  The study of degrees of freedom of signals observed within spatially diverse
broadband multipath fields is an area of ongoing investigation and has a wide
range of applications, including characterising broadband MIMO and cooperative
networks. However, a fundamental question arises: given a size limitation on
the observation region, what is the upper bound on the degrees of freedom of
signals observed within a broadband multipath field over a finite time window?
In order to address this question, we characterize the multipath field as a sum
of a finite number of orthogonal waveforms or spatial modes. We show that (i)
the "effective observation time" is independent of spatial modes and different
from actual observation time, (ii) in wideband transmission regimes, the
"effective bandwidth" is spatial mode dependent and varies from the given
frequency bandwidth. These findings clearly indicate the strong coupling
between space and time as well as space and frequency in spatially diverse
wideband multipath fields. As a result, signal degrees of freedom does not
agree with the well-established degrees of freedom result as a product of
spatial degrees of freedom and time-frequency degrees of freedom. Instead,
analogous to Shannon's communication model where signals are encoded in only
one spatial mode, the available signal degrees of freedom in spatially diverse
wideband multipath fields is the time-bandwidth product result extended from
one spatial mode to finite modes. We also show that the degrees of freedom is
affected by the acceptable signal to noise ratio (SNR) in each spatial mode.
