phd defense 13 may 2011 wireless networking and communications group radio frequency interference...
TRANSCRIPT
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PhD Defense13 May 2011
Wireless Networking and Communications Group
Radio Frequency Interference Modeling and Mitigation in Wireless Receivers
Kapil Gulati
Committee Members:Prof. Jeffrey G. Andrews
Prof. Brian L. Evans (supervisor)Prof. Elmira Popova
Prof. Haris VikaloProf. Sriram Vishwanath
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Wireless Networking and Communications Group
Outline2
Introduction Background System Model Statistical Modeling of Radio Frequency Interference Communication Performance Analysis of Wireless Networks Receiver Design to Mitigate Radio Frequency Interference Conclusion
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Wireless transceivers
Wireless Networking and Communications Group
Introduction3
Wireless CommunicationSources
• Closely located sources• Coexisting protocols
Non-CommunicationSources
Electromagnetic radiations
Computational Platform• Clocks, busses, processors• Co-located transceivers
antenna
baseband processor
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Wireless Networking and Communications Group
Introduction (cont…)4
RFI may severely degrade communication performance Impact of LCD noise on throughput for an IEEE 802.11g
embedded wireless receiver [Shi, Bettner, Chinn, Slattery & Dong, 2006]
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Wireless Networking and Communications Group
Problem Statement5
Designing wireless transceivers to mitigate residual RFI
Guard zone
Example: Dense Wi-Fi Networks
Duration
Channel 11
Channel 11
Channel 9
(a) (a)
(b)(c)
(d)
Residual RFIa) Co-channelb) Adjacent channelc) Out-of-platformd) In-platform
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Wireless Networking and Communications Group
Problem Statement6
Designing wireless transceivers to mitigate residual RFI
Guard zone
Example: Dense Wi-Fi Networks
Duration
Channel 11
Channel 11
Channel 9
Physical (PHY) Layer
Improves: Link communication performance
Transmitsignal Pre-Filter Conventional
Receiver
RFIThermal
noise
Medium Access Control (MAC) LayerOptimize channel access protocols, e.g.,
Improves: Network communication performance
Distribution of Duration
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Wireless Networking and Communications Group
Approach7
Thesis Statement:For interference-limited wireless networks, deriving closed-form non-Gaussian statistics to model tail probabilities of RFI unlocks analysis of network throughput, delay, and reliability tradeoffs and designs of physical layer receivers to increase link spectral efficiency by several bits/s/Hz, without requiring knowledge of the number, locations, or types of interference sources.
Statistical Modeling of Residual RFI
RFI Mitigation in MAC Layer RFI Mitigation in PHY Layer
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Motivates: RFI Mitigation at MAC Layer
Wireless Networking and Communications Group
Contributions8
Statistical Modeling of RFI• Instantaneous statistics of RFI• Applicability to ad hoc, cellular, local area & femtocell networks
Communication Performance Analysis of Wireless Networks• Decentralized wireless networks with temporal correlation• Throughput, delay, and reliability
RFI Mitigation at PHY Layer• Pre-filtering methods mitigate RFI
Contribution #1
Contribution #2
Contribution #3
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Wireless Networking and Communications Group
Statistical Models9
Symmetric Alpha Stable (isotropic, zero-centered) Characteristic function
Gaussian Mixture Model (isotropic, zero-centered) Amplitude distribution
Middleton Class A (without the additive Gaussian component)
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Wireless Networking and Communications Group
Background10
SAS MCA GMM
Statistical Modeling
Statistical-Physical Derivation
[Sousa92][IlowHatzinakos98][YangPetropulu03]
[Middleton77][Middleton99]
No
Interferer Distribution Poisson Poisson -
Interferer Region Entire plane Finite area -
Bounded Pathloss No Yes -
Network Perf.
Used for Analysis [SousaSilvester90][WeberAndrJin05][PintoWin10]
No No
Temporal Dependence Limited No No
Receiver
Design
Example Prior Work [AmbikeIlowHatz94][GonzalesArce98]
[SpauldingMidd77][HaringVinck02]
[EldarYeredor01][KotechaDjuric03]
Include Thermal Noise ? No Yes Yes
Optimal Pre-Filter Myriad not known not known
Opt. Distance Measure Log deviations not known not known
Others RFI Models: Laplacian, Generalized Gaussian, Weibull, Lognormal, … (many more)
Derive RFI statistics for wider range of interference scenarios
Use RFI statistics to analyze performance of networks
Use a distance measure robust to impulsive statistics of RFI
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Interferer locations follow a spatial point process
Intended transmitter-receiver pair is Distance apart
Sum Interference at receiver
Wireless Networking and Communications Group
Initial System Model11
PathlossFadingNarrowband Interferer emissions
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Wireless Networking and Communications Group
Contribution #112
Instantaneous Statistics of Radio Frequency InterferenceField of Poisson interferers distributed over• Case I: Entire plane• Case II: Finite-area annular region• Case III: Infinite-area region with guard zone around receiver
Field of Poisson-Poisson clusters of interferers distributed over• Case I: Entire plane• Case II: Finite-area annular region• Case III: Infinite-area region with guard zone around receiver
Model computational platform noise measurements• Robust to deviations from system model assumptions
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Wireless Networking and Communications Group
Instantaneous Statistics of RFI13
Poisson Field of Interferers Interferers
Poisson-Poisson Cluster Field of Interferers Cluster Centers
Interferers
Closed-form statistics accurately modeling tail probability
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Wireless Networking and Communications Group
Poisson Field of Interferers14
• Cellular networks• Hotspots (e.g. café)
• Sensor networks• Ad hoc networks
• Dense Wi-Fi networks• Networks with contention
based medium access
Symmetric Alpha Stable Middleton Class A (form of Gaussian Mixture)
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Wireless Networking and Communications Group
Poisson-Poisson Cluster Field of Interferers15
• Cluster of hotspots (e.g. marketplace)
• In-cell and out-of-cell femtocell users in femtocell networks
• Out-of-cell femtocell users in femtocell networks
Symmetric Alpha Stable Gaussian Mixture Model
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Wireless Networking and Communications Group
Contribution #216
