Norm Constrained Noise-free Algorithm for Sparse Adaptive Array Beamforming
Keywords:
Array beamforming, constrained LMS algorithm, l1-norm constraint, noise-free normalizing, sparse adaptive beamformingAbstract
In this paper, a reweighted l1-norm constrained noise-free normalized least mean square (NLMS) (RL1- CNFLMS) algorithm is proposed for dealing with sparse adaptive array beamforming. The proposed RL1-CNFLMS algorithm integrates a reweighted l1-norm penalty into the traditional objective function of constrained least mean square least mean square (LMS) (CLMS) algorithm to drive the weighted coefficient vector to sparsity. Besides, the Lagrange multiplier (LM) method and the gradient descent principle are employed during the derivation procedure for getting the update equation. Additionally, we utilize the l1-l2 optimization method to acquire the noise-free a posteriori error signal in normalizing process to achieve a quicker convergence speed, a better signal to interference plus noise ratio (SINR) performance as well as a higher array sparsity with an acceptable computational complexity. Simulation results turn out that by using the noise-free and norm constraint techniques, a fairly comparable beampattern is achieved by using only 38.4%, 39.4% and 69.4% antenna elements in contrast to the constrained NLMS (CNLMS), reweighted l1-norm constrained LMS (RL1- CLMS) and reweighted l1-norm constrained normalized LMS (RL1-CNLMS) algorithms, respectively.
Downloads
References
H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part IV: Optimum Array Processing, John Wiley & Sons, New York, NY, 2002.
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, Sep. 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. 10.1109/TSP.2015.2474302.
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, Y. Li, and J. Yin, “Improved constraint NLMS algorithm for sparse adaptive array beamforming control applications,” Applied Computational Electromagnetics Society Journal, Accepted.
S. A. Vorobyov, A. B. Gershman, and Z. Luo, “Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem,” IEEE Transactions on Signal Processing, vol. 51, no. 2, pp. 313-324, Feb. 2003. 10.1109/tsp.2002.806865.
O. Taheri and S. A. Vorobyov, Reweighted l1-Norm Penalized LMS for Sparse Channel Estimation and its Analysis. Elsevier North-Holland, Inc. 2014.
T. Jiang, X. Zhang, and Y. Li, “Bayesian compressive sensing using reweighted Laplace priors,” AEÜ - International Journal of Electronics and Communications, vol. 97, pp. 178-184, 2018.
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), Prague, Czech Republic, pp. 2864-2867, May 2011.
Y. Wang, Y. Li, and Z. Jin, “An improved reweighted zero-attracting NLMS algorithm for broadband sparse channel estimation,” IEEE International Conference on Electronic Information and Communication Technology, Harbin, China, Aug. 2016.
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, Sept. 2009. 10.1109/LSP.2009.2024736.
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, Jan. 2017. 10.3390/e19010045.
Z. Jin, Y. Li, and J. Liu, “An improved setmembership proportionate adaptive algorithm for a block-sparse system,” Symmetry, vol. 10, no. 3, p. 75, Mar. 2018. 10.3390/sym10030075.
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. 10.1109/TSP.2010.2046897.
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, 2016.
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.
D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
I. Daubechies, M. Defrise, and C. De-Mol, “An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,” Comm. Pure Appl. Math., vol. 57, pp. 1413-1457, 2004.
M. Zibulevsky and M. Elad, “l1-l2 optimization in signal and image processing,” IEEE Signal Process. Mag., pp. 76-88, May 2010.
M. Z. A. Bhotto and A. Antoniou, “A family of shrinkage adaptive filtering algorithms,” IEEE Trans. Signal Process., vol. 61, no. 7, pp. 1689- 1697, 2013.
P. S. R. Diniz, Adaptive Filtering: Algorithms and Practical Implementation. New York, USA: Springer, 2010.
Y. Li, Z. Jiang, W. Shi, X. Han, and B. D. Chen, “Blocked maximum correntropy criterion algorithm for cluster-sparse system identification,” IEEE Transactions on Circuits and Systems II: Express Briefs, 10.1109/TCSII.2019.2891654.
Y. Li, Z. Jiang, O. M. Omer-Osman, X. Han, and J. Yin, “Mixed norm constrained sparse APA algorithm for satellite and network channel estimation,” IEEE Access, vol. 6, pp. 65901-65908, 2018.
Y. Li, Z. Jiang, Z. Jin, X. Han, and J. Yin, “Clustersparse proportionate NLMS algorithm with the hybrid norm constraint,” IEEE Access, vol. 6, pp. 47794-47803, 2018.
K. Yu, Y. Li, and X. Liu, “Mutual coupling reduction of a MIMO antenna array using 3-D novel meta-material structures,” Applied Computational Electromagnetics Society Journal, vol. 33, no. 7, pp. 758-763, 2018.
L. Zhao, F. Liu, X. Shen, G. Jing, Y. Cai, and Y. Li, “A high-pass antenna interference cancellation chip for mutual coupling reduction of antennas in contiguous frequency bands,” IEEE Access, vol. 6, pp. 38097-38105, 2018.
T. Jiang, T. Jiao, Y. Li, and W. Yu, “A low mutual coupling MIMO antenna using periodic multilayered electromagnetic band gap structures,” Applied Computational Electromagnetics Society Journal, vol. 33, no. 3, pp. 305-311, 2018.
