Advanced wireless networks 4g technologies phần 5 pps

The time for which a mobile is in the handoff area depends on system parameters such as the speed and direction of mobile travel and the cell size.. Let X be the elapsed time from the in

CELLULAR SYSTEMS WITH PRIORITIZED HANDOFF 331

The complementary distribution function FCTH(t) is

To simplify the analysis the distribution of THis approximated in References [75, 76] by

a negative exponential distribution with mean ¯TH(1/μH) From the family of negative

exponential distribution functions, a function which best fits the distribution of TH, by

G=

 ∞0

F C

TH(t)− e−μHt dt2

 ∞0

F THC (t) dt

(11.8)

In the sequel the following definitions will be used:

(1) The probability that a new call does not enter service because of unavailability of

channels is called the blocking probability, PB.

(2) The probability that a call is ultimately forced into termination (though not blocked)

is PF This represents the average fraction of new calls which are not blocked butwhich are eventually uncompleted

(3) Pfh is the probability that a given handoff attempt fails It represents the averagefraction of handoff attempts that are unsuccessful

(4) The probability PNthat a new call that is not blocked will require at least one handoffbefore completion because of the mobile crossing the cell boundary is

(5) The probability PHthat a call that has already been handed off successfully willrequire another handoff before completion is

PH= Pr {TM> Th} =

∞

0

e−μMtf Th(t) dt (11.10)

Let the integer random variable K be the number of times that a nonblocked call is

success-fully handed off during its lifetime The event that a mobile moves out of the mobile servicearea during the call will be ignored since the whole service area is much larger than the

cell size A nonblocked call will have exactly K successful handoffs if all of the following

events occur:

(1) It is not completed in the cell in which it was first originated

(2) It succeeds in the first handoff attempt

(3) It requires and succeeds in k− 1 additional handoffs

(4) It is either completed before needing the next handoff or it is not completed but fails

on the (k+ 1)st handoff attempt

The probability function for K is therefore given by

11.2.1 Channel assignment priority schemes

The probability of forced termination can be decreased by giving priority (for channels) tohandoff attempts (over new call attempts) In this section, two priority schemes are described,

and the expressions for PBand Pfhare derived A subset of the channels allocated to a cell is

to be exclusively used for handoff calls in both priority schemes In the first priority scheme,

a handoff call is terminated if no channel is immediately available in the target cell (channel

reservation – CR handoffs) In the second priority scheme, the handoff call attempt is held

in a queue until either a channel becomes available for it, or the received signal power level

becomes lower than the receiver threshold level (channel reservation with queueing – CRQ

handoffs).

11.2.2 Channel reservation – CR handoffs

Priority is given to handoff attempts by assigning Chchannels exclusively for handoff calls

among the C channels in a cell The remaining C − C channels are shared by both new

CELLULAR SYSTEMS WITH PRIORITIZED HANDOFF 333

0 E

Figure 11.21 State-transition diagram for channel reservation – CR handoffs

calls and handoff calls A new call is blocked if the number of available channels in the cell

is less than or equal to Chwhen the call is originated A handoff attempt is unsuccessful if

no channel is available in the target cell We assume that both new and handoff call attemptsare generated according to a Poisson point process with mean rates per cell of Rand Rh,

respectively As discussed previously, the channel holding time THin a cell is approximated

to have an exponential distribution with mean ¯TH(1/μH) We define the state E j of a

cell such that a total of j calls is in the progress for the base station of that cell Let P j

represent the steady-state probability that the base station is in state E j; the probabilitiescan be determined in the usual way for birth-death processes discussed in Chapter 6 Thepertinent state-transition diagram is shown in Figure 11.21

The state equations are

C

k =C−Ch +1

( R +  Rh)C −Ch k −(C−Ch )

Rh k! μHk

Rh j! μ j

H

P0, for j = C − Ch+ 1, , C

(11.14)

The probability of blocking a new call is PB= C

j =C−ChP jand the probability of handoff

attempt failure Pfhis the probability that the state number of the base station is equal to C Thus Pfh= Pc.

11.2.3 Channel reservation with queueing – CRQ handoffs

When a mobile moves away from the base station, the received power generally decreases.When the received power gets lower than a handoff threshold level, the handoff procedure

Delayed Blocked

Handoff attempts

New call originators

Queue of Delayed Handoff Attemps

Channel use record

Delayed Blocked

Handoff attempts

New call originators

Queue of delayed handoff attemps

Channel use record

Calls in progress Forced terminations

Figure 11.22 Call flow diagram for channel reservation with queueing-CRQ handoffs

is initiated The handoff area is defined as the area in which the average received power

level from the base station of a mobile receiver is between the handoff threshold level

(upper bound ) and the receiver threshold level (lower bound ) If the handoff attempt finds

all channels in the target cell occupied, we consider that it can be queued If any channel

is released while the mobile is in the handoff area, the next queued handoff attempt isaccomplished successfully If the received power level from the source cell’s base stationfalls below the receiver threshold level prior to the mobile being assigned a channel in thetarget cell, the call is forced into termination When a channel is released in the cell, it isassigned to the next handoff call attempt waiting in the queue (if any) If more than onehandoff call attempt is in the queue, the first-come-first-served queuing discipline is used.The prioritized queueing is also possible where the fast moving (fast signal level losing)users may have higher priority We assume that the queue size at the base station is unlimited.Figure 11.22 shows a schematic representation of the flow of call attempts through a basestation

The time for which a mobile is in the handoff area depends on system parameters such

as the speed and direction of mobile travel and the cell size We call it the dwell time of a

mobile in the handoff area T Q For simplicity of analysis, we assume that this dwell time

is exponentially distributed with mean ¯T Q(1/μH) We define E j as the state of the base

station when j is the sum of the number of channels being used in the cell and the number of

handoff call attempts in the queue For those states whose state number j is less than equal

to C, the state transition relation is the same as for the CR scheme Let X be the elapsed

time from the instant a handoff attempt joins the queue to the first instant that a channel is

released in the fully occupied target cell For state numbers less than C, X is equal to zero Otherwise, X is the minimum remaining holding time of those calls in progress in the fully

occupied target cell When a handoff attempt joins the queue for a given target cell, otherhandoff attempts may already be in the queue (each is associated with a particular mobile)

