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Aug.  2023

IEEE/CAA Journal of Automatica Sinica

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W. L. Zuo, J. M. Xin, C. N. Liu, N. N. Zheng, and  A. Sano,  “Improved Capon estimator for high-resolution DOA estimation and its statistical analysis,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 8, pp. 1716–1729, Aug. 2023. doi: 10.1109/JAS.2023.123549
Citation: W. L. Zuo, J. M. Xin, C. N. Liu, N. N. Zheng, and  A. Sano,  “Improved Capon estimator for high-resolution DOA estimation and its statistical analysis,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 8, pp. 1716–1729, Aug. 2023. doi: 10.1109/JAS.2023.123549

Improved Capon Estimator for High-Resolution DOA Estimation and Its Statistical Analysis

doi: 10.1109/JAS.2023.123549
Funds:  This work was supported in part by the National Natural Science Foundation of China (62201447) and the Project Supported by Natural Science Basic Research Plan in Shaanxi Province of China (2022JQ-640). This paper was presented in part at 2014 Int. Symposium Nonlinear Theory and Its Applications (NOLTA’2014), Luzern, Switzerland, Sept. 14–18, 2014
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  • Despite some efforts and attempts have been made to improve the direction-of-arrival (DOA) estimation performance of the standard Capon beamformer (SCB) in array processing, rigorous statistical performance analyses of these modified Capon estimators are still lacking. This paper studies an improved Capon estimator (ICE) for estimating the DOAs of multiple uncorrelated narrowband signals, where the higher-order inverse (sample) array covariance matrix is used in the Capon-like cost function. By establishing the relationship between this nonparametric estimator and the parametric and classic subspace-based MUSIC (multiple signal classification), it is clarified that as long as the power order of the inverse covariance matrix is increased to reduce the influence of signal subspace components in the ICE, the estimation performance of the ICE becomes equivalent to that of the MUSIC regardless of the signal-to-noise ratio (SNR). Furthermore the statistical performance of the ICE is analyzed, and the large-sample mean-squared-error (MSE) expression of the estimated DOA is derived. Finally the effectiveness and the theoretical analysis of the ICE are substantiated through numerical examples, where the Cramer-Rao lower bound (CRB) is used to evaluate the validity of the derived asymptotic MSE expression.

     

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  • [1]
    S. Haykin, Array Signal Processing. Englewood Cliffs, USA: Prentice-Hall, 1985.
    [2]
    S. U. Pillai and C. S. Burrus, Array Signal Processing. New York, USA: Springer-Verlag, 1989.
    [3]
    S. Haykin, Advances in Spectrum Analysis and Array Processing, Volumes I–III. Englewood Cliffs, USA: Prentice-Hall, 1991–1995.
    [4]
    D. H. Johnson and D. E. Dudgeon, Array Signal Processing: Concepts and Techniques. Englewood Cliffs, USA: Prentice Hall, 1993.
    [5]
    P. Stoica and R. L. Moses, Introduction to Spectral Analysis. Upper Saddle River, USA: Prentice-Hall, 1997.
    [6]
    P. R. P. Hoole, Smart Antennas and Signal Processing: For Communications, Biomedical and Radar Systems. Ashurst, UK: WIT Press, 2001.
    [7]
    H. L. Van Trees, Optimum Array Processing: Part IV of Detection, Estimation, and Modulation Theory. New York: John Wiley & Sons, 2002.