Decentralized Wireless Network with Temporal CorrelationJoint temporal statistics of interference • Poisson field with temporal correlation• Entire plane• Unbounded pathloss function
Closed-form measures of single-hop communication performance• Local delay• Throughput outage probability• Average network throughput
Extend definition and analysis of transmission capacity • Quantify throughput-delay-reliability tradeoffs
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Wireless Networking and Communications Group
System Model (Temporal Extension)17
Network Model I (Synchronous) User emerge at time slot k and transmit for random duration
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Wireless Networking and Communications Group
System Model (Temporal Extension)18
Network Model II (Asynchronous) Users can emerge at any time slot m
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Wireless Networking and Communications Group
Performance of Decentralized Networks19
Single-hop communication performance measures
Deriving exact closed-form expressions with temporal dependence is an open problem
Performance Measure Key Prior Work Temporal DependenceOutage Probability [Weber, Andrews & Jindal, 2007] IndependentTransmission Capacity [Weber et al., 2005] IndependentLocal Delay [Haenggi, 2010]
[Baccelli & Blaszczyszyn, 2010]• Independent• Complete correlation
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Wireless Networking and Communications Group
Deriving Closed-form Performance Measures20
Problem Formulation
Performance Measures
Power Amplitude and Phase
Laplace Transform Tail Probability
Characteristic Function
Required assumptions
Approximate tails if closed-form not possible
Key Prior Work My Approach
Advantage: Closed-form expressions derived relatively easilyDisadvantage: Asymptotically exact for low outage regimes (simulations also match in high outage regimes)
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Wireless Networking and Communications Group
Joint Temporal Statistics of Interference21
Interference vector Follows a 2n-dimensional symmetric alpha stable
Exact when [Ilow & Hatzinakos, 1998]
Dissertation provides theorems to show Joint amplitude tail probabilities dominated by isotropic component
(i.e., due to users active in time slots 1 through n)
Depends on LDepends on fading and
emissions
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Wireless Networking and Communications Group
Local Delay22
Average time slots to have one successful transmission
Dissertation also derives Throughput outage probability Average network throughput
0 20 40 60 80 1001
1.5
2
2.5
Inverse of SIR threshold for successful detection (T-1)
Lo
cal D
ela
y
Without power control (Simulated)Without power control (Estimated)With power control (Simulated)With power control (Estimated)
= 6
= 4
Network Model II
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0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Outage Constraint ()
Tra
nsm
issi
on
Ca
pa
city
[ in
bp
s/H
z/a
rea
]
Truncated Poisson lifetime distributionNumerically optimized overfeasible lifetime distributions
Wireless Networking and Communications Group
Transmission Capacity (TC)23
Defined assuming temporal independence [Weber et al., 2005]
Extension:
Network Model II
Goodput: ~1.8x
Improved Reliability
Motivates designing MAC protocols that achieve optimum lifetime distribution
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Wireless Networking and Communications Group
Contribution #324
Pre-filter Design to Mitigate RFI
Joint temporal statistics of interference • Poisson field with temporal correlation• Entire plane• Bounded pathloss function
Distance measure robust to impulsive statistics of interference• Scale Correntropy Induced Metric space using zero-order statistics
Pre-filter structures• Modify selection filter (S filter) • Modify combination filter (Ll filter)
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Wireless Networking and Communications Group
Network Model I and II25
Multivariate GMM RFI under bounded pathloss Inphase/quadrature samples dependent but uncorrelated Individually temporally dependent but uncorrelated
Sliding window pre-filters for single-carrier uncoded systems
Prior work on mitigating GMM noise
Map to QAM Constellation
Transmit Pulse Shape Filter Pre-Filter Matched
Filter DemappingBitsReceived Bits
RFIThermal
Noise
Pre-Filter Prior Work Distance Temp. Dep.Bank of Wiener filters [Eldar & Yeredor, 2001] L2 Norm No
Bank of Gaussian Particle filters [Kotecha & Djuric, 2003] L2 Norm No
Order Statistic filters Not based on RFI statistics (Some)
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-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Wireless Networking and Communications Group
Choosing a Distance Measure for GMM26
Correntropy Induced Metric (CIM) [Liu & Principe, 2007]
Prior work did not adapt parameter based on RFI statistics
L2
L1
L0
L2
L1
L0
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Wireless Networking and Communications Group
Zero-Order Statistics of RFI to Scale CIM27
Zero-order statistics (ZOS) [Gonzalez et al., 2006]
Use as approximate Gaussian power
Approximate lower bound on error
Window of received samples
Scale CIM Space
0 200 400 600 800 1000-5
-4
-3
-2
-1
0
1
2
3
4
5
Sample Number
Sam
ple
Val
ue
0 200 400 600 800 1000-5
-4
-3
-2
-1
0
1
2
3
4
5
Sample Number
Gaussian mixture processwith ZOS = 0.2021, variance = 1,mix. probs. = [0.9 0.1], mix. vars. = [0.09 9.17]
Gaussian processwith ZOS = 0.2021 and variance 2
ZOS(I) = 0.1454
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-30 -20 -10 0 10 20 3010
-4
10-3
10-2
10-1
100
Signal-to-Interference ratio (SIR) in dB
Sym
bo
l Err
or
Ra
te (
SE
R)
Matched FilterS Pre-filter (S-CIM)Ll Pre-filter (S-CIM)Approximatelower bound
Wireless Networking and Communications Group
Simulation Results28
>20 dB gain
-30 -20 -10 0 10 20 3010
-4
10-3
10-2
10-1
100
Signal-to-Interference Ratio (SIR) in dBS
ymb
ol E
rro
r R
ate
(S
ER
)
Matched FilterS Pre-filter (L
2 norm)
S Pre-filter (L1 norm)
S Pre-filter (S-CIM)Approximatelower bound
5dB
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Wireless Networking and Communications Group
Conclusions29
Statistical Modeling of RFI• Instantaneous statistics of RFI• Applicability to ad hoc, cellular, local area & femtocell networks
Communication Performance Analysis of Wireless Networks• Decentralized wireless networks with temporal correlation• Unveiled 2x “potential” improvement in network throughput
RFI Mitigation at PHY Layer• Pre-filtering methods mitigate RFI• Improve link efficiency up to 20 dB
Contribution #1
Contribution #2
Contribution #3
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Wireless Networking and Communications Group
Software Release30
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", copyright © 2006-2011 by The University of Texas at Austin.