When any of these first joined the queue, the time that it could remain on the queue without

succeeding is denoted by T Q (according to our previous definition) Let T ibe the remaining

dwell time for that attempt which is in the i th queue position when another handoff attempt

CELLULAR SYSTEMS WITH PRIORITIZED HANDOFF 335

Figure 11.23 State-transition diagram for CRQ priority scheme

joins the queue Under the memoryless assumptions here, the distributions of all T i and T Q

are identical Let N (t) be the state number of the system at time t From the description of

this scheme and the properties of the exponential distribution it follows that

Rh j! μ j

H

P0, for C − Ch+ 1 ≤ j ≤ C

( R +  Rh)(C −C h) j −(C−C h)

Rh C! μ C

The probability of blocking is PB= ∞j =C−Ch P j A given handoff attempt that joins the

queue will be successful if both of the following events occur before the mobile moves out

of the handoff area:

(1) All of the attempts that joined the queue earlier than the given attempt have beendisposed

(2) A channel becomes available when the given attempt is at the front of the queue.Thus the probability of a handoff attempt failure can be calculated as the average fraction ofhandoff attempts whose mobiles leave the handoff area prior to their coming into the queue

front position and getting a channel Noting that arrivals that find k attempts in queue enter position k+ 1, this can be expressed as

Pfh ∞

k=0

wherePfh|k = P r {attempt fails given it enters the queue in position k − 1}.

Since handoff success for those attempts which enter the queue in position k+ 1 requirescoming to the head of the queue and getting a channel, under the memoryless conditionsassumed in this development, we have

whereP (i | i + 1) is the probability that an attempt in position i + 1 moves to position i

before its mobile leaves the handoff area

There are two possible outcomes for an attempt in position i+ 1 It will either be clearedfrom the system or will advance in queue to the next (lower) position It will advance if theremaining dwell time of its mobile exceeds either:

(1) at least one of the remaining dwell times T j , j = 1, 2, , i, for any attempt ahead

of the channel holding times, the random variables, X , T j , ( j = 1, 2, , i) are statistically

independent Therefore, the cumulative distribution of Y iin Equation (11.19) can be writtenas

F Yi(τ) = 1 − {1 − F X(τ)}{1 − F T1(τ)} {1 − F Ti(τ)}

CELLULAR SYSTEMS WITH PRIORITIZED HANDOFF 337

Because of the exponentially distributed variables, this gives

e−(CμH+iμ Q)τ μ Qe−μ Qτdτ = μ Q

C μH+ (i + 1)μ Q , i = 1, 2,

The handoff attempt at the head of the queue will get a channel (succeed) if its remaining

dwell time T1exceeds X Thus

P r {get channel in front position} = P r {T1> X} and

P r {does not get channel in front position} = P r {T1≤ X} (11.21)

=

∞

0

A call which is not blocked will be eventually forced into termination if it succeeds in

each of the first (l − 1) handoff attempts which it requires but fails on the lth Therefore,

where PN and PHare the probabilities of handoff demand of new and handoff calls, as

defined previously Let Pncdenote the fraction of new call attempts that will not be

com-pleted because of either blocking or unsuccessful handoff This is also an important system

performance measure This probability Pnccan be expressed as

Pnc= PB+ PF(1− PB)= PB+ PfhPN(1− PB)

1− PH(1− Pfh) (11.25)where the first and second terms represent the effects of blocking and handoff attemptfailure, respectively In Equation (11.25) we can guess roughly that, when cell size is large,

the probabilities of cell crossing PNand PHwill be small and the second term of Equation(11.25) (i.e the effect of cell crossing) will be much smaller than the first term (i.e effect

of blocking) However, when the cell size is decreased, PN and PH will increase The

noncompleted call probability Pnccan be considered as a unified measure of both blockingand forced termination effects

Another interesting measure of system performance is the weighted sum of PBand PF

CF = (1 − α)PB+ αPF (11.26)whereα is in the interval [(0, 1)] and indicates the relative importance of the blocking and

forced termination effects For some applications PFmay be more important than PBfromthe user’s point of view, and the relative costα can be assigned using the system designer’s

judgment

11.2.4 Performance examples

For the calculations, the average message duration was taken as ¯TM= 120s and the maximum

speed of a mobile of Vmax= 60 miles/h was used The probabilities PBand PFas functions

of (new) call origination rate per unit areaacan be seen in Figure 11.24, with cell radius

R being a parameter A total of 20 channels per cell (C = 20) and one channel per cell for

handoff priority (Ch= 1) was assumed The CRQ scheme was used for this figure, and themean dwell time for a handoff attempt ¯T Qwas assumed to be ¯TH/10 As can be seen, PF

is much smaller than PBand the difference between them decreases as cell size decreases

As expected, for larger R the effect of handoff attempts and forced terminations on system

Figure 11.24 Blocking and forced termination probabilities for CRQ priority scheme

CELLULAR SYSTEMS WITH PRIORITIZED HANDOFF 339

Blocking Forced termination

2 0

Call origination rate density (calls per s/square mile)

Figure 11.25 Blocking and forced termination probabilities for CRQ systems with 20

Figure 11.26 Blocking and forced terminations for priority CR and CRQ schemes (20

channels/cell, one handoff channel/cell, R= 2 miles)

Figure 11.25 shows PBand PFas functions ofa As the effects of increasing priority

given to handoff calls over new calls by increasing Ch, PFdecreases by orders of magnitude

with only small to moderate increase in PB this exchange is important because (as wasmentioned previously) forced terminations are usually considered much less desirable thanblocked calls

Blocking and forced termination probabilities for the two priority schemes are shown

in Figure 11.26 as functions of call origination rate densitya The forced termination

probability PFis smaller for th CRQ scheme, but almost no difference exists in blocking

probability PB We get this superiority of the CRQ priority scheme by queuing the delayed

handoff attempts for the dwell time of the mobile in the handoff area

11.3 CELL RESIDING TIME DISTRIBUTION

In this section we discuss the probability distributions of the residing times T n and Th The

random variable T n is defined as the time (duration) that a mobile resides in the cell in which

its call originated Also This defined as the time a mobile resides in a cell to which its call

is handed off To simplify analysis we approximate the hexagonal cell shape as a circle For

a hexagonal cell having radius R , the approximating circle with the same area has a radius,

Req, which is given by Req=√(3√

3/2π) R ≈ 0.91R and illustrated in Figure 11.27 The

base station is assumed to be at the center of a cell and is indicated by a letter B in the figure The location of a mobile in a cell, which is indicated by a letter A in the figure, is represented by its distance r and direction φ from the base station as shown To find the

distributions of T n and Th, we assume that the mobiles are spread evenly over the area of

the cell Then r and φ are random variables with PDFs

shown in the figure, the distance Z from the mobile to the boundary of approximating circle is Z =√[R2

eq− (r sin θ)2]− r cos θ Because φ is evenly distributed in a circle, Z

is independent ofφ and from the symmetry we can consider the random variable θ is in

q

C

A r

φ

Figure 11.27 Illustration of distance from point A in cell (where call is originated), to point

C on cell boundary (where mobile exits from cell).

