Title: Radio Frequency Interference Sensing and Mitigation in Wireless Receivers
1Radio Frequency Interference Sensing and
Mitigation in Wireless Receivers
Prof. Brian L. Evans Lead Graduate
Students Aditya Chopra, Kapil Gulati, Yousof
Mortazavi and Marcel Nassar In collaboration
with Eddie Xintian Lin, Alberto Alcocer
Ochoa,Chaitanya Sreerama and Keith R. Tinsley at
Intel Labs
- Talk at The University of Texas at Austin
2Outline
2
- Problem definition
- Single carrier single antenna systems
- Radio frequency interference modeling
- Estimation of interference model parameters
- Filtering/detection
- Multi-input multi-output (MIMO) single carrier
systems - Co-channel interference modeling
- Conclusions
- Future work
3Radio Frequency Interference
- Electromagnetic interference
- Limits wireless communication performance
- Applications of RFI modeling
- Sense and mitigate strategies for coexistence of
wireless networks and services - Sense and avoid strategies for cognitive radio
- We focus on sense and mitigate strategies for
wireless receivers embedded in notebooks - Platform noise from users computer subsystems
- Co-channel interference from other in-band
wireless networks and services
4Problem Definition
4
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Within computing platforms, wireless transceivers
experience radio frequency interference from
clocks and 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 estimated model
parameters
We will use noise and interference interchangeably
5Impact of RFI
5
- Impact of LCD noise on throughput for an IEEE
802.11g embedded wireless receiver Shi, Bettner,
Chinn, Slattery Dong, 2006
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6Statistical Modeling of RFI
6
- Radio frequency interference
- Sum of independent radiation events
- Predominantly non-Gaussian impulsive statistics
- Key statistical-physical models
- Middleton Class A, B, C models
- Independent of physical conditions (canonical)
- Sum of independent Gaussian and Poisson
interference - Symmetric Alpha Stable models
- Approximation of Middleton Class B model
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7Assumptions for RFI Modeling
7
- Key assumptions for Middleton and Alpha Stable
modelsMiddleton, 1977Furutsu Ishida, 1961 - Infinitely many potential interfering sources
with same effective radiation power - Power law propagation loss
- Poisson field of interferers with uniform
intensity l - Pr(number of interferers M area R)
Poisson(M lR) - Uniformly distributed emission times
- Temporally independent (at each sample time)
- Limitations
- Alpha Stable models do not include thermal noise
- Temporal dependence may exist
8Our Contributions
8
Mitigation of computational platform noise in
single carrier, single antenna systems Nassar,
Gulati, DeYoung, Evans Tinsley, ICASSP 2008,
JSPS 2009
Computer Platform Noise Modelling Evaluate fit of measured RFI data to noise models Middleton Class A model Symmetric Alpha Stable
Parameter Estimation Evaluate estimation accuracy vs complexity tradeoffs
Filtering / Detection Evaluate communication performance vs complexity tradeoffs Middleton Class A Correlation receiver, Wiener filtering, and Bayesian detector Symmetric Alpha Stable Myriad filtering, hole punching, and Bayesian detector
9Middleton Class A model
9
- Probability Density Function
PDF for A 0.15,?? 0.8
10Symmetric Alpha Stable Model
10
- Characteristic Function
- Closed-form PDF expression only fora 1
(Cauchy), a 2 (Gaussian),a 1/2 (Levy), a 0
(not very useful) - Approximate PDF using inverse transform of power
series expansion - Second-order moments do not exist for a lt 2
- Generally, moments of order gt a do not exist
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PDF for ? 1.5, ? 0, ? 10
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Parameter Description Range
Characteristic Exponent. Amount of impulsiveness
