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

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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

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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

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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

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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

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

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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

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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

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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 | 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 | 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 | 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 | 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 eachIntroduction |Message Passing Receivers | Simulations | Summary

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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

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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

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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 | 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

improvementIntroduction |Message Passing Receivers | Simulations | Summary

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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

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Thank you

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BACK UP

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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

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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

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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

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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