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EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

<strong>Cellular</strong> <strong>Systems</strong><br />

<strong>Cellular</strong> <strong>Concepts</strong><br />

<br />

<br />

<strong>The</strong> <strong>cellular</strong> <strong>concept</strong> <strong>was</strong> a major breakthrough in<br />

solving the problem of spectral congestion and user<br />

capacity. It offered very high capacity in a limited<br />

spectrum allocation without any major technological<br />

changes.<br />

<strong>The</strong> <strong>cellular</strong> <strong>concept</strong> has the following system level<br />

ideas<br />

• Replacing a single, high power transmitter with many<br />

low power transmitters, each providing coverage to<br />

only a small area.<br />

• Neighbouring cells are assigned different groups of<br />

channels in order to minimise interference.<br />

<br />

<br />

Reuse can be done once the total interference from all<br />

users in the cells using the same frequency (cochannel<br />

cell) for transmission suffers from sufficient<br />

attenuation. Factors need to be considered include:<br />

• Geographical separation (path loss)<br />

• Shadowing effect<br />

<strong>The</strong> actual radio coverage of a cell is known as the<br />

cell footprint.<br />

• Irregular cell structure and irregular placing of the<br />

transmitter may be acceptable in the initial system<br />

design. However as traffic grows, where new cells and<br />

channels need to be added, it may lead to inability to<br />

reuse frequencies because of co-channel interference.<br />

• For systematic cell planning, a regular shape is<br />

assumed for the footprint.<br />

<br />

• <strong>The</strong> same set of channels is then reused at different<br />

geographical locations.<br />

When designing a <strong>cellular</strong> mobile communication<br />

system, it is important to provide good coverage and<br />

services in a high user-density area.<br />

• Coverage contour should be circular. However it is<br />

impractical because it provides ambiguous areas with<br />

either multiple or no coverage.<br />

• Due to economic reasons, the hexagon has been chosen<br />

due to its maximum area coverage.<br />

Institute for Infocomm Research 43 National University of Singapore<br />

Institute for Infocomm Research 44 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

R<br />

R<br />

R<br />

2<br />

2<br />

2<br />

Atri = 1.3R<br />

Asq<br />

= 2.0R<br />

Ahex<br />

= 2.6R<br />

• Interference tier : A set of co-channel cells at the same<br />

distance from the reference cell is called an<br />

interference tier. <strong>The</strong> set of closest co-channel cells is<br />

call the first tier. <strong>The</strong>re is always 6 co-channel cells in<br />

the first tier.<br />

• Hence, a conventional <strong>cellular</strong> layout is often defined<br />

by a uniform grid of regular hexagons.<br />

Frequency reuse :<br />

• A <strong>cellular</strong> system which has a total of S duplex<br />

channels.<br />

• S channels are divided among N cells, with each cell<br />

uses unique and disjoint channels.<br />

• If each cell is allocated a group of k channels, then<br />

S = kN .<br />

<br />

Co-ordinates for hexagonal <strong>cellular</strong> geometry<br />

• With these co-ordinates, an array of cells can be laid<br />

out so that the center of every cell falls on a point<br />

specified by a pair of integer co-ordinates.<br />

<br />

Terminology<br />

• Cluster size : <strong>The</strong> N cells which collectively use the<br />

complete set of available frequency is called the<br />

cluster size.<br />

• Co-channel cell : <strong>The</strong> set of cells using the same set of<br />

frequencies as the target cell.<br />

If ( ∆ u , ∆v)<br />

= ( i,<br />

j)<br />

, i,j are known as the shift<br />

parameters, then the distance between the two cell<br />

centres is given by<br />

2<br />

2<br />

D = i + j + ij ⋅ 3R<br />

(Cosine’s Rule)<br />

Institute for Infocomm Research 45 National University of Singapore<br />

Institute for Infocomm Research 46 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

