Robust Direction of Arrival Estimation of Wideband LFM Signals using Dechirping Algorithms with a few Snapshots in the Linear Array
Subject Areas : Electronics Engineering
Abbas Partovi Sangi
1
(
Department of Electrical Engineering, Kazerun Branch, Islamic Azad University, Kazerun, Iran
)
Jasem Jamali
2
(
Department of Electrical Engineering, Kazerun Branch, Islamic Azad University, Kazerun, Iran
)
Mohammad Hossein Fatehi Dindarlou
3
(
Department of Electrical Engineering, Kazerun Branch, Islamic Azad University, Kazerun, Iran
)
Mohammad Mehdi Ghanbarian
4
(
Department of Electrical Engineering, Kazerun Branch, Islamic Azad University, Kazerun, Iran
)
Keywords: LFM signals, FFT Transform, ULA.Dechirping algorithm, MSPICE method,
Abstract :
Wideband linear frequency modulation (LFM) signals are widely used in systems such as radar, sonar and mobile. DOA estimation algorithms LFM signals rely on a large number of time frames (Snapshot). Therefore, they are not suitable for low power and real-time applications. In this paper, we present a low computation based estimation method based on the SPICE algorithm for linear arrays using the Fourier transform FFT. The method is to first develop the dechirping algorithm for LFM signals using the FFT converter, then modify the SPICE algorithm for uniform linear arrays (ULA), then obtain the DOA calculations for a few number of snapshots with low computational volumes. The simulation results of the proposed MSPICE algorithm (i.e. modified SPICE algorithm) show that the proposed algorithm is better than other algorithms such as MUSIC and SPICE. We have shown that the proposed method has acceptable accuracy in both low SNRs and low error in high SNRs. In addition, in terms of computational volume, it is much less than the MUSIC and SPICE methods and will have a good robustness compared to other methods.
[1] B. R. Jackson, S. Rajan, B. J. Liao and S. Wang, "Direction of Arrival Estimation Using Directive Antennas in Uniform Circular Arrays," in IEEE Transactions on Antennas and Propagation, vol. 63, no. 2, pp. 736-747, Feb. 2015, doi: 10.1109/TAP.2014.2384044.
[2] G. Chen, H. Hong, Y. Li, X. Zhu and J. He. “Highly Accurate Multi-Invariance ESPRIT for DOA Estimation with a Sparse Array.” Mathematical Problems in Engineering,pp.1-7, 2019, doi:10.1155/2019/5325817.
[3] F.Heidari, "Estimation for signal reception in mobile smart antennas", Journal of Communication Engineering (JCE),vol.6,no.22, 2016 (in persian).
[4] X. Jing, B. G. Sun, Y. Cao and W. J. Hong. "DOA estimation based on fractional low-order multi-sensor time-frequency analysis in heavy tailed noise", Journal of Physics: Conference Series,vol.1812,no.1, 2021, doi:10.1088/1742-6596/1812/1/012007.
[5] Z. Li, L. Song, H. Shi, et al., "Approaching the capacity of k-user MIMO interference channel with interference counteraction scheme", Ad Hoc Netw.,vol.58,pp.286-291,2017, doi: 10.1016/j.adhoc.2016.02.009
[6] A. Ahmadi and A. Mallahzadeh," Simulation and comparison of array algorithms based on MMSE criterion in different frequency selector feeding conditions", Journal of Communication Engineering (JCE),vol.6,no.24, 2017(in persian).
[7] M. Rahimi.kazeroni and Gh. Ravaei, " Synthesis of linear array of antennas by Newton binomial method to reduce the level of lateral petals of the beam", Journal of Communication Engineering (JCE), vol.6, no.24,2017(in persian).
[8] R. Mulinde, et al., "DOA estimation of wideband LFM RADAR signals," International Radar Conference (RADAR), 2019, pp. 1-6, doi: 10.1109/RADAR41533.2019.171357.
[9] L. Zhang, C.Y. Hung, J. Yu and K.Lu, " Linear Chirp Signal DOA Estimation Using Sparse Time–Frequency Dictionary", Int J Wireless Inf Networks, vol.27,no.5, pp.568-574,2020, DOI:10.1007/s10776-020-00489-1 .
[10] E. Dubrovinskaya, V. Kebkal, O. Kebkal, K. Kebkal and P. Casari,"Underwater Localization via Wideband Direction-of-Arrival Estimation Using Acoustic Arrays of Arbitrary Shape. Sensors (Basel)", in IEEE OCEANS-MTS Conf., 2019,doi: 10.1109/OCEANSE.2019.8867262.
[11] P. Stoica, P. Babu and J. Li, "New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data", IEEE Trans. Signal Process, vol.59,no.1, pp.35–46, 2011, doi: 10.1109/TSP.2010.2086452.
