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Preliminary Results. Mitigating Computer Platform Radio Frequency Interference in Embedded Wireless Transceivers. February 25, 2008. Outline. Problem Definition I: Single Carrier, Single Antenna Communication Systems Noise Modeling Estimation of Noise Model Parameters

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Mitigating computer platform radio frequency interference in embedded wireless transceivers l.jpg

Preliminary Results

Mitigating Computer Platform Radio Frequency Interference inEmbedded Wireless Transceivers

February 25, 2008


Outline l.jpg
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


Slide3 l.jpg

  • Problem Definition

  • 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



Part i single carrier single antenna communication systems l.jpg

PART ISingle Carrier, Single Antenna Communication Systems


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  • 1. Noise Modeling

  • 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


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[Middleton, 1999]

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)


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Probability Density Function for A = 0.15, G = 0.1

Middleton Class A Model

Backup

Probability density function (pdf)


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Symmetric Alpha Stable Model

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 l.jpg
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 l.jpg
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


Results on measured rfi data12 l.jpg
Results on Measured RFI Data

Modeling PDF as Symmetric Alpha Stable process

Normalized MSE = 0.0055


3 filtering and detection system model l.jpg

Nonlinear Filter

Matched Filter

v[n]

Pulse Shape

s[n]

gtx[n]

grx[n]

Λ(.)

3. Filtering and Detection – System Model

Alternate 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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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 l.jpg
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


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Complexity Analysis

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





Probability of error for uncoded transmission l.jpg
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 l.jpg
Chernoff Factors for Coded Transmission

PEP: Pairwise error probability

N: Size of the codeword

Chernoff factor:

Equally likely transmission for symbols


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Part IISingle Carrier, Multiple Antenna Communication Systems


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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 l.jpg
MIMO Receivers in Impulsive Noise 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 l.jpg
Communication Performance Noise

2 x 2 MIMO system

A = 0.1, Γ1 = Γ2 = 10-3

Correlation Coeff. = 0.1

Spatial Multiplexing Mode


Part iii multiple carriers single antenna communication systems l.jpg

Part III NoiseMultiple Carriers, Single Antenna Communication Systems


Motivation l.jpg
Motivation Noise

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 l.jpg
Noise Smearing Noise

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 l.jpg
Conclusion Noise

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 l.jpg
Contributions Noise

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 l.jpg
Future Work Noise

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 l.jpg
References Noise

[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 l.jpg
References (cont…) Noise

[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 l.jpg
Potential Impact Noise

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 l.jpg
Accuracy of Middleton Noise Models Noise

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 l.jpg
Middleton Class A Statistics Noise

Envelope statistics

Envelope for Gaussian signal has Rayleigh distribution

Power Spectral Density


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Symmetric Alpha Stable Process PDF Noise

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 l.jpg
Symmetric Alpha Stable Statistics Noise

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 l.jpg
Estimation of Middleton Class A Model Parameters Noise

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 l.jpg
Estimation of Symmetric Alpha Stable Parameters Noise

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 moments l.jpg

e Probability Density) Plot2 =

e4 =

e6 =

Class A Parameter Estimation Based on Moments

Moments (as derived from the characteristic equation)

Parameter estimates

Odd-order momentsare zero[Middleton, 1999]

2


Slide50 l.jpg

Middleton Class B Model Probability Density) Plot

Envelope Statistics

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


Slide51 l.jpg

Class B Envelope Statistics Probability Density) Plot


Slide52 l.jpg

Parameters for Middleton Class B Noise Probability Density) Plot



Slide54 l.jpg

Expectation Maximization Overview Probability Density) Plot


Slide55 l.jpg

Maximum Likelihood for Sum of Densities Probability Density) Plot


Em estimator for class a parameters using 1000 samples l.jpg

PDFs with 11 summation terms Probability Density) Plot

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 Samples

Iterations for Parameter A to Converge



Slide58 l.jpg

Extreme Order Statistics Probability Density) Plot


Estimator for alpha stable l.jpg
Estimator for Alpha-Stable Probability Density) Plot

0 < p < α


Results for symmetric alpha stable parameter estimator l.jpg
Results for Symmetric Alpha Stable Parameter Estimator Probability Density) Plot

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


Results for symmetric alpha stable parameter estimator61 l.jpg

d Probability Density) Plot = 10

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 Estimator


Wiener filtering linear filter l.jpg

^ Probability Density) Plot

d(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 Filter

Optimal 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 l.jpg
Wiener Filtering – Finite Impulse Response (FIR) Case Probability Density) Plot

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)


Wiener filtering 100 tap fir filter l.jpg

Raised Cosine Pulse Shape Probability Density) Plot

n

Transmitted waveform corrupted by Class A interference

n

Received waveform filtered by Wiener filter

n

Wiener Filtering – 100-tap FIR Filter

Pulse shape10 samples per symbol10 symbols per pulse

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


Slide65 l.jpg

  • Incoherent Detection Probability Density) Plot

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

Small signal approximation


Slide66 l.jpg

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 l.jpg
Coherent Detection – Class A Noise Probability Density) Plot

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


Coherent detection small signal approximation68 l.jpg

Correlation Receiver Probability Density) Plot

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 l.jpg
Volterra Filters Probability Density) Plot

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 l.jpg

[Widrow Probability Density) Plotet al., 1975]

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


Slide71 l.jpg

Region 3 Probability Density) Plot

Region 2

Region 1

Class A (with same power)

Gaussian


Haring s receiver simulation results l.jpg
Haring’s Receiver Simulation Results Probability Density) Plot


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Coherent Detection in Class A Noise with Probability Density) PlotΓ = 10-4

A = 0.1

Correlation Receiver Performance

SNR (dB)

SNR (dB)


Myriad filtering74 l.jpg
Myriad Filtering Probability Density) Plot

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 l.jpg
MAP Detection Probability Density) Plot

Hard decision

Bayesian formulation [Spaulding and Middleton, 1977]

corrupted signal

Decision RuleΛ(X)

H1 or H2

Equally probable source

75


Results l.jpg
Results Probability Density) Plot

76