Instantaneous cross-correlation function type of WD based LFM signals analysis via output SNR inequality modeling

Abstract

Linear canonical transform (LCT) is a powerful tool for improving the detection accuracy of the conventional Wigner distribution (WD). However, the LCT free parameters embedded increase computational complexity. Recently, the instantaneous cross-correlation function type of WD (ICFWD), a specific WD relevant to the LCT, has shown to be an outcome of the tradeoff between detection accuracy and computational complexity. In this paper, the ICFWD is applied to detect noisy single component and bi-component linear frequency-modulated (LFM) signals through the output signal-to-noise ratio (SNR) inequality modeling and solving with respect to the ICFWD and WD. The expectation-based output SNR inequality model between the ICFWD and WD on a pure deterministic signal added with a zero-mean random noise is proposed. The solutions of the inequality model in regard to single component and bi-component LFM signals corrupted with additive zero-mean stationary noise are obtained respectively. The detection accuracy of ICFWD with that of the closed-form ICFWD (CICFWD), the affine characteristic Wigner distribution (ACWD), the kernel function Wigner distribution (KFWD), the convolution representation Wigner distribution (CRWD) and the classical WD is compared. It also compares the computing speed of ICFWD with that of CICFWD, ACWD, KFWD and CRWD.

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

“…), theoretical expansions (time‐frequency analysis [ 92‐99 ] , compressed sensing [ 100 ] , phase retrieval [ 101 ] , etc. ), and practical applications (signal denoising [ 22‐24 , 35 , 36 , 40‐42 , 102‐105 ] , image watermarking [ 106 , 107 ] , weak target detection [ 108 , 109 ] , etc.). The LCT of a signal with the parameter matrix is defined by [ 4 ] where a basis in the LCT domain denotes where the LCT parameters …”

“…Within a well-established output SNR inequality model [22] , it turns out that the CICFCWD outperforms the CWD in detecting noisy linear frequency-modulated (LFM) signals [26−30] , a kind of important non-stationary signals encountered frequently in the fields of nonlinear optics [31] , synthetic aperture radar [32] , satellite communications [33] , and medical imaging [34] . This fact reveals that there is a cause-and-effect relationship between the appropriate LCT free parameters and a good detection performance.…”

“…Our main goal is to establish a mathematical model for this functional relation as accurate as possible, because with a more accurate mathematical model to the output SNR there is a stricter parameters selection strategy so that the CICFCWD achieves a better effect on reducing noise. However, starting from the mathematical expectation for deterministic signals embedded in additive zero‐mean noise processes, the latest expectation‐SNRs [ 22‐24 , 35 , 36 ] were defined in view of amplitude ratio, which may lead to misunderstanding as the standard SNR definition is the ratio of energy. Consequently, the existing LCT free parameters selection strategies do not come up to the demand of practical engineering, leading to a lot of room for detection performance improvement.…”