[12] P. Luo, K. -h. Liu, W. -g. Shi and G. Yan, "2-D DOA estimation of wideband LFM signals for arbitrary planar array," IEEE 10th INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING PROCEEDINGS, 2010, pp. 307-310, doi: 10.1109/ICOSP.2010.5656080.
[13] J. Xu, L. Lan, X. He, S. Zhu, C. Zeng, G. Liao and Y. Zhang,"System Design and Signal Processing for Frequency Diverse Array Radar", JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, vol.30,no.1, pp.1-19, 2021, doi: 10.15918/j.jbit1004-0579.2021.004.
[14] W. DU, D. L. SU, S. G. XIE, et al.,"A fast calculation method for the receiving mutual impedances of uniform circular arrays", IEEE Antennas and Wireless Propagation Letters, vol.11,pp.893–896, 2012, doi: 10.1109/LAWP.2012.2211329.
[15] P. Wang, Y. Li and B. Vucetic, "Millimeter Wave Communications With Symmetric Uniform Circular Antenna Arrays," in IEEE Communications Letters, vol. 18, no. 8, pp. 1307-1310, Aug. 2014, doi: 10.1109/LCOMM.2014.2332334.
[16] Z. Zhang, H.Wang and H.Yao,"Time Reversal and Fractional Fourier Transform-Based Method for LFM Signal Detection in Underwater Multi-Path Channel", Appl. Sci., vol.11,no.2,pp.583,2019, doi:10.3390/app11020583.
[17] G. Ben, X. Zheng, Y. Wang, N. Zhang and X. Zhang,,"A Local Search Maximum Likelihood Parameter Estimator of Chirp Signal", Appl. Sci., vol.11, no.2, pp. 673,2021, doi:10.3390/app11020673.
[18] M. Wang, X. Ma, S. Yan and C. Hao, "An Autocalibration Algorithm for Uniform Circular Array With Unknown Mutual Coupling," in IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 12-15, 2016, doi: 10.1109/LAWP.2015.2425423.
[19] PAN, Y. J., ZHANG, X. F., XIE, S. Y., et al.,"An ultra-fast DOA estimator with circular array interferometer using lookup table method," Radioengineering,vol. 24, no. 3, pp. 850–856,2015, doi:10.13164/re.2015.0850.
[20] V. JAIN and W. D. BLAIR,"Filter design for steady-state tracking of maneuvering targets with LFM waveforms", IEEE Transactions on Aerospace and Electronic Systems, vol. 45, no. 2, pp. 765–773, 2009, doi: 10.1109/TAES.2009.5089558.
[21] P. Wang, H. Li, I. Djurović and B. Himed, "Integrated Cubic Phase Function for Linear FM Signal Analysis," in IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 3, pp. 963-977, July 2010, doi: 10.1109/TAES.2010.5545167.
[22] M. KHODJA, A. BELOUCHRANI and K. ABED-MERAIM, "Performance analysis for time-frequency MUSIC algorithm in presence of both additive noise and array calibration errors", EURASIP Journal on Advances in Signal Processing, vol. 2012, no. 1, pp. 1–11,2012, doi: 10.1186/1687-6180-2012-94.
[23] J J. Lin, X. Ma, S. Yan and C. Hao, "Time-Frequency Multi-Invariance ESPRIT for DOA Estimation," in IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 770-773, 2016, doi: 10.1109/LAWP.2015.2473664.
[24] H. J. ZHANG, G. A. BI, Y. L. CAI, et al.,"DOA estimation of closely-spaced and spectrally-overlapped sources using a STFTbased MUSIC algorithm", Digital Signal Processing, vol. 52, pp. 25–34,2016, doi: 10.1016/j.dsp.2016.01.015
[25] W. YANG and Y. W. SHI,"FRFT based method to estimate DOA for wideband signal", Advanced Materials Research, vols. 712-715, pp. 2716–2720,2013, doi:10.4028/www.scientific.net/AMR.712-715.2716.
[26] Y. CUI and J. F. WANG,"Wideband LFM interference suppression based on fractional Fourier transform and projection techniques", Circuits Systems and Signal Process, vol. 33, no. 2, pp. 613–627,2019, doi: 10.1007/s00034-013-9642-z.
[27] A. Shaw and L. Alirkhis, "Wideband directions of arrival estimation of chirp sources using compressive sensing", Radar sensor technology XXII conference, 2018,pp. 57, doi: 10.1117/12.2316654.
[28] R. TAO, N. ZHANG and Y. WANG,"Analyzing and compensating the effects of range and Doppler frequency migrations in linear frequency modulation pulse compression radar", IET Radar, Sonar and Navigation, 2019, vol. 5, no. 1, pp. 12–22,2019, doi: 10.1049/iet rsn.2019.0265.
