共形相控阵波束形成与DOA估计算法研究
|
摘要
阵列信号处理是信号处理领域的一个重要分支，其最主要研究内容包括自适应波束形成（Adaptive Beamforming,ABF）和波达方向（Direction OfArrive，DOA）估计。ABF和DOA估计可提高阵列天线的性能，在军用与民用方面具有广泛的应用前景。阵列信号处理的基础是阵列结构。由于考虑了空气动力学或水力学，共形阵能进一步提高系统性能。均匀圆阵（Uniform Circular Array,UCA）和球阵（SphericalArray）是共形阵中比较典型的阵列结构，可提供360的方位角覆盖，并且在各个方向上可具有相同的测向性能。此外，它们还能提供俯仰角信息。因此，与均匀线阵和其他的一些平面阵相比，均匀圆阵更适于被应用在雷达、声纳和无线通信等领域，而由于球阵能提供180的俯仰角覆盖范围，其更适于应用在卫星通信领域。本文主要研究了基于均匀圆阵和球形阵列的自适应波束形成和DOA估计算法。主要工作和贡献有：
（1）均匀圆阵常规去相干波束形成算法中模式变换引起噪声功率发生改变，从而导致算法性能下降。针对该问题，提出了一种给同心双圈阵列加权的方法来消除模式变换给噪声功率带来的变化。仿真结果表明该方法大大改善了输出SINR。
（2）提出了一种高效的实值权去相干波束形成算法。该算法可以通过只使用实值权来抑制相干干扰，并且不需进行空间平滑去相干，因此大大减小了计算量。此外，它在低信噪比和小快拍下能快速收敛，并性能稳定。
（3）提出了一种均匀圆阵的相干信源DOA估计的差分算法。该方法具有很强的信源过载能力，且兼顾了相干及非相关信源的分辨。
（4）提出了一种未知互耦条件下的快速DOA估计算法，并给出了一种新的除伪方法。相对于互耦效应存在时常规的盲DOA估计算法，所提算法的计算量显著降低。
（5）提出了一种互耦效应存在时的基于稀疏均匀圆阵的混合算法。与互耦效应存在时已有的计算量较小的二维DOA估计算法不同的是，该算法不需要足够多的阵元来支撑其采用传统的波束空间变换。以阵列流形分解技术为基础，我们提出了一种改进的UCA-RARE来估计方位角，并使用Root-MUSIC算法来估计俯仰角。对于稀疏均匀圆阵来说，与UCA-RARE相比，改进的UCA-RARE能够消除一些由阵列稀疏带来的伪解。阵列流形分解引入的截断误差影响DOA估计精度，因此，我们分析了该误差对DOA估计的影响。
（6）研究了三种球形阵列的阵元分布方式，并讨论了它们的球形模式变换。同时还研究了一种球形ESPRIT算法，完善了该算法并对这三种不同分布方式下的该算法的性能进行了研究。此外还提出了另外两种球形ESPRIT算法，并研究了他们的性能。
The array signal processing，an important branch of signal processing, mainlyincludes adaptive beamforming and DOA estimation techniques. Adaptivebeamforming and DOA estimation techniques, which can improve the performance ofthe array antenna, have broad application prospects in military and civilian applications.The foundation of the array signal processing is the array configuration. Due to theconsideration of aerodynamics or hydraulics, the comformal array is able to furtherimprove the performance of the system. The uniform circular array (UCA) and thespherical array, two typical configurations of the confomal array, are able to provide360o of coverage in the azimuth plane and have uniform performance regardless ofangle of arrival. Moreover, they can provide the elevation angle information. Therefore,compared with the uniform linear array and other planar arrays, the UCA is moresuitable for applications such as radar, sonar, and wireless communications. On theotherhand, due to the180coverage in elevation plane, the spherical array is moresuitable for satellite commulication. In this dissertation, we mainly study thealgorithms of adaptive beamforming and DOA estimation for UCAs and sphericalarrays. Works and contributiones in the dissertation mainly include:
(1) The mode transformation applied to the beamforming of coherent signals willcause the noise power altering. This leads to a degraded performance of theconventional beamforming algorithms. In order to solve this problem, we propose amethod of weighing virtual array of two concentric ring arrays, which significantlyimproves the output SINR.
(2) The conventional beamforming algorithms of coherent signals usually havehigh computation complexity. An effective algorithm that uses real weights withoutphase shift is proposed. The interference is suppressed by using real weightgs and thedecorrelation of the signal sources is realized without spatial smoothing technique.Terefore the computation complexity is reduced. Moreover, this algorithm has rapidconvergency and stable performance in case of low SNR and finite snapshots.
(3) A difference algorithm of DOA estimation for coherent sources with the UCA is proposed. Compared with the conventional DOA estimation algorithms, theproposed algorithm occupies stronger overload ability of signal sources and takes boththe resolution of the coherent and noncoherent signal sources into account.
(4) A fast DOA estimation algorithm in the presence of an unknown mutualcoupling is proposed for UCAs. Meanwhile, a new method to remove the spuriousestimates is presented. Compared with the conventional DOA algorithms in thepresence of the unknown mutual coupling, the computation burden of the proposedalgorithm is greatly reduced.
(5) A novel hybrid approach for2D DOA estimation in the presence of mutualcoupling based on sparse UCA is proposed. Different from the existing2D DOAalgorithms in the presence of mutual coupling, whose computation burdern is low, theproposed algorithm does not require the number of antenna elements to be sufficient toapply the traditional beamspace transoforamtion. Based on the manifold decompositiontechnique, a modified UCA-RARE algorithm is proposed to estimate the azimuth angleand the Root-MUSIC algorithm is employed to estimate the elevation angle. For sparseUCAs, compared with the original UCA-RARE, the modified UCA-RARE is able toavoid spurious estimates which only arise from the sparseness of the array elements.It’s shown that the estimate accuracy usually depends on the truncation errorintroduced by manifold decomposition techniques. Hence, we analyze the truncationerrors for sparse UCAs and derive expressions describing the truncation errors in theDOA estimates.
(6) Three different distributions of a spherical array antenna are introduced andtheir spherical mode transformations are discussed. A modified spherical ESPRITalgorithm is also presented. The performances of this algorithm applied to the threedifferent distributions are evaluated. Moerover, other two kinds of spherical ESPRITalgorithms are proposed. The performances of the proposed spherical ESPRITalgorithms are also studied.
