Variance-SNR Based Noise Suppression on Linear Canonical Choi-Williams Distribution of LFM Signals

By solving the existing expectation-signal-to-noise ratio (expectation-SNR) based inequality model of the closed-form instantaneous cross-correlation function type of Choi-Williams distribution (CICFCWD), the linear canonical transform (LCT) free parameters selection strategies obtained are usually unsatisfactory. Since the second-order moment variance outperforms the first-order moment expectation in accurately characterizing output SNRs, this paper uses the variance analysis technique to improve parameters selection strategies. The CICFCWD’s average variance of deterministic signals embedded in additive zero-mean stationary circular Gaussian noise processes is first obtained. Then the so-called variance-SNRs are defined and applied to model a variance-SNR based inequality. A stronger inequalities system is also formulated by integrating expectation-SNR and variance-SNR based inequality models. Finally, a direct application of the system in noisy one-component and bi-component linear frequency-modulated (LFM) signals detection is studied. Analytical algebraic constraints on LCT free parameters newly derived seem more accurate than the existing ones, achieving better noise suppression effects. Our methods have potential applications in optical, radar, communication and medical signal processing.