Feedback Methods for Multiple-Input
Multiple-Output Wireless Systems
David J. Love
WNCG
The University of Texas at Austin
March 4, 2004
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 Networking and Communication Group
2
Wireless Challenges
 Spectral efficiency


Spectrum very expensive $$$
Maximize data rate per bandwidth
bits/sec/Hz
 Quality


Wireless links fluctuate
Desire SNR to have large mean and low variance
 Limited transmit power
How can we maximize spectral efficiency
and quality?
Wireless Networking and Communication Group
3
Solution: MIMO Wireless Systems
Transmitter
•
•
•
•
•
•
Receiver

Multiple-input multiple-output (MIMO) using multiple antennas at
transmitter and receiver

Antennas spaced

Allow space-time signaling
independent fading
Wireless Networking and Communication Group
4
Capacity
Rate Slope
MIMO Capacity Benefits [Telatar]
8 by 8
antennas
32.3 b/s/Hz
1 by 16
antennas
9 b/s/Hz
min(Tx,Rx) antennas
 Multiply Data Rate
 Multiply throughput $$$
 Multiply # users $$$
Wireless Networking and Communication Group
SNR (dB)
1 by 1 antenna
4.3 b/s/Hz
5
Signal Power
with MIMO
standard
time
Error Rate (log scale)
Signal Quality Through Diversity
1 antenna
Diversity = -slope
4th order
diversity
SNR (dB)
 Antennas provide diversity advantage [Brennan]



Large gains for moderate to high SNR
Reduced fading!
Better user experience $$$
Wireless Networking and Communication Group
6
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
Wireless Networking and Communication Group
7
Space-Time Signaling
time
space
 Design in space and time
 Transmit matrices – transmit one column each
transmission
 Sent over a linear channel
Assumption:
is an i.i.d. complex Gaussian matrix
Wireless Networking and Communication Group
8
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
Wireless Networking and Communication Group
9
 Simplified decoding
 Reduced error rate
 Allows multiuser scheduling
(transmit to group of best users)
Wireless Networking and Communication Group
Error Rate (log scale)
 Channel capacity fundamentally
larger
Capacity
Closed-Loop Performance Benefits
4b/s/Hz
SNR (dB)
12 dB
SNR (dB)
10
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
Wireless Networking and Communication Group
11
Limited Feedback Problem
Data
Transmitter
...
...
 Solution: Send back feedback [Narula et al],[Heath et al]
Receiver
Feedback
 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)
Feedback amount around 5 to 10 bits
Wireless Networking and Communication Group
12
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 Networking and Communication Group
13
Feedback Design Problem
...
...
 Prior work [Narula et al],[Jongren et al]: Quantize channel
Transmitter
Receiver
Quantizer
 Channel quantization fails for MIMO


8x8 MIMO = More than 128 bits of feedback!
Singular value structure sensitive to quantization
Wireless Networking and Communication Group
14
Solution: Limited Feedback Precoding
……
H
F
…
…
Open-Loop
Space-Time
Encoder
FX
X
Receiver
H
Update
precoder
Low-rate feedback path
Choose F
from
codebook
 Use open-loop algorithm with linear transformation
(precoder)
 Restrict to
 Codebook known at transmitter/receiver and fixed
 Convey codebook index when channel changes
bits
Wireless Networking and Communication Group
15
Challenge #1: Codeword Selection
Channel
Realization
H
Codebook
matrix
 Use selection function
 Selection function


such that
depends on
Underlying open-loop algorithm
Performance criterion
 Solution: Use perfect channel knowledge selection but
optimize over codebook
Wireless Networking and Communication Group
16
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
Wireless Networking and Communication Group
17
Communications Vector Quantization
 Let
 Communications Approach: [Love et al]
System parameter to maximize
Design Objective: Improve system performance
 Different than traditional vector quantization
Wireless Networking and Communication Group
18
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 Networking and Communication Group
19
Limited Feedback Beamforming
[Love et al]
unit vector
H
...
f
...
Coding &
Modulation
Detection
and
Decoding
y
s
fs
Feedback
r
Complex
number
 Convert MIMO to SISO
 Beamforming advantages:


Error probability improvement
Resilience to fading
Wireless Networking and Communication Group
20
Challenge #1: Beamformer Selection
 Nearest neighbor union bound [Cioffi]
 Instantaneous channel capacity [Cover & Thomas]
[Love et al]
Wireless Networking and Communication Group
21
Challenge #2: Beamformer Codebook
 Want to maximize
on average
 Average distortion
 Using sing value decomp & Gaussian random matrix
results [James 1964] (
)
channel term
where
codebook term
is a uniformly distributed unit vector
Wireless Networking and Communication Group
22
Codebook as Subspace Code


is a subspace distance – only
depends on subspace not vector

set of lines
 Codebook is a subspace code
 Minimum distance
Wireless Networking and Communication Group
[Sloane et al]
23
Bounding of Criterion
Grassmann
manifold
radius2 metric ball volume [Love et al]

Grassmannian Beamforming Criterion [Love et al]:
Design
by maximizing
Wireless Networking and Communication Group
24
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)
Wireless Networking and Communication Group
25
3 by 3
QPSK
Error Rate (log scale)
Simulation
0.6 dB
SNR (dB)
Wireless Networking and Communication Group
26
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.
Wireless Networking and Communication Group
27
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 Networking and Communication Group
28
Orthogonal Space-Time Block Codes (OSTBC)
f e d c b a
a b* 