（1）均匀圆阵常规去相干波束形成算法中模式变换引起噪声功率发生改变，从而导致算法性能下降。针对该问题，提出了一种给同心双圈阵列加权的方法来消除模式变换给噪声功率带来的变化。仿真结果表明该方法大大改善了输出SINR。
（2）提出了一种高效的实值权去相干波束形成算法。该算法可以通过只使用实值权来抑制相干干扰，并且不需进行空间平滑去相干，因此大大减小了计算量。此外，它在低信噪比和小快拍下能快速收敛，并性能稳定。
（3）提出了一种均匀圆阵的相干信源DOA估计的差分算法。该方法具有很强的信源过载能力，且兼顾了相干及非相关信源的分辨。
（4）提出了一种未知互耦条件下的快速DOA估计算法，并给出了一种新的除伪方法。相对于互耦效应存在时常规的盲DOA估计算法，所提算法的计算量显著降低。
（5）提出了一种互耦效应存在时的基于稀疏均匀圆阵的混合算法。与互耦效应存在时已有的计算量较小的二维DOA估计算法不同的是，该算法不需要足够多的阵元来支撑其采用传统的波束空间变换。以阵列流形分解技术为基础，我们提出了一种改进的UCA-RARE来估计方位角，并使用Root-MUSIC算法来估计俯仰角。对于稀疏均匀圆阵来说，与UCA-RARE相比，改进的UCA-RARE能够消除一些由阵列稀疏带来的伪解。阵列流形分解引入的截断误差影响DOA估计精度，因此，我们分析了该误差对DOA估计的影响。
（6）研究了三种球形阵列的阵元分布方式，并讨论了它们的球形模式变换。同时还研究了一种球形ESPRIT算法，完善了该算法并对这三种不同分布方式下的该算法的性能进行了研究。此外还提出了另外两种球形ESPRIT算法，并研究了他们的性能。
The array signal processing，an important branch of signal processing, mainlyincludes adaptive beamforming and DOA estimation techniques. Adaptivebeamforming and DOA estimation techniques, which can improve the performance ofthe array antenna, have broad application prospects in military and civilian applications.The foundation of the array signal processing is the array configuration. Due to theconsideration of aerodynamics or hydraulics, the comformal array is able to furtherimprove the performance of the system. The uniform circular array (UCA) and thespherical array, two typical configurations of the confomal array, are able to provide360o of coverage in the azimuth plane and have uniform performance regardless ofangle of arrival. Moreover, they can provide the elevation angle information. Therefore,compared with the uniform linear array and other planar arrays, the UCA is moresuitable for applications such as radar, sonar, and wireless communications. On theotherhand, due to the180coverage in elevation plane, the spherical array is moresuitable for satellite commulication. In this dissertation, we mainly study thealgorithms of adaptive beamforming and DOA estimation for UCAs and sphericalarrays. Works and contributiones in the dissertation mainly include:
(1) The mode transformation applied to the beamforming of coherent signals willcause the noise power altering. This leads to a degraded performance of theconventional beamforming algorithms. In order to solve this problem, we propose amethod of weighing virtual array of two concentric ring arrays, which significantlyimproves the output SINR.
(2) The conventional beamforming algorithms of coherent signals usually havehigh computation complexity. An effective algorithm that uses real weights withoutphase shift is proposed. The interference is suppressed by using real weightgs and thedecorrelation of the signal sources is realized without spatial smoothing technique.Terefore the computation complexity is reduced. Moreover, this algorithm has rapidconvergency and stable performance in case of low SNR and finite snapshots.
(3) A difference algorithm of DOA estimation for coherent sources with the UCA is proposed. Compared with the conventional DOA estimation algorithms, theproposed algorithm occupies stronger overload ability of signal sources and takes boththe resolution of the coherent and noncoherent signal sources into account.
(4) A fast DOA estimation algorithm in the presence of an unknown mutualcoupling is proposed for UCAs. Meanwhile, a new method to remove the spuriousestimates is presented. Compared with the conventional DOA algorithms in thepresence of the unknown mutual coupling, the computation burden of the proposedalgorithm is greatly reduced.
(5) A novel hybrid approach for2D DOA estimation in the presence of mutualcoupling based on sparse UCA is proposed. Different from the existing2D DOAalgorithms in the presence of mutual coupling, whose computation burdern is low, theproposed algorithm does not require the number of antenna elements to be sufficient toapply the traditional beamspace transoforamtion. Based on the manifold decompositiontechnique, a modified UCA-RARE algorithm is proposed to estimate the azimuth angleand the Root-MUSIC algorithm is employed to estimate the elevation angle. For sparseUCAs, compared with the original UCA-RARE, the modified UCA-RARE is able toavoid spurious estimates which only arise from the sparseness of the array elements.It’s shown that the estimate accuracy usually depends on the truncation errorintroduced by manifold decomposition techniques. Hence, we analyze the truncationerrors for sparse UCAs and derive expressions describing the truncation errors in theDOA estimates.
(6) Three different distributions of a spherical array antenna are introduced andtheir spherical mode transformations are discussed. A modified spherical ESPRITalgorithm is also presented. The performances of this algorithm applied to the threedifferent distributions are evaluated. Moerover, other two kinds of spherical ESPRITalgorithms are proposed. The performances of the proposed spherical ESPRITalgorithms are also studied.
引文
[1] W.Wirth. Radar techniques using array antennas. NewYork: IET,2001
[2] S.Haykin. Adaptive radar signal processing. New York: John Wiley&Sons,2007
[3] M.L Skolnik. Introduction to Radar Systems. NewYork:McGraw-Hill,1980
[4] E. Brookner. Phased-array radar. Scientific American,1985,252:94-102
[5] W. C. Knight, R. Pridham, and S. M. Kay. Digital signal processing for sonar. Proc. IEEE,1981,69:1451-1506
[6] W.S.Burdic.Underwater acoustic system analysis and edition. New Jersey: Prentice Hall,1991
[7] F.B.Gross. Smart antenna for wireless communications. Newyork:McGraw-Hall,2005
[8] T.S.Rappaport. Smart Antennas. Newyork:IEEE Press,1998
[9] L.C.Codara. Application of antenna arrays to mobile communications, PartⅠ: Performanceimprovement, feasibility, and system considerations. Proc.IEEE,1997,85(7):1031-1060
[10] L.C.Codara. Application of antenna arrays to mobile communications, Part Ⅱ: Beamformingand direction-of-arrival considerations. Proc.IEEE,1997,85(8):1195-1245
[11] J. L. Yen. Array Signal Processing. S. Haykin, Ed. Englewood Cliffs, NJ: Prentice Hall,1985
[12] A. C. Readhead, Radio astronomy by very-long-baseline interferometry. Scientific American,1982,246:52-61
[13] T.Yamazaki, B.W.van Dijk and H.Spekreijse. The accuracy of localizing equivalent dipoles andthe spatio-temporal correlations of background EEG. IEEE Trans.Biomed.Eng.1998,45(9):1114-1121
[14] A. Macovski. Mdeical Imaging. Englewood Cliffs, NJ: Prentice Hall,1983
[15] W. K. Pratt. Digital Image Processing. New York: Wiley and Sons,1978
[16] A. C. Kak. Array Signal Processing. S. Haykin, Ed. Englewood Cliffs, NJ: PrenticeHall,1985
[17] H. Krim, M.Viberg. Two Decades of Array Signal Processing Research. IEEE Signal ProcessingMagazine,1996:67-94
[18]张光义．相控阵雷达系统．北京：国防工业出版社,1994,59-71
[19] D. E. N. Davies. A Transformation between The Phasing Techniques Required for Linear andCircular Aerial Arrays. IEE Proc. F,1965,112(11):2041-2045
[20] Erik De Witte. Design and Development of Spherical Array:[The dissertation for the degree ofDoctor of Philosophy]. London: University College London,2007
[21] B. Rafaely. Analysis and design of spherical microphone arrays. IEEE Transactions on Speechand Audio processing,2005,13(1):29-191