Localization. Analogous to mean
Dispersion. Analogous to variance
11Example Power Spectral Densities
Characteristic Exponent (a) 1.5 Localization
(d) 0 Dispersion (g) 10
Overlap Index (A) 0.15 Gaussian Factor (G)
0.1
Simulated Densities
12Estimation of Noise Model Parameters
12
- Middleton Class A model
- Based on Expectation Maximization Zabin Poor,
1991 - Find roots of second and fourth order polynomials
at each iteration - Advantage Small sample size is required (1000
samples) - Disadvantage Iterative algorithm,
computationally intensive - Symmetric Alpha Stable Model
- Based on Extreme Order Statistics Tsihrintzis
Nikias, 1996 - Parameter estimators require computations similar
to mean and standard deviation computations - Advantage Fast / computationally efficient
(non-iterative) - Disadvantage Requires large set of data samples
(10000 samples)
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13Results on Measured RFI Data
13
13
- 25 radiated computer platform RFI data sets from
Intel - 50,000 samples taken at 100 MSPS
Estimated Parameters for Data Set 18 Estimated Parameters for Data Set 18 Estimated Parameters for Data Set 18
Symmetric Alpha Stable Model Symmetric Alpha Stable Model Symmetric Alpha Stable Model
Localization (d) 0.0065 KL Divergence 0.0308
Characteristic exp. (a) 1.4329 KL Divergence 0.0308
Dispersion (?) 0.2701 KL Divergence 0.0308
Middleton Class A Model Middleton Class A Model Middleton Class A Model
Overlap Index (A) 0.0854 KL Divergence 0.0494
Gaussian Factor (G) 0.6231 KL Divergence 0.0494
Gaussian Model Gaussian Model Gaussian Model
Mean (µ) 0 KL Divergence 0.1577
Variance (s2) 1 KL Divergence 0.1577
KL Divergence Kullback-Leibler divergence
Wireless Networking and Communications Group
14Results on Measured RFI Data
14
- Best fit for 25 data sets under different
platform RFI conditions - KL divergence plotted for three candidate
distributions vs. data set number - Smaller KL value means closer fit
Gaussian
Class A
Alpha Stable
15Video over Impulsive Channels
15
- 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 keyingRaised cosine pulse10
samples/symbol10 symbols/pulse length - Composite of transmitted and received MPEG II
video streams - http//www.ece.utexas.edu/bevans/projects/rfi/tal
ks/video_demo19dB_correlation.wmv - Shows degradation of video quality over impulsive
channels with standard receivers (based on
Gaussian noise assumption)
Additive Class A Noise Value
Overlap index (A) 0.35
Gaussian factor (G) 0.001
SNR 19 dB
Wireless Networking and Communications Group
16Filtering and Detection
- Assumption
- Multiple samples of the received signal are
available - N Path Diversity Miller, 1972
- Oversampling by N Middleton, 1977
16
Impulsive Noise
Pulse Shaping
Pre-Filtering
Matched Filter
Detection Rule
Middleton Class A noise
Symmetric Alpha Stable noise
- Filtering
- Wiener Filtering (Linear)
- Detection
- Correlation Receiver (Linear)
- Bayesian DetectorSpaulding Middleton, 1977
- Small Signal Approximation to Bayesian
detectorSpaulding Middleton, 1977
- Filtering
- Myriad Filtering
- Optimal Myriad Gonzalez Arce, 2001
- Selection Myriad
- Hole Punching Ambike et al., 1994
- Detection
- Correlation Receiver (Linear)
- MAP approximationKuruoglu, 1998
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17Results Class A Detection
17
Communication Performance
Binary Phase Shift Keying
Pulse shapeRaised cosine10 samples per symbol10 symbols per pulse ChannelA 0.35? 0.5 10-3Memoryless
Method Comp. Complexity Detection Perform.
Correl. Low Low
Wiener Medium Low
Bayesian S.S. Approx. Medium High
Bayesian High High
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18Results Alpha Stable Detection
18
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Communication Performance
Same transmitter settings as previous slide
Method Comp. Complexity Detection Perform.
