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Feedback Methods for Multiple-Input Feedback Methods for Multiple-Input Multiple-Output Wireless SystemsMultiple-Output Wireless Systems
David J. Love
WNCG
The University of Texas at Austin
March 4, 2004
Wireless Networking and Communication Group 2
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
Wireless Networking and Communication Group 3
Wireless ChallengesWireless Challenges
Spectral efficiency Spectrum very expensive $$$ Maximize data rate per bandwidth bits/sec/Hz
Quality Wireless links fluctuate Desire SNR to have large mean and low variance
Limited transmit power
How can we maximize spectral efficiency and quality?
Wireless Networking and Communication Group 4
Solution: MIMO Wireless SystemsSolution: MIMO Wireless Systems
Multiple-input multiple-output (MIMO) using multiple antennas at transmitter and receiver
Antennas spaced independent fading
Allow space-time signaling
Receiver•••
Transmitter •••
Wireless Networking and Communication Group 5
SNR (dB)
MIMO Capacity Benefits MIMO Capacity Benefits [Telatar][Telatar]
Multiply Data Rate Multiply throughput $$$ Multiply # users $$$
min(Tx,Rx) antennas
Rat
e S
lope
1 by 1 antenna4.3 b/s/Hz
8 by 8 antennas32.3 b/s/Hz
Cap
acity
1 by 16 antennas9 b/s/Hz
Wireless Networking and Communication Group 6
Signal Quality Through Signal Quality Through DiversityDiversity
Antennas provide diversity advantage [Brennan] Large gains for moderate to high SNR Reduced fading! Better user experience $$$
Sig
nal P
ower
standard
with MIMO
time
1 antenna
4th order diversity
Diversity = -slope
SNR (dB)E
rro
r R
ate
(lo
g s
cale
)
Wireless Networking and Communication Group 7
MIMO Systems are RelevantMIMO Systems are Relevant
Fixed wireless access 802.16.3 standard (optional)
3G cellular HSDPA – (optional)
Local area networks 802.11N Study Group (possibly mandatory)
Mobile Broadband Wireless 802.20 Working Group (possibly mandatory --- too early)
4G Lots of discussion
Wireless Networking and Communication Group 8
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
Wireless Networking and Communication Group 9
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 Performance benefits
Wireless Networking and Communication Group 10
Closed-Loop Performance BenefitsClosed-Loop Performance Benefits
Channel capacity fundamentally larger
Simplified decoding
Reduced error rate
Allows multiuser scheduling (transmit to group of best users)
SNR (dB)
Cap
acity
SNR (dB)
Err
or
Rat
e (
log
sca
le)
4b/s/Hz
12 dB
Wireless Networking and Communication Group 11
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
Wireless Networking and Communication Group 12
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
Wireless Networking and Communication Group 13
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
Wireless Networking and Communication Group 14
Prior work [Narula et al],[Jongren et al]: Quantize channel
Channel quantization fails for MIMO 8x8 MIMO = More than 128 bits of feedback! Singular value structure sensitive to quantization
Feedback Design ProblemFeedback Design Problem
Transmitter Receiver... ...
Quantizer
Wireless Networking and Communication Group 15
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
Wireless Networking and Communication Group 16
Use selection function such that
Selection function depends on Underlying open-loop algorithm Performance criterion
Solution: Use perfect channel knowledge selection but optimize over codebook
Challenge #1: Codeword SelectionChallenge #1: Codeword Selection
Channel Realization
H
Codebookmatrix
Wireless Networking and Communication Group 17
Challenge #2: Codebook DesignChallenge #2: Codebook Design
Codebook design very important
Given: Underlying open-loop algorithm Selection function
Goal: Quantize (in some sense) the perfect channel knowledge precoder
Wireless Networking and Communication Group 18
Communications Vector QuantizationCommunications Vector Quantization
Let
Communications Approach: [Love et al]
System parameter to maximize
Design Objective: Improve system performance
Different than traditional vector quantization
Wireless Networking and Communication Group 19
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
Wireless Networking and Communication Group 20
Convert MIMO to SISO
Beamforming advantages: Error probability improvement Resilience to fading
Limited Feedback BeamformingLimited Feedback Beamforming [Love et al][Love et al]
Coding &Modulation
...Hf
...
