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Message-Passing Based Channel Estimation for Reconfigurable Intelligent Surface Assisted MIMO

Hang Liu*, Xiaojun Yuan†, and Ying-Jun Angela Zhang*

*Department of Information Engineering, The Chinese University of Hong Kong †Center for Intelligent Networking and Communications,

University of Electronic Science and Technology of China

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 1 / 19

Presenter

Hang Liu Department of Information Engineering The Chinese University of Hong Kong Email: lh117@ie.cuhk.edu.hk

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 2 / 19

Overview

1

Reconfigurable Intelligent Surface (RIS)

2

RIS-Assisted MIMO Channel Estimation

3

Bayesian Inference and Result

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 3 / 19

What is Reconfigurable Intelligent Surface (RIS)

One of the key technologies to realize smart radio environments:

• An artificial surface formed by a sub-wavelength array of

sub-wavelength metallic or dielectric scattering particles;

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 4 / 19

What is Reconfigurable Intelligent Surface (RIS)

Main features of RISs:

• (Real-time) configurability: Can modify the direction of the reflected

waves;

• Low-power-consuming, nearly-passive, cheap;
• Easily placed in/on the wall/ceilings.
• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 5 / 19

RIS-Assisted MIMO

• M-antenna Base station;
• K (single-antenna) users;
• An RIS to assisted the communication in between;
• The RIS can be seen as an L-antenna uniform rectangular array;
• Each RIS element induces an independent phase shift on the incident

EM wave: ψ(t) [̟1(t)ejψ1(t), ̟2(t)ejψ2(t), · · · , ̟L(t)ejψL(t)]T ;

• ̟l(t) ∈ {0, 1}: ON/OFF;
• ψl(t) ∈ [0, 2π): phase shift;

BS

User 1 User 2 User K

RIS

RB

H

, UR K

h

,2 UR

h

,1 UR

h

,1 UB

h

,2 UB

h

, UB K

h

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 6 / 19

RIS-Assisted MIMO1

By optimizing the phase shift vector ψ, received power scales as O(L2) for a large L.

• Significant improvement compared to massive MIMO (O(M));
• To optimize ψ, channel state information is critical!
• 1Q. Wu and R. Zhang, ”Intelligent Reflecting Surface Enhanced Wireless Network via Joint Active and Passive

Beamforming”.

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 7 / 19

RIS-Assisted MIMO Channels

• User-to-BS direct channels: hUB,k;
• RIS-to-BS channel: HRB;
• User-to-RIS channels: hUR,k.

BS

User 1 User 2 User K

RIS

RB

H

, UR K

h

,2 UR

h

,1 UR

h

,1 UB

h

,2 UB

h

, UB K

h

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 8 / 19

RIS-Assisted MIMO Channel Estimation

• Dedicate T time slots for uplink RIS channel training⇒ Training

signal matrix X ∈ CK×T ;

• Choose a constant RIS phase shift⇒

ψ(t) = [1, 1, · · · , 1]

• By turning off the RIS, hUB,k can be estimated by using conventional

channel estimation methods for multiuser MIMO systems.

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 9 / 19

RIS-Assisted MIMO Channel Estimation

Received Signal (after canceling the direct channels): Y = HRBHURX + N

• AWGNMatrix
• Passive RIS has very limited signal processing capability;
• Cascaded Channel Estimation: The BS estimates HRB and HUR

from a noisy cascade of them.

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 10 / 19

RIS-to-BS Channel Model

• Block Fading Channel Model: Channel coefficients remain invariant

within the coherence time;

• Channel coherence time is determined by the mobility of the mobile

ends (e.g., the users);

• BS and RIS rarely move after deployment ⇒ quasi-static end-to-end

MIMO channel;

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 11 / 19

RIS-to-BS Channel Model

• (Most of) the channel components (from static scattering clusters)

evolves much more slowly ⇒ slow-varying channel components;

• The remaining ones (from non-static clusters) are fast-varying

channel components;

• Rician fading model: HRB =
• κ

κ+1

¯ HRB

slow−varying

+

• 1

κ+1

• HRB

fast−varying

BS RIS User 1

User-to-RIS Channels User-to-BS Channels Slow-Varying Components in RIS-to-BS Channel Fast-Varying Components in RIS-to-BS Channel

User K Moving Scatterer Static Scatterers

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 12 / 19

User-to-RIS Channel2

• Far-field, Non-LOS channels have sparse coefficients in the angular

domain specified by the angular response due to

• Limited number of scattering clusters;
• Limited angular spread;

Figure: Illustration of limited scatterers. Figure: Sparse Coefficient under the DFT angular response.

2Figures from H. Xie et al., ”Channel estimation for TDD/FDD massive MIMO systems with channel covariance computing,” and J. Zhang et al. ”Blind signal detection in massive MIMO: Exploiting the channel sparsity”.

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 13 / 19

Problem Formulation

Given two (over-complete) angular array response AB and AR

• HUR = ARG with sparse G

HRB = ABSAH

R with sparse S

⇒ Y = HRBHURX + N, = (H0 + ABSR) GX + N.

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 14 / 19

Problem Formulation

Y = (H0 + ABSR) GX + N.

• H0, AB, R, X, and Y are known;
• S and G are two sparse matrices to be estimated;

Joint task of      Linear regression Y = ZX + N; Sparse matrix factorization Z = WG; Matrix calibration W = H0 + ABSR;

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 15 / 19

Bayesian Inference

• Model the channel estimation problem by the Bayesian inference

framework;

• The MMSE estimator is given by the mean of the marginal posteriors;
• Approximate the MMSE estimator by performing message passing
• ver the associated factor graph;

m ' m ' l k l

lk

g

t

mk

z

mt

q

ml

ws

' '

( )

m l

p s

' ' m l

s ( | )

mt mt

p y q

mt

qz

mk

zwg

ml

w ( )

lk

p g

• Introduce Gaussian approximations to reduce complexity;
• Refer to https://arxiv.org/abs/1912.09025 for more details.
• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 16 / 19

Simulation Result3

1/τN (dB) 70 80 90 100 110 NMSE of HRB (dB)

• 30
• 20
• 10

1/τN (dB) 70 80 90 100 110

• Ave. NMSE of hUR,k (dB)
• 30
• 20
• 10

The Proposed Algorithm Concatenate LR Oracle Bound Sequential Channel Estimation

Figure: Normalize MSEs versus the inverse of the noise power.

η

1 1.5 2 2.5

NMSE of HRB (dB)

• 20
• 10

η

1 1.5 2 2.5

• Ave. NMSE of hUR,k (dB)
• 20
• 10

The Proposed Algorithm Concatenate LR Oracle Bound Sequential Channel Estimation

Figure: Normalize MSEs versus the array response sampling resolution.

3The baseline algorithm (the green curves) is from Q.-U.-A. Nadeem et al., ”Intelligent reflecting surface assisted multi-user MISO communication”.

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 17 / 19

Conclusions

• RIS-assisted MIMO systems and channel models;
• Cascaded channel estimation formulation;
• Bayesian inference algorithm and Gaussian approximations;
• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 18 / 19

Thank you

• H. Liu, X. Yuan, Y. J. Zhang

CE for RIS-Assisted MIMO June 8th, 2020 19 / 19