Maximum entropy MIMO wireless channel models with limited information

In this contribution, analytical wireless channel models are derived from the maximum entropy principle, when only limited information about the environment is available. These models are useful in situations where analytical models of the fading characteristics of a multiple-antennas wireless channel are needed, and where the classical Rayleigh fading model is too coarse. The issues of the knowledge of the average channel energy, of an energy upper-bound, and of spatial correlation, are studied. First, analytical models are derived for the cases where these parameters are known deterministically. Frequently, these parameters are unknown, but still known to represent meaningful system characteristics (this includes typical scenarios where the received energy or the spatial correlation varies with the user position). In these cases, consistent analytical channel models are derived, based on maximum entropy distributions of the energy or space correlation parameters. In particular, we show that the entropy-maximizing distribution of the covariance matrices is conveniently handled through its eigenvalues, whereas its eigenvectors are uniformly distributed. Using this technique, the modeler can provide consistent models incorporating correlation of the channel antenna gains without the explicit value of these gains. The results are compared in terms of mutual information to the classical i.i.d. Gaussian model in the SISO case.