Download Radio Frequency Interference Sensing and Mitigation

Wireless Networking and Communications Group
Radio Frequency Interference
Sensing and Mitigation in
Wireless Receivers
Brian L. Evans
Lead Graduate Students
Aditya Chopra, Kapil Gulati, and Marcel Nassar
In collaboration with Eddie Xintian Lin, Alberto Alcocer Ochoa,
Srikathyayani Srikanteswara, and Keith R. Tinsley at Intel Labs
12 Apr 2010
Talk at Intel Labs at Hillsboro, Oregon
Outline
2






Introduction
Problem Definition
Statistical Modeling of Radio Frequency Interference
Receiver Design to Mitigate Radio Frequency Interference
Conclusions
Future work
RFI
Wireless Networking and Communications Group
Introduction
3
(WiMAX Basestation)
(Microwave)
(Wi-Fi)
(WiMAX)
antenna
(Wi-Fi)
(WiMAX Mobile)
Wireless Communication
Sources
•
Closely located sources
•
Coexisting protocols
Non-Communication
Sources
Electromagnetic radiations
baseband processor
(Bluetooth)
•
•
Computational Platform
Clocks, busses, processors
Co-located transceivers
Wireless Networking and Communications Group
Radio Frequency Interference (RFI)
4


Limits wireless communication performance
Impact of LCD noise on throughput for an embedded Wi-Fi
(IEEE 802.11g) receiver [Shi, Bettner, Chinn, Slattery & Dong, 2006]
Wireless Networking and Communications Group
Problem Definition
5



Problem: Co-channel and adjacent channel interference,
and platform noise degrade communication performance
Approach: Statistical modeling of RFI
Solution: Receiver design
Listen to the environment
 Estimate parameters for RFI statistical models
 Use parameters to mitigate RFI


Goal: Improve communication performance
10-100x reduction in bit error rate (this talk)
 10-100x improvement in network throughput (future work)

Wireless Networking and Communications Group
Statistical Modeling of RFI
6


Multiple communication and non-communication sources
System Model

Point process to model interferer locations
 Poisson
(uncoordinated, e.g. ad hoc)
 Poisson-Poisson cluster
(with user clustering, e.g. femtocell)
Interferer
Fading emissions
Pathloss

Sum interference

Goal: Closed form statistics to model tail probability
Tail probability governs
communication performance
Wireless Networking and Communications Group
Statistical Models (isotropic, zero centered)
7

Symmetric Alpha Stable [Furutsu


Characteristic function
Gaussian Mixture Model [Sorenson & Alspach, 1971]


& Ishida, 1961] [Sousa, 1992]
Amplitude distribution
Middleton Class A (w/o Gaussian component) [Middleton, 1977]
Wireless Networking and Communications Group
Poisson Field of Interferers
8
• Sensor networks
• Ad hoc networks
Symmetric Alpha Stable
• Cellular networks
• Hotspots (e.g. café)
• Dense Wi-Fi networks
• Networks with contention
based medium access
Middleton Class A (form of Gaussian Mixture)
Wireless Networking and Communications Group
Poisson-Poisson Cluster Field of Interferers
9
• In-cell and out-of-cell
femtocell users in
femtocell networks
• Cluster of hotspots
(e.g. marketplace)
Symmetric Alpha Stable
Wireless Networking and Communications Group
• Out-of-cell femtocell
users in femtocell
networks
Gaussian Mixture Model
Fitting Measured Laptop RFI Data
10

Statistical-physical models fit data better than Gaussian
0.4
Symmetric Alpha Stable
Middleton Class A
Gaussian Mixture Model
Gaussian
Kullback-Leibler divergence
0.35
0.3
Radiated platform RFI
• 25 RFI data sets from Intel
• 50,000 samples at 100 MSPS
• Laptop activity unknown to us
0.25
Smaller KL divergence
• Closer match in distribution
• Does not imply close match in
tail probabilities
0.2
0.15
0.1
0.05
0
0
5
10
15
Measurement Set
Wireless Networking and Communications Group
20
25
Platform RFI sources
• May not be Poisson distributed
• May not have identical emissions
Results on Measured RFI Data
11