CELL RESIDING TIME DISTRIBUTION 341

If we define new random variables x , y as x = r cos θ, y = r sin θ, then Z = (R2

eq− y2)− x and W = x Since the mobile is assumed to be equally likely to be located anywhere in the

If the speed V of a mobile is constant during its travel in the cell and random variable which

is uniformly distributed on the interval [0, Vmax] with PDF

Vmax

0

B

q

Z C

2Req

Figure 11.28 Illustration of distance from cell entering point ( A on cell boundary), to cell

exiting point (C on cell boundary).

To find the distribution of Th, in the next step we note that, when a handoff call is attempted, it

is always generated at the cell boundary, which is taken as the boundary of the approximating

circle Therefore, to find Thone must recognize that the mobile will move from one point onthe boundary to another The direction of a mobile when it crosses the boundary is indicated

by the angleθ between the direction of the mobile and the direction from the mobile to the

center of a cell as shown in Figure 11.28 [75, 76]

If the mobile moves in any direction with equal probability, the random variableθ has

CELL RESIDING TIME DISTRIBUTION 343

The distance Z as shown in Figure 11.28 is Z = 2Reqcosθ, which has a CDF given by

The time in the cell This the time that a mobile travels the distance Z with speed V , then

Th= Z/V With the same assumption about V , the PDF of This

f Th (t)=

∞

0

50 60 70 80 90 100 110 120 130

Cell radius (miles)

Maximum velocity of mobile = 30 miles/h

40 60

Figure 11.29 Mean channel holding time (s) in cell vs R (average call duration= 120 s)

Table 11.1 The goodness-of-fit G of the approximation

G of this approximation, defined in Equation (11.8), is shown in Table 11.1 for various cell

sizes We see that G is very small for a wide ranges of cell radius R These values support

the use of the approximation in the calculations

11.4 MOBILITY PREDICTION IN PICO- AND MICROCELLULAR NETWORKS

It should be expected that 4G networks will further reduce the size of the cells In a and picocellular network, resources availability varies frequently as users move from oneaccess point to another In order to deterministically guarantee QoS support for a mobileunit, the network must have prior exact knowledge of the mobile’s path, along with arrivaland departure times to every cell along the path With this knowledge, the network canverify the feasibility of supporting the call during its lifetime, as the mobile moves acrossthe network It is impractical, however, to require the users to inform the network of their

micro-exact movement, since they may not know this information a priori Even if the path is

MOBILITY PREDICTION IN PICO- AND MICROCELLULAR NETWORKS 345

known, the exact arrival and departure times to the cells along the path are still hard todetermine in advance Therefore, it becomes crucial to have an accurate mechanism topredict the trajectory of the mobile user

As an example, the virtual connection tree is designed to support QoS guarantees formobile units [77] In this scheme, a number of adjacent cells are grouped into a cell cluster

in a static fashion Upon the admission of a call, the scheme pre-establishes a connectionbetween a root switch and each base station in the cell cluster The scheme does not takeuser mobility into consideration to predict the set of base stations which may potentially

be visited by the mobile unit This may result in an unnecessary resource overloading thatmay underutilize the network resources and cause severe congestion

The shadow cluster (SC) scheme [78] provides a distributed call-admission control

(CAC) based on the estimated bandwidth requirements in the SC An SC is a collection

of base stations to which a mobile unit is likely to attach in the future The admissiondecision is made in a distributed fashion by all the base stations within the SC The schemepartitions the time into predefined intervals and verifies the feasibility of supporting callsover those intervals This requires the communication of large number of messages betweenbase stations during every time interval Moreover, since bandwidth estimates are calculated

at the beginning of each time interval and the admission decisions are made at the end ofeach time interval, admission of new calls is delayed for at least a time equal to the length

of these predefined time intervals

Both of the above two schemes lack the mechanism to predict the mobile’s trajectoryand determine the future cells to which the mobile may hand off Several techniques havebeen proposed in the literature to address this issue In Bharghavan and Mysore [79], aprofile-based algorithm is proposed to predict the next cell that the mobile unit will handoff, using a user profile and a cell profile, which are simply the aggregate values of thehandoff’s history In Liu and Maguire [80], a mobile motion prediction (MMP) algorithm

is proposed to predict the future locations of the mobile unit This algorithm is based on apattern matching technique that exploits the regularity of the users’ movement patterns TheMMP algorithm was further expanded to a two-tier hierarchical location prediction (HLP)algorithm [81] In the latter case, the two-tiered prediction scheme involves both an intercelland an intracell tracking and prediction component The first tier uses an approximatepattern matching technique to predict the global intercell direction and the second tier uses

an extended self-learning Kalman filter to predict the trajectory within the cell using themeasurements received by the mobile unit

In order to support QoS guarantees of multiple classes of services, the scheme must grate call and admission control with the mobility profile of the mobile user The integration

inte-of these two components makes it possible to use mobility prediction to verify the feasibility

of admitting a new call and make sure that the required QoS can be supported during thelifetime of the call In other words we should be able to predict location (space) and timewhen a certain resources well be needed in the network This concept will be referred to

as space time predictive QoS or STP QoS The mobility prediction algorithm must be easy

to implement and maintain, since it will be invoked on a per-user basis Furthermore, theadmission control procedure must be invoked only when needed with minimum overheadand in a distributed fashion, where each network cell, potentially involved in supporting theQoS requirements of the call, participates in the decision process [82, 83]

In this section, we present such a framework, which efficiently integrates mobility diction and CAC, to provide support for PST-QoS guarantees, where each call is guaranteed

pre-its QoS requirements for the time interval that the mobile unit is expected to spend withineach cell it is likely to visit during the lifetime of the call.