<br />

Designing a <strong>cellular</strong> system<br />

Examples: N=3,4,7,9,12,13<br />

Proof : to obtain the area of the cluster and compare<br />

with the area of a single cell.<br />

<br />

<strong>The</strong> cluster size must satisfy<br />

2 2<br />

N = i + ij + j where i, j str non-negative integers.<br />

<br />

Can also verify that<br />

D<br />

Q = = 3N<br />

where Q is the co-channel reuse ratio.<br />

R<br />

Institute for Infocomm Research 47 National University of Singapore<br />

Institute for Infocomm Research 48 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

Handover / Handoff<br />

<br />

Occurs as a mobile moves into a different cell during<br />

an existing call, or when going from one <strong>cellular</strong><br />

system into another.<br />

• It must be user transparent, successful and not too<br />

frequent.<br />

• If the slope of the short-term average received signal<br />

is steep, handover should carry out fast. Information<br />

about vehicle speed is important.<br />

Handover take place<br />

f1<br />

f2<br />

P HO<br />

• Not only involves identifying a new BS, but also<br />

requires that the voice and control signals be allocated<br />

to channels associated with the new BS.<br />

Time taken to<br />

complete handover<br />

P min<br />

<br />

Once a particular signal level P min is specified as the<br />

minimum usable signal for acceptable voice quality<br />

at the BS receiver, a slightly stronger signal level<br />

P HO is used as a threshold at which a handover is<br />

made.<br />

P HO<br />

= P min<br />

+ ∆<br />

• If ∆ is too large ⇒ unnecessary handovers<br />

• If ∆ is too small ⇒ insufficient time to complete<br />

handovers, call may drop due to poor received signal<br />

quality.<br />

• Running average should be used to avoid unwanted<br />

handover due to momentary fading.<br />

<br />

Dwell Time<br />

• <strong>The</strong> time over which a user remains within one cell is<br />

called the dwell time.<br />

• <strong>The</strong> statistics of the dwell time are important for the<br />

practical design of handover algorithms.<br />

• <strong>The</strong> statistics of the dwell time vary greatly,<br />

depending on the speed of the user and the type of<br />

radio coverage.<br />

Institute for Infocomm Research 49 National University of Singapore<br />

Institute for Infocomm Research 50 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

<br />

<br />

Handover indicator<br />

• Each BS constantly monitors the signal strengths of<br />

all of its reverse voice channels to determine the<br />

relative location of each mobile user with respect to<br />

the BS. This information is forwarded to the MSC<br />

who makes decisions regarding handover.<br />

• Mobile assisted handover (MAHO) : <strong>The</strong> mobile<br />

station measures the received power from<br />

surrounding BSs and continually reports the results of<br />

these measurements to the serving BS.<br />

Prioritizing Handover<br />

• Dropped call is considered a more serious event than<br />

call blocking. Channel assignment schemes therefore<br />

must give priority to handover requests.<br />

<br />

which a handover is usually required leaves room for<br />

queueing handover request.<br />

Practical handover<br />

• High speed users and low speed users have vastly<br />

different dwell times which might cause a high<br />

number of handover requests for high speed users.<br />

This will result in interference and traffic<br />

management problem.<br />

• <strong>The</strong> Umbrella Cell approach will help to solve this<br />

problems. High speed users are serviced by large<br />

(macro) cells, while low speed users are handled by<br />

small (micro) cells.<br />

• A fraction of the total available channels in a cell is<br />

reserved only for handover requests. However, this<br />

reduces the total carried traffic. Dynamic allocation<br />

can improve this.<br />

• Queuing of handover requests is another method to<br />

decrease the probability of forced termination of a call<br />

due to a lack of available channel. <strong>The</strong> time span over<br />

Institute for Infocomm Research 51 National University of Singapore<br />

Institute for Infocomm Research 52 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

