low complexity em-based decoding for ofdm systems with impulsive noise
DESCRIPTION
Low Complexity EM-based Decoding for OFDM Systems with Impulsive Noise. Marcel Nassar and Brian L. Evans Wireless Networking and Communications Group The University of Texas at Austin. Asilomar Conference on Signals, Systems, and Computers 2011. Wireless Transceivers. antennas. - PowerPoint PPT PresentationTRANSCRIPT
November 9th, 2010
Low Complexity EM-based Decoding for OFDM Systems with Impulsive
Noise
Asilomar Conference on Signals, Systems, and Computers 2011
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Marcel Nassar and Brian L. Evans
Wireless Networking and Communications Group
The University of Texas at Austin
Wireless Transceivers
Wireless Networking and Communications Group
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Wireless CommunicationSources
Uncoordinated Transmissions
Non-Communication SourcesElectromagnetic radiations
Computational Platform
Clocks, busses, processors
Other embedded transceivers
antennas
baseband processor
3.25 3.3 3.35 3.4 3.45 3.5 3.55 3.6x 10
6
-200
-100
0
100
200
samples IndexV
olta
ge L
evel
Powerline Communications
Wireless Networking and Communications Group
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3.3 3.4 3.5 3.6 3.7 3.8 3.9 4x 10
4
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
time index
volta
ge
Light Dimmers
Receiver
Microwave OvensIngress Broadcast
Stations
Fluorescent Bulbs
Home Devices
Noise Modeling
Modeling the first order statistics of noise Gaussian Mixture Model Middleton Class A Symmetric Alpha Stable
Some Fitted Parameters for GM
Wireless Networking and Communications Group
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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
0.75
0.25
13.7
0.89
0.11
198
0.87
0.13
140
Platform Noise
Powerline Noise
can be estimated during quiet time
Consider an OFDM communication system
Noise Model: a K-term Gaussian Mixture
Assumptions: Channel is fixed during an OFDM symbol Channel state information (CSI) at the receiver Noise is stationary Noise parameters at the receiver
System Model
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impulsive noisenormalized SNRDFT matrix
OFDM symbolreceived symbol circulant channel
Has a product formSymbol Decodable
Exponential in N(N in hundreds)
Problem Statement OFDM detection problem
Transformed detection problem (DFT operation)
Wireless Networking and Communications Group
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• no efficient code representation for• not symbol decodable
• for Gaussian noise, statistics are preserved
• for impulsive noise, dependency is introduced No Product FormExponential in N
Single Carrier (SC) vs. OFDM
-10 -5 0 5 10 15 2010
-6
10-5
10-4
10-3
10-2
10-1
100
SNR
SER
OFDM SystemSingle Carrier System
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𝜋 1=0.9 ,𝜋 2=0.1 ,𝜎21
𝜎12=100
Low SNR: SC better
High SNR: OFDM better
OFDM provides time diversity through the FFT operation
Lot of other reasons to choose OFDM
Gaussian Mixture with
SC outperforms OFDM OFDM outperforms SC
SC vs. OFDM: Intuition
Single Carrier OFDM
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Wireless Networking and Communications Group
N modulated symbols
Impulsive Noise
Time-domain OFDM Symbol
Impulsive Noise
High Amplitude Impulse
High Amplitude Impulse
• Impulse energy concentrated in one symbol• Symbol lost
• Impulse energy spread across symbols• Loss depends on impulse amplitude and SNR
After FFT
Prior Work
Parametric Methods (statistical noise model) Haring 2001: Time-domain MMSE estimate
With noise state information and without it Non-Parametric Methods (no statistical noise model)
Haring 2000: iterative thresholding Low complexity Threshold not flexible
Caire 2008: compressed sensing approach Uses null tones Corrects only few impulses on practical systems
Lin 2011: sparse Bayesian approach Uses null tones
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Gaussian Mixture (GM) Noise
A K-term Gaussian Mixture can be viewed as a Gaussian distribution governed by a latent variable S
The distribution of W is given by:
The latent variable S can be viewed as noise state information (NSI)
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S W
Given perfect noise state information (NSI)
Estimation of time domain OFDM symbols [Haring 2002] Approach:
MMSE With NSI:
MMSE Without NSI:
GM Noise in OFDM Systems
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Exponential in Nn is not identically distributed, taking FFT is suboptimal
(Central Limit Theorem)
Expectation-Maximization Algorithm
Iterative algorithm Finds feature given the observation such that
Uses unobserved data that simplifies the evaluation
Iteration step i : E-step: Average over given and M-step: Choose to maximize this average
Given the right initialization converges to the solution
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Might be difficult to compute directly
Easier to evaluate
EM-Based Iterative Decoding
S is treated as a latent variable, X is the parameter The E-step can be written as:
The M-step can be written as:
The E-step can be interpreted as the detection problem with perfect NSI given by
As a result, we approximate the M-step by the MMSE estimate with perfect NSI
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Exponential in N
Simulation Results
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𝜋 1=0.9 ,𝜋 2=0.1 ,𝜎22
𝜎12=100Gaussian Mixture with
Initialize to MMSE without CSI
Approaches MMSE with CSI
Works well for impulses of around 20dB above background noise
Questions!
Thank you 15
Wireless Networking and Communications Group