Feedback Benefits in MIMO Communication Systems David J. Love Center for Wireless Systems and Applications School of Electrical and Computer Engineering

Feedback Benefits in MIMO Feedback Benefits in MIMO Communication SystemsCommunication Systems

David J. LoveCenter for Wireless Systems and Applications

School of Electrical and Computer Engineering

Purdue University

[email protected]

CWSA – Purdue University 2

Multiple Antenna Wireless SystemsMultiple Antenna Wireless Systems

Multiple-input multiple-output (MIMO) using multiple antennas at transmitter and receiver

Antennas spaced independent fading

Offer improvements in capacity and reliability

Receiver•••

Transmitter •••


Space-Time SignalingSpace-Time Signaling

Design in space and time

Transmit matrices – transmit one column each transmission

Sent over a linear channel

time

space

Assumption: is an i.i.d. complex Gaussian matrix


Role of Channel KnowledgeRole of Channel Knowledge

Open-loop MIMO [Tarokh et al] Signal matrix designed independently of channel Most popular MIMO architecture

Closed-loop MIMO [Sollenberger],[Telatar],[Raleigh et al] Signal matrix designed as a function of channel

Dramatic performance benefits


Transmitter Channel KnowledgeTransmitter Channel Knowledge

Fundamental problem: How does the transmitter find out the current channel conditions?

Observation: Receiver knows the channel

Solution: Use feedback

Transmitter

......

Receiver

Feedback


Solution: Send back feedback [Narula et al],[Heath et al]

Feedback channel rate very limited Rate 1.5 kb/s (commonly found in standards, 3GPP, etc) Update 3 to 7 ms (from indoor coherence times)

Limited Feedback ProblemLimited Feedback Problem

Transmitter Receiver... ...

Data

Feedback

Feedback amount around 5 to 10 bits


SolutionSolution: Limited Feedback Precoding: Limited Feedback Precoding

Use open-loop algorithm with linear transformation (precoder)

Restrict to Codebook known at transmitter/receiver and fixed Convey codebook index when channel changes

bits

HChoose F

from codebook

Updateprecoder

Low-rate feedback path

…Open-Loop Space-Time

EncoderReceiver

…HX

F

……

FX


Convert MIMO to SISO

Beamforming advantages: Error probability improvement Resilience to fading

Example 1: Limited Feedback BeamformingExample 1: Limited Feedback Beamforming

Coding &Modulation

...Hf

...

fs

Detectionand

Decoding

Feedback

y

s

unit vector

r

Complex number


Nearest neighbor union bound [Cioffi]

Instantaneous channel capacity [Cover & Thomas]

[Love et al]

Challenge #1: Beamformer SelectionChallenge #1: Beamformer Selection


Want to maximize on average

Average distortion

Using sing value decomp & Gaussian random matrix results [James 1964] ( )

where is a uniformly distributed unit vector

Challenge #2: Beamformer CodebookChallenge #2: Beamformer Codebook

channel term codebook term


Bounding of CriterionBounding of Criterion

Grassmannian Beamforming Criterion [Love et al]:

Design

by maximizing

Grassmannmanifold

metric ball volume [Love et al]radius2


SimulationSimulation

3 by 3QPSK

SNR (dB)

Err

or R

ate

(log

scal

e)

0.6 dB


Example 2: Limited Feedback Precoded OSTBCExample 2: Limited Feedback Precoded OSTBC

Require

Use codebook:

Space-TimeEncoder

...HF

...

Feedback

C

...

FC

Detectionand

Decoding


Challenge #1: Codeword SelectionChallenge #1: Codeword Selection

Can bound error rate [Tarokh et al]

Choose matrix from from as [Love et al]

Channel Realization

H

Codebookmatrix


Challenge #2: Codebook DesignChallenge #2: Codebook Design

Minimize loss in channel power

Grassmannian Precoding Criterion [Love & Heath]: Maximize minimum chordal distance

Think of codebook as a set (or packing) of subspaces Grassmannian subspace packing



8 by 1Alamouti16-QAM

9.5dB

Open-Loop

16bit channel

8bit lfb precoder

Err

or R

ate

(log

scal

e)

SNR (dB)


Example 3:Limited Feedback Precoded Example 3:Limited Feedback Precoded Spatial MultiplexingSpatial Multiplexing

Assume

Again adopt codebook approach

Coding &Modulation

..HF

...

