non-parametric methods for mitigating interference in ofdm receivers

August 4, 2011

Non-Parametric Methods forMitigating Interference in OFDM

Receivers

American University of Beirut

1

Prof. Brian L. Evans

Department of Electrical and Computer Engineering

The University of Texas at Austin

In collaboration with PhD studentsMs. Jing Lin and Mr. Marcel Nassar

Wireless Networking and Communications Group

Outline

Motivation

System model

Prior work

Sparse Bayesian learning

Proposed algorithms and results

Conclusion


2

3

Mobile Internet Data: The Big Picture

Observations 2x increase/year in data traffic: 1000x increase next 10 years Demand is increasing exponentially but revenues are not Revenue and traffic suddenly decoupled vs. voice service Business models remain fuzzy especially for video

Consequences to industry Restrict data usage (unpopular) OR Decrease cost per bit exponentially (how?) OR Lose money and/or watch network collapse (current status)


Source: J. G. Andrews, "Wireless 1000x?", University of Notre Dame Seminar, May 5, 2011.

Heterogeneity: Make Cells Smaller/Smarter

Demand handled by different networks Macrocells guarantee basic coverage and

require fast dedicated backhaul Picocells target traffic “hotspots” Femtocells must interoperate w/ cellular

networks with minimal coordination


4

Basestation

Range

Power

Build Costs

Oper. Costs

Deployed By

Macrocell 1-10 km

40W $100k High Service Provider

Picocell 100m 1-2W $15-40k Low Service Provider

Femtocell 10m 200mW

$100 Very Low User at Home

Source: J. G. Andrews, "Wireless 1000x?", University of Notre Dame Seminar, May 5, 2011.

Tower-mounted

macrocell

pico

femto

Basestations


Wireless Interference5

Guard zone

Example: Dense Wi-Fi Networks

Duration

Channel 11

Channel 11

Channel 9

(a) (a)

(b)(c)

(d)

Interferencea) Co-channelb) Adjacent channelc) Out-of-platformd) In-platform


In-Platform Interference6

May severely degrade communication performance Impact of LCD noise on throughput for IEEE 802.11g

embedded wireless receiver [Shi, Bettner, Chinn, Slattery & Dong, 2006]

Low-Voltage Power Line Noise


7

0 10 20 30 40 50 60 70 80 90-125

-120

-115

-110

-105

-100

-95

-90

-85

-80

-75

Frequency (kHz)

Pow

er/fr

eque

ncy

(dB

/Hz)

Power Spectral Density Estimate Measurement on 20 Mar 2011 on low-voltage US apartment power outlet at 5:00 amPowerline comm. standards use either 40-90 kHz or 10-500 kHzImpulsive noise is 45-50 dB above the noise floor

[Nassar, Gulati, Mortazavi & Evans, 2011]

Heterogeneity: Receiver’s Perspective


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Wireless CommunicationSources

Uncoordinated Transmissions

Non-CommunicationSources

Electromagnetic radiations

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

Antennas

Baseband Processor

Network heterogeneity leads to the increase of uncoordinated interference at the receiver

Statistical Modeling of Interference


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• Cellular networks• Hotspots (e.g. café)

• Sensor networks• Ad hoc networks

• Dense Wi-Fi networks• Networks with contention

based medium access

Symmetric Alpha Stable Middleton Class A (form of Gaussian Mixture)

[Gulati, Evans, Andrews & Tinsley, 2010]



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• Cluster of hotspots (e.g. marketplace)

• In-cell and out-of-cell femtocell users in femtocell networks

• Out-of-cell femtocell users in femtocell networks

Symmetric Alpha Stable Gaussian Mixture Model

[Gulati, Evans, Andrews & Tinsley, 2010]


Low-voltage power lines Multiple noise sources 1% of impulses exceed

1 ms in duration Amplitude statistics

By derivation, model is Gaussian mixture

Gaussian mixture best fit for tail probabilities


11

Data captured on power outlet in apartment in Austin, Texas USA, 20 Mar 2011Fit blocks of 14 ms of data sampled at 1 MSample/s (blocks of 14000 samples)

[Nassar, Gulati, Mortazavi & Evans, 2011]

Statistical Models of Impulsive Noise

Symmetric Alpha Stable [Furutsu & Ishida, 1961] [Sousa, 1992]

