| The traditional Wigner distribution plays an important role in the time-frequency analysis of signals.It is a two-dimensional function of signal energy on time and frequency,which has a good energy concentration in the time-frequency domain when processing Linear Frequency Modulated(LFM)signals.Linear Canonical Transforms(LCT)is a generalized integral transform with three degrees of freedom.Therefore,by introducing the LCT free parameters into the traditional Wigner distribution,the Wigner distribution in the LCT domain has stronger flexibility in processing LFM signals than the traditional Wigner distribution.Kernel Function type of Wigner Distribution(KFWD)can be obtained by replacing kernel function of Fourier transform with kernel function of LCT.The introduction of LCT free parameters allows KFWD to be more flexible than traditional Wigner distributions.However,KFWD degenerates to the traditional Wigner distribution when processing LFM signals,and thus the detection performance of KFWD is not improved compared with that of the traditional Wigner distribution.In order to improve the detection performance of KFWD without increasing the computational complexity and the complexity of parameters selection,this thesis combines KFWD with τ-Wigner distribution.The Kernel Function type ofτ-Wigner Distribution,KF-τ-WD is defined,the basic properties of KF-τ-WD are derived,and the computational complexity of KFWD and τ-Wigner distribution is analyzed.On this basis,the computational complexity of KF-τ-WD is obtained,and the Heisenberg uncertainty principle is derived.Based on this,the optimal parameter selection strategy of noisy LFM signal detection is formulated.Finally,the correctness of the theoretical analysis is verified by numerical simulation.On the basis of KFWD,the conventional instantaneous auto-correlation function is replaced by the instantaneous Wigner distribution Instantaneous Cross-correlation Function type of Wigner Distribution(ICFWD).ICFWD is widely used in noisy LFM signal detection because of its low computational complexity and good detection performance.In view of the problems of unique parameter selection and unstable detection performance of the noise-containing LFM signal detection method based on the expected output signal-to-noise ratio optimization model of ICFWD,this thesis defines the variance output signal-to-noise ratio of ICFWD,and combines the expected output signal-to-noise ratio of ICFWD to establish a dual-objective optimization model based on the expected output signal-to-noise ratio of ICFWD.The solution of the two-objective optimization model is derived for the single-component LFM signal interfered by zero-mean stationary Gaussian white noise,and the unique parameters selection strategy is obtained.Finally,the correctness of the theoretical analysis is verified by numerical simulation.In conclusion,the above methods solve the bottleneck of the key core technology of noisy LFM signal detection based on Wigner distribution in LCT domain,and provide a mathematical theoretical basis for radar target detection in complex environment. |
