Time Delay Estimation Of Cyclostationary Signals Under Impulsive Noise

Time delay estimation has been widely concerned by scholars as an important issue in the field of signal processing.Not only time delay estimation is widely used in military,civil,scientific and other fields,but also which research and development promotes the development of signal detection and estimation,digital signal processing,adaptive signal processing,etc.There is always a special kind of non-stationary signal in the fields of ocean,communication,astronomy,etc.Its statistical characteristics show periodic transformations with time,which is called cyclostationary signal.The time delay estimation algorithms of traditional cyclostationary signals all assume that the noise is Gaussian and many of the algorithms are based on second-order cyclic statistics.However,the noise in real life does not obey the Gaussian distribution ordinarily and exhibits pulse characteristics.The statistical analysis of these pulse characteristic noises can be described by the mathematical model of a-stable distributed noise.Since cyclostationary signal with a-stable distribution characteristics does not have finite second-order moments,the performance of the cyclostationary signal delay estimation algorithm based on second-order cyclic statistic will degrade or even fail.Firstly,for the delay estimation of cyclostationary signals in impulse noise environment,the generalized correlation entropy is applied to the cyclostationary signal,and the concept of generalized cyclic correlation entropy(GCCE)is defined.The time-delay estimation algorithm of cyclostationary signal based on GCCE is proposed.And using the idea of spectral weighting to improve the algorithm,a generalized cyclic correlation entropy spectral weighting(GCCE-SCOT)algorithm is proposed.The simulation results show that the proposed algorithm is better than the fractional low-order cyclic statistic based delay estimation algorithm.In order to improve the estimation performance of the one-cycle correlation time delay estimation algorithm in low SNR and correlated noise environment,a quadratic cyclic correlation time delay estimation algorithm is proposed.It mainly includes cyclic correlation entropy quadratic correlation(QCCE)algorithm,generalized cyclic correlation entropy quadratic correlation(QGCCE)algorithm and fractional low order cyclic correlation entropy(FLOCCE)algorithm.The simulation results show that the proposed QCCE,QGCCE and FLOCCE delay estimation algorithms are better than the fractional low-order cyclic correlation quadratic correlation(CFCC)algorithm and the performance advantage is more prominent at lower SNR.Finally,aiming at the problem that Doppler frequency shift is inevitable when there is relative motion between the source and the receiver,a variety of delay and Doppler shift joint estimation algorithms for a-stable distributed noise are studied.Firstly,the ambiguity function and the conjugate ambiguity function are combined with the nonlinear preprocessing methods which can effectively suppress the impulse noise.The inverse tangent ambiguity function and the nonlinear transformation ambiguity function are defined,and the inverse tangent conjugate ambiguity and the nonlinear transformation conjugate ambiguity function for non-circular signals is defined,and use these functions to solve the joint estimation problem of delay and Doppler shift in impulse noise environment.Secondly,the cyclic ambiguity function and the conjugated cyclic ambiguity function are combined with the nonlinear preprocessing methods and define the inverse tangent cyclic ambiguity function and the nonlinear transformation cyclic ambiguity function,moreover,define the inverse tangent conjugate cyclic ambiguity function and the nonlinear transformation conjugated cyclic ambiguity function for non-circular signals,and proposed a signal-selective delay and Doppler shift joint estimation algorithm based on these cyclic statistic.The simulation results verify that the proposed performance of the proposed method is better than the estimation algorithm based on fractional low-order statistic,and the new algorithm proposed in this paper does not need to know the prior statistical knowledge of impulse noise in advance,and has the advantage of wider application range.