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13-08-2022

DOA Estimation Based on Second-Order Difference Co-Array for Coprime Arrays

Authors: Ali Sharifzadeh Lari, Dariush Abbasi-Moghadam

Published in: Wireless Personal Communications

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Abstract

In this paper A different approach based on the reconstruction of the data covariance matrix is presented. In the presented approach, by vectorization of the reconstructed matrix, the covariance matrix is reconstructed in two steps. Hence an extensive network of virtual sensors is created, which is introduced as a second-order difference co-array. Then, by using the well-known spatial smoothing technique full-rank covariance matrix is obtained for DOA estimation algorithms. Therefore the MN sources can be detected using a physical array with M + N sensors. The degrees of freedom (DOF) of the second-order difference co-array are significantly increased as opposed to the physical array which provides only N − 1 degrees of freedom. As a result, for a certain number of array elements, in addition to the resolution improvement, the number of detectable targets is sharply increased. Simulation results verify the effectiveness of the proposed method and MUSIC-based or ESPRIT-based DOA estimators could be designed to perform DOA estimation.
Literature
1.
go back to reference H. L. V. 2002 Trees, Detection, Estimation, and Modulation Theory. Part IV., Optimum Array Processing, Wiley- Interscience. H. L. V. 2002 Trees, Detection, Estimation, and Modulation Theory. Part IV., Optimum Array Processing, Wiley- Interscience.
2.
go back to reference T. E. Tuncer and B. Friedlander, Classical and Modern Direction-of-Arrival Estimation, Academic Press, 2009. T. E. Tuncer and B. Friedlander, Classical and Modern Direction-of-Arrival Estimation, Academic Press, 2009.
3.
go back to reference Bienvenu, G., & Kopp, L. (1983). Optimality of high resolution array processing using the eigensystem approach. IEEE Transactions on Acoustics, Speech, and Signal Processing, 31(5), 1235–1247. CrossRef Bienvenu, G., & Kopp, L. (1983). Optimality of high resolution array processing using the eigensystem approach. IEEE Transactions on Acoustics, Speech, and Signal Processing, 31(5), 1235–1247. CrossRef
4.
go back to reference Brillinger, D. R. (1985). A maximum likelihood approach to frequency wavenumber analysis. IEEE Transactions on Acoustics, Speech, and Signal Processing, 33(4), 1076–1085. CrossRef Brillinger, D. R. (1985). A maximum likelihood approach to frequency wavenumber analysis. IEEE Transactions on Acoustics, Speech, and Signal Processing, 33(4), 1076–1085. CrossRef
5.
go back to reference Kumaresan, R., & Tufts, D. W. (1983). Estimating the angles of arrival of multiple plane waves. IEEE Transactions on Aerospace and Electronic Systems, 19(1), 134–138. CrossRef Kumaresan, R., & Tufts, D. W. (1983). Estimating the angles of arrival of multiple plane waves. IEEE Transactions on Aerospace and Electronic Systems, 19(1), 134–138. CrossRef
6.
go back to reference Roy, R., Paulraj, A., & Kailath, T. (1986). ESPRIT—A subspace rotation approach to estimation of parameters of cisoids in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(5), 1340–1342. CrossRef Roy, R., Paulraj, A., & Kailath, T. (1986). ESPRIT—A subspace rotation approach to estimation of parameters of cisoids in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(5), 1340–1342. CrossRef
7.
go back to reference Schmidt, R. O. (1986). Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 34(3), 276–280. CrossRef Schmidt, R. O. (1986). Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 34(3), 276–280. CrossRef
8.
go back to reference Viberg, M., & Ottersten, B. (1991). Sensor array processing based on subspace fitting. IEEE Transactions on Acoustics, Speech, and Signal Processing, 39(5), 1110–1121. CrossRef Viberg, M., & Ottersten, B. (1991). Sensor array processing based on subspace fitting. IEEE Transactions on Acoustics, Speech, and Signal Processing, 39(5), 1110–1121. CrossRef
9.
go back to reference Burg, J. P. (1972). The relationship between maximum entropy spectra and maximum likelihood spectra. Geophys, 37(2), 375–376. CrossRef Burg, J. P. (1972). The relationship between maximum entropy spectra and maximum likelihood spectra. Geophys, 37(2), 375–376. CrossRef
10.
go back to reference Capon, J. (1969). High resolution frequency-wavenumber spectrum analysis. Proceedings of the IEEE, 57, 1408–1418. CrossRef Capon, J. (1969). High resolution frequency-wavenumber spectrum analysis. Proceedings of the IEEE, 57, 1408–1418. CrossRef
11.
