a factor-graph approach to joint ofdm channel estimation and decoding in impulsive noise channels
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A Factor-Graph Approach to Joint OFDM Channel Estimation and Decoding in Impulsive
Noise Channels
Philip Schniter The Ohio State University
Marcel Nassar, Brian L. EvansThe University of Texas at Austin
2
Outline
• Uncoordinated interference in communication systems
• Effect of interference on OFDM systems• Prior work on OFDM receivers in uncoordinated
interference• Message-passing OFDM receiver design• Simulation results
Introduction |Message Passing Receivers | Simulations | Summary
3
Uncoordinated Interference• Typical Scenarios:
– Wireless Networks: Ad-hoc Networks, Platform Noise, non-communication sources
– Powerline Communication Networks: Non-interoperable standards, electromagnetic emissions
• Statistical Models:
: # of comp. comp. probability comp. variance
Interference ModelTwo impulsive components:• 7% of time/20dB above
background• 3% of time/30dB above
background
Gaussian Mixture (GM)
Introduction |Message Passing Receivers | Simulations | Summary
4
OFDM BasicsSystem Diagram
+Source
channel
DFTInverse DFTSymbolMapping 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 | Summary
5
OFDM Symbol StructureData Tones
• Symbols carry information
• Finite symbol constellation
• Adapt to channel conditions
Pilot Tones
• Known symbol (p)• Used to estimate
channelpilots → 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 | Summary
6
Prior OFDM DesignsCategory Referenc
esMethod Limitations
Time-Domain
preprocessing
[Haring2001] Time-domain signal MMSE estimation
• ignore OFDM signal structure
• performance 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 | Summary
7
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 | Summary
8
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 | Summary
9
• 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 | Summary
10
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 | Summary
11
BP over OFDM Factor Graph
LDPC Decoding via BP [MacKay2003]
MC Decoding
Node degree=N+L!!!
Introduction |Message Passing Receivers | Simulations | Summary
12
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 eachIntroduction |Message Passing Receivers | Simulations | Summary
13
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 | Summary
14
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 DecodingLDPC
DecodingGAMP
Design Freedom
Notation : # tones
: # coded bits : # check nodes
: set of used tones
Introduction |Message Passing Receivers | Simulations | Summary
15
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 | Summary
16
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
improvementIntroduction |Message Passing Receivers | Simulations | Summary
17
Summary
• Huge performance gains if receiver account for uncoordinated interference
• The 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
Introduction |Message Passing Receivers | Simulations | Summary
18
Thank you
19
BACK UP
20
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
21
Empirical ModelingWiFi Platform Interference Powerline Systems
[Data provided by Intel] Gaussian HMM
Model1 2
1 2 1 5
Partitioned Markov Chain Model [Zimmermann2002]
1
2
…
Impulsive
Background
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
22
Statistical-Physical ModelingWireless 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
23
Effect of Interference on OFDMSingle 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.
recoveredIn theory, with joint MAP
decodingOFDM Single Carrier
[Haring2002] tens of dBs
(symbol by symbol decoding)DFT
Introduction |Message Passing Receivers | Simulations | Robust Receivers| Summary
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