摘要
对空间谱估计技术进行研究的主要目的是提高空间信源方位角的估计精度以及分辨力,在众多的超分辨算法中,子空间类算法由于其得天独厚的优势:明确的物理概念和良好的估计性能而得到了更多的关注和应用。其中最具代表性也是最常用的两种方法为:多重信号分类算法(MUSIC)和旋转不变子空间算法(ESPRIT)。
将子空间类算法在应用于实际中会发现存在着计算量大的缺陷,而在雷达信号处理中,对算法的实时性又有着较高的要求,虽然有着较好的估计性能,但难以进行实时处理制约了子空间类算法应用和发展。本文从并行处理的角度出发,对子空间类超分辨算法进行高效化进行。然而并行化的实现是并不是简单的将算法分割,而是要依赖于对算法本身的理解和实现步骤的划分。
本文从经典的MUSIC算法入手,分析其性能和计算复杂度,对运算量主要集中的环节——特征分解提出改进算法。该方法针对MUSIC算法的计算复数域上运行,运算量大、不易于特征分解的缺陷,选择一种实值化预处理方法,该方法不仅可以在不影响算法性能的前提下将协方差矩阵化为实对称矩阵,有利于并行化算法的选取,而且处理本身即会减少算法的计算量。之后通过对比分析选取了两种适合并行化处理的特征分解方法,并对其原理进行了分析。
在得到理论依据后,对MUSIC算法进行并行化实现:在构造协方差矩阵、特征分解和谱峰搜索三个阶段分别对其进行并行化改进,从而大大提高算法的实时性。其中在特征分解阶段,分别采用之前所分析的Jacobi方法和QR方法并对其进行并行化改进。通过仿真分析验证了并行算法的有效性,同时通过与经典的MUSIC算法的性能比较,对比分析这两种方法在估计性能及运算量方面的性能。
在得到并行的MUSIC算法之后,本文将此方法推广到ESPRIT算法中。针对ESPRIT算法与MUSIC算法主要的不同之处,即在特征分解阶段ESPRIT算法涉及到对非对称矩阵进行广义特征分解,本文在QR方法的基础上进行改进,采用了Lanczos方法和带原点位移的QR方法,提出了一种适合ESPRIT算法的并行运算方法,通过仿真实验验证了该方法在应用中的可行性,并与ESPRIT算法进行对比分析其性能及运算量。
The main goal of spatial spectral estimation is to study all the algorithms about increasing the accuracy, the angle resolution, and the operation speed in estimating the angles of the spatial signals within bandwidth.During many direction-of-arrival estimation algorithms, subspace-based method is widely used because of the clearness of the physical concept and well estimation performance. Two kinds of the most representative methods are: Multiple Signal Classification (MUSIC) method and Estimation of Signal Parameters via Rotational Invariance Technique (ESPRIT) method.
Nevertheless, it needs huge quantity of computation, which baffles its further application in Modern Radar signal processing which has a high requirement on the speed of processing. Therefore, it is very necessary to study its high-speed implement methods. This article focuses on highly effective of high resolution approach from the aspect of parallel method. The parallel algorithms for sensor array processing algorithm of high-speed realization are complicated, not only depend on the performance of the chips, but also rely on the steps of the algorithm itself.
Starting from MUSIC algorithm, this article made improvement in the stage of covariance matrix decomposition. After analyzing the structure of the array, found a simple and effective method of real value preprocessing, which changed this method from the plural field to the real field, thus reduced the computation greatly with little performance loss. Then selected two eigenvalue decompose methods which are suitable for prarllel proposing.
According to the theoretical basis, this article developed parallel architecture for MUSIC algorithm, during the three stage of MUSIC algorithm: data covariance matrix stage, covariance matrix decomposition stage, power method stage, makes the parallelization improvement separately, thus improve the original method in real time. The effectiveness of the parallel algorithm has been verified through the simulations. At the same time, the advantages and disadvantages of the parallel algorithm has discussed by compared with the MUSIC method.
After obtaining the parallel MUSIC algorithm, this article extends this approach to the ESPRIT algorithm. The parallel ESPRIT algorithm and the parallel MUSIC algorithm are similar except the stage of decomposition, where the ESPRIT algorithm involves decomposition of a generalized asymmetric matrix. This article has used the Lanczos method and the belt zero point displacement's QR method based on the QR method's foundation. The simulation results indicate the feasibility of the application of this method.
