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![Page 1: Limited Feedback Beamforming with Delay: Theory and Practice Huang Kaibin Collaborators: Robert Daniels Prof. Robert W. Heath Jr. Prof. Jeffrey G. Andrews.](https://reader038.fdocuments.net/reader038/viewer/2022110405/56649efa5503460f94c0be93/html5/thumbnails/1.jpg)
Limited Feedback Beamforming with Delay: Theory and Practice
Huang Kaibin
Collaborators: Robert Daniels Prof. Robert W. Heath Jr.
Prof. Jeffrey G. Andrews
Wireless Networking and Communications Group (WNCG)Dept. of Electrical and Computer Engineering
The University of Texas at Austin
08/15/2007
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MIMO: a Personal View1996
1998
2000
2002
2004
2006
2008
Channel capacity(Telatar, Foschini)
Channel capacity(Telatar, Foschini)
Space-time codes(Tarokh, Alamouti, Jafarkani)
Space-time codes(Tarokh, Alamouti, Jafarkani) Gaussian broadcast
Caire & ShamaiVish., Jindal & Goldsmith
Viswanath & TseYu & Cioffi
Gaussian broadcast
Caire & ShamaiVish., Jindal & Goldsmith
Viswanath & TseYu & CioffiMulti-user Diversity
Knopp & HumbletViswanath & TseSharif & Hassibi
Multi-user Diversity
Knopp & HumbletViswanath & TseSharif & Hassibi Diversity-multiplexing tradeoff
(Zheng & Tse, Heath & Paulraj)
Diversity-multiplexing tradeoff(Zheng & Tse, Heath & Paulraj)
IEEE 802.11n(WiFi)
IEEE 802.11n(WiFi)
IEEE 802.16e(WiMax)
IEEE 802.16e(WiMax)
3GPP-LTE3GPP-LTE
1
A new area: MIMO with Limited Feedback
1) Single-user 2) Multi-user 3) Wireless network
A new area: MIMO with Limited Feedback
1) Single-user 2) Multi-user 3) Wireless network
talk scopetalk scope
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Feedback Enhances Communication
no feedback feedback
Here!?
listener speaker listener speaker
In the darkness…
2
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Beamforming Increases Throughput
signal
w1
w2
h1
h2
n
SNR
beamforming weights
no feedback
feedback
feedback
3
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Limited Feedback Concept
Finite-RateFeedback Channel
Adaptive Transmission• Precoder• Beamformer• AMC, etc
CSI
Codebook based quantizer
ReceiverTransmiter
Wireless Channel
S1S2
S3
S4S5
S6
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Limited Feedback Beamforming Increases Throughput
signal
w1
w2
h1
h2
n
SNR
quantizerpartition index
surface of unit hyper-sphere
feedback quantizer
4
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Prior Work on Limited Feedback Beamforming
Narrow-band block fading channels Research focuses on the codebook design.
Grassmannian line packing [Love & Heath 03] [Mukkavilli et al 03]
Lloyd algorithm [Roh & Rao 06][Xia et al 05]
Broadband channels (MIMO-OFDM) Sub-channel grouping [Mondal & Heath 05]
Beamformer interpolation [Choi & Heath 04]
Spatially correlated channels Codebook switching based channel correlation [Mondal & Heath 06]
Temporally correlated channels (considered in this talk) Delta modulated feedback [Roh & Rao 04]
Drawback: multiple feedback streams
1-bit feedback based on subspace perturbation [Banister 03] Drawback: periodic broadcast of matrices
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Limited Feedback Beamforming in Industry
Local Area Networks (IEEE 802.11n)
Optional feature for 600 Mbps
IEEE 802.16e (WiMax)
Codebook based precoding/beamforming
3GPP Long Term Evolution (LTE)
Single- and multi-user limited feedback beamforming
4G
Lots of discussion
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Conventional: Block fading channels (Narula et al 98, Love et al 03, Mukkavilli et al 03, Xia et al 04)
(Pro): Focus on quantizer codebook designs (Con): Omits temporal correlation in wireless channels (Con): Analysis of feedback delay and rate is difficult
New: Temporally-correlated channels Feedback rate (vs. channel coherence time) Feedback compression in time Effect of feedback delay on throughput
Motivation
S1 S2 S3 S4
Channel State
Channel Coherence Time
S1, S2, … are independently distributed.
