Multi-Layer Precoding: A Potential Solution for Full-Dimensional Massive MIMO Systems Ahmed Alkhateeb, Geert Leus*, and Robert W. Heath Jr Wireless Networking and Communications Group Department of Electrical and Computer Engineering The University of Texas at Austin *Delft University of Technology Faculty of EE., Mathematics and Computer Science
Outline Introduction System and Channel Models Multi-Layer Precoding Design Performance Results 2
MIMO is Big! mmWave systems Large arrays are needed at transmitter & receiver Leverage large available bandwidth at high frequency Enable very high data rates Massive MIMO gains Large numbers of users are simultaneously served Ba High sum-rates Simplified multi-user processing Small transmit power Why not we keep scaling MIMO up? 3
Interference Management is Challenging Bas Bas Inter-cell interference Bas MU interference Need high channel state information (CSI) Large channel dimensions Large amount of pilots Basestation cooperation overhead How to manage the interference with limited channel knowledge? 4
Interference Management is Challenging Bas Bas Inter-cell interference Bas MU interference High precoding design complexity Precoders need to be designed to manage different kinds of interference Precoders of different cells need to be jointly designed (usually non-convex problems) Large dimensions add more complexity How to develop low-complexity precoders for large MIMO systems? 5
Multi-Layer Precoding: A Potential Solution F = F (1) F (2) F (3) Inter-cell interference Ba Ba Inter-cell Multi-user Desired signal interference interference MU interference optimization management management Decoupling of Precoding Objectives Low-complexity design Each precoding layer (matrix) is responsible of one objective Dependence on large channel statistics Requires limited CSI Each precoding layer depends on channel statistics larger (slower) than next layers 6
Connection to Prior Work Multi-user hybrid analog/digital precoding [1] Motivated mainly by hardware constraints Leverages the sparse nature of mmWave channels Did not consider out-of-cell interference Joint spatial-division multiplexing [2] Ba Motivated by large channel feedback overhead in FDD Groups the users based on their channel covariance Did not consider out-of-cell interference Pilot decontamination for massive MIMO [3] Leverages the low-dimensional interference subspace to get better desired channel estimate Considered 1-D antenna arrays Requires the knowledge of the interference covariance matrices [1] A. Alkhateeb, G. Leus, and R. W. Heath Jr, “Limited feedback hybrid precoding for multi-user millimeter wave systems,” submitted to IEEE Trans. on Wireless Commu, arXiv:1409.5162 , 2014. [2] A. Adhikary, J. Nam, J.-Y. Ahn, and G. Caire, “Joint spatial division and multiplexing: The large-scale array regime,” IEEE Trans. of IT., vol. 59, no. 10, pp. 6441–6463, October 2013. 7 [3] Y. Haifan, D. Gesbert, M. Filippou, Y. Liu, "A Coordinated Approach to Channel Estimation in Large-Scale Multiple-Antenna Systems," IEEE JSAC, vol.31, no.2, pp.264,273, February 2013
System Model antennas at the BS Base MS’s per cell Base MS k L cells BS has a 2D antenna array of N V vertical elements x N H horizontal elements K single-antenna users are simultaneously served in each cell All BS’s are assumed to be synchronized - TDD - Universal frequency reuse In the downlink, precoder is used by BS c Received signal by user k in cell c 8
Channel Model Kronecker product correlation [1] Azimuth correlation Elevation correlation Using Karhunen-Loeve representation [2] Bas Assuming rank-1 elevation correlation [3] Higher scattering in the street level [1] Ying D, Nam J, Vook FW, Thomas TA, Love DJ, Ghosh A: Kronecker product correlation model and limited feedback codebook design in a 3d channel model. In Proc. IEEE International Conference on Communications . Sydney; 10–14 June 2014. [2] A. Adhikary, J. Nam, J.-Y. Ahn, and G. Caire, “Joint spatial division and multiplexing: The large-scale array regime,” IEEE Transactions on Information Theory, vol. 59, no. 10, pp. 6441–6463, October 2013. [3] Z. Zhong, X. Yin, X. Li, and X. Li, “Extension of ITU IMTadvanced channel models for elevation domains and line-of-sight scenarios,” in Proceedings of the 78th IEEE Vehicular Technology Conference (VTC 9 ’13), pp. 1–5, Las Vegas, Nev, USA, September 2013.
