Indian Institute of Science (IISc), Bangalore, India Interference Modelling in Spatially Distributed Shadowed Wireless Systems Neelesh B. Mehta ECE Department, IISc Project 602 duration: April 2008 to March 2010

Indian Institute of Science, Bangalore Outline Summary of research output Inter-cell interference modeling Our two approaches Results Conclusions

Indian Institute of Science, Bangalore 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 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

Indian Institute of Science, Bangalore 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 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.

Indian Institute of Science, Bangalore Uplink Interference Mobile stations tx. to base station Multiple interferers contribute to UL interference Interference is random –Important to model it correctly Reference cellNeighboring cell Inter-cell interference BS

Indian Institute of Science, Bangalore Wireless Propagation Characteristics Path loss (d) Shadowing (s) –Lognormal distribution Fading (f) –Rayleigh, Ricean, Nakagami-m s s f f P Path lossShadowingFading Rx. power Tx. power

Indian Institute of Science, Bangalore Lognormal Probability Distribution A skewed distribution Several and varied applications in wireless propagation, finance, health care, reliability theory, optics, etc. Lognormal Prob. Distribution x p X (x)

Indian Institute of Science, Bangalore 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

Indian Institute of Science, Bangalore 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

Indian Institute of Science, Bangalore 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

Indian Institute of Science, Bangalore Our Two Methods to Fix Lognormal Parameters Goal: Determine the two parameters μ and σ Lognormal: Developed two methods: Moment-matching method MGF-matching method

Indian Institute of Science, Bangalore Moments of actual interference Moment Matching: Key Results Match the first two moments of total uplink interference Advantage: Closed-form expressions possible

Indian Institute of Science, Bangalore 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 Total interference Complementary CDF

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

Indian Institute of Science, Bangalore 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

Indian Institute of Science, Bangalore 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

Indian Institute of Science, Bangalore Improved Lognormal Approximation Method MGF of the total uplink interference from users in cell k ψ k (s): MGF of the interference from an arbitrary user in cell k Method: Match MGFs at s 1 and s 2 with lognormal’s MGF

Indian Institute of Science, Bangalore 6. Results: CDF and CCDF Matching Accuracy Lognormal approximation is significantly better than Gaussian MGF-based lognormal approximation is better than moment-based lognormal approximation CCDF First-tier interference CDF 30 users/cell on average

Indian Institute of Science, Bangalore 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

Indian Institute of Science, Bangalore 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

Indian Institute of Science, Bangalore 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 Reference cellNeighboring cell It is a random variable. How do we characterize it?

Indian Institute of Science, Bangalore System Model With Power Control 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 x 1 (k),..., x Nk (k) : Reference cell Interfering cell

Indian Institute of Science, Bangalore User Location and Number Modelling Model as a Poisson Spatial Process –Characterized by an intensity parameter (λ) –Analytically tractable model –Probability that N k users occur within a cell of area A equals Analysis approximation

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

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

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

Indian Institute of Science, Bangalore Must model inter-cell interference accurately Cell planning and base station deployment Signal outage probability evaluation Performance of link adaptation Must model inter-cell interference accurately Cell planning and base station deployment Signal outage probability evaluation Performance of link adaptation Sources of Inter-Cell Interference First tier interference Second tier interference

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

Indian Institute of Science, Bangalore 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 cellNeighboring interfering cell

Indian Institute of Science, Bangalore First Tier Interference (Handoff Set Size = 3) Lognormal approximation is still better! CDF CCDF

Indian Institute of Science, Bangalore Second Tier Interference (Handoff Set Size = 2) Second-tier cells are further away CDF CCDF

Indian Institute of Science, Bangalore 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