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Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications by Antonio Napolitano

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4.12 Numerical Results

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

4.12.1 Simulation Setup

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)

(4.304) equation

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) equation

where img and img 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 f2 = Ψ(n)(f1) which are lines with slope ...

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