Capacity of band limited wavefields observed over finite spatial and temporal windows

In this work, we study the channel capacity for broadband transmission in a multipath wavefield observed on the surface of a limited source-free region over a finite temporal window. It has a wide range of applications, such as characterizing broadband distributed or large scale MIMO systems and evaluating the capacity of these systems. In order to address this topic, for given constraints on region size, bandwidth and observation time, the multipath field is characterized as a series of orthogonal basis functions encoded in a finite number of spatial modes. Each of these spatial modes represents an independent channel. We show that for each channel, how the observable time and band limited signals are coupled to a limited region of space. Afterwards, analogous to Shannon's work, we evaluate the capacity of each channel. The derived result indicates that due to the space-frequency coupling relation, for a fixed average signal power over the bandwidth, not all channels have the same capacity. Rather, the lower spatial modes provide large performance gains and channel capacity drops as spatial mode index increases. In addition, different modes provides optimum performance at different radial positions.