1. Statistical Modeling of Co-Channel Interference IEEE Globecom 2009 Wireless Networking and Communications Group 1 st December 2009 Kapil Gulati †, Aditya Chopra †, Brian L. Evans †, and Keith R. Tinsley ‡ † The University of Texas at Austin ‡ Intel Corporation

2. 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 Wireless Networking and Communications Group 2

3. Prior Work Wireless Networking and Communications Group 3

4. Statistical Models  Symmetric Alpha Stable  Characteristic function  Middleton Class A (without Gaussian component)  Amplitude distribution Wireless Networking and Communications Group 4

5. Proposed Contributions Wireless Networking and Communications Group 5

6. System Model  Reception in the presence of interfering signals  Interferers  Distributed according to homogeneous spatial Poisson process  Narrowband emissions Wireless Networking and Communications Group 6

7. System Model (cont…)  Sum interference  Log-characteristic function Wireless Networking and Communications Group 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.

8. Statistical-Physical Modeling Wireless Networking and Communications Group 8

9. Simulation Results  Decay Rates of Tail Probability  Simulation Parameters Wireless Networking and Communications Group 9 Case I: Entire Plane Gaussian and Middleton Class A models are not applicable since mean intensity of interference is infinite

10. Simulation Results (cont…)  Case II: Finite area annular region with receiver at origin Wireless Networking and Communications Group 10 Case II-a: Models with higher accuracy Case II-b: Models with lower accuracy

11. Simulation Results (cont…)  Case III: Finite area annular region & receiver not at origin Wireless Networking and Communications Group 11 Case III-a: Models with higher accuracy Case III-b: Models with lower accuracy

12. Conclusions Wireless Networking and Communications Group 12 Radio Frequency Interference Modeling and Mitigation Software Toolbox http://users.ece.utexas.edu/~bevans/projects/rfi/software/index.html

13. Wireless Networking and Communications Group 13 Thank You, Questions ?

14. Wireless Networking and Communications Group References 14 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.

15. References (cont…) Wireless Networking and Communications Group 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

16. Wireless Networking and Communications Group 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.

17. Backup Slides  Middleton’s approximation/ Applicability of Middleton Class A model Middleton’s approximation/ Applicability of Middleton Class A model  Extensions and new results for Poisson interferer fields 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 Wireless Networking and Communications Group 17

18. Applicability of Middleton Class A model  Model derived using the identity  Accurate model in Case II and Case III when Wireless Networking and Communications Group 18

19. Poisson Field of Interferers  Interferers distributed over parametric annular region  Log-characteristic function Wireless Networking and Communications Group 19

20. Poisson Field of Interferers Wireless Networking and Communications Group 20

21. Poisson Field of Interferers  Simulation Results (tail probability) Wireless Networking and Communications Group 21 Case I Case III Gaussian and Middleton Class A models are not applicable since mean intensity is infinite