feedback benefits in mimo communication systems david j. love center for wireless systems and...
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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
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 •••
CWSA – Purdue University 3
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
CWSA – Purdue University 4
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
CWSA – Purdue University 5
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
CWSA – Purdue University 6
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
CWSA – Purdue University 7
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
CWSA – Purdue University 8
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
CWSA – Purdue University 9
Nearest neighbor union bound [Cioffi]
Instantaneous channel capacity [Cover & Thomas]
[Love et al]
Challenge #1: Beamformer SelectionChallenge #1: Beamformer Selection
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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
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Bounding of CriterionBounding of Criterion
Grassmannian Beamforming Criterion [Love et al]:
Design
by maximizing
Grassmannmanifold
metric ball volume [Love et al]radius2
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SimulationSimulation
3 by 3QPSK
SNR (dB)
Err
or R
ate
(log
scal
e)
0.6 dB
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Example 2: Limited Feedback Precoded OSTBCExample 2: Limited Feedback Precoded OSTBC
Require
Use codebook:
Space-TimeEncoder
...HF
...
Feedback
C
...
FC
Detectionand
Decoding
CWSA – Purdue University 14
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
CWSA – Purdue University 15
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
CWSA – Purdue University 16
SimulationSimulation
8 by 1Alamouti16-QAM
9.5dB
Open-Loop
16bit channel
8bit lfb precoder
Err
or R
ate
(log
scal
e)
SNR (dB)
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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
CWSA – Purdue University 18
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
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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]
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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
CWSA – Purdue University 21
SimulationSimulation
4 by 22 substream16-QAM
16bit channelPerfectChannel
6bit lfbprecoder 4.5dB
Err
or R
ate
(log
scal
e)
SNR per bit (dB)
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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
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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
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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.
CWSA – Purdue University 25
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
CWSA – Purdue University 26
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
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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!
CWSA – Purdue University 28
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.
CWSA – Purdue University 29
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
CWSA – Purdue University 30
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
CWSA – Purdue University 31
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
CWSA – Purdue University 32
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
CWSA – Purdue University 33
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]
CWSA – Purdue University 34
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
CWSA – Purdue University 35
SimulationSimulation
4 by 22 substream16-QAM
16bit channelPerfectChannel
6bit lfbprecoder 4.5dB
Err
or R
ate
(log
scal
e)
SNR per bit (dB)
CWSA – Purdue University 36
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.
CWSA – Purdue University 37
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
CWSA – Purdue University 38
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.
CWSA – Purdue University 39
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.
CWSA – Purdue University 40
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
…
CWSA – Purdue University 41
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
CWSA – Purdue University 42
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
CWSA – Purdue University 43
Beamforming CriterionBeamforming Criterion
[Love et al]
Differentiation maximize
CWSA – Purdue University 45
Precode OSTBC – Cont.Precode OSTBC – Cont.
[Barg et al]
Differentiation maximize
CWSA – Purdue University 46
Precode Spat Mult Criterion – Min SVPrecode Spat Mult Criterion – Min SV
Let
Differentiation maximize
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Precode Spat Mult Criterion – CapacityPrecode Spat Mult Criterion – Capacity
Let
Differentiation maximize
CWSA – Purdue University 48
SM Susceptible to ChannelSM Susceptible to Channel
Decreasing
Fix
Condition number
CWSA – Purdue University 49
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?
CWSA – Purdue University 50
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
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Channel AssumptionsChannel Assumptions
Flat-fading (single-tap)
Antennas widely spaced (channels independent)
BW
frequency (Hz)
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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
CWSA – Purdue University 53
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
CWSA – Purdue University 54
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…