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Mitigating Computer Platform Radio Frequency Interference in Embedded Wireless Transceivers

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### Mitigating Computer Platform Radio Frequency Interference inEmbedded Wireless Transceivers

February 25, 2008

Outline

Problem Definition

I: Single Carrier, Single Antenna Communication Systems

- Noise Modeling
- Estimation of Noise Model Parameters
- Filtering and Detection
- Bounds on Communication Performance

II: Single Carrier, Multiple Antenna Communication Systems

III: Multiple Carrier, Single Antenna Communication Systems

Conclusion and Future Work

- Within computing platforms, wirelesstransceivers experience radio frequencyinterference (RFI) from clocks/busses
- Objectives
- Develop offline methods to improve communication performance in presence of computer platform RFI
- Develop adaptive online algorithms for these methods

Approach

- Statistical modeling of RFI
- Filtering/detection based on estimation of model parameters

Backup

We’ll be using noise and interference interchangeably

- RFI is combination of independent radiation events, and predominantly has non-Gaussian statistics
- Statistical-Physical Models (Middleton Class A, B, C)
- Independent of physical conditions (universal)
- Sum of independent Gaussian and Poisson interference
- Models nonlinear phenomena governing electromagnetic interference
- Alpha-Stable Processes
- Models statistical properties of “impulsive” noise
- Approximation to Middleton Class B noise

Backup

Middleton Class A, B, C Models

Class ANarrowband interference (“coherent” reception) Uniquely represented by two parameters

Class BBroadband interference (“incoherent” reception) Uniquely represented by six parameters

Class CSum of class A and class B (approx. as class B)

Probability Density Function for A = 0.15, G = 0.1

Middleton Class A Model

Backup

Probability density function (pdf)

Characteristic function:

Backup

Parameters

Characteristic exponent indicativeof thickness of tail of impulsiveness

Localization (analogous to mean)

Dispersion (analogous to variance)

No closed-form expression for pdf except for α = 1 (Cauchy), α = 2 (Gaussian), α = 1/2 (Levy) and α = 0 (not very useful)

Could approximate pdf using inverse transform of power series expansion of characteristic function

Backup

2. Estimation of Noise Model Parameters

For the Middleton Class A Model

- Expectation maximization (EM) [Zabin & Poor, 1991]
- Based on envelope statistics [Middleton, 1979]
- Based on moments [Middleton, 1979]

For the Symmetric Alpha Stable Model

- Based on extreme order statistics [Tsihrintzis & Nikias, 1996]

For the Middleton Class B Model

- No closed-form estimator exists
- Approximate methods based on envelope statistics or moments

Backup

Backup

- Complexity
- Iterative algorithm
- At each iteration:
- Rooting a second order polynomial (Given A, maximize K (= AΓ) )
- Rooting a fourth order polynomial (Given K, maximize A)
- Advantage Small sample size required (~1000 samples)
- Disadvantage Iterative algorithm, computationally intensive

Backup

Backup

Complexity

Parameter estimators are based on simple order statistics

AdvantageFast / computationally efficient (non-iterative)

Disadvantage Requires large set of data samples (N ~ 10,000)

Backup

Results on Measured RFI Data

Data set of 80,000 samples collected using 20 GSPS scope

- Measured data is "broadband" noise
- Middleton Class B model would match

PDF is symmetric

- Symmetric Alpha Stable Process expected to work well
- Approximation to Class B model

Matched Filter

v[n]

Pulse Shape

s[n]

gtx[n]

grx[n]

Λ(.)

3. Filtering and Detection – System ModelAlternate Adaptive Model

Impulsive Noise

Signal Model

Multiple samples/copies of the received signal are available:

- N path diversity [Miller, 1972]
- Oversampling by N[Middleton, 1977]

Using multiple samples increases gains vs. Gaussian case because impulses are isolated events over symbol period

Backup

Decision Rule

Filtering and Detection

We assume perfect estimation of noise model parameters

Class A Noise

- Correlation Receiver (linear)
- Wiener Filtering (linear)
- Coherent Detection using MAP (Maximum A posteriori Probability) detector[Spaulding & Middleton, 1977]
- Small Signal Approximation to MAP Detector[Spaulding & Middleton, 1977]

