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


2

Prior Work


3

Statistical Models

Symmetric Alpha Stable Characteristic function

Middleton Class A (without Gaussian component) Amplitude distribution


4

Proposed Contributions


5

System Model

Reception in the presence of interfering signals Interferers

Distributed according to homogeneous spatial Poisson process

Narrowband emissions


6

System Model (cont…)

Sum interference

Log-characteristic function


7

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


8

Simulation Results

Decay Rates of Tail Probability

Simulation Parameters


9

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


10

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


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


Dec

ay R

ate

SimulatedClass A (w/o Gaussian)

Alpha StableGaussian

Simulation Results (cont…)

Case III: Finite area annular region & receiver not at origin


11

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


Dec

ay R

ate


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


Dec

ay R

ate


Conclusions


12

Radio Frequency Interference Modeling and Mitigation Software Toolboxhttp://users.ece.utexas.edu/~bevans/projects/rfi/software/index.html


13

Thank You,Questions ?


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…)


15

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


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


17

Applicability of Middleton Class A model

Model derived using the identity

Accurate model in Case II and Case III when


18

Poisson Field of Interferers

Interferers distributed over parametric annular region

Log-characteristic function


19



20


Simulation Results (tail probability)


21

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

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

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