A p-norm-like Constraint LMS Algorithm for Sparse Adaptive Beamforming
Keywords:
Array beamforming, constrained LMS algorithm, p-norm-like constraint, sparse adaptive beamformingAbstract
In this paper, a p-norm-like constraint normalized least mean square (PNL-CNLMS) algorithm is proposed for sparse adaptive beamforming. The proposed PNL-CNLMS algorithm inherits the good capacity of the conventional constrained least mean square (CLMS) algorithm in adaptive beamforming, i.e., forming ideal beam patterns. Also, the proposed PNL-CNLMS algorithm utilizes a p-norm-like constraint to exploit sparse property of the corresponding antenna array. In the derivation procedure, the Lagrange multiplier approach and the gradient descent method are utilized to obtain the devised updating equation. Numerical simulations reveal the superiority of the proposed PNL-CNLMS algorithm.
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H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part IV: Optimum Array Processing, John Wiley & Sons, New York, NY, 2002.
J. Li and P. Stoica (Eds.), Robust Adaptive Beamforming, John Wiley & Sons, New York, NY, 2005.
O. L. Frost III, “An algorithm for linearly constrained adaptive array processing,” Proc. IEEE, vol. 60, no. 8, pp. 926-935, Aug. 1972.
J. A. Apolinário, Jr., S. Werner, P. S. R. Diniz, and T. I. Laakso, “Constrained normalized adaptive filtering for CDMA mobile communications,” IEEE Signal Processing Conference, Rhodes, Greece, Sept. 1998.
J. F. de Andrade, M. L. R. de Campos, and J. A. Apolinário, “L1-constrained normalized LMS algorithms for adaptive beamforming,” IEEE Transactions on Signal Processing, vol. 63, no. 24, pp. 6524-6539, Dec. 2015.
W. Shi, Y. Li, and S. Luo, “Adaptive antenna array beamforming based on norm penalized NLMS algorithm,” 2018 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting, in press, Boston, America, July 2018.
W. Shi and Y. Li, “Norm-constrained NLMS for sparse controllable adaptive array beamforming,” 2018 International Applied Computational Electromagnetics Society Symposium, in press, Beijing, China, July 2018.
W. Shi, Y. Li, and J. Yin, “Improved constraint NLMS algorithm for sparse adaptive array beamforming control applications,” Applied Computational Electromagnetics Society Journal, Accepted, Mar. 2019.
W. Shi, Y. Li, L. Zhao, and X. Liu, “Controllable sparse antenna array for adaptive beamforming,” IEEE Access, vol. 7, pp. 6412-6423, Jan. 2019. [10] D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
R. Tibshirani, “Regression shrinkage and selection via the lasso,” J. R. Stat. Soc. Ser. B-Stat. Methodol., vol. 58, no. 1, pp. 267-288, Jan. 1996.
Y. Chen, Y. Gu, and A. O. Hero, “Sparse LMS for system identification,” Proc. IEEE International Conference on Acoustic Speech and Signal Processing, (ICASSP’09), pp. 3125-3128, Taipei, Taiwan, Apr. 2009.
O. Taheri and S. A. Vorobyov, “Sparse channel estimation with Lp-norm and reweighted L1-norm penalized least mean squares,” IEEE International Conference on Acoustic Speech and Signal Processing (ICASSP’11), pp. 2864-2867, Prague, Czech Republic, May 2011.
Y. Li, Z. Jiang, O. M. Omer-Osman, X. Han, and J. Yin, “Mixed norm constrained sparse APA algorithm for satellite and network echo channel estimation,” IEEE Access, vol. 6, pp. 65901- 65908, 2018.
W. Shi, Y. Li, and Y. Wang, “Noise-free maximum correntropy criterion algorithm in nongaussian environment,” IEEE Transactions on Circuits and Systems II: Express Briefs, 10.1109/ TCSII.2019.2914511, 2019.
Y. Gu, J. Jin, and S. Mei, “l0-norm constraint LMS algorithm for sparse system identification,” IEEE Signal Process. Lett., vol. 16, no. 9, pp. 774-777, 10.1109/LSP.2009.2024736, Sept. 2009.
