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An Improved 2-D DOA Estimation with L-shaped Arrays Based on PM [Sensors & Transducers (Canada)](Sensors & Transducers (Canada) Via Acquire Media NewsEdge) Abstract: In this paper, an improved two-dimensional (2-D) direction of arrival (DOA) estimation method is proposed for narrow signals impinging on an L-shaped arrays. Based on the propagator method (PM), the computational loads of the proposed method can be significantly smaller since the PM does not require any eigenvalue decomposition of the received data. With a propagator matrix, the proposed method constructs a new extended matrix to estimate the elevation angle, which improves the DOA estimation performance in low SNR. By exploiting the covariance matrix of the received data, another propagator matrix is achieved, then pair matching and peak searching are used to achieve the corresponding 2-D azimuth angles, which reduces the occurrence of estimation failure and errors. In the case of DOA estimation for two signals, at RMSE = 0.2, the proposed method results in a gain improvement of about 5dB over the joint singular value decomposition (SVD) method and 9.5 dB over the PM method. Copyright © 2014 IFSA Publishing, S. L. Keywords: 2-D DOA, L-shaped, PM, low SNR, SVD. (ProQuest: ... denotes formulae omitted.) 1. Introduction Recently, two-dimensional (2-D) direction of arrival (DOA) estimation has received a significant amount of attention [1, 2]. It plays an important role in array processing for improving the quality of the wireless communication [3]. Many effective methods have been proposed for DOA estimation based on the uniform rectangular array (URA) [4] and uniform circular array (UCA) [5]. However, these methods need a large number of sensors to achieve high resolution and give accurate estimates. In reference [6], a 2-D DOA estimation method with two parallel uniform linear arrays is proposed to resolve the uncorrelated signals. However, this method can not resolve signals that have a common direction ß, and since there are only two sensors in the y-axis direction, the accuracy of angles ß may not be high. In reference [7], it has been proven that the L-shaped array has better estimation than many other simple structured arrays. There has been growing interest in developing 2-D DOA estimators by exploiting L-shaped arrays. Tayem et al. proposed a propagator method (PM) based on L-shaped arrays [8]; however, the independent eigenvalue decompositions cause arbitrary ordering of the eigenvalues. Kikuchi et al. [9] proposed a cross correlation matrix method based on ESPRIT, which has problems at low SNR and encounters estimation failure for small angular separation azimuth angles. The joint singular value decomposition (SVD) method [10] can achieve automatic pairing for 2-D angle estimation, but it performs worse in the estimation of azimuth angle when the number of snapshots is small, furthermore they are computationally intensive because of using SVD. This paper proposes an effective method for 2-D DOA estimation of signals with a L-shaped array. The proposed method constructs a new propagator matrix to estimate the elevation angle in the same way as the improved PM method [11] with two parallel uniform linear arrays, which improves the performance in low SNR. And the proposed algorithm can achieve automatically paired twodimensional angle estimation. Finally, numerical simulations show that the proposed method has a higher resolution than the PM method and the joint SVD method of the L-shaped array. This paper is organized as follows. In section 2, the signal model is described. The proposed method is presented in section 3. Then section 4 gives the computer simulation results. Finally, conclusion is presented in Section 5. 