Linear canonical Wigner distribution of noisy LFM signals via variance-SNR based inequalities system analysis

In consideration of the latest second-order moment variance type of signal-to-noise ratio (SNR), the so-called variance-SNR, a new inequality model, namely, the variance-SNR inequality between the closed-form instantaneous cross-correlation function type of Wigner distribution and the classical Wigner distribution, is introduced to characterize the detection performance improvement triggered by linear canonical transform (LCT) free parameters embedded. Combining the newly established variance-SNR inequality model with the previous output SNR inequality model gives a stronger inequalities system. Solving it with respect to noisy one-component linear frequency-modulated signals yields more accurate strategies on determination of parameters. Numerical simulations also verify the correctness and rationality of the results of the theoretical deduction, implying that there is a better noise suppression effect by using the newly derived parameters selection strategies.