techniques. In this respect, mathematical representations are required. While physical models reproduce the properties of the MIMO channel by specifying the locations of obstacles and the array configuration, so-called analytical models provide a mathematical representation of the channel matrix. A major difference between both types of modeling approaches lies in the fact that analytical models only provide a framework, but do not give fully quantitative information, unless they are parametrized by means of extrinsic information. By contrast, models such as the COST 273 model, or a ray-tracing tool, directly yield values of essential characteristics of the MIMO channel (correlations, mutual information, etc.), as a function of geometrical and array parameters. A typical analytical model will mathematically express the 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. Since 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 when analyzing mathematically the impact of correlations on any performance parameter, since 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...