引文
1吕泽均.高分辨阵列测向技术研究.电子科技大学博士论文. 2003年4月:30~36
2陈昊.空间谱估计算法的高速实现.电子科技大学硕士学位论文. 2003年5月: 1~3
3侯煜冠.高频超视距雷达超分辨技术的研究.哈尔滨工业大学硕士学位论文. 2003年7月:3~6
4王永良,陈辉,彭应宁,万群.空间谱估计理论与算法.清华大学出版社. 2004年11月:1-2,83-98,132-138,186-191,204-210
5董照飞.基于DSP的MUSIC算法的实现.现代电子技术. 2006,23:49~52
6郭元曦,桑恩方,王继胜. MUSIC算法在分布式并行处理机上的实现研究.计算机技术与应用. 2007,02(1):112~114
7郭跃.超分辨波达方向估计技术的研究.华中科技大学博士学位论文. 2007年4月:1~5
8 J.P.Burg. Maximum Entropy Spectral Analysis. 37th Ann.Int. Soc. Explar Geophysics meeting, Oklahoma, 1967
9米波雷达超分辨技术.西安电子科技大学电子工程学院探测制导系技术报告. 2005,08:6~7
10黄可生,黄知涛,周一宇.基于信号子空间抽取的DOA估计.信号处理. 2003,19(6):576~579
11 J.A.Cadzow. Multiple Source Location-The Signal Subspace Approach. IEEE Trans. On Acoustics, Speech and Signal Processing.1990, 38(7):1110~1125
12 R.Rajagopal. DOA Estimation with Unknown Noise Field: A Matrix Decomposition Method. IEEE Proceedings F: Radar and Signal Processing. 1991, 138(5):495~501
13 R.Rajagopal. Generalized Algorithms for DOA Estimation in a Passive Sonar. IEEE Proceedings F: Radar and Signal Processing.1993, 140(5):12~20
14 R.D.Degrot. The Constrained MUSIC Problem.IEEE Trans on Signal Processing. 1993, 41(3):1445~1449
15 H.Shimotahira. On The Kernel MUSIC Algorithm.Proc ICASSP. 1995,2:909~912
16 H.Shimotahira. The Kernel MUSIC Algorithm and its Application to the Laser Microvision. IEEE Tencon-Digital Signal Processing Applications.1996:754~758
17 F.Taga, H.Shimotahira. Fast Kernel MUSIC Algorithm.IEICE Trans. 1996,E79-A(8):564~658
18 F.Taga. Smart MUSIC algorithm for DOA estimation.Electronics Letters. 30th January 1997, 33(3):197~201
19 Q.S.Ren, A.J.Willis. Fast root MUSIC algorithm. Electronics Letters. 13th March 1997, 33(6):256~265
20 Weiss, A.J.Friedlander. Direction finding for diversely polarized signals using polynomial rooting.IEEE Trans.SP, 1993, 41(5):198~206
21毛国华,王可人.一种基于DSP的快速MUSIC测向方法研究与实现.电子信息对抗技术. 2007,(22):10~13
22于红旗,黄知涛,周一宇,徐欣.一种基于逐次搜索的快速MUSIC方法.现代雷达. 2008,30(9):74~78
23吴建新,王彤,索志勇.一种快速波达方向估计算法.西安电子科技大学学报(自然科学版) . 2009,36(2):263~268
24 S.Farzaneh, A.R.Sebak. Direction of Arrival Estimation Using Adaptive Null-Forming. Proc. IEEE Radar Conf. 2009:191~195
25 A.Salameh, J.Bagby.Angle of Arrival Estimation without EVD for Coherent Sources. IEEE Transactions on Signal Processing, 2008,43(4):938~949
26 N.Tayem, M.Naraghi-Pour.Unitary Root MUSIC and Unitary MUSIC with Real-Valued Rank Revealing Triangular Factorizationt . Transactions on Acoustics, Speech, and Signal Processing. 2007,ASSP-33(4):806~811
27 A.Thakre, M.Haardt, K.Giridhar. Single Snapshot Spatial Smoothing With Improved Effective Array Aperture. IEEE Signal Processing Letters. 2009,16(6):569~578
28曾耀平.基于数据共轭重排的快速MUSIC算法.电子科技. 2008, 21(4):171~175
29余继周,陈定昌.一种DOA估计的快速子空间算法.微电子技术. 2005, (12):57~60
30唐涛,栾鹏程,吴瑛.基于波束空间SRQ快速测向算法.工程实践及应用技术. 2005,(6):19~23
31周浩,蒋兴舟,袁志勇.基于波束域MUSIC方法的高分辨方位估计.海军工程大学学报. 2007,(4):54~59
32 Chen Hui, Deng Bin, Gao Guoyi, Wang Yi . Beam-Space Algorithms Performance Analysis. IEEE Trans. Signal Processing. 2005,31:348~362
33 Wang Qiong, You Hong . Beamspace Synthetic Spatial Spectrum DOA estimator . Fourth International Conference on Natural Computation. 2008:56~60