Alpha Stable Noise

- Correlation Receiver (linear)
- MAP Approximation
- Myriad Filtering[Gonzalez & Arce, 2001]
- Hole Punching[Ambike et al., 1994]

Backup

Backup

Backup

Coherent Detection – Small Signal Approximation

Expand noise pdf pZ(z) by Taylor series about Sj = 0 (j=1,2)

Optimal decision rule & threshold detector for approximation

Optimal detector for approximation is logarithmic nonlinearity followed by correlation receiver

We use 100 terms of the series expansion ford/dxi ln pZ(xi) in simulations

Backup

Class A Detection - Results

Pulse shapeRaised cosine10 samples per symbol10 symbols per pulse

ChannelA = 0.35G = 0.5 × 10-3Memoryless

K: Constellation Size

N: number of samples per symbol

M: number of retained terms of the series expansion

W: Window Size

Filtering and Detection – Alpha Stable Model

MAP detection: remove nonlinear filter

Decision rule is given by (p(.) is the SαS distribution)

Approximations for SαS distribution:

MAP Detector – PDF Approximation

SαS random variable Z with parameters a , d, gcan be written Z = X Y½[Kuruoglu, 1998]

- X is zero-mean Gaussian with variance 2 g
- Y is positive stable random variable with parameters depending on a

Pdf of Z can be written as amixture model of N Gaussians[Kuruoglu, 1998]

- Mean d can be added back in
- Obtain fY(.) by taking inverse FFT of characteristic function & normalizing
- Number of mixtures (N) and values of sampling points (vi) are tunable parameters

Myriad Filtering

Sliding window algorithm

Outputs myriad of sample window

Myriad of order k for samples x1, x2, … , xN [Gonzalez & Arce, 2001]

- As k decreases, less impulsive noise gets through myriad filter
- As k→0, filter tends to mode filter (output value with highest freq.)

Empirical choice of k: [Gonzalez & Arce, 2001]

Myriad Filtering – Implementation

Given a window of samples x1,…,xN, find β [xmin, xmax]

Optimal myriad algorithm

- Differentiate objective functionpolynomial p(β) with respect to β
- Find roots and retain real roots
- Evaluate p(β) at real roots and extremum
- Output β that gives smallest value of p(β)

Selection myriad (reduced complexity)

- Use x1,…,xN as the possible values of β
- Pick value that minimizes objective function p(β)

Backup

Hole Punching (Blanking) Filter

Sets sample to 0 when sample exceeds threshold [Ambike, 1994]

Intuition:

- Large values are impulses and true value cannot be recovered
- Replace large values with zero will not bias (correlation) receiver
- If additive noise were purely Gaussian, then the larger the threshold, the lower the detrimental effect on bit error rate

Complexity Analysis

N is oversampling factor S is constellation size W is window size

Probability of Error for Uncoded Transmission

Backup

[Haring & Vinck, 2002]

BPSK uncoded transmission

One sample per symbol

A = 0.1, Γ = 10-3

Chernoff Factors for Coded Transmission

PEP: Pairwise error probability

N: Size of the codeword

Chernoff factor:

Equally likely transmission for symbols

Multiple Input Multiple Output (MIMO) Receivers in Impulsive Noise

Statistical Physical Models of Noise

- Middleton Class A model for two-antenna systems[MacDonald & Blum,1997]
- Extension to larger than 2 2 case is difficult

Statistical Models of Noise

- Multivariate Alpha Stable Process
- Mixture of weighted multivariate complex Gaussians as approximation to multivariate Middleton Class A noise[Blum et al., 1997]

MIMO Receivers in Impulsive Noise

Key Prior Work

- Performance analysis of standard MIMO receivers in impulsive noise[Li, Wang & Zhou, 2004]
- Space-time block coding over MIMO channels with impulsive noise[Gao & Tepedelenlioglu,2007]
- Assumes uncorrelated noise at antennas

Our Contributions

- Performance analysis of standard MIMO receivers using multivariate noise models
- Optimal and sub-optimal maximum likelihood (ML) receiver design for 2 2 case

