Optimization of Handover Algorithms for Wireless Networks570176/FULLTEXT01.pdf · Optimization of Handover Algorithms for Wireless Networks ... works, such as cellular systems (e.g.,

Optimization of Handover Algorithms for

Wireless Networks

SILVIA DE LUCIA

Master’s Degree Project

Stockholm, Sweden 2010

Abstract

We are witnessing a continuous development of heterogeneous wireless net-

works, such as cellular systems (e.g., the LTE, or long term evolution of the

third generation wireless system), sensor networks, and satellite networks.

The coexistence of all these networks requires the design of control mech-

anisms to allow the seamless communication from one network to another,

and even between communication standards. The handover is one such con-

trol mechanism. Specifically, the handover is the mechanism of transferring

the connection of a mobile node from an access point (which could be a base

station or a network using some communication standard) to another AP.

During the handover, a node that is being disconnected from an AP and con-

nected to another AP may experience a sudden degradation of the bandwidth

or outage of the communication. This leads to frequent and unnecessary han-

dovers that may reduce significantly the quality of service perceived by the

node. Therefore, in order for the node to achieve high quality of service, an

optimization of the handover algorithm is essential. In this thesis we study

some optimization algorithms for the handover procedure. We show that

the variables available at the node to control the handover are the hysteresis

margin, which is used to compare the quality of signals of the APs, and the

estimation window length, which is the number of samples to estimate with a

desired accuracy these signals. Then, we study two optimization problems in

which the parameters that affect the handover are optimized by considering

as a cost function a convex combination of the probability of outage and the

probability of handover. The first problem is based on a static optimization,

whereas the second problem on a dynamic optimization. We show that both

problems offer better performance with respect to existing algorithms from

the literature. We show that the dynamic optimization gives better results,

but at the cost of an increased computational complexity.

I

Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

1 Introduction to Handover 1

1.1 Handover procedure . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Types of Handover . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Handover initiation . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4 Handover Decison . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.5 Handover in Microcellular Propagation Environment . . . . . 5

1.6 Handover in Multihop Cellular Networks . . . . . . . . . . . . 6

1.7 Handover scenarios in MCNs . . . . . . . . . . . . . . . . . . . 6

1.8 Handover in IP Networks . . . . . . . . . . . . . . . . . . . . . 9

1.9 Mobility in 6LoWPAN . . . . . . . . . . . . . . . . . . . . . . 11

1.9.1 Application methods . . . . . . . . . . . . . . . . . . . 12

1.9.2 Mobile IPv6 on 6LoWPAN . . . . . . . . . . . . . . . . 13

1.9.3 NEMO . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2 Problem Formulation 15

3 Modeling 18

3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.2 Least Square Algorithm: Performance Measures . . . . . . . . 19

3.2.1 Handover decision an probabilities . . . . . . . . . . . . 21

3.3 The effect of the Hysteresis Margin . . . . . . . . . . . . . . . 24

3.3.1 Probability of Base Station Connection . . . . . . . . . 24

3.3.2 Probability of Handover and Probability of Outage . . 26

3.4 Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.1 First Bound . . . . . . . . . . . . . . . . . . . . . . . . 27

3.4.2 Second Approximation: proposed bound . . . . . . . . 28

II

4 Optimization 30

4.1 Pareto Optimization of the Estimate Window Length . . . . . 30

4.2 Static Handover and Outage Pareto Optimization . . . . . . . 31

4.3 Optimization of the Probability of Handover . . . . . . . . . . 32

4.4 Probability of Outage Optimization . . . . . . . . . . . . . . . 33

4.5 Dynamic Handover and Outage Pareto Optimization . . . . . 33

5 Simulation Results 36

5.1 Probability of Handover and Probability of Outage . . . . . . 36

5.2 Estimate Window Length Pareto Optimization Results . . . . 39

5.3 Approximations results . . . . . . . . . . . . . . . . . . . . . . 40

5.3.1 First approximation . . . . . . . . . . . . . . . . . . . 40

5.3.2 Second approximation . . . . . . . . . . . . . . . . . . 41

5.4 Performance Evaluation of Hysteresis Optimization . . . . . . 44

5.4.1 Static Optimization Results . . . . . . . . . . . . . . . 44

5.4.2 Dynamic Optimization Results . . . . . . . . . . . . . 48

5.4.3 Improving Factors . . . . . . . . . . . . . . . . . . . . 50

6 Conclusions 52

III

List of Figures

1.1 Soft and Hard handover . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Signal strength and hysteresis between two adjacent BSs for po-

tential handover. . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Handover scenarios in Microcellular Networks (MCN) . . . . . . . 5

1.4 Handover scenarios in MCN; BS is the base station, MS is the

mobile station, RS is the relay station and a Cell is a coverage

area of the BS . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Optimized vertical handover framework . . . . . . . . . . . . . . 11

3.1 The hysteresis of the handover decision. . . . . . . . . . . . . . . 24

4.1 Trellis diagram for the computation of outage probabilities in the

dynamic optimization. . . . . . . . . . . . . . . . . . . . . . . . 34

4.2 Trellis diagram for the computation of handover probabilities in

the dynamic optimization. . . . . . . . . . . . . . . . . . . . . . 34

4.3 Optimization scheme . . . . . . . . . . . . . . . . . . . . . . . . 34

5.1 Probability of handover versus distance d0 for LS method. The

parameter is the window length nw. . . . . . . . . . . . . . . . . 37

5.2 Probability of outage versus distance d0 for LS method. The pa-

rameter is the window length nw. . . . . . . . . . . . . . . . . . 37

5.3 Maximum values of outage probability versus estimate window

length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.4 Maximum values of handover probability versus estimate window

length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.5 Handover and outage probability evaluate at nw optimum for the

problem having the objective function in (4.6) . . . . . . . . . . . 39

5.6 Probability of BSs connection versus distance for the first bound

proposed in Section 3.4 . . . . . . . . . . . . . . . . . . . . . . . 40

IV

5.7 Probability of handover versus distance evaluated by using the sec-

ond approximation given by equation (3.19) in Chapter 3, with

nw = 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.8 Probability of handover versus distance evaluated by using the sec-

ond approximation given by equation (3.19) in Chapter 3, with

nw = 40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.9 Probability of outage versus distance evaluated by using the second

approximation given by equation (3.19) in Chapter 3, with nw = 10 42

5.10 Probability of outage versus distance evaluated by using the second

approximation given by equation (3.19) in Chapter 3, with nw = 40 42

5.11 Comparison between handover probability values for different

m . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5.12 Comparison between outage probability values for different m 43

5.13 Handover probability evaluated at optimum h for the static opti-

mization problem. . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.14 Outage probability evaluated at optimum h for the static optimiza-

tion problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.15 Objective function evaluated at optimum h for the static optimiza-

tion problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.16 Handover and Outage probabilities evaluated by setting a fixed

histeresis margin h=2: no optimization . . . . . . . . . . . . . 46

5.17 Objective function evaluated by setting h=2: no optimization . . . 46

5.18 Handover and Outage probability evaluated by setting a fixed

histeresis margin h=8: no optimization . . . . . . . . . . . . . 46

5.19 Objective function evaluated by setting h=8: no optimization . . . 47

5.20 Comparison between objective functions evaluate at hopt by apply-

ing dynamic and static optimization techniques with a weigthing

cofficient equal to 0.5 . . . . . . . . . . . . . . . . . . . . . . . . 48







5.23 Improving factor between objective function evaluated by fixing

an hysteresis margin h = 2 and the objective function at hopt

computed by using the static optimization . . . . . . . . . . . . . 51

V



computed by using the dynamic optimization . . . . . . . . . . . 51







5.27 Improving factor between objective function evaluated by using

static and dynamic optimization. The value of the parameter α is

0.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

VI

Chapter 1

Introduction to Handover

In a wireless network the need of managing the receivers mobility and ensur-

ing continuous service led to the develop of procedures for a good network

performance. This is achived by supporting the handover (or handoff ) al-

gorithm, which is a procedure that can be applyed to every kind of wireless

communication network and it is also possible within the same radio system

or between heterogeneous systems wich are standardized by protocols devel-

oped by different standardization bodies. In this chapter, we present the

main characteristics of the handover algorithm.

1.1 Handover procedure

The handover is the key to enable function for mobility and service conti-

nuity among a variety of wireless access technologies. It is is the process

of changing channel (frequency, time slot, spreading code, or combination

of them) associated with the current connection while a communication is

in progress. In cellular telecommunications the term handover refers to the

procedure of transferring a call or a data section while the mobile station is

moving away from a coverage area, called cell, to another cell. This process

is carried out to avoid the interruption of an in-progress call when the mobile

gets outside the range of the cell. In fact a handover initiation is the process

by which a handover is started as a consequence of the fact that the cur-

rent link is unacceptably degraded and/or another base station can provide

a better communication link.

1

CHAPTER 1. INTRODUCTION TO HANDOVER 2

BS0 BS0BS1 BS1MS MS

a. Soft handover b. Hard handover

Figure 1.1: Soft and Hard handover

1.2 Types of Handover

It is possible to distinguish between Hard Handover and Soft Handover.

In the soft handover the mobile station is simultneously connected to two

different base stations (see Fig. 1.1a). On the contrary, in the hard the

connection to the serving base station is interrupted while the new base

station takes on the connection (Fig. 1.1b). Furthermore hard handover can

be divided into intracell handover and intercell handover; the soft handover

can also be divided into multiway soft handover and softer handover. Soft

handover is highly expensive for the network, but offers potentially a higher

performance with respect to the hard handover. Nevertheless, the recent

standardizations of new technologies of Long Term Evolution (LTE) and

High Speed Packet Access (HSPA) suggest the use of hard handover only.

1.3 Handover initiation

The decision to initiate a handover at a mobile station may be based on

different measurements, e.g. the recived signal strenght from the serving base

station and neighboring base stations (BS’s), the distance from BS’s, and the

bit error rate. Handover is critical in cellular communication systems because

neighboring cells are always using a disjoint subset of frequency bands, so

negotiations must take place between the mobile station (MS), the current

BS, and the next potential BS.


Relative signal strength

This method works by selecting the BS from which the strongest signal is

received. The decision is based on the computation of the average of the

measurements of the received signal. It has been observed that this method

generates many unnecessary handovers, even when the signal of the current

BS is still at an acceptable level. Some variations have been proposed, as we

see in the following.