<br />

<br />

A hard handover does “break before make”, ie. <strong>The</strong><br />

old channel connection is broken before the new<br />

allocated channel connection is setup. This obviously<br />

can cause call dropping.<br />

In soft handover, we do “make before break”, ie. <strong>The</strong><br />

new channel connection is established before the old<br />

channel connection is released. This is realized in<br />

CDMA where also BS diversity is used to improve<br />

boundary condition.<br />

A<br />

Hard:<br />

B<br />

Interference and System Capacity<br />

<br />

<br />

In a given coverage area, there are several cells that<br />

use the same set of frequencies. <strong>The</strong>se cells are called<br />

co-channel cells. <strong>The</strong> interference between signals<br />

from these cells is called co-channel interference.<br />

If all cells are approximately of the same size and the<br />

path loss exponent is the same throughout the coverage<br />

area, the transmit power of each BS is almost equal.<br />

We can show that worse case signal to co-channel<br />

interference is independent of the transmitted power.<br />

It becomes a function of the cell radius R, and the<br />

distance to the nearest co-channel cell D’.<br />

A<br />

Soft:<br />

B<br />

(a) Received power at a distance d from the<br />

transmitting antenna is approximated by<br />

−n<br />

⎛ d ⎞<br />

Pr<br />

( d)<br />

= P0<br />

⎜<br />

d<br />

⎟ or<br />

⎝ 0 ⎠<br />

⎛ d ⎞<br />

P r ( d)<br />

( dBm ) = P0 ( dBm ) −10nlog<br />

⎜<br />

⎟<br />

⎝ d0<br />

⎠<br />

(b) Useful signal at the cell boundary is the<br />

weakest, given by P r (R). Interference signal from<br />

the co-channel cell is given to be P r (D′)<br />

.<br />

Institute for Infocomm Research 53 National University of Singapore<br />

Institute for Infocomm Research 54 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

(c) D’ is normally approximated by the base station<br />

separation between the two cells D, unless when<br />

accuracy is needed. Hence<br />

−n<br />

R<br />

SIR =<br />

−n<br />

D<br />

• If only first tier co-channel cells are considered, then<br />

i 0 = 6.<br />

• Unless otherwise stated, normally assuming<br />

for all i.<br />

D i ≈ D<br />

<br />

Outage probability : the probability that a mobile<br />

station does not receive a usable signal.<br />

• For GSM, this is 12 dB and for AMPS, this is 18 dB.<br />

If there is 6 co-channel cells, then<br />

n<br />

( D R) ( 3N<br />

)<br />

SIR = =<br />

6<br />

6<br />

Exercise : please verify this<br />

• For n=4, a minimum cluster size of N=7 is needed to<br />

meet the SIR requirements for AMPS.<br />

n<br />

<br />

For the forward link, a very general case,<br />

−n<br />

R<br />

SIR =<br />

i0<br />

−n<br />

∑ Di<br />

i=<br />

1<br />

where D i is the distance of the ith interfering cell<br />

from the mobile, i 0 is the total number of co-channel<br />

cells exist.<br />

• For n=4, a minimum cluster size of N=4 is required to<br />

meet the SIR requirements for GSM<br />

Institute for Infocomm Research 55 National University of Singapore<br />

Institute for Infocomm Research 56 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

- More accurate SIR can be obtained by computing<br />

the actual distance.<br />

- Aproximation in distance has been made on the<br />

2 nd tier onwards.<br />

- Our computation of outage only based on path loss.<br />

For more accurate modeling, shadowing and fast<br />

fading need to be taken into consideration. This will<br />

not be covered in this course.<br />

Institute for Infocomm Research 57 National University of Singapore<br />

Institute for Infocomm Research 58 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