Latest Toolbox Release: Version 1.6, April 2011Website: http://users.ece.utexas.edu/~bevans/projects/rfi/software
Snapshot of a demo
0 5 10 15 20 25 30 35 4010
-4
10-3
10-2
10-1
100
SNR [in dB]
Sym
bol E
rror
Rat
e
2x2 MIMO systems in Middleton Class A noise
SM with Opt MLSM with SubOpt ML (Two-Piece)SM with SubOpt ML (Four-Piece)SM with Gaussian MLSM with ZF Alamouti
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Wireless Networking and Communications Group
Future Work31
Statistical Modeling Non-Poisson based interferer locations
Communication Performance Analysis of Wireless Networks Multi-hop communications
Receiver Design to Mitigate RFI MAC: Decentralized protocol to control temporal dependence PHY: Use of ZOS scaled CIM as distance measure
Extensions to Single-carrier MIMO Single-antenna OFDM MIMO-OFDM
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Wireless Networking and Communications Group
Related Publications32
Journal Publications• K. Gulati, B. L. Evans, and S. Srikanteshwara, “Interference Modeling and Mitigation
in Decentralized Wireless Networks with Temporal Correlation”, in preparation.• K. Gulati, R. K. Ganti, J. G. Andrews, B. L. Evans, and S. Srikanteshwara, “Throughput,
Delay, and Reliability of Decentralized Wireless Networks with Temporal Correlation”, IEEE Transactions on Wireless Communications, to be submitted.
• 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, Vol. 58, No. 19, Dec 2010.
• M. Nassar, K. Gulati, M. R. DeYoung, B. L. Evans and K. R. Tinsley, “Mitigating Near-Field Interference in Laptop Embedded Wireless Transceivers”, Journal of Signal Processing Systems, Mar. 2009, invited paper.
Conference Publications• M. Nassar, K. Gulati, Y. Mortazavi, and B. L. Evans, “Statistical Modeling of
Asynchronous Impulsive Noise in Powerline Communication Networks”, Proc. IEEE Global Communications Conf., Dec. 5-9, 2011, Houston, Texas, USA, submitted.
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Wireless Networking and Communications Group
Related Publications33
Conference Publications (cont…)• 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, Dallas, Texas USA.
• 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, Hawaii.
• 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.
• 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.
• 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.
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Wireless Networking and Communications Group
34
Thanks !
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Wireless Networking and Communications Group
Selected References35
RFI Modeling1. 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. Applied Physics, 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 Trans. on Signal Proc., vol. 46, no. 6, pp. 1601-1611, Jun. 1998.
4. E. S. Sousa, “Performance of a spread spectrum packet radio network link in a Poisson field of interferers,” IEEE Trans. on Info. 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 Trans. on Signal Proc., 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 Trans. on Vehicular Tech., 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,” Proc. of the IEEE, vol. 97, no. 2, pp. 205–230, Feb. 2009.
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Wireless Networking and Communications Group
Selected References36
Parameter Estimation1. 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 Networks3. M. Haenggi and R. K. Ganti, “Interference in large wireless networks,” in Foundations and Trends in
Networking. Now Publishers Inc., Dec. 2008, vol. 3, no. 2, pp. 127-248.4. F. Baccelli and B. Blaszczyszyn, “Stochastic geometry and wireless networks, volume 1 – theory”, in
Foundations and Trends in Networking. Now Publishers Inc., Mar. 2009, vol. 3, no. 3-4, pp. 249-449.5. F. Baccelli and B. Blaszczyszyn, “Stochastic geometry and wireless networks, volume 2 – applications”,
in Foundations and Trends in Networking. Now Publishers Inc., Mar. 2009, vol. 4, no. 1-2, pp. 1-312.6. R. Ganti and M. Haenggi, “Interference and outage in clustered wireless ad hoc networks,” IEEE Trans.
on Info. Theory, vol. 55, no. 9, pp. 4067–4086, Sep. 2009.7. A. Hasan and J. G. Andrews, “The guard zone in wireless ad hoc networks,” IEEE Trans. on Wireless
Comm., vol. 4, no. 3, pp. 897–906, Mar. 2007.
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Wireless Networking and Communications Group
Selected References37
Communication Performance of Wireless Networks (cont…)6. X. Yang and G. de Veciana, “Inducing multiscale spatial clustering using multistage MAC contention in
spread spectrum ad hoc networks,” IEEE/ACM Trans. on Networking, vol. 15, no. 6, pp. 1387–1400, Dec. 2007.
7. S. Weber, X. Yang, J. G. Andrews, and G. de Veciana, “Transmission capacity of wireless ad hoc networks with outage constraints,” IEEE Trans. on Info. Theory, vol. 51, no. 12, pp. 4091-4102, Dec. 2005.
8. S. Weber, J. G. Andrews, and N. Jindal, “The effect of fading, channel inversion, and threshold scheduling on ad hoc networks,” IEEE Trans. on Info. Theory, vol. 53, no. 11, pp. 4127-4149, Nov. 2007.
9. J. G. Andrews, S. Weber, M. Kountouris, and M. Haenggi, “Random access transport capacity,” IEEE Trans. On Wireless Comm., vol. 9, no. 6, pp. 2101-2111, Jun. 2010.
10. M. Haenggi, “Local delay in static and highly mobile Poisson networks with ALOHA," in Proc. IEEE Int. Conf. on Comm., Cape Town, South Africa, May 2010.
11. F. Baccelli and B. Blaszczyszyn, “A New Phase Transitions for Local Delays in MANETs,” in Proc. of IEEE Int. Conf. on Computer Comm., San Diego, CA, Mar. 14-19 2010, pp. 1-6.
12. R. K. Ganti and M. Haenggi, “Spatial and Temporal correlation of the interference in ALOHA ad hoc networks,” IEEE Comm. Letters, vol. 13, no. 9, pp. 631-633, Sep. 2009.
