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Multiuser MIMO Capacity with Limited Feedback Trellis
Exploration Based Precoder
Sayak Bose and Balasubramaniam Natarajan 1 Dalin Zhu2
1WiCom Group, Electrical and Computer EngineeringKansas State UniversityEmail:[email protected]
2Associate Wireless ResearcherNEC Labs China (NLC)
IEEE International Conference on Computing, Networking andCommunications
January 30 - February 2, 2012
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Outline
1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
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Outline
1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
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Outline
1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
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Outline
1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
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Outline
1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
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Overview
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Overview
Outline
1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 3 / 27
Overview
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Overview
Introduction
Multiple-input Multiple-output (MIMO): use multiple antenna at transmitterand receiver
Benefits
Diversity gain in space (antenna) and time (coding)Maximize data rate per available bandwidth (Bps/HZ)
Important part of various wireless technologies
Fixed wireless 802.16.3 (optional)3G HSDPA (optional)Local area network 802.11n (mandatory)4G (possibly mandatory)
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 4 / 27
Overview
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Overview
Introduction
Multiple-input Multiple-output (MIMO): use multiple antenna at transmitterand receiver
Benefits
Diversity gain in space (antenna) and time (coding)Maximize data rate per available bandwidth (Bps/HZ)
Important part of various wireless technologies
Fixed wireless 802.16.3 (optional)3G HSDPA (optional)Local area network 802.11n (mandatory)4G (possibly mandatory)
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 4 / 27
Overview
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Overview
Introduction
Multiple-input Multiple-output (MIMO): use multiple antenna at transmitterand receiver
Benefits
Diversity gain in space (antenna) and time (coding)Maximize data rate per available bandwidth (Bps/HZ)
Important part of various wireless technologies
Fixed wireless 802.16.3 (optional)3G HSDPA (optional)Local area network 802.11n (mandatory)4G (possibly mandatory)
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 4 / 27
Overview
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Introduction
Multiple-input Multiple-output (MIMO): use multiple antenna at transmitterand receiver
Benefits
Diversity gain in space (antenna) and time (coding)Maximize data rate per available bandwidth (Bps/HZ)
Important part of various wireless technologies
Fixed wireless 802.16.3 (optional)3G HSDPA (optional)Local area network 802.11n (mandatory)4G (possibly mandatory)
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 4 / 27
Overview
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Introduction
Multiple-input Multiple-output (MIMO): use multiple antenna at transmitterand receiver
Benefits
Diversity gain in space (antenna) and time (coding)Maximize data rate per available bandwidth (Bps/HZ)
Important part of various wireless technologies
Fixed wireless 802.16.3 (optional)3G HSDPA (optional)Local area network 802.11n (mandatory)4G (possibly mandatory)
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 4 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel functionPerformance benefits over open loop MIMO
Increased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Overview
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MIMO Architectures
Open loop: Most popular MIMO
Signal matrix independent of channel
Closed loop: Gradually getting popular
Signal matrix as channel function