Hole Punching Low Medium
Selection Myriad Low Medium
MAP Approx. Medium High
Optimal Myriad High Medium
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Use dispersion parameter g in place of noise
variance to generalize SNR
19Video over Impulsive Channels 2
19
- 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 keyingRaised 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/tal
ks/video_demo19dB.wmv
Additive Class A Noise Value
Overlap index (A) 0.35
Gaussian factor (G) 0.001
SNR 19 dB
Wireless Networking and Communications Group
20Video over Impulsive Channels 2
- Structural similarity measure Wang, Bovik,
Sheikh Simoncelli, 2004 - Score is 0,1 where higher means better video
quality
Bit error rates for 50 million bits sent 6 x
10-6 for correlation receiver 0 for RFI
mitigating receiver (Bayesian)
Frame number
21Extensions to MIMO systems
21
Radio Frequency Interference Modeling and Receiver Design for MIMO systems Radio Frequency Interference Modeling and Receiver Design for MIMO systems Radio Frequency Interference Modeling and Receiver Design for MIMO systems Radio Frequency Interference Modeling and Receiver Design for MIMO systems
RFI Model Spatial Corr. Physical Model Comments
Middleton Class A No Yes Uni-variate model Assume independent or uncorrelated noise for multiple antennas
Middleton Class A Receiver design Gao Tepedelenlioglu, 2007 Space-Time CodingLi, Wang Zhou, 2004 Performance degradation in receivers Receiver design Gao Tepedelenlioglu, 2007 Space-Time CodingLi, Wang Zhou, 2004 Performance degradation in receivers Receiver design Gao Tepedelenlioglu, 2007 Space-Time CodingLi, Wang Zhou, 2004 Performance degradation in receivers
Weighted Mixture of Gaussian Densities Yes No Not derived based on physical principles
Weighted Mixture of Gaussian Densities Receiver designBlum et al., 1997 Adaptive Receiver Design Receiver designBlum et al., 1997 Adaptive Receiver Design Receiver designBlum et al., 1997 Adaptive Receiver Design
Bivariate Middleton Class AMcDonald Blum, 1997 Yes Yes Extensions of Class A model to two-antenna systems
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22Our Contributions
22
2 x 2 MIMO receiver design in the presence of
RFIGulati, Chopra, Heath, Evans, Tinsley Lin,
Globecom 2008
RFI Modeling Evaluated fit of measured RFI data to the bivariate Middleton Class A model McDonald Blum, 1997 Includes noise correlation between two antennas
Parameter Estimation Derived parameter estimation algorithm based on the method of moments (sixth order moments)
Performance Analysis Demonstrated communication performance degradation of conventional receivers in presence of RFI Bounds on communication performanceChopra , Gulati, Evans, Tinsley, and Sreerama, ICASSP 2009
Receiver Design Derived Maximum Likelihood (ML) receiver Derived two sub-optimal ML receivers with reduced complexity
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23Results RFI Mitigation in 2 x 2 MIMO
23
Improvement in communication performance over
conventional Gaussian ML receiver at symbol error
rate of 10-2
A Noise Characteristic Improve-ment
0.01 Highly Impulsive 15 dB
0.1 Moderately Impulsive 8 dB
1 Nearly Gaussian 0.5 dB
Communication Performance (A 0.1, ?1 0.01,
?2 0.1, k 0.4)
24Results RFI Mitigation in 2 x 2 MIMO
24
Complexity Analysis for decoding M-level QAM
modulated signal
Receiver Quadratic Forms Exponential Comparisons
Gaussian ML M2 0 0
Optimal ML 2M2 2M2 0
Sub-optimal ML (Four-Piece) 2M2 0 2M2
Sub-optimal ML (Two-Piece) 2M2 0 M2
Complexity Analysis
Communication Performance (A 0.1, ?1 0.01,
?2 0.1, k 0.4)
25Co-Channel Interference Modeling
25
25
- Region of interferer locations determines
interference model Gulati, Chopra, Evans
Tinsley, Globecom 2009