[22] L. Josefsson, P. Persson. Conformal Array Antenna Theory and Design. New York: John Wiley&Sons,2006
[23]龚耀寰.自适应滤波—时域自适应滤波和智能天线.第2版.北京：电子工业出版社,2003
[24] Reed I S, mallet J D, Brennan L E. Rapid convergence rate in adaptive arrays. IEEE Trans.1974,AEs-10:853-863
[25] R. Monzingo, T. Miller. Introduction to adaptive arrays. New York: Wiley and Sons,1980
[26] S. M. Kay, S. L. Marple. Spectrum analysis-a modern perspective. Proc. of the IEEE,1981,11
[27] J. P. Brug. Maximum entropy spectral analysis. Proc. of the37th meeting of the Annual Int.SEG meeting, Oklahoma City, OK,1967
[28] J. Capon. High-resolution frequency-wavenumber spectrum analysis. Proc. of IEEE,1969,57(8):1408-1418
[29] R. O. Schmidt. Multiple emitter location and signal parameter estimation. IEEE Trans. on AP,1986,34(3):276-280
[30] B.D.Rao, K.V. S. Hari. Performance Analysis of Root-MUSIC. IEEE Trans. On ASSP,1989,37(12):1939-1949
[31] R. Roy, T. Kailath. ESPRIT-a subspace rotation approach to estimation of parameters of cissoidsin noise. IEEE Trans. on ASSP,1986,34(10):1340-1342
[32] R. Roy, T. Kailath. ESPRIT-estimation of signal parameters via rotational invariance techniques.IEEE Trans. on ASSP,1989,37(7):984-995
[33] A. J. Weiss, M. Gacish. Direction finding using ESPRIT with interpolated arrays. IEEE Trans.on SP,1991,39(6):1473-1478
[34] P. Stoica, A. Nehorai. MUSIC, Maximum Likelihood, and Cramer-Rao bound. In Proc.ICASSP,1988:2296-2299
[35] J.A.Cadzow. A High Resolution Direction-of-arrival Algorithm for Narrow-band Coherent andIncoherent sources. IEEE Trans.on ASSP,1988,36(7):965-979
[36] H. Chireix. Antennes`a rayonnement z′enithal r′eduit. L’Onde Electrique,1936,15(26):440-456
[37] J. R. Wait. Electromagnetic Radiation from Cylindrical Structures. Pergamon Press, London,1959
[38] A. Hessel. Mutual Coupling Effects in Circular Arrays on Cylindrical Surfaces—ApertureDesign Implications and Analysis. in Proceedings of Phased Array Symposium, PolytechnicInstitute of Brooklyn,1970
[39] P. H. Pathak, W. D. Burnside, R. J. Marhefka. A Uniform GTD Analysis of the Diffraction ofElectromagnetic Waves by a Smooth Convex Surface. IEEE Transactions on Antennas andPropagation,1980,28(5):631-642
[40] L. N. Shestag. A Cylindrical Array for the TACAN System. IEEE Transactions on Antennas andPropagation,1974,22(1):17-25
[41] A. D. Munger, G. Vaughn, J. H. Provencher et al. Conical Array Studies. IEEE Transactions onAntennas and Propagation,1974,22(1):35-43
[42] P. M. Liebman, L. Schwartzman, and Hylas A. E.. Dome Radar—A New Phased Array System.in Proceedings of IEEE International Radar Conference, Washington, D.C.,1975:349-353
[43] M. Kanno, T. Hashimura, T. Katada, et al.. Digital Beam Forming for Conformal Active ArrayAntenna. in IEEE International Symposium on Phased Array Systems and Technology,1996:37-40
[44] H. Steyskal. Pattern Synthesis for a Conformal Wing Array. in IEEE Aerospace ConferenceProceedings,2002,2:819-824
[45] E. Vourch, C. Caille, M. J. Martin, et al. Conformal Array Antenna for LEO ObservationPlatforms. in IEEE AP-S International Symposium Digest,1998:20-23
[46] G. Caille, E. Vourch, M. J. Martin, et al..Conformal Array Antenna for Observation Platforms inLow Earth Orbit. IEEE Antennas and Propagation Magazine,2002,44(3):103-104
[47]黄茜.共形相控阵中的数字波束形成技术研究:[硕士学位论文].成都:电子科技大学.2006
[48] T. J. Shan, T Kailath. Adaptive Beamforming for Coherent Signals and Interference. IEEE Trans.Acoust.,Speech Signal Process.1985,133(3):527-536
[49] S. U. Pillai, B. H. Kwon. Forward-backward Spatial Smoothing Techniques for Coherent SignalIdentification. IEEE Trans. Acoust. Speech Signal Process,1989,37(1):8-15
[50] M. Wax, J. Sheinvald. Direction Finding of Coherent Signals via Spatial Smoothing forUniform Circular Arrays. IEEE Trans. Antennas Propagat.,1994,42(5):613-620
[51] K. Maheswara, V. U. Reddy. Analysis of Spatial Smoothing with Uniform Circular Arrays.IEEE Trans. Signal Processing,1999,47(6):1726-1730
[52] B. K. Lau, Y. H. Leung. Optimum Beaformers for Uniform Circular Arrays in a CorrelatedSignal Environment. Acoustics, Speech, and Signal Processing,2000:3093-3096
[53] B.K. Lau, Y.H. Leung, Yanqun Liu et al. Transformations for Nonideal Uniform Circular ArraysOperating in Correlated Signal Environments. IEEE Trans. Signal Processing,2006,54(1):34-48
[54] C. P. Mathews, M. D. Zoltowski. Eigenstructure techniques for2-D angle estimation withuniform circular arrays. IEEE Trans. Signal Processing,1994,42(9):2395-2407
[55] R. Goossens, H. Rogier, S. Werbrouck. UCA Root-MUSIC with sparse uniform circular arrays.IEEE Trans. Signal Process,2008,56:4095-4099
[56]邓维波,林力,袁楼.一种等间距圆形阵列的超方向性综合方法.哈尔滨工业大学报,2001,33(6):838-841
[57]丁杰伟,傅丰林,阵健.弧形智能天线阵列结构.信号处理，2002,18(3):271-274
[58] R. Vescovo. Constrained and Unconstrained Synthesis of Array factor for Circular arrays.IEEE Trans. Antennas Propagation,1995,43(12):1405-1410
[59] R.Vescovo. Pattern Synthesis with Null Constraints for Circular Arrays of Equally SpacedIsotropic Elements. IEE Proc-Microw Antennas Propag,1996,143(2):103-106
[60] R.Vescovo. Pattern synthesis for arc arrays. Antennas and Propagation Society InternationalSymposium. IEEE,1997,4:2256-2259
[61] F. Ares, S.R.Rengarajan, J.A.F.Lence et al. Synthesis of Antenna Patterns of Circular Arc Arrays.Electronics Letters,1996:1845-1846
[62] P. N. Fletcher, P. Danwood. Beamforming for Circular and Semicircular Array Antennas forLow-cost Wireless LAN Data Communications Systems. IEE Proc-Microw AntennasPropagation.1998,145(2):153-157
[63] K. L. Du. Pattern Analysis of Uniform Circular Array. IEEE Transactions on Antennas andPropagation.2004,52(4):1125-1129
[64] Chan, Pun. On the design of digital broadband beamformer for uniform circular array withfrequency invariant characteristics. Antennas and Propagation Society Symposium,2004. IEEE.2004,3:2796-2799
[65] Griffiths, Cowan, Eiges, Rafik. High-resolution beamforming techniques for circular sonararrays. Oceans Engineering for Today’s Technology and Tomorrow’s Preservation Proceedings.1994:13-16
[66]刘先省，张连堂，周林.给定方向图的圆形阵列综合方法.电子学报.2005,33(2):245-248
[67] H. Steyskal. Circular array with frequency-invariant pattern. in Dig.IEEE Int. Symp. AntennasPropagation,1989,3:1477-1480
[68] M. R. Jones, H. D. Griffiths. Broadband pattern synthesis from a circular array antennas andpropagation. in Proc. Int. Conf. Antennas and Propagation (ICAP)1989,1989,1:55-59
[69] S. C. Chan, K. Carson, S. Pun. On the design of digital broadband beamformer for uniformcircular array with frequency invariant characteristics. in IEEE ISCAS2002, Arizona,USA,2002,1:693-696
[70] Y. Yang, C. Sun, C. Wan. Theoretical and experimental studies on broadband constantbeamwidth beamforming for circular arrays. in Proc. IEEE OCEANS2003,2003,3:1467-1653
[71] Yunhong Li, K.C. Ho, Chiman Kwan. Beampattern Synthesis for Concentric Circular RingArray using MMSE Design. ISCAS,2004:329-332
[72]Yunhong Li. Broadband Beamforming and Direction Finding using Concentric Ring Array.[Thedissertation for the degree of Doctor of Philosophy]. University of Missouri-Columbia.2005.