For measurement set #23
0
Tail Probabilities [P(X > a)]
10
Tail probability governs
communication performance
• Bit error rate
• Outage probability
-5
10
-10
10
Empirical
Middleton Class A
Symmteric Alpha Stable
Gaussian
Gaussian Mixture Model
-15
10
-20
10
0
1
2
3
4
5
6
Threshold Amplitude (a)
Wireless Networking and Communications Group
7
8
9
Receiver Design to Mitigate RFI
12

Design receivers using knowledge of RFI statistics
Guard zone
Physical Layer (this talk)
• Receiver pre-filtering
• Receiver detection
• Forward error correction
Medium Access Control Layer
• Interference sense and avoid
• Optimize guard zone size
(e.g. transmit power control)
Example: Wi-Fi networks
RTS / CTS: Request / Clear to send
Interference statistics similar to Case III
Wireless Networking and Communications Group
RFI Mitigation in SISO systems
13
Interference + Thermal noise
Pulse
Shaping

0
Detection
Rule
Communication performance
10
Binary Phase Shift Keying
Pulse shape
Channel
Raised cosine
A = 0.35
10 samples per symbol
 = 5 × 10-3
10 symbols per pulse
Memoryless
Correlation Receiver
Bayesian Detection
Myriad Pre-filtering
-1
Symbol Error Rate
Matched
Filter
Pre-filtering
10
Method
-2
Comp.
Detection
Complexity Perform.
10
Low
Low
Bayesian detection
High
High
Myriad pre-filtering Medium
-3
10
-40
Correlation
-35
-30
-25
-20
-15
-10
Signal to Noise Ratio (SNR) [in dB]
Wireless Networking and Communications Group
-5
Medium
RFI Mitigation in 2 x 2 MIMO systems
14
Improvement in communication
performance over conventional
Gaussian ML receiver at symbol
error rate of 10-2
Conventional Gaussian
ML Receiver
Vector Symbol Error Rate
-1
10
-2
10
-3
10
-10
A
Noise
Characteristic
Improve
-ment
0.01
Highly Impulsive
~15 dB
0.1
Moderately
Impulsive
~8 dB
Nearly Gaussian
~0.5 dB
Proposed Receivers
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
RFI Mitigation in 2 x 2 MIMO systems
15
Receiver
Quadratic
Forms
Exponential
Comparisons
Complexity Analysis for decoding
M-level QAM modulated signal
Conventional Gaussian
ML Receiver
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
-2
10
-3
10
-10
Complexity Analysis
Proposed Receivers
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
RFI Mitigation Using Error Correction
16

Turbo decoder
-
Parity 1
Decoder 1
Systematic Data
-
Interleaver
Interleaver
-
Parity 2


Decoder 2
-
Interleaver
Decoding depends on the RFI statistics
10 dB improvement at BER 10-5 can be achieved using
accurate RFI statistics [Umehara, 2003]
Wireless Networking and Communications Group
Summary
17



Radio frequency interference affects wireless transceivers
RFI mitigation can improve communication performance
Our contributions
RFI
Modeling
• Co-channel interference in ad hoc, cellular, and femtocell networks
[Gulati, Evans, Andrews & Tinsley, submitted 2009]
[Gulati, Chopra, Evans & Tinsley, Globecom 2009]
• Computational platform noise
[Nassar, Gulati, DeYoung, Evans & Tinsley, ICASSP 2008, JSPS 2009]
• Microwave oven interference
[Nassar, Lin & Evans, submitted 2010]
Receiver
Design
• Single carrier, single antenna systems
[Nassar, Gulati, DeYoung, Evans & Tinsley, ICASSP 2008, JSPS 2009]
• Single carrier, 2 x 2 MIMO systems
[Gulati, Chopra, Heath, Evans, Tinsley & Lin, Globecom 2008]
Wireless Networking and Communications Group
Current and Future Work
18

RFI Modeling
Temporal modeling
 Multi-antenna modeling


Analysis and Bounds on Communication Performance
Physical layer (filtering, detection, and error correction)
 Medium access control layer protocols


RFI Mitigation
Extensions to multicarrier (OFDM) systems
 Extensions to multi-antenna (MIMO) systems
 Extensions to multipath channels

