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Modeling and Analysis of Handoff Algorithms in Multi-Cellular Systems

Modeling and Analysis of Handoff Algorithms in Multi-Cellular Systems. By Chandrashekar Subramanian For EE 6367 Advanced Wireless Communications. Introduction. Handover is an important process of a modern day cellular system

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Modeling and Analysis of Handoff Algorithms in Multi-Cellular Systems

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  1. Modeling and Analysis of Handoff Algorithms in Multi-Cellular Systems By Chandrashekar Subramanian For EE 6367 Advanced Wireless Communications

  2. Introduction • Handover is an important process of a modern day cellular system • Handover ensures continuity and quality of a call between cell boundaries • Handover algorithms must ensure optimum utilization of signalling, radio, and switching resources • This presentation describes a handoff algorithm • Results of simulation of the handoff algorithm are presented • A mathematical analysis based on the algorithm is presented

  3. Basic Handoff Idea • Monitor signal from the communicating base station • If signal (RSSI) falls below a certain threshold value (Tth) initiate handoff process • Tth must be sufficiently higher than minimum acceptable signal strength (Tdrop) •  = Tth - Tdrop • Large  implies unnecessary handoffs may occur • Small  implies very little time for handoff • Requirement: Optimize 

  4. Handoff Strategies • Hard Handoff • First generation cellular systems • RSSI measurements are made by the base station and supervised by the MSC • Base station usually had an additional receiver called locator receiver to monitor users in neighboring cells • MSC handles handoff decisions • Handoff process requires about 10 seconds •  ( = Tth - Tdrop) is usually in the range of 6 to 12 dB

  5. Handoff Strategies • MAHO - Mobile Assisted Handover • Second generation systems • Digital TDMA (GSM) uses MAHO • Mobile measures radio signal strengths from neighboring base stations and reports to serving base station • MAHO is faster • Good for microcell environment where faster handoff is a requirement • Handoff process requires about 1 to 2 seconds •  ( = Tth - Tdrop) is usually in the range of 0 to 6 dB

  6. Model Used • A mobile MS moves from a base station A to another base station B. • d(AB) = D meters • Mobile moves in a straight line and signal measurements are made when mobile is at dk, (k = 1, 2, …, D/ds) MS B A

  7. Propagation Model • The propagation model consists of • Path Loss • Shadow Fading (Lognormal) • Fast Fading (Rayleigh) • Signal levels from base stations A and B are then given by a(d) = K1 - K2log(d) + u(d) b(d) = K1 - K2log(D-d) + v(d) • u(d) and v(d) are iid Gaussian with zero mean and variance s dB (shadow fading process)

  8. Signal Averaging • Measured signals are averaged using and exponential window f(d) f(d) = (1/dav) exp(-d/dav) • dav is the rate of decay of the exponential window • The averaged signals from base stations A and B are given by aMean(d) = f(d)  a(d) bMean(d) = f(d)  b(d) • Let xMean(d) denote the difference in the averaged signals from the base stations: xMean(d) = aMean(d) - bMean(d)

  9. Improvements to Basic Handoff Idea • Using  (=Tth - Tdrop) is not sufficient for optimal performance • Define h (dB) as the hysteresis level to avoid repeated handoffs • Improved Algorithm: (1) If at dk-1, serving BS is A, and at dk, aMean(dk) < Tth and xMean(dk) <-h, Handover to BS B. (2) If at dk-1, serving BS is B, and at dk, bMean(dk) < Tth and xMean(dk) >h, Handover to BS A .

  10. Variable Parameters of Model • dav, rate of decay of the averaging window • Tth, threshold signal level to initiate handoff • h, hysteresis level to avoid repeated handoffs • Efficient algorithm seeks to minimize number of handoffs and delay in handoff by optimal selection of above parameters

  11. Description of Simulations • For purposes of simulation the following values are assumed: D = 2.0 km, ds = 1.0 m, d0 = 20 m. • This gives us K1 = 0.0 and K2 = 30 (Urban) • For various values of the parameters dav, Tth, and h, simulations are done • Purpose of the simulations is to observe how these parameters affect the performance of the handoff algorithms • Performance is measured in terms of (1) number of handoffs, and (2) crossover point

  12. Observations • As the hysteresis level increases, the number of handoffs tends to an ideal value of unity • As the hysteresis level increases, the crossover point increases • For low dav (=5), decreasing T does not seem to have any effect on performance • For higher dav(=15), decreasing T tends to decrease number of handoffs • For higher dav (=15), higher T and lower h gives a good crossover point

  13. Observations • For very high dav (=30), optimum T value tends to give very good performance for low h. • Note: Although in these simulations assume that handoff is instantaneous, we must remember that is not the case. Therefore very low h can often be misleading • In practice a dav of 30 m, an h of 7 dB and a T = -94 dB are considered reasonable values. Simulation indicate the same.

