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Wireless Networking and Communications Group
Radio 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
7 Oct 2009
Talk at The University of Texas at Austin
Outline
22


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
Wireless Networking and Communications Group
Radio Frequency Interference
3



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 user’s computer subsystems
 Co-channel interference from other in-band wireless networks
and services

Problem Definition
44
Backup
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
We will use noise and
interference interchangeably
Statistical modeling of RFI
 Filtering/detection based on estimated model parameters

Wireless Networking and Communications Group
Impact of RFI
55

Impact of LCD noise on throughput for an IEEE 802.11g
embedded wireless receiver [Shi, Bettner, Chinn, Slattery & Dong, 2006]
Backup
Backup
Wireless Networking and Communications Group
Statistical Modeling of RFI
66

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

Wireless Networking and Communications Group
Backup
Backup
Assumptions for RFI Modeling
77

Key assumptions for Middleton and Alpha Stable models
[Middleton, 1977][Furutsu & 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
Wireless Networking and Communications Group
Our Contributions
88
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
Wireless Networking and Communications Group
Middleton Class A model
99
Probability Density Function
f Z ( z)  e
A
where  m2

 m!
Am
m 0
2 m2
e
z2

2
2 m
m

 A
1 
0.7
0.6
Probability density function

0.5
0.4
0.3
0.2
0.1
0
-10
-5
0
Noise amplitude
5
10
PDF for A = 0.15, = 0.8
Parameter
A

Description
Range
Overlap Index. Product of average number of emissions per A  [10-2, 1]
second and mean duration of typical emission
Gaussian Factor. Ratio of second-order moment of Gaussian Γ  [10-6, 1]
component to that of non-Gaussian component
Wireless Networking and Communications Group
Symmetric Alpha Stable Model
1
0
10
Characteristic Function
 ()  e j  ||

0.07
0.06
Probability density function

0.05
Closed-form PDF expression only for
α = 1 (Cauchy), α = 2 (Gaussian),
α = 1/2 (Levy), α = 0 (not very useful)
Approximate PDF using inverse transform
Backup
of power series expansion
Second-order moments do not exist for α < 2
Generally, moments of order > α do not exist
0.04
0.03
0.02
0.01



Parameter
0
-50
0
Noise amplitude
50
PDF for  = 1.5,  = 0,  = 10
Description
Backup
Range
α
Characteristic Exponent. Amount of impulsiveness
α [0,2]
δ
Localization. Analogous to mean
 (, )

Dispersion. Analogous to variance
 (0, )
Wireless Networking and Communications Group
Example Power Spectral Densities
11
Middleton Class A


Symmetric Alpha Stable
Power Spectal Density of S  S noise,  = 1.5,  = 10,  = 0
10
10
8
8
6
6
Power Spectrum Magnitude (dB)
Power Spectrum Magnitude (dB)
Power Spectal Density of Class A noise, A = 0.15,  = 0.1
4
2
0
-2
-4
-6
2
0
-2
-4
-6
-8
-10
4
-8
0
0.1
0.2
0.3
0.4
0.5
0.6
Frequency
0.7
0.8
0.9
Overlap Index (A) = 0.15
Gaussian Factor () = 0.1
Simulated Densities
1
-10
0
0.1
0.2
0.3
0.4
0.5
0.6
Frequency
0.7
0.8
0.9
1
Characteristic Exponent () = 1.5
Localization () = 0
Dispersion () = 10
Estimation of Noise Model Parameters
12

Middleton Class A model

Based on Expectation Maximization [Zabin & Poor, 1991]




Backup
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]



Backup
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)
Wireless Networking and Communications Group
Results on Measured RFI Data
13
25 radiated computer platform RFI data sets from Intel
50,000 samples taken at 100 MSPS


