Linear Canonical Wigner Distribution of Noisy LFM Signals via Multiobjective Optimization Analysis Involving Variance-SNR

The existing output signal-to-noise ratio (SNR) optimization model seems not accurate enough to characterize the closed-form instantaneous cross-correlation function type of Wigner distribution’s optimum detection performance, resulting in an unsatisfactory optimal linear canonical transform free parameters selection strategy. A more appropriate output SNR definition, the so-called variance-SNR, is then proposed to model a new kind of optimization, the variance-SNR optimization model. By integrating these two optimization models, it follows a multiobjective optimization, whose solutions to noisy single component linear frequency-modulated signals are also deduced. The newly derived strategy on determination of the optimal parameters implies the previous one so that there is a better detection performance in terms of noise suppression.