DOA Estimation On Nested Array And The Analysis Of Performance

Direction of arrival estimation method of multiple incident signals is one of the key technologies in array signal processing fields.Traditional DOA estimation methods are all based on uniform array,which have some disadvantages,such as estimating less sources and low estimation precision.In order to sovle these problem,a nested array,which consists of two or more uniform array is proposed.Compared with the uniform array,the proposed array can increase the degrees of freedom and estimate more sensors than sources.Under constraint of fixed total number of sensors,the estimating accuracy has been improved.Thus the DOA estimation algorithm with nested array has received more attention.The details are described as follows:(1)A distributed nested array is proposed,which consists of two independent four level nested sub-arrays,between the two sub-arrays,there exists a base line B.According the array,three identical ULA will be obtained through high order cumulant and Khatri-Rao product operation of the received signals.A spatial smoothing unitary estimation of signal parameters via rotation invariance techniques(ESPRIT)is applied to estimate the DOA.Firstly,according to the received signal,the cumulants matrix can be acquired;Then,the cumulants matrix is vectorized and the spatial smoothing technique is used to recover the rank of the new cumulants matrix;Finally,the DOA estimation is obtained using the dual-size unitary ESPRIT algorithm.The algorithm can improve the degree of freedom efficiently.The simulation results turn out the significance of the proposed algorithm.(2)A new class of two dimensional arrays,namely,the 2qth-order two dimensional nested arrays,whose 2qth-order difference co-array is proved to contain a planar array with virtual sensors,is proposed to ensure that the co-array has the desired degrees of freedom.In order to exploit these increased degrees of freedom of the co-array,which is obtained through high order cumulant and Khatri-Rao product operation of the received signals,a new algorithm for DOA estimation is also developed,which can yet identify statistically independent non-Gaussian sources.Compared to 2qth-order cumulant based method on uniform array,the proposed array with the method not only has higher accuracy,but also estimates more sources than sensors because of that the formed virtual planar array consists of more virtual sensors in DOA estimation aspect.The validity of the proposed method is verified through several numerical examples.(3)A nested L-shaped array is proposed,whose difference co-array can give rise to a virtual two dimensional(2-D)array with O(N~q) x O(N~q) elements.This structure is obtained by two nested linear arrays,one with sensors on the x axis and the other on the y axis.In order to exploit these additional virtual elements a new algorithm for direction of arrival(DOA)estimation is also developed.The multiple level nested array structure and even-order(2qth-order)cumulate method are used to form a virtual planar array that utilizes the more degrees of freedom offered by the difference co-array.Then,azimuth and elevation angles are estimated by utilizing 2-D multiple signal classification(MUSIC)algorithms,which are based on the concept of 2-D spatial smoothing to recover the rank of the spatially smoothed matrix.Under the constraint of fixed total number of sensors,the proposed array structure is shown to have better estimation accuracy than existing alternatives,and more sources have been estimated because the formed virtual planar array consists of more virtual elements.The validity of the proposed algorithm is verified through several numerical simulations.