Estimated Parameters for Data Set #18
0.9
Measured PDF
Measured PDF
Symmetric Alpha Stable Model
Est. -Stable PDF
0.8
Est. Class A PDF
Alpha Stable PDF
Probability Density Function
0.7
Est. Gaussian PDF
0.6
Middleton Class A PDF
Localization (δ)
0.0065
Characteristic exp. (α)
1.4329
Dispersion (γ)
0.2701
KL Divergence
0.0308
0.5
Middleton Class A Model
0.4
Gaussian PDF
0.3
Overlap Index (A)
0.0854
Gaussian Factor (Γ)
0.6231
KL Divergence
0.0494
Gaussian Model
0.2
0.1
0
-6
-4
-2
0
2
4
Noise amplitude
Wireless Networking and Communications Group
Mean (µ)
0
Variance (σ2)
1
KL Divergence
0.1577
6
KL Divergence: Kullback-Leibler divergence
Results 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
0.25
Estimated Alpha Stable model
Gaussian
Estimated Class A model
Estimated Gaussian model
0.2
Kullback-Leibler (KL) Divergence

0.15
Class A
0.1
0.05
Alpha Stable
0
0
5
10
15
Measurement Set Number
20
25
Video 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 keying
Raised cosine pulse
10 samples/symbol
10 symbols/pulse length

Additive Class A Noise
Value
Overlap index (A)
0.35
Gaussian factor ()
0.001
SNR
19 dB
Composite of transmitted and received MPEG II video streams
http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo1
9dB_correlation.wmv

Shows degradation of video quality over impulsive channels with
standard receivers (based on Gaussian noise assumption)
Wireless Networking and Communications Group
Multiple samples of the received signal are available
Filtering and Detection
• N Path Diversity [Miller, 1972]
Assumption
16
• Oversampling by N [Middleton, 1977]
Impulsive Noise
Pulse
Shaping

Matched
Filter
Pre-Filtering
Middleton Class A noise
Symmetric Alpha Stable noise
Filtering
Filtering
Wiener Filtering (Linear)
Backup

Detection


Correlation Receiver (Linear)
Bayesian Detector
Small Signal Approximation to
Bayesian detector
Myriad Filtering


Backup

[Spaulding & Middleton, 1977]

Detection
Rule
Backup
Optimal Myriad
[Gonzalez & Arce, 2001]
Selection Myriad
Hole Punching
Backup
[Ambike et al., 1994]
Detection
Backup
[Spaulding & Middleton, 1977]


Correlation Receiver (Linear)
MAP approximation
[Kuruoglu, 1998]
Wireless Networking and Communications Group
Backup
Results: Class A Detection
17
Communication Performance
Binary Phase Shift Keying
0
10
Pulse shape
Raised cosine
10 samples per symbol
10 symbols per pulse
-1
Bit Error Rate (BER)
10
-2
Method
10
-3
10
Correlation Receiver
Wiener Filtering
Bayesian Detection
Small Signal Approximation
-4
10
-5
10
-35
-30
-25
-20
-15
-10
-5
0
5
10
SNR
Wireless Networking and Communications Group
15
Comp.
Complexity
Channel
A = 0.35
 = 0.5 × 10-3
Memoryless
Detection
Perform.
Correl.
Low
Low
Wiener
Medium
Low
Backup
Bayesian
Medium
S.S. Approx.
High
Backup
Bayesian
High
Backup
High
Results: Alpha Stable Detection
18
Backup
Communication Performance
Same transmitter settings as previous slide
0
10
Bit Error Rate (BER)
Method
-1
Comp.
Complexity
Hole
Punching
Low
Selection
Myriad
Low
MAP
Approx.
Medium
Optimal
Myriad
High
Detection
Perform.
Medium
Backup
10
-2
10
-10
Matched Filter
Hole Punching
MAP
Myriad
-5
0
5
10
15
Medium
Backup
High
Backupc
Medium
20
Generalized SNR (in dB)
Use dispersion parameter  in place of noise variance to generalize SNR
Wireless Networking and Communications Group
Backup
Backup
Video 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 keying
Raised cosine pulse
10 samples/symbol
10 symbols/pulse length

Additive Class A Noise
Value
Overlap index (A)
0.35
Gaussian factor ()
0.001
SNR
19 dB
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_demo1
9dB.wmv
Wireless Networking and Communications Group
Video over Impulsive Channels #2
20

