Research On Radar Signal Detection Based On Linear Canonical Domain τ-Wigner Distribution Output Signal-to-noise Ratio Inequality Modelin

The research focus of signal representation theory is the time-frequency domain representation of nonstationary signals and the nonstationary signal detection methods based on them.In recent years,a large number of classic time-frequency domain representation tools have emerged in the field of non-stationary signal research,such as the Affine Characteristic Wigner distribution(Affine Characteristic Wigner Distribution(ACWD),the Kernel Function Wigner Distribution(KFWD),the Convolution Representation Wigner Distribution(CRWD),the Closed-form Instantaneous Cross-correlation Function Wigner Distribution(CICFWD)and the Instantaneous Cross-correlation Function Wigner Distribution(ICFWD).The results show that ICFWD has certain advantages in detecting noisy Linear Frequency-Modulated(LFM)signals under the condition of very low signal-to-noise ratio,and the detection performance is significantly higher than that of ACWD、KFWD and CRWD.And ICFWD maintains almost the same detection performance as CICFWD,while the parameter complexity is lower than CICFWD.However,the increasingly complex sound,light and electromagnetic environment of modern society puts forward higher requirements for the detection method of LFM signals,and the detection performance of ICFWD still needs to be improved.In order to further improve the detection performance of ICFWD,this paper combines ICFWD with a more flexible τ-Wigner distribution in terms of representation and parameter selection,and proposes a mathematical expression for the Instantaneous Cross-correlation Function τ-Wigner Distribution(ICFτWD).By constructing its expected output signal-tonoise ratio inequality model,the single-and two-component Linear Frequency-Modulated(LFM)signals of white noise interference are solved,and the inequality constraints on the free parameters and parameters of Linear Canonical Transform(LCT)are obtained,according to which,the high-performance detection of ICFτWD is realized.Considering that the standard definition of signal-to-noise ratio is the ratio of second-order moments rather than the ratio of first-order moments,so that the expected output signal-to-noise ratio model is insufficient to accurately depict the causal relationship between parameters and detection performance.In this paper,the output signal-to-noise ratio inequality model of ICFτWD variance is constructed,and the expected output signal-to-noise ratio inequality model is fused to obtain the ICFτWD expectation-variance output signal-to-noise ratio inequality model,which solves the single-and two-component LFM signals of white noise interference,obtains stronger parameter inequality constraints,and further improves the detection performance of ICFτWD.The output signal-to-noise ratio inequality model can overcome the difficulty that the optimization model cannot solve for two-component LFM signals,and numerical simulation experiments verify the correctness of the theoretical analysis and the advantages of the method mentioned in this paper in detecting weak LFM signals.