Abstract
In this paper, we consider the problem of direction of arrival (DOA) estimation on a large sensor array, in the case of missing data resulting from chain failure or employed sub-sampling schemes. Since the missing measurements impair the performance of DOA estimation, we propose to recover the missing entries from the available ones, by applying matrix completion (MC) techniques. We use three well-known MC algorithms SVT, LMaFit, and OptSpace for imputation of the missing entries and then employing MUSIC algorithm to estimate the angles of impinging signals. In addition, we improve the performance of MC techniques, by employing the information theoretic based source enumeration methods, such as MDL and AIC, instead of the heuristic and imprecise rank estimator in current methods. The mean-square error (MSE) of DOA estimation is taken as an assessment criterion for comparing the performance of the aforementioned MC algorithms. Simulation results are conducted to show that in addition to performance improvement achieved by imputation of the missing measurements, the LMaFit algorithm with the proposed rank estimator has the lowest runtime and DOA MSE comparing to the other well-known MC algorithms.
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Notes
In the presence of outliers, other loss functions are employed [18].
The source codes of MC solvers are available at: SVT: http://perception.csl.illinois.edu/matrix-rank/sample_code.html LMaFit: http://lmafit.blogs.rice.edu/ OptSpace: http://web.engr.illinois.edu/~swoh/software/optspace/code.html.
References
Suryaprakash, R.T., Nadakuditi, R.R.: Consistency and MSE performance of MUSIC-based DOA of a single source in white noise with randomly missing data. IEEE Trans. Signal Process. 63(18), 4756–4770 (2015)
Ferréol, A., Larzabal, P., Viberg, M.: On the asymptotic performance analysis of subspace DOA estimation in the presence of modeling errors: case of MUSIC. IEEE Trans. Signal Process. 54(3), 907–920 (2006)
Schmidt, R.O.: Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 34(3), 276–280 (1986)
Wong, K.T., Wu, Y.I., Hsu, Y.S., Song, Y.: A lower bound of DOA-estimates by an array randomly subject to sensor-breakdown. IEEE Sens. J. 12(5), 911–913 (2012)
Zhu, C., Wang, W.Q., Chen, H., So, H.C.: Impaired sensor diagnosis, beamforming, and DOA estimation with difference co-array processing. IEEE Sens. J. 15(7), 3773–3780 (2015)
Wang, M., Wang, W.: DOA estimation of array radar via random interval sub-Nyquist-sampling. In: International Conference on Signal Processing, Communication and Computing (ICSPCC), pp. 1–4. IEEE (2013)
Weng, Z., Wang, X.: Low-rank matrix completion for array signal processing. In: International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 2697–2700. IEEE (2012)
Candès, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9(6), 717–772 (2009)
Cai, J.F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)
Wen, Z., Yin, W., Zhang, Y.: Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm. Math. Progr. Comput. 4(4), 333–361 (2012)
Malek-Mohammadi, M., Babaie-Zadeh, M., Amini, A., Jutten, C.: Recovery of low-rank matrices under affine constraints via a smoothed rank function. IEEE Trans. Signal Process. 62(4), 981–992 (2014)
Keshavan, R.H., Oh, S.: A Gradient Descent Algorithm on the Grassman Manifold for Matrix Completion. arXiv:0910.5260 (2009)
Malek-Mohammadi, M., Jansson, M., Owrang, A., Koochakzadeh, A., Babaie-Zadeh, M.: DOA estimation in partially correlated noise using low-rank, sparse matrix decomposition. In: 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM), pp. 373–376. IEEE (2014)
Wang, M., Zhang, Z., Nehorai, A.: Direction finding using sparse linear arrays with missing data. In: 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 3066–3070 (2017)
Sun, S., Petropulu, A.P., Bajwa, W.U.: Target estimation in colocated MIMO radar via matrix completion. In: Acoustics, International Conference on Speech and Signal Processing (ICASSP), pp. 4144–4148. IEEE (2013)
Kalogerias, D.S., Petropulu, A.P.: Matrix completion in colocated MIMO radar: recoverability, bounds and theoretical guarantees. IEEE Trans. Signal Process. 62(2), 309–321 (2014)
Wax, M., Kailath, T.: Detection of signals by information theoretic criteria. IEEE Trans. Acoust. Speech Signal Process. 33(2), 387–392 (1985)
Wong, R.K., Lee, T.: Matrix Completion with Noisy Entries and Outliers. arXiv:1503.00214 (2015)
Candes, E.J., Plan, Y.: Matrix completion with noise. Proc. IEEE 98(6), 925–936 (2010)
Stoica, P., Nehorai, A.: Music, maximum likelihood, and Cramer–Rao bound. IEEE Trans. Acoust. Speech Signal Process. 37(5), 720–741 (1989)
Grant, M., Boyd, S.: CVX: Matlab Software for Disciplined Convex Programming, version 2.1 (2011). http://cvxr.com/cvx
Ciuonzo, D.: On time-reversal imaging by statistical testing. IEEE Signal Process. Lett. 24(7), 1024–1028 (2017)
Ciuonzo, D., Romano, G., Solimene, R.: Performance analysis of time-reversal MUSIC. IEEE Trans. Signal Process. 63(10), 2650–2662 (2015)
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Setayesh, A., Yazdian, E. & Malek-Mohammadi, M. Direction of arrival estimation with missing data via matrix completion. SIViP 13, 1451–1459 (2019). https://doi.org/10.1007/s11760-019-01482-9
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DOI: https://doi.org/10.1007/s11760-019-01482-9