Research On DOA Estimation Methods Based On Correntropy And Cyclic Correntropy

As an important procedure in passive wireless monitoring and positioning,direction of ar-rival(DOA)estimation has always been a hot issue in the array signal processing field.Ex-isting studies are mostly based on the assumption of the Gaussian noise;however,in practical applications,due to the low-frequency atmospheric noise,the radar backscatter echo,and the discontinuities of sea waves and mountains,the impulsive noise is common in the array.On the other hand,the classical DOA estimation algorithms are based on the point source model.When there is line-of-sight propagation between the source and the observation array,and the direct wave signal strength is sufficiently large,the point source model can effectively approximate the actual communication environment.In this case,the point source as a reasonable assumption greatly simplifies the complexity of DOA estimation.However,with the rapid development of the human society,the space electromagnetic environment is becoming more and more complex,and wireless signals are often scattered,reflected,and diffracted by vehicles,buildings,etc.so that the energy of the array received signal appears within a certain range of space.Therefore,under impulsive noise environments,DOA estimation for point sources,the joint estimation of central DOA and angular spread for distributed sources,and increasing the number of estimable sources by optimizing the array structure are intensively studied.The main contributions are as follows:(1)The DOA estimation of point sources under impulsive noise environments is fully stud-ied.First,the Alpha-stable distribution is used to model the noise distribution.Based on the analysis of the advantages and disadvantages of fractional lower order moment to suppress im-pulsive noise,a new statistic,fractional lower order correntropy,is proposed by considering the correntropy as a theoretical tool.Further,combining with the multiple signal classification(MU-SIC)method,a new high-precision,high-robustness DOA estimation method is proposed under impulsive noise environments.Secondly,to reduce computational complexity,the generalized correntropy is defined,which is applied to replace the covariance matrix of the MUSIC method to suppress the impulsive noise.Combining with the Toeplitz and Unitary transformations,the generalized correntropy is transformed from the complex domain to a real-valued sparse matrix.Further,a novel DOA estimation algorithm with low computational complexity is proposed,which is suitable for the strong impulsive noise and low generalized signal-to-noise ratio envi-ronments.These two algorithms enrich the theory and application of the correntropy and realize the high-precision DOA estimation under impulsive noise environments.(2)The joint estimation of central DOA and angular spread for distributed sources in im-pulsive noise is fully studied.First,inspired by the principle of Hampel identifier detecting and suppressing outliers,and combined with the property that the correntropy can measure the local similarity of random variables,a generalized auto-correntropy operator is proposed,and some important properties are derived.Based on the local entropy theory,a new adaptive kernel size function is proposed to improve the robustness of the kernel function,which only depends on the array output signals and does not need any other prior knowledge.Combining the generalized auto-correntropy operator and the distributed source parameter estimator(DSPE)method,a new joint estimation algorithm of central DOA and angular spread for distributed sources is proposed under impulsive noise environments.Secondly,the complex cyclic correntropy is proposed due to the performance degradation of the existing cyclostationary signal processing methods in im-pulsive noise environments.The important properties of complex cyclic correntropy are also proved.The CDFB kernel function is derived based on the standard normal cumulative distribu-tion function to reduce the dependence of the complex cyclic correntropy on prior knowledge.Therefore,combining the complex cyclic correntropy and DSPE,the CCCS-DSPE algorithm is proposed,which effectively estimates the center DOA and angular spread for coherently dis-tributed sources under both impulsive noise and co-channel interference environments.(3)The problem of increasing the number of estimable sources under impulsive noise en-vironments is fully studied.First,the conjugate co-prime array is proposed,which uses the complex conjugate components of the received data of the co-prime array to increase the num-ber of estimable sources.Based on the conjugate co-prime array,a novel derivative of error function based statistic is derived for suppressing the impulsive noise.Combined with DSPE,a novel parameter estimation algorithm for incoherently distributed sources is proposed.Sec-ondly,to expand the application range of the extended co-prime array,the virtual output signals of the extended co-prime array are reconstructed.The iterative weighting factor derived from the derivative of the error function can effectively suppress the impulsive noise in the cost func-tion.Further,two joint estimation algorithms of central DOA and angular spread are proposed.Simulation results show that the proposed algorithms increase the number of estimable sources and also have distinct advantages in highly impulsive noise environments.