    [8]
    S. M. Kay and S. L. Marple, “Spectrum analysis — A modern perspective,” Proc. IEEE, vol. 69, no. 11, pp. 1380–1419, Nov. 1981. doi: 10.1109/PROC.1981.12184
    [9]
    S. L. Marple Jr, Digital Spectral Analysis. Englewood Cliffs, USA: Prentice-Hall, 1987.
    [10]
    S. M. Kay, Modern Spectral Estimation: Theory and Applications. Englewood Cliffs, USA: Prentice Hall, 1988.
    [11]
    S. Li, R. X. He, B. Lin, and F. Sun, “DOA estimation based on sparse representation of the fractional lower order statistics in impulsive noise,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 860–868, Jun. 2018. doi: 10.1109/JAS.2016.7510187
    [12]
    P. Stoica and R. L. Moses, Spectral Analysis of Signals. Upper Saddle River, USA: Prentice-Hall, 2005.
    [13]
    A. M. Zoubir, M. Viberg, R. Chellappa, and S. Theodoridis, Academic Press Library in Signal Processing, Volume 3: Array and Statistical Signal Processing. New York, USA: Academic Press, 2014.
    [14]
    Y. B. Gao, “Adaptive generalized eigenvector estimating algorithm for hermitian matrix pencil,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 11, pp. 1967–1979, Nov. 2022. doi: 10.1109/JAS.2021.1003955
    [15]
    D. H. Johnson, “The application of spectral estimation methods to bearing estimation problems,” Proc. IEEE, vol. 70, no. 9, pp. 1018–1028, Sept. 1982. doi: 10.1109/PROC.1982.12430
    [16]
    H. Krim and M. Viberg, “Two decades of array signal processing research: The parametric approach,” IEEE Signal Process. Mag., vol. 13, no. 4, pp. 67–94, Jul. 1996. doi: 10.1109/79.526899
    [17]
    L. C. Godara, “Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations,” Proc. IEEE, vol. 85, no. 8, pp. 1195–1245, Aug. 1997. doi: 10.1109/5.622504
    [18]
    B. D. Van Veen and K. M. Buckley, “Beamforming: A versatile approach to spatial filtering,” IEEE ASSP Mag., vol. 5, no. 2, pp. 4–24, Apr. 1988. doi: 10.1109/53.665
    [19]
    V. F. Pisarenko, “The retrieval of harmonics from a covariance function,” Geophys. J. Roy. Astron. Soc., vol. 33, no. 3, pp. 347–366, Sept. 1973. doi: 10.1111/j.1365-246X.1973.tb03424.x
    [20]
    R. O. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 276–280, Mar. 1986. doi: 10.1109/TAP.1986.1143830
    [21]
    D. W. Tufts and R. Kumaresan, “Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood,” Proc. IEEE, vol. 70, no. 9, pp. 975–989, Sept. 1982. doi: 10.1109/PROC.1982.12428
    [22]
    R. Kumaresan and D. W. Tufts, “Estimating the angles of arrival of multiple plane waves,” IEEE Trans. Aerosp. Electron. Syst., vol. AES-19, no. 1, pp. 134–139, Jan. 1983. doi: 10.1109/TAES.1983.309427
    [23]
    R. Roy and T. Kailath, “ESPRIT — Estimation of signal parameters via rotational invariance techniques,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 37, no. 7, pp. 984–995, Jul. 1989. doi: 10.1109/29.32276
    [24]
    P. Stoica and K. C. Sharman, “Novel eigenanalysis method for direction estimation,” IEE Proc. F (Radar Signal Process.), vol. 137, no. 1, pp. 19–26, Feb. 1990. doi: 10.1049/ip-f-2.1990.0004
    [25]
    P. Stoica and K. C. Sharman, “Maximum likelihood methods for direction-of-arrival estimation,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 38, no. 7, pp. 1132–1143, Jul. 1990. doi: 10.1109/29.57542
    [26]
    M. Viberg and B. Ottersten, “Sensor array processing based on subspace fitting,” IEEE Trans. Signal Process., vol. 39, no. 5, pp. 1110–1121, May 1991. doi: 10.1109/78.80966
    [27]
    B. Ottersten, M. Viberg, P. Stoica, and A. Nehorai, “Exact and large sample maximum likelihood techniques for parameter estimation and detection in array processing,” in Radar Array Processing, S. Haykin, J. Litva, and T. J. Shepherd, Eds. Berlin, Germany: Springer-Verlag, 1993, pp. 99–151.