[29] J. SU, H. H. TAO, X. RAO, et al.,"Coherently integrated cubic phase function for multiple LFM signals analysis", Electronics Letters, vol. 51, no. 5, pp. 411–413,2020, doi: 10.1049/el.2020.4164.
[30] P. Stoica, P. Babu and J. Li, "SPICE: A Sparse Covariance-Based Estimation Method for Array Processing," in IEEE Transactions on Signal Processing,vol.59,no.2, pp. 629-638, Feb. 2011, doi: 10.1109/TSP.2010.2090525.
[31] P. Wang, Y. Li and B. Vucetic, "Millimeter Wave Communications With Symmetric Uniform Circular Antenna Arrays," in IEEE Communications Letters, vol. 18, no. 8, pp. 1307-1310, Aug. 2014, doi: 10.1109/LCOMM.2014.2332334.
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[1] B. R. Jackson, S. Rajan, B. J. Liao and S. Wang, "Direction of Arrival Estimation Using Directive Antennas in Uniform Circular Arrays," in IEEE Transactions on Antennas and Propagation, vol. 63, no. 2, pp. 736-747, Feb. 2015, doi: 10.1109/TAP.2014.2384044.
[2] G. Chen, H. Hong, Y. Li, X. Zhu and J. He. “Highly Accurate Multi-Invariance ESPRIT for DOA Estimation with a Sparse Array.” Mathematical Problems in Engineering,pp.1-7, 2019, doi:10.1155/2019/5325817.
[3] F.Heidari, "Estimation for signal reception in mobile smart antennas", Journal of Communication Engineering (JCE),vol.6,no.22, 2016 (in persian).
[4] X. Jing, B. G. Sun, Y. Cao and W. J. Hong. "DOA estimation based on fractional low-order multi-sensor time-frequency analysis in heavy tailed noise", Journal of Physics: Conference Series,vol.1812,no.1, 2021, doi:10.1088/1742-6596/1812/1/012007.
[5] Z. Li, L. Song, H. Shi, et al., "Approaching the capacity of k-user MIMO interference channel with interference counteraction scheme", Ad Hoc Netw.,vol.58,pp.286-291,2017, doi: 10.1016/j.adhoc.2016.02.009
[6] A. Ahmadi and A. Mallahzadeh," Simulation and comparison of array algorithms based on MMSE criterion in different frequency selector feeding conditions", Journal of Communication Engineering (JCE),vol.6,no.24, 2017(in persian).
[7] M. Rahimi.kazeroni and Gh. Ravaei, " Synthesis of linear array of antennas by Newton binomial method to reduce the level of lateral petals of the beam", Journal of Communication Engineering (JCE), vol.6, no.24,2017(in persian).
[8] R. Mulinde, et al., "DOA estimation of wideband LFM RADAR signals," International Radar Conference (RADAR), 2019, pp. 1-6, doi: 10.1109/RADAR41533.2019.171357.
[9] L. Zhang, C.Y. Hung, J. Yu and K.Lu, " Linear Chirp Signal DOA Estimation Using Sparse Time–Frequency Dictionary", Int J Wireless Inf Networks, vol.27,no.5, pp.568-574,2020, DOI:10.1007/s10776-020-00489-1 .
[10] E. Dubrovinskaya, V. Kebkal, O. Kebkal, K. Kebkal and P. Casari,"Underwater Localization via Wideband Direction-of-Arrival Estimation Using Acoustic Arrays of Arbitrary Shape. Sensors (Basel)", in IEEE OCEANS-MTS Conf., 2019,doi: 10.1109/OCEANSE.2019.8867262.
[11] P. Stoica, P. Babu and J. Li, "New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data", IEEE Trans. Signal Process, vol.59,no.1, pp.35–46, 2011, doi: 10.1109/TSP.2010.2086452.
[12] P. Luo, K. -h. Liu, W. -g. Shi and G. Yan, "2-D DOA estimation of wideband LFM signals for arbitrary planar array," IEEE 10th INTERNATIONAL CONFERENCE ON SIGNAL PROCESSING PROCEEDINGS, 2010, pp. 307-310, doi: 10.1109/ICOSP.2010.5656080.
[13] J. Xu, L. Lan, X. He, S. Zhu, C. Zeng, G. Liao and Y. Zhang,"System Design and Signal Processing for Frequency Diverse Array Radar", JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, vol.30,no.1, pp.1-19, 2021, doi: 10.15918/j.jbit1004-0579.2021.004.
[14] W. DU, D. L. SU, S. G. XIE, et al.,"A fast calculation method for the receiving mutual impedances of uniform circular arrays", IEEE Antennas and Wireless Propagation Letters, vol.11,pp.893–896, 2012, doi: 10.1109/LAWP.2012.2211329.