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
Extensions to MIMO systems
21
Radio Frequency Interference Modeling and Receiver Design for MIMO systems
RFI Model
Spatial Physical
Corr.
Model
Comments
Middleton Class A
No
• Uni-variate model
• Assume independent or uncorrelated
noise for multiple antennas
Yes
Receiver design:
[Gao & Tepedelenlioglu, 2007] Space-Time Coding
[Li, Wang & Zhou, 2004] Performance degradation in receivers
Weighted Mixture of
Gaussian Densities
Yes
No
• Not derived based on physical
principles
Receiver design:
[Blum et al., 1997] Adaptive Receiver Design
Bivariate Middleton Class A Yes
Yes
[McDonald & Blum, 1997]
Wireless Networking and Communications Group
• Extensions of Class A model to twoantenna systems
Backup
Our Contributions
22
2 x 2 MIMO receiver design in the presence of RFI
[Gulati, 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
Backup
• Bounds on communication performance
Backup
[Chopra , Gulati, Evans, Tinsley, and Sreerama, ICASSP 2009]
Receiver Design
• Derived Maximum Likelihood (ML) receiver
• Derived two sub-optimal ML receivers with reduced
complexity
Wireless Networking and Communications Group
Backup
Results: RFI Mitigation in 2 x 2 MIMO
23
Improvement in communication
performance over conventional
Gaussian ML receiver at symbol
error rate of 10-2
Vector Symbol Error Rate
-1
10
A
Noise
Characteristic
Improve
-ment
0.01
Highly Impulsive
~15 dB
0.1
Moderately
Impulsive
~8 dB
Nearly Gaussian
~0.5 dB
-2
10
-3
10
-10
Optimal ML Receiver (for Gaussian noise)
Optimal ML Receiver (for Middleton Class A)
Sub-Optimal ML Receiver (Four-Piece)
Sub-Optimal ML Receiver (Two-Piece)
-5
0
5
10
15
SNR [in dB]
Communication Performance
(A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
Wireless Networking and Communications Group
20
1
Results: RFI Mitigation in 2 x 2 MIMO
24
Receiver
Quadratic
Forms
Exponential
Comparisons
Complexity Analysis for decoding
M-level QAM modulated signal
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
Vector Symbol Error Rate
-1
10
Complexity Analysis
-2
10
-3
10
-10
Optimal ML Receiver (for Gaussian noise)
Optimal ML Receiver (for Middleton Class A)
Sub-Optimal ML Receiver (Four-Piece)
Sub-Optimal ML Receiver (Two-Piece)
-5
0
5
10
15
SNR [in dB]
Communication Performance
(A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
Wireless Networking and Communications Group
20
Co-Channel Interference Modeling
25

Region of interferer locations determines interference model
[Gulati, Chopra, Evans & Tinsley, Globecom 2009]
Symmetric Alpha Stable
Wireless Networking and Communications Group
Middleton Class A
Co-Channel Interference Modeling
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
0
0
10
10
P ( Interference amplitude > a)
P ( Interfernce amplitude > a )
Simulated
Symmetric Alpha Stable
-1
10
-2
10
-3
10
-5
10
-10
10
Simulated
Symmetric Alpha Stable
Gaussian
Middleton Class A
-4
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Interference threshold (a)
Wireless Networking and Communications Group
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Interference threshold (a)
0.8
0.9
1
Conclusions
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
Wireless Networking and Communications Group
RFI 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/software/index.html
Wireless Networking and Communications Group
Other 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
Wireless Networking and Communications Group
Future 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
Backup
Wireless Networking and Communications Group
31
Thank You.
Questions ?
Wireless Networking and Communications Group
References
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. 1206–1221, 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
Wireless Networking and Communications Group
References (cont…)
33
Filtering and Detection
[8] A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference EnvironmentPart 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. 55–57, 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. 438–441, 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):220–229, January 2007.
Wireless Networking and Communications Group
Backup 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
Backup
Wireless Networking and Communications Group
Common 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
2.5–2.69
3.3–3.8
5.725–5.85
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
Wireless Networking and Communications Group
Impact of RFI
36

Calculated in terms of desensitization (“desense”)
Interference raises noise floor
 Receiver sensitivity will degrade to maintain SNR

 RX noise floor Interferen ce 
desense  10 log 10 

RX
noise
floor



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)
Wireless Networking and Communications Group
Return
Impact of LCD clock on 802.11g
37