    [28]
    L. C. Liu, Y. Li, and S. M. Kuo, “Feed-forward active noise control system using microphone array,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 5, pp. 946–952, Sept. 2018. doi: 10.1109/JAS.2018.7511171
    [29]
    J. M. Xin and A. Sano, “Computationally efficient subspace-based method for direction-of-arrival estimation without eigendecomposition,” IEEE Trans. Signal Process., vol. 52, no. 4, pp. 876–893, Apr. 2004. doi: 10.1109/TSP.2004.823469
    [30]
    Y. W. Wang, J. Li, and P. Stoica, “Rank-deficient robust Capon filter bank approach to complex spectral estimation,” IEEE Trans. Signal Process., vol. 53, no. 8, pp. 2713–2726, Aug. 2005. doi: 10.1109/TSP.2005.850365
    [31]
    J. Capon, “High-resolution frequency-wavenumber spectrum analysis,” Proc. IEEE, vol. 57, no. 8, pp. 1408–1418, Aug. 1969. doi: 10.1109/PROC.1969.7278
    [32]
    D. H. Johnson and S. DeGraaf, “Improving the resolution of bearing in passive sonar arrays by eigenvalue analysis,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 30, no. 4, pp. 638–647, Aug. 1982. doi: 10.1109/TASSP.1982.1163915
    [33]
    C. D. Seligson, “Comments on ‘High-resolution frequency-wavenumber spectrum analysis’,” Proc. IEEE, vol. 58, no. 6, pp. 947–949, Jun. 1970. doi: 10.1109/PROC.1970.7825
    [34]
    J. Capon and N. R. Goodman, “Probability distributions for estimators of the frequency-wavenumber spectrum,” Proc. IEEE, vol. 58, no. 10, pp. 1785–1786, Oct. 1970. doi: 10.1109/PROC.1970.8014
    [35]
    R. T. Lacoss, “Data adaptive spectral analysis methods,” Geophysics, vol. 36, no. 4, pp. 661–675, Aug. 1971. doi: 10.1190/1.1440203
    [36]
    T. Marzetta, “A new interpretation of Capon’s maximum likelihood method of frequency-wavenumber spectral estimation,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 31, no. 2, pp. 445–449, Apr. 1983. doi: 10.1109/TASSP.1983.1164068
    [37]
    P. Händel, P. Stoica, and T. Söderström, “Capon method for DOA estimation: Accuracy and robustness aspects,” in Proc. IEEE Winter Workshop on Nonlinear Digital Signal Processing, Tampere, Finland, 1993, pp. P_7.1–P_7.5.
    [38]
    P. Stoica, P. Händle, and T. Söderström, “Study of Capon method for array signal processing,” Circ. Syst. Signal Process., vol. 14, no. 6, pp. 749–770, Apr. 1995. doi: 10.1007/BF01204683
    [39]
    C. Vaidyanathan and K. M. Buckley, “Performance analysis of the MVDR spatial spectrum estimator,” IEEE Trans. Signal Process., vol. 43, no. 6, pp. 1427–1437, Jun. 1995. doi: 10.1109/78.388855
    [40]
    C. Vaidyanathan and K. M. Buckley, “Performance analysis of DOA estimation based on nonlinear functions of covariance matrix,” Signal Process., vol. 50, no. 1–2, pp. 5–16, Apr. 1996. doi: 10.1016/0165-1684(96)00005-9
    [41]
