Graphical Models and Message Passing Receivers for Interference Limited Communication Systems

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| Channel𝑡𝑇

+

Single Carrier System: Noise/Interference

0110010

|𝐻|

𝑓

𝑡𝑁𝑇

+

Channel

+

Noise/Interference

0110010

0110010

N sub-bands

frequency selective fading

Implementation complexity

equalizer

Orthogonal Frequency Division Multiplexing (OFDM):

Simpler Equalization


4

Interference in Communication Systems

Wireless LAN in ISM band

Coexisting Protocols Non-

CommunicationSources

Co-Channelinterference

Platform

Powerline Communication

Electromagnetic

emissions

Non-interoperable

standards


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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?


Complementary approach: statistically model and mitigate

UncoordinatedInterference

6

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


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Uncoordinated Interference Modeling

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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


9

Empirical Modeling – WiFi Platform

[Data provided by Intel]

Gaussian HMM Model:

1 2

𝑁 (0 ,𝜎12)𝑁 (0 ,𝜎 2

2)


Gaussian Mixture Model:

0 1 2 3 4 5 6 7 8 910

-20

10-15

10-10

10-5

100

Threshold Amplitude (a)

Tail

Pro

babi

litie

s [P

(X >

a)]

EmpiricalMiddleton Class ASymmteric 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


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Receiver Design

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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:


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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.

recoveredIn theory, with joint MAP

decodingOFDM Single Carrier

[Haring2002] tens of dBs

(symbol by symbol decoding)DFT


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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


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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


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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 !!


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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:


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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


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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


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BP over OFDM Factor Graph

LDPC Decoding via BP [MacKay2003]

MC Decoding

Node degree=N+L!!!


21

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


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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.


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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


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Simulation SettingsInterference Model

Two 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


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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


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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


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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


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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 | Robust Receivers| Summary

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Robust Receiver Design

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Recall - Coded OFDM Factor Graph

contains parameters that might be unknown


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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


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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


33

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

tonesSBL via GAMP

using all tones

EM Parameter estimation

5 TapsGM

noise4-QAMN=256

15 pilots

80 nulls

Settings

Blind EM Parameter Estimation


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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


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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

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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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Thank you

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