Coverage Problems<br />

<br />

Revision:<br />

- Recall that the mean measured value,<br />

⎛ d ⎞<br />

PL(<br />

d)<br />

dB = PL(<br />

d0)<br />

dB + 10n<br />

log<br />

⎜<br />

⎟ or<br />

⎝ d0<br />

⎠<br />

P r ( d)<br />

dB = PtdB<br />

− PL(<br />

d)<br />

dB<br />

[ P ( γ ]<br />

β ( γ ) = P r R)<br />

> - cell boundary coverage,<br />

β ( γ )<br />

∞<br />

= ∫<br />

γ<br />

1<br />

2πσ<br />

X dB<br />

⎛ ⎞<br />

⎜γ<br />

− P<br />

= r ( R)<br />

Q ⎟<br />

⎜ ⎟<br />

⎝<br />

σ X dB ⎠<br />

⎡<br />

2⎤<br />

⎢ 1 ⎛<br />

⎞<br />

⎜ X −<br />

− dB Pr<br />

( R)<br />

exp<br />

⎟ ⎥dX<br />

⎢ ⎜<br />

⎟ ⎥ dB<br />

2<br />

⎢⎣<br />

⎝<br />

σ X dB ⎠ ⎥⎦<br />

where Q(x) is the standard normal distribution.<br />

• must know how to use the table.<br />

<br />

- Measurement shows that at any value of d, the<br />

path loss PL (d)<br />

at a particular location is random<br />

and distributed log-normally (normal in dB) about<br />

this mean value.<br />

Pr ( d)<br />

dB = Pr<br />

( d)<br />

dB + X σ<br />

where X σ is a zero-mean Gaussian distributed<br />

random variable (in dB) with standard deviation σ<br />

(in dB).<br />

Boundary coverage<br />

<br />

Cell coverage<br />

• Proportion of locations within the area defined by the<br />

cell radius R, receiving a signal above the threshold γ.<br />

1<br />

U ( γ ) = ∫ P[ Pr<br />

( r)<br />

> γ ] dA<br />

A<br />

A<br />

1<br />

R 2π<br />

⎛ P r ⎞<br />

Q⎜γ<br />

− r ( )<br />

= ∫ ∫<br />

⎟ ⋅ rdr ⋅ dθ<br />

2<br />

πR<br />

⎜<br />

X<br />

⎟<br />

0 0 ⎝<br />

σ<br />

dB ⎠<br />

2<br />

R ⎛ P r ⎞<br />

Q⎜γ<br />

−<br />

=<br />

r ( )<br />

∫<br />

⎟ ⋅ rdr<br />

R ⎜<br />

X<br />

⎟<br />

0 ⎝<br />

σ<br />

dB ⎠<br />

• <strong>The</strong>refore, there will be a proportion of locations at<br />

distance R (cell radius) where a terminal would<br />

experience a received signal above a threshold γ. (γ is<br />

usually the receiver sensitivity)<br />

<strong>The</strong> solution is given in the Rappaport p.107 (1 st<br />

edition).<br />

Institute for Infocomm Research 59 National University of Singapore<br />

Institute for Infocomm Research 60 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

Solution can be found using the graph provided. (n :<br />

path loss exponent)<br />

<br />

<strong>The</strong> mean signal level at any distance is determined<br />

by path loss and the variance is determined by the<br />

resulting fading distribution (log-normal shadowing,<br />

Rayleigh fading, Nakagami-m, etc). In this course, we<br />

will deal with log-normal shadowing only.<br />

<br />

<strong>The</strong> proportion of locations covered at a given<br />

distance (cell boundary, for example) from BS can be<br />

found directly from the resultant signal pdf/cdf.<br />

<br />

<strong>The</strong> proportion of locations covered within a circular<br />

region defined by a radius R (the cell area, for<br />

example) can be found by integrating the resultant<br />

cdf over the cell area.<br />

Example: if n=4, σ=8 dB, and if the boundary is to<br />

have 75% coverage (75% of the time the signal is to<br />

exceed the threshold at the boundary), then the<br />

area coverage is equal to 94%.<br />

If n=2, σ=8 dB, and if the boundary is to have 75%<br />

coverage, then the area coverage is equal to 91%.<br />

<br />

An operator needs to meet certain coverage criteria.<br />

This is typically the “90% rule” – 90% of a given<br />

geographical area must be covered for 90% of the<br />

time.<br />

Institute for Infocomm Research 61 National University of Singapore<br />

Institute for Infocomm Research 62 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