*
b  a 
Space-time
Receiver
f e d c b a
Transmission 1
 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
Wireless Networking and Communication Group
29
Solution: Limited Feedback Precoded
OSTBC [Love et al]
F
C
...
H
...
...
Space-Time
Encoder
Detection
and
Decoding
FC
Feedback

 Require
 Use codebook:
Wireless Networking and Communication Group
30
Challenge #1: Codeword Selection
Channel
Realization
H
Codebook
matrix
 Can bound error rate [Tarokh et al]
 Choose matrix from
from
Wireless Networking and Communication Group
as [Love et al]
31
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
Wireless Networking and Communication Group
32
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!
Wireless Networking and Communication Group
33
8 by 1
Alamouti
16-QAM
Error Rate (log scale)
Simulation
Open-Loop
16bit
channel
9.5dB
8bit lfb
precoder
Wireless Networking and Communication Group
SNR (dB)
34
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.
Wireless Networking and Communication Group
35
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 Networking and Communication Group
36
Spatial Multiplexing [Foschini]
s
y
Advantage: High-rate signaling technique
Decode
Invert

Detection
and
Decoding
True “multiple-input” algorithm


H
...

{
...,s2Mt,sMt
...
Multiple
independent
streams
...,s1+Mt,s1
(directly/approx)
Disadvantage: Performance very sensitive to channel singular values
Wireless Networking and Communication Group
37
Limited Feedback Precoded SM
F
s
..
H
...
...
Coding &
Modulation
[Love et al]
Detection
and
Decoding
Fs
Feedback
 Assume
 Again adopt codebook approach
Wireless Networking and Communication Group
38
Challenge #1: Codeword Selection
Channel
Realization
H
 Selection functions proposed when
Codebook
matrix
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]
Wireless Networking and Communication Group
39
Challenge #2: Distortion Function
 Min distance, min singular value, MMSE (with trace) [Love
et al]
 MMSE (with det) and capacity [Love et al]
Wireless Networking and Communication Group
40
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
Wireless Networking and Communication Group
41
4 by 2
2 substream
16-QAM
Error Rate (log scale)
Simulation
Perfect
Channel
Wireless Networking and Communication Group
16bit channel
6bit lfb
precoder
4.5dB
SNR per bit (dB)
42
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 twonorm/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.
Wireless Networking and Communication Group
43
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 Networking and Communication Group
44
Multi-Mode Precoding
H
...
H
Adapt precoder
matrix
Feedback
 Fixed rate
 Adaptively vary number of
substreams
 Yields


Detect
&
Decode
Full diversity order
Rate growth of spatial multiplexing
Mode
selector
Capacity Ratio
M: # substreams
FM
...
...
Spatial
Multiplexer
>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.
Wireless Networking and Communication Group
45
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.
Wireless Networking and Communication Group
46
Assorted Areas
 MIMO channel modeling

IEEE 802.11N covariance generation
 Joint source-channel space-time coding
…
Visually important
Visually unimportant
Wireless Networking and Communication Group
Diversity 4
Diversity 2
Diversity 1
47
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
Wireless Networking and Communication Group
48
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
Wireless Networking and Communication Group
49
Beamforming Criterion


[Love et al]

 Differentiation
maximize
Wireless Networking and Communication Group
50
Precode OSTBC Criterion


Let
Wireless Networking and Communication Group
51
Precode OSTBC – Cont.





[Barg et al]
Differentiation
maximize
Wireless Networking and Communication Group
52
Precode Spat Mult Criterion – Min SV
 Let


Differentiation
maximize
Wireless Networking and Communication Group
53
Precode Spat Mult Criterion – Capacity
 Let

 Differentiation
maximize
Wireless Networking and Communication Group
54
SM Susceptible to Channel
 Fix
Decreasing
 Condition number
Wireless Networking and Communication Group
55
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?
Wireless Networking and Communication Group
56
Grassmannian Subspace Packing
 Complex Grassmann manifold
 set of M-dimensional subspaces in
 Packing Problem
 Construct set with maximum
minimum distance
1
 Distance between subspaces
 Chordal
 Projection Two-Norm
 Fubini-Study
2
Column spaces of codebook matrices
represent a set of subspaces in
Wireless Networking and Communication Group
57
Channel Assumptions
BW
frequency (Hz)
 Flat-fading (single-tap)
 Antennas widely spaced (channels independent)
Wireless Networking and Communication Group
58
Solution: Limited Feedback Precoding
F
S
...
H
...
...
Space-Time
Encoder
Detection
and
Decoding
FS
r
Update
Precoder
Low-rate feedback path
H
Choose F
from
codebook
 Use codebook
 Codebook known at transmitter and receiver
 Convey codebook index when channel changes
bits
Wireless Networking and Communication Group
59
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
Wireless Networking and Communication Group
60
Spatial Multiplexing [Foschini]

True “multiple-input” algorithm
Advantage: High-rate signaling technique
}
…



Decode
Invert

Multiple
independent
streams
(directly/approx)
Disadvantage: Performance very sensitive to channel singular values
Wireless Networking and Communication Group
61
Assorted Areas
 MIMO channel modeling

IEEE 802.11N covariance generation
 Joint source-channel space-time coding
…
Visually important
Visually insignificant
Wireless Networking and Communication Group
Diversity 4
Diversity 2
Diversity 1
62