Characteristic function

Gaussian Mixture Model [Sorenson & Alspach, 1971]

Amplitude distribution

Middleton Class A (w/o Gaussian component) [Middleton, 1977]


12

Orthogonal Frequency Division Multiplexing

Divides transmission band into narrow subchannels Null tones at band edges for reducing spectral leakage Null tones in low signal-to-noise ratio (SNR) subchannels Pilot tones for synchronization and channel estimation Power loading per subcarrier to increase data rates

Subchannel processing combats multipath effects Better resilience to impulsive noise vs. single carrier Used in modern data communications standards

Wireless: IEEE802.11a/g/n, cellular LTE Powerline: PRIME, G3, IEEE1901.2Wireless Networking and Communications Group

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Need

Proposed impulsive noise mitigation in OFDM receiver No assumption of a specific impulsive noise model Exploit sparse nature of impulsive noise

System Model


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[Lin, Nassar & Evans, 2011]

OFDM Receivers in Impulsive Noise

DFT spreads out impulsive energy across all tones

SNR of each tone is decreased Receiver performance degrades Noise in each tone is asymptotically Gaussian (as )Wireless Networking and Communications Group

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Parametric Methods

Use parameterized functional forms of noise statistics Need to estimate and track noise parameters

Suffer degradation in performance Due to model mismatch or parameter mismatch When noise statistics are changing rapidly

Not dependent on null tones Higher throughput when noise statistics are slowly varying

Complexity in parameter estimation and tracking OFDM decoders: high complexity for optimality and

low-complexity approximations may work well enoughWireless Networking and Communications Group [Lin, Nassar & Evans, 2011]

Prior Work


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OFDM Systems in Impulsive Noise

Haring2003 SISO Iterative Decoding • high complexity• approaches PEP bound• assumes noise model

Haring2001 SISO MMSE Estimate • with and without CSI• assumes noise model

Haring2000 SISO Iterative Decoding with Threshold Limiter

• threshold not flexible• assumes noise model

Matsuo2002 SISO Iterative Decoding with Threshold Limiter

• threshold selection is ad-hoc•assumes noise model

Caire2008 MIMO Compressed Sensing approach

• very limited number of samples

Parametric Methods

Semi-nonParametric Methods (Threshold Selection)

nonParametric Method


Sparse Bayesian Learning

Underdetermined linear regression : observation vector : sparse weight vector: i.i.d. Gaussian noise w/ variance : overcomplete basis

SBL algorithmParameterized Gaussian prior o: Estimate by computing maximum likelihood (ML) using expectation maximizationEstimate w from posterior mean: Guaranteed to converge to sparse solution Fewer local minima vs. other compressed sampling algorithms


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M: # of known tonesN: total # of tones

Estimation Using Null Tones

Noise observed on null tones is DFT matrix, = , and sparse weight vector and

Estimate e by sparse Bayesian learning Parameterized Gaussian prior imposed on e ML estimation of two hyper-parameters Minimum mean-square estimate of e

Receiver block diagram


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Estimation Using All Tones

Joint estimation of data and noise is DFT matrix and = Treat as a third hyper-parameter to be estimated is relaxed to be continuous variables to guarantee

convergence of expectation maximization algorithm Estimate of sent to channel equalizer and MAP detector with

hard decisions after impulsive noise mitigation Receiver

blockdiagram


20

M: # of known tonesN: total # of tones


Communication Performance Simulations

In different impulsive noise scenarios


21

Gaussian mixture model Middleton Class A model

~6dB

~8dB~6dB

~10dB

~4dB

Parametric (no null tones =>higher throughput)



In different impulsive noise scenarios (continued)


22

Symmetric alpha stable model

~7dB

~4dB




23

Performance of first algorithm as number of known tones decreases SNR is 0 dB 256 tones Middleton Class A noise

In both algorithms, theEM algorithm converges after a few iterations


Comparison

Based on formula for impulsive noise distribution

Needs parameter estimation Good for slowly varying noise

statistics Suffer from model mismatch

in fast varying environments High complexity for optimal

decoders

No assumption of noise statistics

Uses null tones in each OFDM symbol

Robust in fast varying noise environments

Potential reduction in throughput due to null tones (if not already in standard)

