Optimization of resource allocation in FDD massive MIMO systems

Abstract

The performance of massive MIMO systems relies heavily on the availability of Channel State Information at the Transmitter (CSIT). A large amount of work has been devoted to reducing the CSIT acquisition overhead at the pilot training and/or CSI feedback stage. In fact, the downlink communication generally includes three stages, i.e., pilot training, CSI feedback, and data transmission. These three stages are mutually related and jointly determine the overall system performance. Unfortunately, there exist few studies on the reduction of CSIT acquisition overhead from the global point of view. In this paper, we integrate the Minimum Mean Square Error (MMSE) channel estimation, Random Vector Quantization (RVQ) based limited feedback and Maximal Ratio Combining (MRC) precoding into a unified framework for investigating the resource allocation problem. In particular, we first approximate the covariance matrix of the quantization error with a simple expression and derive an analytical expression of the received Signal-to-Noise Ratio (SNR) based on the deterministic equivalence theory. Then the three performance metrics (the spectral efficiency, energy efficiency, and total energy consumption) oriented problems are formulated analytically. With practical system requirements, these three metrics can be collaboratively optimized. Finally, we propose an optimization solver to derive the optimal partition of channel coherence time. Experiment results verify the benefits of the proposed resource allocation schemes under three different scenarios and illustrate the tradeoff of resource allocation between three stages.

Keywords

Massive MIMO / FDD / CSIT / Resource allocation

References

[1] F. Boccardi, R. Jr, A. Lozano, T.L. Marzetta, P. Popovski, Five disruptive technology directions for 5g, IEEE Commun. Mag. 52 (2) (2014) 74-80.

[2] H.Q. Ngo, E.G. Larsson, T.L. Marzetta, Energy and spectral efficiency of very large multiuser mimo systems, IEEE Trans. Commun. 61 (4) (2013) 1436-1449.

[3] T.L. Marzetta, Noncooperative cellular wireless with unlimited numbers of base station antennas, IEEE Trans. Wireless Commun. 9 (11) (2010) 3590-3600.

[4] J. Jose, A. Ashikhmin, T.L. Marzetta, S. Vishwanath, Pilot contamination and precoding in multi-cell tdd systems, IEEE Trans. Wireless Commun. 10 (8) (2011) 2640-2651.

[5] F. Rusek, D. Persson, B.K. Lau, E.G. Larsson, T.L. Marzetta, O. Edfors, F. Tufvesson, Scaling up mimo: opportunities and challenges with very large arrays, Signal Process. Mag IEEE 30 (21) (2012) 40-60.

[6] J.C. Guey, L.D. Larsson,Modeling and evaluation of mimo systems exploiting channel reciprocity in tdd mode, in:Proceedings of the 2005 IEEE Vehicular Technology Conference, 2005.

[7] A. Pitarokoilis, S.K. Mohammed, E.G. Larsson, Uplink performance of time-reversal mrc in massive mimo systems subject to phase noise, IEEE Trans. Wireless Commun. 14 (2) (2015) 711-723.

[8] E. Bjornson, J. Hoydis, M. Kountouris, M. DebbaH, Massive mimo systems with non-ideal hardware: energy efficiency, estimation, and capacity limits, IEEE Trans. Inf. Theor. 60 (11) (2013) 7112-7139.

[9] X. Rao, V.K.N. Lau, Distributed compressive csit estimation and feedback for fdd multi-user massive mimo systems, IEEE Trans. Signal Process. 62 (12) (2014) 3261-3271.

[10] E.G. Larsson, O. Edfors, F. Tufvesson, T.L. Marzetta, Massive mimo for next generation wireless systems, IEEE Commun. Mag. 52 (2) (2014) 186-195.

[11] L. Dai, G. Zhen, Z. Wang, Joint channel estimation and feedback with low overhead for fdd massive mimo systems, in: Proceedings of the 2015 IEEE/CIC International Conference on Communications in China, ICCC), 2016.

[12] P. Zhao, Z. Wang, S. Chen, Angular domain pilot design and channel estimation for fdd massive mimo networks, in: Proceedings of the 2017, IEEE International Conference on Communications, 2017.

[13] A. Adhikary, J. Nam, J.Y. Ahn, G. Caire, Joint spatial division and multiplexingłthe large-scale array regime, IEEE Trans. Inf. Theor. 59 (10) (2013) 6441-6463.

[14] Z. Jiang, A.F. Molisch, G. Caire, Z. Niu, Achievable rates of fdd massive mimo systems with spatial channel correlation, IEEE Trans. Wireless Commun. 14 (5)(2015) 2868-2882.

[15] S. Noh, M. Zoltowski, Y. Sung, D.J. Love, Pilot beam pattern design for channel estimation in massive mimo systems, IEEE J. Selected Topics Signal Process. 8 (5)(2013) 787-801.

[16] A.J. Duly, T. Kim, D.J. Love, J.V. Krogmeier, Closed-loop beam alignment for massive mimo channel estimation, IEEE Commun. Lett. 18 (8) (2013) 1439-1442.

[17] J. Choi, D.J. Love, P. Bidigare, Downlink training techniques for fdd massive mimo systems: open-loop and closed-loop training with memory, IEEE J. Selected Topics Signal Process. 8 (5) (2014) 802-814.

[18] W. Yi, W. Song, Y. Huang, C. Li, L. Yang, Effects of the training duration in massive mimo fdd system over spatially correlated channel, in: Proceedings of the 2015 IEEE 82nd Vehicular Technology Conference, VTC Fall), 2015.

[19] D. Wang, X. Wang, X. Yang, Y. Zhao, W. Wan, Design of downlink training sequences for fdd massive mimo systems, in: Proceedings of the 2015, IEEE International Conference on Communications, 2015.

