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In the field of DoA estimation in array processing, we summarize recent results on an improved MUSIC method (referred to as G-MUSIC), developed in the context where the number of samples N of the observed signal is large, and of the same order of magnitude than the num- ber of sensors. Using results from random matrix theory, we provide a statistical performance analysis of the G-MUSIC method, in terms of consistency, mean square error, and asympto- tic normality, in the context of unknown deterministic source signals. A comparison with the classical MUSIC method is provided in a first scenario with widespace DoA, and in a second scenario with closely spaced DoA.
Array processing, MUSIC, Random matrix theory
Anderson T. (1958). An introduction to multivariate statistical analysis (vol. 2). Wiley New York.
Bai Z., Silverstein J. (1998). No eigenvalues outside the support of the limiting spectral distri- bution of large-dimensional sample covariance matrices. Annals of probability, p. 316–345.
Benaych-Georges F., Nadakuditi R. R. (2012). The singular values and vectors of low rank per- turbations of large rectangular random matrices. Journal of Multivariate Analysis, vol. 111, p. 120–135.
Bianchi P., Debbah M., Maïda M., Najim M. (2011). Performance of statistical tests for single source detection using random matrix theory. IEEE Transactions on Information Theory, vol. 57, no 4, p. 2400-2419.
Couillet R. (2015). Robust spiked random matrices and a robust G-MUSIC estimator. To appear in Journal of Multivariate Analysis.
Couillet R., Kammoun A. (2014). Robust G-MUSIC. In Signal processing conference (eu- sipco), 2014 proceedings of the 22nd european, p. 2155–2159.
Couillet R., Pascal F., Silverstein J. (2015). The random matrix regime of Maronna’s M- estimator with elliptically distributed samples. Journal of Multivariate Analysis, vol. 139, p. 56–78.
Hachem W., Loubaton P., Mestre X., Najim J., Vallet P. (2012a). Large information plus noise random matrix models and consistent subspace estimation in large sensor networks. Random Matrices: Theory and Applications, vol. 1, no 2.
Hachem W., Loubaton P., Mestre X., Najim J., Vallet P. (2012b). A subspace estimator for fixed rank perturbations of large random matrices. Journal of Multivariate Analysis, vol. 114, p. 427–447. (arXiv:1106.1497)
Jonhson B., Abramovich Y., Mestre X. (2008). Music, g-music, and maximum-likelihood performance breakdown. IEEE Transactions on Signal Processing, vol. 56, no 8, p. 3944- 3958.
Krichtman S., Nadler B. (2009). Non-parametric detection of the number of signals: hypothesis testing and random matrix theory. IEEE Transactions on Signal Processing, vol. 57, no 10, p. 3930-3941.
Loubaton P., Vallet P. (2011). Almost sure localization of the eigenvalues in a gaussian infor- mation plus noise model. application to the spiked models. Electron. J. Probab., vol. 16, p. 1934–1959.
Marchenko V., Pastur L. (1967). Distribution of eigenvalues for some sets of random matrices. Mathematics of the USSR-Sbornik, vol. 1, p. 457.
Mestre X., Lagunas M. (2008). Modified subspace algorithms for doa estimation with large arrays. IEEE Transactions on Signal Processing, vol. 56, no 2, p. 598–614.
Nadakuditi R., Edelman A. (2008). Sample eigenvalue based detection of high-dimensional si- gnals in white noise using relatively few samples. IEEE Transactions on Signal Processing, vol. 56, no 7, p. 2625-2637.
Schmidt R. (1986). Multiple emitter location and signal parameter estimation. IEEE Transac- tions on Antennas and Propagation, vol. 34, no 3, p. 276–280.
Stoica P., Nehorai A. (1989). Music, maximum likelihood, and cramer-rao bound. IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 37, no 5, p. 720–741.
Thomas J. K., Scharf L. L., Tufts D. W. (1995). The probability of a subspace swap in the svd. IEEE Transactions on Signal Processing, vol. 43, no 3, p. 730–736.
Vallet P., Loubaton P., Mestre X. (2012, Feb.). Improved Subspace Estimation for Multivariate Observations of High Dimension: The Deterministic Signal Case. IEEE Transactions on Information Theory, vol. 58, no 2. (arXiv: 1002.3234)
Vallet P., Mestre X., Loubaton P. (2015). Performance analysis of an improved music doa estimator. Submitted. (arXiv:1502.02501)
Vinogradova J., Couillet R., Hachem W. (2013). Statistical inference in large antenna arrays under unknown noise pattern. IEEE Transactions on Signal Processing, vol. 61, no 22, p. 5633–5645.