In this framework, efficient support of PST-QoS guarantees is achieved based on anaccurate estimate of mobile’s trajectory as well as the arrival and departure times for eachcell along the path Using these estimates, the network can determine if enough resourcesare available in each cell along the mobile’s path to support the QoS requirements of thecall The framework is designed to easily accommodate dynamic variations in networkresources The basic components of this framework are:

(1) a predictive service model to support timed-QoS guarantees;

(2) a mobility model to determine the mobile’s most likely cluster (MLC); the MLCrepresents a set of cells that are most likely to be visited by a mobile unit during itsitinerary; and

(3) a CAC model to verify the feasibility of supporting a call within the MLC

The service model accommodates different types of applications by supporting integral and fractional predictive QoS guarantees over a predefined time-guarantee period The

MLC model is used to actively predict the set of cells that are most likely to be visited bythe mobile unit For each MLC cell, the mobile’s earliest arrival time latest arrival time andlatest departure time are estimated These estimates are then used by the CAC to determinethe feasibility of admitting a call by verifying that enough resources are available in each

of the MLC cells during the time interval between the mobile’s earliest arrival time and itslatest departure time If available, resources are then reserved for the time interval betweenthe mobile’s earliest arrival time and latest departure time and leased for the time intervalbetween the mobile’s earliest and latest arrival times If the mobile unit does not arrive beforethe lease expires, the reservation is canceled and the resources are returned to the pool ofavailable resources The unique feature of the this frame-work is the ability to combine themobility model with the CAC model to determine the level of PST-QoS guarantees that thenetwork can provide to a call and dynamically adjust these guarantees as the mobile unitmoves across the network

11.4.1 PST-QoS guarantees framework

The first approach, to achieve a high level of QoS support guarantees in mobile environments,

is to allocate resources for the duration of the call in all future cells that the mobile unitwill visit This means that the resources within each cell that is to be visited will be held,possibly for the duration of the call, even if the mobile never moves into the cell This

approach is similar to the one proposed in Talukdar et al [85] and will be referred to as a

predictive space or PS QoS model Clearly, such an approach will result in underutilization

of the network resources as resources are being held, but not used by any call

The second approach is to only reserve resources in all future cells that the mobile unit

may visit for the time interval during which the mobile will reside in each cell If t i and

t i+1represent the expected arrival and departure times of the mobile unit to cell i along the

path, respectively, resources in cell i will only be reserved for the time interval [t i , t i+1][84] Unlike the first approach, this approach is likely to increase resource utilization, sinceresources in every cell remain available to other calls outside the reservation intervals.This approach, however, is only feasible if exact knowledge of the mobile path and arrival

MOBILITY PREDICTION IN PICO- AND MICROCELLULAR NETWORKS 347

and departure times to every cell along the path is available Obtaining exact knowledge

of mobile mobility is not possible in most cases, due to the uncertainty of the mobileenvironments and the difficulty in specifying the mobility profiles of mobile units Anacceptable level of service guarantees, however, can be achieved if the path of the mobilecan be predicted accurately This approach is discussed in this section and will be referred

to as predictive space and time or the PST QoS model The model attempts to achieve

a balance between an acceptable level of service guarantees and a high level of networkresource utilization Based on this model, the required QoS support level is guaranteed by

reserving resources in advance in each cell that is most likely to be visited by the mobile

unit These reservations only extend for a time duration equal to the time interval the mobileunit is expected to spend within a cell, starting from the time of its arrival time to the celluntil its departure time from the cell In order to characterize the set of ‘most likely’ cellsand capture the level of QoS guarantees requested by the application, the service modeluses the following parameters:

(1) the time guarantee period T G;

(2) a cluster-reservation thresholdτ, and a

(3) bandwidth-reservation threshold,γ.

All of these parameters are application-dependent The parameter T G specifies the timeduration for which the required QoS level is guaranteed;τ defines the minimum percentage

of the most likely cells to be visited by the mobile unit that must support the required QoS

level for the guarantee period T G The parameterγ represents the minimum percentage of

the required bandwidth that must be reserved in every cell that is most likely to be visited

To accommodate different types of applications, the service model provides two types

of predictive service guarantees, namely, integral guaranteed service and fractional

guar-anteed service The integral guarguar-anteed service ensures that all cells, which are most likely

to be visited by the mobile unit, can support the requested bandwidth requirements for the

lifetime of the call In this case, T Gmust be equal to the call duration andτ and γ are both

equal to 100 % The fractional guaranteed service, on the other hand, guarantees that at least

τ % of these cells can support at least the γ % of the requested bandwidth requirements for

the next T Ginterval A special case arises when either the value ofτ or γ is zero In this

case, the service is referred to as best effort.

11.4.2 Most likely cluster model

The MLC model considers that the ‘most likely to be visited’ property of a cell is directlyrelated to the position of the cell with respect to the estimated direction of the mobile unit.This likelihood is referred to as directional probability Based on this metric, cells that aresituated along the mobile unit’s direction have higher directional probabilities and are morelikely to be visited than those that are situated outside of this direction

Based on the above, the MLC at any point in time during the lifetime of a call is defined as

a collection of contiguous cells, each of which is characterized by a directional probabilitythat exceeds a certain threshold For each MLC cell, the expected arrival and departuretimes of the mobile are estimated Using these estimates, the feasibility of supporting therequested level of timed-QoS guarantees during the mobile’s residence time within each cellalong path is verified In the following, we present the method used to predict the direction

of a mobile unit and the scheme used to construct its MLC We then describe the algorithmused to estimate the expected times of arrival and departure of the mobile unit to a givencell within the MLC [84].