13. H. Inaltekin, S. B. Wicker, M. Chiang, and H. V. Poor, "On unbounded path-loss models: effects of singularity on wireless network performance," IEEE Journal on Selected Areas in Comm., vol. 27, no. 7, pp. 1078-1092, Sep. 2009.
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Wireless Networking and Communications Group
Selected References38
Receiver Design to Mitigate RFI1. A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment-
Part I: Coherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 19772. 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, Feb 20013. 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 Proc. 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 Trans. on Circuits and Systems II: Analog and Digital Signal Proc., vol. 48, no. 11, pp. 1069-1077, Nov. 2001.
6. J. H. Kotecha and P. M. Djuric, “Gaussian sum particle filtering,” IEEE Trans. on Signal Proc., vol. 51, no. 10, pp. 2602-2612, Oct. 2003.
7. J. G. Gonzalez, J. L. Paredes, and G. R. Arce, "Zero-order statistics: A mathematical framework for the processing and characterization of very impulsive signals," IEEE Trans. on Signal Proc., vol. 54, no. 10, pp. 3839-3851, Oct. 2006.
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Wireless Networking and Communications Group
Selected References39
Receiver Design to Mitigate RFI8. J. G. Gonzalez, J. L. Paredes, and G. R. Arce, "Zero-order statistics: A mathematical framework for
the processing and characterization of very impulsive signals," IEEE Trans. on Signal Proc., vol. 54, no. 10, pp. 3839-3851, Oct. 2006.
9. W. Liu, P. P. Pokharel, and J. C. Principe, "Correntropy: Properties and applications in non-Gaussian signal processing," IEEE Trans. on Signal Proc., vol. 55, no. 11, pp. 5286-5298, 2007.
10. W. Liu, P. P. Pokharel, and J. C. Principe, "Error entropy, correntropy and M-estimation," in Proc. IEEE Workshop on Machine Learning for Signal Proc., Arlington, VA, Sep. 6-8 2006, pp. 179-184.
11. J. Haring and A. J. H. Vinck, "Iterative decoding of codes over complex numbers for impulsive noise channels," IEEE Trans. on Info. Theory, vol. 49, no. 5, pp. 1251-1260, May 2003.
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Wireless Networking and Communications Group
Backup Slides40
Introduction Summary of interference mitigation methods Interference avoidance, alignment, and cancellation methods Femtocell networks
Statistical Modeling of RFI Impact of RFI Computational platform noise modeling results Transients in digital FIR filters Spatial Poisson Point Process Poisson field of interferers Poisson-Poisson cluster field of interferers
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Wireless Networking and Communications Group
Backup Slides (cont…)41
Communication Performance of Wireless Networks Performance Analysis of Wireless Networks Ad hoc networks with guard zones Local Delay Decentralized networks with temporal correlation
Local Delay Throughput Outage Probability Transmission Capacity
Parameter Estimation Expectation maximization overview Extreme order statistics based estimator for Alpha Stable
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Wireless Networking and Communications Group
Backup Slides (cont…)42
Receiver Design to Mitigate RFI Gaussian mixture vs. Alpha Stable Mitigating RFI in SISO systems Mitigating RFI in 2x2 MIMO systems Pre-filtering methods to mitigate RFI
Pre-filtering methods to mitigate GMM distributed RFI Joint temporal statistics Distance Measure Correntropy Induced Metric Zero-order Statistics
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Wireless Networking and Communications Group
Backup Slides (cont…)43
Pre-filtering methods to mitigate GMM RFI (cont…) Pre-filters Computational complexity Applications of ZOS scaled CIM space
OFDM Turbo Decoders
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Wireless Networking and Communications Group
Interference Mitigation Techniques44
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Wireless Networking and Communications Group
Interference Mitigation Techniques (cont…)45
Interference avoidance CSMA / CA
Interference alignment Example:
[Cadambe & Jafar, 2007]
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Wireless Networking and Communications Group
Interference Mitigation Techniques (cont…)46
Interference cancellationRef: J. G. Andrews, ”Interference Cancellation for Cellular Systems: A Contemporary Overview”, IEEE Wireless Communications Magazine, Vol. 12, No. 2, pp. 19-29, April 2005
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Wireless Networking and Communications Group
Femtocell Networks47
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
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Wireless Networking and Communications Group
Common Spectral Occupancy4848
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
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Wireless Networking and Communications Group
Impact of RFI49
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)
49
floor noise RX
ceInterferenfloor noise RXlog10 10desense
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Wireless Networking and Communications Group
Impact of LCD clock on 802.11g50
Pixel clock 65 MHz LCD Interferers and 802.11g center frequencies
50
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
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Results on Measured RFI Data51
25 radiated computer platform RFI data sets from Intel 50,000 samples taken at 100 MSPS
Wireless Networking and Communications Group
0 5 10 15 20 250
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Measurement Set
Kul
lbac
k-Le
ible
r di
verg
ence
Symmetric Alpha StableMiddleton Class AGaussian Mixture ModelGaussian
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Wireless Networking and Communications Group
Results on Measured RFI Data52
For measurement set #23
0 1 2 3 4 5 6 7 8 910
-20
10-15
10-10
10-5
100
Threshold Amplitude (a)
Tai
l Pro
babi
litie
s [P
(X >
a)]
EmpiricalMiddleton Class A
Symmteric Alpha StableGaussianGaussian Mixture Model
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50 100 150 200
-0.5
0
0.5
Inpu
t
50 100 150 200
-1
-0.5
0
0.5
1
Filt
er O
utpu
t
Wireless Networking and Communications Group
