  Imagine a MIMO communication system that fully exploits the propagation
characteristics offered by an electromagnetic channel and ultimately approaches
the limits imposed by wireless communications. This is the concept of
Holographic MIMO communications. Accurate and tractable channel modeling is
critical to understanding its full potential. Classical stochastic models used
by communications theorists are derived under the electromagnetic far-field
assumption, i.e. planar wave approximation over the array. However, such
assumption breaks down when electromagnetically large (compared to the
wavelength) antenna arrays are considered. In this paper, we start from the
first principles of wave propagation and provide a Fourier plane-wave series
expansion of the channel response, which fully captures the essence of
electromagnetic propagation in arbitrary scattering and is also valid in the
(radiative) near-field. The expansion is based on the Fourier spectral
representation and has an intuitive physical interpretation, as it
statistically describes the angular coupling between source and receiver. When
discretized uniformly, it leads to a low-rank semi-unitarily equivalent
approximation of the electromagnetic channel in the angular domain. The
developed channel model is used to compute the ergodic capacity of a
point-to-point Holographic MIMO system with different degrees of channel state
information.
