摘要
基于传感器阵列的高分辨到达角(Direction-of-Arrive, DOA)估计是现代阵列信号处理中的重要研究方向。多数的DOA估计算法均针对理想均匀线阵或均匀网格平面阵设计。随着现代电子技术的发展，非线性阵列由于其在实际应用中更加灵活，且在一定条件下系统性能更好，逐渐成为DOA估计领域的研究热点。
本文针对特定的非线性结构阵列，从快速算法、非均匀阵列噪声、宽带信号处理等几个方面，对相应的DOA估计问题进行了研究。主要研究内容和成果如下：
1、研究了基于流形分离技术的稀疏均匀圆阵快速DOA估计方法。通过引入流形分离技术，避免了波束空间变换所带来的性能损失。利用传播算子法代替奇异值分解，降低了计算量。仿真分析表明，对于阵元数目较少或阵元稀疏的均匀圆阵，该方法与传统的波束空间变换类方法相比，性能明显提高，与基于特征分解的类似方法具有基本相同的性能。
2、基于非均匀噪声下的随机性最大似然方法，研究了一种非均匀噪声稀疏均匀圆阵二维DOA估计方法。首先采用改进的相位模式方法构造非均匀噪声稀疏均匀圆阵的波束空间似然函数，并在分析非均匀噪声稀疏均匀圆阵的波束空间似然函数特点的基础上，修改了Burg的逆迭代算法以适应稀疏均匀圆阵下非均匀噪声自相关矩阵的估计，最后，经过推导非均匀噪声下似然函数的梯度与近似Hessian矩阵，实现了基于MVP(Modified Variable Projection)方法的非均匀噪声下目标二维到达角估计。与稀疏均匀圆阵Root-MUSIC以及传统的均匀噪声随机性最大似然方法相比，该方法对阵列噪声的均匀程度具有更好的鲁棒性，且计算量增加有限。
3、提出了一种基于凸优化的Khatri-Rao子空间非线性阵列宽带DOA估计方法。该方法针对虚拟阵列导向矢量构造聚焦矩阵，利用凸优化工具，在尽量减少聚焦对噪声影响的同时，保持较小的聚焦误差。同时通过引入预处理步骤，增强了算法对非均匀噪声的鲁棒性。与FKR-RSS方法以及传统的RSS方法相比，该方法在估计精度，目标分辨力、多目标处理能力以及对非均匀噪声的鲁棒性方面具有明显的优势，而且其计算量增加有限。
4、基于流形分离技术，提出了一种无需预估角的Khatri-Rao子空间非线性阵列宽带DOA估计方法。该方法将流形分离技术推广到Khatri-Rao子空间虚拟阵列，利用凸优化方法构造与到达角无关的宽带聚焦矩阵，无需预估角且估计性能良好。同时，采用Root-MUSIC算法避免传统算法中的谱峰搜索过程，降低了计算量。研究结果表明，与需要预估角的Khatri-Rao子空间宽带DOA估计方法相比，该方法无需预估角却具有类似的估计精度和目标分辨力，优于无需预估角的传统AMI方法；对于非均匀噪声的情形，该方法也具有良好的鲁棒性。
5、提出了一种基于稀疏恢复的Khatri-Rao子空间非线性阵列宽带DOA估计方法。该方法利用组稀疏模型，构造各频点Khatri-Rao子空间虚拟阵列的稀疏表示，利用稀疏恢复算法实现了对宽带信号的DOA估计。同时，给出了一种迭代方法，以不断修正稀疏恢复算法的正则化参数，提高了算法性能。而且，这种迭代过程可以与网格细化相结合，故并不会带来明显的计算量增加。研究结果表明，无论信号功率谱是否平坦，该方法均具有良好的DOA估计性能，且能够处理频率点数少于目标数的情形。对于非均匀噪声环境，该方法也具有良好的鲁棒性。
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.
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