Symmetric Alpha Stable
Middleton Class A
Wireless Networking and Communications Group
26Co-Channel Interference Modeling
26
26
- Propose unified framework to derive narrowband
interference models for ad-hoc and cellular
network environments - Key result tail probabilities (one minus
cumulative distribution function)
Case 3-a Cellular network (mobile user)
Case 1 Ad-hoc network
Wireless Networking and Communications Group
27Conclusions
27
- Radio Frequency Interference from computing
platform - Affects wireless data communication transceivers
- Models include Middleton and alpha stable
distributions - RFI mitigation can improve communication
performance - Single carrier, single antenna systems
- Linear and non-linear filtering/detection methods
explored - Single carrier, multiple antenna systems
- Optimal and sub-optimal receivers designed
- Bounds on communication performance in presence
of RFI - Results extend to co-channel interference
modeling
28RFI Mitigation Toolbox
28
- Provides a simulation environment for
- RFI generation
- Parameter estimation algorithms
- Filtering and detection methods
- Demos for communication performance analysis
- Latest Toolbox Release
- Version 1.3, Aug 26th 2009
Snapshot of a demo
http//users.ece.utexas.edu/bevans/projects/rfi/s
oftware/index.html
29Other Contributions
29
- Publications
- Journal Articles
- M. Nassar, K. Gulati, M. R. DeYoung, B. L. Evans
and K. R. Tinsley, Mitigating Near-Field
Interference in Laptop Embedded Wireless
Transceivers, J. of Signal Proc. Systems, Mar
2009, invited paper. - Conference Papers
- 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. - K. Gulati, A. Chopra, R. W. Heath Jr., B. L.
Evans, K. R. Tinsley, and X. E. Lin, MIMO
Receiver Design in the Presence of Radio
Frequency Interference, Proc. IEEE Int. Global
Communications Conf., Nov. 30-Dec. 4th, 2008, New
Orleans, LA USA. - A. Chopra, K. Gulati, B. L. Evans, K. R. Tinsley,
and C. Sreerama, Performance Bounds of MIMO
Receivers in the Presence of Radio Frequency
Interference, Proc. IEEE Int. Conf. on
Acoustics, Speech, and Signal Proc., Apr. 19-24,
2009, Taipei, Taiwan, accepted. - K. Gulati, A. Chopra, B. L. Evans and K. R.
Tinsley, Statistical Modeling of Co-Channel
Interference, Proc. IEEE Int. Global
Communications Conf., Nov. 30-Dec. 4, 2009,
Honolulu, HI USA, accepted. - Project Website
- http//users.ece.utexas.edu/bevans/projects/rfi/
index.html
30Future Work
30
- Extend RFI modeling for
- Adjacent channel interference
- Multi-antenna systems
- Temporally correlated interference
- Multi-input multi-output (MIMO) single carrier
systems - RFI modeling and receiver design
- Multicarrier communication systems
- Coding schemes resilient to RFI
- System level techniques to reduce computational
platform generated RFI
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3131
32References
32
- RFI Modeling
- 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 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. - 3 K. Furutsu and T. Ishida, On the theory
of amplitude distributions of impulsive random
noise, J. Appl. Phys., vol. 32, no. 7, pp.
12061221, 1961. - 4 J. Ilow and D . Hatzinakos, Analytic
alpha-stable noise modeling in a Poisson field of
interferers or scatterers, IEEE transactions on
signal processing, vol. 46, no. 6, pp. 1601-1611,
1998. - Parameter Estimation
- 5 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 - 6 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 - RFI Measurements and Impact
- 7 J. Shi, A. Bettner, G. Chinn, K. Slattery
and X. Dong, "A study of platform EMI from LCD
panels - impact on wireless, root causes and
mitigation methods, IEEE International Symposium
on Electromagnetic Compatibility, vol.3, no., pp.