Relative signal strength with threshold

This method allows a MS to hand off only if the current signal is sufficiently

weak (less than threshold) and the other is the stronger of the two. The

effect of the threshold depends on its relative value as compared to the signal

strengths of the two BSs at the point at which they are equal.

Signal strength Signal strength

BS0 BS1

T1

T2

T3

A B C D

h

MS

Figure 1.2: Signal strength and hysteresis between two adjacent BSs for potential

handover.

If the threshold is higher than this value, say T1 in Fig. 1.2, this scheme

performs exactly as the relative signal strength scheme, so the handoff occurs

at position A. If the threshold is lower than this value, say T2 in Fig. 1.2, the

MS would delay handoff until the current signal level crosses the threshold at

position B. In the case of T3, the delay may be so long that the MS drifts too

far into the new cell. This reduces the quality of the communication link from


BS1 and may result in a dropped call. Moreover, this results in additional

interference to cochannel users. Thus, this scheme may create overlapping

cell coverage areas. A threshold is not used alone in actual practice because

its effectiveness depends on prior knowledge of the crossover signal strength

between the current and candidate BSs.

Relative signal strength with hysteresis

This scheme allows a user to hand off only if the new BS is sufficiently

stronger (by a hysteresis margin, h in Fig. 1.2) than the current one. In

this case, the handover would occur at point C. This technique prevents the

so-called ping-pong effect, the repeated handover between two BSs caused

by rapid fluctuations in the received signal strengths from both BSs. The

first handover, however, may be unnecessary if the serving BS is sufficiently

strong.

1.4 Handover Decison

There are numerous methods to perform handover, at least as many as the

type of network entities that maintain the state information. The decision-

making process of handover may be centralized or decentralized (i.e. the

handover decision may be made at the MS or at in the core network). From

the decision process point of view, it is possible to find at least three different

kinds of handoff decisions.

Network-Controlled Handover

In a network-controlled handover protocol, the network makes a handover

decision based on the measurements on the MSs at a number of BSs. In

general, the handover process (including data transmission, channel switch-

ing, and network switching) takes 100–200 ms. Information about the signal

quality for all users is available at a single point in the network that facili-

tates appropriate resource allocation. Network-controlled handoff was used

in first-generation analog systems such as AMPS (advanced mobile phone

system), TACS (total access communication system), and NMT (advanced

mobile phone system).


Mobile-Assisted Handover

In a mobile-assisted handover process, the MS makes measurements that are

transmitted to the network to let it able to make the decision. In analog

systems handover procedure is entirely carried on by the network, in the

circuit-switched GSM (global system mobile) is a mobile assisted procedure.

This mainly means that handover algorithm can operate more efficiently ac-

cording to the larger number of available parameters. The handover time

between handover decision and execution in a circuit-switched GSM is ap-

proximately 1 second.

Mobile-Controlled Handover

In mobile-controlled handover, each MS is completely in control of the han-

dover process. This type of handover has a short reaction time (on the order

of 0.1 second). MS measures the signal strengths from surrounding BSs and

interference levels on all channels. A handover can be initiated if the signal

strength of the serving BS is lower than that of another BS by a certain

threshold.

1.5 Handover in Microcellular Propagation

Environment

In a microcellular propagation environment there are two possible handovers:

handover in line-of-sight (LOS) and handover in non line-of-sight (NLOS).

To study the role of the hysteresis, Murase [8] analized the two cases: for

LOS handover the MS always mantains a LOS with both the serving and the

target BS. This is the case, for example, when a MS traverses along a route

from BS0 to BS2 in Fig. 1.3. NLOS handover, instead, arises when the MS

suddenly loses the LOS component with the serving BS while gaining a LOS

component with the target BS. This phenomenon is called the corner effect,

since it occurs while turning corners in urban microcellular settings as the

one shown in Fig. 1.3 where the MS traverses along a route from BS0 to BS1.

In this case, the average recived signal strength can drop by 25-30 dB over

distance as small as 10 m. Corner effects may also cause link quality imbal-

ances on the forward and reverse channels due to the following mechanism.

Quite often the co-channel interference will arrive via a NLOS propagation


BS0

BS1

BS3

BS2

250 m

Figure 1.3: Handover scenarios in Microcellular Networks (MCN)

path. Hence, as a MS rounds a corner, the recived signal strength at the

sertving BS suffers a large decrease while the NLOS co-channel interference

remains the same, i.e., the corner effect severly degrades the carrier to inter-

ference ratio (C/I). Meanwhile, the corner will cause the same attenuation

to both the desired and interfering signals that are recived at the MS. There-

fore, unless there are other sources of co-channel interference that become

predominant as the MS round the corner, the C/I on the forward channel will

remain about the same. If the handover requests from rapidly moving MSs in

microcellular network are not processed quickly, then excessive dropped calls

will occur. Fast temporal based handover algorithms can partially solve this

problem; these algorithms make use of temporal averaging windows that are

used to detect drops in signal strength. However, the effectiveness of these

algorithms depends on the velocity of the MS. Adaptive handover algorithms

can overcome these problems in propagation environments that are typical

of urban microcellular networks.

1.6 Handover in Multihop Cellular Networks

In conventional cellular systems handover occurs only when a mobile station

(MS) moves to different cell or different sectors of the same cell. The intro-

duction of next generation wireless systems, such as fourth generation (4G),


Cell 1 Cell 2

MS1

MS2MS3

MS4

MS5

BS1 BS2

RS1a

RS1b

RS1c

RS1d

RS2a

RS2b

RS2c

RS2d

Scenario1Scenario2

Scenario3

Scenario5

Scenario4

Figure 1.4: Handover scenarios in MCN; BS is the base station, MS is the mobile

station, RS is the relay station and a Cell is a coverage area of the BS

Third Generation Partnership Project Long-Term Evolution (3GPP LTE),

and IEEE 802.16m includes the development of multihop cellular networks

(MCN) to increase the cell radius or combat the shadowing effect, which is

mainly caused by large obstacles between transceivers.

As shown in Fig. 1.4 in MCN additional handover occur between the BS

and relay stations (RSs) or two different RSs. These additional MCN han-

dovers can cause serious ping pong problems and increase signalling overhead.

Although there are works where relay handover problems is explained, the

main interest of using the multihop concept is not in cellular networks but in

ad-hoc networks; unfortunately doesn’t exist a rich body of literature about

applications of handover in multi-hop networks.

1.7 Handover scenarios in MCNs

There are several possible handover scenarios in MCNs regardless of the RS

deployment structure. Handovers in MCNs can occur when an MS moves

between different BSs, between different RSs, or between a BS and an RS as

shown in Fig. 1.4


Intracell handover

Case 1: intracell RS-RS handover

In this case, an MS performs handover between two different RSs in the

same cell. The BS easily can control the handover process because both

the serving RS and the target RS are under their own control, and inter-BS

information or signaling is not required. To prevent packet loss during the

handover process, automatic retransmission request (ARQ) status should be

consistent between a serving RS and a target RS. In this scenario, transfer of

the ARQ status to the target RS is not required during handover if the ARQ

function is located in the BS. In addition, the current layer 3 (L3) address

can be used after the handover.

Case 2: intracell BS-RS handover

MS changes its communication node from a BS to the RS of the same cell,

or vice versa. In this case, the BS easily can control the handover process as

in case 1, and the ARQ status transfer and the L3 address renewal are not

required.

Intercell handover

Case 3: intercell BS-BS handover

This case is exactly the same as the inter-BS handover in the conventional

cellular systems. The ARQ status should be transferred during the han-

dover process if the ARQ is controlled by the BS, and the L3 address is also

reassigned when the subnet is changed by the handover.

Case 4: intercell RS-RS handover

In case 4, a MS performs handover from an RS to the RS of different cells.

This scenario can cause relatively larger signaling overhead than other sce-

narios because it requires inter-BS signaling and RS-BS signaling in both

cells. In addition, the channel quality of the MS in this handover region can

be seriously attenuated by the intercell interference from the adjacent BSs

and RSs. The ARQ status and the L3 address management are similar to

those of case 3.


Case 5: intercell BS-RS handover

In this case an MS moves from a BS to the RS of different cells, or vice versa.

Inter-BS signaling is also required in this scenario, and the ARQ status and

the L3 address management are the same as scenario 3 except for additional

signaling between the RS and the BS.

Received-Signal-Strength Measurement and Handover

Decision

The received-signal-strength (RSS) measurement process can cause packet-

loss or packet-transmission delay because an MS cannot receive data packets

from the serving BS during the RSS measurement for the neighbor BSs. In

an MCN, the RSS measurement overhead increases because an MS should

measure the RSS of the neighbor RSs, as well as the neighbor BSs. There-

fore, packet-loss or packet-transmission delay caused by handover can be

increased in an MCN compared to a singlehop cellular network (SCN). The

handover decision is based on the RSS measurement result. When the serving

BS receives the measurement report from the MS or the RS, it determines

the handover execution and direction based on the RSS and the resource

availability in the target BS or RS.

Handover Procedures and Signaling

Regardless the exchange of specific messages during the handover execution

which are different according to the scenario, it is possible to say that the

handover procedure consists of several steps such as measurement, handover

decision, handover ranging, association, and resource allocation.

Handover Latency and Service-Interruption Time

There are two important performance metrics of handover schemes:

• handover latency

• service-interruption time

Handover latency is defined as the duration between the time when the

measurement procedure starts and the time when the Handover-Complete


message (which indicates the end of handover process) is transmitted to a

serving BS. To clarify, handover starts with the mesurement procedure per-

formed by the MS and after wich a serving BS determines the handover ex-

ecution and direction, whereas an HandoverComplete message comes before

the Connection release step wich completes the whole handover procedure.

This parameter can be calculated differently according to the scenario.

The service-interruption time can be defined as the duration from suspend-

ing data transmission to resuming data transmission, triggered by the RSS

measurement and handover completion, respectively. In intracell handover

scenarios, the service interruption occurs only during the measurement pro-

cedure if the puncturing or addition finger in the receiving module of an

MS is not considered. However, in intercell handover scenarios, the service

interruption can occur during the measurement and handover execution pro-

cedures.