go back to reference Kaveh, M., & Barabell, A. J. (1986). The statistical performance of the MUSIC and the minimum norm algorithms in resolving plane waves in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(2), 331–341. CrossRef Kaveh, M., & Barabell, A. J. (1986). The statistical performance of the MUSIC and the minimum norm algorithms in resolving plane waves in noise. IEEE Transactions on Acoustics, Speech, and Signal Processing, 34(2), 331–341. CrossRef
12.
go back to reference Stoica, P., & Nehorai, A. (1989). MUSIC, maximum likelihood and Cramer Rao bound. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(12), 720–741. MathSciNetCrossRef Stoica, P., & Nehorai, A. (1989). MUSIC, maximum likelihood and Cramer Rao bound. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(12), 720–741. MathSciNetCrossRef
13.
go back to reference Stoica, P., & Nehorai, A. (1990). MUSIC, maximum likelihood, and Cramer-Rao bound: Further results and comparisons. IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(12), 2140–2150. CrossRef Stoica, P., & Nehorai, A. (1990). MUSIC, maximum likelihood, and Cramer-Rao bound: Further results and comparisons. IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(12), 2140–2150. CrossRef
14.
go back to reference Dogan, M. C., & Mendel, J. M. (1995). Applications of cumulants to array processing - Part I: Aperture extension and array calibration. IEEE Transactions on Signal Processing, 43(5), 1200–1216. CrossRef Dogan, M. C., & Mendel, J. M. (1995). Applications of cumulants to array processing - Part I: Aperture extension and array calibration. IEEE Transactions on Signal Processing, 43(5), 1200–1216. CrossRef
15.
go back to reference Chevalier, P., Albera, L., Ferreol, A., & Comon, P. (2005). On the virtual array concept for higher order array processing. IEEE Transactions on Signal Processing, 53(4), 1254–1271. MathSciNetCrossRef Chevalier, P., Albera, L., Ferreol, A., & Comon, P. (2005). On the virtual array concept for higher order array processing. IEEE Transactions on Signal Processing, 53(4), 1254–1271. MathSciNetCrossRef
16.
go back to reference Chevalier, P., & Ferreol, A. (1999). On the virtual array concept for the fourth-order direction finding problem. IEEE Transactions on Signal Processing, 47(9), 2592–2595. CrossRef Chevalier, P., & Ferreol, A. (1999). On the virtual array concept for the fourth-order direction finding problem. IEEE Transactions on Signal Processing, 47(9), 2592–2595. CrossRef
17.
go back to reference Cardoso, J.-F. (1990). Localisation et identification par la quadricovariance. Traitement du Signal, 7(5), 397–406. Cardoso, J.-F. (1990). Localisation et identification par la quadricovariance. Traitement du Signal, 7(5), 397–406.
18.
go back to reference Chiang, H. H., & Nikias, C. L. (1989). The ESPRIT algorithm with high order statistics (pp. 163–168). Proc. Workshop Higher Order Statistics. Chiang, H. H., & Nikias, C. L. (1989). The ESPRIT algorithm with high order statistics (pp. 163–168). Proc. Workshop Higher Order Statistics.
19.
go back to reference Gönen, E., & Mendel, J. M. (1999). Applications of cumulants to array processing— Part VI: Polarization and direction of arrival estimation with minimally constrained arrays. IEEE Transactions on Signal Processing, 47(9), 2589–2592. CrossRef Gönen, E., & Mendel, J. M. (1999). Applications of cumulants to array processing— Part VI: Polarization and direction of arrival estimation with minimally constrained arrays. IEEE Transactions on Signal Processing, 47(9), 2589–2592. CrossRef
20.
go back to reference Porat, B., & Friedlander, B. (1991). Direction finding algorithms based on higher order statistics. IEEE Transactions on Signal Processing, 39(9), 2016–2024. CrossRef Porat, B., & Friedlander, B. (1991). Direction finding algorithms based on higher order statistics. IEEE Transactions on Signal Processing, 39(9), 2016–2024. CrossRef
21.
go back to reference Shamsunder, S., & Giannakis, G. B. (1993). Modeling of non-Gaussian array data using cumulants: DOA estimation of more sources with less sensors. Signal Processing, 30(3), 279–297. CrossRef Shamsunder, S., & Giannakis, G. B. (1993). Modeling of non-Gaussian array data using cumulants: DOA estimation of more sources with less sensors. Signal Processing, 30(3), 279–297. CrossRef
22.