[73] S. C. Chan., H. H. Chen. Uniform Concentric Circular Arrays With Frequency-InvariantCharacteristics—Theory, Design, Adaptive Beamforming and DOA Estimation. IEEE Trans.Signal Process,2007,55(1):165-177
[74] M. Pesaventoand, J. F. B hme. Direction of arrival estimation in uniform circular arrayscomposed of directional elements. in Proc. Sensor Array and Multichannel Signal ProcessingWorkshop, Aug.2002:503-507
[75] R. Goossens, H. Rogier. A hybrid UCA-RARE/Root-MUSIC approach for2-D direction ofarrival estimation in uniform circular arrays in the presence of mutual coupling. IEEE Trans.Antennas Propag..2007,43:841-849
[76] W. Buhong, H. Hontat, L. Mookseng. Decoupled2D direction of arrival estination usingcompact uniform circular arrays in the presence of elevation-dependent mutual coupling. IEEETrans. Antennas Propag.,2010,58(3):747-755
[77] B. Fridelander. Direction Finding using Spatial Smoothing with Interpolated Arrays. IEEETrans. On Aerospace and Electronic Systems,1992,28(2):574-587
[78] C.QI, Y. Wang, Y. Zhang, et al. DOA estimation and self-calibration algorithm for uniformcircular array. Electronics Letters.2005,41(20):1092-1094
[79] Min Lin, Luxi Yang. Blind calibration and DOA estimation with uniform circular arrays in thepresence of mutual coupling. IEEE Antennas and wireless propagation Letters,2006,5:315-318
[80] J. R. DRISCOLL, D. M. HEALY. Computing Fourier transforms andconvolutions on the2-sphere. Adv. Appl. Math.,1994,15:202-250
[81] G. Arfken, H. J. Weber. Mathematical Methods for Physicists. San Diego, CA: Academic,2001
[82] R.H. HARDIN, N.J. SLOANE. McLaren’s improved snub cube and other new spherical designsin three dimensions. Discrete Comput. Geom,1995,15:429-441
[83] P. LEOPARDI. A Partition of the unit sphere into regions of equal area and small diameter.Electronic Transactions on Numerical Analysis,2006,25:309-327
[84] E. A. RAKHMANOV, E. B. SAFF, Y. M. ZHOU. Minimal discrete energy on the sphere.Mathmatical Research Letters,1994,1:647-662
[85] M. Huang, S. Tan. Spheroidal phase mode processing for antenna arrays. in IEEE Internationalworkshop on Antenna Technology: Small Antennas and Novel Metamaterials,2005
[86] E. DE WITTE, H. GRIFFITH, P. BRENNAN. Phase mode processing for spherical arrays.Electron. Lett.,2003,39:1430-1431
[87] M. Huang, S. Tan. Spherical antenna arrays for phase mode processing. in Proc. IEEEInternational Symposium on Micrwave, Antenna, Propagation and EMC Technologies forWireless Communications,2005
[88] M. Huang and S. Tan. An improved spherical antenna array for wideband phase modeprocessing. Progress In Electromagnetics Research,2006,66:27-40
[89] B. RAFAELY. Spatial Aliasing in Spherical Microphone Arrays. IEEE Trans. Signal Process.,2007,55:1003-1010
[90] R. GOOSSENS, H. ROGIR. Closed-form2D angle estimation with a spherical array viaspherical phase mode excitation and ESPRIT. IEEE International Conference on Acoustics,Speech and Signal Processing2008,2008:2321-2324
[91] R. GOOSSENS, H. ROGIR. Unitary spherical ESPRIT:2-D angle estimation with viasphereical arrays for scalar fields. IET Signal Process.,2008,3:221-231
[92] R. GOOSSENS, I. Bogaert, H. ROGIR. Phase-mode processing for spherical antenna arrayswith a finite number of antenna elements and including mutual coupling. IEEE Trans. AntennasPropag.,2009,57(12):3783-3790
[93] Panayiotis Ioannides, Constantine A. Balanis. Wideband beamforming using circular arrays.IEEE Antennas and Propagation Society, AP-S International Symposium,2004,3:2627-2630
[94]何子述，夏威等.现代数字信号处理及其应用.北京:清华大学出版社，2009
[95] Simon Haykin. Adaptive filter theory. Third Edition. NJ: Prencice-Hall,1996
[96]王永良，陈辉，彭应宇等.空间谱估计理论与算法.北京:清华大学出版社，2004
[97] Xie Julan, He Zishu. Beamforming of coherent signals for weighed two concentric ring arrays.Intelligent Signal Processing and Communication Systems,2007:850-853
[98] O L. Frost. An Algorithm for Linearly Constrained Adaptive Processing. Proc IEEE,1972,60(8):926-935
[99]谢菊兰,何子述,夏威等.一种高效的实值权均匀圆阵去相干波束形成算法.系统工程与电子技术.2008,30(12):9-11
[100] Y.-H. Choi. Simple Adaptive Beamforming with Only Real Weights Based on Covariancedifferencing. Electronics Letters,2007,43(10):552-553
[101] E. W. Weisstein. Jacobi-anger expansion. Wolfram MathWorld [Online]. Available: http//www.mathworld. wolfram.com/Jacobi–Anger Expansion. Html
[102] F. Belloni, A. Richter, V. Koivunen,. Beamspace transform for UCA: Error analysis and biasreduction. IEEE Trans. Signal Process.,2006,54(8):3078-3089
[103] Elio D. Di Claudio. Asymptotically Perfect Wideband Focusing of Multiring Circular Arrays.IEEE Trans. Signal Process,2005,53(10):3661-3673
[104]张贤达.矩阵分析与应用.北京:清华大学出版社,2004,61-64
[105]高世伟,保铮.利用数据矩阵分解实现对空间相关信号源的超分辨处理.通信学报,1988,9(1):4-13
[106]谢菊兰,李会勇,何子述.均匀圆阵相干信源DOA估计的差分算法.电子科技大学学报.已录用
[107] Julan Xie, Zishu He, Huiyong Li. A Fast DOA Estimation Algorithm for Uniform CircularArrays in the Presence of Unknown Mutual Coupling. Progress In Electromagnetics ResearchJournals C.2011,21:257-271
[108] S. Marcos, A. Marsal, M. Benidir. Propagator method for source bearing estimation. SignalProcessing,1995,42(2):121-138
[109] S. Marcos, M. Benidir. On a high resolution array processing method non-based on theeigenanlysis approach. Acoustics, Speech, and Signal Processing,1990InternationalConference on,1990,5:2955-2958
[110] AKKAR Salem, GHARSALLAH Ali, HARABI Ferid. Concentric circular array for DOAsestimation of coherent sources with ESPRIT algorithm. Design and Technology of IntegratedSystems in Nanoscale Era (DTIS),20105th International Conference on,2010:1-6
[111] ZHAO Hui, WANG Hongjin. MODE-SUMWE algorithm for estimating DOA of coherentsignals on uniform circular array. Networks Security Wireless Communications and TrustedComputing (NSWCTC),2010,2:318-320
[112] K. M. REDDY, V. U. REDDY. Analysis of interpolated arrays with spatial smoothing. Signalprocessing,1996,54(4):267-272
[113]穆世强,陈天麒.圆阵中相干信号的高分辨阵列测向技术.电子科技大学学报,1993,22(4):350-355
[114] XU Dihua, CHEN Jianwen. A novel DOA estimation for uniform circular arrays in correlatedenvironment without interpolation. ISPACS2006,2006:650-652
[115]韩芳明,张守宏.用改进的MUSIC算法实现相干多径信号分离.系统电子与工程技术,2004,26(6):721-713
[116]高书彦,陈辉,王永良等.基于均匀圆阵的模式空间矩阵重构算法.电子与信息学报，2007,29(12):2832-2835
[117] KAREEM Al Jabr, HYUCK M Kwon, NIZAR Tayem. Modified UCA-ESPRIT for estimatingDOA of coherent signals using one snapshot.Vehicular Technology Conference,2008. VTCSpring2008. IEEE,2008:290-293
[118]齐崇英,王永良,张永顺等.色噪声背景下相干信源DOA的空间差分平滑算法.电子学报,2005,33(7):1315-1318
[119] Deyuan Gao, Buhong Wang, Ying Guo. Comments on “Blind Calibration and DOA EstimationWith Uniform Circular Arrays in the Presence of Mutual coupling”. IEEE Antennas andwireless propagation Letters,2006,5:566-569
