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# Modeling and Analysis of Handoff Algorithms in Multi-Cellular Systems - PowerPoint PPT Presentation

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

By

Chandrashekar Subramanian

For

EE 6367

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 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 Multi-Cellular Systems

• Hard Handoff

• First generation cellular systems

• RSSI measurements are made by the base station and supervised by the MSC

• MSC handles handoff decisions

• Handoff process requires about 10 seconds

•  ( = Tth - Tdrop) is usually in the range of 6 to 12 dB

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 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 Multi-Cellular Systems

• The propagation model consists of

• Path Loss

• 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 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 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 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 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 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

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 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... 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... 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 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 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... 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... 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... 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. 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 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 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.