Performance benefits over open loop MIMOIncreased system capacity
Simplify decoding
Diversity gain easily obtainable
Intelligent interference cancellation among multiple users
Problem: Transmitter requires channel state information (CSI)
Solution: Precoding - Receiver has channel knowledge, use feedback to exploitCSI at the transmitter
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 5 / 27
Background
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Outline
1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 6 / 27
Background
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Linear Precoding for Single user (M= 1) MIMO
Limited feedback (phase indices)
inputs
S/PH
F
Linear
receiversP/S
outputs
Optimal precoder matrix Fi requires iterative waterfilling of user covariancematrix
Transmit Ms
Mt streams,
Determine precoder matrix F based on channel matrix H
Send precoder matrix F to transmitter via feedback channel
Linear detection applied to effective channel HF
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 7 / 27
Background
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Linear Precoding for Single user (M= 1) MIMO
Limited feedback (phase indices)
inputs
S/PH
F
Linear
receiversP/S
outputs
Optimal precoder matrix Fi requires iterative waterfilling of user covariancematrix
Transmit Ms
Mt streams,
Determine precoder matrix F based on channel matrix H
Send precoder matrix F to transmitter via feedback channel
Linear detection applied to effective channel HF
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 7 / 27
Background
d f l ( )
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Linear Precoding for Single user (M= 1) MIMO
Limited feedback (phase indices)
inputs
S/PH
F
Linear
receiversP/S
outputs
Optimal precoder matrix Fi requires iterative waterfilling of user covariancematrix
Transmit Ms
Mt streams,
Determine precoder matrix F based on channel matrix H
Send precoder matrix F to transmitter via feedback channel
Linear detection applied to effective channel HF
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 7 / 27
Background
L P d f S l (M 1) MIMO
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Linear Precoding for Single user (M= 1) MIMO
Limited feedback (phase indices)
inputs
S/PH
F
Linear
receiversP/S
outputs
Optimal precoder matrix Fi requires iterative waterfilling of user covariancematrix
Transmit Ms
Mt streams,
Determine precoder matrix F based on channel matrix H
Send precoder matrix F to transmitter via feedback channel
Linear detection applied to effective channel HF
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 7 / 27
Background
Li P di f Si l (M 1) MIMO
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Linear Precoding for Single user (M= 1) MIMO
Limited feedback (phase indices)
inputs
S/PH
F
Linear
receiversP/S
outputs
Optimal precoder matrix Fi requires iterative waterfilling of user covariancematrix
Transmit Ms
Mt streams,
Determine precoder matrix F based on channel matrix H
Send precoder matrix F to transmitter via feedback channel
Linear detection applied to effective channel HF
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 7 / 27
Background
Li P di f M l i (M 1) MIMO
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Linear Precoding for Multi user (M 1) MIMO
Linear
receivers
P/S
S/P MF
S/P1F
MH
1H
Limited feedback (phase indices)
Limited feedback (phase indices)
1x
Mx
y
Optimal capacity achieved by spatio-temporal vector coding in MU-MIMOdispersive channel [? ]
Optimal precoder matrix Fi requires iterative waterfilling of user covariancematrix regarding other users signal as (multiple access) interference (MAI)
Eigen modes of user covariance matrix require matching the eigen modes ofH
Hi
Rn +
Mj=1,j=iHjRjH
Hj
1Hi, where Rn is AWGN channel noise
covariance
Send precoder matrix Fi to transmitter via feedback channel for that user
Linear detection applied to effective channel HiFi
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 8 / 27
Background
Li P di f M lti (M 1) MIMO
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Linear Precoding for Multi user (M 1) MIMO
