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Interference Modelling in Spatially Distributed Shadowed Wireless Systems

Interference Modelling in Spatially Distributed Shadowed Wireless Systems. Neelesh B. Mehta ECE Department, IISc. Project 602 duration: April 2008 to March 2010. Outline. Summary of research output Inter-cell interference modeling Our two approaches Results Conclusion s.

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Interference Modelling in Spatially Distributed Shadowed Wireless Systems

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  1. Interference Modelling in Spatially Distributed Shadowed Wireless Systems Neelesh B. Mehta ECE Department, IISc Project 602 duration: April 2008 to March 2010

  2. Outline • Summary of research output • Inter-cell interference modeling • Our two approaches • Results • Conclusions

  3. Summary of Output: Conference Publications • Sarabjot Singh and Neelesh B. Mehta, “An Alternate Model for Uplink Interference in CDMA Systems with Power Control,” National Conference on Communications (NCC), Guwahati, India, Jan. 2009. • Neelesh B. Mehta, Sarabjot Singh, and Andreas F. Molisch, “An Accurate Model For Interference From Spatially Distributed Shadowed Users in CDMA Uplinks,” IEEE Global Telecommunications Conf. (Globecom), Honolulu, USA, Nov.\ 2009

  4. Summary of Output: Journal Publications • Sarabjot Singh, Neelesh B. Mehta, Andreas F. Molisch, and Abhijit Mukhopadhyay, “Moment-Matched Lognormal Modeling of Uplink Interference with Power Control and Cell Selection,” IEEE Trans. on Wireless Communications, March 2010. • Neelesh B. Mehta, Sarabjot Singh, Abhijit Mukhopadhyay, and Andreas F. Molisch, “Accurately Modeling the Interference From Spatially Distributed Shadowed Users in CDMA Uplinks,” To be submitted to IEEE Trans. on Communications, 2010.

  5. Uplink Interference Inter-cell interference • Mobile stations tx. to base station • Multiple interferers contribute to UL interference • Interference is random • Important to model it correctly 2 BS 2 2 Reference cell Neighboring cell 1 2 2 1 1 2 2 1 1 1 2 2 2 2 2

  6. Wireless Propagation Characteristics • Path loss (d) • Shadowing (s) • Lognormal distribution • Fading (f) • Rayleigh, Ricean, Nakagami-m s f P Rx. power Tx. power Path loss Shadowing Fading

  7. Lognormal Probability Distribution Lognormal Prob. Distribution • A skewed distribution • Several and varied applications in wireless propagation, finance, health care, reliability theory, optics, etc. pX(x) x

  8. Conventional Model: Gaussian Approximation • Problem: Closed-form tractable expressions for probability distribution of sum are not known • Conventional solution: Model as a Gaussian RV • [Chan, Hanly’01; Tse,Viswanath’05] • Two justifications given: • Central limit theorem • Less randomness in the presence of power control and cell site selection

  9. Our Approach: Approximate As A Lognormal • Related literature supports this approach • Works much better given number of summands • [Mehta et al'07, Fenton-Wilkinson’60, Schleher‘77, Schwartz-Yeh‘82, Beaulieu-Xie’04] • ‘Permanence' of lognormal sums • [W. A. Janos ‘70, R. Barakat’76] Model inter-cell interference as a lognormal random variable

  10. Unique Feature of Our Problem: Several Sources of Randomness • User locations are random within a cell • Use Poisson point process model • Number of users is also random • Interferer’s transmit power is random • Power control • Cell site selection

  11. Our Two Methods to Fix Lognormal Parameters Lognormal: Goal: Determine the two parameters μ and σ • Developed two methods: • Moment-matching method • MGF-matching method

  12. Moment Matching: Key Results • Match the first two moments of total uplink interference • Advantage: Closed-form expressions possible Moments of actual interference

  13. CCDF Matching: To See Tail Behaviour • Lognormal tracks the actual CCDF very well • Better than conventional Gaussian Ave. # of users/cell= 10 First tier interference Complementary CDF Total interference