    C. Vaidyanathan and K. M. Buckley, “Performance analysis of the enhanced minimum variance spatial spectrum estimator,” IEEE Trans. Signal Process., vol. 46, no. 8, pp. 2202–2206, Aug. 1998. doi: 10.1109/78.705432
    [42]
    M. Hawkes and A. Nehorai, “Acoustic vector-sensor beamforming and Capon direction estimation,” IEEE Trans. Signal Process., vol. 46, no. 9, pp. 2291–2304, Sept. 1998. doi: 10.1109/78.709509
    [43]
    J. Benesty, J. D. Chen, and Y. T. Huang, “A generalized MVDR spectrum,” IEEE Signal Process. Lett., vol. 12, no. 12, pp. 827–830, Dec. 2005. doi: 10.1109/LSP.2005.859517
    [44]
    P. Stoica and A. Nehorai, “MUSIC, maximum likelihood, and Cramer- Rao bound,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 37, pp. 720–741, May 1989. doi: 10.1109/29.17564
    [45]
    U. Nickel, “Algebraic formulation of Kumaresan-Tufts superresolution method, showing relation to ME and MUSIC methods,” IEE Proc. F (Commun.,Radar Signal Process.), vol. 135, no. 1, pp. 7–10, Feb. 1988. doi: 10.1049/ip-f-1.1988.0002
    [46]
    A. Jakobsson, S. L. Marple, and P. Stoica, “Computationally efficient two-dimensional capon spectrum analysis,” IEEE Trans. Signal Process., vol. 48, no. 9, pp. 2651–2661, Sept. 2000. doi: 10.1109/78.863072
    [47]
    P. Stoica, Z. S. Wang, and J. Li, “Robust capon beamforming,” IEEE Signal Process. Lett., vol. 10, no. 6, pp. 172–175, Jun. 2003. doi: 10.1109/LSP.2003.811637
    [48]
    J. Li, P. Stoica, and Z. S. Wang, “On robust Capon beamforming and diagonal loading,” IEEE Trans. Signal Process., vol. 51, no. 7, pp. 1702–1715, Jul. 2003. doi: 10.1109/TSP.2003.812831
    [49]
    R. Abrahamsson, A. Jakobsson, and P. Stoica, “A Capon-like spatial spectrum estimator for correlated sources,” in Proc. 12th European Signal Processing Conf., Vienna, Austria, 2004, pp. 1265–1268.
    [50]
    L. Du, T. Yardibi, J. Li, and P. Stoica, “Review of user parameter-free robust adaptive beamforming algorithms,” Digital Signal Process., vol. 19, no. 4, pp. 567–582, Jul. 2009. doi: 10.1016/j.dsp.2009.02.001
    [51]
    J. Yang, X. C. Ma, C. H. Hou, and Y. C. Liu, “Shrinkage-based Capon and APES for spectral estimation,” IEEE Signal Process. Lett., vol. 16, no. 10, pp. 869–872, Oct. 2009. doi: 10.1109/LSP.2009.2026203
    [52]
    P. Lopez-Dekker and J. J. Mallorqui, “Capon and APES-based SAR processing: Performance and practical considerations,” IEEE Trans. Geosci. Remote Sens., vol. 48, no. 5, pp. 2388–2402, May 2010. doi: 10.1109/TGRS.2009.2038902
    [53]
    A. Aubry, V. Carotenuto, and A. De Maio, “A new optimality property of the Capon estimator,” IEEE Signal Process. Lett., vol. 24, no. 11, pp. 1706–1708, Jul. 2017. doi: 10.1109/LSP.2017.2729658
    [54]
    R. Chellappa and S. Theodoridis, Academic Press Library in Signal Processing, Volume 7: Array, Radar and Communications Engineering. New York, USA: Academic Press, 2017.