Fs

Feedback

s

...Detection

andDecoding



Selection functions proposed when known

Use unquantized selection functions over MMSE (linear receiver) [Sampath et al], [Scaglione et al] Minimum singular value (linear receiver) [Heath et al] Minimum distance (ML receiver) [Berder et al] Instantaneous capacity [Gore et al]

Channel Realization

H

Codebookmatrix


Challenge #2: Distortion FunctionChallenge #2: Distortion Function

Min distance, min singular value, MMSE (with trace) [Love et al]

MMSE (with det) and capacity [Love et al]


Codebook CriterionCodebook Criterion

Grassmannian Precoding Criterion [Love & Heath]:

Maximize

Min distance, min singular value, MMSE (with trace) – Projection two-norm distance

MMSE (with det) and capacity – Fubini-Study distance



4 by 22 substream16-QAM

16bit channelPerfectChannel

6bit lfbprecoder 4.5dB

Err

or R

ate

(log

scal

e)

SNR per bit (dB)


ConclusionsConclusions

Limited feedback allows closed-loop MIMO Beamforming Precoded OSTBC Precoded spatial multiplexing

Large performance gains available with limited feedback

Limited feedback application IEEE 802.16e IEEE 802.11n


Codebook as Subspace CodeCodebook as Subspace Code

is a subspace distance – only depends on subspace not vector

Codebook is a subspace code

Minimum distance [Sloane et al]

set of lines


Beamforming SummaryBeamforming Summary

Contribution #1: Framework for beamforming when channel not known a priori at transmitter Codebook of beamforming vectors Relates to codes of Grassmannian lines

Contribution #2: New distance bounds on Grassmannian line codes Contribution #3: Characterization of feedback-diversity relationship

More info:D. J. Love, R. W. Heath Jr., and T. Strohmer, “Grassmannian Beamforming for Multiple-Input Multiple-Output Wireless Systems,” IEEE Trans. Inf. Th., vol. 49, Oct. 2003.

D. J. Love and R. W. Heath Jr., “Necessary and Sufficient Conditions for Full Diversity Order in Correlated Rayleigh Fading Beamforming and Combining Systems,” accepted to IEEE Trans. Wireless Comm., Dec. 2003.


OutlineOutline

Introduction MIMO Background MIMO Signaling Channel Adaptive (Closed-Loop) MIMO

Limited Feedback Framework

Limited Feedback Applications Beamforming Precoded Orthogonal Space-Time Block Codes Precoded Spatial Multiplexing

Other Areas of Research


Constructed using orthogonal designs [Alamouti, Tarokh et al] Advantages

Simple linear receiver Resilience to fading

Do not exist for most antenna combs (complex signals) Performance loss compared to beamforming

Orthogonal Space-Time Block Codes (OSTBC)Orthogonal Space-Time Block Codes (OSTBC)

Space-timeReceiver f e d c b af e d c b a ⎥

⎦

⎤⎢⎣

⎡

− *

*

ab

ba

Transmiss ion 1


Feedback vs Diversity AdvantageFeedback vs Diversity Advantage

Question: How does feedback amount affect diversity advantage?

Theorem [Love & Heath]: Full diversity advantage if and only if bits of feedback

Proof similar to beamforming proof.

Precoded OSTBC save at least bits compared to beamforming!


Precoded OSTBC SummaryPrecoded OSTBC Summary

Contribution #1: Method for precoded orthogonal space-time block coding when channel not known a priori at transmitter Codebook of precoding matrices Relates to Grassmannian subspace codes with chordal distance

Contribution #2: Characterization of feedback-diversity relationship

More info:D. J. Love and R. W. Heath Jr., “Limited feedback unitary precoding for orthogonal space

time block codes,” accepted to IEEE Trans. Sig. Proc., Dec. 2003.

D. J. Love and R. W. Heath Jr., “Diversity performance of precoded orthogonal space-time

block codes using limited feedback,” accepted to IEEE Commun. Letters, Dec. 2003.


OutlineOutline






True “multiple-input” algorithm Advantage: High-rate signaling technique

Decode

Invert (directly/approx)

Disadvantage: Performance very sensitive to channel singular values

Spatial Multiplexing Spatial Multiplexing [Foschini][Foschini]

{Multiple independentstreams

...H

...

s

Detectionand

Decoding

...,s1+Mt,s1

...,s2Mt,sMt

y


Limited Feedback Precoded SMLimited Feedback Precoded SM [Love et al][Love et al]

Assume

Again adopt codebook approach

Coding &Modulation

..HF

...

Fs

Feedback

s

...Detection

andDecoding



Selection functions proposed when known

Use unquantized selection functions over MMSE (linear receiver) [Sampath et al], [Scaglione et al] Minimum singular value (linear receiver) [Heath et al] Minimum distance (ML receiver) [Berder et al] Instantaneous capacity [Gore et al]

Channel Realization

H

Codebookmatrix


Challenge #2: Distortion FunctionChallenge #2: Distortion Function

Min distance, min singular value, MMSE (with trace) [Love et al]

MMSE (with det) and capacity [Love et al]


Codebook CriterionCodebook Criterion

Grassmannian Precoding Criterion [Love & Heath]:

Maximize

Min distance, min singular value, MMSE (with trace) – Projection two-norm distance

MMSE (with det) and capacity – Fubini-Study distance



4 by 22 substream16-QAM

16bit channelPerfectChannel

6bit lfbprecoder 4.5dB

Err

or R

ate

(log

scal

e)

SNR per bit (dB)


Precoded Spatial Multiplexing SummaryPrecoded Spatial Multiplexing Summary

Contribution #1: Method for precoding spatial multiplexing when channel not known a priori at transmitter Codebook of precoding matrices Relates to Grassmannian subspace codes with projection two-

norm/Fubini-Study distance

Contribution #2: New bounds on subspace code density

More info:D. J. Love and R. W. Heath Jr., “Limited feedback unitary precoding for spatial multiplexing systems,” submitted to IEEE Trans. Inf. Th., July 2003.