[120] Min Lin, Luxi Yang. Reply to the comments on “Blind Calibration and DOA Estimation WithUniform Circular Arrays in the Presence of Mutual coupling”. IEEE Antennas and wirelesspropagation Letters,2006,5:568-569
[121] B.Friedlander, A.J.Weiss. Direction finding in the presence of mutual coupling. IEEETrans.Antennas Propag.,1991,39:273-284
[122] Helmut Lütkepohl. Handbook of Matrices. New York:Wiley,1996
[123] R. Goossens, H. Rogier.2-D direction of arrival estimation combining UCA-RARE andMUSIC for uniform circular arrays subject to mutual coupling. in Proc. Int. Conf. onElectromagnetics in Advanced Applications,2005:791-794
[124] T. T. Zhang, Y. L. Lu, H. T. Hui. Compensation for the mutual coupling effect in uniformcircular arrays for2D DOA estimations employing the maximum likelihood technique. IEEETrans. Aerosp. Electron. Sys.,2008,44:1215-1221
[125] H.T.Hui. Improved compensation for the mutual coupling effect in a dipole array for directionfinding. IEEE Trans.Antennas Propag.,2003,51(9):2498-2503
[126] Julan Xie, Zishu He, Huiyong Li et al.2D DOA Estimation with Sparse Uniform CircularArrays in the Presence of Mutual Coupling. EURASIP Journal on Advances in SignalProcessing.2011, doi:10.1186/1687-6180-2011-127
[127] M. A. Doron, E. Doron. Wavefield modeling and array processing—Part I: spatial sampling.IEEE Trans. Signal Processing,1994,42(10):2549-2559
[128] M. A. Doron, E. Doron. Wavefield modeling and array processing—Part II: Algorithms. IEEETrans. Signal Processing,1994,42(10):2560-2570
[129] M. A. Doron, E. Doron. Wavefield modeling and array processing—Part III: Resolutioncapacity. IEEE Trans. Signal Processing,1994,42(10):2571-2580
[130]C. Mario, R. Andreas and K. Visa.Unified array manifold decomposition based on sphericalharmonics and2-D Fourier basis. IEEE Trans. Signal Processing,2010,58(9):4634-4645
[131] F. Belloni, A. Richter, and V. Koivunen. Performance of root-MUSIC algorithm usingreal-world arrays.14th Eur. Signal Processing Conf.(EUSIPCO), Florence, Italy,2006:4-8
[132] F. Belloni, A. Richter, V. Koivunen. Extension of root-MUSIC to non-ULA arrayconfigurations. presented at the IEEE Int. Conf.Acoustics, Speech, Signal Processing (ICASSP),France,2006:14-19
[133] F. Belloni, A. Richter, V. Koivunen. DoA estimation via manifold separation for arbitrary arraystructures. IEEE Trans. Signal Process,2007,55(10):4800-4810
[134] Gupta I. J, Ksienski A. A. Effect of mutual coupling on the performance of adaptive arrays.IEEE Trans Antennas Propagat,1983,31(5):785-791
[135] T. Rahim and D.E.N.Davies. Effect of directional elements on the directional response ofcircular antenna arrays. Microwaves, Optics and Antennas, IEE Proceedings H,1982,129(1):18-22
[136] A. L. Swindlehurst, T. Kailath. A performance analysis of subspace-based methods in thepresence of model errors—I: The MUSIC algorithm. IEEE Trans. Signal Process.,1992,40(7):1758-1774
[137] A. L. Swindlehurst, T. Kailath. A performance analysis of subspace-based methods in thepresence of model errors—II: Multidimensional algorithm. IEEE Trans. Signal Process.,1993,41(9):2882-2890
[138] H. TEUTSCH. Modal array signal processing: principles and applications of acousticwavefield decomposition. Springer,2007
[139] J. MEYER, G. ELKO. Handing spatiall aliasing in spherical array application. Hands-FreeSpeech Commum. Microphone Arrays,2008:8-15
[140] L. MARANTIS, E. DE WITTE, P. BRENNAN. Comparison of various spherical antennaarray element distributions. Antennas and Propagation,2009. EuCAP2009.3rd EuropeanConference on,2009:2980–2984
[141] Julan Xie, L. Marantis, P. V. Brennan. Spherical ESPRIT-Based2-D Direction Finding withDifferent Distributions of a Spherical Array Antenna. Antennas&Propagation Conference,2009. LAPC2009. Loughborough.2009:661-664
[142] W. FREEDEN. On integral formulas of the (unit) sphere and their application to numericalcomputation of integrals. Computing,1980,25:205-208
[143] C.R. Rao, H. Toutenburg, A. Fieger, etc. Linear Models: Least Squares and Alternatives.Springer,1999
[2] S.Haykin. Adaptive radar signal processing. New York: John Wiley&Sons,2007
[3] M.L Skolnik. Introduction to Radar Systems. NewYork:McGraw-Hill,1980
[4] E. Brookner. Phased-array radar. Scientific American,1985,252:94-102
[5] W. C. Knight, R. Pridham, and S. M. Kay. Digital signal processing for sonar. Proc. IEEE,1981,69:1451-1506
[6] W.S.Burdic.Underwater acoustic system analysis and edition. New Jersey: Prentice Hall,1991
[7] F.B.Gross. Smart antenna for wireless communications. Newyork:McGraw-Hall,2005
[8] T.S.Rappaport. Smart Antennas. Newyork:IEEE Press,1998
[9] L.C.Codara. Application of antenna arrays to mobile communications, PartⅠ: Performanceimprovement, feasibility, and system considerations. Proc.IEEE,1997,85(7):1031-1060
[10] L.C.Codara. Application of antenna arrays to mobile communications, Part Ⅱ: Beamformingand direction-of-arrival considerations. Proc.IEEE,1997,85(8):1195-1245
[11] J. L. Yen. Array Signal Processing. S. Haykin, Ed. Englewood Cliffs, NJ: Prentice Hall,1985
[12] A. C. Readhead, Radio astronomy by very-long-baseline interferometry. Scientific American,1982,246:52-61
[13] T.Yamazaki, B.W.van Dijk and H.Spekreijse. The accuracy of localizing equivalent dipoles andthe spatio-temporal correlations of background EEG. IEEE Trans.Biomed.Eng.1998,45(9):1114-1121
[14] A. Macovski. Mdeical Imaging. Englewood Cliffs, NJ: Prentice Hall,1983
[15] W. K. Pratt. Digital Image Processing. New York: Wiley and Sons,1978
[16] A. C. Kak. Array Signal Processing. S. Haykin, Ed. Englewood Cliffs, NJ: PrenticeHall,1985
[17] H. Krim, M.Viberg. Two Decades of Array Signal Processing Research. IEEE Signal ProcessingMagazine,1996:67-94
[18]张光义．相控阵雷达系统．北京：国防工业出版社,1994,59-71
[19] D. E. N. Davies. A Transformation between The Phasing Techniques Required for Linear andCircular Aerial Arrays. IEE Proc. F,1965,112(11):2041-2045
[20] Erik De Witte. Design and Development of Spherical Array:[The dissertation for the degree ofDoctor of Philosophy]. London: University College London,2007
[21] B. Rafaely. Analysis and design of spherical microphone arrays. IEEE Transactions on Speechand Audio processing,2005,13(1):29-191
[22] L. Josefsson, P. Persson. Conformal Array Antenna Theory and Design. New York: John Wiley&Sons,2006
[23]龚耀寰.自适应滤波—时域自适应滤波和智能天线.第2版.北京：电子工业出版社,2003
[24] Reed I S, mallet J D, Brennan L E. Rapid convergence rate in adaptive arrays. IEEE Trans.1974,AEs-10:853-863
[25] R. Monzingo, T. Miller. Introduction to adaptive arrays. New York: Wiley and Sons,1980
[26] S. M. Kay, S. L. Marple. Spectrum analysis-a modern perspective. Proc. of the IEEE,1981,11