Transients in Digital FIR Filters53
25-Tap FIR Filter• Low pass• Stopband freq. 0.22 (normalized)
Input Output
Freq = 0.16
Interference duration = 10 * 1/0.22 Interference duration = 100 x 1/0.22
Transients
Transients Significant w.r.t. Steady State
100 200 300 400 500 600
-0.5
0
0.5
Inpu
t
100 200 300 400 500 600-1
-0.5
0
0.5
1
Filt
er O
utpu
t
Transients Ignorable w.r.t. Steady State
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Wireless Networking and Communications Group
Homogeneous Spatial Poisson Point Process54
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Wireless Networking and Communications Group
Poisson Field of Interferers55
Applied to wireless ad hoc networks, cellular networksClosed Form Amplitude Distribution
Model Interference Region Key Prior WorkSymmetric Alpha Stable Spatial Entire plane [Sousa, 1992]
[Ilow & Hatzinakos, 1998][Yang & Petropulu, 2003]
Middleton Class A Spatio-temporal Finite area [Middleton, 1977, 1999]Other Interference Statistics – closed form amplitude distribution not derived
Statistics Interference Region Key Prior WorkMoments Spatial Finite area [Salbaroli & Zanella, 2009]Characteristic Function Spatial Finite area [Win, Pinto & Shepp,2009]
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Wireless Networking and Communications Group
Poisson Field of Interferers56
Interferers distributed over parametric annular space
Log-characteristic function
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Wireless Networking and Communications Group
Poisson Field of Interferers57
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Wireless Networking and Communications Group
Poisson Field of Interferers58
Simulation Results (tail probability)
0.1 0.2 0.3 0.4 0.5 0.6 0.710
-3
10-2
10-1
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[ P (
|Y| >
y)
]
Simulated
Symmetric Alpha Stable
0.1 0.2 0.3 0.4 0.5 0.6 0.710
-15
10-10
10-5
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[ P (
|Y| >
y)
]
SimulatedSymmetric Alpha StableGaussianMiddleton Class A
Gaussian and Middleton Class A models are not applicable since mean intensity is infinite
Case I: Entire Plane Case III: Infinite-area with guard zone
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Wireless Networking and Communications Group
Poisson Field of Interferers59
Simulation Results (tail probability)
Case II: Finite area annular region
0 0.1 0.2 0.3 0.4 0.5 0.6 0.710
-15
10-10
10-5
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[P(|
Y| >
y)]
SimulatedSymmetric Alpha StableGaussianMiddleton Class A
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Wireless Networking and Communications Group
Poisson-Poisson Cluster Field of Interferers60
Applied to femtocell networks, cellular and ad hoc networks with user clustering
Clustering due to Geographical factors (femtocell networks) Medium Access Control (MAC) layer protocols
[Yang & de Veciana, 2007] Prior Work
Closed form amplitude distribution not derived
Statistics Interference Region Key Prior WorkOutage Probability Spatial Entire Plane [Ganti & Haenggi, 2009]Characteristic Function Temporal - [Furutsu & Ishida, 1961]
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Wireless Networking and Communications Group
Poisson-Poisson Cluster Field of Interferers61
Cluster centers distributed as spatial Poisson process over
Interferers distributed as spatial Poisson process
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Wireless Networking and Communications Group
Poisson-Poisson Cluster Field of Interferers62
Log-Characteristic function Return
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Wireless Networking and Communications Group
Poisson-Poisson Cluster Field of Interferers63
Simulation Results (tail probability)
0.1 0.2 0.3 0.4 0.5 0.6 0.710
-12
10-10
10-8
10-6
10-4
10-2
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[ P (
|Y| >
y)
]
SimulatedSymmetric Alpha Stable
GaussianGaussian Mixture Model
0.1 0.2 0.3 0.4 0.5 0.6 0.710
-4
10-3
10-2
10-1
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[ P (
|Y| >
y)
]
Simulated
Symmetric Alpha Stable
Gaussian and Gaussian mixture models are not applicable since mean intensity is infinite
Case I: Entire Plane Case III: Infinite-area with guard zone
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Wireless Networking and Communications Group
Poisson-Poisson Cluster Field of Interferers64
Simulation Results (tail probability)
Case II: Finite area annular region
0 0.1 0.2 0.3 0.4 0.5 0.6 0.710
-15
10-10
10-5
100
Interference amplitude (y)
Tai
l Pro
babi
lity
[P(|
Y| >
y)]
SimulatedSymmetric Alpha StableGaussianGaussian Mixture Model
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Summary of Contribution #1
• Sensor networks• Ad hoc networks
• Dense Wi-Fi networks
• Cluster of hotspots (e.g. marketplace)
• In-cell and out-of-cell femtocell users
• Out-of-cell femtocell users
• Cellular networks• Hotspots (e.g. café)
Symmetric Alpha Stable
Poisson field of interferers
• Ad hoc networks• Cellular networks
Poisson-Poisson Cluster field of
interferers• Femtocell networks
Gaussian Mixture Model
65
Wireless Networking and Communications Group
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Wireless Networking and Communications Group
Performance Analysis of Wireless Networks66
Interference statistics useful for Communication performance analysis of wireless networks Deriving network strategies to improve performance
Both Physical (PHY) and Medium Access Control (MAC) Layer Communication performance measures
Outage Probability
Key Prior WorkDerives bounds in Poisson field of interferers [Weber, Andrews & Jindal, 2007]Proposed WorkImprove analysis based on tail probabilities of statistical models
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Wireless Networking and Communications Group
Performance Analysis of Wireless Networks (cont…)67
Proposed Contribution #2 [future work]
Spatial Throughput [Weber, Andrews & Jindal, 2007]Expected spatial density of successful transmissions
Limitation: Quality-of-service constraints not included
Transmission Capacity [Weber, Yang, Andrews & de Veciana, 2005]
Enables quantitative design tradeoffs for both PHY and MAC layer techniquesLimitation: Only simultaneous single hop transmissions captured