go back to reference Chevalier, P., Ferréol, A., & Albera, L. (2006). High-resolution direction finding from Higher order statistics: The 2q-MUSIC algorithm. IEEE Transactions on Signal Processing, 54(8), 2986–2997. CrossRef Chevalier, P., Ferréol, A., & Albera, L. (2006). High-resolution direction finding from Higher order statistics: The 2q-MUSIC algorithm. IEEE Transactions on Signal Processing, 54(8), 2986–2997. CrossRef
23.
go back to reference Pal, P., & Vaidyanathan, P. P. (2012). Multiple level nested array: An efficient geometry for 2qth order cumulant based array processing. IEEE Transactions on Signal Processing, 60(3), 1253–1269. MathSciNetCrossRef Pal, P., & Vaidyanathan, P. P. (2012). Multiple level nested array: An efficient geometry for 2qth order cumulant based array processing. IEEE Transactions on Signal Processing, 60(3), 1253–1269. MathSciNetCrossRef
24.
go back to reference Hoctor, R. T., & Kassam, S. A. (1990). The unifying role of the coarray in aperture synthesis for coherent and incoherent imaging. Proceedings of the IEEE, 78(4), 735–752. CrossRef Hoctor, R. T., & Kassam, S. A. (1990). The unifying role of the coarray in aperture synthesis for coherent and incoherent imaging. Proceedings of the IEEE, 78(4), 735–752. CrossRef
25.
go back to reference Moffet, A. (1968). Minimum-redundancy linear arrays. IEEE Transactions on Antennas and Propagation, 16(2), 172–175. CrossRef Moffet, A. (1968). Minimum-redundancy linear arrays. IEEE Transactions on Antennas and Propagation, 16(2), 172–175. CrossRef
26.
go back to reference Bloom, G. S., & Golomb, S. W. (1977). Application of numbered undirected graphs. Proceedings of the IEEE, 65(4), 562–570. CrossRef Bloom, G. S., & Golomb, S. W. (1977). Application of numbered undirected graphs. Proceedings of the IEEE, 65(4), 562–570. CrossRef
27.
go back to reference Pal, P., & Vaidyanathan, P. P. (2010). Nested arrays: A novel approach to array processing with enhanced degrees of freedom. IEEE Transactions on Signal Processing, 58(8), 4167–4181. MathSciNetCrossRef Pal, P., & Vaidyanathan, P. P. (2010). Nested arrays: A novel approach to array processing with enhanced degrees of freedom. IEEE Transactions on Signal Processing, 58(8), 4167–4181. MathSciNetCrossRef
28.
go back to reference Gupta, I. J., & Ksienski, A. A. (1983). Effect of mutual coupling on the performance of adaptive arrays. IEEE Transactions on Antennas and Propagation, AP-31(5), 785–791. CrossRef Gupta, I. J., & Ksienski, A. A. (1983). Effect of mutual coupling on the performance of adaptive arrays. IEEE Transactions on Antennas and Propagation, AP-31(5), 785–791. CrossRef
29.
go back to reference Zhang, Y., Hirasawa, K., & Fujimoto, K. (1987). Signal bandwidth consideration of mutual coupling effects on adaptive array performance. IEEE Transactions on Antennas and Propagation, AP-35(3), 337–339. CrossRef Zhang, Y., Hirasawa, K., & Fujimoto, K. (1987). Signal bandwidth consideration of mutual coupling effects on adaptive array performance. IEEE Transactions on Antennas and Propagation, AP-35(3), 337–339. CrossRef
30.
go back to reference Chen, T., Shi, L., & Guo, L. (2019). Sparse DOA estimation algorithm based on fourth-order cumulants vector exploiting restricted non-uniform linear array. IEEE Access, 7, 9980–9988. CrossRef Chen, T., Shi, L., & Guo, L. (2019). Sparse DOA estimation algorithm based on fourth-order cumulants vector exploiting restricted non-uniform linear array. IEEE Access, 7, 9980–9988. CrossRef
31.
go back to reference Zhou, Y., Li, J., Nie, W., & Li, Y. (2021). The fourth-order difference co-array construction by expanding and shift nested array: Revisited and improved. Signal Processing, 188, 108198. CrossRef Zhou, Y., Li, J., Nie, W., & Li, Y. (2021). The fourth-order difference co-array construction by expanding and shift nested array: Revisited and improved. Signal Processing, 188, 108198. CrossRef
32.
