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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

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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

Multi-Layer Precoding: A Potential Solution for Full-Dimensional Massive MIMO Systems

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Outline

Introduction System and Channel Models Multi-Layer Precoding Design Performance Results

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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 High sum-rates Simplified multi-user processing Small transmit power

MIMO is Big!

Why not we keep scaling MIMO up?

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Interference Management is Challenging

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?

Bas Bas Bas

MU interference Inter-cell interference

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Interference Management is Challenging

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?

Bas Bas Bas

MU interference Inter-cell interference

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Multi-Layer Precoding: A Potential Solution

Decoupling of Precoding Objectives

Each precoding layer (matrix) is responsible of one objective

Dependence on large channel statistics

Each precoding layer depends on channel statistics larger (slower) than next layers

Ba Ba

MU interference Inter-cell interference

F = F(1)F(2)F(3)

Inter-cell interference management Desired signal

ptimization

Multi-user interference management

Low-complexity design Requires limited CSI

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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]

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. [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 Ba

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System Model

BS has a 2D antenna array of NV vertical elements x NH 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

Base Base

L cells

MS’s per cell

MS k

antennas at the BS

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Channel Model

Kronecker product correlation [1] Using Karhunen-Loeve representation [2] Assuming rank-1 elevation correlation [3]

Bas

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 ’13), pp. 1–5, Las Vegas, Nev, USA, September 2013.

Elevation correlation Azimuth correlation

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Insights from Large Channel Characteristics

Channel covariance matrices have directional structure [1], [2]

In the elevation direction, signal and interference may occupy different subspaces Signal and interference are contained in low-dimensional subspaces

Ba Ba

Interference subspace

Cell c [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 Conference (VTC ’13), pp. 1–5, Las Vegas, Nev, USA, September 2013.

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Multi-Layer Precoding Design (1/3)

The SINR of user k in cell c is In the design

Leverage the Kronecker structure of the channel Focus on multi-layer precoding in the elevation direction

Desired signal power Inter-cell interference Multi-user interference Minimize inter-cell interference Requires large-scale channel statistics Maximize effective signal power Requires large-scale channel statistics Minimize multi-user interference Requires instantaneous channel

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Multi-Layer Precoding Design (2/3)

First layer: To avoid inter-cell interference, is designed such that After the first layer

Inter-cell interference Expectation over different scheduled users Interference null-space

B B

Interference subspace

Intuition

Cell c

Time

Due to the expectation

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Multi-Layer Precoding Design (3/3)

Second layer

Training: Acquires effective channel elevation covariance eigenvectors (reduced rank) 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) After the third layer

Conjugate beamforming of the effective channel covariance Effective channel is of K x K dimensions Penalty of interference management

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Achievable Rates

Assume The achievable rate of user k in cell c with Asymptotic optimality Performance approaches single-user rate

ucck 2 R
UNI

, 8k
?

Rck log2 ✓ 1 + PkhA

cckk2cck

2 G

◆ ✓ ◆

where G
Uc
= 4

✓

max(Uc)

min(Uc) +

min(Uc)

max(Uc) + 2

◆1

and
the maximum and minimum

lim

NV!1 r/NV=const.

Rck = ˚ Rckwith and

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Simulation Results

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

Setup: 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

Ba Ba Ba Ba

Multi-layer precoding gain Small difference between exact and

approx. int. covariance

knowledge

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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.

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Questions?

Ahmed Alkhateeb

The University of Texas at Austin

Thank You