[27] J. P. Brug. Maximum entropy spectral analysis. Proc. of the37th meeting of the Annual Int.SEG meeting, Oklahoma City, OK,1967
[28] J. Capon. High-resolution frequency-wavenumber spectrum analysis. Proc. of IEEE,1969,57(8):1408-1418
[29] R. O. Schmidt. Multiple emitter location and signal parameter estimation. IEEE Trans. on AP,1986,34(3):276-280
[30] B.D.Rao, K.V. S. Hari. Performance Analysis of Root-MUSIC. IEEE Trans. On ASSP,1989,37(12):1939-1949
[31] R. Roy, T. Kailath. ESPRIT-a subspace rotation approach to estimation of parameters of cissoidsin noise. IEEE Trans. on ASSP,1986,34(10):1340-1342
[32] R. Roy, T. Kailath. ESPRIT-estimation of signal parameters via rotational invariance techniques.IEEE Trans. on ASSP,1989,37(7):984-995
[33] A. J. Weiss, M. Gacish. Direction finding using ESPRIT with interpolated arrays. IEEE Trans.on SP,1991,39(6):1473-1478
[34] P. Stoica, A. Nehorai. MUSIC, Maximum Likelihood, and Cramer-Rao bound. In Proc.ICASSP,1988:2296-2299
[35] J.A.Cadzow. A High Resolution Direction-of-arrival Algorithm for Narrow-band Coherent andIncoherent sources. IEEE Trans.on ASSP,1988,36(7):965-979
[36] H. Chireix. Antennes`a rayonnement z′enithal r′eduit. L’Onde Electrique,1936,15(26):440-456
[37] J. R. Wait. Electromagnetic Radiation from Cylindrical Structures. Pergamon Press, London,1959
[38] A. Hessel. Mutual Coupling Effects in Circular Arrays on Cylindrical Surfaces—ApertureDesign Implications and Analysis. in Proceedings of Phased Array Symposium, PolytechnicInstitute of Brooklyn,1970
[39] P. H. Pathak, W. D. Burnside, R. J. Marhefka. A Uniform GTD Analysis of the Diffraction ofElectromagnetic Waves by a Smooth Convex Surface. IEEE Transactions on Antennas andPropagation,1980,28(5):631-642
[40] L. N. Shestag. A Cylindrical Array for the TACAN System. IEEE Transactions on Antennas andPropagation,1974,22(1):17-25
[41] A. D. Munger, G. Vaughn, J. H. Provencher et al. Conical Array Studies. IEEE Transactions onAntennas and Propagation,1974,22(1):35-43
[42] P. M. Liebman, L. Schwartzman, and Hylas A. E.. Dome Radar—A New Phased Array System.in Proceedings of IEEE International Radar Conference, Washington, D.C.,1975:349-353
[43] M. Kanno, T. Hashimura, T. Katada, et al.. Digital Beam Forming for Conformal Active ArrayAntenna. in IEEE International Symposium on Phased Array Systems and Technology,1996:37-40
[44] H. Steyskal. Pattern Synthesis for a Conformal Wing Array. in IEEE Aerospace ConferenceProceedings,2002,2:819-824
[45] E. Vourch, C. Caille, M. J. Martin, et al. Conformal Array Antenna for LEO ObservationPlatforms. in IEEE AP-S International Symposium Digest,1998:20-23
[46] G. Caille, E. Vourch, M. J. Martin, et al..Conformal Array Antenna for Observation Platforms inLow Earth Orbit. IEEE Antennas and Propagation Magazine,2002,44(3):103-104
[47]黄茜.共形相控阵中的数字波束形成技术研究:[硕士学位论文].成都:电子科技大学.2006
[48] T. J. Shan, T Kailath. Adaptive Beamforming for Coherent Signals and Interference. IEEE Trans.Acoust.,Speech Signal Process.1985,133(3):527-536
[49] S. U. Pillai, B. H. Kwon. Forward-backward Spatial Smoothing Techniques for Coherent SignalIdentification. IEEE Trans. Acoust. Speech Signal Process,1989,37(1):8-15
[50] M. Wax, J. Sheinvald. Direction Finding of Coherent Signals via Spatial Smoothing forUniform Circular Arrays. IEEE Trans. Antennas Propagat.,1994,42(5):613-620
[51] K. Maheswara, V. U. Reddy. Analysis of Spatial Smoothing with Uniform Circular Arrays.IEEE Trans. Signal Processing,1999,47(6):1726-1730
[52] B. K. Lau, Y. H. Leung. Optimum Beaformers for Uniform Circular Arrays in a CorrelatedSignal Environment. Acoustics, Speech, and Signal Processing,2000:3093-3096
[53] B.K. Lau, Y.H. Leung, Yanqun Liu et al. Transformations for Nonideal Uniform Circular ArraysOperating in Correlated Signal Environments. IEEE Trans. Signal Processing,2006,54(1):34-48
[54] C. P. Mathews, M. D. Zoltowski. Eigenstructure techniques for2-D angle estimation withuniform circular arrays. IEEE Trans. Signal Processing,1994,42(9):2395-2407
[55] R. Goossens, H. Rogier, S. Werbrouck. UCA Root-MUSIC with sparse uniform circular arrays.IEEE Trans. Signal Process,2008,56:4095-4099
[56]邓维波,林力,袁楼.一种等间距圆形阵列的超方向性综合方法.哈尔滨工业大学报,2001,33(6):838-841
[57]丁杰伟,傅丰林,阵健.弧形智能天线阵列结构.信号处理，2002,18(3):271-274
[58] R. Vescovo. Constrained and Unconstrained Synthesis of Array factor for Circular arrays.IEEE Trans. Antennas Propagation,1995,43(12):1405-1410
[59] R.Vescovo. Pattern Synthesis with Null Constraints for Circular Arrays of Equally SpacedIsotropic Elements. IEE Proc-Microw Antennas Propag,1996,143(2):103-106
[60] R.Vescovo. Pattern synthesis for arc arrays. Antennas and Propagation Society InternationalSymposium. IEEE,1997,4:2256-2259
[61] F. Ares, S.R.Rengarajan, J.A.F.Lence et al. Synthesis of Antenna Patterns of Circular Arc Arrays.Electronics Letters,1996:1845-1846
[62] P. N. Fletcher, P. Danwood. Beamforming for Circular and Semicircular Array Antennas forLow-cost Wireless LAN Data Communications Systems. IEE Proc-Microw AntennasPropagation.1998,145(2):153-157
[63] K. L. Du. Pattern Analysis of Uniform Circular Array. IEEE Transactions on Antennas andPropagation.2004,52(4):1125-1129
[64] Chan, Pun. On the design of digital broadband beamformer for uniform circular array withfrequency invariant characteristics. Antennas and Propagation Society Symposium,2004. IEEE.2004,3:2796-2799
[65] Griffiths, Cowan, Eiges, Rafik. High-resolution beamforming techniques for circular sonararrays. Oceans Engineering for Today’s Technology and Tomorrow’s Preservation Proceedings.1994:13-16
[66]刘先省，张连堂，周林.给定方向图的圆形阵列综合方法.电子学报.2005,33(2):245-248
[67] H. Steyskal. Circular array with frequency-invariant pattern. in Dig.IEEE Int. Symp. AntennasPropagation,1989,3:1477-1480
[68] M. R. Jones, H. D. Griffiths. Broadband pattern synthesis from a circular array antennas andpropagation. in Proc. Int. Conf. Antennas and Propagation (ICAP)1989,1989,1:55-59
[69] S. C. Chan, K. Carson, S. Pun. On the design of digital broadband beamformer for uniformcircular array with frequency invariant characteristics. in IEEE ISCAS2002, Arizona,USA,2002,1:693-696
[70] Y. Yang, C. Sun, C. Wan. Theoretical and experimental studies on broadband constantbeamwidth beamforming for circular arrays. in Proc. IEEE OCEANS2003,2003,3:1467-1653
[71] Yunhong Li, K.C. Ho, Chiman Kwan. Beampattern Synthesis for Concentric Circular RingArray using MMSE Design. ISCAS,2004:329-332
[72]Yunhong Li. Broadband Beamforming and Direction Finding using Concentric Ring Array.[Thedissertation for the degree of Doctor of Philosophy]. University of Missouri-Columbia.2005.