626-631, 14-18 Aug. 2006
33References (cont)
33
- Filtering and Detection
- 8 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 - 9 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 - 10 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 - 11 S. Ambike, J. Ilow, and D. Hatzinakos,
Detection for binary transmission in a mixture
of Gaussian noise and impulsive noise modelled as
an alpha-stable process, IEEE Signal Processing
Letters, vol. 1, pp. 5557, Mar. 1994. - 12 J. G. Gonzalez and G. R. Arce, Optimality
of the myriad filter in practical impulsive-noise
environments, IEEE Trans. on Signal Proc, vol.
49, no. 2, pp. 438441, Feb 2001. - 13 E. Kuruoglu, Signal Processing In Alpha
Stable Environments A Least Lp Approach, Ph.D.
dissertation, University of Cambridge, 1998. - 14 J. Haring and A.J. Han Vick, Iterative
Decoding of Codes Over Complex Numbers for
Impulsive Noise Channels, IEEE Trans. On Info.
Theory, vol 49, no. 5, May 2003 - 15 Ping Gao and C. Tepedelenlioglu.
Space-time coding over mimo channels with
impulsive noise, IEEE Trans. on Wireless Comm.,
6(1)220229, January 2007.
34Backup Slides
34
- Most backup slides are linked to the main slides
- Miscellaneous topics not covered in main slides
- Performance bounds for single carrier single
antenna system in presence of RFI
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35Common Spectral Occupancy
35
Return
Standard Carrier (GHz) Wireless Networking Interfering Clocks and Busses
Bluetooth 2.4 Personal Area Network Gigabit Ethernet, PCI Express Bus, LCD clock harmonics
IEEE 802. 11 b/g/n 2.4 Wireless LAN (Wi-Fi) Gigabit Ethernet, PCI Express Bus, LCD clock harmonics
IEEE 802.16e 2.52.69 3.33.8 5.7255.85 Mobile Broadband(Wi-Max) PCI Express Bus,LCD clock harmonics
IEEE 802.11a 5.2 Wireless LAN (Wi-Fi) PCI Express Bus,LCD clock harmonics
36Impact of RFI
36
- Calculated in terms of desensitization
(desense) - Interference raises noise floor
- Receiver sensitivity will degrade to maintain SNR
- Desensitization levels can exceed 10 dB for
802.11a/b/g due to computational platform noise
J. Shi et al., 2006 - Case Sudy 802.11b, Channel 2, desense of 11dB
- More than 50 loss in range
- Throughput loss up to 3.5 Mbps for very low
receive signal strengths ( -80 dbm)
Return
37Impact of LCD clock on 802.11g
37
- Pixel clock 65 MHz
- LCD Interferers and 802.11g center frequencies
Return
LCD Interferers 802.11g Channel Center Frequency Difference of Interference from Center Frequencies Impact
2.410 GHz Channel 1 2.412 GHz 2 MHz Significant
2.442 GHz Channel 7 2.442 GHz 0 MHz Severe
2.475 GHz Channel 11 2.462 GHz 13 MHz Just outside Ch. 11. Impact minor
38Middleton Class A, B and C Models
38
Return
- Class A Narrowband interference (coherent
reception) Uniquely represented by 2 parameters - Class B Broadband interference (incoherent
reception) Uniquely represented by six
parameters - Class C Sum of Class A and Class B (approx. Class
B)
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39Middleton Class B Model
39
- Envelope statistics
- Envelope exceedence probability density (APD),
which is 1 cumulative distribution function
(CDF)
Return
40Middleton Class B Model (cont)
40
- Middleton Class B envelope statistics
Return
41Middleton Class B Model (cont)
41
- Parameters for Middleton Class B model
Return
42Accuracy of Middleton Noise Models
42
Return
Magnetic Field Strength, H (dB relative to
microamp per meter rms)?
e0 (dB gt erms)?
Percentage of Time Ordinate is Exceeded
P(e gt e0)?