go back to reference Vaidyanathan, P. P., & Pal, P. (2011). Sparse sensing with co-prime samplers and arrays. IEEE Transactions on Signal Processing, 59(2), 573–586. MathSciNetCrossRef Vaidyanathan, P. P., & Pal, P. (2011). Sparse sensing with co-prime samplers and arrays. IEEE Transactions on Signal Processing, 59(2), 573–586. MathSciNetCrossRef
33.
go back to reference Qin, S., Zhang, Y. D., & Amin, M. G. (2015). Generalized Coprime Array Configurations for Direction-of-Arrival Estimation. IEEE Transactions on Signal Processing, 63(6), 1377–1390. MathSciNetCrossRef Qin, S., Zhang, Y. D., & Amin, M. G. (2015). Generalized Coprime Array Configurations for Direction-of-Arrival Estimation. IEEE Transactions on Signal Processing, 63(6), 1377–1390. MathSciNetCrossRef
34.
go back to reference Tan, Z., Eldar, Y. C., & Nehorai, A. (2014). Direction of arrival estimation using Co-prime arrays: A super-resolution viewpoint. IEEE Transactions on Signal Processing, 62(21), 5565–5576. MathSciNetCrossRef Tan, Z., Eldar, Y. C., & Nehorai, A. (2014). Direction of arrival estimation using Co-prime arrays: A super-resolution viewpoint. IEEE Transactions on Signal Processing, 62(21), 5565–5576. MathSciNetCrossRef
35.
go back to reference Liu, K., & Zhang, Y. D. (2018). Coprime array-based DOA estimation in unknown nonuniform noise environment. Digital Signal Processing, 76, 66–74. MathSciNetCrossRef Liu, K., & Zhang, Y. D. (2018). Coprime array-based DOA estimation in unknown nonuniform noise environment. Digital Signal Processing, 76, 66–74. MathSciNetCrossRef
36.
go back to reference B. Liao, C. Guo, L. Huang, J. Wen, (2016) Matrix completion based direction-of-arrival estimation in nonuniform noise. In: Proceedings of 2016 IEEE International Conference on Digital Signal Processing (DSP), Beijing, China, pp. 66–69. B. Liao, C. Guo, L. Huang, J. Wen, (2016) Matrix completion based direction-of-arrival estimation in nonuniform noise. In: Proceedings of 2016 IEEE International Conference on Digital Signal Processing (DSP), Beijing, China, pp. 66–69.
37.
go back to reference Qin, Si., Zhang, Y. D., Amin, M. G., & Himed, B. (2017). DOA estimation exploiting a uniform linear array with multiple co-prime frequencies. Signal Processing, 130, 37–46. CrossRef Qin, Si., Zhang, Y. D., Amin, M. G., & Himed, B. (2017). DOA estimation exploiting a uniform linear array with multiple co-prime frequencies. Signal Processing, 130, 37–46. CrossRef
38.
go back to reference Mei, F., Xu, H., Cui, W., Ba, B., & Wang, Y. (2021). A transformed coprime array With reduced mutual coupling for DOA estimation of non-circular signals. IEEE Access, 9, 125984–125998. CrossRef Mei, F., Xu, H., Cui, W., Ba, B., & Wang, Y. (2021). A transformed coprime array With reduced mutual coupling for DOA estimation of non-circular signals. IEEE Access, 9, 125984–125998. CrossRef
39.
go back to reference Lu, A., Guo, Y., Li, N., & Yang, S. (2020). Efficient gridless 2-D direction-of-arrival estimation for coprime array based on decoupled atomic norm minimization. IEEE Access, 8, 57786–57795. CrossRef Lu, A., Guo, Y., Li, N., & Yang, S. (2020). Efficient gridless 2-D direction-of-arrival estimation for coprime array based on decoupled atomic norm minimization. IEEE Access, 8, 57786–57795. CrossRef
40.
go back to reference Chen, Z., Fan, C., & Huang, X. (2020). Interpolation-based direction-of-arrival estimation for coprime arrays via covariance matrix fitting. IEEE Access, 8, 149133–149141. CrossRef Chen, Z., Fan, C., & Huang, X. (2020). Interpolation-based direction-of-arrival estimation for coprime arrays via covariance matrix fitting. IEEE Access, 8, 149133–149141. CrossRef
Metadata
Title
DOA Estimation Based on Second-Order Difference Co-Array for Coprime Arrays
Authors
Ali Sharifzadeh Lari
Dariush Abbasi-Moghadam
Publication date
13-08-2022
Publisher
Springer US
Published in
Wireless Personal Communications
Print ISSN: 0929-6212
Electronic ISSN: 1572-834X
DOI
https://doi.org/10.1007/s11277-022-09858-w