Multipath fading channels have recently been shown to provide a diversity benefit for wireless data transfer, which may be exploited through the use of multiple-input multiple-output (MIMO) systems. This has prompted a significant volume of research aimed at modelling the wireless channel, and designing so-called ``Space-Time'' codes to achieve the predicted information capacity.
MIMO wireless models predominantly consider transmit and receive elements as point-wise in nature, following stochastic and geometric results from beam-forming literature. We present a generalized point-wise model for MIMO systems which provides details on the necessary and sufficient conditions for ``dense'' scattering. For large dimension point-wise models, the channel information capacity is shown to be dominated by the eigenvalues of the channel covariance. The channel covariance is determined by the angular diversity of the communication link.
A novel continuous modelling approach is introduced, which allows us to consider volumes in space, and abstract the point-wise features from the MIMO model. It is shown that spatially diverse systems have a fundamental limit to their information theoretic capacity which is a property of the environment, and not governed by the number of antenna elements. Theoretical results are provided which relate the connection strengths (channel gains) between continuous basis functions to the standard point-wise modelling approach. It is shown that the basis expansion provides a Fourier dual to the point-wise approach.
Continuous models for wireless channels are provided for both direct (no scattering) and scattering cases, and the capacity of the wireless channel is shown to improve in the presence of scattering bodies through the availability of additional communication modes. A numerical algorithm for calculating the connection strengths of continuous modes is provided and supported by a comparison with the well-known Ray Tracing channel modelling technique.