Considerations on MCNs handover

Several design principles can affect the performance of handover schemes in

an MCN. The location and number of RSs in a cell for an MCN have the

most direct impact on the performance of handover in terms of throughput

and handover latency. With an appropriate handover scheme it is possible,

for example, improve the overall cell throughput, simplifie the handover pro-

cess, reduce handover signaling overhead and handover latency, and improve

significantly the service-interruption time. The choice of the scheme should

be a compromise between technical issues and network complexity.

1.8 Handover in IP Networks

Cellular networks are evolving to provide not only the traditional voice ser-

vice but also data services. IP appears to be the base technology of future

networks, to provide all kind of services and through different access tech-

nologies, both fixed and mobile. In Ip networks the management of terminal

mobility is achived by using the Mobile IP (MIP) protocol wich makes use

of two addresses for the mobile:

• a long term address (home address)

• a short-term local address (care of address, CoA)


The home address belongs to the MT’s home domain, while CoA belongs

to the visiting network and it is used by the mobile when it is away from

the home network. The home address is used as endpoint identifier for the

transport layer, while the CoA is used as location identifier.

Enhanced Mobile Internet Protocols

The basic MIP scheme is not efficient in certain circumstances, this due

to an handover delay introduction wich is often unaccetable for real time

applications. Wether to make faster some procedures like movement detec-

tion, new CoA configuration and location update, and to improve mobile

communications, enhancements to the Mobile IP technique, such as MIPv6,

Faster MIPv6 (FMIPv6) and Hierarchical MIPv6 (HMIPv6), are being de-

veloped. All these protocols are host-based in the sense that the MTs needs

to implement mobility-related functionality to perform handover and loca-

tion management signaling when they move between network subnets. Re-

cently the Internet Engineering Task Force IETF specified a network-based

localized mobility management protocol that allows MTs to move between

subnets within the same access network without requiring changes in their

IPv6 protocol stack. This protocol is called Proxy MIPv6. Although the

current trend in network-layer mobility management protocol design is to

enhance the level of coordination between distinct network entities, efficient

handover is required also for close interaction of functions inside the entities

themselves. This interaction is essential to reduce the delays associated with

handover operation.

IEEE 802.21 based vertical handover framework

The IEEE 802.21 is the standard that provides services facilitating handovers

between heterogeneous networks and an optimized handover framework that

leverages genric link-layer intelligence independent of the specifics of mo-

bile nodes or radio access networks. In this regard, the mobility manage-

ment protocol stack of the network elements engaged in handover signaling

is readdressed, and a logical entity is introduced between the link and up-

per layers. This entity, called MIH function (MIHF), provides tree kind of

services: event, command and information services to its users. To provide

these services a group of primitives included in a media-independent service


Upper Layers

MIH_SAP

MIHF

MIH_LINK_SAP

802.11 802.16 3GPP DVB

Mobile terminal

Figure 1.5: Optimized vertical handover framework

access point (SAP) MIH-SAP are used; on the other hand, to communicate

with link layers the MIHF uses primitives that are defined in the media-

dependant MIH-LINK-SAP and mapped to technology-specific primitives.

The architecture is shown in Fig. 1.5. MIHF facilitates handover initiation

(network discovery, network selection, handover negotiation) and handover

preparation (link 2 and link 3 connectivity, resource reservation).

1.9 Mobility in 6LoWPAN

Today’s increasing use of embedded devices, also called smart objects, that

are universally becoming IP enabled and an integral part of the internet

(Internet-connected), led to the definition of the so-called Internet of Things.

6LoWPAN is a set of standards defined by the Internet Engineering Task

Force (IETF) enabling the efficient use of IPv6 over low-pass, low-rate wire-

less networks on simple embedded devices through an adaptation layer and

the optimization of related protocols [3]. There is a wide range of applications

where 6LoWPAN technology may be used, for example home and building

automation, real-time environmental monitoring and forecasting, industrial


automation, personal health and fitness. In these scenarios is useful to con-

sider the mobility because in some cases, such as with body area networks,

the network itself may even be mobile. Mobility is often associated with

topology change so there are several reasons why it happens:

• Physical Movement: the devices change their point of attchment.

• Radio Channel: change in radio propagation may be caused by en-

vironmental change and this often require different topology.

• Network performance: in a wireless network poor signal strength,

node congestion and collisions cause packet loss and delay that reduce

network performance and induce a node to change its attachment point.

• Sleep schedules: in a wireless embedded network, to save battery

power, node use sleep schedules. If a node is attached to a sleeping

router it will move to a better point of attachment.

• Node failure: the failure of a router causes a topology change for

nodes using it as their default router.

In IP networks, mobility is the change of the attachment point of the node.

Mobility may be distinguish in two kinds [3]:

• Roaming: node moves to another network typically without packets

stream.

• Handover: node changes its attachment point during the packets trans-

mission to and from the network. In order for the mobile node to com-

municate again, this process may include operations at specific link

layers as well as at the IP layer.

Further, it is possible to distinguish between micro-mobility and macro-

mobility; in 6LoWPAN micro-mobility refers to the mobility of a node within

a LoWPAN where the IPv6 prefix does not change thus such a mobility re-

quires only the handover, macro-mobility, instead, refers to mobility between

LoWPANs in which the IPv6 changes, and it requires both routing and han-

dover. Another class of mobility is the network mobility that concerns the

changing of the attachment point of an entire network.


Solutions for mobility

As well known each node manage the mobility involving different layers of

the protocol stack. Depending on the type of mobility that occurred and

the handover and roaming prcedures that are in use there are more or less

layers involved. If the node movement is contained within the same LoWPAN

network the link layer may be able to deal with the mobility without any

noticeable change to the network layer. Common link layers that deal with

the mobility include cellular systems such as GPRS or UMTS which perform

handovers maintaining the same IP address; low-power wireless link-layer

technologies such as IEEE 802.15.4 tend to leave mobility to be dealt with

by the network layer. Networks such as IEEE 802.15.4 work in a manner

that all topology changes are node-controlled rather than network-controlled

(such as in cellular systems). If the node moves between different LoWPANs

it needs to change the IPv6 address; if a node acts as a client, a simple way

to deal with such an address change is for the applications to restart when

detecting a change in IP address. A real challenge is to manage the macro-

mobility if a node acts as a server: a way to deal with this in 6LoWPAN

applications is making use at application layer of session initiation protocol

(SIP), uniform resource identifiers (URIs) or a domain name server (DNS).

1.9.1 Application methods

If the LoWPAN network layer does not use mechanisms for the mobility, the

handover causes effects at the application layer. Dealing with mobility at

this layer may even provide better optimization for some applications. For

an application server communicating with mobile 6LoWPAN Nodes with

changing IP address to function, it needs to use some sort of unique and

stable identifier for each node. Examples include the EUI-64 of the node’s

interface, a URI, a universally unique identifier (UUID) or for example a

domanin name.

1.9.2 Mobile IPv6 on 6LoWPAN

As explained in the previous section, the mobility of nodes on the Internet

is managed by using the MIP protocol. As 6LoWPAN is an adaption for

IPv6, it would make sense to apply MIPv6 for dealing with the mobility in

6LoWPAN Nodes while maintaining a costant IPv6 address. The limit to


the use of the MIPv6 for 6LoWPAN is due to the node complexity, power

consumption and limited bandwidth of wireless links that make it difficult to

apply on this field. In order to be applied to 6LoWPAN Node mobility, the

MIPv6 would be to be implemented on LoWPAN Nodes but this problem is

still under investigation. In this regards there are some proposals:

• To full MIPv6 messages are compressed and decompressed by edge

routers; this technique would need a standardization;

• The edge router or some other entity on the visited network would

proxy MIPv6 functions on behalf of the LoWPAN Nodes (proxy method).

1.9.3 NEMO

IP, IPv4, IPv6 were not designed to take into account mobility of users and

terminals. But some IP-layer protocols, such as MIPv6, that the IETF has

defined to enable terminal mobility in IP networks exists. Nevertheless, these

protocols do not support the movement of a complete network that moves

as a whole changing its point of attachment to the fixed infrastructure, that

is, network mobility. A solution to this problem is provided by a working

group called NEMO or network mobility [4]. The NEMO protocol works

by introducing a new logical entity called the mobile router that is able to

deal with MIPv6 and is responsible for handling its function for the entire

mobile network. The network consists of a number of nodes called mobile

network nodes (MNNs) and each node does not need to run Mobile IP be-

cause the router are attached to runs Mobile IP. When the entire LoWPAN,

including edge router and MNNs associated to it, move togheter to a new

point of attachment, applying NEMO means having benefits because inside

the LoWPAN no change can be noticed due to network mobility. The edge

router, in fact, acts as a NEMO mobile router: using MIPv6 binds its new

care-of address in the visited network, and in addition the home LoWPAN

prefix. This means that the LoWPAN continues to use the same prefix as in

the home network.

Chapter 2

Problem Formulation

The handover is the procedure that allows user’s mobility in the context of

heterogeneous -or not- wireless networks by ensuring continuity of service; in

this scenario outage events, that are defined as periods in which the recived

signal level is not sufficiently high to prevent the session interruption, must

be considered to achive a good quality of service. In a wireless network, it is

necessary to minimize outage events, because they reduce the quality of the

communicaiton, and optimize the number of handovers, because they are very

expensive to manage. This thesis focus on the probability of handover and the

probability of outage optimization with respect to important parameters in

the handover initiation: the estimate window length and hysteresis margin.