Soviet high power over-the-horizon radar
interference Middleton, 1999
Fluorescent lights in mine shop office
interference Middleton, 1999
43Symmetric Alpha Stable PDF
43
- 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 ? 0
Return
44Symmetric Alpha Stable Model
44
- Heavy tailed distribution
Return
Density functions for symmetric alpha stable
distributions for different values of
characteristic exponent alpha a) overall density
and b) the tails of densities
45Parameter Estimation Middleton Class A
45
- Expectation Maximization (EM)
- E Step Calculate log-likelihood function \w
current parameter values - M Step Find parameter set that maximizes
log-likelihood function - EM Estimator for Class A parameters Zabin
Poor, 1991 - Express envelope statistics as sum of weighted
PDFs - Maximization step is iterative
- Given A, maximize K ( AG). Root 2nd order
polynomial. - Given K, maximize A. Root 4th order polynomial
Return
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Results
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46Expectation Maximization Overview
46
Return
47Results EM Estimator for Class A
47
Return
Iterations for Parameter A to Converge
Normalized Mean-Squared Error in A
K A G
PDFs with 11 summation terms 50 simulation runs
per setting
1000 data samples Convergence criterion
48Results EM Estimator for Class A
48
Return
- For convergence for A ? 10-2, 1, worst-case
number of iterations for A 1 - Estimation accuracy vs. number of iterations
tradeoff
49Parameter Estimation Symmetric Alpha Stable
49
- Based on extreme order statistics Tsihrintzis
Nikias, 1996 - PDFs of max and min of sequence of i.i.d. data
samples - PDF of maximum
- PDF of minimum
- Extreme order statistics of Symmetric Alpha
Stable PDF approach Frechets distribution as N
goes to infinity - Parameter Estimators then based on simple order
statistics - Advantage Fast/computationally efficient
(non-iterative) - Disadvantage Requires large set of data samples
(N10,000)
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Results
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50Parameter Est. Symmetric Alpha Stable Results
50
Return
- Data length (N) of 10,000 samples
- Results averaged over 100 simulation runs
- Estimate a and mean g directly from data
- Estimate variance g from a and d estimates
Mean squared error in estimate of characteristic
exponent a
51Parameter Est. Symmetric Alpha Stable Results
51
Return
Mean squared error in estimate of dispersion
(variance) ?
Mean squared error in estimate of localization
(mean) ?
52Extreme Order Statistics
52
Return
53Parameter Estimators for Alpha Stable
53
Return
0 lt p lt a
54Filtering and Detection
54
- System model
- Assumptions
- Multiple samples of the received signal are
available - N Path Diversity Miller, 1972
- Oversampling by N Middleton, 1977
- Multiple samples increase gains vs. Gaussian case
- Impulses are isolated events over symbol period
Impulsive Noise
Pulse Shaping
Pre-Filtering
Matched Filter
Detection Rule
N samples per symbol
55Wiener Filtering
55
- Optimal in mean squared error sense in presence
of Gaussian noise
Return
Model
d(n) desired signald(n) filtered
signale(n) error w(n) Wiener filter x(n)
corrupted signalz(n) noise
Design
Minimize Mean-Squared Error E e(n)2
56Wiener Filter Design
56
- Infinite Impulse Response (IIR)
- Finite Impulse Response (FIR)
- Weiner-Hopf equations for order p-1
Return
desired signal d(n)power spectrum ?(e j
?) correlation of d and x rdx(n)autocorrelat
ion of x rx(n)Wiener FIR Filter w(n)
corrupted signal x(n)noise z(n)?
57Results Wiener Filtering
57
Return
Pulse shape10 samples per symbol10 symbols per
pulse
ChannelA 0.35? 0.5 10-3SNR -10
dBMemoryless
58MAP Detection for Class A
58
- Hard decision
- Bayesian formulation Spaulding Middleton,
1977 - Equally probable source
Return
59MAP Detection for Class A Small Signal Approx.