2. Signal Model Fig. 1 shows the L-shape array configuration which uses x-z plane. Each linear array consists of N omnidirectional element sensors with adjacent spacing d. Suppose that there are K far-field narrow band signal s*(t) (k= impinging on the arrays, where X is the carrier wavelength. The signal Sk(t) has an elevation angle Ok and an azimuth angle (pk. Let the N x 1 signal vectors received at the X and Z subarray be Xi(t) = [*i(f), x2(t),..., xnÍOY, and Zi(t) = [z\(t), z2(t),..., zidt)Y, respectively, where the superscript T denotes the transpose. Also let the (N-1) x l signal vectors received at the X and Z subarrays be X2(t) = [x\(t)jc2(t),...jcN-\(t)Y and Z2(t)=[zi(í), z2(t),..., zN.i(t)Y, respectively. These received vectors at the Z and X subarray can be rewritten as ... (1) ... (2) ... (3) ... (4) ... (5) ... (6) ... (7) where ... nzl(í), nz2(í), nxl(í) and nx2(i) are additive white Gaussian noise vectors whose elements have mean zero and variance o2. The matrix Oj and 02 is a K*K diagonal matrix containing information bout the elevation angle Ok and azimuth angle (fk, respectively. 3. Proposed Method 3.1. Estimation of Elevation Angles Combining the signal vector Zi(t) and Z2(t), obtain a (2N -1) x 1 vector as ... (8) where Nz(0 = [nl,(0,<2(0f. Partition the matrix A as ... (9) where Ai and A2 are the matrices of dimension K*K and (2N-\-K)xK, respectively. Assume that Z(t) are constant for J samples, then the covariance matrix of the received data in Z subarray can be written as ... (10) where the superscript H denotes the conjugate transpose. As in [11], Rz is partitioned as Rz= [Rzi R^], where Rzi and Rz2 are matrices of dimension (2N-\)xKand (2N-\)x(2N-\-K), respectively. And in the noiseless case ... (11) where Pz is the propagator matrix. And the matrix Pz . . . , can be estimated by ... (12) With Pz, construct a new extended matrix as follow ... (13) Then partition Pci as ... (14) where Px and Py are the matrices of dimension NxK and (N-l)xK, respectively. Let Pi denote the first N rows of Px, and we have ... (15) ... (16) Define a new matrix as ... (17) where the superscript # denotes the pseudoinverse transpose. Then perform the eigenvalue decomposition of *Py, and the eigenvalues are corresponding to the elevation angle Ok(k =1, ... ,K). 3.2. Estimation of Azimuth Angles Define a (2AM) x l vector as ... (18) where Nx(0 = [nTxl(t),nTx2(t)f. The covariance matrix of the received data in X subarray is ... (19 which is partitioned as Rx= [Rxi R^], where Rxi and Rx2 are matrices of dimension (2N-])*K and (2N-1 ) x (2N-1-K), respectively. And the propagator matrix can be estimated by ... (20) then define a new matrix Pc2 , and partition PC2 as ... (21) where Px2 and Py2 are the matrices of dimension N*K and (N-l)xK, respectively. Let Qx denote the first N rows of Px2, then the /¿h azimuth angle (pk can be found from the maximum peaks of the following formula ... (21) (15) 3.3. Summary of the Algorithm In this paper, the 2-D DOAs of multiple signals are estimated at two different stages. First, with the improved PM method [11], a new propagator matrix Pci is constructed, which use fully all elements of the array. It can obtain good performance in 2-D DOA estimation of elevation angles, especially under low SNR situation. Second, the matrix Qx is achieved to associate the azimuth angles with the corresponding elevation angles in the proposed method, and the peak searching procedure improves the performance of DOA estimation. 4. Numerical Results Computer simulations are carried out to illustrate the performance of the proposed method. The elements of each ULA with N = l\ sensors were separated by a half-wavelength. 