Insights from Large Channel Characteristics Channel covariance matrices have directional structure [1], [2] Signal and interference are contained in low-dimensional subspaces Interference subspace Ba Ba Cell c In the elevation direction, signal and interference may occupy different subspaces [1] Y. Haifan, D. Gesbert, M. Filippou, Y. Liu, "A Coordinated Approach to Channel Estimation in Large-Scale Multiple-Antenna Systems," IEEE JSAC , vol.31, no.2, pp.264,273, February 2013 [2] Z. Zhong, X. Yin, X. Li, and X. Li, “Extension of ITU IMTadvanced channel models for elevation domains and line-of-sight scenarios,” in Proceedings of the 78th IEEE Vehicular Technology 10 Conference (VTC ’13), pp. 1–5, Las Vegas, Nev, USA, September 2013.
Multi-Layer Precoding Design (1/3) The SINR of user k in cell c is Desired signal power Inter-cell interference Multi-user interference In the design Leverage the Kronecker structure of the channel Focus on multi-layer precoding in the elevation direction Minimize inter-cell interference Maximize effective signal power Minimize multi-user interference Requires large-scale channel statistics Requires large-scale channel statistics Requires instantaneous channel 11
Multi-Layer Precoding Design (2/3) First layer: Inter-cell interference To avoid inter-cell interference, is designed such that Intuition Interference subspace B B Expectation over different scheduled users Cell c Interference null-space Time After the first layer Due to the expectation 12
Multi-Layer Precoding Design (3/3) Second layer Training: Acquires effective channel elevation covariance eigenvectors (reduced rank) Conjugate beamforming of the effective channel covariance Remark: No uplink inter-cell interference during training phase due to first layer After the second layer Third layer Training: Instantaneous effective channels (reduced-rank channel) Effective channel is of K x K dimensions After the third layer Penalty of interference management 13
Achievable Rates Assume U NI � � • u cck 2 R , 8 k c � ? � The achievable rate of user k in cell c 1 + P k h A cck k 2 � cck ✓ �◆ � R ck � log 2 G U c � 2 � � with ✓ ◆ ◆ � 1 ✓ � 2 max ( U c ) � 2 min ( U c ) � � = 4 min ( U c ) + max ( U c ) + 2 where G U c � 2 � 2 � � � � and the maximum and minimum Asymptotic optimality R ck with and R ck = ˚ lim N V !1 r/N V =const . Performance approaches single-user rate 14
Simulation Results Ba Multi-layer precoding gain Ba Ba Small difference Ba between exact and approx. int. covariance Setup: knowledge Poisson layout of BS’s and MS’s MS poisson density is 30 times higher than BS densities Inter-site distance=200 m, antenna height=50 m MS’s are associated to the nearest BS BS randomly selects K=4 MS’s to be served Performance is averaged over100 realizations Interference covariance is averaged over 20 realizations Pathloss exponent=3.5 Considerable gains compared with interference-limited massive MIMO systems Gains are mainly due to inter-cell interference management Gains increase with the number of antennas Very close performance to the case with exact interference covariance matrix Cell edge users may be blocked if the number of antennas is not large enough 15
Conclusion and Future Work Multi-layer precoding Manages inter-cell and multi-user interference Requires limited channel knowledge Enables low-complexity designs (precoding objectives decoupling) Approaches the single-user rates in some special cases Future extensions Performance analysis for more general channel settings, e.h., including angle spread Investigating solutions to improve cell-edge users in the non-asymptotic regime Evaluating the impact of channel estimation errors Approximation using hybrid analog/digital architecture Ahmed Alkhateeb, Geert Leus, and Robert W. Heath Jr, "Multi-Layer Precoding for Full-Dimensional Massive MIMO Systems," in Proc. of Asilomar Conference on Signals, Systems and Computers , Pacific Grove, CA, November 2014. 16
Thank You Questions? Ahmed Alkhateeb The University of Texas at Austin 17
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