Graphical Models and Message Passing Receivers for Interference Limited Communication Systems Marcel...
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Transcript of Graphical Models and Message Passing Receivers for Interference Limited Communication Systems Marcel...
Graphical Models and Message Passing Receivers for Interference Limited
Communication SystemsMarcel Nassar
PhD Defense
Committee Members:Prof. Gustavo de Veciana
Prof. Brian L. Evans (supervisor)Prof. Robert W. Heath Jr.
Prof. Jonathan PillowProf. Haris Vikalo
April 17, 2013
2
Outline
• Uncoordinated interference in communication systems
• Effect of interference on OFDM systems
• Prior work on receivers in uncoordinated interference
• Message-passing receiver design
• Learning interference model parameters: robust receivers
• Summary and future work
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
3
Modern Communication Systems
𝑓
|𝐻| Channel𝑡
𝑇
+
Single Carrier System:
Noise/Interference
0110010
|𝐻|
𝑓
𝑡
𝑁𝑇
+
Channel
+
Noise/Interference
0110010
0110010
N sub-bands
frequency selective fading
Implementation complexity
equalizer
Orthogonal Frequency Division Multiplexing (OFDM):
Simpler Equalization
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
4
Interference in Communication Systems
Wireless LAN in ISM band
Coexisting Protocols Non-
CommunicationSources
Co-Channelinterference
Platform
Powerline Communication
Electromagnetic
emissions
Non-interoperable
standards
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
5
Interference Management
• An active area of research …– Orthogonal Access – MAC Layer Access: Co-existence [Rao2002] [Andrews2009]
– Precoding Techniques: Inter-cell interference cancellation [Boudreau2009], network MIMO (CoMP) [Gesbert2007], Interference Alignment [Heath2013]
– Successive Interference Cancellation [Andrews2005]
• What about residual interference? • What about non-communicating sources?• What about non-cooperative sources?
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
Complementary approach: statistically model and mitigate
UncoordinatedInterference
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Thesis Contributions
Thesis Statement:Receivers can leverage interference models to enhance decoding and increase spectral efficiency in interference limited systems.
• Contribution I: Uncoordinated Inference Modeling
• Contribution II: Receiver Design• Contribution III: Robust Receiver Design
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
7
Uncoordinated Interference Modeling
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Statistical-Physical Modeling
Wireless Systems Powerline Systems
Rural, Industrial, Apartments [Middleton77,Nassar11]
Dense Urban, Commercial[Nassar11]
WiFi, Ad-hoc[Middleton77, Gulati10]
WiFi Hotspots [Gulati10] Gaussian Mixture (GM)
: # of comp.
comp. probability
comp. variance
Middleton Class-A
A Impulsive Index
Mean Intensity
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
9
Empirical Modeling – WiFi Platform
[Data provided by Intel]
Gaussian HMM Model:
1 2
𝑁 (0 ,𝜎12)𝑁 (0 ,𝜎 2
2)
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
Gaussian Mixture Model:
0 1 2 3 4 5 6 7 8 910
-20
10-15
10-10
10-5
100
Threshold Amplitude (a)
Tai
l Pro
babi
litie
s [P
(X >
a)]
EmpiricalMiddleton Class A
Symmteric Alpha StableGaussianGaussian Mixture Model
10
1 2 1 5
Markov Chain Model
[Zimmermann2002]1
2
…
Impulsive
Background
Empirical Modeling – Powerline Systems
Measurement Data
[Katayama06] Proposed Model
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
11
Receiver Design
12
OFDM Basics
System Diagram
+Source
channel
DFTInverse DFT
SymbolMapping 𝑓
|𝐻|
0111 …
1+i 1-i -1-i 1+i …
noise +interference
Noise Model
where
total noisebackground noiseinterference
GM or GHMM
and
Receiver Model
LDPC Coded
• After discarding the cyclic prefix:
• After applying DFT:
• Subchannels:
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
13
Effect of GM Interference on OFDM
Single Carrier (SC) OFDM
• Impulse energy concentrated• Symbol lost with high probability• Symbol errors independent• Min. distance decoding is MAP-
optimal• Minimum distance decoding
under GM:
• Impulse energy spread out• Symbol lost ??• Symbol errors dependent• Disjoint minimum distance is
sub-optimal• Disjoint minimum distance
decoding:
Single Carrier vs. OFDM
Impulse energy high → OFDM sym. lost
Impulse energy low → OFDM sym.
