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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

Sayak et al. (K-State and NLC) Multiuser Trellis: MIMO-MAC Capacity ICNC12 1 / 27
http://goforward/http://find/http://goback/

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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



5 Conclusion


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Outline

1 Overview

2 Background



5 Conclusion


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Outline

1 Overview

2 Background



5 Conclusion


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Outline

1 Overview

2 Background



5 Conclusion


Overview

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Overview

Outline

1 Overview

2 Background



5 Conclusion


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)


Overview

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Overview

Introduction


Benefits





Overview

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Overview

Introduction


Benefits





Overview

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Introduction


Benefits





Overview

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Introduction


Benefits





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


Overview

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MIMO Architectures




Signal matrix as channel function

Performance benefits over open loop MIMOIncreased system capacity

Simplify decoding






Overview

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MIMO Architectures






Simplify decoding






Overview

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MIMO Architectures






Simplify decoding






Overview

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MIMO Architectures






Simplify decoding






Overview

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MIMO Architectures






Simplify decoding






Overview

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MIMO Architectures






Simplify decoding






Overview

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MIMO Architectures






Simplify decoding






Overview

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MIMO Architectures






Simplify decoding






Overview

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MIMO Architectures






Simplify decoding






Overview

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MIMO Architectures






Simplify decoding






Background

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Outline

1 Overview

2 Background



5 Conclusion


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


Background

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inputs

S/PH

F

Linear

receiversP/S

outputs


Transmit Ms

Mt streams,





Background

d f l ( )

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inputs

S/PH

F

Linear

receiversP/S

outputs


Transmit Ms

Mt streams,





Background

L P d f S l (M 1) MIMO

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inputs

S/PH

F

Linear

receiversP/S

outputs


Transmit Ms

Mt streams,





Background

Li P di f Si l (M 1) MIMO

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inputs

S/PH

F

Linear

receiversP/S

outputs


Transmit Ms

Mt streams,





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



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


Background

Li P di f M lti (M 1) MIMO

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Linear

receivers

P/S

S/P MF

S/P1F

MH

1H



1x

Mx

y




Hi

Rn +

Mj=1,j=iHjRjH

Hj


covariance




Background

Li P di f M lti (M 1) MIMO

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Linear

receivers

P/S

S/P MF

S/P1F

MH

1H



1x

Mx

y




Hi

Rn +

Mj=1,j=iHjRjH

Hj


covariance




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Background


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Linear

receivers

P/S

S/P MF

S/P1F

MH

1H



1x

Mx

y




Hi

Rn +

Mj=1,j=iHjRjH

Hj


covariance




Background

Role of Limited Feedback

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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}


Background


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H(K)F(K)Symbols


Precoder

Linear

Rx

Form F(k)

Online

Choose F(k)

From codebook

H

Detection

&

Decode






Background


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H(K)F(K)Symbols


Precoder

Linear

Rx

Form F(k)

Online

Choose F(k)

From codebook

H

Detection

&

Decode






Background


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H(K)F(K)Symbols


Precoder

Linear

Rx

Form F(k)

Online

Choose F(k)

From codebook

H

Detection

&

Decode






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 [? ]


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


Proposed Multiuser Trellis Based Precoding

Outline

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Outline

1 Overview

2 Background



5 Conclusion



MU-MIMO System Model

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U O Syste ode

Linear

receivers

P/S

S/PMF

S/P1F

MH

1H



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


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)



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



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



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


Simulation Results

Outline

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1 Overview

2 Background



5 Conclusion


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)


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


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



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%


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


Conclusion

Outline

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1 Overview

2 Background



5 Conclusion


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


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.


Conclusion

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Thank You!


Conclusion

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Questions?


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