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The authors propose a new physically motivated model that allows the study of the interaction between the antennas and the propagation channel for multiple-input multiple-output (MIMO) systems. The key tools employed in the model are the expansion coefficients of the electromagnetic field in spherical vector waves and the scattering matrix representation of the properties of the antenna. The authors derive the expansion of the MIMO channel matrix, H, in spherical vector wave modes of the electromagnetic field of the antennas as well as the propagation channel. The authors also introduce the channel scattering dyadic, C, with a corresponding correlation model for co-polarised and cross-polarised elements and introduce the concept of mode-to-mode channel mapping, the M-matrix, between the receive and transmit antenna modes. The M-matrix maps the modes excited by the transmitting antenna to the modes exciting the receive antennas and vice versa. The covariance statistics of this M-matrix are expressed as a function of the double-directional power-angular spectrum (PAS) of co-polarised and cross-polarised components of the electromagnetic field. Their approach aims at gaining insights into the physics governing the interaction between antennas and channels and it is useful for studying the performance of different antenna designs in a specified propagation channel as well as for modelling the propagation channel. It can furthermore be used to quantify the optimal properties of antennas in a given propagation channel. The authors illustrate the developed methodology by analysing the interaction of a 2 × 2 system of slant polarised half-wavelength dipole antennas with some basic propagation channel models.