Random Access Transport Capacity [Andrews, Weber, Kountouris & Haenggi, 2010]Includes multihop transmissionsBridges gap between asymptotic throughput scaling and transmission capacity
Local Delay [Haenggi, 2010][Baccelli & Blaszczyszyn, 2010]Expected number of retransmissions for successful reception of packet
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Wireless Networking and Communications Group
Ad hoc Networks with Guard Zones (GZs)68
System Model Return
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Wireless Networking and Communications Group
Point Processes for Networks with GZs69
Modified Matern hardcore [Baccelli, 2009]
Neighbor set (received power based) [Baccelli, 2009]
Neighbor set (distance based) [Hasan & Andrews, 2007]
Limitation: Underestimates intensity
Simple Sequential Inhibition [Busson, Chelius & Gorce, 2009] Even intensity expression not known
1 2 3
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Wireless Networking and Communications Group
Ad hoc networks with GZ: Prior Work70
Transmission Capacity, Optimum GZ size[Hasan & Andrews, 2007] AS1: Poisson distributed AS2: Sum interference is Gaussian AS3: Distance based GZ creation
Limitation: Gaussian assumption may not be valid Plan of Work: Use Middleton Class A statistics
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Wireless Networking and Communications Group
Ad hoc networks with GZ: Prior Work71
Outage Probability [Baccelli, 2009] AS1: Poisson distributed AS2: Received power based GZ creation
Limitation: Closed form for Rayleigh fading only
Return
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Wireless Networking and Communications Group
Probability of Successful Transmission72
Return
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Wireless Networking and Communications Group
Local Delay: Definition73
Expected time slots till packet is successfully received Probability of success
Conditional Local Delay – Geometric with mean Local Delay
Return
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Wireless Networking and Communications Group
Local Delay: Prior Work74
Prior Work [Haenggi, 2010][Baccelli, 2010]
Phase transition for static Poisson networks Due to SINR model for connectivity Avoided by using adaptive coding [Baccelli, 2010]
Poisson Networks with ALOHAStatic Highly Mobile
Finite for transmit probability (for ALOHA) below a threshold
Finite local delay
Minimum Local Delay:
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Wireless Networking and Communications Group
Local Delay75
Return
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Wireless Networking and Communications Group
Local Delay (cont…)76
0 20 40 60 80 1001
1.5
2
2.5
Inverse of SIR threshold for successful detection (T-1)
Lo
cal D
ela
y
Without power control (Simulated)Without power control (Estimated)With power control (Simulated)With power control (Estimated)
= 6
= 4
Network Model IINetwork Model I
Return
0 20 40 60 80 1001
1.02
1.04
1.06
1.08
1.1
1.12
1.14
1.16
1.18
1.2
Inverse of SIR threshold for successful detection (T-1)
Lo
cal D
ela
y
(Simulated) With rayleigh fading(Estimated) With rayleigh fading(Simulated) Without fading(Estimated) Without fading
= 4
= 6
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Wireless Networking and Communications Group
Throughput Outage Probability77
Derived closed-form expressions using joint tail probability
0 20 40 60 80 100
10-2
10-1
100
101
Inverse of SIR threshold for successful detection (T-1)
Pro
b (
# s
ucc
ess
es
in L
ma
x tim
e s
lots
< s
)
s = 1 (Simulated)s = 1 (Estimated)s = 2 (Simulated)s = 2 (Estimated)s = 3 (Simulated)s = 3 (Estimated)s = 4 (Simulated)s = 4 (Estimated)
Network Model II
Return
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Wireless Networking and Communications Group
Throughput Outage Probability (cont…)78
Network Model I
Return
0 20 40 60 80 10010
-3
10-2
10-1
100
Inverse of SIR threshold for successful detection (T-1)
Th
rou
gh
pu
t ou
tag
e p
rob
ab
ility
[Pro
b (
# s
ucc
ess
es
in L
ma
x tim
e s
lots
< s
)]
s = 1 (Simulated)s = 1 (Estimated)s = 2 (Simulated)s = 2 (Estimated)s = 3 (Simulated)s = 3 (Estimated)s = 4 (Simulated)s = 4 (Estimated)
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Wireless Networking and Communications Group
Average Network Throughput79
Return
Network Model II
20 40 60 80 100 120 140 160 180 2000
0.1
0.2
0.3
0.4
0.5
Inverse of SIR threshold for successful detection (T-1)
Ave
rag
e N
etw
ork
Th
rou
gh
pu
t (Ca
v )[in
bp
s/H
z/a
rea
]
= 0.01 (Simulated) = 0.01 (Estimated) = 0.005 (Simulated) = 0.005 (Estimated)
= 0.005
= 0.01
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Wireless Networking and Communications Group
Transmission Capacity80
Defined assuming temporal independence [Weber et al., 2005]
Extension:
0 0.2 0.4 0.6 0.8 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Outage Constraint ()
Tra
nsm
issi
on
Ca
pa
city
[ in
bp
s/H
z/a
rea
]
Truncated Poisson lifetime distributionOptimized over all lifetime distributions
Lmax
= 20
Lmax
= 40
Network Model II
Goodput: ~1.8x
Improved Reliability
Motivates designing MAC protocols that achieve optimum lifetime distribution
Return
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Wireless Networking and Communications Group
Transmission Capacity (cont…)81
Optimal Lifetime distribution (via numerical optimization)
Network Model II
0 5 10 15 20 25 30 35 400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Time slots
Pro
ba
bili
ty D
en
sity
Fu
nct
ion
of L
ifetim
e Using fmincon function in MATLAB• Active set algorithm
Return
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Wireless Networking and Communications Group
Expectation Maximization Overview8282
Return
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Wireless Networking and Communications Group
Extreme Order Statistics8383
Return
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Wireless Networking and Communications Group
Parameter Estimators for Alpha Stable8484
0 < p < α
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Wireless Networking and Communications Group
Particle Filtering85
Ref: P. Djuric et. al., “Particle Filtering,” IEEE Signal Processing Magazine, vol. 20, no. 5, September 2003, pp: 19-38.
