American Institute of Mathematical Sciences

Advanced
2016, 6(3): 297-304. doi: 10.3934/naco.2016012

A low-complexity zero-forcing Beamformer design for multiuser MIMO systems via a dual gradient method

Bin Li 1, , Hai Huyen Dam 1, and  Antonio Cantoni 2,

1. 

Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, WA 6845
2. 

School of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009

Received  March 2015 Revised  September 2016 Published  September 2016

In this paper, we consider the zero-forcing beamforming (ZFBF) under the per-antenna power constraints (PAPC). Our objective is to maximize the minimum user information rate. Traditionally, ZFBF under PAPC with a max-min performance measure can be transformed into a second order cone problem and then solved by applying the interior point method. However, it is expensive to realize this design in practice due to high computational complexity per iteration. An alternative low complexity zero-forcing beamformer design is proposed for MU-MIMO systems by applying a dual gradient method. Different from the step size rule in the literature, a backtracking line search is adopted. A numerical example is provided to show the effectiveness of the proposed method.
Keywords: a gradient method, Zero-forcing beamforming, MIMO systems, a backtracking line search..
Mathematics Subject Classification: Primary: 90B18; Secondary: 90C2.
Citation: Bin Li, Hai Huyen Dam, Antonio Cantoni. A low-complexity zero-forcing Beamformer design for multiuser MIMO systems via a dual gradient method. Numerical Algebra, Control and Optimization, 2016, 6 (3) : 297-304. doi: 10.3934/naco.2016012
References:
[1]

S. J. Benson, Y. Ye and X. Zhang, Solving large-scale sparese semidefinite programs for combinational optimization, SIAM J. Optim., 10 (2000), 443-461. doi: 10.1137/S1052623497328008.

[2]

S. Boyd and L. Vandenberghe, Covex Optimization, Cambrige, UK: Cambrige University Press, 2004. doi: 10.1017/CBO9780511804441.

[3]

G. Caire and S. Shamai (Shitz), On the achievable throughput of multiatenna Gaussian broadcast channel, IEEE Trans. Inf. Theory., 49 (2003), 1691-1706. doi: 10.1109/TIT.2003.813523.

[4]

H. H. Dam and A. Cantoni, Interior point method for optimum zero-forcing beamforming with per-antenna power constraints and optimal step size, Signal Process., 106 (2015), 10-14.

[5]

K. Karakayali, R. Yates, G. Foschini and R. Valenzuela, Optimal zero-forcing beamforming with per-antenna power constraints, IEEE International Symposium on Information Theory, Nice, France, (2007), 101-105.

[6]

S. R. Lee, J. S. Kim, S. H. Moon, H. B. Kong and I. Lee, Zero-forcing beamforming in multiuser MISO downlink systems under per-antenna power constraint and equal-rate metric, IEEE Trans. Wireless Commun., 12 (2013), 228-236.

[7]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A global optimal zero-forcing beamformer esign with signed Power-of-Two coefficients, Journal of Industrial and Management Optimization, 12 (2016), 625-636.

[8]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A first-order optimal zero-forcing beamformer design for multiuser MIMO systems via a regularized dual accelerated gradient method, IEEE Commun. Lett., 19 (2015), 195-198.

[9]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, Some interesting properties for zero-forcing beamforming under per-antenna power constraints in rural areas, J. Glob. Optim., 62 (2015), 877-886. doi: 10.1007/s10898-014-0237-4.

[10]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A primal-dual interior point method for optimal zero-forcing beamformer design under per-antenna power constraints, Optim. Lett., 8 (2014), 1829-1843. doi: 10.1007/s11590-013-0673-y.

[11]

B. Li, C. Z. Wu, H. H. Dam, A. Cantoni and K. L. Teo, A parallel low complexity zero-forcing beamformer design for multiuser MIMO systems via a regularized dual decomposition method, IEEE Trans. Signal Process., 63 (2015), 4179-4190. doi: 10.1109/TSP.2015.2437846.

[12]

H. Suzuki, D. Robertson, N. L. Ratnayake and K. Ziri-Castro, Prediction and measurement of multiuser MIMO-OFDM channel in rural Australia, IEEE 75th Vehicular Technology Conference, (2012), 1-5.