The direction-prediction method used by MLC to predict the mobile user’s direction is

based on the history of its movement It is clear, however, that the prediction method usedshould not be greatly affected by small deviations in the mobile direction Furthermore, themethod should converge rapidly to the new direction of the mobile unit To take the aboveproperties into consideration, a first-order autoregressive filter, with a smoothing factorα,

is used More specifically, let D0be the current direction of the mobile unit when the call ismade Notice that, when the mobile is stationary within a cell, it is assumed that the currentcell is the only member of the MLC, so reservations are done only within the current cell

If D t represents the observed direction of the mobile unit at time t and ˜ D t represents the

estimated direction at time t , the predicted direction ˜D t+1at t + 1 is obtained as ˜D t+1=(1− α) ˜D t + αD t In order to track the actual direction of the mobile unit more accurately,the smoothing factorα is computed as α = cE2

s /σ s+1where 0< c < 1, E s = D s − ˜D s isthe prediction error, andσ s is the average of the past square prediction errors at time s σ s

can be expressed asσ s+1 = cE2

s + (1 − c) σ s

The directional probability, at any point in time t, of any cell being visited next by a

mobile unit, can be derived based on the current cell, where the mobile resides, and theestimated direction ˜D t of the mobile unit at time t The basic property of this probability

distribution is that for a given direction, the cell that lies on the estimated direction fromthe current cell has the highest probability of being visited in the future [83] Consider a

mobile unit currently residing at cell i coming from cell m and let j = 1, 2, , represent a set of adjacent cells to cell i Each cell j is situated at an angle ω i j from the x-axis passing

by the center of cell i , as presented in Figure 11.30 If we define the directional path from

i to j as the direct path from the center of cell i to the center of cell j, the directionality

D i j for a given cell j can be expressed as

MOBILITY PREDICTION IN PICO- AND MICROCELLULAR NETWORKS 349

whereφ i j is an integer representing the deviation angle between the straight path to

des-tination and the directional path from i to j , while θ i j represents the angle between the

directional path from m to i and the directional path from i to j

Based on its directionality D i j , the directional probability P i → j of cell j being visited next by a mobile unit currently at cell i can be expressed as P i → j = D i j / k D ik where k is

a cell at the same ring as j with respect to i A cell k is said to be at ring L with respect to cell

i if it is located at a ring L cells away from i For a given cell i, the directional probabilities

P i → jprovide the basis upon which MLCs are formed as the mobile units moves across the

network

11.4.2.1 Forming the most likely cluster

Starting from the cell where the call originated, a mobile unit is expected to progresstoward its destination The mobile unit, however, can temporarily deviate from its long-term direction to the destination, but is expected to converge back at some point in timetoward its destination This mobility behavior can be used to determine the cells that arelikely to be visited by a mobile unit

Let us define the forward span as the set of cells situated within an angle with respect

to the estimated direction ˜D tof the mobile unit as illustrated in Figure 11.31 Based on thedirectional probabilities and the definition of a forward span, the MLC of a given mobile

unit u currently located at cell i , denoted as CMLC

i (u), can be expressed as CMLC

{cells j | φ i j ≤ δ i , j = 1, 2, } where φ i jis the deviation angle between the straight path

to destination and the directional path from i to j The angle δ i is defined such that P i → j ≥ μ,

whereμ represents a system defined threshold on the likelihood that cell is to be visited.

More specifically,δ ican be expressed asδ i = max |φ i j | such that P i → j ≥ μ.

The next step in the process of forming the MLC is to decide on the size of the MLC

window, WMLC, which represents the number of adjacent rings of cells to be included in theMLC Define Ringi , j to be the ring at which cell j is located with respect to cell i Therefore,

on the performance of the scheme Increasing the MLC window size, by including morerings, increases the likelihood of supporting the required QoS if the mobile moves alongthe predicted direction ˜D (t) On the other hand, if the mobile deviates from the predicted

direction, increasing the MLC window size may not ensure the continued support of thecall, as the mobile unit may move out from the MLC A possible approach is to rewardusers who move within the predicted direction by increasing their MLC window size up

to a maximum Rmax The value of Rmaxdepends on the value of the guarantee period T G

Higher values of T G result in larger values of Rmax.When the user deviates from the estimated direction, the MLC window size is decreased

by an amount proportional to the degree of deviation As a result, support of the predictableusers’ QoS requirements can be achieved with high probability, whereas users with unpre-dictable behavior do not unnecessarily overcommit the network resources The algorithmdynamically updates the size of the MLC window based on the observed movement pat-terns of the mobile users If tis the measure of the mobile’s deviation with respect to the

estimated direction at time t, defined as  t+1= β t + (1 − β)| ˜D t − D t | with 0 < β < 1

and0equal to zero, the MLC window size WMLCat time t can be defined as follows:

The method can be easily extended to cellular network with cells of different sizes When

a cellular network has cells of different sizes, the definition of rings is different The rings

are imaginary circles centered at the current cell The radius of the first ring R1is equal tothe distance from the center of the current cell to the center of the neighboring cell whose

center is farthest away Consequently, the radius of a ring i , where i = 1, 2, , is equal

i × R1 Any cell that has its center within the boundaries of a ring is considered in that ring

The time of arrival and residence time of the mobile can be estimated for each MLC

cell Based on these estimates, the feasibility of supporting the requested level of timed-QoSguarantees within the residence time can then be verified The cell residence time within cell

j for a mobile unit currently in cell i is characterized by three parameters, namely, expected

earliest arrival time [TEA(i , j)], expected latest arrival time [TLA(i , j)], and expected latest

departure time [TLD(i , j)] Consequently, [TEA(i , j), TLD(i , j) ] is the expected residence

time of the mobile unit within cell j This interval is referred to as the resource reservation interval (RRI), while the interval [TEA(i , j), TLA(i , j)] is referred to as the resource leasing

interval (RLI) Resources are reserved for the entire duration of RRI However, if the mobiledoes not arrive to cell before RLI expires, all resources are released and the reservation iscanceled This is necessary to prevent mobile units from holding resources unnecessarily

In order to derive these time intervals, one can adopt the method used in the SC andconsider all possible paths from the current cell to each cell in the cluster [78] This methodcan be complex, since there are many possible paths that a mobile unit may follow to reach

a cell The approach taken in the MLC model is based on the concept of most likely paths[84]

Consider a mobile unit u, currently located at cell m, and let CMLC

m (u) denote its MLC Define G = (V, E) to be a directed graph, where V is a set of vertices and E a set of edges.

