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The study of degrees of freedom of signals observed within spatially diversebroadband multipath fields is an area of ongoing investigation and has a widerange of applications, including characterising broadband MIMO and cooperativenetworks. However, a fundamental question arises: given a size limitation onthe observation region, what is the upper bound on the degrees of freedom ofsignals observed within a broadband multipath field over a finite time window?In order to address this question, we characterize the multipath field as a sumof a finite number of orthogonal waveforms or spatial modes. We show that (i)the "effective observation time" is independent of spatial modes and differentfrom actual observation time, (ii) in wideband transmission regimes, the"effective bandwidth" is spatial mode dependent and varies from the givenfrequency bandwidth. These findings clearly indicate the strong couplingbetween space and time as well as space and frequency in spatially diversewideband multipath fields. As a result, signal degrees of freedom does notagree with the well-established degrees of freedom result as a product ofspatial degrees of freedom and time-frequency degrees of freedom. Instead,analogous to Shannon's communication model where signals are encoded in onlyone spatial mode, the available signal degrees of freedom in spatially diversewideband multipath fields is the time-bandwidth product result extended fromone spatial mode to finite modes. We also show that the degrees of freedom isaffected by the acceptable signal to noise ratio (SNR) in each spatial mode.

Band Limited Signals Observed Over Finite Spatial and Temporal Windows: An Upper Bound to Signal Degrees of Freedom