Wireless Networking and Communications Group
Related Publications
19
Journal Publications
• K. Gulati, B. L. Evans, J. G. Andrews, and K. R. Tinsley, “Statistics of Co-Channel
Interference in a Field of Poisson and Poisson-Poisson Clustered Interferers”, IEEE
Transactions on Signal Processing, submitted Nov. 29, 2009.
• M. Nassar, K. Gulati, M. R. DeYoung, B. L. Evans and K. R. Tinsley, “Mitigating NearField Interference in Laptop Embedded Wireless Transceivers”, Journal of Signal
Processing Systems, Mar. 2009, invited paper.
Conference Publications
• M. Nassar, X. E. Lin, and B. L. Evans, “Stochastic Modeling of Microwave Oven
Interference in WLANs”, Int. Global Comm. Conf., Dec. 6-10, 2010, submitted.
• K. Gulati, B. L. Evans, and K. R. Tinsley, “Statistical Modeling of Co-Channel
Interference in a Field of Poisson Distributed Interferers”, Proc. IEEE Int. Conf. on
Acoustics, Speech, and Signal Proc., Mar. 14-19, 2010.
• 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.
Cont…
Wireless Networking and Communications Group
Related Publications
20
Conference Publications (cont…)
• 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.
• 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.
• 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.
Software Releases
• K. Gulati, M. Nassar, A. Chopra, B. Okafor, M. R. DeYoung, N. Aghasadeghi, A. Sujeeth,
and B. L. Evans, "Radio Frequency Interference Modeling and Mitigation Toolbox in
MATLAB", version 1.4.1 beta, Apr. 11, 2010.
Wireless Networking and Communications Group
UT Austin RFI Modeling & Mitigation Toolbox
21


Freely distributable toolbox in MATLAB
Simulation environment for RFI modeling and mitigation
RFI generation
 Measured RFI fitting
 Parameter estimation algorithms
 Filtering and detection methods
 Demos for RFI modeling and mitigation


Latest Toolbox Release
Snapshot of a demo
Version 1.4.1 beta, Apr. 11, 2010
http://users.ece.utexas.edu/~bevans/projects/rfi/software/index.html
Wireless Networking and Communications Group
Usage Scenario #1
22
RFI Toolbox
RFI Generation
• RFI_MakeDataClassA.m
• RFI_MakeDataAlphaStable.m
….
….
Parameter Estimation
• RFI_EstMethodofMoments.m
• RFI_EstAlphaS_Alpha.m
….
….
User System Simulator
(e.g. WiMAX simulator)
Wireless Networking and Communications Group
Receivers
• RFI_myriad_opt.m
• RFI_BiVarClassAMLRx.m
….
….
Usage Scenario #2
23
Measured RFI data
RFI Toolbox
SISO Communication
Performance DEMO
Statistical Modeling DEMO
MIMO Communication
Performance DEMO
Wireless Networking and Communications Group
File Transfer DEMO
24
Thanks !
Wireless Networking and Communications Group
References
25
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. 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.
3. 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.
4. E. S. Sousa, “Performance of a spread spectrum packet radio network link in a Poisson field of
interferers,” IEEE Transactions on Information Theory, vol. 38, no. 6, pp. 1743–1754, Nov. 1992.
5. X. Yang and A. Petropulu, “Co-channel interference modeling and analysis in a Poisson field of
interferers in wireless communications,” IEEE Transactions on Signal Processing, vol. 51, no. 1, pp.
64–76, Jan. 2003.
6. E. Salbaroli and A. Zanella, “Interference analysis in a Poisson field of nodes of finite area,” IEEE
Transactions on Vehicular Technology, vol. 58, no. 4, pp. 1776–1783, May 2009.
7. M. Z. Win, P. C. Pinto, and L. A. Shepp, “A mathematical theory of network interference and its
applications,” Proceedings of the IEEE, vol. 97, no. 2, pp. 205–230, Feb. 2009.
Wireless Networking and Communications Group
References
26
Parameter Estimation
1. 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 .
2. 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.
Communication Performance of Wireless Networks
1. R. Ganti and M. Haenggi, “Interference and outage in clustered wireless ad hoc networks,” IEEE
Transactions on Information Theory, vol. 55, no. 9, pp. 4067–4086, Sep. 2009.
2. A. Hasan and J. G. Andrews, “The guard zone in wireless ad hoc networks,” IEEE Transactions on
Wireless Communications, vol. 4, no. 3, pp. 897–906, Mar. 2007.
3. X. Yang and G. de Veciana, “Inducing multiscale spatial clustering using multistage MAC contention
in spread spectrum ad hoc networks,” IEEE/ACM Transactions on Networking, vol. 15, no. 6, pp.
1387–1400, Dec. 2007.
4. S. Weber, X. Yang, J. G. Andrews, and G. de Veciana, “Transmission capacity of wireless ad hoc
networks with outage constraints,” IEEE Transactions on Information Theory, vol. 51, no. 12, pp.
4091-4102, Dec. 2005.
Wireless Networking and Communications Group
References
27
Communication Performance of Wireless Networks (cont…)
5. S. Weber, J. G. Andrews, and N. Jindal, “Inducing multiscale spatial clustering using multistage MAC
contention in spread spectrum ad hoc networks,” IEEE Transactions on Information Theory, vol.
53, no. 11, pp. 4127-4149, Nov. 2007.
6. J. G. Andrews, S. Weber, M. Kountouris, and M. Haenggi, “Random access transport capacity,” IEEE
Transactions On Wireless Communications, Jan. 2010, submitted. [Online]. Available:
http://arxiv.org/abs/0909.5119
7. M. Haenggi, “Local delay in static and highly mobile Poisson networks with ALOHA," in Proc. IEEE
International Conference on Communications, Cape Town, South Africa, May 2010.
8. F. Baccelli and B. Blaszczyszyn, “A New Phase Transitions for Local Delays in MANETs,” in Proc. of
IEEE INFOCOM, San Diego, CA,2010, to appear.
Receiver Design to Mitigate RFI
1. A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference EnvironmentPart I: Coherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 1977
2. 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
Wireless Networking and Communications Group
References
28
Receiver Design to Mitigate RFI (cont…)
3. 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.
4. G. R. Arce, Nonlinear Signal Processing: A Statistical Approach, John Wiley & Sons, 2005.
5. Y. Eldar and A. Yeredor, “Finite-memory denoising in impulsive noise using Gaussian mixture
models,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 48,
no. 11, pp. 1069-1077, Nov. 2001.
6. J. H. Kotecha and P. M. Djuric, “Gaussian sum particle ltering,” IEEE Transactions on Signal
Processing, vol. 51, no. 10, pp. 2602-2612, Oct. 2003.
7. 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.
8. 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.
RFI Measurements and Impact
1.
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
Backup Slides
29