[20] W. Yi, C. Li, Y. Huang, D. Wang, B. Tian, L. Yang, Energy-efficient optimization for downlink massive mimo fdd systems with transmit-side channel correlation, IEEE Trans. Veh. Technol. 65 (9) (2016) 7228-7243.

[21] J. So, D. Kim, Y. Lee, Y. Sung, Pilot signal design for massive mimo systems: a received signal-to-noise-ratio-based approach, IEEE Signal Process. Lett. 22 (5) (2014) 549-553.

[22] W. Kai, W. Wang, G. Lu, X. Gao,Compressive csi acquisition and non-orthogonal pilot design for downlink massive mimo systems, in:Proceedings of the 2016 IEEE Global Communications Conference, 2016.

[23] P.-H. Kuo, H.T. Kung, P.-A. Ting,Compressive sensing based channel feedback protocols for spatially-correlated massive antenna arrays, in:Proceedings of the 2012 IEEE Wireless Communications and Networking Conference (WCNC), 2012, pp. 492-497.

[24] J. Choi, Z. Chance, D.J. Love, U. Madhow, Noncoherent trellis coded quantization: a practical limited feedback technique for massive mimo systems, IEEE Trans. Commun. 61 (12) (2013) 5016-5029.

[25] Y. Jang, G. Kong, M. Jung, S. Choi, I.-M. Kim, Deep autoencoder based csi feedback with feedback errors and feedback delay in fdd massive mimo systems, IEEE Wireless Commun. Lett. 8 (3) (2019) 833-836.

[26] C.-K. Wen, W.-T. Shih, S. Jin, Deep learning for massive mimo csi feedback, IEEE Wireless Commun. Lett. 7 (5) (2018) 748-751.

[27] M.B. Mashhadi, D. Gündüz, Pruning the pilots: deep learning-based pilot design and channel estimation for mimo-ofdm systems, IEEE Trans. Wireless Commun. 20 (10)(2021) 6315-6328.

[28] J. Guo, C.-K. Wen, S. Jin, Deep learning-based csi feedback for beamforming in single-and multi-cell massive mimo systems, IEEE J. Sel. Area. Commun. 39 (7)(2021) 1872-1884.

[29] K. Kong, W.-J. Song, M. Min, Knowledge distillation-aided end-to-end learning for linear precoding in multiuser mimo downlink systems with finite-rate feedback, IEEE Trans. Veh. Technol. 70 (10) (2021) 11095-11100.

[30] J. Jang, H. Lee, S. Hwang, H. Ren, I. Lee, Deep learning-based limited feedback designs for mimo systems, IEEE Wireless Commun. Lett. 9 (4) (2019) 558-561.

[31] M. Kobayashi, N. Jindal, G. Caire, Optimized training and feedback for mimo downlink channels, in: 2009 IEEE Information Theory Workshop on Networking and Information Theory, 2009, pp. 226-230.

[32] M. Kobayashi, G. Caire, N. Jindal, How much training and feedback are needed in mimo broadcast channels?, in: 2008 IEEE International Symposium on Information Theory, 2008, pp. 2663-2667.

[33] W. Santipach, M.L. Honig, Optimization of training and feedback overhead for beamforming over block fading channels, IEEE Trans. Inf. Theor. 56 (12) (2010) 6103-6115.

[34] L. Chen, G. Wei, Energy-efficient power allocation for training-based multiple-input multiple-output system with and without feedback, IET Commun. 7 (15) (2013) 1697-1707.

[35] Y. Zhang, R. Y. Fei, R. Yang, Z. Chen, Z. Wang, Energy-efficient dynamic power allocation in multi-antenna transmissions with imperfect channel estimation and feedback, Electron. Lett. 51 (21).

[36] D.W.K. Ng, E.S. Lo, R. Schober, Energy-efficient resource allocation in ofdma systems with large numbers of base station antennas, IEEE Trans. Wireless Commun. 11 (9) (2012) 3292-3304.

[37] L. Zhao, H. Zhao, F. Hu, K. Zheng, J. Zhang,Energy efficient power allocation algorithm for downlink massive mimo with mrt precoding, in:Proceedings of the 2013 IEEE 78th Vehicular Technology Conference (VTC Fall), 2013.

[38] Y. Kim, G. Miao, T. Hwang, Energy efficient pilot and link adaptation for mobile users in tdd multi-user mimo systems, Wireless Commun. IEEE Trans. on 13 ( 2014) 382-393.

[39] V. Raghavan, V.V. Veeravalli, Ensemble properties of rvq-based limited-feedback beamforming codebooks, IEEE Trans. Inf. Theor. 59 (12) (2013) 8224-8249.

[40] R. Couillet, M. Debbah, J. W. Silverstein,A Deterministic Equivalent for the Capacity Analysis of Correlated Multi-User Mimo Channels, CoRR.

[41] N. Jindal, Mimo broadcast channels with finite-rate feedback, IEEE Trans. Inf. Theor. 52 (11) (2006) 5045-5060.

[42] J.A.T. Thomas, M. Cover, Elements of Information Theory, Wiley, New York, 2006.

[43] K. Kim, T. Kim, D.J. Love, I.H. Kim, Differential feedback in codebook-based multiuser mimo systems in slowly varying channels, IEEE Trans. Commun. 60 (2)(2012) 578-588.

[44] J.H. Kotecha, A.M. Sayeed, Transmit signal design for optimal estimation of correlated mimo channels, IEEE Trans. Signal Process. 52 (2) (2004) 546-557.

[45] B. Hassibi, B. Hochwald, How much training is needed in multiple-antenna wireless links? IEEE Trans. Inf. Theor. 49 (4) (2003) 951-963.