In addition, the performance and the efficiency of the proposed method are not affected significantly by the correlation between the received signals, which permits us to estimate not only wideband incoherent signals but also wideband coherent signals. The simulation results for DOA estimation of wideband signals using the proposed method will be shown and analyzed to verify its performance.
Nghiên cứu khoa học công nghệ A NOVEL METHOD FOR DOA ESTIMATION OF WIDEBAND SIGNALS BASED ON TOTAL FORWARD-BACKWARD MATRIX PENCIL ALGORITHM Han Trong Thanh1*, Vu Van Yem1 Abstract: Direction Of Arrival (DOA) estimation for wideband signals has been drawing a lot of research interest recently In this paper, a novel method based on Total Forward-Backward Matrix Pencil (TFBMP) algorithm to estimate the direction of arrival of wideband signals using a Uniform Linear Antenna Array (ULA) is proposed TFBMP is an extension of Matrix Pencil algorithm that works directly on signal samples received by an M – element ULA One of the most remarkable advantages of the method is that it can extract the DOA information with one snapshot, which means that the sampling frequency in real time receivers as well as implementation cost of the system can be considerably reduced In addition, the performance and the efficiency of the proposed method are not affected significantly by the correlation between the received signals, which permits us to estimate not only wideband incoherent signals but also wideband coherent signals The simulation results for DOA estimation of wideband signals using the proposed method will be shown and analyzed to verify its performance Keywords: Direction of arrival (DOA); Wideband signal; Matrix Pencil (TFBMP), Uniform Linear Antenna Array (ULA) Total Forward-Backward INTRODUCTION Wideband signals are widely used in wireless localization system such as Radar, Sonar or Direction Finding (DF) systems Several techniques to estimate the Direction Of Arrival of wideband signals have been investigated recently [1-9] In order to that most of them decompose the incident wideband signals into narrowband bins, and then extract the DOA information by using high resolution DOA techniques such as MUSIC, ESPRIT [1-4] In [10-14], the Matrix Pencil algorithm was proposed as a high – resolution technique to estimate the DOA of the incoming radio signals Matrix Pencil (MP) has some advantages in comparison to the other super – resolution methods for DOA estimation such as MUSIC, ESPRIT, which generally have to calculate the signal covariance matrix Unlike other algorithms, Matrix Pencil works directly on signal samples and does not require independent data samples Furthermore, the Matrix Pencil algorithm offers some benefits such as less processing power and faster executing than some other ones [12] One of the most remarkable advantages of this technique is that it can extract the DOA information with one snapshot Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Điện tử, 10 - 2015 225 Kỹ thuật điện tử The Total Forward – Backward Matrix Pencil (TFBMP) algorithm is an extension of the Matrix Pencil Method [15] The Total Forward – Backward is the preprocessing technique to break the correlative property of the received signals [16-17] Therefore, this fact helps the Matrix Pencil method to estimate the DOA information of the incoming signals with the higher accuracy [18], especially in a high correlative environment TFBMP was utilized for the high – resolution frequency estimator In some scenarios, it provides better estimation results than the other methods such as Fourier technique [15] In [18], the DOA information of the narrowband coherent incoming signals can be successfully determined However, the DOA of wideband signals had not been mentioned yet In this paper, we propose a method based on the TFBMP to estimate the DOA information of wideband incoming signals received by an M – element Uniform Linear Antenna (ULA) array In order to that we have to divide the received wideband signals into several narrowband bins by using the Discrette Fourier Transform (DFT) method [4,9] and then estimate the DOA information of incoming signals in each bin The performance of this method will be assessed in many cases that depend on the characteristics of incoming signals as well as number of snapshots of data The paper is organized as follows Section II describes the model of the incoming signals In section III, we present in detail the TFBMP technique for DOAs estimation of wideband signals The simulation results are shown in the section IV The conclusion is given in the section V SIGNAL MODEL Fig Antenna array in the coordinate system In this research, an element Uniform Linear Antenna Array (ULA) is used This is one of the most convenient mathematical