Communication Performance

2 x 2 MIMO system

A = 0.1, Γ1 = Γ2 = 10-3

Correlation Coeff. = 0.1

Spatial Multiplexing Mode

Motivation

Impulse noise with impulse event followed by “flat” region

- Coding and interleaving may improve communication performance
- In multicarrier modulation, impulsive event in time domain spreads out over all subsymbols thereby reducing effect of impulse

Complex number (CN) codes [Lang, 1963]

- Transmitter forms s = GS, where S contains transmitted symbols,G is a unitary matrix and s contains coded symbols
- Receiver multiplies received symbols by G-1
- Gaussian noise unaffected (unitary transformation is rotation)
- Orthogonal frequency division multiplexing (OFDM) is special case of CN codes when G is inverse discrete Fourier transformmatrix

Noise Smearing

Smearing effect

- Impulsive noise energy distributes over longer symbol time
- Smearing filters maximize impulse attenuation and minimize intersymbol interference for impulsive noise [Beenker, 1985]
- Maximum smearing efficiency is where N is number of symbols used in unitary transformation
- As N, distribution of impulsive noise becomes Gaussian

Simulations [Haring, 2003]

- When using a transformation involving N = 1024 symbols, impulsive noise case approaches case where only Gaussian noise is present

Backup

Conclusion

Radio frequency interference from computing platform

- Affects wireless data communication transceivers
- Models include Middleton noise models and alpha stable processes
- Cancellation can improve communication performance

Initial RFI cancellation methods explored

- Linear (Wiener) and Non-linear filtering (Myriad, Hole Punching)
- Optimal detection rules (significant gains at low bit rates)

Preliminary work

- Performance bounds in presence of RFI
- RFI mitigation in multicarrier, MIMO communication systems

Contributions

Publications

M. Nassar, K. Gulati, A. K. Sujeeth, N. Aghasadeghi, B. L. Evans and K. R. Tinsley, “Mitigating Near-field Interference in Laptop Embedded Wireless Transceivers”, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., Mar. 30-Apr. 4, 2008, Las Vegas, NV USA, accepted for publication.

Software Releases

RFI Mitigation Toolbox

Version 1.1 Beta (Released November 21st, 2007)

Version 1.0 (Released September 22nd, 2007)

http://users.ece.utexas.edu/~bevans/projects/rfi/software.html

Project Web Site

http://users.ece.utexas.edu/~bevans/projects/rfi/index.html

Future Work

Single carrier, single antenna communication systems

- Fixed-point (embedded) methods for parameter estimation and detection methods
- Estimation and detection for Middleton Class B model

Single carrier, multiple antenna communication systems

- MIMO receiver design in presence of RFI
- Performance bounds for MIMO receivers in presence of RFI

Multicarrier Modulation and Coding

- Explore unitary coding schemes resilient to RFI
- Investigate multi-layered coding

References

[1] D. Middleton, “Non-Gaussian noise models in signal processing for telecommunications: New methods and results for Class A and Class B noise models”, IEEE Trans. Info. Theory, vol. 45, no. 4, pp. 1129-1149, May 1999

[2] S. M. Zabin and H. V. Poor, “Efficient estimation of Class A noise parameters via the EM [Expectation-Maximization] algorithms”, IEEE Trans. Info. Theory, vol. 37, no. 1, pp. 60-72, Jan. 1991

[3] G. A. Tsihrintzis and C. L. Nikias, "Fast estimation of the parameters of alpha-stable impulsive interference", IEEE Trans. Signal Proc., vol. 44, Issue 6, pp. 1492-1503, Jun. 1996

[4] A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment-Part I: Coherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 1977

[5] A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment-Part II: Incoherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 1977

[6] B. Widrow et al., “Principles and Applications”, Proc. of the IEEE, vol. 63, no.12, Sep. 1975.

[7] J.G. Gonzalez and G.R. Arce, “Optimality of the Myriad Filter in Practical Impulsive-Noise Environments”, IEEE Trans. on Signal Processing, vol 49, no. 2, Feb 2001

References (cont…)

[8] S. Ambike, J. Ilow, and D. Hatzinakos, “Detection for binary transmission in a mixture of gaussian noise and impulsive noise modeled as an alpha-stable process,” IEEE Signal Processing Letters, vol. 1, pp. 55–57, Mar. 1994.

