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 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

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

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 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

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)

A B

MS

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)

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)

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

.

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

Absolute Signal Values vs. Distance

-110-88

-66-44

-220

2244

6688

110

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Distance in meters

Sig

nal V

alue

in d

B

a(d) b(d) x(d) = a(d) - b(d)

Averaged Signal Values vs. Distance

-110

-88

-66

-44

-22

0

22

44

66

88

110

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Distance in meters

Ave

rag

ed S

ign

al V

alu

es

aMean(d) bMean(d) x(d) = aMean(d) - bMean(d)

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

dav = 5 m

0102030405060

0 5 10 15

h in dB

Nu

mb

er o

f H

and

off

s

T = -90 T = -92 T = -94

T = -95 T = -96

dav = 5 m

1000

1100

1200

1300

1400

1500

0 5 10 15

h in dB

Cro

sso

ver

Po

int

in

met

ers

T = -90 T = -92 T = -94

T = -95 T = -96

dav = 10 m

0

10

20

30

0 5 10 15

h in dB

Num

ber

of

Han

doffs

T = -90 T = -92 T = -94

T = -95 T = -96

dav = 10

100011001200130014001500

0 5 10 15

h in dB

Cro

ssov

er P

oint

in

met

ers

T = -90 T = -92 T = -94

T = -95 T = -96

dav = 15

05

1015202530

0 5 10 15

h in dB

Nu

mb

er o

f H

and

off

s

T = -90 T = -92 T = -94

T = -95 T = -96

dav = 15

100011001200130014001500

0 5 10 15

h in dB

Cro

ssov

er P

oint

in

met

ers

T = -90 T = -92 T = -94

T = -95 T = -96

dav = 20

0

5

10

15

20

0 5 10 15

h in dB

Num

ber

of

Han

doffs

T = -90 T = -92 T = -94

T = -95 T = -96

dav = 20 m

100011001200130014001500

0 5 10 15

h in dB

Cro

sso

ver

Po

int

in m

eter

s

T = -90 T = -92 T = -94

T = -95 T = -96

dav = 30 m

0

5

10

15

20

0 5 10 15

h in dB

Nu

mb

er o

f H

and

off

s

T = -90 T = -92 T = -94

T = -95 T = -96

dav = 30 m

100011001200130014001500

0 5 10 15

h in dB

Cro

ssov

er P

oint

in

met

ers

T = -90 T = -92 T = -94

T = -95 T = -96

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

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.

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

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.

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

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

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}

Averaged Signal Values vs. Distance

-110

-88

-66

-44

-22

0

22

44

66

88

110

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Distance in meters

Ave

rag

ed S

ign

al V

alu

es

aMean(d) bMean(d) x(d) = aMean(d) - bMean(d)

R1 R2

R3 R4

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}

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

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)

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

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

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.

Thank You!