Linear
receivers
P/S
S/P MF
S/P1F
MH
1H
Limited feedback (phase indices)
Limited feedback (phase indices)
1x
Mx
y
Optimal capacity achieved by spatio-temporal vector coding in MU-MIMOdispersive channel [? ]
Optimal precoder matrix Fi requires iterative waterfilling of user covariancematrix regarding other users signal as (multiple access) interference (MAI)
Eigen modes of user covariance matrix require matching the eigen modes ofH
Hi
Rn +
Mj=1,j=iHjRjH
Hj
1Hi, where Rn is AWGN channel noise
covariance
Send precoder matrix Fi to transmitter via feedback channel for that user
Linear detection applied to effective channel HiFi
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 8 / 27
Background
Li P di f M lti (M 1) MIMO
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Linear Precoding for Multi user (M 1) MIMO
Linear
receivers
P/S
S/P MF
S/P1F
MH
1H
Limited feedback (phase indices)
Limited feedback (phase indices)
1x
Mx
y
Optimal capacity achieved by spatio-temporal vector coding in MU-MIMOdispersive channel [? ]
Optimal precoder matrix Fi requires iterative waterfilling of user covariancematrix regarding other users signal as (multiple access) interference (MAI)
Eigen modes of user covariance matrix require matching the eigen modes ofH
Hi
Rn +
Mj=1,j=iHjRjH
Hj
1Hi, where Rn is AWGN channel noise
covariance
Send precoder matrix Fi to transmitter via feedback channel for that user
Linear detection applied to effective channel HiFi
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 8 / 27
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Background
Linear Precoding for Multi user (M 1) MIMO
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Linear Precoding for Multi user (M 1) MIMO
Linear
receivers
P/S
S/P MF
S/P1F
MH
1H
Limited feedback (phase indices)
Limited feedback (phase indices)
1x
Mx
y
Optimal capacity achieved by spatio-temporal vector coding in MU-MIMOdispersive channel [? ]
Optimal precoder matrix Fi requires iterative waterfilling of user covariancematrix regarding other users signal as (multiple access) interference (MAI)
Eigen modes of user covariance matrix require matching the eigen modes ofH
Hi
Rn +
Mj=1,j=iHjRjH
Hj
1Hi, where Rn is AWGN channel noise
covariance
Send precoder matrix Fi to transmitter via feedback channel for that user
Linear detection applied to effective channel HiFi
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 8 / 27
Background
Role of Limited Feedback
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Role of Limited Feedback
H(K)F(K)Symbols
Low-rate feedback pathUpdate
Precoder
Linear
Rx
Form F(k)
Online
Choose F(k)
From codebook
H
Detection
&
Decode
Challenges with feedback:Feedback requirements Number of subcarriers (MIMO-OFDM), andNumber ofMtMr, and Number of users (for MU-MIMO)Transmitter has CSI via a limited rate feedback channel (Sub-optimal)
Two basic approaches:
Finite codebook (offline)Restrict F to lie in finite codebook F = {F1,F1, ,FC}
Trellis exploration (online)Exploit channel information through trellis searchRestrict F to lie in finite phase space = {1, 2, , L}
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 9 / 27
Background
Role of Limited Feedback
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Role of Limited Feedback
H(K)F(K)Symbols
Low-rate feedback pathUpdate
Precoder
Linear
Rx
Form F(k)
Online
Choose F(k)
From codebook
H
Detection
&
Decode
Challenges with feedback:Feedback requirements Number of subcarriers (MIMO-OFDM), andNumber ofMtMr, and Number of users (for MU-MIMO)Transmitter has CSI via a limited rate feedback channel (Sub-optimal)
Two basic approaches:
Finite codebook (offline)Restrict F to lie in finite codebook F = {F1,F1, ,FC}
Trellis exploration (online)Exploit channel information through trellis searchRestrict F to lie in finite phase space = {1, 2, , L}
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 9 / 27
Background
Role of Limited Feedback
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Role of Limited Feedback
H(K)F(K)Symbols
Low-rate feedback pathUpdate
Precoder
Linear
Rx
Form F(k)
Online
Choose F(k)
From codebook
H