models for array processing due to its simplicity and regularity The ULA model can be described as a set of isotropic antenna elements spaced at a uniform interval along some line in space The reference point has been defined as the origin of the three – Dimensional – 226 H T Thanh, V V Yem “A novel method for DOA … matrix pencil method.” Nghiên cứu khoa học công nghệ Cartesian – coordinate system shown in Fig.1 In Fig.1, we assume that the incoming signals at the far field of the array impinging on the ULA are wideband and have DOA information in both elevation and azimuth ( ) However, this work concerns about the signals in the same plane with antenna array This means that we estimate the DOA of signals of interest in azimuth, , and In practice, there are several radio signals crossing the antenna array simultaneously The received signal at each antenna element will be the sum of all arriving radio signals In case of signals approaching the array from some azimuth directions , according to [4-6], the wideband signal received at the antenna element can be modeled as (1) where is the incoming signal; is noise at the antenna element, which is assumed to be uncorrelated with the signal sources and is white noise in both temporal and spatial domain; , in which is the distance between the element and the reference point, and is the speed of the signal propagation Assuming the array manifolds of different DOAs are independent In other words, array manifolds with different DOAs should span a dimensional subspace Moreover, considering the number of signal sources is either known or can be estimated The bandwidths of the wideband sources need not be identical, but there should be some frequency band where and are minimum and maximum angular frequency of wideband signal spectrum, respectively In order to ensure the Fourier transform of the output signal at each antenna element has a good resolution, we suppose the observation time is long enough Then the DFT of the element output is (2) Equation (2) describes the received wideband signals at each antenna element in frequency domain In order to estimate the DOA information, this signal is splitted into several narrowband bins using filter banks or the DFT technique If the intersection of the frequency bands of all incoming signals is , then the output of the filter bank or DFT module can be written in frequency vector form as follows: (3) where is number of bins and (4) Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Điện tử, 10 - 2015 227 Kỹ thuật điện tử (5) In which is the denotes transpose matrix, steering matrix: with , (6) The columns of the matrix are the frequency The array manifold is defined as array manifolds at (7) where and is the DOA of the incoming signal DOA ESTIMATION BASED ON TFBMP In , Equation (2) can be rewritten as bin, let (8) According to [15,18], the DOA information could be extracted by using TFBMP with the following steps Step – Hankel Matrix Establishment: The Hankel matrix of could be written as: X0 X Ym X M L 1 X1 X2 XL XL X L 1 X M 1 ( M L ) x ( L 1) (9) where are the Pencil parameter Because of the efficient noise filtering issue described in [10], is chosen with the conditions as: , if is even (10) , if is odd Step – Complex conjugate Matrix Establishment: Based on Equation (9), the matrix is established as: X L 1 * XL * X * XL * Yb L 1 X M 1 * X M * X0 * X * X M L 1 * ( M L )( L 1) where symbol denotes the complex conjugate Step – All Data Matrix Establishment: The “All data” matrix defined as follow: (11) can be (12) 228 H T Thanh, V V Yem “A novel method for DOA … matrix pencil method.” Nghiên cứu khoa học công nghệ The matrix will be processed to get the DOA information For noisy data, based on [10], the best way is to perform a Singular Value Decomposition (SVD) on The SVD of is given as: (13) where the characters denotes conjugate transpose and are unitary matrices and is the diagonal matrix which is composed by the singular values (SVs) of : where The matrix can be divided into two subspace and is a diagonal matrix This matrix has largest SVs in main diagonal and displays the signal subspace as , ,…, ,…, , where is the variance of noise of relative SVs is the diagonal matrix with smallest SVs in main diagonal: , ,…, , where is the variance of noise of relative SVs This matrix characterizes the additive noise subspace Similar to the above analysis, can also be separated into two spaces: noise subspace and signal subspace as: (14) Step – All Data Matrix Decomposition: Based on the properties of SVD operation can be rewritten as follow: , where and are matrices, are obtained from In matlab, and and are matrix can be presented as (15) and (16) (17) Step – DOA Estimation: As above analysis, the DOA information could be gathered