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Low Complexity EM-based Decoding for OFDM Systems with Impulsive Noise

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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

- antennas

- Computational Platform
- Clocks, busses, processors
- Other embedded transceivers

- Non-Communication Sources
- Electromagnetic radiations

- baseband processor

- Wireless Communication
- Sources
- Uncoordinated Transmissions

Wireless Networking and Communications Group

- Microwave Ovens

- Ingress Broadcast Stations

- Receiver

- Home Devices

- Light Dimmers

- Fluorescent Bulbs

Wireless Networking and Communications Group

- Modeling the first order statistics of noise
- Gaussian Mixture Model
- Middleton Class A
- Symmetric Alpha Stable

- Some Fitted Parameters for GM

Platform Noise

Powerline Noise

Wireless Networking and Communications Group

- 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

impulsive noise

OFDM symbol

normalized SNR

received symbol

DFT matrix

circulant channel

can be estimated during quiet time

Wireless Networking and Communications Group

- OFDM detection problem
- Transformed detection problem (DFT operation)

Exponential in N

(N in hundreds)

- no efficient code representation for
- not symbol decodable

Has a product formSymbol Decodable

- for Gaussian noise, statistics are preserved
- for impulsive noise, dependency is introduced

No Product FormExponential in N

Wireless Networking and Communications Group

Gaussian Mixture with

- Low SNR: SC better
- High SNR: OFDM better
- OFDM provides time diversity through the FFT operation
- Lot of other reasons to choose OFDM

SC outperforms OFDM

OFDM outperforms SC

Wireless Networking and Communications Group

Single Carrier

OFDM

N modulated symbols

Time-domain OFDM Symbol

High Amplitude Impulse

High Amplitude Impulse

Impulsive Noise

Impulsive Noise

After FFT

- Impulse energy concentrated in one symbol
- Symbol lost

- Impulse energy spread across symbols
- Loss depends on impulse amplitude and SNR

Wireless Networking and Communications Group

- Parametric Methods (statistical noise model)
- Haring 2001: Time-domain MMSE estimate
- With noise state information and without it

- Haring 2001: Time-domain MMSE estimate
- 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

- Haring 2000: iterative thresholding

Wireless Networking and Communications Group

- 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)

S

W

Wireless Networking and Communications Group

- Given perfect noise state information (NSI)
- Estimation of time domain OFDM symbols [Haring 2002]
- Approach:
- MMSE With NSI:
- MMSE Without NSI:

Exponential in N

(Central Limit Theorem)

n is not identically distributed,

taking FFT is suboptimal

Wireless Networking and Communications Group

- 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

Might be difficult to compute directly

Easier to evaluate

Wireless Networking and Communications Group

- 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

Exponential in N

Wireless Networking and Communications Group

Gaussian Mixture with

- Initialize to MMSE without CSI
- Approaches MMSE with CSI
- Works well for impulses of around 20dB above background noise

Wireless Networking and Communications Group

Questions!

Wireless Networking and Communications Group