[9] J. G. Gonzalez and G. R. Arce, “Optimality of the myriad filter in practical impulsive-noise enviroments,” IEEE Trans. on Signal Proc, vol. 49, no. 2, pp. 438–441, Feb 2001.

[10] E. Kuruoglu, “Signal Processing In Alpha Stable Environments: A Least Lp Approach,” Ph.D. dissertation, University of Cambridge, 1998.

[11] J. Haring and A.J. Han Vick, “Iterative Decoding of Codes Over Complex Numbers for Impuslive Noise Channels”, IEEE Trans. On Info. Theory, vol 49, no. 5, May 2003

[12] G. Beenker, T. Claasen, and P. van Gerwen, “Design of smearing filters for data transmission systems,” IEEE Trans. on Comm., vol. 33, Sept. 1985.

[13] G. R. Lang, “Rotational transformation of signals,” IEEE Trans. Inform. Theory, vol. IT–9, pp. 191–198, July 1963.

[14] Ping Gao and C. Tepedelenlioglu. “Space-time coding over mimo channels with impulsive noise”, IEEE Trans. on Wireless Comm., 6(1):220–229, January 2007.

[15] K.F. McDonald and R.S. Blum. “A physically-based impulsive noise model for array observations”, Proc. IEEE Asilomar Conference on Signals, Systems& Computers, vol 1, 2-5 Nov. 1997.

Potential Impact

Improve communication performance for wireless data communication subsystems embedded in PCs and laptops

- Achieve higher bit rates for the same bit error rate and range, and lower bit error rates for the same bit rate and range
- Extend range from wireless data communication subsystems to wireless access point

Extend results to multipleRF sources on single chip

Accuracy of Middleton Noise Models

Magnetic Field Strength, H (dB relative to

microamp per meter rms)

ε0 (dB > εrms)

Percentage of Time Ordinate is Exceeded

P(ε > ε0)

Soviet high power over-the-horizon radar interference [Middleton, 1999]

Fluorescent lights in mine shop office interference [Middleton, 1999]

Middleton Class A Statistics

Envelope statistics

Envelope for Gaussian signal has Rayleigh distribution

Power Spectral Density

Symmetric Alpha Stable Process PDF

Closed-form expression does not exist in general

Power series expansions can be derived in some cases

Standard symmetric alpha stable model for localization parameter d = 0

Symmetric Alpha Stable Statistics

Example: exponent a = 1.5, “mean” d = 0and “variance” g = 10

×10-4

Probability Density Function

Power Spectral Density

Estimation of Middleton Class A Model Parameters

Expectation maximization

- E: Calculate log-likelihood function w/ current parameter values
- M: Find parameter set that maximizes log-likelihood function

EM estimator for Class A parameters[Zabin & Poor, 1991]

- Expresses envelope statistics as sum of weighted pdfs

Maximization step is iterative

- Given A, maximize K (with K = AΓ). Root 2nd-order polynomial.
- Given K, maximize A. Root4th-order poly. (after approximation).

Backup

Backup

Estimation of Symmetric Alpha Stable Parameters

Based on extreme order statistics [Tsihrintzis & Nikias, 1996]

PDFs of max and min of sequence of independently and identically distributed (IID) data samples follow

- PDF of maximum:
- PDF of minimum:

Extreme order statistics of Symmetric Alpha Stable pdf approach Frechet’s distribution as N goes to infinity

Parameter estimators then based on simple order statistics

- AdvantageFast / computationally efficient (non-iterative)
- Disadvantage Requires large set of data samples (N ~ 10,000)

Backup

Backup

Backup

Class A Parameter Estimation Based on APD (Exceedance Probability Density) Plot

e4 =

e6 =

Class A Parameter Estimation Based on MomentsMoments (as derived from the characteristic equation)

Parameter estimates

Odd-order momentsare zero[Middleton, 1999]

2

Envelope Statistics

Envelope exceedance probability density (APD) which is 1 – cumulative distribution function