In effect, a variety of parameters such as bit error rate (BER), carrier-to-

interference ratio (C/I), distance, traffic load, signal strength, and various

combination of them have been suggested in literature for evaluating the link

quality and deciding when a handover should be performed, as we explained

in the previous chapter. Signal strength measurement is one of the most

common criterion, and it is considered in this work. To improve performance,

optimization with respect to some key parameters of the handover algorithm

are studied in this thesis. We consider the LS algorithm proposed in [1],

and we will first evaluate the probabilities of handover (PH) and outage (PO)

for a mobile station (MS) moving between a certain number of base stations

(BSs); then we will study an optimization of the probabilities with respect to

the value of the estimate window length nw, which is the number of samples

to use to make an estimate of the power of the received signals from the base

stations. This parameter plays a foundamental role in terms of performance

since it affects PH and PO. As will be shown in Chapter 5, an increase of

16

CHAPTER 2. PROBLEM FORMULATION 17

nw causes a decrease of PH and an increase of PO, thus a suitable balance

between higher values of PO and lower values of PH has to be found. The

optimal nw is obtained by solving a static optimization problem, which makes

use of the following objective function:

Fobj(n, nw) = α · PH(n, nw) + (1 − α) · PO(n, nw),

where PH(n) is the handover probability at time n, PO(n) is the outage

probability at time n, α is a weighting coefficient. We study how to chose

nw so that the objective function is minimized at each time n. Moreover, we

study the case when an hysteresis margin h is introduced (see the previous

chapter). We then study how to optimize the objective function for such an

hysteresis margin. We will consider two optimizations: a static one and a

dynamic one. Static optimization means that the minimization looks only at

present time and does not take into account what happens in future moments,

that is what is done in the dynamic one. By using the hysteresis margin, the

cost function is defined as follows:

J(n, h(n)) = α · PH(h(n), n) + (1 − α)PO(h(n), n). (2.1)

The static optimization problem is expressed by:

minh(n)

J(n, h(n)),

Notice that the left hand side of (2.1) depend on h(n). The obtained results

will be discussed in Chapter 5. The dynamic optimization problem uses the

following cost function:

J(b(n), h(n)) =l+K∑

n=l

α · PH(h(l), l) + (1 − α)PO(h(l), l),

where the objective function is defined over the finite time interval [l, l + K]

and it also depends on the histeresys margin and base station b(n) at wich

the mobile is connected to in the future evolutions. Hence the constrained

optimization problem can be written as:

minh(n)

J(b(n), h(n))

s.t b(l + 1) = f(b(n), h(n)).

CHAPTER 2. PROBLEM FORMULATION 18

In Chapter 4, how to solve this problem will be studied. The evaluation of

the handover and outage probability after the introduction of the histeresis

margin, implies the computation of joint probabilities composed by a large

number of elements, and this could be temporally and computationally pro-

hibitive; for this reason some approximations of both handover and outage

probability will be proposed in Chapter 4.

Chapter 3

Modeling

To provide high quality of service in mobile communication systems is ness-

esary to develop and optimize algorithms that manage critical procedures in

wireless networks such as handover procedure. In this chapter, we study the

analytical model of the expressions of the probability of outage and of the

probability of handover. These expressions will be then used to optimize the

handover.

3.1 System Model

A system model, consisting of two BSs and a mobile terminal moving from

one base station to the other is assumed. A typical lognormal fading envi-

ronment is considered, where the attenuation of the power of the transmitted

signals follow a lognormal distribution.In this scenario the probability of out-

age Po and the probability of handover Ph are evaluated along the trip from

the current to the target BS at regular time intervals. The number of han-

dovers and outages should be minimized but the decision to make a handover

should not be delayed too long should be correctly taken, since the quality of

the communication link can degrade. Using the LS algorithm proposed in [1]

which is based on the least squares (LS) estimate of path-loss parameters for

each MS-BS link, it is necessary to know only the distance of the MS from

the surrounding BS’s.

19

CHAPTER 3. MODELING 20

3.2 Least Square Algorithm: Performance Mea-

sures

The handover problem is formulated here for the case of two BS’s, BS0 and

BS1, separated by D meters, and with an MS moving from BS0 to BS1

along a straight line at a constant speed v. The mobile measures the signal

strength from each BS at constant time intervals T (frame period). The

value of the power of the received signal level is the sum of two terms—one

due to path loss and the other due to lognormal (shadow) fading. Rayleigh

fading, which has a much shorter correlation distance with respect to shadow

fading, is neglected here because it gets averaged out at the time scale under

consideration. Hence, the signal levels [in decibels, p0(n) and p1(n)] the

mobile terminal receives from BS0 and BS1 at time nT, are given by

ps(n) = αs − βs log[ds(n)] + us[ds(n)], s = 0, 1 (3.1)

where d0 and d1 are the distances of the MS from BS0 and BS1, respectively.

Notice that d0(n) = vTn and d1(n) = D − d0(n), n=1,2. . . N with N =

⌊D/(vT )⌋ (⌊z⌋ stands for the highest integer less than or equal to the real

z). In (3.1), αs − βs log[ds(n)] is due to the path loss and αs and βs are

the parameters of the mean signal strength for the MS-BS link. u0 and u1

model the shadow fading processes. They are zero-mean stationary Gaussian

processes, independent of each other. According to [1] for the fading process

is assumed an exponential autocorrelation function

rus(∆) = E[us(d)us(d − ∆)] = σ2

use−|∆|/d s = 0, 1

where d is the decorrelation distance. This model is appropriate for cellular

environments, wich are widely used in system performance evaluation, but

as shown in [1] it can be extended to microcell and picocell system models.

Let ls(n), s=0,1 be a linear estimate of the signal strength received from the

BSs, obtained from the sequence ps(i), i = 1, 2 . . . n

ls(n) =n

∑

i=nb

ps(i) · Gs(n, i) + Gs,∞(n)

where nb = max 1, n − nw + 1 and nw is the estimation window length.

The analyzed handover algorithm makes use of the LS estimate of the path-

loss parameters, assuming that the distances are known. In a nonuniform


propagation environment the estimate of αs and βs should be carried for

each link; the estimate of the coefficients, here denoted by αs(n) and βs(n),

minimize the function

n∑

i=nb

(ps(i) − αs(n) + βs(n) log(ds(i)))2 (3.2)

By setting to zero the first-order partial derivatives of (3.2) with respect to

αs and βs, the following system of equations turns out:

n∑

i=nb

(ps(i) − αs(n) + βs(n) log ds(i)) = 0

n∑

i=nb

(ps(i) − αs(n) + βs(n) log ds(i)) log ds(i) = 0

whose solutions are

αs(n) =1

Ds(n) − Cs(n)2· [Ps(n)Ds(n) − Qs(n)Cs(n)]

βs(n) =1

Ds(n) − Cs(n)2· [Ps(n)Cs(n) − Qs(n)]

where

Ps(n)=

1

n − nb + 1

n∑

i=nb

ps(i)

Qs(n)=

1

n − nb + 1

n∑

i=nb

ps(i) log ds(i)

Cs(n)=

1

n − nb + 1

n∑

i=nb

log ds(i)

Ds(n) ,1

n − nb + 1

n∑

i=nb

(log ds(i))2.

Let

As(n, i)=

1

n − nb + 1· Ds(n) − Cs(n) log ds(i)

Ds(n) − Cs(n)2

Bs(n, i)=

1

n − nb + 1· Cs(n) − log ds(i)

Ds(n) − Cs(n)2


it follows

ls(n) =n

∑

i=nb

ps(i)As(n, i) − ps(i)Bs(n, i) log ds(n)

and

Gs(n) = As(n, i) − Bs(n, i) log ds(n)

G∞(n) = 0.

Considering that the decision process is expressed by

y(n) = l0(n) − l1(n),

it follows that for the LS algorithm the decision variable to start the handover

has the following expression:

y(n) =n

∑

i=nb

p0(i) · G0(n, i) −n

∑

i=nb

p1(i) · G1(n, i) (3.3)

3.2.1 Handover decision an probabilities

The handover decision is taken on the base of the process y(mK) defined as

y(mK) , l0(mK) − l1(mK), m = 1, 2, · · ·N/K − 1

every KT seconds (considering KT as the period of signalling multiframe

with K integer).

Let define the following connection rule based on y(mK)

b(mK) =

0, if y(mK) > 0

1, if y(mK) < 0

where b(mK) is the BS the mobile is connected to at time samples n =

mK + 1, · · · (m + 1)K. A handover occurs every time b(mK) 6= b(m + 1)K.

To evaluate performance of the algorithm, the probability of outage PO and

the probability of handover PH are defined as

PO(mK + k) = P [pbmK(mK + k) < β]

PH(mK) = P [b(mK) 6= b(mK − K)] .


Since in the described scenario is reasonable to assume that the mobile is

initially assigned to BS0, the following expressions hold:

PO(mK + k) =

P [p0(k) < β] , if m = 0

P [p0(mK + k) < β, y(mK) > 0] +

P [p1(mK + k) < β, y(mK) < 0] , if m > 1

PH(mK) =

P [y(k) < β] , if m = 1

P [y(mK) > 0, y(mK − K) < 0] +

P [y(mK) < 0, y(mK − K) > 0] , if m > 2

PO(n + 1) =

P [p0(n) < β] , if n = 0

P [p0(n + 1) < β, y(n) > 0] +

P [p1(n + 1) < β, y(n) < 0] , if n > 1

PH(n) =

P [y(n) < β] , if n = 1

P [y(n) > 0, y(n − 1) < 0] +

P [y(n) < 0, y(n − 1) > 0] , if n > 2

The above probabilities can be evaluated numerically by integrating a bivari-

ate Gaussian probability density function. To compute them is necessary to

know means, variances and correlation coefficients of every variable. Con-

sider that σ2y(n) is the variance of the decision process y(n), σ2

p0(n) is the

variance of the signal level p0 and σ2p1

(n) is the variance of the signal level

p1, then

σ2y(n) =

n∑

i=nb

n∑

j=nb

ru0(i − j) · G0(n, i) · G0(n, j) + ru1(i − j) · G1(n, i) · G1(n, j)

(3.4)

σ2p0

(n) = σ2u0

σ2p1

(n) = σ2u1

where rus(l) , rus

(lvT )=σ2us

exp(− |l| /(d/vT )) is the autocorrelation func-

tion of us(n).