  14. CDF Matching: To See Head Behaviour Ave. number of users/cell= 10 • Lognormal significantly better than Gaussian • Gaussian CDF high for small value of interference • Off by 2 orders of magnitude CDF Total interference

  15. With Cell Selection (Handoff Set Size = 2) • Moment matching based lognormal approximation is better than Gaussian even with cell site selection • Shown for first-tier interference

  16. Further Improvement Using MGF Matching • Key idea: Match moment generating function instead of moments • Advantage: Gives the parametric flexibility to match both portions of distribution well • Technical enabler: Can evaluate MGF relatively easily when users are distributed as per a Poisson spatial process • Benefit from the extensive theory on Poisson processes

  17. Improved Lognormal Approximation Method • MGF of the total uplink interference from users in cell k • ψk(s): MGF of the interference from an arbitrary user in cell k • Method: Match MGFs at s1 and s2 with lognormal’s MGF

  18. 6. Results: CDF and CCDF Matching Accuracy 30 users/cell on average • Lognormal approximation is significantly better than Gaussian • MGF-based lognormal approximation is better than moment-based lognormal approximation CCDF CDF First-tier interference

  19. Conclusion • Goal: Model inter-cell interference in uplink of CDMA systems • Showed: Lognormal is better than the conventional Gaussian • New methods: To determine parameters of approximating lognormal • First method :Based on moment-matching • Second improved method: MGF-based moment matching

  20. Extensions Two model generalizations: • Extend the femto cells • Multiple femto cells within a macrocell • Hybrid macrocell/microcell cellular layouts Two other improvements: • Include peak power constraints • Better cell area approximation techniques

  21. Inter-Cell Interference in CDMA Uplinks • Spreading codes diminish interference but do not annul it • Sum of signals from many users served by other BSs • Undergoes shadowing/fading It is a random variable. How do we characterize it? Reference cell Neighboring cell

  22. System Model With Power Control Interfering cell Reference cell • Fading-averaged inter-cell interference • Path loss and shadowing model: • Interference power (with power control) at BS 0 from users served by BS k, located at x1(k), . . . , xNk(k) :

  23. User Location and Number Modelling • Model as a Poisson Spatial Process • Characterized by an intensity parameter (λ) • Analytically tractable model • Probability that Nk users occur within a cell of area A equals Analysis approximation

  24. Signal Interferers Sum of Fixed Number of Lognormals: CDF • Percentile (CDF) plot comparison S-Y method Moment matching CDF Simulations Mehta et al [Mehta, Wu, Molisch, & Zhang, IEEE Trans. Wireless 2007]

  25. Sum of Fixed Number of Lognormals: CCDF • Various approaches exist to accurately characterize the approximating lognormal Complementary CDF Fenton-Wilkinson Log scale S-Y Simulation Mehta et al [Mehta, Wu, Molisch, & Zhang, IEEE Trans. Wireless 2007]

  26. CCDF Matching (Denser User Population) • Lognormal approximation is still significantly better • In sync with literature on sums of fixed number of lognormals Ave. # of users/cell= 30 First tier interference Complementary CDF Total interference

  27. Sources of Inter-Cell Interference 2 • First tier interference • Second tier interference 2 2 1 2 2 1 1 2 2 1 1 2 1 2 2 2 2 • Must model inter-cell interference accurately • Cell planning and base station deployment • Signal outage probability evaluation • Performance of link adaptation

  28. CDF Matching (Denser User Population) Ave. number of users/cell= 30 • Lognormal better than Gaussian even for denser populations! • However, inaccuracy does increase CDF Total interference

  29. With Cell Site Selection & Power Control • Serving base station chosen by a user need not be the geographically closest one • Due to shadowing • Depends on soft handoff set size • The number of neighboring base stations a user tracks Reference cell Neighboring interfering cell

  30. First Tier Interference (Handoff Set Size = 3) • Lognormal approximation is still better! CDF CCDF

  31. Second Tier Interference (Handoff Set Size = 2) • Second-tier cells are further away CDF CCDF

  32. Zero Tier Interference (Handoff Set Size = 2) • Even users located within reference cell can cause inter-cell interference • Gaussian does well in this case! CDF CCDF

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