Study On DOA Estimation For Nonlinear Array

Direction-of-arrive (DOA) estimation based on the sensor array plays an important role in themodern array signal processing. Most of the high-resolution DOA estimation algorithms have beendeveloped for ideal uniform linear arrays and uniform rectangular arrays. With the development of theelectronic technique, DOA estimation for the nonlinear array becomes a research focus because of themore flexibility in the applications and the better performance in certain situations.This thesis focus on the DOA estimation for the nonlinear arrays in several topics, such as thelow computational complexity algorithm, the nonuniform noise and the wideband array processing. Insummary, the main contents and contributions of this thesis are listed as follows:1、 A low computational complexity DOA estimation algorithm for sparse uniform circulararray (UCA) is presented based on the manifold separation technique (MST). By employing the MST,the proposed method can avoid the performance degradation of DOA estimation caused by thebeamspace transform (BT) and reduce the computational complexity by utilizing the propagatormethod (PM) and the polynomial rooting instead of the singular value decomposition (SVD) and thespectrum searching. Simulations show that this method offers better performance than theconventional BT based method when the elements of the UCA are few or sparse and has almost thesame performance to the similar method based on the SVD.2、 A DOA estimation algorithm for sparse UCA in presence of the nonuniform noise isdeveloped based on the stochastic maximum-likelihood method for the nonuniform noise. First of all,the beamspace likelihood function for sparse UCA in the nonuniform noise is constructed with themodified phase-mode principle. Second, based on the analysis to the beamspace likelihood function ofsparse UCA in the nonuniform noise, Burg’s inverse iteration algorithm is modified to estimate thenoise covariance matrix of the nonuniform noise on the sparse UCA. At last, by deriving the gradientand the asymptotic Hessian matrix of the likelihood function in the nonuniform noise, the angleparameters are estimated based on the MVP (Modified Variable Projection) method. The simulationresults show that compared with sparse UCA root-MUSIC and the traditional maximum-likelihoodalgorithm, the proposed method is more robust under the nonuniform noise with limitedcomputational burden increased.3、 A convex optimization based Khatri-Rao subspace wideband Direction-of-Arrive (DOA)estimation algorithm is proposed. For minimizing the distortion of the noise caused by the focusing procedure and maintaining the acceptable focusing error, the steering vectors of the virtual array areused to compute the wideband focusing matrix with the convex optimization. Then, the robustness ofthe proposed method to the nonuniform noise is enhanced by utilizing a pre-processing step.Compared with the FKR-RSS and conventional RSS method, this method shows significantadvantage in the estimation accuracy, targets resolution and capability of dealing with multiple targets.The computational complexity of the proposed method is similar to FKR-RSS. The proposed methodalso shows the robustness to the nonuniform noise.4、 Based on the manifold separation technique, a Khatri-Rao subspace wideband DOAestimation algorithm without preliminary angle estimation for nonlinear arrays is proposed. Utilizingthe steering vectors of the Khatri-Rao subspace virtual array, the proposed method compute thewideband focusing matrix regardless of DOAs with convex optimization based on the manifoldseparation technique so that the preliminary angle estimation can be avoided and the algorithm stillperforms well. On the other hand, this method can avoid expensive spectrum searching in theconventional methods to reduce the computational complexity with polynomial rooting. Simulationsshow that the proposed method performs close to the preliminary angle estimation needed Khatri-Raosubspace wideband DOA estimation algorithms with accurate preliminary angle information, andwhen the preliminary angle estimation is coarse, this method have better performance. In presence ofthe nonuniform noise, the proposed method also performs well.5、 A sparse recovery based Khatri-Rao subspace wideband DOA estimation algorithm isproposed. This method propose the sparse representation of the Khatri-Rao subspace virtual arraybased on the group sparse model and achieve the wideband DOA estimation by sparse recovery. Theproposed method has good robustness to the spectrum distribution of the signals. On the other hand,to improve the performance of the algorithm, an iteration based regularization parameter updatingmethod is proposed which can be combined with the grid refinement. Therefore, the computationalcomplexity increasing caused by the updating processing is limited. Simulations show that theproposed method performs well, whether the spectrum of the signals is flat or not. The proposedmethod can also deal with the situation of less frequency bins than number of targets and thenonuniform noise.