[73] S. C. Chan., H. H. Chen. Uniform Concentric Circular Arrays With Frequency-InvariantCharacteristics—Theory, Design, Adaptive Beamforming and DOA Estimation. IEEE Trans.Signal Process,2007,55(1):165-177
[74] M. Pesaventoand, J. F. B hme. Direction of arrival estimation in uniform circular arrayscomposed of directional elements. in Proc. Sensor Array and Multichannel Signal ProcessingWorkshop, Aug.2002:503-507
[75] R. Goossens, H. Rogier. A hybrid UCA-RARE/Root-MUSIC approach for2-D direction ofarrival estimation in uniform circular arrays in the presence of mutual coupling. IEEE Trans.Antennas Propag..2007,43:841-849
[76] W. Buhong, H. Hontat, L. Mookseng. Decoupled2D direction of arrival estination usingcompact uniform circular arrays in the presence of elevation-dependent mutual coupling. IEEETrans. Antennas Propag.,2010,58(3):747-755
[77] B. Fridelander. Direction Finding using Spatial Smoothing with Interpolated Arrays. IEEETrans. On Aerospace and Electronic Systems,1992,28(2):574-587
[78] C.QI, Y. Wang, Y. Zhang, et al. DOA estimation and self-calibration algorithm for uniformcircular array. Electronics Letters.2005,41(20):1092-1094
[79] Min Lin, Luxi Yang. Blind calibration and DOA estimation with uniform circular arrays in thepresence of mutual coupling. IEEE Antennas and wireless propagation Letters,2006,5:315-318
[80] J. R. DRISCOLL, D. M. HEALY. Computing Fourier transforms andconvolutions on the2-sphere. Adv. Appl. Math.,1994,15:202-250
[81] G. Arfken, H. J. Weber. Mathematical Methods for Physicists. San Diego, CA: Academic,2001
[82] R.H. HARDIN, N.J. SLOANE. McLaren’s improved snub cube and other new spherical designsin three dimensions. Discrete Comput. Geom,1995,15:429-441
[83] P. LEOPARDI. A Partition of the unit sphere into regions of equal area and small diameter.Electronic Transactions on Numerical Analysis,2006,25:309-327
[84] E. A. RAKHMANOV, E. B. SAFF, Y. M. ZHOU. Minimal discrete energy on the sphere.Mathmatical Research Letters,1994,1:647-662
[85] M. Huang, S. Tan. Spheroidal phase mode processing for antenna arrays. in IEEE Internationalworkshop on Antenna Technology: Small Antennas and Novel Metamaterials,2005
[86] E. DE WITTE, H. GRIFFITH, P. BRENNAN. Phase mode processing for spherical arrays.Electron. Lett.,2003,39:1430-1431
[87] M. Huang, S. Tan. Spherical antenna arrays for phase mode processing. in Proc. IEEEInternational Symposium on Micrwave, Antenna, Propagation and EMC Technologies forWireless Communications,2005
[88] M. Huang and S. Tan. An improved spherical antenna array for wideband phase modeprocessing. Progress In Electromagnetics Research,2006,66:27-40
[89] B. RAFAELY. Spatial Aliasing in Spherical Microphone Arrays. IEEE Trans. Signal Process.,2007,55:1003-1010
[90] R. GOOSSENS, H. ROGIR. Closed-form2D angle estimation with a spherical array viaspherical phase mode excitation and ESPRIT. IEEE International Conference on Acoustics,Speech and Signal Processing2008,2008:2321-2324
[91] R. GOOSSENS, H. ROGIR. Unitary spherical ESPRIT:2-D angle estimation with viasphereical arrays for scalar fields. IET Signal Process.,2008,3:221-231
[92] R. GOOSSENS, I. Bogaert, H. ROGIR. Phase-mode processing for spherical antenna arrayswith a finite number of antenna elements and including mutual coupling. IEEE Trans. AntennasPropag.,2009,57(12):3783-3790
[93] Panayiotis Ioannides, Constantine A. Balanis. Wideband beamforming using circular arrays.IEEE Antennas and Propagation Society, AP-S International Symposium,2004,3:2627-2630
[94]何子述，夏威等.现代数字信号处理及其应用.北京:清华大学出版社，2009
[95] Simon Haykin. Adaptive filter theory. Third Edition. NJ: Prencice-Hall,1996
[96]王永良，陈辉，彭应宇等.空间谱估计理论与算法.北京:清华大学出版社，2004
[97] Xie Julan, He Zishu. Beamforming of coherent signals for weighed two concentric ring arrays.Intelligent Signal Processing and Communication Systems,2007:850-853
[98] O L. Frost. An Algorithm for Linearly Constrained Adaptive Processing. Proc IEEE,1972,60(8):926-935
[99]谢菊兰,何子述,夏威等.一种高效的实值权均匀圆阵去相干波束形成算法.系统工程与电子技术.2008,30(12):9-11
[100] Y.-H. Choi. Simple Adaptive Beamforming with Only Real Weights Based on Covariancedifferencing. Electronics Letters,2007,43(10):552-553
[101] E. W. Weisstein. Jacobi-anger expansion. Wolfram MathWorld [Online]. Available: http//www.mathworld. wolfram.com/Jacobi–Anger Expansion. Html
[102] F. Belloni, A. Richter, V. Koivunen,. Beamspace transform for UCA: Error analysis and biasreduction. IEEE Trans. Signal Process.,2006,54(8):3078-3089
[103] Elio D. Di Claudio. Asymptotically Perfect Wideband Focusing of Multiring Circular Arrays.IEEE Trans. Signal Process,2005,53(10):3661-3673
[104]张贤达.矩阵分析与应用.北京:清华大学出版社,2004,61-64
[105]高世伟,保铮.利用数据矩阵分解实现对空间相关信号源的超分辨处理.通信学报,1988,9(1):4-13
[106]谢菊兰,李会勇,何子述.均匀圆阵相干信源DOA估计的差分算法.电子科技大学学报.已录用
[107] Julan Xie, Zishu He, Huiyong Li. A Fast DOA Estimation Algorithm for Uniform CircularArrays in the Presence of Unknown Mutual Coupling. Progress In Electromagnetics ResearchJournals C.2011,21:257-271
[108] S. Marcos, A. Marsal, M. Benidir. Propagator method for source bearing estimation. SignalProcessing,1995,42(2):121-138
[109] S. Marcos, M. Benidir. On a high resolution array processing method non-based on theeigenanlysis approach. Acoustics, Speech, and Signal Processing,1990InternationalConference on,1990,5:2955-2958
