Limited Feedback Beamforming with Delay: Theory and Practice Huang Kaibin Collaborators: Robert Daniels Prof. Robert W. Heath Jr. Prof. Jeffrey G. Andrews

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

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

Feedback Enhances Communication

no feedback feedback

Here!?

listener speaker listener speaker

In the darkness…

2

Beamforming Increases Throughput

signal

w1

w2

h1

h2

n

SNR

beamforming weights

no feedback

feedback

feedback

3

Limited Feedback Concept

Finite-RateFeedback Channel

Adaptive Transmission• Precoder• Beamformer• AMC, etc

CSI

Codebook based quantizer

ReceiverTransmiter

Wireless Channel

S1S2

S3

S4S5

S6

Limited Feedback Beamforming Increases Throughput

signal

w1

w2

h1

h2

n

SNR

quantizerpartition index

surface of unit hyper-sphere

feedback quantizer

4

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

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

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

Outline

Part I: Theory Channel Markov model

Feedback compression and rate

Feedback delay

Part II: Practice Experiment setup

Measurement results

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

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

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

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

Outline



Feedback delay


Measurement results

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]

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

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

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

Proposition 2: The average capacity converges as

where

Result 2: Ergodic Capacity

Truncation of state transitions

· >

Instantaneous Capacity


Quantization

Regions

Quantization

Regions

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]


Codebook lookupCodebook lookup

Partial CSI

• 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

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


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


Outline



Feedback delay


Measurement results

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

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)

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

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

where

Result 1: Ergodic Capacity with Feedback Delay



Quantization

Regions

Quantization

Regions

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

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

• Feedback delay D• Finite rate• Free of error

• Feedback delay D• Finite rate• Free of error



Codebook lookupCodebook lookup

Partial CSI



Partial CSI: BeamformerPartial CSI: Beamformer


CSIQuantizer

Quantized Channel State

Feedback Channel

Jn

un

hn

Receiver

Forward-Link ChannelTransmitter

Beamform. Vector

Generator

wn

RX CSI

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

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

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.

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

Outline



Feedback delay


Measurement results

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

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

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

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)

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

Channel Temporal Statistics (Mobility)Antennas:

Mounted on oscillating table fans

Oscillation Period:TX Period = 13.75 secondsRX Period = 11.25 seconds

Outline



Feedback delay


Measurement results

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

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

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

Results - Throughput Gain

Using adaptive MCSUsing adaptive MCS

Results - Transition Probability Matrix

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

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.

Thank you!

Documents

Limited Feedback Beamforming with Delay: Theory and Practice Huang Kaibin Collaborators: Robert Daniels Prof. Robert W. Heath Jr. Prof. Jeffrey G. Andrews