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Off-grid DOA estimation via a deep learning framework

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Abstract

Direction-of-arrival (DOA) estimation problem is one of the most important tasks for array signal processing. Conventional methods are limited by either the computational complexity or the resolution. In this paper, a novel deep learning (DL) framework for super-resolution DOA estimation is developed, where the grid mismatch problem is fully considered into the DL DOA estimation and the offset between the real DOA and the discrete sampling grid is thereby trained as a part of the network output. Specifically, we first model the DOA estimation problem as a multi-classification task and obtain the on-grid estimation result with a resolution of 1° as the first output. Then we designed another regression module to estimate the offset between target angles and the corresponding grids. By combining both on-grid and offset estimation results, the accurate off-grid estimation is achieved. In addition, the method of fusing low-level features and high-level features by skip connection is adopted between the on-grid estimation module and the offset estimation module. The high-level features in the first part of the network are combined with the original input to improve the training speed and the estimation accuracy. Herein, our training dataset contains a large number of off-grid signal data, which is close to the practical application. Also, the utilization of the off-grid part information improves DOA estimation performance compared to existing DL-based methods, achieving more accurate DOA estimations. Numerous simulation results have demonstrated the superiority of the proposed method in DOA estimation precision, and a good performance advantage maintains even when using a limited number of snapshots. Further, we test the proposed method on the real millimeter-wave radar system, and it outperforms the other state-of-the-art methods, especially for two adjacent targets in the same range and Doppler bin.

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References

  1. Krim H, Viberg M. Two decades of array signal processing research: the parametric approach. IEEE Signal Process Mag, 1996, 13: 67–94

    Article  Google Scholar 

  2. Lan L, Liao G S, Xu J W, et al. Range-angle-dependent beamforming for FDA-MIMO radar using oblique projection. Sci China Inf Sci, 2022, 65: 152305

    Article  MathSciNet  Google Scholar 

  3. Ge S, Li K, Rum S N B M. Deep learning approach in DOA estimation: a systematic literature review. Mobile Inform Systems, 2001. doi: https://doi.org/10.1155/2021/6392875

  4. Schmidt R. A signal subspace approach to multiple emitter location spectral estimation. Dissertation for Ph.D. Degree. Palo Alto: Stanford University. 1981

    Google Scholar 

  5. Roy R, Paulraj A, Kailath T. Estimation of signal parameters via rotational invariance techniques — ESPRIT. In: Proceedings of the IEEE Military Communications Conference: Communications-Computers: Teamed for the 90’s, 1986. 1–5

  6. Rao B D, Hari K V S. Performance analysis of Root-Music. IEEE Trans Acoust Speech Signal Process, 1989, 37: 1939–1949

    Article  Google Scholar 

  7. Ottersten B, Viberg M, Kailath T. Performance analysis of the total least squares ESPRIT algorithm. IEEE Trans Signal Process, 1991, 39: 1122–1135

    Article  MATH  Google Scholar 

  8. Shi B H, Jiang X Y, Chen N, et al. Fast ambiguous DOA elimination method of DOA measurement for hybrid massive MIMO receiver. Sci China Inf Sci, 2022, 65: 159302

    Article  Google Scholar 

  9. Qin G D, Bao D, Liu G G, et al. Cross-correlation matrix Root-MUSIC algorithm for bistatic multiple-input multiple-output radar. Sci China Inf Sci, 2015, 58: 1–10

    Article  Google Scholar 

  10. Donoho D L. Compressed sensing. IEEE Trans Inform Theor, 2006, 52: 1289–1306

    Article  MathSciNet  MATH  Google Scholar 

  11. Yang Z, Li J, Stoica P, et al. Sparse methods for direction-of-arrival estimation. Acad Press Lib Signal Process, 2018, 7: 509–581

    Google Scholar 

  12. 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

    Article  MathSciNet  MATH  Google Scholar 

  13. Wipf D P, Rao B D. An empirical Bayesian strategy for solving the simultaneous sparse approximation problem. IEEE Trans Signal Process, 2007, 55: 3704–3716

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu Z M, Huang Z T, Zhou Y Y. An efficient maximum likelihood method for direction-of-arrival estimation via sparse Bayesian learning. IEEE Trans Wireless Commun, 2012, 11: 1–11

    Article  Google Scholar 

  15. Hu N, Ye Z F, Xu D Y, et al. A sparse recovery algorithm for DOA estimation using weighted subspace fitting. Signal Process, 2012, 92: 2566–2570

