DOA Estimation Based On The Sparsity Of Fractional Lower Order Statistics

Direction of Arrival (DOA) estimation is a technology in which to judge the orientation of the signal source, is widely used in many fields. In recent years, Compressed Sensing (CS) theory has been applied to DOA estimation. DOA estimation based on compressed sensing has higher performance than conventional array signal DOA estimation method, with high accuracy and need less sampling data, and does not affect by coherent source signal. In order to suppress the influence of environmental noise to the performance of DOA estimation based on compressed sensing, there have been many improved algorithms in compressed sensing DOA estimation, but these improved algorithms are based on Gaussian noise background assumptions. If in non-Gaussian impulse noise environment, because these algorithms do not match the mathematical model of the physical environment, lead to impulse noise can not be effectively inhibited, DOA estimation performance will severely degrade. In this paper, we introduce Alpha Stable Distribution to describe the impulse noise, in which second order statistics does not exist, we use Fractional Lower Order Statistics as a mathematical tool to describe the statistical characteristics of the array receive signal, and try to combine it with compressed sensing DOA estimation algorithm. Through the study of fractional lower order correlation matrix established by array receive signal, we found the sparsity of fractional lower order correlation matrix’s column vector on direction of signal arrival, and the sparsity of fractional lower order correlation matrix’s eigenvector correspond to big eigenvalue on direction of signal arrival. Baesd on the sparsity of the column vector we propose two DOA estimation algorithm:FLOM-SCV algorithm and FLOM-MCV algorithm, as well as based on the sparsity of the eigenvector we propose another DOA estimation algorithm:FLOM-EIG algorithm. Simulation results show that these three DOA estimation algorithm’s performance is much better than the DOA estimation algorithm based on sparsity of covariance matrix under impulse noise environment, indicating that DOA estimation algorithm based on sparsity of fractional lower order statistics can better suppress impulse noise affect than traditional algorithm based on second order statistics. Finally, for solve the problem of DOA estimation based on compressed sensing that increasing angular resolution will also bring a significant increase in the amount of computation, we introduce an adaptive thinning method for redundancy dictionary, it can effectively reduce the computation, and further introduce FLOM-EIG algorithm based on dictionary thinning. The simulation show that the algorithm can provide high-performance and high-resolution DOA estimation results under impulse noise conditions.