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

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

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

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Handoff Strategies n 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 – ( = T th - T drop ) is usually in the range of 6 to 12 dB

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Handoff Strategies n 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 – ( = T th - T drop ) is usually in the range of 0 to 6 dB

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

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Propagation Model n The propagation model consists of –Path Loss –Shadow Fading (Lognormal) –Fast Fading (Rayleigh) n Signal levels from base stations A and B are then given by a(d) = K 1 - K 2 log(d) + u(d) b(d) = K 1 - K 2 log(D-d) + v(d) n u(d) and v(d) are iid Gaussian with zero mean and variance s dB (shadow fading process)

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

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Improvements to Basic Handoff Idea n Using (=T th - T drop ) is not sufficient for optimal performance n Define h (dB) as the hysteresis level to avoid repeated handoffs n Improved Algorithm: (1)If at d k-1, serving BS is A, and at d k, aMean(d k ) < T th and xMean(d k ) <-h, Handover to BS B. (2)If at d k-1, serving BS is B, and at d k, bMean(d k ) h, Handover to BS A.

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Variable Parameters of Model n d av, rate of decay of the averaging window n T th, threshold signal level to initiate handoff n h, hysteresis level to avoid repeated handoffs n Efficient algorithm seeks to minimize number of handoffs and delay in handoff by optimal selection of above parameters

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Description of Simulations n For purposes of simulation the following values are assumed: D = 2.0 km, d s = 1.0 m, d 0 = 20 m. n This gives us K1 = 0.0 and K2 = 30 (Urban) n For various values of the parameters d av, T th, and h, simulations are done n Purpose of the simulations is to observe how these parameters affect the performance of the handoff algorithms n Performance is measured in terms of (1) number of handoffs, and (2) crossover point

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

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Observations n For very high d av (=30), optimum T value tends to give very good performance for low h. n 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 n In practice a d av of 30 m, an h of 7 dB and a T = -94 dB are considered reasonable values. Simulation indicate the same.

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Mathematical Model n Notation –P ho (k) = probability of handoff in k th interval –P B/A (k) = probability of handing off from BS A to BS B –P A/B (k) = probability of handing off from BS B to BS A –P A (k) = probability of mobile being assigned to BS A at d k –P B (k) = probability of mobile being assigned to BS B at d k n a(d k ), b(d k ), x(d k ), mean the averaged signals henceforth. n k is the k th interval, i.e., when mobile is at d k

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Equations... n Recursively we can compute P ho (k) as: P ho (k) = P A (k-1)P B/A (k) + P B (k-1)P A/B (k) P A (k) = P A (k-1)[1-P B/A (k)] + P B (k-1)P A/B (k) P B (k) = P B (k-1)[1-P A/B (k)] + P A (k-1)P B/A (k) n Initial values: P A (0) = 1 and P B (0) = 0 n k = 1, 2, …, D/d s n Once we can determine P B/A (k) and P A/B (k), the model is complete.

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

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Approximation n If X and Y are related events and if we can decompose Y as Y = Y 1 Y 2 and Y 1 Y 2 =, i.e., Y 1 and Y 2 are mutually exclusive n Recall P{X/Y}= P{X/Y 1 Y 2 } = P{X/Y 1 }P{Y 1 }/P{Y} + P{X/Y 2 }P{Y 2 }/P{Y} where P{Y} = P{Y 1 } + P{Y 2 } n Now, A(k-1) = {x(d k-1 ) < -h}, {a(d k-1 ) < T} n Both cannot be true because then A could not be serving at d k-1 n Break A(k-1) into two mutually exclusive subevents

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Using the Approximation n We write A(k-1) = A 1 (k-1) A 2 (k-1) where,A 1 (k-1) = {x(d k-1 ) -h} A 2 (k-1) = {x(d k-1 ) < -h, a(d k-1 ) T} n Let regions, R1 denote {x(d k-1 ) -h} R2 denote {x(d k-1 ) < -h} R3 denote {a(d k-1 ) T} R4 denote {a(d k-1 ) < T}

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R1R2 R3R4

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Still More Equations... n From plot we see that P{A 2 (k-1)} P{A 1 (k-1)} n Actually R3 R2 =, i.e., P {A 2 (k-1)} = 0 n Using Bayes Theorem, P B/A (k)= P{B(k)/A 1 (k-1)}P{A 1 (k-1)}/[P{A 1 (k-1)+P{A 2 (k-1)}] = P{B(k)/A 1 (k-1)} = P{x(d k ) < -h, a(d k ) < T / x(d k-1 ) -h} = P{x(d k ) < -h / x(d k-1 ) - h} X P{a(d k ) < T/ x(d k-1 ) - h, x(d k ) < -h}

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Few More Equations... n Since correlation between current states is much higher than that between current and past state, rewrite last equation as P B/A (k)= P{x(d k ) < -h / x(d k-1 ) - h} X P{a(d k ) < T/ x(d k ) < -h} = P 1 P 2 Similarly, P A/B (k)= P{x(d k ) > h / x(d k-1 ) h} X P{b(d k ) h} = P 3 P 4

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Last Few Equations... n P i s can be calculated using Gaussian distributions as: n P 1 = P{x(d k ) < -h, x(d k-1 ) -h} / P{x(d k-1 ) -h} n P 2 = P{a(d k ) < T, x(d k ) < -h} / P{x(d k ) < -h} n 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 P i s n Thus we can evaluate P ho (k)

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

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Conclusions n Described an algorithm for MAHO n Used algorithm to study variable parameters n Presented an equivalent mathematical model to study the algorithm Future Work n The simulation and analytical model can be extended to study cases involving more than two base stations n 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

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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.

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