Abstract：Focusing on the problem of poor accuracy and low resolution of traditional Direction Of Arrival (DOA) estimation algorithm in the presence of non-uniform noise, based on the Matrix Complement theory, a Weighted L1 Sparse Reconstruction DOA estimation algorithm is developed under the Second-order Statistical domain (MC-WLOSRSS) in this paper. Following the matrix completion approach, the regularization factor is firstly introduced to reconstruct the signal covariance matrix reconstruction as a noise-free covariance matrix. After that, the multi-vector problem of the noise-free covariance matrix can be transformed into a single vector one by exploiting sum-average operation for matrix in the second-order statistical domain. Finally, the DOA can be complemented by employing the sparse reconstruction weighted L1 norm. Numerical simulations show that the proposed algorithm outperforms the traditional DOA algorithms such as MUltiple SIgnal Classification (MUSIC), Improved L1-SRACV (IL1-SRACV), L1-norm-Singular Value Decomposition (L1-SVD) subspace and sparse reconstruction weighted L1 methods in the following respects: suppressing the influence of the non-uniform noise significantly, bettering DOA estimation performance, as well as improving estimation accuracy and resolution with low Signal-Noise Ratio (SNR).
VAN TREES H L. Optimum Array Processing: Part IV of Detection, Estimation and Modulation Theory[M]. New York, NY, USA: John Wiley & Sons, 2002: 917-1317.
[2]
SCHMIDT R. Multiple emitter location and signal parameter estimation[J]. IEEE Transactions on Antennas & Propagation, 1986, 34(3): 276-280. doi: 10.1109/TAP.1986. 1143830.
[3]
LIAO B, HUANG L, GUO C, et al. New approaches to direction-of-arrival estimation with sensor arrays in unknown nonuniform noise[J]. IEEE Sensors Journal, 2016, 16(24): 8982-8989. doi: 10.1109/JSEN.2016.2621057.
[4]
TIAN Y, SHI H, and XU H. DOA estimation in the presence of unknown nonuniform noise with coprime array[J]. Electronics Letters, 2016, 53(2): 113-115. doi: 10.1049/ el.2016.3944.
[5]
HU R, FU Y, CHEN Z, et al. Robust DOA estimation via sparse signal reconstruction with impulsive noise[J]. IEEE Communications Letters, 2017, 21(6): 1333-1336. doi: 10.1109/LCOMM.2017.2675407.
[6]
MALIOUTOV D, CETIN M, and WILLSKY A S. A sparse signal reconstruction perspective for source localization with sensor arrays[J]. IEEE Transactions on Signal Processing, 2005, 53(8): 3010-3022. doi: 10.1109/TSP.2005.850882.
[7]
PAL P and VAIDYANATHAN P P. A grid-less approach to underdetermined direction of arrival estimation via low rank matrix denoising[J]. IEEE Signal Processing Letters, 2014, 21(6): 737-741. doi: 10.1109/LSP.2014.2314175.
[8]
PESAVENTO M and GERSHMAN A B. Maximum- likelihood direction-of-arrival estimation in the presence of unknown nonuniform noise[J]. IEEE Transactions on Signal Processing, 2002, 49(7): 1310-1324. doi: 10.1109/78.928686.
[9]
HE Z Q, SHI Z P, and HUANG L. Covariance sparsity-aware DOA estimation for nonuniform noise[J]. Digital Signal Processing, 2014, 28(1): 75-81. doi: 10.1016/j.dsp.2014.02. 013.
[10]
YIN J H and CHEN T Q. Direction-of-arrival estimation using a sparse representation of array covariance vectors[J]. IEEE Transactions on Signal Processing, 2011, 59(9): 4489-4493. doi: 10.1109/TSP.2011.2158425.
[11]
LIAO B, GUO C, HUANG L, et al. Matrix completion based direction-of-arrival estimation in nonuniform noise[C]. IEEE International Conference on Digital Signal Processing, Beijing, China, 2017: 66-69. doi: 10.1109/ICDSP.2016. 7868517.
[12]
CANDES E J and RECHT B. Exact matrix completion via convex optimization[J]. Foundations of Computational Mathematics, 2009, 9(6): 717-772. doi: 10.1007/s10208-009- 9045-5.
[13]
CANDES E J and PLAN Y. Matrix completion with noise[J]. Proceedings of the IEEE, 2009, 98(6): 925-936. doi: 10.1109 /JPROC.2009.2035722.
[14]
JIANG X, ZHONG Z, LIU X, et al. Robust matrix completion via alternating projection[J]. IEEE Signal Processing Letters, 2017, 24(5): 579-583. doi: 10.1109/LSP. 2017.2685518.
[15]
CANDES E J, WAKIN M B, and BOYD S P. Enhancing sparsity by reweighted L1 minimization[J]. Journal of Fourier Analysis & Applications, 2008, 14(5): 877-905. doi: 10.1007/ s00041-008-9045-x.
FANG Qingyuan, HAN Yong, JIN Ming, et al. DOA estimation based on eigenvalue reconstruction of noise subspace[J]. Journal of Electronics & Information Technology, 2014, 36(12): 2876-2881. doi: 10.3724/SP.J.1146.2013.02014.
[17]
SUN S and PETROPULU A P. Waveform design for MIMO radars with matrix completion[J]. IEEE Journal of Selected Topics in Signal Processing, 2015, 9(8): 1400-1414. doi: 10.1109/JSTSP.2015.2469641.
[18]
CAI J F, CANDES E J, and SHEN Z. A singular value thresholding algorithm for matrix completion[J]. SIAM Journal on Optimization, 2010, 20(4): 1956-1982. doi: 10.1137/080738970.
[19]
HOR R A and JOHNSON C R. Matrix Analysis[M]. Cambridge, U.K: Cambridge University Press, 1985: 1-162.
[20]
GRANT M and BOYD S. CVX: Matlab software for disciplined convex programming, version 2.1[OL]. http:// cvxr.com/cvx, Jun.2015.
FENG Mingyue, HE Minghao, XU Jing, et al. High accuracy DOA estimation under low SNR condition for wideband underdetermined signals[J]. Journal of Electronics & Information Technology, 2017, 39(6): 1340-1347. doi: 10.11999/JEIT160921.
[22]
OTTERSTEN B, STOICA P, and ROY R. Covariance matching estimation techniques for array signal processing applications[J]. Digital Signal Processing, 1998, 8(3): 185-210. doi: 10.1006/dspr.1998.0316.
[23]
TIAN Y, SUN X, and ZHAO S. DOA and power estimation using a sparse representation of second-order statistics vector and l0-norm approximation[J]. Signal Processing, 2014, 105(12): 98-108. doi: 10.1016/j.sigpro.2014.05.014.
[24]
LOBO M, VANDENBERGHE L, BOYD S, et al. Application of second-order cone programming[J]. Linear Algebra and its Applications, 1998, 284(1/3): 193-228. doi: 10.1016/S0024- 3795(98)10032-0.
[25]
LIAO B, CHAN S C, HUANG L, et al. Iterative methods for subspace and DOA estimation in nonuniform noise[J]. IEEE Transactions on Signal Processing, 2016, 64(12): 3008-3020. doi: 10.1109/TSP.2016.2537265.