<strong>Cellular</strong> Traffic<br />

- Call holding time (H) : the average duration of a call.<br />

- Request rate (λ) : average number of call requests per<br />

unit time.<br />

<br />

<strong>The</strong> basic consideration in the design of a <strong>cellular</strong><br />

system is the sizing of the system. Sizing has two<br />

components to be considered.<br />

- Coverage area<br />

- Traffic handling capability<br />

• After the system is sized, channels are assigned to<br />

cells using the assignment schemes mentioned before.<br />

<br />

Traffic flow or intensity A<br />

• Measured in Erlang, which is defined as the callminute<br />

per minute.<br />

• Total offered traffic for such a system is given as<br />

A = λ ⋅ H<br />

Exercise : <strong>The</strong>re are 3000 calls per hour in a cell,<br />

each lasting an average of 1.76 min.<br />

<br />

Terminology in traffic theory<br />

Offered traffic A = (3000/60)(1.76) = 88 Erlangs<br />

- Trunking : exploits the statistical characteristics of<br />

the users calling behaviour. Any efficient<br />

communication system relies on trunking to<br />

accommodate a large number of users with a limited<br />

number of channels.<br />

- Grade of service (GoS) : A user is allocated a channel<br />

on a per call basis. GoS is a measure of the ability of<br />

a user to access a trunked system during the busiest<br />

hour. It is typically given as the likelihood that a call<br />

is blocked (also known as blocking probability<br />

mentioned before).<br />

- Trunking theory : is used to determine the number of<br />

channels required to service a certain offered traffic<br />

at a specific GoS.<br />

<br />

<br />

<br />

If the offered traffic exceeds the maximum possible<br />

carried traffic, blocking occurs. <strong>The</strong>re are three<br />

different strategies to be used.<br />

- Blocked calls cleared<br />

- Blocked calls delayed<br />

Trunking efficiency : is defined as the carried traffic<br />

intensity in Erlangs per channel, which is a value<br />

between zero and one. It is a function of the number<br />

of channels per cell and the specific GoS parameters.<br />

Call arrival process: it is widely accepted that calls<br />

have a Poisson arrival.<br />

Institute for Infocomm Research 63 National University of Singapore<br />

Institute for Infocomm Research 64 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

