Limited Feedback Beamforming with Delay: Theory and Practice

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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 View
1996
Channel capacity (Telatar, Foschini)
1998
Gaussian broadcast Caire Shamai Vish., Jindal
Goldsmith Viswanath Tse Yu Cioffi
Space-time codes (Tarokh, Alamouti, Jafarkani)
2000
2002
Multi-user Diversity Knopp Humblet Viswanath
Tse Sharif Hassibi
Diversity-multiplexing tradeoff (Zheng Tse,
Heath Paulraj)
2004
IEEE 802.16e (WiMax)
2006
IEEE 802.11n (WiFi)
3GPP-LTE
2008
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3
Feedback Enhances Communication
In the darkness
Here!
?
listener
speaker
listener
speaker
no feedback
feedback
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4
Beamforming Increases Throughput
beamforming weights
no feedback
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5
Limited Feedback Concept

• Adaptive Transmission
• Precoder
• Beamformer
• AMC, etc

Receiver
Transmiter
CSI
Finite-Rate Feedback Channel
Codebook based quantizer
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Limited Feedback Beamforming Increases Throughput
quantizer
partition index
feedback quantizer
surface of unit hyper-sphere
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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 06Xia 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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Motivation

• 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

Important for designing practical limited
feedback systems
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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 sequence
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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 Channel
Markov Chain
Feedback rate, compression, delay
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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 Model
Unit Hyper-Sphere
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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

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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
CSI

Quantization
Extensively studied Love et al 04 Mukkavilli
et al 03
Compression (frequency)
Compression (time)
Compression (space)
Adaptive Codebooks Mondal and Heath 05
Incremental Feedback Roh 04Banister 03
Subspace Interpolation Choi et al 04
Finite-Rate Feedback
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Aperiodic Feedback

• 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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Truncation of Channel State Transitions
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 Feedback
Transition Truncation
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Result 2 Ergodic Capacity

• Proposition 2 The average capacity converges as
• where

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Case Study Beamforming for 21 Channel

• i.i.d CN(0,1) vector
• Clarks correlation function

Partial CSI Beamformer
Partial CSI

• Finite rate
• Free of error

Codebook lookup
Grassmanian codebook Love Heath 03 Xia
Giannakis 05
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Case Study Beamforming for 21 Channel
Significant reduction on average feedback rates
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Case Study Beamforming for 21 Channel
Feedback compression causes no loss on ergodic
capacity
? 1e-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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Recap System Model

• Feedback delay exists due to
• Propagation
• Signal processing
• Protocol

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How to Model Delay ?
CSI Variation at Receiver
Feedback Delay Model
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Convergence of CSI Index Markov Chain
Transition probability matrix
Stationary Distribution
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Result 1 Ergodic Capacity with Feedback Delay

• Theorem 1 The ergodic capacity with a feedback
  delay of D symbols is
• where

Quantization Regions
Instantaneous Capacity
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Result 2 Feedback Capacity Gain

• Def Feedback Capacity Gain
• Theorem 2 The feedback capacity gain ?C
  decreases at least exponentially with the
  feedback delay D as

?2 is the 2nd largest eigenvalue of P
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Result 2 Feedback Capacity Gain
D Feedback Delay

• Remarks

• ? depends on
• Type of System
• precoding, beamforming etc.
• CSI Quantization Codebook

• ? increases inversely with
• Channel Coherence Time

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Case Study Beamforming for 21 Channel

• i.i.d CN(0,1) vector
• Clarks correlation function

Partial CSI Beamformer
Partial CSI

• Feedback delay D
• Finite rate
• Free of error

Codebook lookup
Grassmanian codebook Love Heath 03 Xia
Giannakis 05
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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

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Design Example

• Requirement A
• Delay 0.4 ms
• Capacity gain 1 bps/Hz
• Requirement B
• Speed 140 km/h
• Delay 0.27 ms

Vehicular speed 43 km/h

• Parameters (WiMax)
• Carrier 2.3 GHz
• Symbol rate 1.5 MHz

Capacity gain 0.6 bps/Hz
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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
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IEEE 802.11n Transmitter
Extended Training Non-beamformed training
symbols to measure true channel
Frame Format
Bit Parsing Unnecessary for our experiment with
only 1 spatial stream
Transmission Process
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IEEE 802.11n Receiver
Header Decoding Any problems with header
decoding result in dropped measurements
Receiver Header Processing
Receiver Data Processsing
Equalization Maximal ratio combining for
experiments
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Feedback Channel Construction

• Wired Feedback Advantages (for measurements)
• Low latency (compared to Hydra over-the-air
  feedback)
• High reliability (no dropped feedback packets
  due to frame synchronization errors)
• 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 seconds RX
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
Collecting CSI
CDD
Sounding
LF-BF
TX
RX

• Send a packet with cyclic delay diversity from
  the uninformed transmitter (baseline case).
• Send a sounding packet from the transmitter.
• Estimate the MIMO channel using the sounding
  packet.
• Select a beamformer from a codebook and return
  the index over the wired feedback channel.
• Send data packets using beamforming with a
  desired feedback delay.
• Repeat steps 1-5 for 1000 iterations and measure
  the bit error of each packet.

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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

Throughput Curve Fitting SNR binning with cubic
spline interpolation
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Results - Throughput Gain
Using 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!