statistical modeling of co-channel interference ieee globecom 2009 wireless networking and...

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