Pixel clock 65 MHz
LCD Interferers and 802.11g center frequencies
LCD
Interferers
Return
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
Wireless Networking and Communications Group
Middleton Class A, B and C Models
38
Return
[Middleton, 1999]

Class A

Class B

Class C
Narrowband interference (“coherent” reception)
Uniquely represented by 2 parameters
Broadband interference (“incoherent” reception)
Uniquely represented by six parameters
Sum of Class A and Class B (approx. Class B)
Wireless Networking and Communications Group
Backup
Middleton Class B Model
39

Envelope statistics

Return
Envelope exceedence probability density (APD), which is 1 – cumulative
distribution function (CDF)
(1) m Aˆm  m 
 m

P1 (   0 ) B  I  1  ˆ0 
.  1 
;2;ˆ0 
 . 1F1 1 
m!
2 
2



m 0
where, 1F1 is the confluent hypergeometric function

ˆ0 
 0 Ni
2GB
P1 (   0 ) B  II  e
A
Aˆ     ;
2 GB
;
 AB

ABm  02 /( 2 mB2 )
e

m  0 m!
Wireless Networking and Communications Group
GB 
2
0  B
1
 4 
' 



B
'
4(1  B )  2  

0  B
Middleton Class B Model (cont…)
40
Middleton Class B envelope statistics
Return
Exceedance Probability Density Graph for Class B
Parameters: A = 10-1, A = 1,  = 5, N = 1,  = 1.8

Normalized Envelope Threshold (E0 / Erms )

B
B
I
4.5
4
3.5

3
2.5
PB-II

B
2
1.5

1
PB-I
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
P(E > E0)
Wireless Networking and Communications Group
0.7
0.8
0.9
1
Middleton Class B Model (cont…)
41

Parameters for Middleton Class B model
Parameters
Return
Description
Typical Range
AB
Impulsive Index
AB  [10-2, 1]
B
Ratio of Gaussian to non-Gaussian intensity
ΓB  [10-6, 1]
NI
Scaling Factor
NI  [10-1, 102]
Spatial density parameter
α  [0, 4]
Effective impulsive index dependent on α
A α  [10-2, 1]
Inflection point (empirically determined)
εB > 0

A
B
Wireless Networking and Communications Group
Accuracy of Middleton Noise Models
42
ε0 (dB > εrms)
Magnetic Field Strength, H (dB relative to
microamp per meter rms)
Return
P(ε > ε0)
Soviet high power over-the-horizon radar
interference [Middleton, 1999]
Wireless Networking and Communications Group
Percentage of Time Ordinate is Exceeded
Fluorescent lights in mine shop office
interference [Middleton, 1999]
Symmetric 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
Wireless Networking and Communications Group
Return
Symmetric Alpha Stable Model
44

Heavy tailed distribution
Density functions for symmetric alpha stable distributions for different values of
characteristic exponent alpha: a) overall density and b) the tails of densities
Wireless Networking and Communications Group
Return
Parameter Estimation: Middleton Class A
45

Expectation Maximization (EM)



Return
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


 2
Am
m
A
2e 
z
e
2
w( z )  
m  0 m! m

0

z2

Backup
z0
z0
w( z )    j p j ( z | A, )
j 0
A j e A
j 
;
j!

p j ( z | A, )  2 z
Maximization step is iterative
 Given A, maximize K (= A). Root 2nd order polynomial.
 Given K, maximize A. Root 4th order polynomial
Wireless Networking and Communications Group
Results
e
z2
 2j
 2j
Backup
Expectation Maximization Overview
46
Return
Wireless Networking and Communications Group
Results: EM Estimator for Class A
47
Return
Normalized Mean-Squared Error in A
-3
x 10
A = 0.01
A = 0.1
A=1
NMSE( Aest ) 
A  Aest
A
2
A = 0.01
A = 0.1
A=1
30
25
Number of Iterations
est
) / A |2
2.4
Fractional MSE = | (A - A
Number of Iterations taken by the EM Estimator for A
Fractional MSE of Estimator for A
2.6
2.2
Iterations for Parameter A to Converge
2
1.8
1.6
1.4
20
15
1.2
K = A 10
1
0.8
1e-006
1e-005
0.0001
K
0.001
0.01
PDFs with 11 summation terms
50 simulation runs per setting
Wireless Networking and Communications Group
1e-006
1e-005
0.0001
K
1000 data samples
Convergence criterion:
0.001
0.01
ˆ A
ˆ
A
n
n 1
 10 7
ˆ
An 1
Results: EM Estimator for Class A
48
Return
• For convergence for
A  [10-2, 1], worstcase number of
iterations for A = 1
• Estimation accuracy
vs. number of
iterations tradeoff
Wireless Networking and Communications Group
Parameter 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
Return
PDF of maximum f M :N ( x)  N F N 1 ( x) f X ( x)
f m:N ( x)  N [1  F ( x)] N 1 f X ( x)
 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