from It can be seen that the can be extracted from matrix In order to that, two matrices and are created by deleting the last and the first columns from After that, the matrix will be established, in which is Moore – Penrose pseudo – inverse of as (18) is a matrix This matrix has the eigenvalues which is the value of Therefore, by using the values of the generalized eigenvalues of , angles of arrival can be estimated as (19) where is the imaginary part of Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Điện tử, 10 - 2015 229 Kỹ thuật điện tử SIMULATION RESULTS The proposed method is simulated using Matlab to examine its performance for DOA estimation of far field wideband incoming signals which are assumed as a sum of complex exponentials as follow: (20) where the amplitude is a Rayleigh random variable; the phase is uniformly distributed in and is the number of frequency components of wideband incoming signal In our research, we suppose that the wideband signals impinge on an – element antenna array These signals are based on IEEE 802.15.4a standard [19] and they can be divided into 11 bins ( ), in which and are the minimum and maximum frequency of wideband signal spectrum, respectively In our simulation, we choose the Pencil parameter and inter – spacing of antenna array , where with is the frequency center of the selected narrowband signal bin Table The DOAs (Degrees) estimated in each narrow bins Bin Bin Bin Bin Bin Bin Bin Bin Bin Bin 10 Bin 11 9.56 10.09 9.96 10.28 10.38 9.91 10.04 10.06 10.05 9.71 10.25 -29.71 30.28 29.73 30.33 30.01 29.91 29.49 29.80 30.11 29.83 29.88 59.85 60.58 58.96 60.43 60.13 60.16 60.67 59.96 60.05 60.18 59.86 In the first simulation, the proposed method is executed to estimate the DOAs of three incoming signal at in the AWGN channel with SNR = 10dB The simulation results in each bin are presented in the table In this table, we can see that the DOAs are estimated accurately for all bins However, in order to get the best result, the average value in each row is calculated and choosed as the final estimated DOA information The final result is plotted in Figure 230 H T Thanh, V V Yem “A novel method for DOA … matrix pencil method.” Nghiên cứu khoa học công nghệ Fig DOA estimation with snapshot Fig Estimation accuracy of DOA estimation with one snapshot However, we need to note that the estimated DOAs in the simulation are the numerical values as in Eq.19 Therefore, in order to demonstrate visually the results, we illustrate the DOA in XOY plane, in which the X – Axis is the DOA of incoming signal and the Y – Axis is the indicating factor This factor is set to corresponding to the estimated DOA in X - Axis In Figure 2, it can be seen that the DOAs are estimated accurately by the proposed method with very small error Figure presents the performance of the proposed method in the AWGN channel with the variable SNRs from −10dB to 20dB The simulation result also indicates that the proposed method works well in white noise environment although with one snapshot Figure illustrates the DOA estimation accuracy of the TFBMP and the original MP method with the above incoming signals From this figure, it is easy to see that TFBMP is more efficient than MP Obviously, DOA estimation with only one snapshot is the remarkable advantage in comparison with other super high resolution methods In similar situation, the DOA information could not be estimated by the MUSIC algorithm as shown in Fig.5 The fact is due to the inaccurate estimate of the correlation matrix Fig DOA estimation accuracy of TFBMP and MP Fig.5 DOA estimation using MUSIC with one snapshot The angle resolution of this method is also a factor to be assessed In order to that this algorithm is performed to estimate the DOA of some pairs of incoming wideband signals whose SNRs are set to 10dB with one snapshot The simulation results are stored in Table If we consider the RMSE of desired results less than degrees, from Table 2, it can be seen that this method will work well with the resolution approximately degrees This result is similar to the MP However, the Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Điện tử, 10 - 2015 231 Kỹ thuật điện tử resolution of this method is less than other super high resolution algorithms such as MUSIC Obviously, this is the drawback of the method Table Angle resolution for wideband signals Assumed DOA (Degrees) Estimated DOA (Degrees) RMSE (Degrees) 41 40 40.3756 -10.9878 36.0566 42 40 46.4804 40.3794 3.1795 43 40 42.1109 39.5665 0.6994 44 40 44.6997 40.1236 0.5024 Moreover, in order to evaluate the influence of the number of snapshot on the performance of this algorithm, this method is executed with the same inputs as above with 1000 snapshots The simulation results plotted in Figure and Figure show