基于压缩感知的阵列DOA估计

发布时间：2018-07-06 13:30

本文选题：压缩感知 + 阵列DOA估计　；参考：《哈尔滨工业大学》2013年硕士论文

【摘要】：随着压缩感知理论的兴起与发展，其应用于阵列DOA（Direction of Arrival）估计时候，表现出来的少快拍（单快拍）、低信噪比条件下仍有较好性能，以及天然的解相干能力等优势，是传统DOA估计算法所不具备的，因此使用压缩感知理论进行阵列DOA估计，能克服传统方法的许多不足，具有十分重要的意义。本文首先介绍了基于压缩感知的阵列DOA估计的研究现状，及压缩感知和阵列DOA估计的基本原理和数学模型，然后从空间网格划分方式、贪婪算法的DOA估计的性能以及DOA解相干算法三个方面来进行研究。由于把空间信号当成稀疏信号，阵列流型矩阵充当了压缩感知模型中的测量矩阵的角色，这就要求阵列流型满足稀疏重构条件。文中分析了目前存在的等角度与等正弦的空间网格划分方法对阵列流型任意两列之间的正交性的影响，并提出了一种“类正弦”的划分方式。分析表明，空间参考角度在不同范围时，三种网格划分方式对正交性的影响不同，因此，不同的观测空间要采用不同的网格划分方式。随后本文选取贪婪算法中的三种典型代表：OMP（Orthogonal MatchingPursuit）、ROMP（Regularized Orthogonal Matching Pursuit）和CoSaMP（CompressiveSampling Matching Pursuit）算法进行DOA估计性能研究。首先在单快拍SMV模型下，仿真它们的均方根误差与成功分辨概率随信噪比和阵元个数的变化情况。结果表明OMP算法性能最好；ROMP算法由于采用了阈值思想，，容易产生虚假信号；CoSaMP算法不太稳定，一旦角度估计错误，往往就会产生很大的偏差。然后在多快拍MMV模型下，分析了OMP算法的性能。结果表明，贪婪算法不同于传统的子空间类算法，只有在增加很少量快拍数的时候对算法性能有所提高，快拍数过多对算法性能没有任何改善作用。最后本文选取了传统解相干算法中基于奇异值分解的ESVD-ESPRIT算法，分析其在单快拍时候的解相干性能，并与OMP算法比较。发现在低信噪比时，OMP算法性能较好，而高信噪比时ESVD-ESPRIT算法较好。因此，综合两种算法的解相干思想，将ESVD-ESPRIT算法引入OMP算法的迭代过程中，同时利用了CoSaMP算法的回溯思想，提出了一种新的解相干算法。仿真分析表明，该新算法性能优于OMP和ESVD-ESPRIT算法。
[Abstract]:With the rise and development of compression sensing theory, its application in DOA (Direction of Arrival) estimation) shows the advantages of less fast beat (single shot), better performance under low SNR, and natural decoherence ability, etc. The traditional DOA estimation algorithm does not have the traditional DOA estimation algorithm, so it is of great significance to use compressed sensing theory to estimate array DOA, which can overcome many shortcomings of traditional methods. This paper first introduces the research status of array DOA estimation based on compressed sensing, and the basic principle and mathematical model of compressed sensing and array DOA estimation. The performance of DOA estimation of greedy algorithm and DOA decoherence algorithm are studied. Because the spatial signal is regarded as a sparse signal, the array flow pattern matrix acts as the measurement matrix in the compression sensing model, which requires the array flow pattern to satisfy the sparse reconstruction condition. In this paper, the influence of the existing equal-angle and equal-sinusoidal spatial mesh generation method on the orthogonality between any two columns of the array flow pattern is analyzed, and a kind of "sinusoid" partition method is proposed. The analysis shows that the three grid methods have different effects on orthogonality when the spatial reference angle is in different range. Then, the DOA estimation performance of three typical greedy algorithms, namely: OMP (orthogonal matching pursuit) ROMP (regulated orthogonal matching pursuit) and CoSaMP (Compressive sampling pursuit) algorithm, is studied in this paper. Firstly, the RMS error and the successful resolution probability of the SMV model are simulated with SNR and the number of array elements. The results show that the OMP algorithm has the best performance. Because of the threshold thought, it is easy to generate false signals and CoSaMP algorithm is not stable. Once the angle estimation is wrong, there is often a big deviation. Then, the performance of OMP algorithm is analyzed under multi-shot MMV model. The results show that the greedy algorithm is different from the traditional subspace algorithm, only when a very small number of beats is increased, the algorithm performance is improved, and too many beats have no effect on the performance of the algorithm. Finally, the ESVD-Esprit algorithm based on singular value decomposition (SVD) is selected in the traditional decoherence algorithm to analyze the decoherence performance of the ESVD-Esprit algorithm in the case of single shot, and to compare it with the OMP algorithm. It is found that the performance of OMP algorithm is better than that of ESVD-ESPRIT algorithm with high SNR. Therefore, the ESVD-Esprit algorithm is introduced into the iterative process of OMP algorithm, and a new decoherence algorithm is proposed by using the backtracking idea of CoSaMP algorithm. Simulation results show that the proposed algorithm outperforms OMP and ESVD-ESPRIT.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：TN911.7

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