MIMO Channel Rank via the Aperture-Bandwidth Product

An abstract progressive scattering model for multiple-input, multiple-output (MIMO) wireless communication systems is developed. In the model, the transmitted signal reflects off multiple groups of scatterers on its way from transmit array to receive array. The model is then used to predict the effective degrees of freedom (EDOF) of different stages of propagation within the channel. Using properties of the Karhunen-Loeve expansion of random processes, it is shown that the EDOF of a given stage are controlled by the product of observed spatial bandwidth and observing aperture. Simulated results are then provided to demonstrate how the individual stages interact with each other to determine the EDOF and eigenvalue distribution of the overall MIMO system. These results give additional insight into the behavior of known propagation channels such as keyhole channels and single-bounce channels with receiver-side spatial correlation.