    [55]
    J. C. Chen, K. Yao, and R. E. Hudson, “Source localization and beamforming,” IEEE Signal Process. Mag., vol. 19, no. 2, pp. 30–39, Mar. 2002. doi: 10.1109/79.985676
    [56]
    Y.-S. Yoon, M. G. Amin, and F. Ahmad, “MVDR beamforming for through-the-wall radar imaging,” IEEE Trans. Aerosp. Electron. Syst., vol. 47, no. 1, pp. 347–366, Jan. 2011. doi: 10.1109/TAES.2011.5705680
    [57]
    S. D. Somasundaram, “Wideband robust Capon beamforming for passive sonar,” IEEE J. Ocean. Eng., vol. 38, no. 2, pp. 308–322, Apr. 2013. doi: 10.1109/JOE.2012.2223560
    [58]
    K. Luo and A. Manikas, “Superresolution multitarget parameter estimation in MIMO Radar,” IEEE Trans. Geosci. Remote Sens., vol. 51, no. 6, pp. 3683–3693, Jun. 2013. doi: 10.1109/TGRS.2012.2226466
    [59]
    T. Tirer and A. J. Weiss, “High resolution direct position determination of radio frequency sources,” IEEE Signal Process. Lett., vol. 23, no. 2, pp. 192–196, Feb. 2016. doi: 10.1109/LSP.2015.2503921
    [60]
    M. D. Hossain and A. S. Mohan, “Eigenspace time-reversal robust Capon beamforming for target localization in continuous random media,” IEEE Antennas Wirel. Propag. Lett., vol. 16, pp. 1605–1608, Jan. 2017. doi: 10.1109/LAWP.2017.2653809
    [61]
    L. S. Yang, M. R. McKay, and R. Couillet, “High-dimensional MVDR beamforming: Optimized solutions based on spiked random matrix models,” IEEE Trans. Signal Process., vol. 66, no. 7, pp. 1933–1947, Apr. 2018. doi: 10.1109/TSP.2018.2799183
    [62]
    P. Chevalier, J.-P. Delmas, and M. Sadok, “Third-order Volterra MVDR beamforming for non-Gaussian and potentially non-circular interference cancellation,” IEEE Trans. Signal Process., vol. 66, no. 18, pp. 4766–4781, Sept. 2018. doi: 10.1109/TSP.2018.2860551
    [63]
    L. Zhang, L. Huang, B. Li, M. Huang, J. M. Yin, and W. M. Bao, “Fast-moving jamming suppression for UAV navigation: A minimum dispersion distortionless response beamforming approach,” IEEE Trans. Veh. Technol., vol. 68, no. 8, pp. 7815–7827, Aug. 2019. doi: 10.1109/TVT.2019.2924951
    [64]
    S. R. Tuladhar and J. R. Buck, “Unit circle rectification of the minimum variance distortionless response beamformer,” IEEE J. Ocean. Eng., vol. 45, no. 2, pp. 500–510, Apr. 2020. doi: 10.1109/JOE.2018.2876584
    [65]
    N. L. Owsley, “Signal subspace based minimum-variance spatial array processing,” in Proc. IEEE 19th Asilomar Conf. Circuit, Systems and Computers, Pacific Grove, USA, 1985, pp. 94–97.
    [66]
    J. P. Burg, “The relationship between maximum entropy spectra and maximum likelihood spectra,” Geophysics, vol. 37, no. 2, pp. 375–376, Apr. 1972. doi: 10.1190/1.1440265
    [67]
    V. F. Pisarenko, “On the estimation of spectra by means of non-linear functions of the covariance matrix,” Geophys. J. Roy. Astronon. Soc., vol. 28, no. 5, pp. 511–531, Jun. 1972. doi: 10.1111/j.1365-246X.1972.tb06146.x
    [68]
    G. Borgiotti and L. Kaplan, “Superresolution of uncorrelated interference sources by using adaptive array techniques,” IEEE Trans. Antennas Propag., vol. 27, no. 6, pp. 842–845, Nov. 1979. doi: 10.1109/TAP.1979.1142176
    [69]
    M. Lagunas-Hernandez and A. Gasull-Llampallas, “An improved maximum likelihood method for power spectral density estimation,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 32, no. 1, pp. 170–173, Feb. 1984. doi: 10.1109/TASSP.1984.1164292
    [70]
    C. L. Byrne and A. K. Steele, “Stable nonlinear methods for sensor array processing,” IEEE J. Ocean. Eng., vol. 10, no. 3, pp. 255–259, Jul. 1985. doi: 10.1109/JOE.1985.1145111