    Article  Google Scholar 

  16. Ma Y N, Cao X B, Wang X R. Off-grid DOA estimation with arbitrary-spaced linear array using single snapshot. In: Proceedings of the IEEE Radar Conference (RadarConf), Boston, 2019. 1–6

  17. Ling Y, Gao H T, Zhou S, et al. Robust sparse Bayesian learning-based off-grid DOA estimation method for vehicle localization. Sensors, 2020, 20: 302

    Article  Google Scholar 

  18. Zhu H, Leus G, Giannakis G B. Sparsity-cognizant total least-squares for perturbed compressive sampling. IEEE Trans Signal Process, 2011, 59: 2002–2016

    Article  MathSciNet  MATH  Google Scholar 

  19. Yang Z, Xie L H, Zhang C S. Off-grid direction of arrival estimation using sparse Bayesian inference. IEEE Trans Signal Process, 2013, 61: 38–43

    Article  MathSciNet  MATH  Google Scholar 

  20. Gretsistas A, Plumbley M D. An alternating descent algorithm for the off-grid DOA estimation problem with sparsity constraints. In: Proceedings of the 20th European Signal Processing Conference (EUSIPCO), Bucharest, 2012. 874–878

  21. Duan H P, Qian Z G, Wang Y Y. Off-grid DOA estimation based on noise subspace fitting. In: Proceedings of the IEEE International Conference on Digital Signal Processing (DSP), Singapore, 2015. 675–678

  22. Zhang Y, Ye Z F, Xu X, et al. Off-grid DOA estimation using array covariance matrix and block-sparse Bayesian learning. Signal Process, 2014, 98: 197–201

    Article  Google Scholar 

  23. Liu D H, Zhao Y B. Real-valued sparse Bayesian learning algorithm for off-grid DOA estimation in the beamspace. Digital Signal Process, 2022, 121: 103322

    Article  Google Scholar 

  24. Dai J S, Bao X, Xu W C, et al. Root sparse Bayesian learning for off-grid DOA estimation. IEEE Signal Process Lett, 2017, 24: 46–50

    Article  Google Scholar 

  25. Wang Q L, Zhao Z Q, Chen Z M, et al. Grid evolution method for DOA estimation. IEEE Trans Signal Process, 2018, 66: 2374–2383

    Article  MathSciNet  MATH  Google Scholar 

  26. Chen T, Shi L, Guo L M. Gridless direction of arrival estimation exploiting sparse linear array. IEEE Signal Process Lett, 2020, 27: 1625–1629

    Article  Google Scholar 

  27. Wu S, Yuan Y, Huang L, et al. Grid-less DOA estimation of coherent sources based on the covariance matrix recovery. Phys Commun, 2021, 46: 101345

    Article  Google Scholar 

  28. Du J X, Feng X A, Yan M. DOA estimation based on support vector machine — large scale multiclass classification problem. In: Proceedings of the IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Xi’an, 2011. 1–4

  29. Pastorino M, Randazzo A. A smart antenna system for direction of arrival estimation based on a support vector regression. IEEE Trans Antennas Propagat, 2005, 53: 2161–2168

    Article  Google Scholar 

  30. El Gonnouni A, Martinez-Ramon M, Rojo-Alvarez J L, et al. A support vector machine MUSIC algorithm. IEEE Trans Antennas Propagat, 2012, 60: 4901–4910

    Article  MathSciNet  MATH  Google Scholar 

  31. Pan J J, Wang Y D, Le Bastard C, et al. DOA finding with support vector regression based forward C backward linear prediction. Sensors, 2017, 17: 1225

    Article  Google Scholar 

  32. Hasan M I, Saquib M. Low complexity single source 2-D DOA estimation based on reduced dimension SVR. In: Proceedings of the 22nd Annual Wireless and Microwave Technology Conference (WAMICON), Clearwater, 2022. 1–4

  33. Lo T, Leung H, Litva J. Radial basis function neural network for direction-of-arrivals estimation. IEEE Signal Process Lett, 1994, 1: 45–47

    Article  Google Scholar 

  34. LeCun Y, Bengio Y, Hinton G. Deep learning. Nature, 2015, 521: 436–444

    Article  Google Scholar 

  35. He K M, Zhang X Y, Ren S Q, et al. Deep residual learning for image recognition. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, 2017. 6450–6458

