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Statistical Modeling of Co-Channel Interference
IEEE Globecom 2009
Wireless Networking and Communications Group
1st December 2009
Kapil Gulati†, Aditya Chopra†, Brian L. Evans†, and Keith R. Tinsley ‡
†The University of Texas at Austin ‡ Intel Corporation
Problem Definition
Large-scale random wireless networks Dense spatial reuse of radio spectrum Co-channel interference becoming a dominant noise source
Statistical modeling of co-channel interference Field of Poisson distributed interferers
[Win, Pinto & Shepp, 2009][Baccelli & Błaszczyszyn, 2009][Haenggi & Ganti, 2009]
Finite- and infinite-area region containing interferers[Middleton, 1977][Sousa, 1992][Ilow & Hatzinakos, 1998][Yang & Petropulu, 2003]
Benefits Designing interference-aware receivers Communication performance analysis of wireless networks
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Prior Work
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Statistical Models
Symmetric Alpha Stable Characteristic function
Middleton Class A (without Gaussian component) Amplitude distribution
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Proposed Contributions
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System Model
Reception in the presence of interfering signals Interferers
Distributed according to homogeneous spatial Poisson process
Narrowband emissions
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System Model (cont…)
Sum interference
Log-characteristic function
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is the interferer index,is the location of the receiver,
are distances of interferers from receiver,is the power pathloss exponent, is the i.i.d random amplitude variations due to fading.
Statistical-Physical Modeling
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Simulation Results
Decay Rates of Tail Probability
Simulation Parameters
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Case I: Entire Plane
8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 100
1
2
3
4
5
6
Interference Amplitude
Dec
ay R
ate
Simulated
Alpha Stable
Gaussian and Middleton Class A models are not applicable since mean intensity of interference is infinite
Simulation Results (cont…)
Case II: Finite area annular region with receiver at origin
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Case II-a: Models with higher accuracy Case II-b: Models with lower accuracy
8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 100
1
2
3
4
5
6
Interference Amplitude
Dec
ay R
ate
SimulatedClass A (w/o Gaussian)Alpha StableGaussian
8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 100
1
2
3
4
5
6
Interference Amplitude
Dec
ay R
ate
SimulatedClass A (w/o Gaussian)
Alpha StableGaussian
Simulation Results (cont…)
Case III: Finite area annular region & receiver not at origin
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Case III-a: Models with higher accuracy Case III-b: Models with lower accuracy
8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 100
1
2
3
4
5
6
7
Interference Amplitude
Dec
ay R
ate
SimulatedClass A (w/o Gaussian)Alpha StableGaussian
8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 100
2
4
6
8
10
12
14
16
18
Interference Amplitude
Dec
ay R
ate
SimulatedClass A (w/o Gaussian)Alpha StableGaussian
Conclusions
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Radio Frequency Interference Modeling and Mitigation Software Toolboxhttp://users.ece.utexas.edu/~bevans/projects/rfi/software/index.html
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Thank You,Questions ?
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References14
RFI Modeling[1] D. Middleton, “Non-Gaussian noise models in signal processing for telecommunications: New
methods and results for Class A and Class B noise models”, IEEE Trans. Info. Theory, vol. 45, no. 4, pp. 1129-1149, May 1999.
[2] K.F. McDonald and R.S. Blum. “A physically-based impulsive noise model for array observations”, Proc. IEEE Asilomar Conference on Signals, Systems& Computers, vol 1, 2-5 Nov. 1997.
[3] K. Furutsu and T. Ishida, “On the theory of amplitude distributions of impulsive random noise,” J. Appl. Phys., vol. 32, no. 7, pp. 1206–1221, 1961.
[4] J. Ilow and D . Hatzinakos, “Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers”, IEEE transactions on signal processing, vol. 46, no. 6, pp. 1601-1611, 1998.
[5] F. Baccelli and B. Błaszczyszyn, “Stochastic geometry and wireless networks, volume 1 — theory,” in Foundations and Trends in Networking. Now Publishers Inc., 2009, vol. 3, no. 3–4, to appear.
[6] F. Baccelli and B. Błaszczyszyn, “Stochastic geometry and wireless networks, volume 2— applications,” in Foundations and Trends in Networking. Now Publishers Inc., 2009, vol. 4, no. 1–2, to appear.
[7] M. Haenggi and R. K. Ganti, “Interference in large wireless networks,” in Foundations and Trends in Networking. Now Publishers Inc., Dec. 2009, vol. 3, no. 2, to appear.
[8] 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.
References (cont…)
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RFI Modeling (cont…)[9] 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.[10] 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.
[11] 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.
Parameter Estimation[12] 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
[13] G. A. Tsihrintzis and C. L. Nikias, "Fast estimation of the parameters of alpha-stable impulsive interference", IEEE Trans. Signal Proc., vol. 44, Issue 6, pp. 1492-1503, Jun. 1996
RFI Measurements and Impact[14] 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
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References (cont…)16
Filtering and Detection[15] A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment-
Part I: Coherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 1977[16] A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment
Part II: Incoherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 1977[17] 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[18] 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.
[19] J. G. Gonzalez and G. R. Arce, “Optimality of the myriad filter in practical impulsive-noise environments,” IEEE Trans. on Signal Proc, vol. 49, no. 2, pp. 438–441, Feb 2001.
[20] E. Kuruoglu, “Signal Processing In Alpha Stable Environments: A Least Lp Approach,” Ph.D. dissertation, University of Cambridge, 1998.
[21] 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
[22] 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.
Backup Slides Middleton’s approximation/ Applicability of Middleton Class A model Extensions and new results for Poisson interferer fields
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, submitted.
Extensions for Poisson-Poisson cluster interferer fields
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, to be submitted. http://users.ece.utexas.edu/~bevans/papers/index.html
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Applicability of Middleton Class A model
Model derived using the identity
Accurate model in Case II and Case III when
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Poisson Field of Interferers
Interferers distributed over parametric annular region
Log-characteristic function
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Poisson Field of Interferers
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Poisson Field of Interferers
Simulation Results (tail probability)
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Case I Case III
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