Advantage:
Disadvantage:
Fast/computationally efficient (non-iterative)
Requires large set of data samples (N~10,000)
Results
Wireless Networking and Communications Group
Backup
Parameter Est.: Symmetric Alpha Stable Results
50
Return
MSE in estimates of the Characteristic Exponent (  )
0.09
• Data length (N) of 10,000 samples
0.08
• Results averaged over 100
simulation runs
Mean Squared Error (MSE)
0.07
0.06
0.05
• Estimate α and “mean”  directly
from data
0.04
0.03
• Estimate “variance”  from α and δ
estimates
0.02
0.01
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Characteristic Exponent: 
1.6
1.8
2
Mean squared error in estimate
of characteristic exponent α
Wireless Networking and Communications Group
Parameter Est.: Symmetric Alpha Stable Results
51
6
6
5
5
4
3
2
1
0
0
Return
MSE in estimates of the Dispersion Parameter ()
7
Mean Squared Error (MSE)
Mean Squared Error (MSE)
MSE in estimates of the Dispersion Parameter ()
7
4
3
2
1
0.2
0.4
0.6
0.8
1
1.2
1.4
Characteristic Exponent: 
1.6
1.8
2
Mean squared error in estimate
of localization (“mean”) 
Wireless Networking and Communications Group
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Characteristic Exponent: 
1.6
1.8
Mean squared error in estimate
of dispersion (“variance”) 
2
Extreme Order Statistics
52
Return
Wireless Networking and Communications Group
Parameter Estimators for Alpha Stable
53
Return
0<p<α
Wireless Networking and Communications Group
Filtering and Detection
54

System model
Impulsive Noise
Pulse
Shaping

Matched
Filter
Detection
Rule
Assumptions


Pre-Filtering
Multiple samples of the received signal are available
 N Path Diversity [Miller, 1972]
N samples per symbol
 Oversampling by N [Middleton, 1977]
Multiple samples increase gains vs. Gaussian case

Impulses are isolated events over symbol period
Wireless Networking and Communications Group
Wiener Filtering
55

Optimal in mean squared error sense in presence of
Gaussian noise
Model
^
z(n)
d(n)
^
x(n)
w(n)
Design
x(n)
d(n)
d(n)
^
w(n)
d(n)
e(n)
Wireless Networking and Communications Group
d(n):
d(n):
e(n):
w(n):
x(n):
z(n):
desired signal
filtered signal
error
Wiener filter
corrupted signal
noise
Minimize Mean-Squared
Error E { |e(n)|2 }
Return
Wiener Filter Design
56

Infinite Impulse Response (IIR)
H

e )
jω 2
MMSE
Φdx (e )
Φd (e )
jω
=
Φx (e jω )
jω
=
Φd (e jω ) + Φz (e jω )
Finite Impulse Response (FIR)

Weiner-Hopf equations for order p-1
rx 0 )

rx 1)



rx  p  1)
rx 1)


rx  p  2 )
... rx  p  1)  w( 0 )  = rdx ( 0 ) 

 

w(
1
)
r
(
1
)

  dx

 

 

 
 

 

 

w(p

1
)
r
(p

1
)
... rx 0)  
  dx

p 1
 w(l)r (k  l) = r
x
dx
(k) k = 0,1,..., p - 1
l =0
Wireless Networking and Communications Group
Return
desired signal:
d(n)
power spectrum: (e j )
correlation of d and x: rdx(n)
autocorrelation of x: rx(n)
Wiener FIR Filter: w(n)
corrupted signal: x(n)
noise: z(n)
Results: Wiener Filtering
57