And for the expectations it results

my(n) =n

∑

i=nb

(α0 − β0 log(d0(i))) · G0(n, i) − (α1 − β1 log(d1(i))) · G1(n, i)


mp0(n) = α0 − β0 log(d0(n))

mp1(n) = α1 − β1 log(d1(n))

By defining z(n) = y(n)−my(n) for n = mK the normalized correlation

coefficients of the handover decision variable y are given by

ρy(mK) =E [z(mK) · z(mK − K)]

σz(mK)σz(mK − K)

ρp0,y(mK + k) =E [u0(mK + k) · z(mK)]

σu0σz(mK)

ρp1,y(mK + k) =E [u1(mK + k) · z(mK)]

σu1σz(mK)

and from (3.1) and (3.3)

E [z(n) · z(n − K)] =n

∑

i=nb

n−K∑

j=n′b

ru0(i − j) · G0(n, i) · G0(n − K, j)

+ru1(i − j) · G1(n, i) · G1(n − K, j)

where n′b = max 1, n − K − nw + 1

E [u0(n + k) · z(n)] =n

∑

i=nb

ru0(n + k − i) · G0(n, i)

E [u1(n + k) · z(n)] = −n

∑

i=nb

ru1(n + k − i) · G1(n, i)

Given the expressions above, we can evaluate the performances of the

LS algorithm in terms of probability of outage and probability of handover;

moreover the expected number of outages and handovers along the trip are

simply given by

O =N−1∑

n=1

PO(n)

O =

N/K−1∑

m=1

PH(mK)


3.3 The effect of the Hysteresis Margin

Up to now LS algorithm was analyzed in the absence of any hysteresis mar-

gin but in handover decision criteria some hysteresis margin is allowed to

avoid the ping-pong effect that may occur in the edge of cells and hence fre-

quent handover requests from single user. The value of the hysteresis margin

plays a key role in handover performance and affects the coverage of cellular

system, therefore it must be chosen to optimize handover performance: if

this margin is too small numerous unnecessary handovers may be processed,

on the contrary if it is too high the long handover delay may result in a

dropped-call or low QoS. In the proposed algorithm handover decisions are

based on the comparison of y(n) with an hysteresis margin h(n) as will be

explained in next sections. For the same scenario of a MT moving between

only two BSs, BS0 and BS1, let define by ε(n) the event of the MT being

connected to BS1 at time n, namely ε(n)=b(n) = 1, and anlogously let

ε(n)=b(n) = 0, where the event ε(n) is defined as follows:

ε(n) = y(n) < −h(n) ∪ y(n) < h(n), ε(n − 1) (3.5)

and its complementary is

ε(n) = y(n) > h(n) ∪ y(n) > −h(n), ε(n − 1) (3.6)

b(n)

y(n)h(n)-h(n)

1

Figure 3.1: The hysteresis of the handover decision.

3.3.1 Probability of Base Station Connection

Let L(h(n)) = y(n) ≤ −h(n), M(h(n)) = −h(n) < y(n) ≤ h(n), N (h(n)) =

y(n) ≥ h(n); from (3.5) and (3.6), by using the previous definitions and


considering that L(h(n)) ⊆ N (h(n)) it follows that

ǫ(n) = L(h(n)) + N (h(n))ǫ(n − 1)

= L(h(n)) + M(h(n))ǫ(n − 1)

= L(h(n)) + M(h(n))L(h(n − 1))

+ M(h(n))M(h(n − 1))ǫ(n − 2)

The proof is obtained considering that

ǫ(n) = L(h(n)) + N (h(n))ǫ(n − 1)

= L(h(n)) + L(h(n)) + M(h(n)) ǫ(n − 1)

= L(h(n)) + L(h(n))ǫ(n − 1) + M(h(n))ǫ(n − 1)= L(h(n)) Ω + ǫ(n − 1) + M(h(n))ǫ(n − 1)= L(h(n)) + M(h(n))ǫ(n − 2),

where Ω is the probability space. Since it results that

ǫ(n − 1) = L(h(n − 1)) + N (h(n − 1))ǫ(n − 2)

= L(h(n − 1)) + M(h(n)) ǫ(n − 2),

it follows

ǫ(n) = L(h(n)) + M(h(n)) L(h(n − 1)) + M(h(n − 1)ǫ(n − 2))= L(h(n)) + M(h(n))L(h(n − 1)) + M(h(n − 1))M(h(n − 1)ǫ(n − 2)).

By iterating the procedure until time 0 ≤ m ≤ n it results

ǫ(n) =n

∑

j=m+1

L(h(j))n

∏

k=j+1

M(h(k)) +n

∏

k=m+1

M(h(k))ǫ(m) (3.7)

ǫ(n) =n

∑

j=m+1

N (h(j))n

∏

k=j+1

M(h(k)) +n

∏

k=m+1

M(h(k))ǫ(m), (3.8)

And in term of probabilities

Pr [ǫ(n)] =n

∑

j=1

Pr

L(h(j))n

∏

k=j+1

M(h(k))

+Pr

n∏

k=1

M(h(k))ǫ(0)

(3.9)


Pr [ǫ(n)] =n

∑

j=1

Pr

N (h(j))n

∏

k=j+1

M(h(k))

+Pr

n∏

k=1

M(h(k))ǫ(0)

(3.10)

The proof follows from (3.7) and (3.8) by setting m = 0 and observing

that ǫ(n) and ǫ(n) are given by the sum of events mutually exclusive. The

computation of the probabilities (3.9) and (3.10) is given by a multivari-

ate Gaussian distribution, since the events L(h(j)), M(h(k)), N (h(j)) are

defined over Gaussian (cross correlated) random variables.

3.3.2 Probability of Handover and Probability of Out-

age

Based on the events L(h(n)), M(h(n)), N (h(n)) the handover probability

at time n is given by

PH(n) = PH01(n) + PH10(n) (3.11)

where

PH01(n) = Pr [N (n)ǫ(n − 1)] · Pr [ǫ(n − 1)] (3.12)

PH10(n) = Pr [L(n)ǫ(n − 1)] · Pr [ǫ(n − 1)] (3.13)

Considering that P0(n) = p0(n) < β and P1(n) = p1(n) ≤ β the

expression of the probability of outage is given by

PO(n) = PO0(n) + PO1(n) (3.14)

where

PO0(n) = Pr [P0(n)|ǫ(n)] =Pr [P0(n)|ǫ(n)]

Pr [ǫ(n)], (3.15)

PO1(n) = Pr [P1(n)|ǫ(n)] =Pr [P1(n)|ǫ(n)]

Pr [ǫ(n)]. (3.16)

By combining (3.12),(3.13),(3.15),(3.16) with (3.9) and (3.10) come out

once again multivariate Gaussian distributions; since the use of these distri-

butions may be computationally prohibitive, in the following some bounds

to approximate the probabilities are provided.


3.4 Approximations

To obtain efficient performance, in this chapter we propose some bounds

to approximate the probabilities and their optimizations with respect to the

estimate window lenght and hysteresis margin that, as seen in previous chap-

ters, play a crucial role in terms of performance.

3.4.1 First Bound

To make calculation of Gaussian distribution faster, in this subsection we

study a simple bound to the computation of the probability. Considers a

Gaussian vector y ∈ Rn having average µ and covariance matrix Σ given by

σ2y1

ρy1y2σy1σy2 · · · ρy1ynσy1σyn

ρy1y2σy1σy2 σ2y2

· · · ρy2ynσy2σyn

......

. . ....

ρy1ynσy1σyn

ρy2ynσy2σyn

· · · σ2yn

which is a n-by-n symmetric positive definite matrix.

Let λmax and λmin be the maximum and minimum eigenvalue of Σ, re-

spectively. Consider the sets Yl =

yl ∈[

yl, yl

]

for l = 1...n. Then

Pr Y1Y2 . . .Yn ≤ λn2max√detΣ

n∏

l=1

Pr

yl ∈[

σlyl√λmax

,σlyl√λmax

]

, (3.17)

Pr Y1Y2 . . .Yn ≥ λn2min√detΣ

n∏

l=1

Pr

yl ∈[

σlyl√λmin

,σlyl√λmin

]

. (3.18)

The bounds (3.17), (3.18) are obtained by considering that for every x ∈ Rn

it holds‖x‖2

λmax

≤ xT Σ−1x ≤ ‖x‖2

λmin

and

Pr Y1Y2 . . .Yn =

∫ y1

y1

∫ y2

y2

· · ·∫ yn

yn

e−12(y−µ)T Σ−1(y−µ)

√

detΣ(2π)2dy1 . . . dyn

≤∫ y1

y1

∫ y2

y2

· · ·∫ yn

yn

e−12

‖y−µ‖2

λmax

√

detΣ(2π)2dy1 . . . dyn.


We will show in Chapter 5 that this approximation works only for low values

of the hysteresis margin. Therefore, we need an alternative approximation,

as we discuss next. The graphic that shows this trend will be reported in

Chapter 5.

3.4.2 Second Approximation: proposed bound

In this section we focus on evaluating the probabilities of handover and outage

by using the following approximation: given a Gaussian vector y ∈ Rn having

average µ and covariance matrix Σ, the probability of y is expressed by:

Pr Y1Y2 . . .Yn = Pr YnYn−1 . . .Yn−m · Pr Yn−m−1 · · ·Pr Y1 (3.19)

Where m is such that m ≤ n and Σn−m is the matrix obtained by taking the

first n − m rows and n − m columns of Σ. Make use of this bounds means

to consider the first n − m components of the Gaussian vector related and

the rest of them as if they were independent. In other words, m indicates

the number of components belonging to the joint probability which are effec-

tively considered to be joint. This make sense considering that at a generic

instant time nT there will be a strong correlation with more recent instants

time (n-1)T, (n-2)T, (n-3)T and a weaker correlation with those passed. By

starting from the expression of the probability given in (3.14), here we study

some expressions that we need to use in the probability of handover for the

simulator. By combining (3.12) with (3.9) after simple algebra and for a

generic time nT it results that the first term of the product in (3.12) is given

by:

Pr [N (n)ǫ(n − 1)] =

= P N (h(n))L(h(n))= P N (h(n))L(h(n − 1))M(h(n))= P N (h(n))L(h(n − 2))M(h(n − 1))M(h(n))= P N (h(n))L(h(n − 3))M(h(n − 2))M(h(n − 1))M(h(n))...

= P N (h(n))L(h(n − 2))M(h(n − 2)) · · ·M(h(n − i)) · · ·M(h(n)) ,

therefore by applying the equation (3.19) to these joint probability and by

considering the events correlated up till the time (n − 4) (according to the

approximation), for example for the last expression, we obtain:


P N (h(n))L(h(n − 2))M(h(n − 2)) · · ·M(h(n − i)) · · ·M(h(n)) =

P N (h(n)))M(h(n))M(h(n − 1))M(h(n − 2))M(h(n − 3) ··M(h(n − 4)) · · · M(h(n − i))L(h(n − 2)) (3.20)

Analogously, from (3.13) and (3.10) we have:

Pr [L(n)ǫ(n − 1)] =

= P L(h(n))N (h(n))= P L(h(n))N (h(n − 1))M(h(n))= P L(h(n))N (h(n − 2))M(h(n − 1))M(h(n))= P L(h(n))N (h(n − 3))M(h(n − 2))M(h(n − 1))M(h(n))...