recovered
In theory, with joint MAP decoding
OFDM Single Carrier [Haring2002] tens of dBs
(symbol by symbol decoding)
DFT
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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OFDM Symbol StructureData Tones
• Symbols carry information
• Finite symbol constellation
• Adapt to channel conditions
Pilot Tones
• Known symbol (p)• Used to estimate
channel
pilots → linear channel estimation → symbol detection → decoding
Null Tones
• Edge tones (spectral masking)
• Guard and low SNR tones
• Ignored in decoding
Coding• Added redundancy
protects against errors
But, there is unexploited information and dependencies
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
15
Prior WorkCategory Referenc
esMethod Limitations
Time-Domain
preprocessing
[Haring2001] Time-domain signal MMSE estimation
• ignore OFDM signal structure
• performance vs DFT rx degrades with increasing SNR and modulation order
[Zhidkov2008,Tseng2012]
Time-domain signal
thresholding
Sparse Signal
Reconstruction
[Caire2008,Lampe2011]
Compressed sensing
• utilize only known tones• don’t use interference
models• complexity
[Lin2011] Sparse Bayesian Learning
Iterative Receivers
[Mengi2010,Yih2012]
Iterative preprocessing
& decoding
• Suffer from preprocessing limitations
• Ad-hoc design[Haring2004] Turbo-like receiver
All don’t consider the non-linear channel estimation, and don’t use code structure
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
16
Joint MAP-Decoding• The MAP decoding rule of LDPC coded OFDM is:
• Can be computed as follows:
non iid & non-Gaussian
depends on linearly-mixed N noise samples and L
channel taps
LDPC code
Very high dimensional integrals and summations !!
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Belief Propagation on Factor Graphs
• Graphical representation of pdf-factorization• Two types of nodes:
• variable nodes denoted by circles• factor nodes (squares): represent variable
“dependence “• Consider the following pdf:
• Corresponding factor graph:
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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• Approximates MAP inference by exchanging messages on graph
• Factor message = factor’s belief about a variable’s p.d.f.
• Variable message = variable’s belief about its own p.d.f.
• Variable operation = multiply messages to update p.d.f.
• Factor operation = merges beliefs about variable and forwards
• Complexity = number of messages = node degrees
Belief Propagation on Factor Graphs
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Coded OFDM Factor Graph
unknown channel
taps
Unknown interference samples
Information bits
Coding & Interleavin
gBit loading
& modulatio
n
Symbols
Received Symbols
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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BP over OFDM Factor Graph
LDPC Decoding via BP [MacKay2003]
MC Decoding
Node degree=N+L!!!
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Generalized Approximate Message Passing[Donoho2007,Rangan2010]
Estimation with Linear Mixing
Decoupling via Graphs
• If graph is sparse use standard BP
• If dense and ”large” → Central Limit Theorem
• At factors nodes treat as Normal
• Depend only on means and variances of incoming messages
• Non-Gaussian output → quad approx.
• Similarly for variable nodes• Series of scalar MMSE estimation
problems: messages
observations
variables
• Generally a hard problem due to coupling
• Regression, compressed sensing, …
• OFDM systems:
coupling
Interference subgraph
channel subgraphgiven given
and and
3 types of output channels for each
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Proposed Message-Passing Receiver
Schedule
1. coded bits to symbols
2. symbols to 3. Run channel GAMP4. Run noise
“equalizer”5. to symbols6. Symbols to coded
bits7. Run LDPC decoding
Turbo Iteration:
1. Run noise GAMP2. MC Decoding3. Repeat
Equalizer Iteration:
Initially uniform
GAMP
GAMP
LDPC Dec.
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
23
Receiver Design & Complexity
• Not all samples required for sparse interference estimation
• Receiver can pick the subchannels:• Information provided• Complexity of MMSE estimation
• Selectively run subgraphs• Monitor convergence (GAMP
variances)• Complexity and resources
• GAMP can be parallelized effectively
Operation Complexity per iteration
MC Decoding
LDPC Decoding
GAMP
Design Freedom
Notation: # tones
: # coded bits: # check nodes
: set of used tones
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Simulation Settings
Interference ModelTwo impulsive components:• 7% of time/20dB above
background• 3% of time/30dB above
backgroundTwo types of temporal dynamics:• i.i.d. samples• Hidden Markov Model
Receiver Parameters15 GAMP iterations5 turbo iterations
FFT Size 256 (PLC) FFT Size1024 (Wireless)
50 LDPC iterations
DefinitionsSER: Symbol Error Rate
BER: Bit Error RateSNR: Signal to “noise +
interference” power ratio
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Simulation - Uncoded Performance
Matched Filter Bound: Send only one symbol
at tone k
within 1dB of MF Bound
15db better than DFT
5 TapsGM
noise4-QAMN=256
15 pilots
80 nulls
Settings
use LMMSE channel estimate
2.5dB better than SBL
use only known tones, requires matrix inverse
performs well when
interference dominates
time-domain signal
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Simulation – Modeling Gain
amplitude accuracy is not
important using all tones gives
8dB gain
flat ch.N=25660 nulls
Settings
amplitude accuracy gives
7db gain
correct marginal: 4dB gaintemporal dependency: extra
4dB
