A Hierarchical Position Prediction Algorithm for Efficient Management of Resources in Cellular Networks Tong Liu, Paramvir Bahl, Imrich Chlamtac 2 1 3

A Hierarchical Position Prediction Algorithm A Hierarchical Position Prediction Algorithm for Efficient Management of Resources in for Efficient Management of Resources in

Cellular Networks Cellular Networks

Tong Liu, Paramvir Bahl, Imrich Chlamtac 22 11 33

Tellabs Wireless Systems DivisionMicrosoft ResearchErik Jonsson School of Engineering and Computer Science, The University of Texas at Dallas

11

22

33

GLOBECOM ‘97, November 1997

Main MessagesMain Messages

… mobility prediction is a promising technique for improving resource efficiency and connection reliability in cellular networks.

… theoretical richness of stochastic signal processing field makes it feasible for predicting random intercell movement…

Bi-levelstochasticmovementmodel

Approximate pattern matching

Extended, self-learningKalman Filtering

Intercell movementprediction

OutlineOutline

Mobility prediction - Problem and Framework Related work in literature Hierarchical Position Prediction

User Mobility Model - A Global View Approximate Pattern Matching User Mobility Model - A Local View Extended, Self-learning Kalman Filtering Prediction Performance

Conclusions

Mobility Prediction - Problem DescriptionMobility Prediction - Problem Description

NMn

n

n

n

n

u

u

u

fu

u

2

1

11

^

1

^

,

Global Prediction: Next-cell(s) Crossing

nn cellu ?

Local Prediction: Dynamic State

][ [n]

][ [n]

][ ][

naa

nvv

nynx

u

yx

yxn

?

Mobility Prediction - Problem DescriptionMobility Prediction - Problem Description

?

Mobility Prediction - FrameworkMobility Prediction - Framework

Movement Observation

Movement Model Cell Geometry

Prediction Algorithm

Position Speed Cell siteTime

Improve lifetime connectivity and radio resource efficiency- Bandwidth Reservation - QoS Control- Optimal Routing - Position/velocity Based Handoff

Global

Local

Global

Local

Related Work in Literature Related Work in Literature

Recently Crossed Cells

Pattern Matching

Next Cell

Tabbane (JSAC, 1995)Liu and Maguire (ICUPC,1995)Liu , Munro and Barton (ICUPC, 1996)

Next-cell prediction based on movement pattern

Prediction Performance

Historical Movement Pattern

Related Work in Literature Related Work in Literature

Cell TransitionProbability Matrix

Look Up Table

Next Cell

Bar-Noy, Kessler and Sidi (Jour. Of Wireless Networks, 1995)Akyildiz and Ho(Proc. ACM SIGCOMM, 1995)Liu and Maguire (ICUPC,1995)


