Robust Adaptive Beamforming Using Least Mean Mixed Norm Algorithm
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Robust Adaptive Beamforming Using Least Mean Mixed Norm AlgorithmAbstract
This paper proposes an accurate and rapidlyconvergent algorithm for enhanced adaptive beamforming based on the combination of the least mean mixed norm (LMMN) algorithm with initialization using sample matrix inversion (SMI). The algorithm uses a mixing parameter which controls the proportions of the error norms and offers an extra degree of freedom within the adaptation. Monte Carlo simulations show that the misadjustment curve has a minimum at = 0:40 which means that the proposed algorithm has an optimum steady-state performance at this mixing parameter value. The convergence of the algorithm is further improved by employing SMI to initialize the weights vector in the LMMN update equation. This makes the proposed SMI-initialized LMMN algorithm have a better steady state performance when compared to the least mean squares (LMS) algorithm and better stability properties when compared to the least mean fourth (LMF) algorithm. Simulation results obtained show that the developed SMI-initialized LMMN algorithm outperforms other algorithms in terms of computational efficiency, numerical accuracy, and cosnvergence rate.
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References
L. C. Godara, “Applications of antenna arrays to mo-
bile communications I:. performance improvement,
feasibility, and system considerations,” Proceedings
of the IEEE, Vol. 85, No. 7, 1031-1060, 1997.
L. C. Godara, “Application of antenna arrays to
mobile communications, Part II: Beamforming and
direction-of-arrival considerations,” Proceedings of
IEEE, Vol. 85, No. 8, 1195-1245, 1997.
M. Mouhamadou, P. Vaudon, and M. Rammal,
“Smart antenna array patterns synthesis: null steer-
ing and multi-user beamforming by phase control,”
Progress In Electromagnetics Research, PIER 60,
-106, 2006.
F. Gozasht, G. Dadashzadeh, and S. Nikmhr, “A
comprehensive performance study of circular and
hexagonal array geometries in the LMS algorithm
for smart antenna applications,” Progress In Elec-
tromagnetics Research, PIER 68, 281-296, 2007.
F. E. Fakoukakis, S. G. Diamantis, A. P. Orfanides,
and G. A. Kyriacou, “Development of an adaptive
and a switched beam smart antenna system for wire-
less communications,” Journal of Electromagnetic
Waves and Applications, Vol. 20, No. 3, 399-408,
M. I. Dessouky, H. Sharshar, and Y. A. Albagory,
“A novel tapered beamforming window for uniform
concentric circular arrays,” Journal of Electromag-
netic Waves and Applications, Vol. 20, No. 14, 2077-
, 2006.
R. Vescovo, “Beam scanning with null and excitation
constraints for linear arrays of antennas,” Journal of
Electromagnetic Waves and Applications, Vol. 21,
No. 2, 267-277, 2007.
R. M. Shubair and R. S. Nuaimi, “Displaced sensor
array for improved signal detection under grazing
incidence conditions,” Progress In Electromagnetics
Research, PIER 79, 427-441, 2008.
Y.-J. Gu, Z.-G. Shi, K. S. Chen, and Y. Li, “Robust
adaptive beamforming for steering vector uncertain-
ties based on equivalent DOAs method,” Progress
In Electromagnetics Research, PIER 79, 277-290,
Gu Y.-J., Shi Z.-G, Chen K. S, and Li Y., “Robust
adaptive beamforming for a class of Gaussian steer-
ing vector mismatch,” Progress In Electromagnetics
Research, PIER 81, 315-328, 2008.
R. M. Shubair and A. Merri, “Robust algorithms
for direction finding and adaptive beamforming: per-
formance and optimization,” Proceedings of IEEE
International Midwest Symposium of Circuits & Sys-
tems (MWSCAS 2004), Hiroshima, Japan, 589-592,
July 25-28, 2004.
L. C. Godara, “Improved LMS algorithm for adap-
tive beamforming,” IEEE Transactions on Antennas
and Propagation, Vol. 38, No. 10, 1631-1635.
J. A. Chambers, O. Tanrikulu, and A. G. Constan-
tinides, “Least mean mixed-norm adaptive filtering,”
IEE Electronic Letters, Vol. 30, No. 9, 1994.
O. Tanrikulu O. and J. A. Chambers, “Convergence
and steady-state properties of the least-mean mixed
norm (LMMN) adaptive algorithm,” IEE Proceed-
ings on Vision, Image and Signal Processing, Vol.
, No. 3, 137-142, 1996.
S. A. Jimaa, M. E. Jadah, and B. S. Sharif, “Least
mean mixed-norm adaptive filtering for impulsive
DS-CDMA channels,” Proceedings of IEEE Inter-
national Symposium on Signal Processing and In-
formation Technology (ISSPIT 2004), 9-12, 2004.
E. M. Al Ardi, R. M. Shubair, and M. E. Al Mualla,
“Investigation of high-resolution DOA estimation
algorithms for optimal performance of smart antenna
systems,” Proceedings of IEE International Confer-
ence on Third Generation Mobile Communications
(3G’03), 460-464, 2003.
E. M. Al Ardi, R. M. Shubair, and M. E. Al
Mualla, “Performance evaluation of direction finding
algorithms for adaptive antenna arrays,” Proceedings
of IEEE International Conference on Electronics,
Circuits, and Systems (ICECS’03), Vol. 2, 735-738,
M. Samahi M. and R. M. Shubair, “Performance
of smart antenna systems for signal detection and
estimation in multipath fading environment,” Pro-
SHUBAIR, JIMAA, OMAR: ROBUST ADAPTIVE BEAMFORMING USING LEAST MEAN MIXED NORM ALGORITHM
ceedings of IEEE International Conference on Inno-
vations in Information Technology (IIT’06), 2006.
E. M. Al Ardi, R. M. Shubair, and M. E. Al Mualla,
“Direction of arrival estimation in a multipath envi-
ronment: an overview and a new contribution,” Ap-
plied Computational Electromagnetics Society Jour-
nal: Special Issue on Phased and Adaptive Array
Antennas, Vol. 21, No. 3, 226-239, 2006.
J. M. Samhan, R. M. Shubair, M. A. Al Qutayri,
“Design and implementation of an adaptive smart
antenna system,” Proceedings of IEEE International
Conference on Innovations in Information Technol-
ogy (IIT’06), 2006.
R. M. Shubair, M. A. Al Qutayri, and J. M. Samhan,
“A setup for the evaluation of the MUSIC and LMS
algorithms for a smart antenna system,” Journal of
Communications (JCM), Academy Publisher, Vol. 2,
No. 4, 71-77, 2007.
H. L. Van Trees, Detection, Estimation, and Modu-
lation Theory, Part IV: Optimum Array Processing.
John Wiley & Sons, 2002.
S. Haykin, Adaptive Filter Theory. Prentice-Hall, 4th
Ed., 2002.