Detection
&
Decode
Challenges with feedback:Feedback requirements Number of subcarriers (MIMO-OFDM), andNumber ofMtMr, and Number of users (for MU-MIMO)Transmitter has CSI via a limited rate feedback channel (Sub-optimal)
Two basic approaches:
Finite codebook (offline)Restrict F to lie in finite codebook F = {F1,F1, ,FC}
Trellis exploration (online)Exploit channel information through trellis searchRestrict F to lie in finite phase space = {1, 2, , L}
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 9 / 27
Background
Role of Limited Feedback
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Role of Limited Feedback
H(K)F(K)Symbols
Low-rate feedback pathUpdate
Precoder
Linear
Rx
Form F(k)
Online
Choose F(k)
From codebook
H
Detection
&
Decode
Challenges with feedback:Feedback requirements Number of subcarriers (MIMO-OFDM), andNumber ofMtMr, and Number of users (for MU-MIMO)Transmitter has CSI via a limited rate feedback channel (Sub-optimal)
Two basic approaches:
Finite codebook (offline)Restrict F to lie in finite codebook F = {F1,F1, ,FC}
Trellis exploration (online)Exploit channel information through trellis searchRestrict F to lie in finite phase space = {1, 2, , L}
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 9 / 27
Background
Prior Work on Precoding and Limited Feedback
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Prior Work on Precoding and Limited Feedback
Prior work on precoding
MMSE precoding [Sampath et. al.][Scaglione et. al]Quantized feedback for orthogonal space-time block code [? ]ML based precoding [Berder et. al]
Prior work on finite codebook based limited feedback
Limited feedback unitary precoding [? ]Random and correlated random codebook for MU-MIMO Channels [? ]
Prior work on trellis exploration based limited feedback
Trellis exploration based preocder for SU-MIMO [? ]
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 10 / 27
Background
Key Contributions
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Key Contributions
Multiuser trellis based precoding to improve MU-MIMO system capacity inthe uplink
Complexity analysis and feedback savings for the proposed approach
Performance comparison with codebook based precoding in MU-MIMO
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Proposed Multiuser Trellis Based Precoding
Outline
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Outline
1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
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Proposed Multiuser Trellis Based Precoding
MU-MIMO System Model
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U O Syste ode
Linear
receivers
P/S
S/PMF
S/P1F
MH
1H
Limited feedback (phase indices)
Limited feedback (phase indices)
1x
Mx
y
Received signal:
y =Mi=1
HiFixi + n i= 1, ,M
n AWGNSayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 13 / 27
Proposed Multiuser Trellis Based Precoding
Multiuser MIMO-MAC Capacity Analysis
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p y y
Generate for of sum-capacity for multi-user Gaussian vector channel
C=Maxtr(Ri)=Ei1
N+ log2
det(Rn +M
i=1 HiRiHHi )
det(Rn)
Transmitted symbol with Precoding : si = Fixi
Input covariance matrix for the i-th user Ri = Exix
H
i
Noise covariance matrix Rn = EnnH
MU MIMO-MAC Capacity with Precoding
Ri = EFixi (Fixi)
H= FiiF
Hi
C= maxtr(Ri)=Ei
1
N+ log2
det(Rn +Ei
NMt
Mi=1 HiFiF
Hi H
Hi )
det(Rn)
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 14 / 27
Proposed Multiuser Trellis Based Precoding
Custom-designed Precoder Per User
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g
Precoder for i-th user:
Fi =
Fi1,1 Fi1,2 Fi1,Mt
Fi2,1 Fi2,2 Fi2,Mt
...... . . .
...FiMt,1 F
iMt,2
FiMt,Mt
Fim,p U[0, 2]
i =
Ei
NMt exp(j2
l
1
L ), wherel= 1, 2, , L
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 15 / 27
Proposed Multiuser Trellis Based Precoding
Multiuser Trellis Exploration
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p
iF
1,1
iF
2,1
i
NMNMtt
F1,1
i
NMNMtt
F,
i
1
i
2
i
L
Metric to maximize through trellis explorationi = arg
mini(l) i=1, ,L
ViUi2FVi eigen vector of input covariance matrix Ri
Ri = ViiVHi .