Next-cell prediction based on Markov Chain model

Current Cell ID

Prediction of Random Intercell MovementPrediction of Random Intercell Movement

Cell Geometry

Position Speed


Pattern Template

Linear Dynamic System

Approximate Pattern Matching

Extended Self-Learning Kalman Filter

Recent Crossed Cells

RSS Measurement

Next Cells

User Mobility Model - A Global ViewUser Mobility Model - A Global View

User Mobility Pattern

ProfileUser

7pm) - (5pm UMP

5pm) - (9am UMP

9am) - (7am UMP

3

2

1

Editing Process

inserting

changingdeleting

iUMP User Actual Path

UAP

Editing Operation UMP

b1 b2 b3b1 b2 b3

a

UAPSpatialCost

Insertion

deletion

change

b1 b3 b4b2 b1 b3 b4

b1 b2b3 b3b4 b4

b1 b2a

2IabW

2DbW

2CabW

User Mobility Model - A Global ViewUser Mobility Model - A Global View

otherwise

2,1 of celladjacent theis 1

otherwise 1

deletedbeen have 0

otherwise

2,1 of celladjacent theis 1

P

11

21

niaaW

bbW

nibaW

bbbUAFor

iCab

iDb

iIab

n

i

i

i

Spatial Cost

Approximate Pattern MatchingApproximate Pattern Matching

}),({min

)min(),( :DistanceEdit

ThresholdUMPUAPdAugUMPMatched

WWWUMPUAPd

ii

kkI

jjD

iiI

if } ),(

,),(

,),(min{

if ),(

),(

1

1.0 )0,(

0 0),0( :Induction

; :Assume

12121

21121

121121

121121

2121

2121

baWbbbaaad

Wbbbaaad

Wbbbaaad

babbbaaad

bbbaaad

mi

iiad

nj bd

bbbUMPaaaUAP

jiDbji

Iaji

bCaji

jiji

ji

i

j

mm

j

i

ji

User Mobility Model - A Local ViewUser Mobility Model - A Local View

S 1

Sm

S2 MovingDynamics

CommandsTime correlatedrandom acceleration

r(t)+

U(t) a(t) F( )

Measurement noise

Nonlinear measurement

-Amax S1 S2 Sm Amax

P( a(t)/S1 ) P( a(t)/S2 ) P( a(t)/Sm )

+

Dynamic EquationsDynamic Equations

Continuous-time dynamic equation:

2

|2

2 ),()()(.

0 ,)]()([)(

)](),([)(

)](),([)(

)](),(),(),([)(:

)()()()(.

m

mr

Tyx

Tyx

Tyx

withtwtrtr

etrtrER

trtrtr

tututu

tvtytvtxtxwhere

trGtuEtxFtx

Discrete-time dynamic equation:

Tyxn

Tyxn

Tyyxxn

nnnn

nwnwWnunuU

nrnvnynrnvnxXwhere

WBUAXX

)]( ),([ ,)]( ),([

)]( ),( ),( ),( ),( ),([

1

Observation ModelObservation Model

d0

d1

d2

dB

rp

idrpp

dB

ibyaxd

i

o

iioi

iii

8~4deviation standard with the

variablerandomGaussian mean zero a is

constants are 4)~2( and where

1,2,3 withlog10

)(t measuremen RSS

3,2,1 with , )()( 22

nnXX

nnn

nnn

Tn

XXX

hH

HXZ

XhZ

pppZ

n of estimate optimal theis , |with

:equationn observatio Linearized

)( :equation n observatio Nonlinear

],,[ :n vectorobservatio time-Discrete

*

210

*

Adaptive Dynamic State EstimatorAdaptive Dynamic State Estimator

)/(),/()()/(

)/()(

)1for stateunknown of estimation ( feature learning External

)(

:filterKalman

1111

111

^^

^^

11

^^

1

^

nin

m

ininnn

in

n

in

ininn

i

nnnnnnn

ZSPZSzfconstZSP

ZSPSUU

,...miS

UHBXHAZKUBXAX

Adaptive Dynamic State EstimatorAdaptive Dynamic State Estimator

m

1i

1

/

1/1

1

^

1

,11

1)/( from evaluated is (const)constant The .3

.for )1()1( and

forunity near p valueaby edapproximat becan parameter This ions.considerat

Markov-semi from obtained is )/(y Probabilit 2.

matrix. covianceerror t measuremen is and matrix, covariance

edisturbancGaussian theis and matrix, estimation state theis where

][ :ce varian

)()(:mean

on with distributiGaussian a has )/ 1.