Parametric Methods Non-Parametric Methods

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Conclusions and Future Work

Proposed impulsive noise reduction algorithms Assume real-valued OFDM symbols (G3, PRIME, ADSL) Use null + pilot tones to give 4-6 dB SNR gain in simulation Use all tones to give 8-10 dB SNR gain in simulation

Future work Extend to complex-valued OFDM symbols (802.11a/b/n, LTE) Track impulsive noise OFDM symbol to OFDM symbol Incorporate knowledge of noise statistics Add channel estimation Analyze performance with coding and with correlated noise


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References

G. Caire, T. Al-Naffouri, and A. Narayanan, “Impulse noise cancellation in OFDM: an application of compressed sensing,” Proc. IEEE Int. Sym. on Info. Theory, 2008, pp. 1293–1297.

K. Furutsu and T. Ishida, “On the theory of amplitude distributions of impulsive random noise,” J. Appl. Phys., vol. 32, no. 7, pp. 1206–1221, 1961.

K. Gulati, B. Evans, J. Andrews, and K. Tinsley, “Statistics of cochannel interference in a field of Poisson and Poisson-Poisson clustered interferers,” IEEE Trans. on Signal Proc., vol. 58, no. 12, pp. 6207–6222, 2010.

J. Haring and A. Vinck, “Iterative decoding of codes over complex numbers for impulsive noise channels,” IEEE Trans. Info. Theory, vol. 49, no. 5, pp. 1251–1260, 2003.

J. Lin, M. Nassar, and B. L. Evans, “Non-Parametric Impulsive Noise Mitigation in OFDM Systems Using Sparse Bayesian Learning,” Proc. IEEE Int. Global Communications Conf., Dec. 5-9, 2011.

D. Middleton, “Statistical-Physical Models of Electromagnetic Interference”, IEEE Trans. On Electromagnetic Compatibility, vol. 19, no. 3, Aug. 1977, pp. 106-127.

D. Middleton, “Non-Gaussian noise models in signal processing for telecommunications: new methods an results for Class a and Class b noise models,” IEEE Trans. on Info. Theory, vol. 45, no. 4, pp. 1129–1149, 1999.


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References

M. Nassar, K. Gulati, M. DeYoung, B. Evans, and K. Tinsley, “Mitigating near-field interference in laptop embedded wireless transceivers,” Journal of Signal Proc. Sys., pp. 1–12, 2009.

M. Nassar, K. Gulati, Y. Mortazavi, and B. L. Evans, “Statistical Modeling of Asynchronous Impulsive Noise in Powerline Communication Networks”, Proc. IEEE Int. Global Communications Conf., Dec. 5-9, 2011.

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.

H. W. Sorenson and D. L. Alspach, “Recursive Bayesian estimation using Gaussian sums”, Automatica, vol. 7, no. 4, July 1971, pp. 465-479.

E. S. Sousa, “Performance of a spread spectrum packet radio network link in a Poisson field of interferers,” IEEE Trans. on Info. Theory, vol. 38, no. 6, pp. 1743–1754, Nov. 1992.

D. Wipf and B. Rao, “Sparse Bayesian learning for basis selection,” IEEE Trans. Signal Proc., vol. 52, no. 8, pp. 2153–2164, 2004.


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BACK UP SLIDES28


Interference Mitigation Techniques (cont…)

Interference cancellationRef: J. G. Andrews, ”Interference Cancellation for Cellular Systems: A Contemporary Overview”, IEEE Wireless Communications Magazine, Vol. 12, No. 2, pp. 19-29, April 2005


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Return

Femtocell Networks

Reference:V. Chandrasekhar, J. G. Andrews and A. Gatherer, "Femtocell Networks: a Survey", IEEE Communications Magazine, Vol. 46, No. 9, pp. 59-67, September 2008


