基于辅助阵元的非圆信号自校正算法及其性能分析

doi:10.3969/j.issn.1000-436x.2014.02.020

摘要/Abstract

摘要：

针对非圆信号空间谱测向中方位依赖幅相误差的校正问题，基于辅助阵元自校正算法(ISM, instrumental sensor method)基本原理，提出一种改进的ISM算法：NC-ISM算法。该算法通过利用最大非圆率信号的扩展数据模型，提高了信号利用率，使其估计精度较一般的ISM算法有明显提升，最大可分辨信源数也增加一倍。对该算法的理论性能进行研究，证明了其参数估计的统计一致性，并采用一阶误差分析方法推导了辅助阵元模型误差影响下参数估计的均方误差表达式，从而为工程应用提供理论支撑。仿真结果验证了理论推导的正确性，同时表明，该算法较ISM算法在辅助阵元模型误差与低信噪比下都有更强的顽健性。

关键词: 方位依赖幅相误差, 辅助阵元自校正, 非圆信号, 统计一致性, 辅助阵元模型误差

Abstract:

An improved direction-finding algorithm for noncircular sources was proposed in the presence of angularly dependent gain and phase errors, which is called NC-ISM based on the fundamental principle of ISM (instrumental sen-sor method). Through the application of the extended data model of non-circular signals with maximum rate, the pro-posed algorithm enhances the information utilization leading to advancement of estimation accuracy and twice the num-ber of sources that can be distinguished. The performance study on NC-ISM proved the statistical consistency of the pa-rameter estimation, and a theoretical derivation for the closed-form expression of the mean square error (MSE) of NC-ISM estimation was presented under the influence of modeling errors of instrumental sensors by the first-order analysis. Therefore, the analysis can provide theoretical support for practical applications. The simulation results not only verify the effectiveness of theoretical derivation, but also illustrate that NC-ISM is more robust than ISM with respect to signal-to-noise ratio as well as modeling errors.

Key words: angularly dependent gain and phase error, ISM, noncircular signal, statistical consistency, modeling error of instrumental sensor

尹洁昕,吴瑛,王鼎. 基于辅助阵元的非圆信号自校正算法及其性能分析[J]. 通信学报, 2014, 35(2): 153-165.

Jie-xin YIN,Ying WU,Ding WANG. Auto-calibration method and performance analysis for noncircular sources based on instrumental sensors[J]. Journal on Communications, 2014, 35(2): 153-165.

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参考文献 19

[1]	王永良，陈辉，彭应宁等. 空间谱估计理论与算法[M]．北京：清华大学出版社， 2005 WANG Y L , CHEN H PENG Y N et al. The Theory and Calculation of Spatial Spectrum Estimation[M]. Beijing： Tsinghua University Press， 2005
[2]	CHARGE P , WANG Y SAILLARD J . A noncircular sources direction finding method using polynomial rooting[J]. Signal Process, 2001,81(6): 1765-1770.
[3]	HARRDT M , ROMER F . Enhancements of unitary ESPRIT for noncircular sources[A]. ICASSP 2004-2[C]. Canada, 2004.101-104.
[4]	刘剑，黄知涛周一宇， . 基于扩展传播算子的非圆信号测向方法[J]. 信号处理， 2008,24(4): 556-560. LIU J , HUANG Z T , ZHOU Y Y . Extended propagator method for direction estimation of noncircular signals[J]. Signal Processing, 2008,24(4): 556-560.
[5]	CHARGE P , WANG Y D , SAILLARD J . A direction finding method under sensor gain and phase uncertainties[A]. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing[C]. Istanbul, Turkey, 2000.3045-3048.
[6]	WANG B H , WANG Y L , CHEN H . Array Calibration of angularly dependent gain and phase uncertainties with instrumental sensors[A]. IEEE International Symposium on Phased Array Systems and Technology[C]. Wuhan, China, 2003.182-186.
[7]	王布宏，王永良，陈辉等. 方位依赖阵元幅相误差校正的辅助阵元法[J]. 中国科学F辑：信息科学， 2004,34(8): 906-918. WANG B H , WANG Y L CHEN H et al. Array calibration of angularly dependent gain and phase uncertainties with carry-on instrumental sensors[J]. Science in China Series F: Information Sciences, 2004,34(8): 906-918.
[8]	LIAO B , LIAO G S . Method for array gain and phase uncertainties calibration based on ISM and ESPRIT[J]. Journal of Systems Engineering and Electronics, 2009,20(2): 223-228.
[9]	王鼎，潘苗，吴瑛 . 基于辅助阵元的方位依赖幅相误差最大似然自校正：针对确定信号模型[J]. 通信学报， 2011,32(2): 34-47. WANG D , PAN M WU Y . Maximum likelihood self-calibration for direction-dependent gain-phase errors with carry-on instrumental sensors:case of deterministic signal model[J]. Journal on Communications, 2011,32(2): 34-47.
[10]	YANG L , HO K C . Alleviating sensor position error in source location using calibration emitters at inaccurate locations[J]. IEEE Transactions on Signal Processing, 2010,58(1): 67-83.
[11]	刘凯，梁国龙，嵇建飞 . 随机阵列误差影响下的声矢量阵噪声特性和阵增益[J]. 哈尔滨工程大学学报， 2011,32(5): 624-631. LIU K , LIANG G L JI J F . Noise characteristics and array gain of an acoustic vector-sensor array influenced by random array errors[J]. Journal of Harbin Engineering University, 2011,32(5): 624-631.
[12]	侯青松，郭英，王布宏 . 共形阵列天线振动条件下稳健的DOA估计及位置误差校正[J]. 信号处理， 2010,26(11): 1756-1760. HOU Q S , GUO Y WANG B H . Robust direction finding and position errors calibration for conformal array antenna in the presence of vibration[J]. Signal Processing, 2010,26(11): 1756-1760.
[13]	刘剑， . 非圆信号波达方向估计算法研究[D]．长沙：国防科学技术大学， 2007 LIU J . DOA Estimation Algorithms for Noncircular Signals Using Sensor arrays[D]． Changsha: National University of Defense Technology, 2007.
[14]	PICINBONO B . On circularity[J]. IEEE Trans Signal Processing, 1994,24(12): 3473-3482.
[15]	赵悦，孙明磊，谢俊好 . 基于最大非圆率信号的改进SWEDE算法[J]．信号处理， 2011,27(5): 697-702. ZHAO Y , SUN M L , XIE J H . Improved SWEDE for signals with maximum noncircularity rate[D]． Signal Processing, 2011,27(5): 697-702.
[16]	刘剑，于红旗，黄知涛 . 模型误差对非圆信号测向MUSIC算法性能的影响[J]．电子学报， 2008,36(12): 105-107. LIU J , YU H Q , HUANG Z T . Performance analysis of the MUSIC algorithm for noncircular signals with modeling errors[J]． Acta Electronica Sinica, 2008,36(12): 105-107.
[17]	ABEIDA H , DELMAS J P . MUSIC-like estimation of direction of arrival for noncircular sources[J]. IEEE Transactions on Signal Processing, 2006,54(7): 2678-2690.
[18]	FERRéOL A , LARZABAL P . On the resolution probability of MUSIC in presence of modeling errors[J]. IEEE Transactions on Signal Processing, 2008,56(5): 1945-1953.
[19]	王鼎，吴瑛 . 未预期模型误差影响下秩减估计器的性能分析[J]. 通信学报， 2011,32(8): 81-90. WANG D , WU Y . Performance analysis of rank reduction estimator in the presence of unexpected modeling errors[J]. Journal on Communications, 2011,32(8): 81-90.