Introduction
Interference avoidance , alignment, and cancellation methods
 Femtocell networks

Backup

Statistical Modeling of RFI
Computational platform noise
 Impact of RFI
 Assumptions for RFI Modeling
 Transients in digital FIR filters
 Poisson field of interferers
 Poisson-Poisson cluster field of interferers

Backup
Backup
Backup
Backup
Backup
Wireless Networking and Communications Group
Backup
Backup
Backup Slides (cont…)
30


Gaussian Mixture vs. Alpha Stable
Middleton Class A, B, and C models
Middleton Class A model
 Expectation maximization overview
 Results: EM for Middleton Class A



Backup
Backup
Backup
Extreme order statistics based estimator for Alpha Stable
Video over impulsive channels
Demonstration #1
 Demonstration #2

Backup
Backup
Symmetric Alpha Stable

Backup
Backup
Backup
Wireless Networking and Communications Group
Backup
Backup Slides (cont…)
31

RFI mitigation in SISO systems
Our contributions
 Results: Class A Detection
 Results: Alpha Stable Detection

Backup
Backup

RFI mitigation in MIMO systems





Backup
Our contributions
Backup
Performance bounds for SISO systems
Performance bounds for MIMO systems
Extensions for multicarrier systems
Turbo codes in impulsive channels
Wireless Networking and Communications Group
Backup
Backup
Backup
Backup
Interference Mitigation Techniques
32

Interference avoidance


CSMA / CA
Interference alignment

Example:
[Cadambe & Jafar, 2007]
Wireless Networking and Communications Group
Return
Interference Mitigation Techniques (cont…)
33

Interference cancellation
Return
Ref: J. G. Andrews, ”Interference Cancellation for Cellular Systems: A Contemporary
Overview”, IEEE Wireless Communications Magazine, Vol. 12, No. 2, pp. 19-29, April 2005
Wireless Networking and Communications Group
Femtocell Networks
34
Reference:
V. Chandrasekhar, J. G. Andrews and A. Gatherer, "Femtocell Networks: a Survey", IEEE
Communications Magazine, Vol. 46, No. 9, pp. 59-67, September 2008
Wireless Networking and Communications Group
Return
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
Assumptions for RFI Modeling
38

