Higher-Order Statistics-Based Non-uniform Linear Array for Underdetermined DoA Estimation of Non-circular Signals

H. Abeida, J. Delmas, Music-like estimation of direction of arrival for noncircular sources. IEEE Trans. Signal Process. 54(7), 2678–2690 (2006) H. Abeida, J. Delmas, Statistical performance of music-like algorithms in re-solving noncircular sources. IEEE Trans. Signal Process. 56(9), 4317–4329 (2008) A. Ahmed, Y.D. Zhang, B. Himed, Effective nested array design for fourth-order cumulant-based DOA estimation, in IEEE Radar Conference (RadarConf) (2017), pp. 0998–1002 H. Alquran, M. Alqudah, I. Abu-Qasmieh, A. Al-Badarneh, S. Almashaqbeh, ECG classification using higher order spectral estimation and deep learning techniques. Neural Netw. World 29(4), 207–219 J.-F. Cardoso, E. Moulines, Asymptotic performance analysis of direction-finding algorithms based on fourth-order cumulants. IEEE Trans. Signal Process. 43(1) (1995) P. Chevalier, L. Albera, A. Ferreol, P. Comon, On the virtual array concept for higher order array processing. IEEE Trans. Signal Process. 53(4), 1254–1271 (2005) P. Chevalier, A. Ferreol, L. Albera, High-resolution direction finding from higher order statistics: the \(2q\)-MUSIC algorithm. IEEE Trans. Signal Process. 54(8), 2986–2997 (2006) Z. Chen, Y. Ding, S. Ren, Z. Chen, A novel noncircular MUSIC algorithm based on the concept of the difference and sum coarray. Sensors 18(2), 344 (2018) P. Charge, Y. Wang, J. Saillard, A non-circular sources direction finding method using polynomial rooting. Signal Process. 81, 1765–1770 (2001) H. Cox, Resolving power and sensitivity to mismatch of optimum array processors. J. Acoust. Soc. Am. 50, 771–785 (1973) J.-P. Delmas, H. Abeida, Stochastic Cramer–Rao bound for noncircular signals with application to DOA estimation. IEEE Trans. Signal Process. 52(11), 3192–3199 (2004) M.C. Dogan, J.M. Mendel, Applications of cumulants to array processing part I: aperture extension and array calibration. IEEE Trans. Signal Process. 43(5), 1200–1216 (1995) J. Eriksson, E. Ollila, V. Koivunen, Essential statistics and tools for complex random variables. IEEE Trans. Signal Process. 58(10), 5400–5408 (2010) A. Ferreol, P. Chevalier, New insights into second and fourth-order direction finding for non-circular sources, in Proceedings of IEEE Sensor Array Multichannel Signal Process (Spain, 2014), pp. 465–468 A. Ferreol, P. Chevalier, Higher Order Direction Finding for Arbitrary Non Circular Sources: The NC-2qMUSIC Algorithm (EUSIPCO, Aalborg, 2010) F.F. Gao, A. Nallanathan, Y. Wang, Improved music under the coexistence of both circular and noncircular sources. IEEE Trans. Signal Process. 56(7), 3033–3038 (2008) X. Gou, Z. Liu, X. Yougen, Biquaternion cumulant-MUSIC for DOA estimation of noncircular signals. Signal Process. 93(4), 874–881 (2013) P. Gounon, C. Adnet, J. Galy, Localization angulaire de signaux non circulaires. Traitement du Signal 15(1), 17–23 (1998) P. Gupta, M. Agrawal, Study of DoA estimation algorithm for underdetermined cases, in OCEANS 2018, MTS/IEEE (Kobe, Japan, 2018) P. Gupta, M. Agrawal, Noncircularity-exploitation to design the sparse array for DoA estimation, in OCEANS 2018, MTS/IEEE (Charleston, US, 2018) P. Gupta, M. Agrawal, Design and analysis of the sparse array for DoA estimation of noncircular signals. IEEE Trans. Signal Process. (2018). https://doi.org/10.1109/TSP.2018.2883035 