In this section, simulation results are reported to corroborate the theoretical results of the previous sections on the spectral cross-correlation density estimation.

The spectral cross-correlation density function between complex-envelope signals x(t) and y(t) is measured, where x(t) and y(t) are the input and output signals, respectively, of a linear time-variant system that models the channel between transmitter and receiver in relative motion with constant relative radial speed, that is (Section 7.3)

In (4.304), a is the (possibly complex) scaling amplitude, d the delay, s the time-scale factor, and ν the frequency shift.

For an ACS input process x(t) the Loève bifrequency cross-spectrum between y(t) and x(t) is given by (see (7.276))

(4.305)

where and are the cyclic spectra and the set of cycle frequencies, respectively, of x(t). Therefore, if s ≠ 1, x(t) and y(t) are not jointly ACS (even if they are singularly ACS) but are jointly SC and exhibit joint spectral correlation on curves f_{2} = Ψ^{(n)}(f_{1}) which are lines with slope ...

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