A vertexv i ∈ V represents MLC cell i For each cell i and j in CMLC(u), an edge ( v i,v j)

MOBILITY PREDICTION IN PICO- AND MICROCELLULAR NETWORKS 351

is in E if and only if j is a reachable direct neighbor of i Each directed edge is ( v i,v j) in

G is assigned a cost 1 /P i → j.

A path  between MLC cells i and k is defined as a sequence of edges (v i , v i+1),

(v i+1, v i+2), , (v k−1, v k ) The cost of a path between MLC cells i and k is derived from

the cost of its edges so that the least costly path represents the most likely path to be followed

by the mobile A k-shortest paths algorithm [86] is then used to obtain the set K of k-most

likely paths to be followed by the mobile unit.

For each path ∈ K between MLC cell i and j, we define the path residence time as

the sum of the residence time of each cell in the path Let s and1 in K , represent the

paths with the shortest and longest path residence time, respectively. sis used to derive theexpected earliest arrival time , while1is used to derive expected latest arrival TLA(i , j).

So, TEA(i , j) and TLA(i , j) can be expressed, respectively, as

n are three consecutive cells in the path The value of d(m , k, n) depends on whether cell

k is the cell where the call originated, an intermediate cell or the last cell in the path, i.e.

dO(k , n), if k is the originating cell

dI(m , k, n), if k is the intermediate cell

dLI (k , n), if m = n

dL(m , k), if k is the last cell, k= j

(11.39)

When k is the originating cell, the pdf f Y (y) of the distance Y , within cell k as shown in

Figure 11.32, is derived, assuming that the mobile units are evenly spread over a cell area of

v

ω 1

Figure 11.32 Distance Y in originating cell k.

radius R travel along a constant direction within the cell and can exit from the cell from any point along the border with cell n Therefore, the position of the mobile unit is determined by

the angleν and the distance r from the center of the cell ν is uniformly distributed between

0 and 2π; r is uniformly distributed between 0 and R Since ν is uniformly distributed,

φ is also uniformly distributed between 0 and π Therefore, d (k, n) is equal to the mean

distance E [Y ] of the PDF f Y(y) Based on these assumptions the PDF f Y(y)in a cell where

the call originates can be obtained using the standard methods as described in [75]:

y · f Y (y) dy=8R

When k is an intermediate cell, the PDF f Y(y) of the distance Y , within cell k, as shown in

Figure 11.33, is derived assuming that the mobile units enter cell k from cell m at any point along the arc AB of cell k This arc is defined by the angles β1andβ2: The mobile travels

along a constant direction within the cell and can exit from cell k to n from any point along the arc CD of cell k , which is defined by the angles ω1andω2 The direction of the mobile

is indicated by the angleφ, which is uniformly distributed; d (m, k, n) is equal to the mean

distance E [Y ] of the PDF f Y(y), which is derived in Aljadhai and Znati [84] (see also the

A

B C

D

φ 0

Y R

Cell n’s border

Cell k’s border

φ 0

MOBILITY PREDICTION IN PICO- AND MICROCELLULAR NETWORKS 353

Appendix for details) as

!β

2− ω22

"

− sin

!β

1− ω22

"

− sin

!β

2− ω12

"

+ sin

!β

1− ω12

!ω

1− β22

"

− sin

!ω

1− β12

"

− sin

!ω

2− β12

"

+ sin

!ω

2− β12

"*

for β2≤ ω1

(11.41)The mean distance in the last cell in the path is derived as follows:

The estimates of TEA(i , j), TLD(i , j) and TLD(i , j) for a mobile u currently located at cell i

are used to compute RLI and RRI for each cell j ∈ CMLC

i (u) The CAC uses these values

to verify the feasibility of supporting u’s call in each cell j ∈ CMLC

i (u).

A good agreement between the results of the analytical model of the distance, based onEquations (11.40) and (11.41), and the simulation results of mobile units traveling alongthe same path, is demonstrated in Aljadhai and Znati: [84]

used: voice, audio, and video, requiring Bvoice= 1 BU, Baudio= 5 BUs and Bvideo=

10 BUs, respectively The probabilities of each type are, Pvoice = 0.7, Paudio= 0.2, and Bvideo= 0.1.

(4) Mobile units may have one of three different speeds: 70, 90 or 105 km/h Theprobability of each speed is 1/3.

(5) In the SC scheme, the time is quantized in time interval of length 10 s

(6) A reference scheme, referred to as clairvoyant scheme (CS), is introduced In thisscheme, the exact behavior of every mobile unit is assumed to be known at theadmission time CS reserves bandwidth in exactly the cells that the mobile unit willvisit and for the exact residence time interval in every cell Therefore, CS producesthe maximum utilization and minimum blocking ratio for a specific dropping ratio,which is zero in this case.

Since mobile units can appear anywhere along a cell, the residence time within the initialcell (the cell in which the call originates) is selected to be uniformly distributed betweenzero, and a duration equal to cell length/speed The initial direction probability is assumed

to be 0.5 for both possible directions, i.e left and right directions After the first handoff, thedirection and position of the call become known and, therefore, it is possible to determinethe arrival and departure time in other cells

Figure 11.34 shows the blocking ratio and Figure 11.35 utilization of the three schemes

as functions of the call arrival rate As expected, CS produces the maximum utilizationand minimum blocking ratio assuming a zero dropping ratio condition The utilization inthe MLC CAC is better than SC as the call arrival rate exceeds 0.06 for all mean callholding times Moreover, the call blocking in MLC CAC is much less than that of the

SC scheme This behavior shows that, by simply reserving bandwidth between the earliestarrival time and latest departure time at a cell, the MLC scheme accepts more calls andincreases utilization Moreover, the increase in the utilization in the SC scheme is very slowwhen the call arrival rate is greater than 0.06 The reason for this behavior is that the SCbases its estimates on the exponential holding time PDF, which decreases as time increases.Therefore, the bandwidth estimates decreases as the distance to a future cell increases

As a result, the chance of dropping the call in subsequent cells is increased unless theminimum survivability estimate is increased In Figures 11.34 and 11.35, the MLC CACalways outperforms the SC regardless of the mean holding time

0 0.1 0.2 0.3 0.4 0.5 0.6

CAC (130

CS (130 sec)

CAC (180 CS CAC (130

CS (130 sec)

CAC (180 CS

Shadow cluster (130 s)

CAC (130 s)

CS (130 s)

Shadow cluster (180 s) CAC (180 s)