59
- Expand noise PDF pZ(z) by Taylor series about Sj
0 (j1,2)? - Approximate MAP detection rule
- Logarithmic non-linearity correlation receiver
- Near-optimal for small amplitude signals
Return
We use 100 terms of the series expansion
ford/dxi ln pZ(xi) in simulations
60Incoherent Detection
60
- Bayesian formulation Spaulding Middleton,
1997, pt. II - Small signal approximation
Return
Correlation receiver
61Filtering for Alpha Stable Noise
61
- Myriad filtering
- Sliding window algorithm outputs myriad of a
sample window - Myriad of order k for samples x1,x2,,xN
Gonzalez Arce, 2001 - As k decreases, less impulsive noise passes
through the myriad filter - As k?0, filter tends to mode filter (output value
with highest frequency) - Empirical Choice of k Gonzalez Arce, 2001
- Developed for images corrupted by symmetric alpha
stable impulsive noise
Return
62Filtering for Alpha Stable Noise (Cont..)
62
- Myriad filter implementation
- Given a window of samples, x1,,xN, find ß ?
xmin, xmax - Optimal Myriad algorithm
- Differentiate objective function polynomial p(ß)
with respect to ß - Find roots and retain real roots
- Evaluate p(ß) at real roots and extreme points
- Output ß that gives smallest value of p(ß)
- Selection Myriad (reduced complexity)
- Use x1, , xN as the possible values of ß
- Pick value that minimizes objective function p(ß)
Return
63Filtering for Alpha Stable Noise (Cont..)
63
- Hole punching (blanking) filters
- Set sample to 0 when sample exceeds threshold
Ambike, 1994 - Large values are impulses and true values can be
recovered - Replacing large values with zero will not bias
(correlation) receiver for two-level
constellation - If additive noise were purely Gaussian, then the
larger the threshold, the lower the detrimental
effect on bit error rate - Communication performance degrades as
constellation size (i.e., number of bits per
symbol) increases beyond two
Return
64MAP Detection for Alpha Stable PDF Approx.
64
- SaS random variable Z with parameters a , d, g
can 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 a mixture model of N
GaussiansKuruoglu, 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
Return
65Results Alpha Stable Detection
65
Return
66Complexity Analysis for Alpha Stable Detection
66
Return
Method Complexity per symbol Analysis
Hole Puncher Correlation Receiver O(NS) A decision needs to be made about each sample.
Optimal Myriad Correlation Receiver O(NW3S) Due to polynomial rooting which is equivalent to Eigen-value decomposition.
Selection Myriad Correlation Receiver O(NW2S) Evaluation of the myriad function and comparing it.
MAP Approximation O(MNS) Evaluating approximate pdf(M is number of Gaussians in mixture)
67Bivariate Middleton Class A Model
67
- Joint spatial distribution
Return
Parameter Description Typical Range
Overlap Index. Product of average number of emissions per second and mean duration of typical emission
Ratio of Gaussian to non-Gaussian component intensity at each of the two antennas
Correlation coefficient between antenna observations
68Results on Measured RFI Data
68
Return
- 50,000 baseband noise samples represent broadband
interference
Estimated Parameters Estimated Parameters Estimated Parameters
Bivariate Middleton Class A Bivariate Middleton Class A Bivariate Middleton Class A
Overlap Index (A) 0.313 2D-KL Divergence1.004
Gaussian Factor (G1) 0.105 2D-KL Divergence1.004
Gaussian Factor (G2) 0.101 2D-KL Divergence1.004
Correlation (k) -0.085 2D-KL Divergence1.004
Bivariate Gaussian Bivariate Gaussian Bivariate Gaussian
Mean (µ) 0 2D-KL Divergence1.6682
Variance (s1) 1 2D-KL Divergence1.6682
Variance (s2) 1 2D-KL Divergence1.6682
Correlation (k) -0.085 2D-KL Divergence1.6682