Important for designing practical limited feedback systems
6
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Outline
Part I: Theory Channel Markov model
Feedback compression and rate
Feedback delay
Part II: Practice Experiment setup
Measurement results
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System Model
CSI {H1, H2, … } is a correlated sequenceCSI {H1, H2, … } is a correlated sequence
7
Index Jn
Feedback Channel(delay, error free)
BeamformingChannel
EstimationHn
CSI (beamformer)
12
3
CSI quantizer
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Proposed Approach: Assumption and Overview
The CSI index Jn varies as a discrete-time finite-state Markov chain
Accurate for slowly time-varying SISO channel (Wang & Moayeri 95)
Temporally Correlated
MIMO ChannelMarkov Chain
Feedback rate, compression,
delay
8
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Proposed Approach: CSI Index Markov Chain Definition of Markov state space
Partition channel space using existing codebook-design techniques (Love et al 03, Xia et al 05, Rho & Rao 05)
Computation of stationary and transition probabilities Monte Carlo simulation (next slide)
Markov Channel ModelMarkov Channel Model
S1S2
S3
S4
S6
S5
p33
p13
p63
p64
p43
Unit Hyper-SphereUnit Hyper-Sphere
Codebook Members
S1S2
S3
S4S5
S6
9
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Proposed Approach: CSI Index Markov Chain
Computation of stationary and transition probabilities Generate a long channel sequence
Compute CSI index sequence
Compute stationary probability {pn}
Compute transition probability {pnm} S1S2
S3
S4
S6
S5
p33
p13
p63
p64
p43
9
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Outline
Part I: Theory Channel Markov model
Feedback compression and rate
Feedback delay
Part II: Practice Experiment setup
Measurement results
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Overview of Feedback Compression
QuantizationQuantization
Compression(frequency)
Compression(frequency)
Compression(time)
Compression(time)
Compression(space)
Compression(space)
Finite-Rate Feedback
CSI
Extensively studied [Love et al 04] [Mukkavilli et al 03]
Adaptive Codebooks[Mondal and Heath 05]
Subspace Interpolation[Choi et al 04]
Incremental Feedback[Roh 04][Banister 03]
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Aperiodic Feedback
Feedback? Yes No No Yes No No
Temporally Correlated
Static(Feedback is unnecessary)
Fast fading(Compression is ineffective)
Channel State
1
2
3
4
5
Symbol 1 Symbol 2 Symbol 4 Symbol 5 Symbol 6Symbol 3
Time Variation of Quantized Channel
• Motivation: Infrequent channel state changes due to temporal correlation• Proposed: aperiodic feedback triggered by channel state changes• Conventional: periodic feedback per block
• Motivation: Infrequent channel state changes due to temporal correlation• Proposed: aperiodic feedback triggered by channel state changes• Conventional: periodic feedback per block
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0.7
0.2
0.08
1.8e-22e-3
Symbol 1 Symbol 2
Channel State
1
2
3
4
5
probability
Truncation of Channel State Transitions
neighborhood of Channel State 1
Feedback Compression = 2 ! 1 bit
Truncation Threshold: = 0.02
Motivation: Given a current state, the next state belongs to a subset of the state space with high probability
Motivation: Given a current state, the next state belongs to a subset of the state space with high probability
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Result 1: Average Feedback Rate
Proposition 1: The time-average feedback rate converges with time as
where
Aperiodic FeedbackAperiodic Feedback
20 40 60 80 100 120 140 160 180 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time (symbols)
Fe
ed
ba
ck
Ra
te (
bit
s/s
ym
bo
l)
20 40 60 80 100 120 140 160 180 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time (symbols)
Fe
ed
ba
ck
Ra
te (
bit
s/s
ym
bo
l)
Transition TruncationTransition Truncation
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Proposition 2: The average capacity converges as
where
Result 2: Ergodic Capacity
Truncation of state transitions
· >
Instantaneous Capacity
Instantaneous Capacity
Quantization
Regions
Quantization
Regions
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Case Study: Beamforming for 2£1 Channel
• Finite rate• Free of error
• Finite rate• Free of error
Grassmanian codebook [Love & Heath 03] [Xia & Giannakis 05]
Grassmanian codebook [Love & Heath 03] [Xia & Giannakis 05]
Codebook lookupCodebook lookup
Partial CSI
• i.i.d CN(0,1) vector• Clark’s correlation function
• i.i.d CN(0,1) vector• Clark’s correlation function
Partial CSI: BeamformerPartial CSI: Beamformer
CSIQuantizer
Quantized Channel State
Feedback Channel
Jn
un
hn
Receiver
Forward-Link ChannelTransmitter
Beamform. Vector
Generator
wn
RX CSI
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10-3
10-2
10-1
100
Normalized Doppler, fDT
S
Av
era
ge
Fe
ed
ba
ck
Ra
te (
bit
s/T
s)
N = 8
N = 64
N = 256
Compression (colors, = 1e-6)Reference (black, = 0)Nt = 2
Compression Ratio > 3Compression Ratio > 3
Compression Ratio = 2Compression Ratio = 2
Significant reduction on average feedback rates Significant reduction on average feedback rates
Case Study: Beamforming for 2£1 Channel
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Feedback compression causes no loss on ergodic capacity Feedback compression causes no loss on ergodic capacity
0 1 2 3 4 5 6 7 8 9 101
1.5
2
2.5
3
3.5
4
4.5
5
SNR (dB)
Erg
od
ic C
ap
ac
ity
(b
ps
/Hz)
w/o Feedback Compression
w/ Feedback Compression
fd = 5e-3
Nt = 4
N = 64
fd = 4e-3
Nt = 2
N = 64
= 1e-6
Case Study: Beamforming for 2£1 Channel
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Outline
Part I: Theory Channel Markov model
Feedback compression and rate
Feedback delay
Part II: Practice Experiment setup
Measurement results
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Recap: System Model
7
Feedback delay exists due to• Propagation• Signal processing• Protocol
Feedback delay exists due to• Propagation• Signal processing• Protocol
Index Jn
Feedback Channel(delay, error free)
BeamformingChannel
EstimationHn
CSI (beamformer)
12
3
CSI quantizer
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How to Model Delay ?