100-tap FIR Filter
Return
Raised Cosine
Pulse Shape
n
Transmitted waveform corrupted by Class A interference
n
Pulse shape
10 samples per
symbol
10 symbols per
pulse
Channel
A = 0.35
 = 0.5 × 10-3
SNR = -10 dB
Memoryless
Received waveform filtered
by Wiener filter
n
Wireless Networking and Communications Group
MAP Detection for Class A
58


Hard decision
Bayesian formulation [Spaulding & Middleton, 1977]
H1
H1 : X = S1 + Z
Λ( X ) =
H 2 : X = S2 + Z

p(H 2 )p( X | H 2 )
p(H 1 )p( X | H1 )
H2
Equally probable source
Λ( X ) =
pZ ( X  S 2 )
pZ ( X  S1 )


H1


1
H2
Wireless Networking and Communications Group
1
Return
MAP Detection for Class A: Small Signal Approx.
59

Expand noise PDF pZ(z) by Taylor series about Sj = 0 (j=1,2)
p Z ( X )
pZ ( X  S j )  p Z ( X )  p Z ( X )  S j = p Z ( X )  
s ji
xi
i=1


)
Τ
Approximate MAP detection rule
N
d
1   s2i
ln p Z (xi )
dx
i=1
i
Λ( X ) 
N
d
1   s1i
ln p Z (xi )
dx
i=1
i

H1


1
N
We use 100 terms of the
series expansion for
d/dxi ln pZ(xi) in simulations
H2
Logarithmic non-linearity
+ correlation receiver

Near-optimal for small amplitude signals
Wireless Networking and Communications Group
Correlation Receiver
Return
Incoherent Detection
60

Bayesian formulation [Spaulding & Middleton, 1997, pt. II]
H1 : X(t) = S1(t,θ)+ Z(t)
H 2 : X(t) = S 2 (t,θ)+ Z(t)
Λ( X ) =
θ =  a  where a : amplitude and φ : phase
 
 φ
 

 p( X | H
2
)p(θp(θ
θ
 p( X | H
θ
1
)p(θp(θ
=
Return
p2 ( X ) H1
1
p1( X )
H2
Small signal approximation
2
2
N
 N

l(x
)
cos
ω
t
+
l(x
)
sin
ω
t
2 i
2 i
 i
 i
 i=1
  i=1

2
2
N
 N

 l(x i )cosω1ti  +  l(x i )sin ω1ti 
 i=1
  i=1

where l(x i ) =
H1


1
H2
d
ln pZ (xi )
dxi
Wireless Networking and Communications Group
Correlation receiver
Filtering for Alpha Stable Noise
61

Myriad filtering
Return
Sliding window algorithm outputs myriad of a sample window
 Myriad of order k for samples x1,x2,…,xN [Gonzalez & Arce, 2001]


2
g M x1 ,, xN )  ˆk  arg min  k 2  xi   )
N





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]
k ( ,  ) 

i 1

2 

1

Developed for images corrupted by symmetric alpha stable
impulsive noise
Wireless Networking and Communications Group
Filtering for Alpha Stable Noise (Cont..)
62

Myriad filter implementation
Given a window of samples, x1,…,xN, find β  [xmin, xmax]
 Optimal Myriad algorithm

1.
Differentiate objective function polynomial p(β) with respect to β

p(  )   k 2  xi   )
N
i 1
2.
3.
4.