Marginal PDFs of measured data compared with
estimated model densities
69System Model
69
Return
- 2 x 2 MIMO System
- Maximum Likelihood (ML) receiver
- Log-likelihood function
Sub-optimal ML Receivers approximate
70Sub-Optimal ML Receivers
70
- Two-piece linear approximation
- Four-piece linear approximation
Return
Approximation of
chosen to minimize
71Results Performance Degradation
71
- Performance degradation in receivers designed
assuming additive Gaussian noise in the presence
of RFI
Return
- Simulation Parameters
- 4-QAM for Spatial Multiplexing (SM) transmission
mode - 16-QAM for Alamouti transmission strategy
- Noise ParametersA 0.1, ?1 0.01, ?2 0.1, k
0.4
Severe degradation in communication performance
in high-SNR regimes
72Performance Bounds (Single Antenna)
72
Return
System Model
Case I Shannon Capacity in presence of additive white Gaussian noise
Case II (Upper Bound) Capacity in the presence of Class A noise Assumes that there exists an input distribution which makes output distribution Gaussian (good approximation in high SNR regimes)
Case III (Practical Case) Capacity in presence of Class A noise Assumes input has Gaussian distribution (e.g. bit interleaved coded modulation (BICM) or OFDM modulation Haring, 2003)
73Performance Bounds (Single Antenna)
73
- Channel capacity in presence of RFI
Return
System Model
Capacity
ParametersA 0.1, G 10-3
74Performance Bounds (Single Antenna)
74
- Probability of error for uncoded transmissions
Return
Haring Vinck, 2002
BPSK uncoded transmission One sample per symbol A
0.1, G 10-3
75Performance Bounds (Single Antenna)
75
- Chernoff factors for coded transmissions
Return
PEP Pairwise error probability N Size of the
codeword Chernoff factor Equally likely
transmission for symbols
76System Model
76
Return
77Performance Bounds (2x2 MIMO)
77
Return
System Model
Case I Shannon Capacity in presence of additive white Gaussian noise
Case II (Upper Bound) Capacity in presence of bivariate Middleton Class A noise. Assumes that there exists an input distribution which makes output distribution Gaussian for all SNRs.
Case III (Practical Case) Capacity in presence of bivariate Middleton Class A noise Assumes input has Gaussian distribution
78Performance Bounds (2x2 MIMO)
78
- Channel capacity in presence of RFI for 2x2 MIMO
Return
System Model
Capacity
ParametersA 0.1, G1 0.01, G2 0.1, k 0.4
79Performance Bounds (2x2 MIMO)
79
- Probability of symbol error for uncoded
transmissions
Return
Pe Probability of symbol error S Transmitted
code vector D(S) Decision regions for MAP
detector Equally likely transmission for symbols
ParametersA 0.1, G1 0.01, G2 0.1, k 0.4
80Performance Bounds (2x2 MIMO)
80
- Chernoff factors for coded transmissions
Return
PEP Pairwise error probabilityN Size of the
codewordChernoff factorEqually likely
transmission for symbols
ParametersG1 0.01, G2 0.1, k 0.4
81Performance Bounds (2x2 MIMO)
81
- Cutoff rates for coded transmissions
- Similar measure as channel capacity
- Relates transmission rate (R) to Pe for a length
T codes
Return
82Performance Bounds (2x2 MIMO)
82
Return
83Extensions to Multicarrier Systems
83
Return
- Impulse noise with impulse event followed by
flat region - Coding may improve communication performance
- In multicarrier modulation, impulsive event in
time domain spreads over all subcarriers,
reducing effect of impulse - Complex number (CN) codes Lang, 1963
- Unitary transformations
- Gaussian noise is unaffected (no change in 2-norm
Distance) - Orthogonal frequency division multiplexing (OFDM)
is a special case Inverse Fourier Transform - As number of subcarriers increase, impulsive
noise case approaches the Gaussian noise case
Haring 2003