  14. Mathematical Model • Notation • Pho(k) = probability of handoff in kth interval • PB/A(k) = probability of handing off from BS A to BS B • PA/B(k) = probability of handing off from BS B to BS A • PA(k) = probability of mobile being assigned to BS A at dk • PB(k) = probability of mobile being assigned to BS B at dk • a(dk), b(dk), x(dk), mean the averaged signals henceforth. • k is the kth interval, i.e., when mobile is at dk

  15. Equations... • Recursively we can compute Pho(k) as: Pho(k) = PA(k-1)PB/A(k) + PB(k-1)PA/B(k) PA(k) = PA(k-1)[1-PB/A(k)] + PB(k-1)PA/B(k) PB(k) = PB(k-1)[1-PA/B(k)] + PA(k-1)PB/A(k) • Initial values: PA(0) = 1 and PB(0) = 0 • k = 1, 2, …, D/ds • Once we can determine PB/A(k) and PA/B(k), the model is complete.

  16. More Equations... • Let A(k-1) denote the event BS A is serving at dk-1 • Let B(k) denote the event BS B is serving at dk • Then (recall algorithm) PB/A(k) = P{B(k)/A(k-1)} = P{x(dk) < -h, a(dk) < T / A(k-1)} Similarly, PA/B(k) = P{A(k)/B(k-1)} = P{x(dk) > h, b(dk) < T / B(k-1)} • No approximation used thus far

  17. Approximation • If X and Y are related events and if we can decompose Y as Y = Y1 Y2 and Y1  Y2 = , i.e., Y1 and Y2 are mutually exclusive • Recall P{X/Y} = P{X/Y1 Y2} = P{X/Y1}P{Y1}/P{Y} + P{X/Y2}P{Y2}/P{Y} where P{Y} = P{Y1} + P{Y2} • Now, A(k-1) = {x(dk-1) < -h} , {a(dk-1) < T} • Both cannot be true because then A could not be serving at dk-1 • Break A(k-1) into two mutually exclusive subevents

  18. Using the Approximation • We write A(k-1) = A1(k-1)  A2(k-1) where, A1(k-1) = {x(dk-1)  -h} A2(k-1) = {x(dk-1) < -h, a(dk-1)  T} • Let regions, R1 denote {x(dk-1)  -h} R2 denote {x(dk-1) < -h} R3 denote {a(dk-1)  T} R4 denote {a(dk-1) < T}

  19. R1 R2 R3 R4

  20. Still More Equations... • From plot we see that P{A2(k-1)}  P{A1(k-1)} • Actually R3  R2 = , i.e., P {A2(k-1)} = 0 • Using Bayes Theorem, PB/A(k)= P{B(k)/A1(k-1)}P{A1(k-1)}/[P{A1(k-1)+P{A2(k-1)}] = P{B(k)/A1(k-1)} = P{x(dk) < -h, a(dk) < T / x(dk-1)  -h} = P{x(dk) < -h / x(dk-1)  - h} X P{a(dk) < T/ x(dk-1)  - h, x(dk) < -h}

  21. Few More Equations... • Since correlation between current states is much higher than that between current and past state, rewrite last equation as PB/A(k)= P{x(dk) < -h / x(dk-1)  - h} X P{a(dk) < T/ x(dk) < -h} = P1P2 Similarly, PA/B(k)= P{x(dk) > h / x(dk-1)  h} X P{b(dk) < T/ x(dk) > h} = P3P4

  22. Last Few Equations... • Pi’s can be calculated using Gaussian distributions as: • P1 = P{x(dk) < -h, x(dk-1)  -h} / P{x(dk-1)  -h} • P2 = P{a(dk) < T, x(dk) < -h} / P{x(dk) < -h} • Since a(), b(), x() are all Gaussian random variables, and using a joint Gaussian density function with an appropriate correlation coefficient we can evaluate the Pi’s • Thus we can evaluate Pho(k)

  23. Final Equation. • Probability of having more than one handoff in an interval is negligible • For a trip from A to B, number of handoffs is equal to the number of intervals in which handoff occurs. D/ds Number of Handoffs =  Pho(k) k = 1 • Thus we can use this mathematical model to study the handoff algorithm

  24. Conclusions • Described an algorithm for MAHO • Used algorithm to study variable parameters • Presented an equivalent mathematical model to study the algorithm Future Work • The simulation and analytical model can be extended to study cases involving more than two base stations • Study can be made about handoff behavior when mobile is moving in a random path. This would be a step closer to a real world situation

  25. References [1] R. Vijayan, and J.M. Holtzman, “A Model for Analyzing Handoff Algorithms”, IEEE Trans. On Vehicular Technology, Vol. 42, No. 3, pp. 351-356, August 1993. [2] N. Zhang, and J.M. Holtzman, “Analysis of Handoff Algorithms Using Both Absolute and Relative Measurements”, IEEE Trans. On Vehicular Technology, Vol. 45, No. 1, pp. 174-179, February 1996. [3] S. Agarwal, and J.M. Holtzman, “Modeling and Analysis of Handoff Algorithms in Multi-Cellular Systems”, 1997 IEEE 47th Vehicular Technology Conference, Phoenix, AZ., Vol. 1, pp. 300-304, May 1997.

  26. Thank You!

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