fs
Detectionand
Decoding
Feedback
y
s
unit vector
r
Complex number
Wireless Networking and Communication Group 21
Nearest neighbor union bound [Cioffi]
Instantaneous channel capacity [Cover & Thomas]
[Love et al]
Challenge #1: Beamformer SelectionChallenge #1: Beamformer Selection
Wireless Networking and Communication Group 22
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
Wireless Networking and Communication Group 23
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
Wireless Networking and Communication Group 24
Bounding of CriterionBounding of Criterion
Grassmannian Beamforming Criterion [Love et al]:
Design
by maximizing
Grassmannmanifold
metric ball volume [Love et al]radius2
Wireless Networking and Communication Group 25
Feedback vs Diversity AdvantageFeedback vs Diversity Advantage
Question: How does the feedback amount affect diversity advantage?
Diversity Theorem [Love & Heath]: Full diversity advantage if and only if bits of feedback
Proof Sketch:
1. Use: Gaussian matrices are isotropically random
2. Bound by selection diversity (known full diversity)
Wireless Networking and Communication Group 26
SimulationSimulation
3 by 3QPSK
SNR (dB)
Err
or R
ate
(log
scal
e)
0.6 dB
Wireless Networking and Communication Group 27
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.
Wireless Networking and Communication Group 28
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
Wireless Networking and Communication Group 29
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
Transmission 1
Wireless Networking and Communication Group 30
Solution: Limited Feedback Precoded Solution: Limited Feedback Precoded OSTBC OSTBC [Love et al][Love et al]
Require
Use codebook:
Space-TimeEncoder
...HF
...
Feedback
C
...
FC
Detectionand
Decoding
Wireless Networking and Communication Group 31
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
Wireless Networking and Communication Group 32
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
Wireless Networking and Communication Group 33
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!
Wireless Networking and Communication Group 34
SimulationSimulation
8 by 1Alamouti16-QAM
9.5dB
Open-Loop
16bit channel
8bit lfb precoder
Err
or R
ate
(log
scal
e)
SNR (dB)
Wireless Networking and Communication Group 35
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.
Wireless Networking and Communication Group 36
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
Wireless Networking and Communication Group 37
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
Wireless Networking and Communication Group 38
Limited Feedback Precoded SMLimited Feedback Precoded SM [Love et al][Love et al]
Assume
Again adopt codebook approach
Coding &Modulation
..HF
...
Fs
Feedback
s
...
Detectionand
Decoding
Wireless Networking and Communication Group 39
Challenge #1: Codeword SelectionChallenge #1: Codeword Selection
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
Wireless Networking and Communication Group 40
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]
Wireless Networking and Communication Group 41
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
Wireless Networking and Communication Group 42
SimulationSimulation
4 by 22 substream16-QAM
16bit channelPerfectChannel
6bit lfbprecoder 4.5dB
Err
or R
ate
(log
scal
e)
SNR per bit (dB)
Wireless Networking and Communication Group 43
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.
Wireless Networking and Communication Group 44
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
Wireless Networking and Communication Group 45
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.
Wireless Networking and Communication Group 46
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.
Wireless Networking and Communication Group 47
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
…
Wireless Networking and Communication Group 48
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
Wireless Networking and Communication Group 49
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
Wireless Networking and Communication Group 50
Beamforming CriterionBeamforming Criterion
[Love et al]
Differentiation maximize
Wireless Networking and Communication Group 52
Precode OSTBC – Cont.Precode OSTBC – Cont.
[Barg et al]
Differentiation maximize
Wireless Networking and Communication Group 53
Precode Spat Mult Criterion – Min SVPrecode Spat Mult Criterion – Min SV
Let
Differentiation maximize
Wireless Networking and Communication Group 54
Precode Spat Mult Criterion – CapacityPrecode Spat Mult Criterion – Capacity
Let
Differentiation maximize
Wireless Networking and Communication Group 55
SM Susceptible to ChannelSM Susceptible to Channel
Decreasing
Fix
Condition number
Wireless Networking and Communication Group 56
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?
Wireless Networking and Communication Group 57
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
Wireless Networking and Communication Group 58
Channel AssumptionsChannel Assumptions
Flat-fading (single-tap)
Antennas widely spaced (channels independent)
BW
frequency (Hz)
Wireless Networking and Communication Group 59
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
Wireless Networking and Communication Group 60
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
Wireless Networking and Communication Group 61
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…