[110] AKKAR Salem, GHARSALLAH Ali, HARABI Ferid. Concentric circular array for DOAsestimation of coherent sources with ESPRIT algorithm. Design and Technology of IntegratedSystems in Nanoscale Era (DTIS),20105th International Conference on,2010:1-6
[111] ZHAO Hui, WANG Hongjin. MODE-SUMWE algorithm for estimating DOA of coherentsignals on uniform circular array. Networks Security Wireless Communications and TrustedComputing (NSWCTC),2010,2:318-320
[112] K. M. REDDY, V. U. REDDY. Analysis of interpolated arrays with spatial smoothing. Signalprocessing,1996,54(4):267-272
[113]穆世强,陈天麒.圆阵中相干信号的高分辨阵列测向技术.电子科技大学学报,1993,22(4):350-355
[114] XU Dihua, CHEN Jianwen. A novel DOA estimation for uniform circular arrays in correlatedenvironment without interpolation. ISPACS2006,2006:650-652
[115]韩芳明,张守宏.用改进的MUSIC算法实现相干多径信号分离.系统电子与工程技术,2004,26(6):721-713
[116]高书彦,陈辉,王永良等.基于均匀圆阵的模式空间矩阵重构算法.电子与信息学报，2007,29(12):2832-2835
[117] KAREEM Al Jabr, HYUCK M Kwon, NIZAR Tayem. Modified UCA-ESPRIT for estimatingDOA of coherent signals using one snapshot.Vehicular Technology Conference,2008. VTCSpring2008. IEEE,2008:290-293
[118]齐崇英,王永良,张永顺等.色噪声背景下相干信源DOA的空间差分平滑算法.电子学报,2005,33(7):1315-1318
[119] Deyuan Gao, Buhong Wang, Ying Guo. Comments on “Blind Calibration and DOA EstimationWith Uniform Circular Arrays in the Presence of Mutual coupling”. IEEE Antennas andwireless propagation Letters,2006,5:566-569
[120] Min Lin, Luxi Yang. Reply to the comments on “Blind Calibration and DOA Estimation WithUniform Circular Arrays in the Presence of Mutual coupling”. IEEE Antennas and wirelesspropagation Letters,2006,5:568-569
[121] B.Friedlander, A.J.Weiss. Direction finding in the presence of mutual coupling. IEEETrans.Antennas Propag.,1991,39:273-284
[122] Helmut Lütkepohl. Handbook of Matrices. New York:Wiley,1996
[123] R. Goossens, H. Rogier.2-D direction of arrival estimation combining UCA-RARE andMUSIC for uniform circular arrays subject to mutual coupling. in Proc. Int. Conf. onElectromagnetics in Advanced Applications,2005:791-794
[124] T. T. Zhang, Y. L. Lu, H. T. Hui. Compensation for the mutual coupling effect in uniformcircular arrays for2D DOA estimations employing the maximum likelihood technique. IEEETrans. Aerosp. Electron. Sys.,2008,44:1215-1221
[125] H.T.Hui. Improved compensation for the mutual coupling effect in a dipole array for directionfinding. IEEE Trans.Antennas Propag.,2003,51(9):2498-2503
[126] Julan Xie, Zishu He, Huiyong Li et al.2D DOA Estimation with Sparse Uniform CircularArrays in the Presence of Mutual Coupling. EURASIP Journal on Advances in SignalProcessing.2011, doi:10.1186/1687-6180-2011-127
[127] M. A. Doron, E. Doron. Wavefield modeling and array processing—Part I: spatial sampling.IEEE Trans. Signal Processing,1994,42(10):2549-2559
[128] M. A. Doron, E. Doron. Wavefield modeling and array processing—Part II: Algorithms. IEEETrans. Signal Processing,1994,42(10):2560-2570
[129] M. A. Doron, E. Doron. Wavefield modeling and array processing—Part III: Resolutioncapacity. IEEE Trans. Signal Processing,1994,42(10):2571-2580
[130]C. Mario, R. Andreas and K. Visa.Unified array manifold decomposition based on sphericalharmonics and2-D Fourier basis. IEEE Trans. Signal Processing,2010,58(9):4634-4645
[131] F. Belloni, A. Richter, and V. Koivunen. Performance of root-MUSIC algorithm usingreal-world arrays.14th Eur. Signal Processing Conf.(EUSIPCO), Florence, Italy,2006:4-8
[132] F. Belloni, A. Richter, V. Koivunen. Extension of root-MUSIC to non-ULA arrayconfigurations. presented at the IEEE Int. Conf.Acoustics, Speech, Signal Processing (ICASSP),France,2006:14-19
[133] F. Belloni, A. Richter, V. Koivunen. DoA estimation via manifold separation for arbitrary arraystructures. IEEE Trans. Signal Process,2007,55(10):4800-4810
[134] Gupta I. J, Ksienski A. A. Effect of mutual coupling on the performance of adaptive arrays.IEEE Trans Antennas Propagat,1983,31(5):785-791
[135] T. Rahim and D.E.N.Davies. Effect of directional elements on the directional response ofcircular antenna arrays. Microwaves, Optics and Antennas, IEE Proceedings H,1982,129(1):18-22
[136] A. L. Swindlehurst, T. Kailath. A performance analysis of subspace-based methods in thepresence of model errors—I: The MUSIC algorithm. IEEE Trans. Signal Process.,1992,40(7):1758-1774
[137] A. L. Swindlehurst, T. Kailath. A performance analysis of subspace-based methods in thepresence of model errors—II: Multidimensional algorithm. IEEE Trans. Signal Process.,1993,41(9):2882-2890
[138] H. TEUTSCH. Modal array signal processing: principles and applications of acousticwavefield decomposition. Springer,2007
[139] J. MEYER, G. ELKO. Handing spatiall aliasing in spherical array application. Hands-FreeSpeech Commum. Microphone Arrays,2008:8-15
[140] L. MARANTIS, E. DE WITTE, P. BRENNAN. Comparison of various spherical antennaarray element distributions. Antennas and Propagation,2009. EuCAP2009.3rd EuropeanConference on,2009:2980–2984
[141] Julan Xie, L. Marantis, P. V. Brennan. Spherical ESPRIT-Based2-D Direction Finding withDifferent Distributions of a Spherical Array Antenna. Antennas&Propagation Conference,2009. LAPC2009. Loughborough.2009:661-664
[142] W. FREEDEN. On integral formulas of the (unit) sphere and their application to numericalcomputation of integrals. Computing,1980,25:205-208
[143] C.R. Rao, H. Toutenburg, A. Fieger, etc. Linear Models: Least Squares and Alternatives.Springer,1999