= P L(h(n))N (h(n − 2))M(h(n − 2)) · · ·M(h(n − i)) · · ·M(h(n)) ,

hence again it is possible to apply the approximation to have:

P L(h(n))N (h(n − 2))M(h(n − 2)) · · ·M(h(n − i)) · · ·M(h(n)) =

P L(h(n)))M(h(n))M(h(n − 1))M(h(n − 2))M(h(n − 3) ··M(h(n − 4)) · · · M(h(n − i))N (h(n − 2)) (3.21)

In this way the approximation has been applied to the other joint proba-

bilities involved, as the probabability of outage and base station connection

probabilities.

For comparison purposes in Chapter 5 we illustrate the results obtained by

using a different value of m which indicates the number of the joint compo-

nents in the provided approximation. Will be shown how chosing a smaller

value of m can degrade noticeably the performance.

Chapter 4

Optimization

We formulate a static optimization problem with respect the estimate window

length and both static and dynamic optimizazion problems with respect to

hysteresis margin.

4.1 Pareto Optimization of the Estimate Win-

dow Length

One of the most important parameters of LS algorithm is the estimate win-

dow lenght (nw). The variation of this parameter causes opposite effects on

the handover and outage probability; we will show that an increase of nw de-

termines a decrease of handover probability (PH) and an increase of outage

probability (PO) hence is necessary to find a tradeoff between lower values

of PH and higher values of PO. An approach to solve the problem is to use

an objective function defined in terms of outage and handover probabilities,

is given by:

Fobj(nw) = α · PH(nw) + (1 − α) · PO(nw), (4.1)

where PH(n) is the handover probability at time n, PO(n) is the outage prob-

ability at time n, α is a weighting coefficient to tradeoff the performance in

terms of outages or handovers. The objective function is therefore a weighted

sum of handover and outage probability. The (4.1) is used in the following

minimization problem

minnw

Fobj(nw).

31

CHAPTER 4. OPTIMIZATION 32

The optimization problem expressed above is an unconstrained static op-

timization problem: the optimum value of nw can be evaluated for each

instant time nT not taking into account optimum values chosen at previous

and next time instants. The choice of the optimum value is carried out by

considering that given a value of α included between the interval [0.01,0.99]

it is possible to determine the minimum value of the objective function with

respect to the parameter nw for each instant value nT. As in D/2 falls the

worst case for values of handover and outage probability, for the parameter

n such a value is assumed in the formulated minimization problem. Ones

the optimum values of nw are evaluated it results that nwopt ⇒ nwopt(a),

in D/2; by plotting handover and outage probability evaluated in nwopt(a)

PH(nwopt(a)), PO(nwopt(a)) a fair value of the weighting coefficient can be

choosen graphically. The results will be shown in Section 5.2.

4.2 Static Handover and Outage Pareto Op-

timization

LS algorithm uses an hysteresis for the handover decision. It is easy to see

that performance of LS can be improved by adapting the hysteresis. To

select the hysteresis level, we could use a simplified method similar to the

one proposed for the estimate window length. The optimization problem is

formulated by considering the following cost function:

fobj(n, h(n)) = α · PH(n, h(n)) + (1 − α) · PO(n, h(n)), (4.2)

which has to be minimized with respect to the values that h assumes in each

n, thus we have to find

minh(n)

fobj(n, h(n))

without any constrains. As it is a static optimization problem, to solve it

we need to find the optimum value of h that, for every n, minimizes the

objective function, without considering what happens in the past and in the

future. Consider the following values:

• α ∈ [0, 01; 0, 99]

• h ∈ [2; 10]

the optimization algorithm can be described as follows:


1. for each value of α we evaluate PH and PO for every value of n and

every value of h. The values are collected in a matrix of dimensions

[n × h];

2. as probabilities values are known it is possible to compute numerically

the cost function and find its minimum value corresponding to a specific

value of h. The minimum-find is processed for each n and so optimum

values of h are known.

3. finally, by iterating step 2 for each value of α, it is possible to see the

variation of the cost function evaluated in hoptimum with respect to n,a.

The results obtained by applying the above algorithm will be presented

in Chapter 5.

4.3 Optimization of the Probability of Han-

dover

In this section we propose the optimization of the handover probability un-

der outage constraints. More specifically, here we investigate the following

dynamic optimization problem:

minh(n)

n+m∑

l=n

PHb(l)(l)

s.t POb(l)(l) ≤ Pout, l = n, · · · , n + m

b(l + 1) = f(b(l), h(l)), l = n, · · · , n + m.

In such a problem, the decision variables are the hysteresis thresholds h(l)

for l = n, . . . , n+m, which we collect in the vector h(n) = [h(n)...h(n+m)]T .

The problem is posed such that at each time instant n, the mobile station tries

to minimize the probability of handover from the current moment up until

a future instant that is m sampling times from n. The handover probability

is minimized taking into account outage events, which motivates the outage

probability constraint for ensuring an adequate quality of the communication.

In other words, we impose that at each time instant l, l = n, . . . , n + m, the

outage probability must be below a maximum value Pout. The last constraint

of the optimization problem gives the base station b(l+1) at which the mobile


station is connected to at time l+1 when a hysteresis threshold h(l) is decided

at time l. Such a mobile station will then determine the computation of the

handover probability PHb(l+1)(l+1) at time l+1. Such an optimization involves

a prediction of the future evolutions of the wireless channel. The memory

of the channel is finite owing to the coherence time of the channel. That is

why a prediction can be done up to some time m. The dynamic optimization

we are proposing by problem (23) is motivated by the fact that choosing a

hysteresis threshold h(n) at time n determines the handover decisions and

outage events of the future times. Therefore, an optimization of the handover

looking just at a present time may have negative consequences in the future.

4.4 Probability of Outage Optimization

Here is proposed the optimization problem

minh(n)

m∑

l=n

PO(l)

s.t PH(l) ≤ Phan, l = n, · · · ,m

b(l + 1) = f(b(l), h(l)), l = n, · · · ,m.

4.5 Dynamic Handover and Outage Pareto

Optimization

A better approach consists in solving an optimization problem. The objective

function is defined in terms of outage and handover probabilities:

J(b(n), h(n)) =l+K∑

n=l

z · PH(h(l), l) + (1 − z)PO(h(l), l),

where PH(n) is the handover probability at time n, PO(n) is the outage

probability at time n, z is a weighting coefficient to tradeoff the performance

in terms of outages or handovers, and K is the time horizon. The objective

function is therefore a weighted sum of handover and outage probability. In

the notation adopted for the cost function, we have evidenced the dependance

on the hysteresis h(n) and base station b(n) at which the mobile station is

connected to. Thus, we can express the following optimization problem


minh(n)

J(b(n), h(n)) (4.3)

s.t b(l + 1) = f(b(n), h(n)).

This is a dynamic optimization problem, thus getting the optimal input

h(n) of the system. The main idea is to find the optimal value of h at each

time instant n. algorithm.

0

1

PO0(n+1) PO0(n+2)

PO1(n)

PO0(n+1) PO0(n+2)

PO0(n)

PO1(n+1) PO1(n+1)

PO1(n+1) PO1(n+2)

n n+1 n+2 n+3

Figure 4.1: Trellis diagram for the computation of outage probabilities in the

dynamic optimization.

0

1

1-PH01(n+1) 1-PH01(n+2)

PH01(n)

PH10(n+1) PH10(n+2)

1-PH01(n)

PH01(n+1) PH01(n+1)

1-PH10(n+1) 1-PH10(n+2)

n n+1 n+2 n+3

Figure 4.2: Trellis diagram for the computation of handover probabilities in the

dynamic optimization.

We solve (4.3) through the use of dynamic programming, [2], for a case

of a MT moving between two BSs on a straight line and for a fixed speed v.


BS0 BS1

Optimization Interval

Cells boundary

Figure 4.3: Optimization scheme

The dynamic programming optimization can be performed with the help of

a trellis structure, where each stage of the BS0 BS1 trellis is associated to

a time instant and the possible values that the state of the system assume.

The starting stage of the trellis is associated with the state of the system

at the time n − 1, and the ending stage with the states of the system at

the time n + K. Optimization is only needed in a region which is close to

the cells boundaries, so we take into account a path of Dis = 500m, whose

left side is 750 m far from BS0, as shown in Figure ??. The coherence

interval is assumed to be d = 20m, which implies that predicted values of

the wireless channel coefficients are valid only up to 20 meters far from the

starting point. This means that, if the current BS and the hystereis value

are assumed to be known at time n − 1, future values of these parameters

can be predicted up to the time instant n + 3. In fact, assuming a sampling

distance dc = v · Tc = 6.24m, where v = 13m/s and Tc = 0.48s are the speed

of the MT and the sampling interval, respectively, it follows that the number

of prediction stages (and thus the number of stages of the trellis diagram) is:

d

dc

= 4

The optimization algorithm is as follows:

1. we assume that at distance 750 meters the system is at the generic

time instant n − 1 where the MT is still connected to BS0 with the

maximum value of the hysteresis margin;

2. since the channel coefficients are valid up to 4 samples from this starting

point, we compute through dynamic programming the costs of each

reverse path as a function of the hysteresis which is assumed to be the

same for each path of the four stages of the trellis;


3. for any path starting from b(n − 1) and ending to one of the possible

values of b(n + 3), we compute the objective function as a function of

the hysteresis;

4. for each path we then compute the hysteresis value that minimize the

cost function corresponding to the path;

5. once the hysteresis levels are known, it is possible to compute numeri-

cally the objective function associated to each path, and thus the actual

cost path;

6. the values of b(n) and h(n) are computed selecting the path with the

minimum cost;

7. the system goes in the next state, when a new vale of the fading pa-

rameters is produced. The trellis is updated removing the last stage,

and adding a new one.

The procedure described above is performed a number of times given by

Dis

dc

= 80

To go in the details of the expressions, we assume that at time ni − 1 the

minimum value of the hysteresis is known and that the probability of the

MT being connected to BS0 is equal to 1.