Vi is obtained at the receiver by eigen decomposing FiFHi
Ui eigen vector of desired user matrix with additional interference Ti
Ti = HHi
Rn +
Mj=1,j=i
HjRjHHj
1
Hi
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 16 / 27
Proposed Multiuser Trellis Based Precoding
Complexity Analysis and Feedback Bits
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y y
Dominating factor for complexity:
Computation of{RiFi}Mi=0Number of complex additions: LMIN2MtMr
Number of complex multiplications: LM(M 1)IN3MrM2t
L = ||, N block size, I Number of iterations through trellisNumber of feedback bits/user/transmission:Kb = NMrMtlog2L where, b = log2L specifies one phase element of
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 17 / 27
Simulation Results
Outline
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1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 18 / 27
Simulation Results
Simulation Parameters
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Block length N 10Number of users M 5Number of phases L 4, 8
Channel model i.i.d Rayleigh fadingChannel memory 4
Dispersive (STVC) Channel powers 0dB, 0.25dB, 0.6dB, 1dBNon-dispersive Channel power 0dB
Energy allocation Equal per userNumber of trellis search I 3
Assumptions:perfect CSI is always available at the receiver
Limited rate feedback channel is perfect (noiseless)
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 19 / 27
Simulation Results
Ergodic Sum-capacity: STVC with Full CSIT vs. STVC with
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Trellis Aided Limited Feedback
0 5 10 15 201
2
3
4
5
6
7
8
9
10
11
SNR (dB)
To
talCapacity(bps/transmission)
Mt=2 Mr=2 STVC
Mt=2 Mr=2 Trellis with L=8
Mt=2 Mr=2 Trellis with L=4
2 2 Multiuser MIMO-MAC
0 5 10 15 202
4
6
8
10
12
14
16
18
SNR (dB)
To
talCapacity(bps/transmission)
Mt=3 Mr=3 STVC
Mt=3 Mr=3 Trellis with L=8
Mt=3 Mr=3 Trellis with L=4
3 3 Multiuser MIMO-MACSayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 20 / 27
Simulation Results
Feedback Performance
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Limited feedback bits Kb for different L in trellis exploration based precoder
2 2 3 3Kb(L = 8) 120 270Kb(L = 4) 80 180
Feedback bit savings compared to 10-bit quantized channel information(standard practice):Kb = 1764 bits/user/transmission
Trellis approach with 2 2 MIMO:Feedback bit savings with L = 8, 53.12%, and with L = 4, 68.75%Trellis approach with 3 3 MIMO:Feedback bit savings with L = 8, 84.7%, and with L = 4, 89.8%
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 21 / 27
Simulation Results
Sum-capacity Comparison: Trellis vs. Codebook
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(Non-dispersive 3 3 MIMO-MAC)
0 5 10 15 200
2
4
6
8
10
12
14
16
18
20
SNR (dB)
Capacity(bps/transmission)
Ideal Precoding
Correlated Random Codebook
Random Codebook
Trellis
No CSIT
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Conclusion
Outline
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1 Overview
2 Background
3 Proposed Multiuser Trellis Based Precoding
4 Simulation Results
5 Conclusion
Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 23 / 27
Conclusion
Conclusion
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Trellis exploration aided precoding improves the multi-user MIMO dispersivechannel capacity with equal user power allocation;
Number of feedback bits/user/transmission relative to the quantized CSIbits/user/transmission decreases with increase in the order (MtMr) of MIMO
for the same number of users.The trellis based precoder in a non-dispersive channel provides high capacitygain over random codebook based linear precoding with equal user powerallocation.
Sum-rate capacity improvement occurs at the cost of added receiver
complexity due to trellis search
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Conclusion
References
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[1] J. Wang and K. Yao. Multiuser spatio-temporal coding for wireless communications. In IEEEWireless Communications and Networking Conference., volume 1, pages 276279, March 2002.
[2] G. Jongren and M. Skoglund. Utilizing quantized feedback information in orthogonal space-timeblock coding. In IEEE Globecomm conference, volume 2, pages 995999, December 2000.
[3] D. J. Love and R. W. Heath. Limited feedback unitary precoding for spatial multiplexing. In IEEETransactions on Information Theory, volume 51, pages 29672976, August 2005.
[4] F. Kaltenberger, M. Kountouris, D. Gesbert, and R. Knopp. On the trade-off between feedback andcapacity in measured mu-mimo channels. In IEEE Transactions on Wireless Communications,
volume 8(9), pages 48664875, September 2009.[5] D. Zhu and B. Natarajan. Trellis exploration algorithm aided precoder design in maximizing mimo
capacity with limited feedback. In IEEE Globecomm conference, 2009.
[6] R. W. Heath Jr, D.J. Love, and J. Choi. Precoding and interpolation for spatial multiplexingmimo-ofdm with limited feedback. In WNCG, The University of Texas at Austin, July 2004.
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Conclusion
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Thank You!
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Conclusion
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Questions?
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