2

Find roots and retain real roots
Evaluate p(β) at real roots and extreme points
Output β that gives smallest value of p(β)
Selection Myriad (reduced complexity)
1.
2.
Use x1, …, xN as the possible values of β
Pick value that minimizes objective function p(β)
Wireless Networking and Communications Group
Return
Filtering for Alpha Stable Noise (Cont..)
63

Hole punching (blanking) filters

Set sample to 0 when sample exceeds threshold [Ambike, 1994]
 x[n]
h hp  
 0




x[n]  Thp
x[n] > Thp
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
Wireless Networking and Communications Group
Return
MAP Detection for Alpha Stable: PDF Approx.
64

SαS random variable Z with parameters  , , can be
written Z = X Y½ [Kuruoglu, 1998]



X is zero-mean Gaussian with variance 2 
Y is positive stable random variable with parameters depending on 
PDF of Z can be written as a mixture model of N Gaussians
[Kuruoglu, 1998]
N
p ,0, z ) 
 2e
i 1



fY vi2 )
 f v )
N
i 1

z2
2vi2
Y
2
i
Mean 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
Wireless Networking and Communications Group
Return
Results: Alpha Stable Detection
65
Return
Wireless Networking and Communications Group
Complexity Analysis for Alpha Stable Detection
66
Return
Method
Complexity
per symbol
Analysis
Hole Puncher +
Correlation Receiver
O(N+S)
A decision needs to be made about each
sample.
Optimal Myriad +
Correlation Receiver
O(NW3+S)
Due to polynomial rooting which is
equivalent to Eigen-value decomposition.
Selection Myriad +
Correlation Receiver
O(NW2+S)
Evaluation of the myriad function and
comparing it.
MAP Approximation
O(MNS)
Evaluating approximate pdf
(M is number of Gaussians in mixture)
Wireless Networking and Communications Group
Bivariate Middleton Class A Model
67

Joint spatial distribution
Parameter
Description
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
Wireless Networking and Communications Group
Return
Typical Range
Results on Measured RFI Data
68
Return

50,000 baseband noise samples represent broadband interference
1.4
1.2
Probability Density Function
Estimated Parameters
Measured PDF
Estimated Middleton
Class A PDF
Equi-power
Gaussian PDF
1
Bivariate Middleton Class A
Overlap Index (A)
0.313
0.8
Gaussian Factor (1)
0.105
0.6
Gaussian Factor (2)
0.101
Correlation (k)
-0.085
0.4
2DKL Divergence
1.004
Bivariate Gaussian
0.2
0
-4
-3
-2
-1
0
1
2
3
4
Noise amplitude
Marginal PDFs of measured data compared
with estimated model densities
Wireless Networking and Communications Group
Mean (µ)
0
Variance (1)
1
Variance (2)
1
Correlation (k)
-0.085
2DKL Divergence
1.6682
System Model
69
Return

2 x 2 MIMO System

Maximum Likelihood (ML) receiver

Log-likelihood function
Wireless Networking and Communications Group
Sub-optimal ML Receivers
approximate
Sub-Optimal ML Receivers
70

Two-piece linear approximation
Return

Four-piece linear approximation
Approxmation of  (z)
5
4.5
(z)
 1(z)
4
 2(z)
3.5
3
2.5
2
1.5
1
0.5
0
-5
-4
-3
-2
-1
0
z
chosen to minimize
Wireless Networking and Communications Group
Approximation of
1
2
3
4
5
Results: Performance Degradation
71

Performance degradation in receivers designed assuming
additive Gaussian noise in the presence of RFI
Return
0
10
Simulation Parameters
• 4-QAM for Spatial Multiplexing (SM)
transmission mode
• 16-QAM for Alamouti transmission
strategy
• Noise Parameters:
A = 0.1, 1= 0.01, 2= 0.1, k = 0.4
-1
Vector Symbol Error Rate
10
-2
10
-3
10
-4
10
-5
10
-10
SM with ML (Gaussian noise)
SM with ZF (Gaussian noise)
Alamouti coding (Gaussian noise)
SM with ML (Middleton noise)
SM with ZF (Middleton noise)
Alamouti coding (Middleton noise)
-5
0
5
10
15
SNR [in dB]
Wireless Networking and Communications Group
20
Severe degradation in
communication performance in
high-SNR regimes
Performance Bounds (Single Antenna)
72

Channel capacity
C
max
{ f X ( x ), E { X 2 } Es }


I ( X ;Y )
h(Y )  h(Y | X )
h(Y )  h( N )
Return
System Model
Y  X N
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])
Wireless Networking and Communications Group
Performance Bounds (Single Antenna)
73