    [71]
    M. A. Lagunas, M. E. Santamaria, A. Gasull, and A. Moreno, “Maximum likelihood filters in spectral estimation problems,” Signal Process., vol. 10, no. 1, pp. 19–34, Jan. 1986. doi: 10.1016/0165-1684(86)90062-9
    [72]
    J. Munier and G. Y. Delisle, “Spatial analysis in passive listening using adaptive techniques,” Proc. IEEE, vol. 75, no. 11, pp. 1458–1471, Nov. 1987. doi: 10.1109/PROC.1987.13908
    [73]
    M. K. Ibrahim, “New high-resolution pseudospectrum estimation method,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 35, no. 7, pp. 1071–1072, Jul. 1987. doi: 10.1109/TASSP.1987.1165236
    [74]
    M. D. Zoltowski and F. Haber, “A multiply constrained minimum variance approach to multiple source parameter estimation,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 35, no. 9, pp. 1358–1360, Sept. 1987. doi: 10.1109/TASSP.1987.1165291
    [75]
    P. S. Naidu and V. V. Krishna, “Improved maximum likelihood spectrum for direction of arrival (DOA) estimation,” in Proc. 1988 IEEE Int. Conf. Acoustics, Speech, and Signal Processing, New York, USA, 1988, pp. 2901–2904.
    [76]
    M. A. Lagunas and F. Vallverdu, “Rayleigh estimates for high resolution direction finding,” in Underwater Acoustic Data Processing, Y. T. Chan, Ed. Dordrecht, the Netherlands: Springer, 1989, pp. 267–271.
    [77]
    J. Choi, I. Song, S. I. Park, and J. S Yun, “Direction of arrival estimation with unknown number of signal sources,” in Proc. IEEE Int Conf Communication Systems, Singapore, Singapore, 1992, pp. 30–34.
    [78]
    U. Nickel, “Radar target parameter estimation with array antennas,” in Radar Array Processing, S. Haykin, J. Litva, and T. J. Shepherd, Eds. Berlin, Germany: Springer, 1993, pp. 47–98.
    [79]
    A. Hassanien, S. Shahbazpanahi, and A. B. Gershman, “A generalized Capon estimator for localization of multiple spread sources,” IEEE Trans. Signal Process., vol. 52, no. 1, pp. 280–283, Jan. 2004. doi: 10.1109/TSP.2003.820089
    [80]
    B. D. Van Veen, W. Van Drongelen, M. Yuchtman, and A. Suzuki, “Localization of brain electrical activity via linearly constrained minimum variance spatial filtering,” IEEE Trans. Biomed. Eng., vol. 44, no. 9, pp. 867–880, Sept. 1997. doi: 10.1109/10.623056
    [81]
    M.-X. Huang, J. J. Shih, R. R. Lee, D. L. Harrington, R. J. Thoma, M. P. Weisend, F. Hanlon, K. M. Paulson, T. Li, K. Martin, G. A. Miller, and J. M. Canive, “Commonalities and differences among vectorized beamformers in electromagnetic source imaging,” Brain Topogr., vol. 16, no. 3, pp. 139–158, Mar. 2004.
    [82]
    M. Costa and V. Koivunen, “Application of manifold separation to polarimetric Capon beamformer and source tracking,” IEEE Trans. Signal Process., vol. 62, no. 4, pp. 813–827, Feb. 2014. doi: 10.1109/TSP.2013.2294598
    [83]
    C. D. Richmond, “Capon algorithm mean-squared error threshold SNR prediction and probability of resolution,” IEEE Trans. Signal Process., vol. 53, no. 8, pp. 2748–2764, Aug. 2005. doi: 10.1109/TSP.2005.850361
    [84]
    A. K. Steele, C. L. Byrne, J. L. Riley, and M. Swift, “Performance comparison of high resolution bearing estimation algorithms using simulated and sea test data,” IEEE J. Ocean. Eng., vol. 18, no. 4, pp. 438–446, Oct. 1993. doi: 10.1109/48.262294
    [85]
    R. Klemm, “High-resolution analysis of non-stationary data ensembles,” in Signal Processing: Theories and Applications, M. Kunt and F. de Coulon, Eds. Amsterdam, the Netherlands: North-Holland, 1980, pp. 711–714.
