Instantaneous cross-correlation function-[formula omitted]-Wigner distribution: Theory and application

Abstract

To raise the noisy linear frequency-modulated (LFM) signal detection threshold without sacrificing the computing performance, this study employs the well-known τ-Wigner distribution (τ-WD) in extending further the notion of the instantaneous cross-correlation function WD (ICFWD) to the so-called ICF-τ-WD. We extend some essential properties of the ICFWD to those of the ICF-τ-WD. We analyze the computational complexities of the ICFWD and τ-WD, based on which we derive the computational complexity of the ICF-τ-WD. We address an important concern regarding the ICF-τ-WD’s optimal parameters selection for the noisy single component LFM signal processing, in accordance with the output signal-to-noise ratio (SNR) optimization models including the single-objective (expectation-SNR) optimization model and the double-objective (expectation-SNR and variance-SNR) optimization model. We also provide numerical simulations for verifying the advantage of the double-objective optimization model over the single-objective one and the ICF-τ-WD over the ICFWD in the improvement of detection performance.