Benefits of Rich Scattering in MIMO Channels: A Graph-Theoretical Perspective

In this letter, the impact of scattering on a multiple-input multiple-output (MIMO) propagation environment is studied based on a recently-proposed graph-theoretical channel model. An old result that rich scattering in MIMO propagation environments is a requisite for the channel matrix to have full rank (equivalently for the channel capacity to scale linearly with the number of antennas) is verified. Then, novel insights on the importance of scattering in MIMO channels from a graph-theoretical perspective are provided. By showing that the adjacency matrix of the whole propagation channel has same spectrum (eigenvalues) as the sub-graph inter-connecting the scatterers, it is inferred that all graph-theoretical properties of the propagation graph are contained in the scattering fraction of the channel. In particular, it is inferred that the channel model can be almost-surely reconstructed from the sole knowledge of the spectrum of the sub-graph interconnecting the scatterers. These results may find application in MIMO channel modeling in settings where full pilot-based channel estimation is infeasible or impractical, as in high-mobility scenarios.