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Return


Problem Statement31

Designing wireless transceivers to mitigate residual RFI

Guard zone

Example: Dense Wi-Fi Networks

Duration

Channel 11

Channel 11

Channel 9

Physical (PHY) Layer

Improves: Link communication performance

Transmitsignal Pre-Filter Conventional

Receiver

RFIThermal

noise

Medium Access Control (MAC) LayerOptimize channel access protocols, e.g.,

Improves: Network communication performance

Distribution of Duration

Poisson Field of Interferers

Interferers distributed over parametric annular space

Log-characteristic function


32

Return

Poisson Field of Interferers


33

Return

Poisson-Poisson Cluster Field of Interferers

Cluster centers distributed as spatial Poisson process over

Interferers distributed as spatial Poisson process


34

Return

Poisson-Poisson Cluster Field of Interferers

Log-Characteristic function


35

Return

Gaussian Mixture vs. Alpha Stable

Gaussian Mixture vs. Symmetric Alpha Stable


36

Gaussian Mixture Symmetric Alpha StableModeling Interferers distributed with Guard

zone around receiver (actual or virtual due to pathloss function)

Interferers distributed over entire plane

Pathloss Function

With GZ: singular / non-singularEntire plane: non-singular

Singular form

Thermal Noise

Easily extended(sum is Gaussian mixture)

Not easily extended (sum is Middleton Class B)

Outliers Easily extended to include outliers Difficult to include outliers

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Middleton Class A model

Probability Density Function

1

2!)(

2

2

02

2

2

Am

where

em

Aezf

m

z

m m

mA

Zm

-10 -5 0 5 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Noise amplitude

Pro

babi

lity

dens

ity fu

nctio

n

PDF for A = 0.15, = 0.8

A

Parameter

Description RangeOverlap Index. Product of average number of emissions per second and mean duration of typical emission

A [10-2, 1]

Gaussian Factor. Ratio of second-order moment of Gaussian component to that of non-Gaussian component

Γ [10-6, 1]

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Home Power Line Noise Measurement


38

0 10 20 30 40 50 60 70 80 90-125

-120

-115

-110

-105

-100

-95

-90

-85

-80

-75

Frequency (kHz)

Pow

er/fr

eque

ncy

(dB

/Hz)

Power Spectral Density Estimate



39

0 10 20 30 40 50 60 70 80 90-125

-120

-115

-110

-105

-100

-95

-90

-85

-80

-75

Frequency (kHz)

Pow

er/fr

eque

ncy

(dB

/Hz)


Spectrally-ShapedBackground Noise



40

0 10 20 30 40 50 60 70 80 90-125

-120

-115

-110

-105

-100

-95

-90

-85

-80

-75

Frequency (kHz)

Pow

er/fr

eque

ncy

(dB

/Hz)



Narrowband Noise



41

0 10 20 30 40 50 60 70 80 90-125

-120

-115

-110

-105

-100

-95

-90

-85

-80

-75

Frequency (kHz)

Pow

er/fr

eque

ncy

(dB

/Hz)



Narrowband Noise

Periodic and Asynchronous Noise

Analytical Models for Powerline Noise


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Expectation Maximization Overview


4343

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Video over Impulsive Channels

Video demonstration for MPEG II video stream 10.2 MB compressed stream from camera (142 MB uncompressed) Compressed file sent over additive impulsive noise channel Binary phase shift keying

Raised cosine pulse10 samples/symbol10 symbols/pulse length

Composite of transmitted and received MPEG II video streamshttp://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB_correlation.wmv Shows degradation of video quality over impulsive channels with

standard receivers (based on Gaussian noise assumption)Wireless Networking and Communications Group

Additive Class A Noise ValueOverlap index (A) 0.35Gaussian factor () 0.001SNR 19 dB

Return

http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB_correlation.wmv

http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB_correlation.wmv

Video over Impulsive Channels #2

Video demonstration for MPEG II video stream revisited 5.9 MB compressed stream from camera (124 MB uncompressed) Compressed file sent over additive impulsive noise channel Binary phase shift keying

Raised cosine pulse10 samples/symbol10 symbols/pulse length

Composite of transmitted video stream, video stream from a correlation receiver based on Gaussian noise assumption, and video stream for a Bayesian receiver tuned to impulsive noise

http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB.wmv


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Additive Class A Noise ValueOverlap index (A) 0.35Gaussian factor () 0.001SNR 19 dB

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Video over Impulsive Channels #2

Structural similarity measure [Wang, Bovik, Sheikh & Simoncelli, 2004]

Score is [0,1] where higher means better video quality

Frame number

Bit error rates for ~50 million bits sent:

6 x 10-6 for correlation receiver

0 for RFI mitigating receiver (Bayesian)

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non-parametric methods for mitigating interference in ofdm receivers

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