[13]

L. Vandenberghe, Lecture Notes: Optimization Methods for Large-Scale Systems, UCLA, Spring 2013-2014.

[14]

A. Wiesel, Y. C. Eldar and S. Shamai (Shitz), Linear precoding via conic optimizaiton for fixed MIMO receivers, IEEE Trans. Signal Process., 54 (2006), 161-176.

[15]

A. Wiesel, Y. C. Eldar and S. Shamai (Shitz), Zero-forcing precoding and generalized inverses, IEEE Trans. Signal Process., 56 (2008), 4409-4418. doi: 10.1109/TSP.2008.924638.

show all references

References:
[1]

S. J. Benson, Y. Ye and X. Zhang, Solving large-scale sparese semidefinite programs for combinational optimization, SIAM J. Optim., 10 (2000), 443-461. doi: 10.1137/S1052623497328008.

[2]

S. Boyd and L. Vandenberghe, Covex Optimization, Cambrige, UK: Cambrige University Press, 2004. doi: 10.1017/CBO9780511804441.

[3]

G. Caire and S. Shamai (Shitz), On the achievable throughput of multiatenna Gaussian broadcast channel, IEEE Trans. Inf. Theory., 49 (2003), 1691-1706. doi: 10.1109/TIT.2003.813523.

[4]

H. H. Dam and A. Cantoni, Interior point method for optimum zero-forcing beamforming with per-antenna power constraints and optimal step size, Signal Process., 106 (2015), 10-14.

[5]

K. Karakayali, R. Yates, G. Foschini and R. Valenzuela, Optimal zero-forcing beamforming with per-antenna power constraints, IEEE International Symposium on Information Theory, Nice, France, (2007), 101-105.

[6]

S. R. Lee, J. S. Kim, S. H. Moon, H. B. Kong and I. Lee, Zero-forcing beamforming in multiuser MISO downlink systems under per-antenna power constraint and equal-rate metric, IEEE Trans. Wireless Commun., 12 (2013), 228-236.

[7]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A global optimal zero-forcing beamformer esign with signed Power-of-Two coefficients, Journal of Industrial and Management Optimization, 12 (2016), 625-636.

[8]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A first-order optimal zero-forcing beamformer design for multiuser MIMO systems via a regularized dual accelerated gradient method, IEEE Commun. Lett., 19 (2015), 195-198.

[9]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, Some interesting properties for zero-forcing beamforming under per-antenna power constraints in rural areas, J. Glob. Optim., 62 (2015), 877-886. doi: 10.1007/s10898-014-0237-4.

[10]

B. Li, H. H. Dam, A. Cantoni and K. L. Teo, A primal-dual interior point method for optimal zero-forcing beamformer design under per-antenna power constraints, Optim. Lett., 8 (2014), 1829-1843. doi: 10.1007/s11590-013-0673-y.

[11]

B. Li, C. Z. Wu, H. H. Dam, A. Cantoni and K. L. Teo, A parallel low complexity zero-forcing beamformer design for multiuser MIMO systems via a regularized dual decomposition method, IEEE Trans. Signal Process., 63 (2015), 4179-4190. doi: 10.1109/TSP.2015.2437846.

[12]

H. Suzuki, D. Robertson, N. L. Ratnayake and K. Ziri-Castro, Prediction and measurement of multiuser MIMO-OFDM channel in rural Australia, IEEE 75th Vehicular Technology Conference, (2012), 1-5.

[13]

L. Vandenberghe, Lecture Notes: Optimization Methods for Large-Scale Systems, UCLA, Spring 2013-2014.

[14]

A. Wiesel, Y. C. Eldar and S. Shamai (Shitz), Linear precoding via conic optimizaiton for fixed MIMO receivers, IEEE Trans. Signal Process., 54 (2006), 161-176.

[15]

A. Wiesel, Y. C. Eldar and S. Shamai (Shitz), Zero-forcing precoding and generalized inverses, IEEE Trans. Signal Process., 56 (2008), 4409-4418. doi: 10.1109/TSP.2008.924638.

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