WSN PPT.ppt

Feedback Methods for Multiple-Input
Multiple-Output Wireless Systems
David J. Love
WNCG
The University of Texas at Austin
March 4, 2004

Wireless Networking and Communication Group 2
Outline
 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 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?

Solution: 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 •
•
•

SNR (dB)
MIMO Capacity Benefits [Telatar]
 Multiply Data Rate
 Multiply throughput $$$
 Multiply # users $$$
min(Tx,Rx) antennas
Rate
Slope
1 by 1 antenna
4.3 b/s/Hz
8 by 8
antennas
32.3 b/s/Hz
Capacity
1 by 16
antennas
9 b/s/Hz

Signal Quality Through Diversity
 Antennas provide diversity advantage [Brennan]
 Large gains for moderate to high SNR
 Reduced fading!
 Better user experience $$$
Signal
Power
standard
with MIMO
time
1 antenna
4th order
diversity
Diversity = -slope
SNR (dB)
Error
Rate
(log
scale)

MIMO 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

Space-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

Role 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

Closed-Loop Performance Benefits
 Channel capacity fundamentally
larger
 Simplified decoding
 Reduced error rate
 Allows multiuser scheduling
(transmit to group of best users)
SNR (dB)
Capacity
SNR (dB)
Error
Rate
(log
scale)
4b/s/Hz
12 dB

Transmitter 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

 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 Problem
Transmitter Receiver
...
...
Data
Feedback
Feedback amount around 5 to 10 bits

Outline
 Introduction
 MIMO Background
 MIMO Signaling
 Beamforming

 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 Problem
Transmitter Receiver
...
...
Quantizer

Solution: 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
H
Choose F
from
codebook
Update
precoder
Low-rate feedback path
…
Open-Loop
Space-Time
Encoder
Receiver
…
H
X
F
…
…
FX

 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 Selection
Channel
Realization
H
Codebook
matrix

Challenge #2: Codebook Design
 Codebook design very important
 Given:
 Underlying open-loop algorithm
 Selection function
 Goal: Quantize (in some sense) the perfect channel
knowledge precoder

Communications Vector Quantization
 Let
 Communications Approach: [Love et al]
System parameter to maximize
Design Objective: Improve system performance
 Different than traditional vector quantization

Outline
 Introduction
 MIMO Background
 MIMO Signaling
 Channel adaptive (Closed-Loop) MIMO
 Beamforming

 Convert MIMO to SISO
 Beamforming advantages:
 Error probability improvement
 Resilience to fading
Limited Feedback Beamforming [Love et al]
Coding &
Modulation
...
H
f
...
fs
Detection
and
Decoding
Feedback
y
s
unit vector
r
Complex
number

 Nearest neighbor union bound [Cioffi]
 Instantaneous channel capacity [Cover & Thomas]
[Love et al]
Challenge #1: Beamformer Selection

 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 Codebook
channel term codebook term

Codebook 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

Bounding of Criterion

Grassmannian Beamforming Criterion [Love et al]:
Design
by maximizing
Grassmann
manifold
metric ball volume [Love et al]
radius2

Feedback 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)

Simulation
3 by 3
QPSK
SNR (dB)
Error
Rate
(log
scale)
0.6 dB

Beamforming 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.

Outline
 Introduction
 MIMO Background
 MIMO Signaling
 Beamforming

 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)
Space-time
Receiver f e d c b a
f e d c b a 





 *
*
a
b
b
a
Transmission 1

Solution: Limited Feedback Precoded
OSTBC [Love et al]

 Require
 Use codebook:
Space-Time
Encoder
...
H
F
...
Feedback
C
...
FC
Detection
and
Decoding

 Can bound error rate [Tarokh et al]
 Choose matrix from from as [Love et al]
Channel
Realization
H
Codebook
matrix

Challenge #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

Feedback 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!

Simulation
8 by 1
Alamouti
16-QAM
9.5dB
Open-Loop
16bit
channel
8bit lfb
precoder
Error
Rate
(log
scale)
SNR (dB)

Precoded 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.

Outline
 Introduction
 MIMO Background
 MIMO Signaling
 Beamforming

 True “multiple-input” algorithm
 Advantage: High-rate signaling technique
 Decode
Invert (directly/approx)
 Disadvantage: Performance very sensitive to channel singular values
Spatial Multiplexing [Foschini]
{
Multiple
independent
streams
...
H
...
s
Detection
and
Decoding
...,s1+Mt,s1
...,s2Mt,sMt
y

Limited Feedback Precoded SM [Love et al]
 Assume
 Again adopt codebook approach
Coding &
Modulation
..
H
F
...
Fs
Feedback
s
... Detection
and
Decoding

 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
Codebook
matrix

Challenge #2: Distortion Function
 Min distance, min singular value, MMSE (with trace) [Love
et al]
 MMSE (with det) and capacity [Love et al]

Codebook 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

Simulation
4 by 2
2 substream
16-QAM
16bit channel
Perfect
Channel
6bit lfb
precoder 4.5dB
Error
Rate
(log
scale)
SNR per bit (dB)

Precoded 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.

Outline
 Introduction
 MIMO Background
 MIMO Signaling
 Beamforming

Multi-Mode Precoding
 Fixed rate
 Adaptively vary number of
substreams
 Yields
 Full diversity order
 Rate growth of spatial multiplexing Capacity
Ratio
Spatial
Multiplexer
...
...
H
FM
M: # substreams Adapt precoder
matrix
... H
Mode
selector
Feedback
Detect
&
Decode
>98%
>85%
SNR (dB)
D. J. Love and R. W. Heath Jr., “Multi-Mode Precoding for MIMO Wireless Systems Using
Linear Receivers,” submitted to IEEE Transactions on Signal Processing, Jan. 2004.

Space-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,” submitted
to IEEE Transactions on Wireless Communications, Nov. 2003.

Assorted Areas
 MIMO channel modeling
 IEEE 802.11N covariance generation
 Joint source-channel space-time coding
Diversity 4
Diversity 2
Diversity 1
Visually important
Visually unimportant
…

Future 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

Conclusions
 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

Beamforming Criterion

 [Love et al]

 Differentiation maximize

Precode OSTBC Criterion
 Let


Precode OSTBC – Cont.



 [Barg et al]

Precode Spat Mult Criterion – Min SV
 Let


Precode Spat Mult Criterion – Capacity
 Let


SM Susceptible to Channel
Decreasing
 Fix
 Condition number

Vector 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?

Grassmannian 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

Channel Assumptions
 Flat-fading (single-tap)
 Antennas widely spaced (channels independent)
BW
frequency (Hz)

Solution: Limited Feedback Precoding
 Use codebook
 Codebook known at transmitter and receiver
 Convey codebook index when channel changes
Space-Time
Encoder
...
H
r
F
... H
Low-rate feedback path
S
Update
Precoder
...
Choose F
from
codebook
FS
Detection
and
Decoding
bits

Communications Vector Quantization
 Let
 VQ Approach:
Design Objective: Approximate optimal solution
 Communications Approach: [Love et al]
System parameter to maximize
Design Objective: Improve system performance

 True “multiple-input” algorithm
 Advantage: High-rate signaling technique

 Decode
Invert (directly/approx)
 Disadvantage: Performance very sensitive to channel singular values
Spatial Multiplexing [Foschini]
}Multiple
independent
streams
…

Assorted Areas
 MIMO channel modeling
 IEEE 802.11N covariance generation
 Joint source-channel space-time coding
Diversity 4
Diversity 2
Diversity 1
Visually important
Visually insignificant
…

WSN PPT.ppt

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