DOA (Direction of Arrival) estimation is a major problem in array signal processing applications. Recently, compressive sensing algorithms, including convex relaxation algorithms and greedy algorithms, have been recognized as a kind of novel DOA estimation algorithm. However, the success of these algorithms is limited by the RIP (Restricted Isometry Property) condition or the mutual coherence of measurement matrix. In the DOA estimation problem, the columns of measurement matrix are steering vectors corresponding to different DOAs. Thus, it violates the mutual coherence condition. The situation gets worse when there are two sources from two adjacent DOAs. In this paper, an algorithm based on OMP (Orthogonal Matching Pursuit), called ILS-OMP (Iterative Local Searching-Orthogonal Matching Pursuit), is proposed to improve DOA resolution by Iterative Local Searching. Firstly, the conventional OMP algorithm is used to obtain initial estimated DOAs. Then, in each iteration, a local searching process for every estimated DOA is utilized to find a new DOA in a given DOA set to further decrease the residual. Additionally, the estimated DOAs are updated by substituting the initial DOA with the new one. The simulation results demonstrate the advantages of the proposed algorithm.
References
[1]
Stoica, P.; Moses, R.L. Introduction to Spectral Analysis; Prentice-Hall: Englewood Cliffs, NJ, USA, 1997.
[2]
Capon, J. High-resolution frequency-wavenumber spectrum analysis. Proc. IEEE 1969, 57, 1408–1418.
[3]
Li, J.; Stoica, P. An adaptive filtering approach to spectral estimation and SAR imaging. IEEE Trans. Signal Process. 1996, 44, 1469–1484.
[4]
Schmidt, R. Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. 1986, 34, 276–280.
[5]
Roy, R.; Kailath, T. ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Trans. Acoust. Speech Signal Process. 1989, 37, 984–995.
[6]
Stoica, P.; Nehorai, A. MUSIC, maximum likelihood, and Cramer-Rao bound: Further results and comparisons. IEEE Trans. Acoust. Speech Signal Process. 1990, 38, 2140–2150.
[7]
Zooghby, A.H.E.; Christodoulou, C.G.; Georgiopoulos, M. A neural network-based smart antenna for multiple source tracking. IEEE Trans. Antennas Propag. 2000, 48, 768–776.
[8]
Donelli, M.; Viani, F.; Rocca, P.; Massa, A. An innovative multiresolution approach for DOA estimation based on a support vector classification. IEEE Trans. Antennas Propag. 2009, 57, 2279–2292.
[9]
Malioutov, D.; Cetin, M.; Willsky, A.S. A sparse signal reconstruction perspective for source localization with sensor arrays. IEEE Trans. Signal Process. 2005, 53, 3010–3022.
[10]
Karabulut, G.Z.; Kurt, T.; Yongacoglu, A. Estimation of directions of arrival by matching pursuit (EDAMP). EURASIP J. Wirel. Commun. Netw. 2005, 2005, doi:10.1155/WCN.2005.197.
[11]
Carlin, M.; Rocca, P.; Oliveri, G.; Viani, F.; Massa, A. Directions-of-arrival estimation through bayesian compressive sensing strategies. IEEE Trans. Antennas Propag. 2013, 61, 3828–3838.
[12]
Candes, E.J.; Romberg, J.; Tao, T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 2006, 52, 489–509.
[13]
Chen, S.; Donoho, D.L.; Michael, A.S. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 1998, 20, 33–61.
[14]
Tropp, J.A.; Gilbert, A.C. Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 2007, 53, 4655–4666.
[15]
Needell, D.; Tropp, J.A. CoSaMP: Iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 2008, 26, 301–321.
[16]
Hayashi, K.; Nagahara, M.; Tanaka, T. A user's guide to compressed sensing for communications systems. IEICE Trans. Commun. 2013, E96-B, 685–712.
[17]
Candes, E.J.; Tao, T. Near-optimal signal recovery from random projections: Universal encoding strategies? IEEE Trans. Inf. Theory 2006, 52, 5406–5425.
[18]
Baraniuk, R.G.; Cevher, V.; Duarte, M.F.; Hegde, C. Model-based compressive sensing. IEEE Trans. Inf. Theory 2010, 56, 1982–2001.
[19]
Lu, Z.; Zoubir, A.M. Generalized bayesian information criterion for source enumeration in array processing. IEEE Trans. Signal Process. 2013, 61, 1470–1480.
[20]
Chen, J.; Huo, X. Theoretical results on sparse representations of multiple-measurement vectors. IEEE Trans. Signal Process. 2006, 54, 4634–4643.
[21]
Chi, Y.; Scharf, L.L.; Pezeshki, A.; Calderbank, A.R. Sensitivity to basis mismatch in compressed sensing. IEEE Trans. Signal Process. 2011, 59, 2182–2195.