Channel capacity in presence of RFI
Return
Channel Capacity
15
System Model
X: Gaussian, N: Gaussian
Y:Gaussian, N:ClassA (A = 0.1,  = 10-3)
Y  X N
Capacity (bits/sec/Hz)
X:Gaussian, N:ClassA (A = 0.1,  = 10-3)
Capacity
10
C


5
max
{ f X ( x ), E { X 2 } E s }
I ( X ;Y )
h(Y )  h(Y | X )
h(Y )  h( N )
Parameters
A = 0.1, Γ = 10-3
0
-40
-30
-20
-10
SNR [in dB]
0
Wireless Networking and Communications Group
10
20
Performance Bounds (Single Antenna)
74

Probability of error for uncoded transmissions
Probability of error (Uncoded Transmission)
0

10
m
A
Pe  e  A  PeAW GN ( m2 )
m 0 m!
-1
10
[Haring & Vinck, 2002]
-2
10
Probability of error
Return
m

2
A
m 
1 
-3
10
-4
10
BPSK uncoded transmission
-5
10
One sample per symbol
-6
10
AWGN
-7
10
-40
A = 0.1, Γ = 10-3
Class A: A = 0.1,  = 10-3
-30
-20
-10
dmin /  [in dB]
0
Wireless Networking and Communications Group
10
20
Performance Bounds (Single Antenna)
75

Chernoff factors for coded transmissions
Return
Chernoff factors for real channel with various parameters of A and MAP decoding
0
10
PEP  P(c  c ' )
 min
l
-1
Chernoff Factor
10
N
'
C
(
c
,
c
 k k , l)
k 1
PEP: Pairwise error probability
N: Size of the codeword
-2
10
'
Chernoff factor: min C (ck , ck , l )
Gaussian
l
Class A: A = 0.1,  = 10-3
Equally likely transmission for
symbols
Class A: A = 0.3,  = 10-3
Class A: A = 10,  = 10-3
-3
10
-20
-15
-10
-5
0
dmin /  [in dB]
5
Wireless Networking and Communications Group
10
15
System Model
76
Return
Wireless Networking and Communications Group
Performance Bounds (2x2 MIMO)
77

Channel capacity
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
Wireless Networking and Communications Group
Performance Bounds (2x2 MIMO)
78
Channel capacity in presence of RFI for 2x2 MIMO
25
Mutual Information (bits/sec/Hz)

20
Return
System Model
Channel Capacity with Gaussian noise
Upper Bound on Mutual Information with Middleton noise
Gaussian transmit codebook with Middleton noise
Capacity
15
10
5
Parameters:
0
-40
A = 0.1, 1 = 0.01, 2 = 0.1, k = 0.4
-30
-20
-10
0
SNR [in dB]
Wireless Networking and Communications Group
10
20
Performance 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
Parameters:
A = 0.1, 1 = 0.01,2 = 0.1, k = 0.4
Wireless Networking and Communications Group
Performance Bounds (2x2 MIMO)
80
Chernoff factors for coded transmissions

0
10
PEP  P( s  s ' )
 min
l
-2
10
Chernoff Factor
Return
N
 C (s , s , l )
t
'
t
t 1
-4
10
-6
10
-8
10
-30
Middleton noise (A = 0.5)
Middleton noise (A = 0.1)
Middleton noise (A = 0.01)
Gaussian noise
-20
-10
0
10
20
30
d2t / N0 [in dB]
Parameters:
1 = 0.01,2 = 0.1, k = 0.4
Wireless Networking and Communications Group
40
PEP: Pairwise error probability
N: Size of the codeword
C (ck , ck' , l )
Chernoff factor: min
l
Equally likely transmission for symbols
Performance 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

Wireless Networking and Communications Group
Return
Performance Bounds (2x2 MIMO)
82
Cutoff rate
Return
4
3.5
Cutoff Rate [bits/transmission]

3
BPSK, Middleton noise
BPSK, Gaussian noise
QPSK, Middleton noise
QPSK, Gaussian noise
16QAM, Middleton noise
16QAM, Gaussian noise
2.5
2
1.5
1
0.5
0
-30
-20
-10
0
10
SNR [in dB]
Wireless Networking and Communications Group
20
30
40
Extensions to Multicarrier Systems
83

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]

Wireless Networking and Communications Group
Return