PDFs with 11 summation terms

50 simulation runs per setting

Convergence criterion:

Example learning curve

Normalized Mean-Squared Error in A

×10-3

EM Estimator for Class A Parameters Using 1000 SamplesIterations for Parameter A to Converge

Estimator for Alpha-Stable

0 < p < α

Results for Symmetric Alpha Stable Parameter Estimator

Data length (N) was 10,000 samples

Results averaged over 100 simulation runs

Estimate αand “mean” δ directly from data

Estimate “variance” γ from α and δ estimates

Continued next slide

Mean squared error in estimate of characteristic exponent α

g = 5

Mean squared error in estimate of dispersion (“variance”) g

Mean squared error in estimate of localization (“mean”) d

Results for Symmetric Alpha Stable Parameter Estimatord(n)

^

d(n): desired signald(n): filtered signale(n): error w(n): Wiener filter x(n): corrupted signalz(n): noise

d(n):

^

d(n)

z(n)

d(n)

x(n)

w(n)

d(n)

x(n)

e(n)

w(n)

Wiener Filtering – Linear FilterOptimal in mean squared error sense when noise is Gaussian

Model

Design

Minimize Mean-Squared Error E { |e(n)|2 }

Wiener Filtering – Finite Impulse Response (FIR) Case

Wiener-Hopf equations for FIR Wiener filter of order p-1

General solution in frequency domain

desired signal: d(n)power spectrum:F(e j w)correlation of d and x:rdx(n)autocorrelation of x:rx(n)Wiener FIR Filter:w(n) corrupted signal:x(n)noise:z(n)

n

Transmitted waveform corrupted by Class A interference

n

Received waveform filtered by Wiener filter

n

Wiener Filtering – 100-tap FIR FilterPulse shape10 samples per symbol10 symbols per pulse

ChannelA = 0.35G = 0.5 × 10-3SNR = -10 dBMemoryless

- Bayes formulation[Spaulding & Middleton, 1997, pt. II]

Small signal approximation

- Optimal Structure:

Incoherent Correlation Detector

The optimal detector for the small signal approximation is basically the correlation receiver preceded by the logarithmic nonlinearity.

Coherent Detection – Class A Noise

Comparison of performance of correlation receiver (Gaussian optimal receiver) and nonlinear detector [Spaulding & Middleton, 1997, pt. II]

Coherent Detection –Small Signal Approximation

Near-optimal for small amplitude signals

Suboptimal for higher amplitude signals

AntipodalA = 0.35G = 0.5×10-3

Communication performance of approximation vs. upper bound[Spaulding & Middleton, 1977, pt. I]

Volterra Filters

Non-linear (in the signal) polynomial filter

By Stone-Weierstrass Theorem, Volterra signal expansion can model many non-linear systems, to an arbitrary degree of accuracy. (Similar to Taylor expansion with memory).

Has symmetry structure that simplifies computational complexity Np = (N+p-1) C p instead of Np. Thus for N=8 and p=8; Np=16777216 and (N+p-1) C p = 6435.

Adaptive Noise Cancellation

Computational platform contains multiple antennas that can provide additional information regarding the noise

Adaptive noise canceling methods use an additional reference signal that is correlated with corrupting noise

s : signals+n0 :corrupted signaln0 : noisen1 : reference inputz : system output

Coherent Detection in Class A Noise with Γ = 10-4

A = 0.1

Correlation Receiver Performance

SNR (dB)

SNR (dB)

Myriad Filtering

Myriad Filters exhibit high statistical efficiency in bell-shaped impulsive distributions like the SαS distributions.

Have been used as both edge enhancers and smoothers in image processing applications.

In the communication domain, they have been used to estimate a sent number over a channel using a known pulse corrupted by additive noise. (Gonzalez 1996)

In this work, we used a sliding window version of the myriad filter to mitigate the impulsiveness of the additive noise. (Nassar et. al 2007)

74

MAP Detection

Hard decision

Bayesian formulation [Spaulding and Middleton, 1977]

corrupted signal

Decision RuleΛ(X)

H1 or H2

Equally probable source

75

Results

76

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