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Simulation – Tone Map Design
Tone Map Design
• How to allocate tones? • Limited resources → select
tones?• Optimal solution not
known…….• Dictionary coherence
• For same node type
Typical configuration performs significantly
worse
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Simulation - Coded Performance
10 TapsGM
noise16-QAMN=1024
150 pilots
Rate ½L=60k
Settings
one turbo iteration gives 9db over DFT
5 turbo iterations gives 13dB over
DFT
Integrating LDPC-BP into JCNED by passing back bit LLRs gives 1 dB
improvement
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Robust Receiver Design
30
Recall - Coded OFDM Factor Graph
contains parameters that might be unknown
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
31
Learning the Interference Model
model training
Θ̂
parameterestimate
Detection
01010011
Θ̂
01010011
Detection
joint estimation & detection
Training-Based
quiet period
Robust Receiver
corruptedtransmissio
n
corruptedtransmissio
n
• Computationally simpler detection
• For slowly varying environments• Suffer from model mismatch in
rapidly varying environments
• More computation for parameter estimation (but not always)
• Adapts to rapidly varying environment
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
32
Parameter Estimation via EM Algorithm
EM AlgorithmSimplifies ML Estimation by:• Marginalize over latent• Maximize w.r.t parametersMarginalization easy for directly observed GM and GHMM samples
EM for Robust ReceiversApproximate
marginalization using GAMP messages
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Sparse Bayesian Learning via GAMP
Sparse Bayesian Learning• Bayesian approach to compressive
sensing
• Use data to fit via EM• If e is sparse lot of end up zero• Requires big matrix inverse• Use only null tones• Linear channel estimation
Prior:
SBL via GAMP• Integrate into GAMP
estimation functions• Linear input estimator• Can include all tones and
codeIntroduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Simulation Result – SBL via GAMP
SBL via EM using only null
tones
SBL via GAMP using all
tones
EM Parameter estimation
5 TapsGM
noise4-QAMN=256
15 pilots
80 nulls
Settings
Blind EM Parameter Estimation
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
35
FPGA Test System for G3 PLC Receiver
NI PXIe-7965R(Virtex 5)
NI PXIe-1082Real-time host
• Simplified message-passing receiver using only null tones
• In collaboration with Karl Nieman
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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Summary
• Significant performance gains if receiver accounts for uncoordinated interference
• Proposed solution combines all available information to perform approximate-MAP inference
• Asymptotic complexity similar to conventional OFDM receiver
• Can be parallelized
• Highly flexible framework: performance vs. complexity tradeoff
• Robust for fast-varying interference environments
37
Future Work
• Temporal Modeling of Uncoordinated Interference – Wireless Networks– Powerline Networks– Tractable Inference
• Pilot and null tone allocation in impulsive noise– Coherence not optimal– Trade-off between channel and noise estimation
• Extension to different interference and noise models– Cyclostationary noise– ARMA models for spectrally shaped noise
• Mitigation of narrowband interferers– Sparse in frequency domain
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Related Publications
M. Nassar, K. Gulati, Y. Mortazavi, and B. L. Evans, "Statistical Modeling of Asynchronous Impulsive Noise in Powerline Communication Networks", Proc. IEEE Int. Global Comm. Conf.. Dec. 5-9, 2011, Houston, TX USA.
M. Nassar, X. E. Lin and B. L. Evans, "Stochastic Modeling of Microwave Oven Interference in WLANs", Proc. IEEE Int. Comm. Conf., Jun. 5-9, 2011, Kyoto, Japan.
M. Nassar, A. Dabak, I. H. Kim, T. Pande and B. L. Evans, "Cyclostationary Noise Modeling In Narrowband Powerline Communication For Smart Grid Applications“, Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, March 25-30, 2012, Kyoto, Japan. M. Nassar, J. Lin, Y. Mortazavi, A. Dabak, I. H. Kim and B. L. Evans, "Local Utility Powerline Communications in the 3-500 kHz Band: Channel Impairments, Noise, and Standards", IEEE Signal Processing Magazine, Sep. 2013
M. Nassar and B. L. Evans, "Low Complexity EM-based Decoding for OFDM Systems with Impulsive Noise", Proc. Asilomar Conf. on Signals, Systems and Computers, Nov. 6-9, 2011, Pacific Grove, CA USA.
M. Nassar, K. Gulati, M. R. DeYoung, B. L. Evans and K. R. Tinsley, "Mitigating Near-Field Interference in Laptop Embedded Wireless Transceivers", Journal of Signal Processing Systems, Mar. 2009, invited paper.
J. Lin, M. Nassar and B. L. Evans, "Non-Parametric Impulsive Noise Mitigation in OFDM Systems Using Sparse Bayesian Learning", Proc. IEEE Int. Global Comm. Conf., Dec. 5-9, 2011, Houston, TX USA.
M. Nassar, P. Schniter and B. L. Evans, ``Message-Passing OFDM Receivers for Impulsive Noise Channels'', IEEE Transactions on Signal Processing, to be submitted.
J. Lin, M. Nassar, and B. L. Evans, ``Impulsive Noise Mitigation in Powerline Communications using Sparse Bayesian Learning'', IEEE Journal on Selected Areas in Communications, vol. 31, no. 7, Jul. 2013, to appear.
K. F. Nieman, J. Lin, M. Nassar, B. L. Evans, and K. Waheed, ``Cyclic Spectral Analysis of Power Line Noise in the 3-200 kHz Band'', Proc. IEEE Int. Symp. on Power Line Communications and Its Applications, Mar. 24-27, 2013, Johannesburg, South Africa. Won Best Paper Award.
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