Research On The Theory Of Instantaneous Cross-correlation Function Type τ-Wigner Distribution And Its Radar Signal Detectio

With the development of communication technology,non-stationary signal detection has become a hot topic in recent years.Wigner Distribution(WD)is an important time-frequency representation for detecting non-stationary signals.It has a good performance in detecting the Linear Frequency-Modulated(LFM)signal which is often encountered in satellite,communication,radar and sonar system.However,WD cannot provide high enough signal representation flexibility in extremely noisy environments.Instantaneous Cross-correlation Function type of Wigner Distribution(ICFWD)has six Linear Canonical Transform free parameters,which has strong flexibility in signal representation.It has the characteristics of high real-time processing efficiency and good detection performance.However,due to the increasing complexity of sound,light and electromagnetic environments in modern society,ICFWD’s performance need to be improved.To raise the noisy LFM signal detection threshold without sacrificing the computing performance,this thesis employs the known τ-Wigner Distribution(τ-WD)in extending further the notion of ICFWD to the so-called Instantaneous Cross-correlation Function type ofτ-Wigner Distribution(ICF-τ-WD).This thesis extends some essential properties of ICFWD to ICF-τ-WD,analyzes the computational complexities of ICFWD and τ-WD,based on which we derive the computational complexity of ICF-τ-WD.The single-objective(expectation-SNR)optimization model and double-objective(expectation-SNR and variance-SNR)optimization model are established.The important problem of selecting optimal parameters for ICF-τ-WD in processing single component LFM signal with additive zero mean noise is solved,and the optimal selection strategies for ICF-τ-WD free parameters under two models are obtained respectively.Numerical simulation results show that the detection performance of the double-objective optimization model is better than that of the single-objective optimization model,and the detection performance of ICF-τ-WD is better than that of ICFWD.The proposal of ICF-τ-WD enriches the existing time-frequency distribution system,provides a new idea of time-frequency representation,and lays a theoretical foundation for the high-performance detection of weak LFM signals.