300 Monte Carlo trials were performed for each experiment. In the first simulation, there are K= 2 signals impinging on the array. The DOAs of elevation and azimuth angles are (45°, 45°) and (60°, 30°). The number of the snapshots is 200 with a SNR of 10 dB. Fig. 2 shows that the proposed method can estimate the DOAs of all the signals. In the second simulation, there are K= 2 signals impinging on the array from the DOAs (65°, 70°) and (40°, 55°). Fig. 3 shows the root mean square error (RMSE) of the joint elevation and azimuth angle estimation versus the SNR in dB, using the proposed 210method, the PM method and the joint SVD method. The number of the snapshots is 500, and the SNR is varied from -5 dB to 30 dB. The RMSE is defined as ... (23) where P is the number of the independent trials. It can be observed that at RMSE = 0.2, the proposed method achieves a gain improvement of about 5 dB over the joint SVD method, and about 9.5 dB over the PM method. In the third simulation, Fig. 4 describes the detection probability versus the number of signals. The snapshot is 100 and SNR is 3 dB, respectively. The result illustrates that the success rate of the proposed method is better than that of the joint SVD method and the PM method, when the number of snapshots is small and the SNR is low. 5. Conclusion A new method for estimating 2-D angles of wave arrival is proposed using L-shaped ULAs. The proposed method constructs a new propagator matrix to estimate the elevation angle, which improves the performance in low SNR. Then the automatic pair matching method is used to achieve the corresponding 2-D angles. Simulation results show that the proposed method has better 2-D DOA estimation accuracy. Acknowledgements The authors would like to thank Dr. Tang Lan for her valuable advice. This work is supported by Industry-academic Joint Technological Innovations Fund Project of Jiangsu Province (BY2012187). References [1]. K. Yohan, Kim Yeungjun, Hyunll Yoo, et al, 2-D DOA estimation with cell searching for a mobile relay station with uniform circular array, IEEE Transactions on Communications, Vol. 58, Issue 10, 2010, pp. 2805-2809. [2]. J. Bach Andersen, Antenna arrays in mobile communications: gain, diversity, and channel capacity, IEEE Antennas and Propagation Magazine, Vol. 42, Issue 2,2000, pp. 12-16. [3]. E. Ben Dor, T. S. Rappaport, Qiao Yijun, et al, Millimeter-wave 60 GHz outdoor and vehicle AOA propagation measurements using a broadband channel sounder, in Proceedings of the IEEE Global Telecommunications Conference, 2011, pp. 1-6. [4]. M. D. Zoltowski, K. T. Wong, ESPRIT-based 2-D direction finding with a sparse uniform array of electromagnetic vector sensors, IEEE Transactions on Signal Processing, Vol. 48, Issue 8, 2000, pp. 2195-2204. [5]. R. J. Weber, Huang Yikun, Performance analysis of direction of arrival estimation with a uniform circular array, IEEE Aerospace Conference, 2012, pp. 1-7. [6]. Q. Y. Yin, R. W. Newcomb, L. H. Zou, Estimating 2D D of arrival via two parallel linear arrays, in Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, Vol. 3, 1989, pp. 2803-2806. [7]. Y. Hua, T. K. Sarkar, D. D. Weiner, An L-shaped array for estimating 2-D directions of wave arrival, IEEE Transactions on Antennas and Propagation, Vol. 39, Issue 2, 1991, pp. 143-146. [8]. N. Tayem, H. M. Kwon, L-shaped 2-dimensional arrival angle estimation with propagator method, IEEE Transactions on Antennas and Propagation, Vol. 53, Issue 5,2005, pp. 1622-1630. [9]. S. Kikuchi, H. Tsuji, A. Sano, Pair-matching method for estimating 2-D angle of arrival with a crosscorrelation matrix, IEEE Antennas and Wireless Propagation Letters, Vol. 5, Issue 1,2006, pp. 35-40. [10]. Gu Jianfeng, Wei Ping, Joint SVD of two crosscorrelation matrices to achieve automatic pairing in 2-D angle estimation problems, IEEE Antennas and Wireless Propagation Letters, Vol. 6, 2007, pp. 553-556. [11]. Li Jianfeng, Zhang Xiaofei, Chen Han, Improved two-dimensional DOA estimation algorithm for twoparallel uniform linear arrays using propagator method, Signal Processing, Vol. 92, Issue 12, 2012, pp. 3032-3038. Chunhua Yu, Xinggan Zhang, Xiaojun Qiu, and Yechao Bai School of Electronic Science and Engineering, Nanjing University, Nanjing 210046, China Tel: +86-13382029502, fax: +86-25-8968-7772 E-mail: [email protected] Received: 25 June 2014 /Accepted: 29 August 2014 /Published: 30 September 2014 (c) 2014 IFSA Publishing, S.L. |