:sAssumption

nin

ninai

n

nnn

nTnn

Tnnn

inninn

ninn

ZSP

im-/-pi

SUSUP

R

QM

RHQAAMH

SBUHSXAH

ZSf(z

Recursive AlgorithmRecursive Algorithm

11/1/ ][

:MatrixGain Kalman Compute

nnnnTnnnn HMHRHMK

n

in

ininn ZSPSUU

1

^)/()(

:Input ticDeterminis Update

)]([

: With Estimate State Dynamic Update

1/^

1/^

/^

nnnnnnnn

n

XhzKXX

z

:AheadProject

//1

^

//1

QAAMM

UBAXXT

nnnn

nnnnn

] [

:Matrix MMSE Update

1// nnnnnn MHKI-M

Prediction of Next Cell Prediction of Next Cell

Trajectory

Direction

56

cell 0

cell 6

cell 1

cell 2

cell 3

cell 4

cell 5

17

1

1

17

,6..2,1 with

][][)/(

:direction moving of change dramatic no Assuming

)(

)(tan :Direction

,6..2,1 with

)/()/(

:yProbabilit crossing-Cell

6..2,1 with

)}/({maxargcell/Next

:celllnext theof Prediction

1

i

QQXcellP

nv

nv

i

dXfXcellP

i

XcellPX

iini

x

y

nni

nii

n

i

i

Hierarchical Position PredictionHierarchical Position Prediction

User Profile)( 21 nbbbUMP Approximate Pattern Matching

Global Prediction

)( 1 nk bb kt

User MobilityBuffer size:L

UAP Forming)( kLk aa

)( 1

^

kkLk aaaUAP

Optimum AdaptiveFiltering

Local Prediction of Next Cell

Dynamic state

1

^

ka

RSS measurement

LocalPrediction

Global Prediction

Significance of Local PredictionSignificance of Local Prediction

MovementPattern 2

MovementPattern 1

---Crossed Cell ---Uncrossed Cell

A practical situation necessitates looking-ahead mode for movement pattern identification

Prediction Performance - Simulation ParametersPrediction Performance - Simulation Parameters

Mhz 50.........9....................signal.... RF of Wavelength

dB 1..........antenna...station mobile ofgain Power

dB ....6..........antenna...station base ofgain Power

w......20..........power..... ansmissionstation tr Base

dB .....5shadowing. random ofdeviation Standard

] 80 ......[30,........................................range..... Speed

10.....)........./constant(1on accelerati Random

/.5.........0).(on accelerati random of Variance

/7.5) 2.5, ...(0,input..... driving ticdeterminis theof States

/ ..10..............................on accelerati Maximum

5t.......0.measuremen RSS of interval Sampling

km .....2..............................cell...... a of Radiance

..30..............................sites..... cell ofNumber

.............................................Geometry Cell

22

2

2

miles/hr

s

sm

sm

sm

s

lsHexagonCel

m

Prediction Performance - Trajectory TrackingPrediction Performance - Trajectory Tracking

2000 0 2000 4000 6000 8000 10000 12000 14000 16000 180000.5

0

0.5

1

1.5

2

2.5x 10

4

Xdirection [meter]

Ydi

rect

ion

[met

er]

Uesr1

Uesr2

Uesr3

Actual trajectory

Predicted trajectory

1

2

3

4

5

6

7

8

9

12

1314

Cell ID

20

19

Prediction Performance - Speed EstimationPrediction Performance - Speed Estimation

0 500 1000 1500 2000 2500 3000 3500 4000 45000

5

10

15

20

25

Time second

Speed

mete

r/secon

d

Predicted Speed

Actual Speed

Local Prediction of Next CellLocal Prediction of Next Cell

User1 Current cell ID 1 2 3 4 20 Prediction ratio

Predicted cell ID 6 3 4 20 75%

User2 Current cell ID 1 6 5 8 9 19

Predicted cell ID 6 5 7 9 19 80%

User3 Current cell ID 1 6 7 12 14

Predicted cell ID 6 7 12 14 100%


Parametric Behavior of Next-cell Prediction

dB4

dB5

dB6

dB7


Global PredictionGlobal Prediction

d(UAP,UMP1)

2

2

2

Current Cell

C8

C9

C10

d(UAP,UMP2)

3

Global Prediction

C9

C10C18C17C16

C17C16

Determine Edit Distance:

Prediction Result:

UAPUMP1

1

2C

5C

8C

10

^

C

9C

2C 5C 8C 12C 14C

0 0 0 0 0

0 1 2 3 4

1

0

1

1

1

1 2 3

0 1 2 3

10 2 3

UAPUMP2

1

2C

5C

8C

10

^

C

9C

2C 5C 4C 9C 19C

0 0 0 0 00 1 2 3 4

1

0

1

1

1

2 1

0 1 2

21

18C 17C 16C

0 0 0

5 6 74 5 6

4 5 6

2 3 4 5

2 2 3 4 5

3

ConclusionConclusion

Hierarchical Movement Model Top level: Movement Pattern subject to random editing

operations Bottom level: A linear dynamic system driven by the

combination of a semi-Markovian process and Color Gaussian Noise.

Hierarchical Position Prediction Algorithm Approximate Pattern Matching Extended Self-learning Kalman Filter

Documents

A Hierarchical Position Prediction Algorithm for Efficient Management of Resources in Cellular Networks Tong Liu, Paramvir Bahl, Imrich Chlamtac 2 1 3