Analysis of Degrees of Freedom of Wideband Random Multipath Fields Observed Over Time and Space Windows

TL;DR

This paper investigates the intrinsic degrees of freedom in wideband multipath wavefields over finite regions, revealing a complex coupling between space, time, and bandwidth that affects channel capacity.

Contribution

It models the wavefield as orthogonal waveforms, showing that observable bandwidth and observation time depend on spatial order, extending classical degrees of freedom analysis.

Findings

Observable wavefield bandwidth is limited within an effective bandwidth.

Observation time varies with spatial order.

Classical time-bandwidth product does not directly extend to space-time-bandwidth product.

Abstract

In multipath systems, available degrees of freedom can be considered as a key performance indicator, since the channel capacity grows linearly with the available degrees of freedom. However, a fundamental question arises: given a size limitation on the observable region, what is the intrinsic number of degrees of freedom available in a wideband random multipath wavefield observed over a finite time interval? In this paper, we focus on answering this question by modelling the wavefield as a sum of orthogonal waveforms or spatial orders. We show that for each spatial order, (i) the observable wavefield is band limited within an effective bandwidth rather than the given bandwidth and (ii) the observation time varies from the given observation time. These findings show the strong coupling between space and time as well as space and bandwidth. In effect, for spatially diverse multipath wavefields, the classical degrees of freedom result of "time-bandwidth" product does not directly extend to "time-space-bandwidth" product.