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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

Modeling and Analysis of Handoff Algorithms in Multi-Cellular Systems

By

Chandrashekar Subramanian

For

EE 6367

Advanced Wireless Communications


Introduction
Introduction Multi-Cellular Systems

  • 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


Basic handoff idea
Basic Handoff Idea Multi-Cellular Systems

  • 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 


Handoff strategies
Handoff Strategies Multi-Cellular Systems

  • 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


Handoff strategies1
Handoff Strategies Multi-Cellular Systems

  • 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


Model used
Model Used Multi-Cellular Systems

  • 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


Propagation model
Propagation Model Multi-Cellular Systems

  • 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)


Signal averaging
Signal Averaging Multi-Cellular Systems

  • 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)


Improvements to basic handoff idea
Improvements to Basic Handoff Idea Multi-Cellular Systems

  • 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

    .


Variable parameters of model
Variable Parameters of Model Multi-Cellular Systems

  • 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


Description of simulations
Description of Simulations Multi-Cellular Systems

  • 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


Observations
Observations Multi-Cellular Systems

  • 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


Observations1
Observations Multi-Cellular Systems

  • 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.


Mathematical model
Mathematical Model Multi-Cellular Systems

  • 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


Equations
Equations... Multi-Cellular Systems

  • 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.


More equations
More Equations... Multi-Cellular Systems

  • 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


Approximation
Approximation Multi-Cellular Systems

  • 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


Using the approximation
Using the Approximation Multi-Cellular Systems

  • 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}


R1 Multi-Cellular Systems

R2

R3

R4


Still more equations
Still More Equations... Multi-Cellular Systems

  • 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}


Few more equations
Few More Equations... Multi-Cellular Systems

  • 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


Last few equations
Last Few Equations... Multi-Cellular Systems

  • 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)


Final equation
Final Equation. Multi-Cellular Systems

  • 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


Conclusions
Conclusions Multi-Cellular Systems

  • 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


References
References Multi-Cellular Systems

[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.


Thank you

Thank You! Multi-Cellular Systems


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