P. Gupta, M. Agrawal, DOA estimation of non-circular signals using fourth order cumulant in underdetermined cases, in 2018 IEEE International Workshop on Signal Processing Systems (SiPS) (Cape Town, 2018) P. Gupta, M. Agrawal, Computation of weight function of 2qth order virtual array to analyse the estimation performance, in Eleventh IEEE Sensor Array ANS Multichannel Signal Processing Workshop (Hangzhou, China, 2020) P. Han, H. Xu, B. Ba, Y. Zhang, Direction-of-arrival estimation in a mixture of multiple circular and non-circular signals using nested array. IEEE Access 8, 105237–105249 (2020) M. Haardt, F. Roemer, Enhancements of unitary ESPRIT for non-circular sources, in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (2004) J. He, L. Li, T. Shu, Sparse nested arrays with spatially spread orthogonal dipoles: high accuracy passive direction finding with less mutual coupling. IEEE Trans. Aerosp. Electron. Syst. 57(4), 2337–2345 (2021). https://doi.org/10.1109/TAES.2021.3054056 Z.T. Huang, Z.M. Liu, J. Liu, Y.Y. Zhou, Performance analysis of music for non-circular signals in the presence of mutual coupling. IET Radar Sonar Navig. 4(5), 703–711 (2010) C. Liu, P.P. Vaidyanathan, Super nested arrays: linear sparse arrays with reduced mutual coupling-part I: fundamentals. IEEE Trans. Signal Process. 64(15), 3997–4012 (2016). https://doi.org/10.1109/TSP.2016.2558159 C. Liu, P.P. Vaidyanathan, Tensor MUSIC in multidimensional sparse arrays, in 2015 49th Asilomar Conference on Signals, Systems and Computers (2015), pp. 1783–1787. https://doi.org/10.1109/ACSSC.2015.7421458 J. Li, Y. Wang, C. Le Bastard, W. Zongze, S. Men, Low-complexity highorder propagator method for near-field source localization. Sens. MDPI 19(1), 54 (2019) J. Liu, Z. Huang, Y. Zhou, Extended \(2q\)-MuSiC algorithm for noncircular signals. Signal Process. 88, 1327–1339 (2008) M. Nasrolahzadeh, Z. Mohammadpoory, J. Haddadnia, A novel method for early diagnosis of Alzheimer’s disease based on higher-order spectral estimation of spontaneous speech signals. Cognit. Neurodyn. 10, 495–503 (2016) H. Ould-Baba, J. Antoni, V. Robin, Multidimensional Independent Component Analysis with Higher-Order Cumulant Matrices for Vector Sources with Possibly Differing Dimensions. (hal-01006087v1) (2014) P. Pal, P.P. Vaidyanathan, Multiple level nested array: an efficient geometry for \(2q\)th order cumulant based array processing. IEEE Trans. Signal Process. 60(3), 1253–1269 (2012) P. Pal, P.P. Vaidyanathan, Nested arrays: a novel approach to array processing with enhanced degrees of freedom. IEEE Trans. Signal Process. 58(8), 4167–4181 (2010) Z. Peng, Y. Ding, S. Ren, X. Wang, Extended transformed nested arrays for DoA estimation of non-circular sources. IEEE Access 8, 162350–162362 (2020). https://doi.org/10.1109/ACCESS.2020.3021077 B. Porat, B. Friedlander, Direction finding algorithms based on higher order statistics. IEEE Trans. Signal Process. 39(9), 2016–2024 (1991) W. Rao, D. Li, J.Q. Zhang, A tensor-based approach to L-shaped arrays processing with enhanced degrees of freedom. IEEE Signal Process. Lett. 25(2), 1–5 (2018). https://doi.org/10.1109/LSP.2017.2783370 Q. Shen, W. Liu, W. Cui, S. Wu, Extension of co-prime arrays based on the fourth-order difference coarray concept. IEEE Signal Process. Lett. 23(5), 615–619 (2016) L. Shen, Z. Liu, X. Gou, Y. Xu, Polynomial-rooting based fourth-order MUSIC for direction-of-arrival estimation of noncircular signals. J. Syst. Eng. Electron. 