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| Energy-efficiency Optimization of Pilot Duration and Power Allocation for Downlink Massive MIMO FDD Systems |
| WANG Yi LIN Yan LI Chunguo HUANG Yongming YANG Luxi |
| (School of Information Science and Engineering, Southeast University, Nanjing 210096, China) |
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Abstract An energy-efficient resource allocation method is provided for the downlink massive Multiple-Input Multiple-Output (MIMO) Frequency Division Duplexing (FDD) system, which jointly evaluates the channel estimation stage and data transmission stage. The optimization problem is established based on the Energy Efficiency (EE) maximization by adjusting the pilot duration, pilot power and data power under the constraint of total transmit energy and spectral efficiency requirement. Since the analytical expression of the involved objective function is intractable, a closed-form expression is deduced using deterministic equivalent approximation technology. Based on this, the original non-convex fractional optimization problem is transformed into an equivalent problem in subtractive form by the means of fraction programming. Then, a lower bound of the transformed objective function is employed, which induces a relatively easy-to-solve equivalent problem. Finally, a three-layer iterative algorithm is developed. Numerical results validate the effectiveness and relatively fast convergence speed of the proposed algorithm.
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Received: 11 March 2016
Published: 09 October 2016
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| Fund: The National 863 Program of China (2015AA01A703), The National Natural Science Foundation of China (61372101, 61271018, 61671144), Research Project of Jiangsu Province (BE2015156), The Natural Science Research Project of Jiangsu Province for Colleges and Universities (16KJB510008) |
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Corresponding Authors:
WANG Yi
E-mail: yiwang@seu.edu.cn
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| [1] |
MARZETTA T L. Noncooperative cellular wireless with unlimited numbers of base station antennas[J]. IEEE Transactions on Wireless Communications, 2010, 9(11): 3590-3600. doi: 10.1109/TWC.2010.092810.091092.
|
| [2] |
RUSEK F, PERSSON D, LAU B K, et al. Scaling up MIMO: opportunities and challenges with very large arrays[J]. IEEE Signal Processing Magazine, 2013, 30(1): 40-60. doi: 10.1109/ MSP.2011.2178495.
|
| [3] |
HOYDIS J, BRINK S T, and DEBBAH M. Massive MIMO in the UL/DL of cellular networks: how many antennas do we need?[J]. IEEE Journal on Selected Areas in Communications, 2013, 31(2): 160-171. doi: 10.1109/JSAC.2013.130205.
|
| [4] |
LARSSON E, EDFORS O, TUFVESSON F, et al. Massive MIMO for next generation wireless systems[J]. IEEE Communications Magazine, 2014, 52(2): 186-195. doi: 10. 1109/MCOM.2014.6736761.
|
| [5] |
NGO H Q, LARSSON E G, and MARZETTA T L. Energy and spectral efficiency of very large multiuser MIMO systems [J]. IEEE Transactions on Communications, 2013, 61(4): 1436-1449. doi: 10.1109/TCOMM.2013.020413.110848.
|
| [6] |
BOCCARDI F, HEATH R W, LOZANO A, et al. Five disruptive technology directions for 5G[J]. IEEE Communications Magazine, 2014, 52(2): 74-80. doi: 10.1109/ MCOM.2014.6736746.
|
| [7] |
JIANG Z, A MOLISCH F, CAIRE G, et al. Achievable rates of FDD massive MIMO systems with spatial channel correlation[J]. IEEE Transactions on Wireless Communications, 2015, 14((5): 2868-2882. doi: 10.1109/ TWC. 2015.2396058
|
| [8] |
DULY A, KIM T, LOVE D J, et al. Closed-loop beam alignment for massive MIMO channel estimation[J]. IEEE Communications Letters, 2014, 18(8): 1439-1442. doi: 10. 1109/LCOMM.2014.2316157
|
| [9] |
CHOI J, LOVE D J, and BIDIGARE P. Downlink training techniques for FDD massive MIMO systems: Open-loop and closed-loop training with memory[J]. IEEE Journal of Selected Topics in Signal Processing, 2014, 8(5): 802-814. doi: 10.1109/JSTSP.2014.2313020.
|
| [10] |
WANG Y, SONG W, HUANG Y, et al. Effects of the training duration in massive MIMO FDD System over spatially correlated channel[C]. IEEE Vehicular Technology Conference, Boston, MA, USA, 2015: 1-5.
|
| [11] |
WANG D, WANG X, YANG H, et al. Design of downlink training sequences for FDD massive MIMO systems[C]. IEEE International Conference on Communications, London, UK, 2015: 4570-4575.
|
| [12] |
ADHIKARY A, NAM J, AHN J Y, et al. Joint spatial division and multiplexing: The large-scale array regime[J]. IEEE Transactions on Information Theory, 2013, 59(10): 6441-6463. doi: 10.1109/TIT.2013.2269476.
|
| [13] |
LI G Y, XU Z K, XIONG C, et al. Energy-efficient wireless communications: Tutorial, survey, and open issues[J]. IEEE Wireless Communications, 2011, 18(6): 28-35. 10.1109/ MWC.2011.6108331.
|
| [14] |
NG D, LO E, and SCHOBER R. Energy-efficient resource allocation in OFDMA systems with large numbers of base station antennas[J]. IEEE Transactions on Wireless Communications, 2012, 11(9): 3292-3304. doi: 10.1109/TWC. 2012.072512.111850.
|
| [15] |
ZHAO L, ZHAO H, HU F, et al. Energy efficient power allocation algorithm for downlink massive MIMO with MRT precoding[C]. IEEE Vehicular Technology Conference, Las Vegas, NV, USA, 2013: 1-5.
|
| [16] |
KIM Y, MIAO G, and T HWANG. Energy efficient pilot and link adaptation for mobile users in TDD multi-user MIMO systems[J]. IEEE Transactions on Wireless Communications, 2014, 13(1): 382-393. doi: 10.1109/TWC.2013.120113. 130677.
|
| [17] |
BJORNSON E, HOYDIS J, KOUNTOURIS M, et al. Massive MIMO systems with non-ideal hardware: energy efficiency, estimation, and capacity limits[J]. IEEE Transactions on Information Theory, 2014, 60(11): 7112-7139. doi: 10.1109/TIT.2014.2354403.
|
| [18] |
SANTIPACH W and HONIG M. Optimization of training and feedback overhead for beamforming over block fading channels[J]. IEEE Transactions on Information Theory, 2010, 56(12): 6103-6115. doi: 10.1109/TIT.2010.2081150.
|
| [19] |
TRUONG K T and HEATH R W. Effects of channel aging in massive MIMO systems[J]. Journal of Communications and Networks, 2013, 15(4): 338-351. doi: 10.1109/JCN.2013. 000065.
|
| [20] |
DINKELBACH W. On nonlinear fractional programming[J]. Management Science, 1967, 13(7): 492-498. doi: 10.1287/ mnsc.13.7.492.
|
| [21] |
HE S, HUANG Y, JIN S, et al. Coordinated beamforming for energy efficient transmission in multicell multiuser systems[J]. IEEE Transactions on Communications, 2013, 61(12): 4961-4971. doi: 10.1109/TCOMM.2013.110313.130350.
|
| [22] |
BOYD S and VANDENBERGHE L. Convex Optimization [M]. Cambridge, U.K.: Cambridge Univ. Press, 2004: 143-289.
|
|
|
|