Over an observation period T, divide this time into<br />

n sub-intervals.<br />

- only one arrival can occur in any one sub-interval.<br />

- call arrivals are independent from each other.<br />

- the probability that an arrival occurs in one of<br />

the sub-intervals is proportional to the subinterval<br />

length.<br />

<strong>The</strong> probability of exactly k arrivals in n subintervals<br />

can be evaluated using the binomial<br />

distribution. In the limit when n→∞ , this<br />

approach to a Poisson Process, with its mean equal<br />

to λ T .<br />

(Refer to tutorial 1 and extend the <strong>concept</strong> from<br />

Poisson distribution to Poisson Process)<br />

( λT<br />

)<br />

k<br />

pk<br />

= exp<br />

k!<br />

( − λT<br />

)<br />

- <strong>The</strong> probability that a call terminates within one<br />

subinterval is proportional to its length.<br />

- <strong>The</strong> call termination occurs independently of which<br />

subinterval is considered.<br />

<strong>The</strong> probability that the holding time h is less than<br />

or equal t is given as<br />

n<br />

⎛ µ t ⎞<br />

1 − Fh ( t)<br />

= 1 − P(<br />

h ≤ t)<br />

= P(<br />

h > t)<br />

= lim ⎜1<br />

− ⎟ = exp µ<br />

n→∞⎝<br />

n ⎠<br />

∴Fh ( t)<br />

= 1−<br />

exp( − µ t) ⇒ fh(<br />

t)<br />

= µ exp( − µ t)<br />

This gives a mean holding time of H =1 µ .<br />

( − t)<br />

Markov chain : probability that the next state is x n+ 1<br />

depends only upon the current state x n and not any<br />

previous value. A special case is the birth-death<br />

process.<br />

<br />

Mean inter-arrival time<br />

( τ ≤ t) = 1−<br />

P( τ > t) = 1−<br />

P( no ) = 1−<br />

( − λt)<br />

λ exp( − λt)<br />

Fτ<br />

( t)<br />

= P<br />

arrival exp<br />

∴ fτ<br />

( t)<br />

=<br />

<br />

Block calls cleared : Assuming that there are altogether<br />

C trunks, and<br />

• An infinite subscriber population<br />

<br />

Memoryless property of the negative exponential<br />

distribution : the past history of an exponentially<br />

distributed random variable has no influence in<br />

predicting its future.<br />

• Poisson call arrivals with rate λ calls/sec<br />

• Exponentially distributed call durations with mean<br />

H =1/ µ .<br />

<br />

Call holding time : it is normally assume that it has a<br />

negative exponential distribution.<br />

• Blocked calls are cleared.<br />

Institute for Infocomm Research 65 National University of Singapore<br />

Institute for Infocomm Research 66 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