OutlineOutline






Multi-Mode PrecodingMulti-Mode Precoding

Fixed rate Adaptively vary number of

substreams Yields

Full diversity order Rate growth of spatial multiplexing C

apac

ity R

atio

SpatialMultiplexer

......

HFM

M: # substreams Adapt precodermatrix

...

H

Modeselector

Feedback

Detect&

Decode

>98%

>85%

SNR (dB)D. J. Love and R. W. Heath Jr., “Multi-Mode Precoding for MIMO Wireless Systems UsingLinear Receivers,” submitted to IEEE Transactions on Signal Processing, Jan. 2004.


Space-Time Chase DecodingSpace-Time Chase Decoding

Decode high rate MIMO signals “costly” Existing decoders difficult to implement

Solution([Love et al] with Texas Instruments): Space-time version of classic Chase decoder [Chase] Use linear or successive decoder as “initial bit estimate” Perform ML decoding over set of perturbed bit estimates

D. J. Love, S. Hosur, A. Batra, and R. W. Heath Jr., “Space-Time Chase Decoding,” submittedto IEEE Transactions on Wireless Communications, Nov. 2003.


Assorted AreasAssorted Areas

MIMO channel modeling IEEE 802.11N covariance generation

Joint source-channel space-time coding

Diversity 4Diversity 2Diversity 1

Visually important

Visually unimportant

…


Future Research AreasFuture Research Areas

Coding theory Subspace codes Binary transcoding Reduced complexity Reed-Solomon

UWB & cognitive (or self-aware) wireless Capacity MIMO (???) Multi-user UWB

Cross layer optimization (collaborative) Sensor networks Broadcast channel capacity schemes


ConclusionsConclusions

Limited feedback allows closed-loop MIMO Beamforming Precoded OSTBC Precoded spatial multiplexing

Diversity order a function of feedback amount

Large performance gains available with limited feedback

Multi-mode precoding & Efficient decoding for MIMO signals


Beamforming CriterionBeamforming Criterion

[Love et al]

Differentiation maximize


Precode OSTBC CriterionPrecode OSTBC Criterion

Let


Precode OSTBC – Cont.Precode OSTBC – Cont.

[Barg et al]



Precode Spat Mult Criterion – Min SVPrecode Spat Mult Criterion – Min SV

Let



Precode Spat Mult Criterion – CapacityPrecode Spat Mult Criterion – Capacity

Let



SM Susceptible to ChannelSM Susceptible to Channel

Decreasing

Fix

Condition number


Vector Quantization RelationshipVector Quantization Relationship

Observation: Problem appears similar to vector quantization (VQ)

In VQ, 1. Choose distortion function 2. Minimize distortion function on average

VQ distortion chosen to improve fidelity of quantized signal

Can we define a distortion function that ties to communication system performance?


Grassmannian Subspace PackingGrassmannian Subspace Packing

Complex Grassmann manifold set of M-dimensional subspaces in

Packing Problem Construct set with maximum

minimum distance Distance between subspaces

Chordal Projection Two-Norm Fubini-Study

Column spaces of codebook matrices represent a set of subspaces in

1

2


Channel AssumptionsChannel Assumptions

Flat-fading (single-tap)

Antennas widely spaced (channels independent)

BW

frequency (Hz)


SolutionSolution: Limited Feedback Precoding: Limited Feedback Precoding

Use codebook Codebook known at transmitter and receiver Convey codebook index when channel changes

Space-TimeEncoder

...H

r

F

...

H

Low-rate feedback path

S

UpdatePrecoder

...

Choose Ffrom

codebook

FS

Detectionand

Decoding

bits


Communications Vector QuantizationCommunications Vector Quantization

Let

VQ Approach:

Design Objective: Approximate optimal solution

Communications Approach: [Love et al]

System parameter to maximize

Design Objective: Improve system performance


True “multiple-input” algorithm Advantage: High-rate signaling technique

Decode

Invert (directly/approx)

Disadvantage: Performance very sensitive to channel singular values

Spatial Multiplexing Spatial Multiplexing [Foschini][Foschini]

} Multiple independentstreams…


Assorted AreasAssorted Areas

MIMO channel modeling IEEE 802.11N covariance generation

Joint source-channel space-time coding

Diversity 4Diversity 2Diversity 1

Visually important

Visually insignificant

…

Documents

Feedback Benefits in MIMO Communication Systems David J. Love Center for Wireless Systems and Applications School of Electrical and Computer Engineering