25(6), 942–948 (2014). https://doi.org/10.1109/JSEE.2014.00108 J. Shi, F. Wen, T. Liu, Nested MIMO radar: coarrays, tensor modeling, and angle estimation. IEEE Trans. Aerosp. Electron. Syst. 57(1), 573–585 (2021). https://doi.org/10.1109/TAES.2020.3034012 W. Si, Z. Peng, C. Hou, F. Zeng, Improved nested arrays with sumdifference coarray for DOA estimation. IEEE Sens. J. 19(16), 6986–6997 (2019) J. Steinwandt, F. Roemer, M. Haardt, Analytical performance assessment of ESPRIT-type algorithms for coexisting circular and strictly non-circular signals, in Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (Shanghai, China, 2016), pp. 2931–2935 J. Steinwandt, F. Roemer, M. Haardt, G. Del Galdo, R-dimensional ESPRIT-type algorithms for strictly second-order non-circular sources and their performance analysis. IEEE Trans. Signal Process. 62(18), 4824–4838 (2014) T.E. Tuncer, B. Friedlander, Classical and Modern Direction-of-Arrival Estimation (Academic Press, Cambridge, 2009) Q. Wang, X. Wang, H. Chen, X. Zhu, W. Liu, W. Yan, L. Wang, An effective localization method for mixed far-field and near-field strictly non-circular sources. Digital Signal Process. 94, 125–136 (2019) L. Wan, K. Liu, Y.-C. Liang, T. Zhu, DOA and polarization estimation for non-circular signals in 3-D millimeter wave polarized massive MIMO systems. IEEE Trans. Wirel. Commun. 20(5), 3152–3167 (2021). https://doi.org/10.1109/TWC.2020.3047866 T. Wang, B.P. Ng, M.H. Er, DOA estimation of amplitude modulated signals with less array sensors than sources, in Proceedings of IEEE ICASSP (Kyoto, 2012), pp. 2565–2568 Y. Wang, W. Wu, X. Zhang, W. Zheng, Transformed nested array designed for DOA estimation of non-circular signals: reduced sumdifference co-array redundancy perspective. IEEE Commun. Lett. 24(6), 1262–1265 (2020) W. Xie, X.Y. Zhang, L.B. Chen, J.H. Yin, Q. Wan, Fast DOA estimation algorithm for noncircular sources with central symmetrical array, in Proceedings of 12th International Conference on Signal Processing (ICSP) (2014), pp. 267–270 W. Yunfei, S. Jinqing, Z. Xiaofei, H. Yi, D. Xiangrui, Noncircular signals for nested array: sum-difference co-array and direction of arrival estimation algorithm. IET Radar Sonar Navig. 14(1), 27–35 (2020) F. Yan, M. Jin, X. Qiao, Low-complexity DOA estimation based on compressed MUSIC and its performance analysis. IEEE Trans. Signal Process. 61(8), 1915–1930 (2013). https://doi.org/10.1109/TSP.2013.2243442 X.M. Yang, G.J. Li, Z. Zheng, DoA estimation of non-circular signal based on sparse representation. Wirel. Pers. Commun. 82, 2363–2375 (2015) A. Zoubir, P. Chargé, Y. Wang, Non-circular sources localization with ESPRIT, in Proceedings of the 6th European Conference on Wireless Technology (2003) H. Zheng, C. Zhou, Y. Gu, Z. Shi, Two-dimensional DOA estimation for coprime planar array: a coarray tensor-based solution, in ICASSP 2020—2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2020), pp. 4562–4566. https://doi.org/10.1109/ICASSP40776.2020.9053860 Y. Zhang, B.P. Ng, MUSIC-like DOA estimation without estimating the number of sources. IEEE Trans. Signal Process. 58(3), 1668–1676 (2010). https://doi.org/10.1109/TSP.2009.2037074 C. Zhou, Y. Gu, Y.D. Zhang, Z. Shi, T. Jin, X. Wu, Compressive sensing-based coprime array direction-of-arrival estimation. IET Commun. 11(11), 1719–1724 (2017)