Under steady state conditions<br />

Pn = n ⋅ P n<br />

λδ ⋅ − 1 µδ<br />

Solving for different values of n, we have<br />

n<br />

λ<br />

λ 1 ⎛ λ ⎞<br />

P 1 = P 0 , …, Pn<br />

= Pn<br />

−1<br />

= ⎜ ⎟ P0<br />

, …<br />

µ<br />

nµ<br />

n!<br />

⎝ µ ⎠<br />

C<br />

From ∑ P n = 1, we get<br />

n=<br />

0<br />

1<br />

P0<br />

=<br />

C n<br />

1 ⎛ λ ⎞<br />

∑ ⎜ ⎟<br />

n=<br />

0 n!<br />

⎝ µ ⎠<br />

<strong>The</strong> probability of blocking for C trunked channel is<br />

C<br />

1 ⎛ λ ⎞<br />

⎜ ⎟ 1<br />

C<br />

C<br />

A<br />

1 ⎛ λ ⎞ C!<br />

⎟ =<br />

⎝ µ<br />

GoS = P = ⎜<br />

⎠<br />

c P<br />

= C!<br />

0<br />

C!<br />

C<br />

⎝ µ ⎠ C n<br />

1 ⎛ λ ⎞ 1 n<br />

∑ ⎜ ⎟ ∑ A<br />

n=<br />

n ⎝ ⎠ n=<br />

0 n!<br />

0 ! µ<br />

which is the Erlang B formula, and A = λ H = λ µ .<br />

• Must know how to use the table.<br />

Examples on Erlang B models<br />

<br />

1. <strong>The</strong>re are 3000 calls per hour in a cell, each lasting<br />

an average of 1.76 minutes. For a 2% blocking<br />

probability, how many channels are needed in the<br />

cell?<br />

2. A cell contains 50 channels. <strong>The</strong> average call<br />

duration is 100s. How many calls per hour can be<br />

handle if PB=2%?<br />

Blocked calls delayed : in this model, the blocked<br />

calls are allowed to queue up and wait to be served.<br />

Normally assume that the queue is infinitely long<br />

(M/M/C/∞)<br />

At steady state,<br />

λδ ⋅ Pn − 1 = nµδ<br />

⋅ P n for k ≤ C<br />

λδ ⋅ Pn − 1 = Cµδ<br />

⋅ P n for k ≥ C<br />

This leads to<br />

⎧<br />

n<br />

1 ⎛ λ ⎞<br />

⎪ ⎜ ⎟ P0<br />

n ≤ C<br />

n!<br />

⎝ µ<br />

P = ⎠<br />

n ⎨ n<br />

⎪ 1 ⎛ λ ⎞ 1<br />

≥<br />

⎪<br />

⎜ ⎟ P n C<br />

−<br />

⎩C!<br />

n C 0<br />

⎝ µ ⎠ C<br />

From = 1<br />

n∑ ∞ P n , we get<br />

= 0<br />

Institute for Infocomm Research 67 National University of Singapore<br />

Institute for Infocomm Research 68 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

P<br />

0<br />

=<br />

C<br />

∑ − 1<br />

n=<br />

0<br />

1 ⎛ λ ⎞<br />

⎜ ⎟<br />

n!<br />

⎝ µ ⎠<br />

n<br />

1<br />

1 ⎛ λ ⎞<br />

+ ⎜ ⎟<br />

C!<br />

⎝ µ ⎠<br />

C<br />

1<br />

⎛ λ ⎞<br />

⎜1<br />

− ⎟<br />

⎝ µ C ⎠<br />

<strong>The</strong> probability that the call will not have<br />

immediate access to a channel (i.e. having nonzero<br />

delay)<br />

Pr( delay<br />

> 0) = ∑ ∞ P<br />

=<br />

k<br />

k C<br />

C<br />

A 1<br />

= P<br />

C!<br />

A<br />

1−<br />

C<br />

where A = λ / µ . This is the Erlang C formula.<br />

- This probability of non-zero delay that can be<br />

tolerated is also known to be the GoS parameter of<br />

the Erlang C system.<br />

- If no channels are immediately available, the call<br />

is delayed, and the probability that the delayed<br />

call is forced to wait more than t seconds is given<br />

by the probability that a call is delayed, multiplied<br />

by the conditional probability that the delay is<br />

greater than t seconds (the delay threshold).<br />

Pr(delay > t)<br />

= Pr(delay > 0) Pr(delay > t delay > 0)<br />

= Pr(delay > 0) exp[ −(<br />

C − A)<br />

t / H ]<br />

- <strong>The</strong> average delay D for all calls in a queued<br />

system is given by<br />

∞<br />

H<br />

D = ∫ Pr(delay > t)<br />

dt = Pr(delay > 0)<br />

0<br />

C − A<br />

or the average delay for those calls which are<br />

queue is given by H /( C − A)<br />

.<br />

0<br />

Note: Proof for<br />

Pr( delay > t delay > 0) = exp[ −(<br />

C − A)<br />

t / H ]<br />

Consider C=1, this corresponding to the M/M/1 queue<br />

model. <strong>The</strong> waiting time W consists of the service times of<br />

the existing N customers in the system, ie.,<br />

W = S1 + S2<br />

+ L+<br />

S N where S i follows exponential<br />

distribution fS ( t)<br />

= µ exp( − µ t)<br />

and W is the sum of these N<br />

i<br />

independent random variables. Note that implicity we<br />

assume that N > 0 .<br />

λ λ n<br />

Also can easily show that P n = (1 − )( ) , i.e. n follows a<br />

µ µ<br />

geometric distribution (memoryless property).<br />

<strong>The</strong> pdf of W is then given by<br />

Erlang(<br />

n+<br />

1, µ )<br />

64748 4<br />

∞<br />

∞ n<br />

( µ t)<br />

−µ<br />

t λ λ n<br />

fW<br />

( t)<br />

= ∑ f<br />

W | n<br />

( t,<br />

n)<br />

Pn<br />

= ∑ µ e ⋅ (1 − )( )<br />

n=<br />

0<br />

n=<br />

0 n!<br />

µ µ<br />

−(<br />

µ −λ)<br />

t<br />

= ( µ − λ)<br />

e<br />

Note that µ = 1/ H , A = λH<br />

, integrate this from t to ∞ will<br />

obtain Pr( delay > t delay > 0)<br />

For M/M/C queue, the system behaves as an M/M/1 queue<br />

with higher service rate C µ (rather than µ ).<br />

Institute for Infocomm Research 69 National University of Singapore<br />

Institute for Infocomm Research 70 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