  36. Liu P F, Qiu X P, Huang X J. Recurrent neural network for text classification with multi-task learning. In: Proceedings of the 25th International Joint Conference on Artificial Intelligence (IJCAI), New York, 2016. 2873–2879

  37. Redmon J, Divvala S, Girshick R, et al. You only look once: unified, real-time object detection. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, 2016. 779–788

  38. Zhuang Z H, Xu L, Li J Y, et al. Machine-learning-based high-resolution DOA measurement and robust directional modulation for hybrid analog-digital massive MIMO transceiver. Sci China Inf Sci, 2020, 63: 180302

    Article  MathSciNet  Google Scholar 

  39. Yao R G, Qin Q N, Wang S Y, et al. Deep learning assisted channel estimation refinement in uplink OFDM systems under time-varying channels. In: Proceedings of the International Wireless Communications and Mobile Computing (IWCMC), Harbin, 2021. 1349–1353

  40. Qi C H, Dong P H, Ma W Y, et al. Acquisition of channel state information for mmWave massive MIMO: traditional and machine learning-based approaches. Sci China Inf Sci, 2021, 64: 181301

    Article  Google Scholar 

  41. Kase Y, Nishimura T, Ohgane T, et al. DOA estimation of two targets with deep learning. In: Proceedings of the 15th Workshop on Positioning, Navigation and Communications (WPNC), Bremen, 2018. 1–5

  42. Wu L L, Liu Z M, Huang Z T. Deep convolution network for direction of arrival estimation with sparse prior. IEEE Signal Process Lett, 2019, 26: 1688–1692

    Article  Google Scholar 

  43. Papageorgiou G, Sellathurai M, Eldar Y. Deep networks for direction-of-arrival estimation in low SNR. IEEE Trans Signal Process, 2021, 69: 3714–3729

    Article  MathSciNet  MATH  Google Scholar 

  44. Liu Z M, Zhang C, Yu P S. Direction-of-arrival estimation based on deep neural networks with robustness to array imperfections. IEEE Trans Antennas Propagat, 2018, 66: 7315–7327

    Article  Google Scholar 

  45. Ahmed A M, Eissa O, Sezgin A. Deep autoencoders for DOA estimation of coherent sources using imperfect antenna array. In: Proceedings of the 3rd International Workshop on Mobile Terahertz Systems (IWMTS), Essen, 2020. 1–5

  46. Gao Y, Xu J, Jia X. Joint number and DOA estimation via the eigen-beam mCapon method for closely spaced sources. Sci China Inf Sci, 2015, 58: 129302

    Article  Google Scholar 

  47. Yan F G, Jin M, Zhou H J, et al. Low-degree root-MUSIC algorithm for fast DOA estimation based on variable substitution technique. Sci China Inf Sci, 2020, 63: 159206

    Article  MathSciNet  Google Scholar 

  48. Elbir A M. DeepMUSIC: multiple signal classification via deep learning. IEEE Sensors Letters, 2020, 4: 1–4

    Article  Google Scholar 

  49. Hoang D T, Lee K. Deep learning-aided coherent direction-of-arrival estimation with the FTMR algorithm. IEEE Trans Signal Process, 2022, 70: 1118–1130

    Article  MathSciNet  Google Scholar 

  50. Kingma D P, Ba J. Adam: a method for stochastic optimization. In: Proceedings of the 3rd International Conference on Learning Representations (ICLR), San Diego, 2014

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61901112).

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Authors and Affiliations

  1. State Key Lab of Millimeter Waves, Southeast University, Nanjing, 211100, China

    Yan Huang, Yanjun Zhang & Wei Hong

  2. Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing, 210096, China

    Jun Tao

  3. School of Information Science and Technology, Northwest University, Xi’an, 710069, China

    Cai Wen

  4. National Key Lab of Radar Signal Processing, Xidian University, Xi’an, 710071, China

    Guisheng Liao

Authors
  1. Yan Huang
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  2. Yanjun Zhang
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  3. Jun Tao
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  4. Cai Wen
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  5. Guisheng Liao
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  6. Wei Hong
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Correspondence to Yan Huang or Jun Tao.

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Huang, Y., Zhang, Y., Tao, J. et al. Off-grid DOA estimation via a deep learning framework. Sci. China Inf. Sci. 66, 222305 (2023). https://doi.org/10.1007/s11432-022-3750-5

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