The New Methods Of DOA Estimation Based On Fractional Lower Order Cyclic Statistics

The signal of DOA estimation is an important research content of the array signal processing. The task of DOA estimation is to determine the spatial location of the signals that are in a region of space at the same time, and is widely used in signal processing areas about radar, sonar, seismic waves, ECG and so on. There are many DOA estimation algorithms, and in them the eigenspace algorithm represented by MUSIC and ESPRIT are the typical representative. Although under certain conditions the MUSIC and the ESPRIT algorithm can get very good results, the resolution of the traditional eigenspace algorithm is lower, and this algorithm do not have frequency selective and so on disadvantages. In view of this, the method based on DOA estimation of the cyclostationary signal has been widely attention and development.In communications, astronomy, oceans, and other signals, there is a special class of non-stationary signals and the performance of their non-stationary nature is cycle stable, which means that their statistical properties changes in one or more cycle (each cycle can not pass around). In view of this, DOA estimation method based on the cyclostationarity properties took into account the information of time-domain and spatial-domain, with many advantages that the traditional DOA estimation methods do not have: On the one hand, this algorithm can inhibit the interference and noise that are not cyclic correlation; on the other hand, is still valid when the number of array are less than the source. The DOA estimation methods based on the second-order cyclic correlation are Cyclic-MUSIC,Cyclic-ESPRIT and SC-SSF etc. In them, Cyclic-MUSIC and Cyclic-ESPRIT is applicable to the signal of narrowband; SC-SSF is applicable to the signal of broadband. However, in nature there are a lot of noises with notable pulse characteristic, they are a significant departure from the traditional Gaussian distribution. These noises usually use alpha-stable distribution model to depict stochastic signals with a remarkable impulsive characteristic. Because of the second-order statistics of the alpha-stable distributed noise doesn't exist, which result in noticeable degradation or even failure of the performance of algorithms based on the second-order statistics.Focusing on this question, this paper firstly presents a new concept referred to as the fractional lower order cyclic correlation matrix and based on it presents algorithms in two forms, which are called fractional lower order moment total least squares cyclic ESPRIT. Simulation results show that the proposed algorithms can effectually give DOA estimation under impulsive-noise conditions, and they performance is superior to the Cyclic-ESPRIT based on second order cyclic correlation. The new algorithms have potential applications.Secondly, this paper presents an algorithm of Direction of Arrival (DOA) estimation based on the fractional lower order cyclic correlation. The algorithm uses the phase shift characteristics of the fractional lower order cyclic correlation and transforms the DOA estimation problem of the wideband cyclostationary signals into an issue of the narrowband cyclostationary signals that the "centre frequency" isε. Simulation results show that the proposed algorithm can give accurate DOA estimation under both Gaussian and impulsive-noise conditions, and its performance is superior to the SC-SSF (Spectral Correlation-Signal Subspace Fitting) based on second order cyclic correlation.