APPENDIX: DISTANCE CALCULATION IN AN INTERMEDIATE CELL 355

0.2 0.3 0.4 0.5

CS (

Shadow cluster (130 sec) Shadow cluster (180 sec) CAC (130 s

CS (13 CA

CS (

Shadow cluster (130 s) Shadow cluster (180 s) CAC (130 s)

CS (130 s) CAC (180 s)

CS (180 s)

Call arrival rate (call/cell/s)Figure 11.35 Utilization in three systems

APPENDIX: DISTANCE CALCULATION IN AN INTERMEDIATE CELL

Given an intermediate cell on the path of the mobile unit, the PDF of the distance can bederived based on the anglesβ and ω, as shown in Figure 11.33 The entry point to the

cell is assumed to be the point E, as shown in Figure 11.33 The mobile unit move in adirection evenly distributed leading to the next cell (Figure 11.33), where 2ψ is the range of

the direction angleφ The angle β is uniformly distributed between β1andβ2 Therefore,

If Y is the distance traveled from E to X , as in Figure 11.33 then, Y becomes Y = 2R cos φ

and gives in Equation (11.47) the following four cases

"

1−2arco cos

 y 2R

"

≤ y ≤ 2R cos

!

ψ12

"

!

ψ12

"

≤ y ≤ 2R cos

!

ψ12

!

ψ22

"

− sin

!

ψ12

"*

(11.52)

The mean distance E [Y ] for cell id(m , i, j) for a mobile path entering cell i from cell

m and exiting cell i to cell j is

!ψ22

"

− sin

!

ψ12

"*

APPENDIX: DISTANCE CALCULATION IN AN INTERMEDIATE CELL 357

!

β2− ω22

"

− sin

!

β1− ω12

"

− sin

!β

2− ω12

"

+ sin

!β

1− ω22

!

ω1− β22

"

− sin

!

ω1− β12

"

− sin

!ω

2− β12

"

+ sin

!ω

2− β12

"

1−2arc cos

 y 2R

"

≤ y ≤ 2R cos

!

ψ12

"

!

ψ22

"

≤ y ≤ 2R cos

!

ψ12

!ψ22

"

− sin

!ψ12

"*

(11.58)

The mean distance E [Y ] for cell id(m , i, j) for a mobile path entering cell i from cell

m and exiting cell i to cell j is

!ψ22

"

− sin

!

ψ12

"*

β2− ω22

"

− sin

!

β1− ω12

"

− sin

!β

2− ω12

"

+ sin

!β

1− ω22

!

ω1− β22

"

− sin

!

ω1− β12

"

− sin

!ω

2− β12

"

+ sin

!ω

2− β12

"

1−2arc cos

 y 2R

− ψ1

!ψ22

"

1−2arc cos

 y 2R

"

≤ y ≤ 2R

(11.66)

APPENDIX: DISTANCE CALCULATION IN AN INTERMEDIATE CELL 359

The mean distance E[Y | β] is

!ψ22

"

− sin

!ψ12

"*

(11.68)

The mean distance E [Y ] for cell id(m , i, j) for a mobile path entering cell i from cell m

and exiting cell i to cell j is

!

ψ22

"

− sin

!

ψ12

!

β2− ω22

"

− sin

!

β1− ω12

"

− sin

!β

2− ω12

"

+ sin

!β

1− ω22

!

ω1− β22

"

− sin

!

ω1− β12

"

− sin

!ω

2− β12

"

+ sin

!ω

2− β12

"

1−2arc cos

 y 2R

"

≤ y ≤ 2R

(11.72)

1−2arco cos

 y 2R

!

ψ22

"

− sin

!

ψ12

"*

(11.78)

The mean distance E[Y ] for cell id(m , i, j) for a mobile path entering cell i from cell m

and exiting cell i to cell j is

!ψ22

"

− sin

!

ψ12

"*

β2− ω22

"

− sin

!

β1− ω12

"

− sin

!β

2− ω12

"

+ sin

!β

1− ω22

!

ω1− β22

"

− sin

!

ω1− β12

"

− sin

!ω

2− β12

"

+ sin

!ω

2− β12

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Adaptive Resource

Management

12.1 CHANNEL ASSIGNMENT SCHEMES

A given radio spectrum (or bandwidth) can be divided into a set of disjoint or noninterferingradio channels All such channels can be used simultaneously while maintaining an accept-able received radio signal In order to divide a given radio spectrum into such channels,many techniques such as frequency division (FDMA/OFDMA), time division (TDMA/THUWB), or code division (CDMA/MC CDMA) can be used, as discussed in Chapter 2 InFDMA, the spectrum is divided into disjoint frequency bands, whereas in TDMA the chan-nel separation is achieved by dividing the usage of the channel into disjoint time periodscalled time slots In CDMA, the channel separation is achieved by using different spreadingcodes The major criteria in determining the number of channels with a certain quality thatcan be used for a given wireless spectrum is the level of received signal quality that can beachieved in each channel

If Si(k) is the set (i ) of wireless terminals that communicate with each other using the same channel k, then due to the physical characteristics of the radio environment, the same channel k can be reused simultaneously by another set j if the members of sets i and j

are spaced sufficiently apart All such sets which use the same channel are referred to asco-channel sets or simply co-channels The minimum distance at which co-channels can

be reused with acceptable interference is called the ‘co-channel reuse distance’ D For

illustration see Figure 12.1

This is possible because, due to propagation path loss in the radio environment, the

average power received from a transmitter at distance d is proportional to PTd −αwhereα

is a number in the range 3–5 depending on the physical environment, and PTis the average

transmitter power Thus, by adjusting the transmitter power level and/or the distance d

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D R

1

1 1

1

1 1

1 1

1 1

1

1 1

1

1 1

1 1

3

3 3

Figure 12.1 Examples of frequency reuse factor (a) Uniform hexagonal cellular layout

with reuse 7 (b) Macrocell layout with reuse 3 (c) Street microcell layoutwith reuse 2

between co-channels, a channel can be reused by a number of co-channels if the CIR

(carrier-to-interference ratio) in each co-channel is above the required value CIRmin In

general, for a wireless station R at distance d from a transmitter T , using the same reference radio channel as the set of other transmitters T i at distances d i from R, we have

where N0represents the background noise To achieve a certain level of CIR at the reference

station R, different methods can be used.