34 K.C.Huarng, C.C.Yeh. A unitary transformation method for angle of arrival estimation. IEEE Trans.Acoust.,Speech,Signal Processing. 1991,39:975~977
35 M.D.Zoltowski, G.M.Kautz, S.D.Silverstein. Beamspace root-MUSIC. IEEE Trans. Signal Processing. 1993,41:344~364
36 P.Marius, B.Alex. Unitary Root-MUSIC with a real-valued eigendecomposition: a theoretical and experimental performance study. IEEE Trans On Signal Processing. 2000,48(5):1306~1314
37杨洁,刘聪锋.实值空间的ESPRIT算法及其实现.西安邮电学院学报.2008,25(1):8~11
38刘志刚,汪晋宽,王福利.实值循环ESPRIT算法.通信学报. 2006,27(5):45~51
39 J.P.Carde. Fast Algorithm for Root-MUSIC with Real-Valued Eigendecomposition. IEEE Transactions on Acoustics, Speech, and Signal Processing. 2003,37(7):965~983
40 M.Zhang, W.Yang. A Novel Approach of Resolution Enhancement with Application in Array Processing of Single Snapshot.IEEE Transactions on Antennas and Propagation. 1991,39(8):1125~1129
41 B.M.Radich, K.M.Buckley. Single-Snapshot DOA Estimation and Source Number Detection. IEEE Signal Processing Letters. 1997,4(8):109~111
42 R. K.Howell.d-MUSIC, A Real Time Algorithm for Estimating the DOA of Coherent Sources Using a Single Array Snapshot.IEEE Trans on ASSP. 1999,37(12):1939~1949
43 J.T.Kim, D.S.Han. Fast DOA Estimation Algorithm using Pseudo Covariance Matrix.IEEE Trans. on ASSP,2003, 34(10):1340~1342
44 J.T.Kim, S.H.Moon, D.S.Han, M.J.Cho.Fast DOA Estimation Algorithm Using Pseudocovariance Matrix.IEEE Transactions on Antennas and Propagation. April 2005,53(4):1346~1351
45 A.Moghaddamjoo, T.C.Chang. A Fast DOA Estimation Algorithm Based on Directory Data Domain Least Square Approach. IEEE Transactions on Signal Processing. 1999,40(3):692~694
46 T.Liang, H.K.Kwan. A novel approach to fast DOA estimation of multiple spatial narrowband signals. The 2002 45th Midwest Symposium on Circuits and Systems, Tulsa, Oklahoma. 2002,(2):452~460
47陈四根,杨莘元.等距线阵信号傅里叶变换研究.哈尔滨工程大学学报. 2003, 24(4):440~443.
48袁国靖,丁君,郭陈江.一种快速高分辨率的DOA估计方法——FFT-BMUSIC法.微波学报. 2005,21(1):10~13.
49曾浩,谭晓衡,杨士中,刘玲. DFT在二维DOA估计的MUSIC法中的应用.重庆大学学报. 2005,28(8):68~71.
50 A.A.Beex, M.P.Fargues. Highly Parallel Recursive/Iterative Toeplitz Eigenspace Decomposition. IEEE Transcations on Acoustics, Speech And Signal Processing. November. 1989,37(11):1765~1770
51 M.Marc, F.J.Vanpoucke, E.F.Deprettere. Parallel and Adaptive High-Resolution Direction Finding. IEEE Transactions on Signal Processing. September 1994, 42(9):2439~2448
52朱军,薛杰.多DSP并行处理技术在信号DOA估计中的应用.微机发展. 2000, (1):26~28
53刘晶,栾晓明,陆娜,简容坤.基于多DSP并行结构实现MUSIC算法的设计.自动化技术与应用. 2008,27(3):19~22
54郭跃,王宏远,陈思捷,姚华熊.阵列测向中的精确高速并行谱峰搜索算法.微电子学与计算机. 2007,24(12):50~54
55王飞,王建业,张安堂,张陆游.实对称矩阵特征值分解高速并行算法的FPGA实现.空军工程大学学报(自然科学版). 2002,l9(6):67~74
56吴仁彪.一种通用的高分辨率波达方向估计预处理新方法.电子科学学刊. 1993,15(3):305~309
57李小波,薛王伟,孙志勇.一种求解复Hermite矩阵特征值的方法.数据采集与处理. 2005,(20):105~110
58陈昊.空间谱算法的高速实现.电子科技大学硕士学位论文. 2003年4月:14~16
59马连达.高分辨波束形成及快速算法研究.哈尔滨工程大学硕士学位论文. 2008年1月:45~47
60裴智勇,吴卫国,李晓彬.求解非对称矩阵广义特征问题的Lanczos-QR方法.武汉理工大学学报. 2002,26(3):411~413
61 C.Rajakumar, C.R.Rogers. The Lanczos algorithm applied to unsymmetric generalized eigenvalue problem.Int. J Numer.1991(32):1009~1026
62贾仲孝,熊西文.非对称实矩阵特征问题的广义Lanczos方法的收敛性.大连理工大学学报. 1990,30(1):2~7