信噪比/dB	信号1		信号2
信噪比/dB	NC-ISM	ISM	NC-ISM	ISM
10	0.235	0.398	0.138	0.237
11	0.213	0.356	0.120	0.207
12	0.189	0.316	0.110	0.185
13	0.165	0.280	0.097	0.161
14	0.147	0.251	0.088	0.148
15	0.132	0.221	0.077	0.133
16	0.116	0.195	0.069	0.117
17	0.104	0.175	0.061	0.108
18	0.095	0.158	0.055	0.094
19	0.082	0.142	0.050	0.082
20	0.074	0.124	0.044	0.072

信噪比/dB	信号1		信号2
信噪比/dB	NC-ISM	ISM	NC-ISM	ISM
10	3.690	5.714	10.08	18.32
11	3.307	5.027	8.828	15.98
12	2.980	4.481	7.972	14.25
13	2.580	3.939	7.102	12.45
14	2.308	3.587	6.324	11.28
15	2.066	3.096	5.683	10.30
16	1.846	2.767	4.974	9.027
17	1.623	2.495	4.474	8.337
18	1.477	2.232	3.971	7.234
19	1.283	2.006	3.610	6.257
20	1.160	1.740	3.267	5.563

模型误差功率/dB	实验值		理论值
模型误差功率/dB	NC-ISM	ISM	NC-ISM	ISM
-40	0.158	0.279	0.160	0.278
-39	0.178	0.310	0.180	0.312
-38	0.206	0.351	0.202	0.350
-37	0.233	0.390	0.230	0.392
-36	0.253	0.441	0.255	0.440
-35	0.287	0.490	0.286	0.494
-34	0.308	0.552	0.310	0.554
-33	0.362	0.625	0.360	0.622
-32	0.410	0.695	0.404	0.697
-31	0.446	0.786	0.449	0.782
-30	0.506	0.872	0.509	0.878

模型误差功率/dB	实验值		理论值
模型误差功率/dB	NC-ISM	ISM	NC-ISM	ISM
-40	2.360	3.873	2.361	3.826
-39	2.645	4.300	2.650	4.293
-38	2.979	4.937	2.973	4.817
-37	3.416	5.385	3.336	5.405
-36	3.743	6.089	3.743	6.064
-35	4.207	6.768	4.199	6.804
-34	4.535	7.589	4.712	7.635
-33	5.310	8.676	5.286	8.566
-32	6.002	9.796	5.932	9.612
-31	6.665	11.22	6.655	10.78
-30	7.353	12.01	7.467	12.10