Return
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Wireless Networking and Communications Group
Gaussian Mixture vs. Alpha Stable86
Gaussian Mixture vs. Symmetric Alpha Stable
Gaussian Mixture Symmetric Alpha StableModeling Interferers distributed with Guard
zone around receiver (actual or virtual due to PL)
Interferers distributed over entire plane
Pathloss Function
With GZ: singular / non-singularEntire 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
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Wireless Networking and Communications Group
RFI Mitigation in SISO Systems8787
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
Mitigation of computational platform noise in single carrier, single antenna systems [Nassar, Gulati, DeYoung, Evans & Tinsley, ICASSP 2008, JSPS 2009]
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Wireless Networking and Communications Group
Filtering and Detection8888
Pulse Shaping Pre-Filtering Matched
FilterDetection
Rule
Impulsive Noise
Middleton Class A noise Symmetric Alpha Stable noise
Filtering Wiener Filtering (Linear)
Detection Correlation Receiver (Linear) Bayesian Detector
[Spaulding & Middleton, 1977] Small Signal Approximation to
Bayesian detector[Spaulding & Middleton, 1977]
Filtering Myriad Filtering
Optimal Myriad [Gonzalez & Arce, 2001]
Selection Myriad Hole Punching
[Ambike et al., 1994]
Detection Correlation Receiver (Linear) MAP approximation
[Kuruoglu, 1998]
AssumptionMultiple samples of the received signal are available• N Path Diversity [Miller, 1972]• Oversampling by N [Middleton, 1977]
Return
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Wireless Networking and Communications Group
Results: Class A Detection8989
Pulse shapeRaised cosine
10 samples per symbol10 symbols per pulse
ChannelA = 0.35
= 0.5 × 10-3
Memoryless
Method Comp. Complexity
Detection Perform.
Correl. Low LowWiener Medium LowBayesian S.S. Approx.
Medium High
Bayesian High High-35 -30 -25 -20 -15 -10 -5 0 5 10 15
10-5
10-4
10-3
10-2
10-1
100
SNR
Bit
Err
or R
ate
(BE
R)
Correlation ReceiverWiener FilteringBayesian DetectionSmall Signal Approximation
Communication Performance
Binary Phase Shift KeyingReturn
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Wireless Networking and Communications Group
Results: Alpha Stable Detection9090
Use dispersion parameter g in place of noise variance to generalize SNR
Method Comp. Complexity
Detection Perform.
Hole Punching
Low Medium
Selection Myriad
Low Medium
MAP Approx.
Medium High
Optimal Myriad
High Medium
-10 -5 0 5 10 15 20
10-2
10-1
100
Generalized SNR (in dB)
Bit
Err
or R
ate
(BE
R)
Matched FilterHole PunchingMAPMyriad
Communication Performance
Same transmitter settings as previous slideReturn
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Wireless Networking and Communications Group
RFI Mitigation in 2x2 MIMO Systems9191
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
2 x 2 MIMO receiver design in the presence of RFI[Gulati, Chopra, Heath, Evans, Tinsley & Lin, Globecom 2008]
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92Wireless Networking and Communications Group
Bivariate Middleton Class A Model
Joint spatial distribution
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
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93Wireless Networking and Communications Group
Results on Measured RFI Data
50,000 baseband noise samples represent broadband interference
Estimated Parameters
Bivariate Middleton Class A
Overlap Index (A) 0.313
2D-KL Divergence
1.004
Gaussian Factor (G1) 0.105
Gaussian Factor (G2) 0.101
Correlation (k) -0.085
Bivariate Gaussian
Mean (µ) 0
2D-KL Divergence
1.6682
Variance (s1) 1
Variance (s2) 1
Correlation (k) -0.085
-4 -3 -2 -1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
1.2
1.4
Noise amplitude
Pro
ba
bili
ty D
en
sity
Fu
nct
ion
Measured PDFEstimated MiddletonClass A PDFEqui-powerGaussian PDF
Marginal PDFs of measured data compared with estimated model densities
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94
2 x 2 MIMO System
Maximum Likelihood (ML) receiver
Log-likelihood function
Wireless Networking and Communications Group
System Model
Sub-optimal ML Receiversapproximate
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Wireless Networking and Communications Group
Sub-Optimal ML Receivers95
Two-piece linear approximation
Four-piece linear approximation
-5 -4 -3 -2 -1 0 1 2 3 4 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
z
Ap
pro
xma
tion
of
(z)
(z)
1(z)
2(z)
chosen to minimizeApproximation of
Return
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96Wireless Networking and Communications Group
Results: Performance Degradation
Performance degradation in receivers designed assuming additive Gaussian noise in the presence of RFI
-10 -5 0 5 10 15 2010
-5
10-4
10-3
10-2
10-1
100
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
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)
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
Severe degradation in communication performance in
high-SNR regimes
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Wireless Networking and Communications Group
Results: RFI Mitigation in 2 x 2 MIMO 97
-10 -5 0 5 10 15 20
10-3
10-2
10-1
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
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)
97
A Noise Characteristic
Improve-ment
0.01 Highly Impulsive ~15 dB0.1 Moderately
Impulsive ~8 dB
1 Nearly Gaussian ~0.5 dB
Improvement in communication performance over conventional Gaussian ML receiver at symbol
error rate of 10-2
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
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Wireless Networking and Communications Group
Results: RFI Mitigation in 2 x 2 MIMO 9898
Complexity AnalysisReceiver
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 for decoding M-level QAM modulated signal
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
-10 -5 0 5 10 15 20
10-3
10-2
10-1
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
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)
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Wireless Networking and Communications Group
Pre-filtering Methods to Mitigate RFI99
Pre-filtering based on statistical models
Gaussian Mixture Filtering (MMSE objective function) Non-linear combination of banks of Weiner filter Non-linear combination of banks of Gaussian Particle Filters
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Wireless Networking and Communications Group
Pre-filtering for Gaussian mixture noise100
Closed form objective function or filter structure for BER optimality not known
