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

摘要

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