    [86]
    P. Stoica, J. Li, and X. Tan, “On spatial power spectrum and signal estimation using the Pisarenko framework,” IEEE Trans. Signal Process., vol. 56, no. 10, pp. 5109–5119, Oct. 2008. doi: 10.1109/TSP.2008.928935
    [87]
    C. N. Liu, J. M. Xin, Y. Nishio, N. N. Zheng, and A. Sano, “Modified Capon beamformer for high-resolution direction-of-arrival estimation,” in Proc. Int. Symp. Nonlinear Theory and Its Applications, Luzern, Switzerland, 2014, pp. 116–119.
    [88]
    J. M. Xin, N. N. Zheng, and A. Sano, “Simple and efficient nonparametric method for estimating the number of signals without eigendecomposition,” IEEE Trans. Signal Process., vol. 55, no. 4, pp. 1405–1420, Apr. 2007. doi: 10.1109/TSP.2006.889982
    [89]
    G. H. Golub and C. F. Van Loan, Matrix Computations. 2nd ed. Baltimore, USA: Johns Hopkins University Press, 1989.
    [90]
    P. Shaman, “The inverted complex Wishart distribution and its application to spectral estimation,” J. Multivar. Anal., vol. 10, no. 1, pp. 51–59, Mar. 1980. doi: 10.1016/0047-259X(80)90081-0
    [91]
    B. Musicus, “Fast MLM power spectrum estimation from uniformly spaced correlations,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 33, no. 5, pp. 1333–1335, Oct. 1985. doi: 10.1109/TASSP.1985.1164696
    [92]
    T. Ekman, A. Jakobsson, and P. Stoica, “On efficient implementation of the Capon algorithm,” in Proc. 8th Europ. Signal Process. Conf., Tampere, Finland, 2000.
    [93]
    L. Wei and S. L. Marple, “Fast algorithms for least-squares-based minimum variance spectral estimation,” Signal Process., vol. 88, no. 9, pp. 2181–2192, Sept. 2008. doi: 10.1016/j.sigpro.2008.03.004
    [94]
    Z.-S. Liu, H. Li, and J. Li, “Efficient implementation of Capon and APES for spectral estimation,” IEEE Trans. Aerosp. Electron. Syst., vol. 34, no. 4, pp. 1314–1319, Oct. 1998. doi: 10.1109/7.722716
    [95]
    G.-O. Glentis, “A fast algorithm for APES and Capon spectral estimation,” IEEE Trans. Signal Process., vol. 56, no. 9, pp. 4207–4220, Sept. 2008. doi: 10.1109/TSP.2008.925940
    [96]
    C. S. Withers and S. Nadarajah, “The nth power of a matrix and approximation for large n,” N. Z. J. Math., vol. 38, pp. 171–178, 2008.
    [97]
    G.-O. Glentis, “Efficient algorithms for adaptive Capon and APES spectral estimation,” IEEE Trans. Signal Process., vol. 58, no. 1, pp. 84–96, Jan. 2010. doi: 10.1109/TSP.2009.2028935
    [98]
    T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms for Signal Processing. Upper Saddle River, USA: Prentice-Hall, 2000.
