Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

2.7 Numerical Results

In this section, simulation experiments are carried out, aimed at corroborating the theoretical results of the previous sections.

2.7.1 Aliasing in Cycle-Frequency Domain

In the simulation experiments, a GACS signal is obtained as the output of the Doppler channel existing between a transmitter and a receiver with constant relative radial acceleration, when the input signal is a cyclostationary PAM signal (Section 2.2.6.1). In this case, an analytical condition on the sampling frequency can be deduced, which limits aliasing. Starting from (2.179a) specialized for x ≡ y and ACS signals, it follows that aliasing in the cycle-frequency domain can be avoided, provided that f_s ≥ 4B, where B is the monolateral bandwidth of x(t) (Theorem 1.3.7), (Izzo and Napolitano 1996). Since 2B is the maximum allowable cycle frequency for an ACS signal with bandwidth B, condition f_s ≥ 4B prevents replicas in (2.179a) with p ≠ 0 from contributing to the discrete-time cyclic autocorrelation function in the “principal domain” . If x(t) is not strictly bandlimited, with approximate monolateral bandwidth B, then 2B is the maximum cycle frequency at which x(t) exhibits a significant degree of cyclostationarity. For the chirp-modulated signal y(t) in (2.99) with x(t) ACS, the effect of the chirp modulation is to rotate by an angle θ, where tan θ = γ, the support lines of the cyclic autocorrelation ...