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
Return
Transients in Digital FIR Filters
39
Input
Freq = 0.16
25-Tap FIR Filter
• Low pass
• Stopband freq. 0.22 (normalized)
Interference duration = 100 x 1/0.22
Interference duration = 10 * 1/0.22
0.5
Input
Input
0.5
0
-0.5
0
-0.5
50
100
150
200
1
100
200
300
400
500
600
100
200
300
400
500
600
1
Transients
0.5
0
-0.5
-1
Filter Output
Filter Output
Return
Output
0.5
0
-0.5
-1
50
100
150
200
Transients Significant w.r.t. Steady State
Wireless Networking and Communications Group
Transients Ignorable w.r.t. Steady State
Poisson Field of Interferers
40

Interferers distributed over parametric annular space

Log-characteristic function
Wireless Networking and Communications Group
Return
Poisson Field of Interferers
41
Return
Wireless Networking and Communications Group
Poisson Field of Interferers
Return
42
Simulation Results
(tail probability)

Case III: Infinite-area with guard zone
Case I: Entire Plane
0
0
10
10
Gaussian and Middleton Class A
models are not applicable since
mean intensity is infinite
-1
10
-2
10
-5
10
-10
10
-15
-3
10
Tail Probability [ P (|Y| > y) ]
Tail Probability [ P (|Y| > y) ]
Simulated
Symmetric Alpha Stable
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Interference amplitude (y)
Wireless Networking and Communications Group
10
Simulated
Symmetric Alpha Stable
Gaussian
Middleton Class A
0.1
0.2
0.3
0.4
Interference amplitude (y)
0.5
0.6
0.7
Poisson Field of Interferers
43
Simulation Results (tail probability)
Case II: Finite area annular region
0
10
Tail Probability [P(|Y| > y)]

-5
10
-10
10
Simulated
Symmetric Alpha Stable
Gaussian
Middleton Class A
-15
10
0
0.1
0.2
0.3
0.4
0.5
Interference amplitude (y)
Wireless Networking and Communications Group
0.6
0.7
Return
Poisson-Poisson Cluster Field of Interferers
44

Cluster centers distributed as spatial Poisson process over

Interferers distributed as spatial Poisson process
Wireless Networking and Communications Group
Return
Poisson-Poisson Cluster Field of Interferers
45

Log-Characteristic function
Wireless Networking and Communications Group
Return
Poisson-Poisson Cluster Field of Interferers
Return
46
Simulation Results
(tail probability)

Case III: Infinite-area with guard zone
Case I: Entire Plane
0
0
10
10
Simulated
Symmetric Alpha Stable
-2
Gaussian and Gaussian mixture
models are not applicable since
mean intensity is infinite
-1
10
-2
10
-3
10
Tail Probability [ P (|Y| > y) ]
Tail Probability [ P (|Y| > y) ]
10
-4
10
-6
10
-8
10
-10
10
-12
-4
10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Interference amplitude (y)
Wireless Networking and Communications Group
10
Simulated
Symmetric Alpha Stable
Gaussian
Gaussian Mixture Model
0.1
0.2
0.3
0.4
Interference amplitude (y)
0.5
0.6
0.7
Poisson-Poisson Cluster Field of Interferers
47
Simulation Results (tail probability)
Case II: Finite area annular region
0
10
Tail Probability [P(|Y| > y)]

-5
10
-10
10
Simulated
Symmetric Alpha Stable
Gaussian
Gaussian Mixture Model
-15
10
0
0.1
0.2
0.3
0.4
0.5
Interference amplitude (y)
Wireless Networking and Communications Group
0.6
0.7
Return
Gaussian Mixture vs. Alpha Stable
48

Gaussian Mixture vs. Symmetric Alpha Stable
Gaussian Mixture
Symmetric Alpha Stable
Modeling
Interferers distributed with Guard Interferers distributed over
zone around receiver (actual or
entire plane
virtual due to pathloss function)
Pathloss
Function
With GZ: singular / non-singular
Entire plane: non-singular
Singular form
Thermal
Noise
Easily extended
(sum is Gaussian mixture)
Not easily extended
(sum is Middleton Class B)
Outliers
Easily extended to include outliers Difficult to include outliers
Wireless Networking and Communications Group
Return
Middleton Class A, B and C Models
49
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
Middleton Class A model
50
Probability Density Function
f Z ( z)  e
A
where  m2

 m!
Am
m 0
2 m2
e
z2

2
2 m
m

 A
1 
Return
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
Expectation Maximization Overview
51
Return
Wireless Networking and Communications Group
Results: EM Estimator for Class A
Return
52
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
53
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
Symmetric Alpha Stable Model
54
Characteristic Function
 ()  e j  ||