[15] P. Wang, Y. Li and B. Vucetic, "Millimeter Wave Communications With Symmetric Uniform Circular Antenna Arrays," in IEEE Communications Letters, vol. 18, no. 8, pp. 1307-1310, Aug. 2014, doi: 10.1109/LCOMM.2014.2332334.
[16] Z. Zhang, H.Wang and H.Yao,"Time Reversal and Fractional Fourier Transform-Based Method for LFM Signal Detection in Underwater Multi-Path Channel", Appl. Sci., vol.11,no.2,pp.583,2019, doi:10.3390/app11020583.
[17] G. Ben, X. Zheng, Y. Wang, N. Zhang and X. Zhang,,"A Local Search Maximum Likelihood Parameter Estimator of Chirp Signal", Appl. Sci., vol.11, no.2, pp. 673,2021, doi:10.3390/app11020673.
[18] M. Wang, X. Ma, S. Yan and C. Hao, "An Autocalibration Algorithm for Uniform Circular Array With Unknown Mutual Coupling," in IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 12-15, 2016, doi: 10.1109/LAWP.2015.2425423.
[19] PAN, Y. J., ZHANG, X. F., XIE, S. Y., et al.,"An ultra-fast DOA estimator with circular array interferometer using lookup table method," Radioengineering,vol. 24, no. 3, pp. 850–856,2015, doi:10.13164/re.2015.0850.
[20] V. JAIN and W. D. BLAIR,"Filter design for steady-state tracking of maneuvering targets with LFM waveforms", IEEE Transactions on Aerospace and Electronic Systems, vol. 45, no. 2, pp. 765–773, 2009, doi: 10.1109/TAES.2009.5089558.
[21] P. Wang, H. Li, I. Djurović and B. Himed, "Integrated Cubic Phase Function for Linear FM Signal Analysis," in IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 3, pp. 963-977, July 2010, doi: 10.1109/TAES.2010.5545167.
[22] M. KHODJA, A. BELOUCHRANI and K. ABED-MERAIM, "Performance analysis for time-frequency MUSIC algorithm in presence of both additive noise and array calibration errors", EURASIP Journal on Advances in Signal Processing, vol. 2012, no. 1, pp. 1–11,2012, doi: 10.1186/1687-6180-2012-94.
[23] J J. Lin, X. Ma, S. Yan and C. Hao, "Time-Frequency Multi-Invariance ESPRIT for DOA Estimation," in IEEE Antennas and Wireless Propagation Letters, vol. 15, pp. 770-773, 2016, doi: 10.1109/LAWP.2015.2473664.
[24] H. J. ZHANG, G. A. BI, Y. L. CAI, et al.,"DOA estimation of closely-spaced and spectrally-overlapped sources using a STFTbased MUSIC algorithm", Digital Signal Processing, vol. 52, pp. 25–34,2016, doi: 10.1016/j.dsp.2016.01.015
[25] W. YANG and Y. W. SHI,"FRFT based method to estimate DOA for wideband signal", Advanced Materials Research, vols. 712-715, pp. 2716–2720,2013, doi:10.4028/www.scientific.net/AMR.712-715.2716.
[26] Y. CUI and J. F. WANG,"Wideband LFM interference suppression based on fractional Fourier transform and projection techniques", Circuits Systems and Signal Process, vol. 33, no. 2, pp. 613–627,2019, doi: 10.1007/s00034-013-9642-z.
[27] A. Shaw and L. Alirkhis, "Wideband directions of arrival estimation of chirp sources using compressive sensing", Radar sensor technology XXII conference, 2018,pp. 57, doi: 10.1117/12.2316654.
[28] R. TAO, N. ZHANG and Y. WANG,"Analyzing and compensating the effects of range and Doppler frequency migrations in linear frequency modulation pulse compression radar", IET Radar, Sonar and Navigation, 2019, vol. 5, no. 1, pp. 12–22,2019, doi: 10.1049/iet rsn.2019.0265.
[29] J. SU, H. H. TAO, X. RAO, et al.,"Coherently integrated cubic phase function for multiple LFM signals analysis", Electronics Letters, vol. 51, no. 5, pp. 411–413,2020, doi: 10.1049/el.2020.4164.
[30] P. Stoica, P. Babu and J. Li, "SPICE: A Sparse Covariance-Based Estimation Method for Array Processing," in IEEE Transactions on Signal Processing,vol.59,no.2, pp. 629-638, Feb. 2011, doi: 10.1109/TSP.2010.2090525.
[31] P. Wang, Y. Li and B. Vucetic, "Millimeter Wave Communications With Symmetric Uniform Circular Antenna Arrays," in IEEE Communications Letters, vol. 18, no. 8, pp. 1307-1310, Aug. 2014, doi: 10.1109/LCOMM.2014.2332334.