Chapter 5

Simulation Results

The performance measures for the handover algorithm studied in this the-

sis are evaluated in this chapter. First the results obtained by using LS

algorithm without any hysteresis margin and with the optimization of the

window length nw are presented; then by applying the hysteresis margin will

be presented the computation of the proposed handover and outage proba-

bility approximations will be studied. Finally, the results of the optimization

algorithms will be presented.

5.1 Probability of Handover and Probability

of Outage

In this section the probability of handover and the probability of outage

evaluted by using (3.2.1) and (3.2.1) are studied. According to the used

model explained in Chapter 2, these figures are obtained by considering that

at the beginning the mobile station (MS) is connected to the base station 0

(BS0). For the numerical computations, the following set of values has been

assumed:

D = 2000m

β0 = β1 = 33.8

KT = 0.48s

σ0 = σ1 = 6dB

K = 1

β = −100dBm

α0 = α1 = 10

These values are consistent with a typical LTE cellular environment.

38

CHAPTER 5. SIMULATION RESULTS 39

0 500 1000 1500 20000

0.05

0.1

0.15

0.2

0.25

distance BS0 − MS

Pro

b. h

ando

ver

n

w=5

nw

=15

nw

=25

nw

=35

nw

=45

Figure 5.1: Probability of handover versus distance d0 for LS method. The pa-

rameter is the window length nw.

0 500 1000 1500 20000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

distance BS0 − MS

Pro

b. o

utag

e

n

w=5

nw

=15

nw

=25

nw

=35

nw

=45

Figure 5.2: Probability of outage versus distance d0 for LS method. The param-

eter is the window length nw.


As reported in Figure 5.1, when the mobile station (MS) is close to the

base station 0 (BS0) the probability of handover is very low and this is

due to that the MS remains attached to the current BS until it goes out of

the coverage area of the considered BS. When the mobile is approximately

midway between the two BSs PH assumes the highest values. Then, near the

BS1 the probability value goes back again to zero because the mobile is get its

coverage area. Regard the outage probability, wich is shown in figure 5.2, it

can be observed that it follows the same trand of PH as the maximum values

fall in D/2 as well. Although the two probabilities behave differently under

varying of parameter nw, that means a trade-off between the two trends is

needed, an increase of nw does not yield any handover delay. (In other words,

the LS estimate of path-loss parameters provides an unbiased estimate of the

mean signal strength). This is a fundamental aspect because it is important

to keep the handover delay small to prevent dropped calls and to prevent an

increase in co-channel interference due to distortion of the cell boundaries.

The result of the proposed solution to estimate an appropriate value of nw

will be given in next sections.

5 10 15 20 25 30 35 40 450.054

0.056

0.058

0.06

0.062

0.064

0.066

0.068

0.07

Estimate window length

Max

imum

val

ues

of P

O

Figure 5.3: Maximum values of outage probability versus estimate window length.


5 10 15 20 25 30 35 40 450.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Estimate window length

Max

imum

val

ues

of P

H

Figure 5.4: Maximum values of handover probability versus estimate window

length.

Figures 5.3 and 5.4 show the trend of the maximum value of the handover

and outage probability, such a value is assumed when the mobile is at same

distance (D/2) from the two base stations.


5.2 Estimate Window Length Pareto Opti-

mization Results

In this section we present the result of the solution to the optimization prob-

lem with respect to the estimate window length. The result is obtained by

considering the objective function expressed in (4.1).

0.054 0.056 0.058 0.06 0.062 0.064 0.066 0.068 0.070.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Outage probability

Han

dove

r P

roba

bilit

y

Figure 5.5: Handover and outage probability evaluate at nw optimum for the

problem having the objective function in (4.6)

The graph shown in figure 5.5 is parameterized with respect to the weight-

ing coefficient α. The probabilities on the axes are evaluated at the optimum

value of the parameter nw wich depends on values of α. High values of han-

dover probability are obteined for α ∼= 0 and low values for α ∼= 1, on the

contrary the outage probability has an opposite trend. In other words it

is possible to choose the appropriate value of the weighting coefficient for

a given value of handover and/or outage probability. Of course α can be

choosen close to zero, for example, if the specific application requires that

the outage probability is more important otherwise it should be choosen close

to one.


5.3 Approximations results

In the following we present results of the approximations provided in the

previous chapter to compute handover and outage probability.

5.3.1 First approximation

0 500 1000 1500 20000

0.2

0.4

0.6

0.8

1

1.2

1.4

distance BS0 − MS

Pr

BS

h=0

h=2

h=4

Figure 5.6: Probability of BSs connection versus distance for the first bound

proposed in Section 3.4

As exhibited in Chapter 4 in the first approximation appear the deter-

minant, maximum and minimum eigenvalue of the covariance matrix Σ. By

using this approximation to plot the base station’s probability connection it

results that the error accumulated in each instant time nT yield a value of the

probability higher than one for hysteresis values different by zero (Fig.5.6).

Althought this result does not allow to apply the approximation to solve

optimization problems using high level of the hysteresis margin, it may be

implemented on applications wich make use of low values of the parameter

h because it noticeably reduces the probabilities computing time.


5.3.2 Second approximation

This section evaluates the performance of the approximation proposed in

Section 4.2.

0 500 1000 1500 20000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

distance MS−BS0

Pha

ndov

er

nw

=10, v=40, m=4

h=2h=4h=6h=8

Figure 5.7: Probability of handover versus distance evaluated by using the second

approximation given by equation (3.19) in Chapter 3, with nw = 10

0 500 1000 1500 20000

0.005

0.01

0.015

0.02

0.025

distance MS−BS0

Pha

ndov

er

nw

=40, v=40, m=4

h=2h=4h=6h=8

Figure 5.8: Probability of handover versus distance evaluated by using the second



Figures 5.7, 5.8 exhibit the trends of the handover probability for different

levels of the hysteresis margin. As it can be seen the number of components

considered correlated is indicated by the value of m which is set to four. The

difference between the two graphs is due to the choice of different values of

estimate window length which is small (nw = 10) in the first case and bigger

(nw = 40) in the second case. It is important to notice that an increase

of nw yield a decrease of the handover probability, as would be expected.

This means that the approximation works according to LS algorithm. Fur-

thermore also by using the approximation the requirement of not having any

handover delay is achived. In Fig. 5.8 the probability value decrease so much

that for some values of h it is practically equal to zero.

0 500 1000 1500 20000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

distance MS−BS0

Pou

tage

nw

=10, v=40 m=4

h=2h=4h=6h=8h=10

Figure 5.9: Probability of outage versus distance evaluated by using the second


Fig. 5.9 and 5.10 illustrate the trend of the outage probability with

respect to different levels of the hysteresis. According to the expected be-

haviour, values increase with the growth of parameters h and nw grow. The

small shift of the curves is a consequence of the fact that the probability is

computing by using the approximation. In order to prove that the better

choice of the parameter m is to take m = 4 a comparison between the values

assumed by the probability of handover and the probability of outage is pro-

vided. As it can be noticed in Fig 5.11 and 5.12 by using a value of m equal


0 500 1000 1500 2000−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

distance MS−BS0

Pou

tage

nw

=40, v=40 m=4

Figure 5.10: Probability of outage versus distance evaluated by using the second


to 4 gives results that are much better than those obtained by setting m = 3.

This confirms that if we consider less joint elements to compute probabilities,

this will influence performance in a negative manner. In particular, given a

value of h, for example h = 2, on the handover probability there is a 18%

decrease if we pass from the case m = 4 to the case m = 3.


0 500 1000 1500 20000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

distance MS−BS0

Pha

ndov

er

nw

=10, v=40, m=4

h=2h=4h=6h=8

(a) Handover probability for m=4

0 500 1000 1500 20000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

distance MS−BS0

Pha

ndov

er

nw

=10, v=40, m=3

h=2h=4h=6h=8h=10

(b) Handover probability for m=3

Figure 5.11: Comparison between handover probability values for different

m


0 500 1000 1500 20000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

distance MS−BS0

Pou

tage

nw

=10, v=40 m=4

h=2h=4h=6h=8h=10

(a) Outage probability for m=4

0 500 1000 1500 20000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

distance MS−BS0

Pou

tage

nw

=10, v=40, m=4

h=2h=4h=6h=8h=10

(b) Outage probability for m=3

Figure 5.12: Comparison between outage probability values for different m


5.4 Performance Evaluation of Hysteresis Op-

timization

The formulation of the minimization problems with respect to the optimum

value of hysteresis margin is developed in Chapter 4. In this section we

investigate both static and dynamic optimization effects on the functions

involved.

5.4.1 Static Optimization Results

In Section 4.7 we introduced the static optimization problem with respect

to the hysteresis margin and formulated an algorithm to find optimum val-

ues of h along the trip of the mobile station (MS). In this subsection we

report results obtained by applying the algorithm to minimize statically the

approximated probabilities.

0

50

100

150

0

0.5

10

0.02

0.04

0.06

0.08

Values of nValues of a

Ph(

a,n,

h* )

Figure 5.13: Handover probability evaluated at optimum h for the static opti-

mization problem.

Fig. 5.13 illustrates the trend of handover probability evaluated in hopt:

decreasing the value of a from 1 to 0 the trend tends to lower values. The

same analysis can be performed for the outage probability in Fig 5.14, even

if it follows an opposite trend with respect to the variation of a and it can be

seen how a deacrease of a yield a weak increase of PO. This does not match


0

50

100

150

0

0.5

10

0.02

0.04

0.06

0.08

0.1


Po(

a,n,

h* )

Figure 5.14: Outage probability evaluated at optimum h for the static optimiza-

tion problem.

the trend shown by the probabilities evaluated in nw optimum, in that case,

infact, an increase of a yielded an increase of PO and a decrease of PH . Fig.

5.15 shows the effect achived by applying the minimization on the objective

function: as the value of the weighting coefficient a decreases, the value of F

evaluated in hopt decreases. The reason why F has this trend is due to that

F (h∗) is the waighting sum of PH(h∗) and PO(h∗) and a decrease of PH(h∗) is

much deep compared to the weak increase of PO(h∗). Furthermore, according

to the model, maximum values of F are achived in correspondence to n = 52,

which indicates that the MS is situated at same distance from the current

and the target BS.