S1S2
S3
S4
S6
S5
t
t+2 t+1
CSI Variation at ReceiverCSI Variation at Receiver
Feedback Delay ModelFeedback Delay Model
S1 S3 S3 S5 S1S6
S1 S3 S3 S5S6 S6
S1 S3 S3 S5S6S6
D = 1 (symbol)
D = 2 (symbol)
RX CSI
TX CSI (D =1)
TX CSI (D =2)
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Convergence of CSI Index Markov ChainTransition
probability matrix
Transition probability matrix
StationaryDistribution
StationaryDistribution
Channel StateValue = probability
Short Feedback Delay Long Feedback Delay
TX CSITX CSI
2
3
4
1
RX CSI
.25
.25
.25
.25
0.1
0.1
0.1
0.7
0
0
0
1
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Theorem 1: The ergodic capacity with a feedback delay of D symbols is
where
Result 1: Ergodic Capacity with Feedback Delay
Instantaneous Capacity
Instantaneous Capacity
Quantization
Regions
Quantization
Regions
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Def: Feedback Capacity Gain
Theorem 2: The feedback capacity gain C decreases at least exponentially with the feedback delay D as
Result 2: Feedback Capacity Gain
2 is the 2nd largest eigenvalue of P2 is the 2nd largest eigenvalue of P
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Result 2: Feedback Capacity Gain
Remarks: D: Feedback DelayD: Feedback Delay
depends on Type of System
precoding, beamforming etc.
CSI Quantization Codebook
depends on Type of System
precoding, beamforming etc.
CSI Quantization Codebook
increases inversely with Channel Coherence Time
increases inversely with Channel Coherence Time
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• Feedback delay D• Finite rate• Free of error
• Feedback delay D• Finite rate• Free of error
Grassmanian codebook [Love & Heath 03] [Xia & Giannakis 05]
Grassmanian codebook [Love & Heath 03] [Xia & Giannakis 05]
Codebook lookupCodebook lookup
Partial CSI
• i.i.d CN(0,1) vector• Clark’s correlation function
• i.i.d CN(0,1) vector• Clark’s correlation function
Partial CSI: BeamformerPartial CSI: Beamformer
Case Study: Beamforming for 2£1 Channel
CSIQuantizer
Quantized Channel State
Feedback Channel
Jn
un
hn
Receiver
Forward-Link ChannelTransmitter
Beamform. Vector
Generator
wn
RX CSI
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Feedback Capacity Gain Feedback capacity gain decreases exponentially with feedback
delay;
Decreasing rate is determined by Doppler
Parameters (WiMax): Carrier = 2.3 GHz
Symbol rate = 1.5 MHz
0 0.07 0.13 0.2 0.27 0.33 0.4 0.46 0.5310
-1
100
Feedback Delay (ms)
Fe
ed
ba
ck C
ap
aci
ty G
ain
(b
/s/H
z) fs = (90, 120, 150) Hz
fs = 300 Hz
fs = 750 Hz
fs = 1.5 KHz Nt = 2, Nr = 1, N = 16
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Design ExampleRequirement A:
Delay · 0.4 ms Capacity gain ¸ 1 bps/Hz
Requirement B: Speed = 140 km/h Delay = 0.27 ms
Parameters (WiMax): Carrier = 2.3 GHz
Symbol rate = 1.5 MHz
Vehicular speed · 43 km/h Vehicular speed · 43 km/h
Capacity gain = 0.6 bps/Hz Capacity gain = 0.6 bps/Hz
0 0.07 0.13 0.2 0.27 0.33 0.4 0.46 0.5310
-1
100
Feedback Delay (ms)
Fe
ed
ba
ck C
ap
aci
ty G
ain
(b
/s/H
z) fs = (90, 120, 150) Hz
fs = 300 Hz
fs = 750 Hz
fs = 1.5 KHz Nt = 2, Nr = 1, N = 16
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Summary of Theory
We proposed an analytical framework for designing practical limited feedback beamforming system
Feedback rate
Feedback compression
Feedback delay
Observations Feedback rate increases (e.g. linearly) with Doppler.