0.06
Probability density function

Return
0.07
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
Parameter Estimation: Symmetric Alpha Stable
55


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)
Wireless Networking and Communications Group
Parameter Estimators for Alpha Stable
56
Return
0<p<α
Wireless Networking and Communications Group
Parameter Est.: Symmetric Alpha Stable Results
57
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
58
MSE in estimates of the Dispersion Parameter ()
7
6
6
5
5
Mean Squared Error (MSE)
Mean Squared Error (MSE)
MSE in estimates of the Dispersion Parameter ()
7
4
3
2
1
0
0
Return
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
59
Return
Wireless Networking and Communications Group
Video over Impulsive Channels
60

Video demonstration for MPEG II video stream
Return

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
Video over Impulsive Channels #2
61

Video demonstration for MPEG II video stream revisited
Return

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
62

Structural similarity measure [Wang, Bovik, Sheikh & Simoncelli, 2004]

Return
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
Our Contributions
Return
63
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
Assumption
Filtering and Detection
Multiple samples of the received signal are available
• N Path Diversity [Miller, 1972]
• Oversampling by N [Middleton, 1977]
64
Impulsive Noise
Pulse
Shaping

Matched
Filter
Pre-Filtering
Middleton Class A noise
Symmetric Alpha Stable noise
Filtering
Filtering
Wiener Filtering (Linear)

Detection


Correlation Receiver (Linear)
Bayesian Detector
[Spaulding & Middleton, 1977]

Detection
Rule
Small Signal Approximation to
Bayesian detector
[Spaulding & Middleton, 1977]
Myriad Filtering



Optimal Myriad
[Gonzalez & Arce, 2001]
Selection Myriad
Hole Punching
[Ambike et al., 1994]
Detection


Correlation Receiver (Linear)
MAP approximation
[Kuruoglu, 1998]
Wireless Networking and Communications Group
Return
Results: Class A Detection
65
Communication Performance
Binary Phase Shift Keying
Return
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
Bayesian
Medium
S.S. Approx.
High
Bayesian
High
High
Results: Alpha Stable Detection
66
Return
Communication Performance
Same transmitter settings as previous slide
0
10
Bit Error Rate (BER)
Method
-1
Comp.
Complexity
Detection
Perform.
Hole
Punching
Low
Medium
Selection
Myriad
Low
Medium
MAP
Approx.
Medium
High
Optimal
Myriad
High
Medium
10
-2
10
-10
Matched Filter
Hole Punching
MAP
Myriad
-5
0
5
10
15
20
Generalized SNR (in dB)
Use dispersion parameter  in place of noise variance to generalize SNR
Wireless Networking and Communications Group
MAP Detection for Class A
67


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.
68

Expand noise PDF pZ(z) by Taylor series about Sj = 0 (j=1,2)
Return
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
Incoherent Detection
69

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
70

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..)
71

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..)
72

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.
73

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
74
Return
Wireless Networking and Communications Group
Complexity Analysis for Alpha Stable Detection
75
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
Extensions to MIMO systems
Return
76
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
Our Contributions
Return
77
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
• Bounds on communication performance
[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
Bivariate Middleton Class A Model
78

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
Return
79

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
Return
80

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
81

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
82

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
Results: RFI Mitigation in 2 x 2 MIMO
Return
83
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
Return
84
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
Performance Bounds (Single Antenna)
85

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)
86

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)
87

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)
88

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
Performance Bounds (2x2 MIMO)
89
Return
Wireless Networking and Communications Group
Performance Bounds (2x2 MIMO)
90

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)
91
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)
92

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)
93
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)
94

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)
95
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
96

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
Turbo Codes in Presence of RFI
97
Return
Parity 1
Systematic Data
Decoder 1
-

Gaussian channel:

Parity 2
Decoder 2
-

1
Middleton Class A channel:
Extrinsic
Information
Leads to a 10dB improvement at
BER of 10-5 [Umehara03]
Independent of
channel
statistics
Wireless Networking and Communications Group
A-priori
Information
Depends on
channel
statistics
Independent
of channel
statistics