Finite-memory minimum mean squared error (MMSE) filter [Eldar & Yeredor, 2001] Filtering Gaussian signal in Gaussian mixture noise Non-linear combination of bank of Wiener filters Good for highly impulsive noise
Gaussian sum particle filters [Kotecha & Djuric, 2003] Bank of Gaussian particle filters
Order-statistic filtering Linear combination of ordered data
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Wireless Networking and Communications Group
Order Statistic Filtering101
Linear combination of order statistics Return
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Wireless Networking and Communications Group
Joint Temporal Statistics102
Bounded Pathloss Function
Network Model II
Return
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Wireless Networking and Communications Group
Distance Measure103
Example: Constant signal in noise
Optimal distance measure depends on noise statistics Not known for GMM noise
0 10 20 30 40 50 60 70 80 90 100-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Sample Number
Sam
ple
Val
ues
(x)
L2 Norm
L1 Norm
0 10 20 30 40 50 60 70 80 90 100-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
Sample Number
Sam
ple
Val
ues
(x)
L1 Norm
L2 Norm
Impulsive NoiseNearly Gaussian Noise
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Wireless Networking and Communications Group
Correntropy Induced Metric (CIM)104
Sample estimator of Correntropy [Liu and Principe, 2007]Return
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Wireless Networking and Communications Group
Zero-Order Statistics105
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Wireless Networking and Communications Group
Zero-Order Statistics (cont…)106
“Gaussian part” of non-Gaussian random process
0 2 4 6 8 10 12 1410
-6
10-5
10-4
10-3
10-2
10-1
100
Amplitude threshold
CC
DF
Gaussian with variance 2ZOS(i)
Gaussian mixture process withmix. probs. [0.7 0.2 0.1]mix vars. [1 10 20]
Return
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Wireless Networking and Communications Group
Pre-filters 107
Sliding windowSelection Pre-filter Modified Ll Pre-filter
Selection Pre-filter
Adaptive Update with J(error)
Training data
J(x) Optimal forL2 Norm Gaussian
L1 Norm Laplacian
CIM N/A
Ll Pre-filter
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Wireless Networking and Communications Group
Simulation Results108
-30 -20 -10 0 10 20 3010
-4
10-3
10-2
10-1
100
Signal-to-Interference ratio (SIR) in dB
Sym
bo
l Err
or
Ra
te (
SE
R)
Matched FilterS Pre-filter (S-CIM)Ll Pre-filter (S-CIM)Approximatelower bound
-30 -20 -10 0 10 20 3010
-4
10-3
10-2
10-1
100
Signal-to-Interference Ratio (SIR) in dBS
ymb
ol E
rro
r R
ate
(S
ER
)
Matched FilterS Pre-filter (L
2 norm)
S Pre-filter (L1 norm)
S Pre-filter (S-CIM)Approximatelower bound
Return
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Wireless Networking and Communications Group
Simulation Results (cont…)109
-30 -20 -10 0 10 20 3010
-4
10-3
10-2
10-1
100
Signal-to-Interference Ratio (SIR) in dB
Sym
bo
l Err
or
Ra
te (
SE
R)
Matched FilterLl Pre-filter (L
2 norm)
Ll Pre-filter (L1 norm)
Ll Pre-filter (S-CIM)Approximatelower bound
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Wireless Networking and Communications Group
Simulation Results (cont…)110
Gaussian distributed interference
-10 -5 0 5 1010
-4
10-3
10-2
10-1
100
Signal-to-Interference Ratio (SIR) in dB
Sym
bo
l Err
or
Ra
te (
SE
R)
Matched FilterS Pre-filter (S-CIM)Ll Pre-filter (S-CIM)Approximate lower bound
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Wireless Networking and Communications Group
Computational Complexity111
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Wireless Networking and Communications Group
Computational Complexity (cont…)112
Zero-order statistics from N received samples N-1 multiplications 1 table lookup to evaluate Nth root
Correntropy Induced Metric (additional over L2 norm) 1 multiplication 1 exponential evaluation (table lookup) 1 subtraction 1 square root evaluation (table lookup)
Not required if max/min operation on distance is being performed
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Wireless Networking and Communications Group
Pre-filtering in OFDM Systems113
OFDM transmissions with nyquist sampling at receiver
-10 -5 0 5 10 15 20 2510
-4
10-3
10-2
10-1
100
Signal-to-Interference Ratio (SIR) in dB
Sym
bo
l Err
or
Ra
te (
SE
R)
Matched FilterClippingBlankingApproximatelower bound
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Wireless Networking and Communications Group
Pre-filtering in OFDM Systems (cont…)114
OFDM transmissions with 7x oversampling at receiver
-10 -5 0 5 10 15 20 2510
-4
10-3
10-2
10-1
100
Signal-to-Interference Ratio (SIR) in dB
Sym
bo
l Err
or
Ra
te (
SE
R)
Matched FilterClippingBlankingLl Pre-filter (S-CIM)Approximatelower bound
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Turbo Decoder
Decoder 1Parity 1Systematic Data
Decoder 2
Parity 2
1
-
-
-
-
A-priori Information
Depends on channel statistics
Independent of channel statistics
Independent of channel statistics
Extrinsic Information
115
Wireless Networking and Communications Group
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Wireless Networking and Communications Group
Turbo Decoder (cont…)116
Gaussian noise
Non-Gaussian noise (requires knowledge of noise statistics)
Proposed: Based on ZOS scaled CIM spaceS-CIM instead of L2 norm
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Wireless Networking and Communications Group
Turbo Decoder (Preliminary Results)117
-30 -25 -20 -15 -10 -5 010
-4
10-3
10-2
10-1
100
Signal-to-Interference Ratio (SIR) in dB
Sym
bo
l Err
or
Ra
te (
SE
R)
L2 Norm
S-CIMApproximatelower bound
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Wireless Networking and Communications Group
ESPL Research in RFI Modeling and Mitigation118
ESPL Research in RFI Modeling and Mitigation
RFI Modeling
Student Methods Antennas Carrier Multipath Time Samples Measured FittingKapil Statistical Physical Single Single No Dependent Computational Platform NoiseAditya Statistical Physical Multiple Single Yes IndependentMarcel Statistical Physical Single Multiple No Dependent Computational Platform Noise
Receiver Design in the Presence of RFI
Student Antennas Carrier Coding Multipath FocusKapil Single / Multiple Single No No Filtering methodsAditya Single / Multiple Single No Yes Detection methodsMarcel Single / Multiple Single / Mulitple Yes No Filtering and decoding
Multipath indicates if multiple paths from interferer to receiver.
Measured Fitting indicates the pure simulation-based measured fitting results, butdoes not include possible results from measured data from the underlying model assumed:(a) co-channel / adjacent channel (Kapil)(b) multi-antenna (Aditya)(c) correlated fitting (Marcel)).
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