    [99]
    J. M. Xin and A. Sano, “Efficient subspace-based algorithm for adaptive bearing estimation and tracking,” IEEE Trans. Signal Process., vol. 53, no. 12, pp. 4485–4505, Dec. 2005. doi: 10.1109/TSP.2005.859329
    [100]
    T.-J. Shan, M. Wax, and T. Kailath, “On spatial smoothing for direction-of-arrival estimation of coherent signals,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 33, no. 4, pp. 806–811, Aug. 1985. doi: 10.1109/TASSP.1985.1164649
    [101]
    S. U. Pillai and B. H. Kwon, “Forward/backward spatial smoothing techniques for coherent signal identification,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 37, no. 1, pp. 8–15, Jan. 1989. doi: 10.1109/29.17496
    [102]
    J. M. Xin and A. Sano, “MSE-based regularization approach to direction estimation of coherent narrowband signals using linear prediction,” IEEE Trans. Signal Process., vol. 49, no. 11, pp. 2481–2497, 2001. doi: 10.1109/78.960396
    [103]
    P. Stoica and A. Nehorai, “Performance study of conditional and unconditional direction-of-arrival estimation,” IEEE Trans. Acoust.,Speech,Signal Process., vol. 38, no. 10, pp. 1783–1795, Oct. 1990. doi: 10.1109/29.60109
    [104]
    A. J. Barabell, “Improving the resolution performance of eigenstructure-based direction-finding algorithms,” in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, Boston, USA, 1983, pp. 336–339.
    [105]
    Z. Yang, L. H. Xie, and C. S. Zhang, “A discretization-free sparse and parametric approach for linear array signal processing,” IEEE Trans. Signal Process., vol. 62, no. 19, pp. 4959–4973, Oct. 2014. doi: 10.1109/TSP.2014.2339792
    [106]
    C. Qian, L. Huang, N. D. Sidiropoulos, and H. C. So, “Enhanced PUMA for direction-of-arrival estimation and its performance analysis,” IEEE Trans. Signal Process., vol. 64, no. 16, pp. 4127–4137, Aug. 2016. doi: 10.1109/TSP.2016.2543206
    [107]
    J. Zhu, L. Han, R. S. Blum, and Z. W. Xu, “Multi-snapshot Newtonized orthogonal matching pursuit for line spectrum estimation with multiple measurement vectors,” Signal Process., vol. 165, pp. 175–185, Dec. 2019. doi: 10.1016/j.sigpro.2019.07.012
    [108]
    D. Zachariah, P. Stoica, and M. Jansson, “Comments on ‘Enhanced PUMA for direction-of-arrival estimation and its performance analysis’,” IEEE Trans. Signal Process., vol. 65, no. 22, pp. 6113–6114, Nov. 2017. doi: 10.1109/TSP.2017.2742982
    [109]
    P. Stoica and T. Söderström, “Statistical analysis of a subspace method for bearing estimation without eigendecomposition,” IEE Proc. F (Radar Signal Process.), vol. 139, no. 4, pp. 301–305, Aug. 1992. doi: 10.1049/ip-f-2.1992.0042
    [110]
    G. M. Wang, J. M. Xin, N. N. Zheng, and A. Sano, “Computationally efficient subspace-based method for two-dimensional direction estimation with L-shaped array,” IEEE Trans. Signal Process., vol. 59, no. 7, pp. 3197–3212, Jul. 2011. doi: 10.1109/TSP.2011.2144591
    [111]
    K. B. Petersen and M. S. Pedersen, “The matrix cookbook,” Nov. 14, 2008. [Online]. Available: http://faculty.bicmr.pku.edu.cn/~wenzw/bigdata/matrix-cook-book.pdf, 2012.
    [112]
    P. H. M. Janssen and P. Stoica, “On the expectation of the product of four matrix-valued Gaussian random variables,” IEEE Trans. Autom. Control, vol. 33, no. 9, pp. 867–870, Sept. 1988. doi: 10.1109/9.1319

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    • Higher-order inverse array covariance matrix based improved Capon DOA estimation
    • ICE and MUSIC are equivalent regardless of the SNR with large power order
    • The asymptotic MSE expressions of DOA estimates are derived explicitly

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