Y. Li, Y. Wang, R. Yang, et al., “A soft parameter function penalized normalized maximum correntropy criterion algorithm for sparse system identification,” Entropy, vol. 19, no. 1, p. 45, 10.3390/e19010045, Jan. 2017.
Y. Li, Z. Jiang, W. Shi, X. Han, and B. Chen, “Blocked maximum correntropy criterion algorithm for cluster-sparse system identifications,” IEEE Transactions on Circuits and Systems II: Express Briefs, 10.1109/TCSII.2019.2891654, 2019.
D. Angelosante, J. A. Bazerque, and G. B. Giannakis, “Online adaptive estimation of sparse signals: Where RLS meets the l1-norm,” IEEE Transactions on Signal Processing, vol. 58, no. 7, pp. 3436-3447, Mar. 2010.
O. Taheri and S. A. Vorobyov, “Reweighted l1-norm penalized LMS for sparse channel estimation and its analysis,” Elsevier Signal Processing, vol. 104, pp. 70-79, May 2014.
Y. Li, Y. Wang, and T. Jiang, “Sparse-aware set-membership NLMS algorithms and their application for sparse channel estimation and echo cancelation,” AEU - International Journal of Electronics and Communications, vol. 70, no. 7, pp. 895-902, 2016.
Y. Li, Y. Wang, and T. Jiang, “Norm-adaption penalized least mean square/fourth algorithm for sparse channel estimation,” Signal Processing, vol. 128, pp. 243-251, Nov. 2016.
I. S. Caballero, C. J. P. Prieto, and A. A. Rodriguez, “Sparse deconvolution using adaptive mixed-Gaussian models,” Signal Processing, vol. 54, no. 2, pp. 161-172, Oct. 1996.
B. D. Rao and K. K. Delgado, “An affine scaling methodology for best basis selection,” IEEE Transactions on Signal Processing, vol. 47, no. 1, pp. 187-200, 1999.
F. Wu and F. Tong, “Gradient optimization pnorm-like constraint LMS algorithm for sparse system estimation,” Signal Processing, vol. 93, no. 4, pp. 967-971, Apr. 2013.
P. S. R. Diniz, Adaptive Filtering: Algorithms and Practical Implementation, New York, USA: Springer, 2010.
Q. Wu, Y. Li, Y. Zakharov, W. Xue, and W. Shi, A kernel affine projection-like algorithm in reproducing kernel hilbert space, IEEE Transactions on Circuits and Systems II: Express Briefs, 10.1109/TCSII.2019.2947317, 2019.
X. Zhang, T. Jiang, Y. Li, and X. Liu, “An offgrid DOA estimation method using proximal splitting and successive nonconvex sparsity approximation,” IEEE Access, vol. 7, pp. 66764- 66773, 2019.
X. Zhang, T. Jiang, Y. Li, and Y. Zakharov, “A novel block sparse reconstruction method for DOA estimation with unknown mutual coupling,” IEEE Communications Letters, vol. 23, no. 10, pp. 1845-1848, 2019.
F. Liu, J. Guo, L. Zhao, G. L. Huang, Y. Li, and Y. Yin, “Dual-band metasurface-based decoupling method for two closely packed dual-band antennas,” IEEE Transactions on Antennas and Propagation, 10.1109/TAP.2019.2940316, 2019.
J. Guo, F. Liu, L. Zhao, Y. Yin, G. L. Huang, and Y. Li, “Meta-surface antenna array decoupling designs for two linear polarized antennas coupled in H-Plane and E-Plane,” IEEE Access, vol. 7, pp. 100442-100452, 2019.
S. Luo, Y. Li, Y. Xia, and L. Zhang, “A low mutual coupling antenna array with gain enhancement using metamaterial loading and neutralization line structure,” Applied Computational Electromagnetics Society Journal, vol. 34, no. 3, pp. 411-418, 2019.
S. Luo, Y. Li, C. Y. D. Sim, Y. Xia, and X. Liu, “MIMO antenna array based on metamaterial frequency selective surface,” International Journal of RF and Microwave Computer-Aided Engineering, Submitted, 2019.
T. Jiang, T. Jiao, and Y. Li, “A low mutual coupling MIMO antenna using periodic multilayered electromagnetic band gap structures,” Applied Computational Electromagnetics Society Journal, vol. 33, no. 3, 2018.