To investigate the impact of a static optimization, we show PH , PO and

Fobj plots obtained by fixing a specific value of h. For comparison purposes

first we set h = 2 (this value is suggested in [1]), then we show graphs

obtained by setting h = 8. In the first case, as it can be seen in Fig. 5.18,

PH and PO assume almost same values, hence in the trend of the objective

function in Fig. 5.17 it is not easy to see the weak increase. In second case,

instead, PH and PO have different values and that is why a decrease of a

yield a decrease of cost function. By comparing plot in Fig 5.15 and plot in

Fig. 5.17 it is evident the advantage achived by using the static optimization

technique.


0

50

100

150

0

0.5

10

0.02

0.04

0.06

0.08


F(a

,n,h

* )

Figure 5.15: Objective function evaluated at optimum h for the static optimiza-

tion problem.


0

50

100

150

0

0.5

10

0.02

0.04

0.06

0.08


Ph(

a,n,

h)

(a) Handover probability

0

50

100

150

0

0.5

10

0.02

0.04

0.06

0.08


Po(

a,n,

h)

(b) Outage probability

Figure 5.16: Handover and Outage probabilities evaluated by setting a fixed

histeresis margin h=2: no optimization

0

50

100

150

0

0.5

10

0.02

0.04

0.06

0.08


F(a

,n,h

)

Figure 5.17: Objective function evaluated by setting h=2: no optimization


0

50

100

150

0

0.5

10

0.002

0.004

0.006

0.008

0.01

0.012

Values of n

h=8

Values of a

Ph(

a,n,

h)

(a) Handover probability

0

50

100

150

0

0.5

10

0.02

0.04

0.06

0.08

Values of n

h=8

Values of a

Po(

a,n,

h)

(b) Outage probability

Figure 5.18: Handover and Outage probability evaluated by setting a fixed

histeresis margin h=8: no optimization

0

50

100

150

0

0.5

10

0.02

0.04

0.06

0.08

Values of n

h=8

Values of a

F(a

,n,h

)

Figure 5.19: Objective function evaluated by setting h=8: no optimization


5.4.2 Dynamic Optimization Results

The theoretical analysis of an hysteresis dynamic optimization is developed

in previous chapter. In this subsection we evaluate results obtained by Mat-

Lab for the dynamic optimization of handover and outage probabilties. In

this case the optimization is carried out taking into account the influence

of the channel from the current time instant to the next four time instants.

The objective functions are evaluated in a region which is close to the cells

boundaries, so we take into account a path of Dis = 500m, whose left side

is 750 m far from BS0. Notice that if we compare the objective function

obtained by using a dynamic optimization technique, values are lower than

those assumed by applying the static one. In this case we use different values

of the weighting coefficient α which are significant to show that the opti-

mization works well by weighting differently the probabilities involved. In

particular we choose

• α = 0.2, in this case bigger weight is given to the probability of han-

dover;

• α = 0.5, in this case same weight is given to the probabilities;

• α = 0.8, in this case bigger weight is given to the probability of outage;

As shown in Fig. 5.20 and Fig. 5.21 where α = 0.8 and α = 0.5 re-

spectively, by using dynamic optimization, better performance are achived

mostly in the region close to the BS1. When the mobile node is going out

from the coverage area of the BS0 dynamic thecnique works worst and this

is due to that in the middle of the path the recived signal strength varations

are really fast and looking at the future does not improve what the mobile

node knows about the channel. As can be seen in Fig. 5.21 even when the

mobile is close to BS0 the dynamic optimization works better. In the case

of Fig. 5.22 the dynamic technique works better than the static one for each

distance. In this plots the value of the estimate window length nw is setted

to 40.


700 800 900 1000 1100 1200 13000.01

0.02

0.03

0.04

0.05

0.06

0.07

distance MN−BS0

Obj

ectiv

func

tion

at h

opt

alpha=0.8

dynamicstatic

Figure 5.20: Comparison between objective functions evaluate at hopt by applying

dynamic and static optimization techniques with a weigthing cofficient equal to

0.5

700 800 900 1000 1100 1200 13000.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

distance MN−BS0

Obj

ectiv

e fu

nctio

n at

hop

t

alpha=0.5

dynamicstatic



0.8


700 800 900 1000 1100 1200 13000.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0.02alpha=0.2

distance MN−BS0

Obj

ectiv

e fu

nctio

n at

hop

t

dynamicstatic



0.2


5.4.3 Improving Factors

To show the improvement obtained by applying the optimization methods

proposed in this thesis, in this subsection we show the improving factors

achived by comparing objective functions obtained in the follow cases:

1. fixed level of the hysteresis margin (h = 2) and static optimization;

2. fixed level of the hysteresis margin (h = 2) and dynamic optimization;

3. fixed level of the hysteresis margin (h = 8) and optimization;

4. fixed level of the hysteresis margin (h = 8) and dynamic optimization;

5. static vs dynamic optimization.

Fig. 5.23 shows the improving factor obtained by comparing the objective

function at hopt for the static optimization and the objective function eval-

uated at h = 2 without any optimization. The value of the weighting coef-

ficient is α equal to 0.2. As it is shown there is a drammatic improvement

which is expressed in percentage. Notice that this factor is really high be-

cause the worst case for the objective function is the choice h = 2 as we

assumed in this comparison. The improvement obtained if we compare the

same objective function at h = 2 (no optimization) with the objective func-

tion evaluate at hopt by applying dynamic optimization, is shown in Fig.

5.24. The improvement in this case is even higher than the one obtained

in Fig. 5.23 and this is the proof that dynamic optimization works better

than the static one. As shown in previous sections the choice of h = 2 is

the worst choice among fixed values of the parameter h; this result also in

the improvement that we can obtain by applying optimization methods. Fig.

5.25 shows the improving factor obtained by comparing the objective func-

tion at hopt for the static optimization and the objective function evaluated

at h = 8 without any optimization. The value of the weighting coefficient is

α equal to 0.2. This factor is smaller than the improving factor obtained in

the previous comparison. The same can be observed if we compare objective

function for dynamic optimization with the objective function at h = 8 (Fig.

5.26). The improvement is certainly smaller in the comparison between ob-

jective functions evaluated at hopt for static and dynamic optimization, as

shown in Fig. and this confirms that static optimization works always very

well but the dynamic one is even better.


700 800 900 1000 1100 1200 1300200

300

400

500

600

700

800

Impr

ovin

g fa

ctor

(%

)

distance MN−BS0

alpha=0.2

Figure 5.23: Improving factor between objective function evaluated by fixing an

hysteresis margin h = 2 and the objective function at hopt computed by using the

static optimization

700 800 900 1000 1100 1200 1300200

300

400

500

600

700

800

900

1000

distance MN−BS0

Impr

ovin

g fa

ctor

(%

)

alpha=0.2



dynamic optimization


700 800 900 1000 1100 1200 130010

15

20

25

30

35

40

45

50

55

60

distance MN−BS0

Impr

ovin

g fa

ctor

(%

)

alpha=0.2




700 800 900 1000 1100 1200 130020

40

60

80

100

120

140

distance MN−BS0

Impr

ovin

g fa

ctor

(%

)

alpha=0.2





700 800 900 1000 1100 1200 13000

20

40

60

80

100

120

distance MN−BS0

Impr

ovin

g fa

ctor

(%

)

alpha=0.2

Figure 5.27: Improving factor between objective function evaluated by using static

and dynamic optimization. The value of the parameter α is 0.2

Chapter 6

Conclusions

The contribution of this thesis regards two aspects. First, to overcome the

limitation due to limited computational resources we studied an approxi-

mation to compute the probability of handover and probability of outage

evaluated along the trip of a mobile station moving between two base sta-

tions. The numerical results show that the approximated probabilities follow

a good behavior. Starting by a well known model, we have then studied some

optimization problems of these probabilities with respect to parameters that

play a crucial role in term of algorithms performance. Without considering

any hysteresis margin we provided an optimization of the estimate window

length which is the number of samples to estimate with a desired accuracy

these probabilities by solving a static minimization problem. We showed that

this optimization allows to choose a fair value of the weighting coefficient and

the choice is based on the considered application. Then we formulated other

two optimization problems with respect to the level of the hysteresis mar-

gin, an important parameter that should be properly choosen to avoid the

so called ping pong effect which is a frequent connection and disconnection

with the same base station by the mobile node. This could be expensive for

the network in terms of traffic load. We proved that by formulating different

optimization problems better performance can be obtained with respect to

existing algorithms. Results show that performance achived by choosing a

fixed value of the hysteresis margin are worst compared to the performance

achived by appling the studied optimizations:

• static optimization outperforms significantly a non optimized handover;

• dynamic optimization outperform the static one at the cost of an in-

61

CHAPTER 6. CONCLUSIONS 62

creased computational complexity.

We can see that static optimization works always very well but the dynamic

one is even better. We obtained drammatic improving factors that show this

results.

Future works

In this thesis we show how the algorithm is sensitive to the variations of

the estimate window length and the level of the hysteresis margin, and we

studied an optimization of the algorithm with respect to these parameters.

However, as the window length and the hysteresis affects differently the in-

volved probabilities, could be useful to do a joint optimization of these two

parameters to choose fair values for both of them.

Bibliography

[1] N. Benvenuto, F. Santucci: A Least Squares Path-Loss Estimation Ap-

proach to Handover Algorithms, IEEE Transaction on Vehicular Tech-

nology, Vol. 48, No. 2, March 1999.

[2] Dimitri P. Bertsekas: Dynamic programming and optimal control.,

Athena scientific, 1995.

[3] Zach Shelby, Carsten Bormann: 6LoWPAN: The Wireless Embedded

Internet. WILEY, 2009.

[4] Carlos J. Bernardos, Antonio De La Oliva, Marıa Calderon, Dirk von

Hugo, and Holger Kahle:NEMO: Network Mobility. Bringing ubiquity

to the Internet access. Demonstration at IEEE INFOCOM 2006, April

2006.

[5] M. Gudmundson: Radio Communication Systems. IEEE Elettronics

Letters, Vol. 27, No. 23, November 1991.

[6] Gordon L. Stuber: Principles of Mobile Communication. Kluwer Aca-

demic Publishers, 1996.

[7] D. Culler, D. Estrin, M. Srivastava: Overview of Sensor Networks, IEEE

Computer Society, August 2004.

[8] A. Murase, I. C. Symington and E. Green: Handover criterion for

macro and microcellular systems, IEEE Vehicular Technology Confer-

ence, Saint Louis, May 1991.

63

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