In general we can represent the residual interference signal power as

I → Ir(d , θ, f, t) = (1 − Cf)(1− Cp)(1− C θ)(1− Ct)I (d , θ, f, t) (12.1a)

CHANNEL ASSIGNMENT SCHEMES 369

where Cf, Cp, C θ and Ctare frequency, propagation (distance+ shadowing + fading), angle

(space) and time isolation coefficients, respectively I (d , θ, f, t) is the interference signal

power without any suppression techniques [1] For perfect isolation at least one of thesecoefficients is equal to one and the interference has no influence on the received signal In

practice, it is rather difficult and economically impractical to reach the point where C i = 1.Instead, the product (1− Cr) (1− C θ) (1− Ct) depending on these coefficients should bekept as low as possible with an affordable effort measured by cost, power consumption andphysical size of the hardware required for the solution

Coefficient Cfis related to frequency assignment in the cellular network while coefficient

Cp is related to the propagation conditions Cf= 1 if the interfering signal frequency is

different from the frequency of the useful signal Cp= 1 if, due to propagation losses, theinterfering signal cannot reach the site of the useful reference signal In general, the samefrequency can be used in two cells only if the propagation losses between the two cells arehigh enough so that the interfering signals are attenuated to the acceptable level Coefficient

C θis related to antenna beamforming and the possibilities of reducing the interference level

by spatial filtering Finally, interference cancellation and equalization in time domain canalso be used to reduce the level of interference

In this chapter we will focus on two methods for reducing the interference level First, the

distance between interfering stations using the co-channel and the reference station R can

be increased to reduce the co-channel interference level Many channel allocation schemes

are based on this idea of physical separation Another solution to reduce the CIR at R is

to reduce the interfering powers transmitted from interfering stations and/or to increase

the desired signal’s power level P This is the idea behind power control schemes These

two methods present the underlying concept for channel assignment algorithms in cellular

systems Each of these algorithms uses a different method to achieve a CIRminat each mobileterminal by separating co-channels and/or by adjusting the transmitter power

12.1.1 Different channel allocation schemes

Channel allocation schemes can be divided into a number of different categories depending

on the comparison basis For example, when channel assignment algorithms are comparedbased on the way in which co-channels are separated, they can be divided into fixed channelallocation (FCA), dynamic channel allocation (DCA), and hybrid channel allocation (HCA)

In FCA schemes, the area is partitioned into a number of cells, and a number of channels

are assigned to each cell according to some reuse pattern, depending on the desired signal

quality In DCA, all channels are placed in a pool and are assigned to new calls as needed

such that the criterion is satisfied At the cost of higher complexity, DCA schemes provideflexibility and traffic adaptability However, DCA strategies are less efficient than FCAunder high load conditions To overcome this drawback, HCA techniques were designed

by combining FCA and DCA schemes Channel assignment schemes can be implemented

in many different ways For example, a channel can be assigned to a radio cell based on

the coverage area of the radio cell and its adjacent cells such that the CIRminis maintainedwith high probability in all radio cells Channels could be also assigned by taking the localCIR measurements of the mobile’s and base station’s receiver into account That is, instead

of allocating a channel blindly to a cell based on worst-case conditions (such as lettingco-channels be located at the closest boundary), a channel can be allocated to a mobilebased on its local CIR measurements [2, 3]

Channel assignment schemes can be implemented in centralized or distributed fashion Inthe centralized schemes the channel is assigned by a central controller, whereas in distributedschemes a channel is selected either by the local base station of the cell from which the call

is initiated or selected autonomously by the mobile In a system with cell-based control,each base station keeps information about the current available channels in its vicinity Herethe channel availability information is updated by exchange of status information betweenbase stations In autonomously organized distributed schemes, the mobile chooses a channelbased on its local CIR measurements without the involvement of a central call assignmententity This scheme is simpler but less efficient The channel assignment based on localassignment can be done for both FCA and DCA schemes

12.1.2 Fixed channel allocation

In the FCA strategy a set of nominal channels is permanently allocated to each cell for itsexclusive use Here a definite relationship is assumed between each channel and each cell,

in accordance with co-channel reuse constraints [4–8]

The total number of available channels in the system C is divided into sets, and the minimum number of channel sets N (reuse factor) required to serve the entire coverage area is related to the reuse distance s as follows [5]: N = σ2/3, for hexagonal cells.

Here σ is defined as D /R, where R is the radius of the cell and D is the physical

distance between the two cell centres [4] N can assume only the integer values 3, 4, 7,

9, , as generally presented by the series, (i + j)2 − i j, with i and j being integers [4] Figure 12.1(a) and 4(b) gives the allocation of channel sets to cells for N = 3 and N = 7,

respectively

In the simple FCA strategy, the same number of nominal channels is allocated to eachcell This uniform channel distribution is efficient if the traffic distribution of the system isalso uniform In that case, the overall average blocking probability of the mobile system isthe same as the call blocking probability in a cell Because traffic in cellular systems can benonuniform with temporal and spatial fluctuations, a uniform allocation of channels to cellsmay result in high blocking in some cells, while others might have a sizeable number ofspare channels This could result in poor channel utilization So, the number of channels in

a cell can match the load in it by nonuniform channel allocation [9, 10] or static borrowing[11, 12]

In nonuniform channel allocation the number of nominal channels allocated to eachcell depends on the expected traffic profile in that cell Thus, heavily loaded cells areassigned more channels than lightly loaded ones In Zhang and Yum [9] an algorithm,

called nonuniform compact pattern allocation, is proposed for allocating channels to cells

according to their traffic distributions The technique attempts to allocate channels to cells

in such a way that the average blocking probability in the entire system is minimized Asimilar technique for nonuniform channel allocation is also employed in the algorithms

proposed in Oh et al [10].

Simulation results in Zhang and Yum [9] show that the blocking probability using form compact pattern allocation is always lower than the blocking probability of uniformchannel allocation Also, for the same blocking probability, the system can carry on average

nonuni-10 % (maximum 22 %) more traffic with the use of the nonuniform pattern allocation [9]

In the static borrowing schemes proposed in References [11, 12], unused channels fromlightly loaded cells are reassigned to heavily loaded ones at distances greater than the

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