Feedback compression significantly reduces feedback rate.
Feedback capacity gain diminishes at least exponentially with feedback delay.
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Motivation for Measurement Results
Validate the analytical model
Channel Markov chain assumption
Shannon capacity gain vs. throughput (QAM, adaptive MCS)
Verify theoretical results
Evaluate the impact of practical factors
Synchronization errors
Channel estimation errors
Frequency offset
Phase noise
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Outline
Part I: Theory Channel Markov model
Feedback compression and rate
Feedback delay
Part II: Practice Experiment setup
Measurement results
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Measurement Setup: Hydra Prototype
Operating Frequency 2.5 GHz
Symbol Rate 1 MHz
Maximum Transmit Power 7.5 mW
Antennas L-Shaped Microstrip
RF/Baseband Universal Software Radio Peripheral
Software Architecture GNU Radio and Click
Physical Layer IEEE 802.11n Draft 2.0
see http://hydra.ece.utexas.edu for more details
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IEEE 802.11n Transmitter
Frame Format
Transmission Process
Extended Training:Non-beamformed training symbols
to measure true channel
Bit Parsing:Unnecessary for our experiment with
only 1 spatial stream
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IEEE 802.11n Receiver
Receiver Data Processsing
Receiver Header ProcessingHeader Decoding:
Any problems with header decoding result in dropped measurements
Equalization:Maximal ratio combining for experiments
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Feedback Channel Construction
Wired Feedback Advantages (for measurements):1. Low latency (compared to Hydra over-the-air feedback)2. High reliability (no dropped feedback packets due to frame synchronization errors)3. “Perfect” CSI returned to transmitter (floating point samples)
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Measurement Topology
Wireless Path:10 m wireless path between
transmitter and receiver obstructed by cubicles and office equipment
Usage Scenario:Typical wireless local area network
(WLAN) environment
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Channel Temporal Statistics (Mobility)Antennas:
Mounted on oscillating table fans
Oscillation Period:TX Period = 13.75 secondsRX Period = 11.25 seconds
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Outline
Part I: Theory Channel Markov model
Feedback compression and rate
Feedback delay
Part II: Practice Experiment setup
Measurement results
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Measurement Procedure
RXCDDSoundingLF-BF
1. Send a packet with cyclic delay diversity from the uninformed transmitter (baseline case).
2. Send a sounding packet from the transmitter.
3. Estimate the MIMO channel using the sounding packet.
4. Select a beamformer from a codebook and return the index over the wired feedback channel.
5. Send data packets using beamforming with a desired feedback delay.
6. Repeat steps 1-5 for 1000 iterations and measure the bit error of each packet.
Collecting CSI
TX
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Measure Throughput Gain
IEEE 802.11n Modulation and Coding Schemes (Single Stream)
Translation to Throughput:
Optimal Adaptation:Measurements taken for each MCS over all SNR
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Results - BER Scatter Plot
Sample Measurement:• MCS 4 (16-QAM w/ 3/4 coding rate)• 5-bit Grassmannian codebook
Sample Measurement:• MCS 4 (16-QAM w/ 3/4 coding rate)• 5-bit Grassmannian codebook
Throughput Curve Fitting:SNR binning with cubic spline
interpolation
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Results - Throughput Gain
Using adaptive MCSUsing adaptive MCS
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Results - Transition Probability Matrix
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Results - Feedback Delay
Best Fit:Least squares mapping of
measured data to an exponential decay function
Theoretical Upper Bound:Analytically derived (earlier) upper bound using transition probability
matrix calculation
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Conclusions
We proposed an analytical framework for designing limited feedback beamforming systems Allocate feedback bandwidth Compress CSI feedback Compute allowable mobility range, and signal processing and
protocol delay.
Theoretical result on feedback delay is validated using measurement data. More experiments are being carried for verifying other
theoretical results.
The proposed framework can be extended to other types of limited feedback systems e.g. precoding.
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Thank you!