that when we increase the number of snapshots, the accuracy of this method increases significantly However, it can be observed that when the number of snapshots is more than 300, the accuracy of the algorithm seems to be invariable On the other hand, when the number of snapshot is increased, the computation time also significantly increases Therefore, the trade – off between the computation time and the accuracy of the algorithm should be taken into account Fig DOA estimation with 1000 snapshots Fig Estimation accuracy of DOA estimation with the different number of snapshot CONCLUSIONS We propose an efficient method for DOA estimation of wideband signals by using Total Forward – Backward Matrix Pencil algorithm The remarkable advantage of the proposed method is that it can extract accurately the DOA information with only one snapshot This fact reduces significantly the computation time in comparison with other high resolution algorithms as well as the sampling frequency and the size of buffer in real time receivers Therefore, the 232 H T Thanh, V V Yem “A novel method for DOA … matrix pencil method.” Nghiên cứu khoa học công nghệ proposed method is one of the practical ways to estimate the DOAs information of wideband signals in real application Acknowledgment: This research is carried out in the framework of the project titled “Design and Implementation of an Earth Station based on Software Defined Radio in the satellite communication system” in the national program on space technology under the grant number VT/CN-02/14-15 This research is funded by the Vietnam Academy of Science and Technology The authors would like to thank the Vietnam Academy of Science and Technology and the Ministry of Science and Technology, Vietnam for their financial support REFERENCES [1] Schmidt R O "Multiple emitter location and signal parameter estimation," IEEE Transactions on Antennas and Propagation, vol 34 (1986), pp 276-280 [2] Hirata A., Morimoto T., and Kawasaki Z "DOA estimation of ultra-wideband EM waves with MUSIC and interferometry," IEEE antennas and wireless propagation letters, vol.2 (2003), pp 190-193 [3] Zhou L., Zhao Y.-j., and Cui H "High resolution wideband DOA estimation based on modified MUSIC algorithm," in International Conference on Information and Automation, (2008), pp 20-22 [4] Ottersten B and Kailath T "Direction-of-arrival estimation for wide-band signals using the ESPRIT algorithm," IEEE Transactions on Acoustics, Speech and Signal Processing, vol 38 (1990), pp 317-327 [5] Yoon Y.-S., Kaplan L M., and McClellan J H "Direction-of-arrival estimation of wideband sources using arbitrary shaped multidimensional arrays," in IEEE International Conference on Acoustics, Speech, and Signal Processing, vol (2004), pp ii-221-4 [6] Liu Z.-M., Huang Z.-T., and Zhou Y.-Y "Direction-of-arrival estimation of wideband signals via covariance matrix sparse representation," IEEE Transactions on Signal Processing, vol 59 (2011), pp 4256-4270 [7] Xia B and Wang W "Estimation method of DOA for DS-UWB signal," Journal of University of Electronic Science and Technology of China, vol 36 (2007), pp 190-192 [8] Wang F and Zhang X "Joint estimation of TOA and DOA in IR-UWB system using sparse representation framework," ETRI Journal, vol 36 (2014), pp 460-468 [9] Yoon Y.-S., Kaplan L M., and McClellan J H "TOPS: new DOA estimator for wideband signals," IEEE Transactions on Signal Processing, vol 54 (2006), pp 1977-1989 Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san Viện Điện tử, 10 - 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Backward Matrix Pencil Method,” in Proc.International Conference on Communications and Electronics (ICCE), Danang, Vietnam (2014), pp 718 - 722 [19] Karapistoli E., Pavlidou F.-N., et al "An overview of the IEEE 802.15 4a standard," IEEE Communications Magazine, vol 48 (2010), pp 47-53 Nhận ngày 21 tháng 07 năm 2015 Hoàn thiện ngày 10 tháng 08 năm 2015 Chấp nhận đăng ngày 07 tháng 09 năm 2015 Address: School of Electronics and Telecommunications, Hanoi University of Science and Technology, Vietnam * 234 Email: Thanh.hantrong@hust.edu.vn; H T Thanh, V V Yem “A novel method for DOA … matrix pencil method.” ... snapshot CONCLUSIONS We propose an efficient method for DOA estimation of wideband signals by using Total Forward – Backward Matrix Pencil algorithm The remarkable advantage of the proposed method. .. subspace and is a diagonal matrix This matrix has largest SVs in main diagonal and displays the signal subspace as , ,…, ,…, , where is the variance of noise of relative SVs is the diagonal matrix. .. computation time and the accuracy of the algorithm should be taken into account Fig DOA estimation with 1000 snapshots Fig Estimation accuracy of DOA estimation with the different number of snapshot