Channel Assignment Strategies<br />

<br />

Channel allocation schemes can affect the performance<br />

of the system.<br />

Fixed Channel Allocation (FCA) :<br />

• Channels are divided in sets.<br />

• A set of channels is permanently allocated to each cell<br />

in the network. Same set of channels must be<br />

assigned to cells separated by a certain distance to<br />

reduce co-channel interference.<br />

• Any call attempt within the cell can only be served by<br />

the unused channels in that particular cell. <strong>The</strong><br />

service is blocked if all channels have used up.<br />

• Most easiest to implement but least flexibility.<br />

• An modification to this is ‘borrowing scheme’. Cell<br />

(acceptor cell) that has used all its nominal channels<br />

can borrow free channels from its neighboring cell<br />

(donor cell) to accommodate new calls.<br />

• Borrowing can be done in a few ways: borrowing from<br />

the adjacent cell which has largest number of free<br />

channels, select the first free channel found, etc.<br />

Institute for Infocomm Research 71 National University of Singapore<br />

• To be available for borrowing, the channel must not<br />

interfere with existing calls. <strong>The</strong> borrowed channel<br />

should be returned once the channel becomes free.<br />

Dynamic Channel Allocaton (DCA) :<br />

• Voice channels are not allocated to any cell<br />

permanently. All channels are kept in a central pool<br />

and are assigned dynamically to new calls as they<br />

arrive in the system.<br />

• Each time a call request is made, the serving BS<br />

requests a channel from the MSC. It then allocates a<br />

channel to the requested cell following an algorithm<br />

that takes into acount the likelihood of future blocking<br />

within the cell, the reuse distance of the channel and<br />

other cost functions ⇒ increase in complexity<br />

• Centralized DCA scheme involves a single controller<br />

selecting a channel for each cell. Distributed DCA<br />

scheme involves a number of controllers scattered<br />

across the network.<br />

• For a new call, a free channel from central pool is<br />

selected based on either the co-channel distance,<br />

signal strength or signal to noise interference ratio.<br />

Flexible channel assignment<br />

Institute for Infocomm Research 72 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

<br />

• Divide the total number of channels into two groups,<br />

one of which is used for fixed allocation to the cells,<br />

while the other is kept as a central poor to be shared<br />

by all users.<br />

• Mix the advantages the FCA and DCA, available<br />

schemes are scheduled and predictive.<br />

Channels need to be assigned to users to accommodate<br />

- new calls<br />

- handovers<br />

With the objective of increasing capacity and<br />

minimizing probability of a blocked call.<br />

<br />

System Expansion Techniques<br />

As demand for wireless services increases, the number<br />

of channels assigned to a cell eventually becomes<br />

insufficient to support the required number of users.<br />

More channels must therefore be made available per<br />

unit area.<br />

• This can be accomplished by dividing each initial cell<br />

area into a number of smaller cells, a technique<br />

known as cell-splitting.<br />

• It can also be accomplished by having more channels<br />

per cell, i.e. by having a smaller reuse factor.<br />

However, to have a smaller reuse factor, the cochannel<br />

interference must be reduced. This can be<br />

done by using antenna sectorization.<br />

<br />

Cell splitting<br />

• Cell splitting increases the number of BSs in order to<br />

increase capacity. <strong>The</strong>re will be a corresponding<br />

reduction in antenna height and transmitter power.<br />

• Cell splitting accommodates a modular growth<br />

capability. This in turn leads to capacity increase<br />

Institute for Infocomm Research 73 National University of Singapore<br />

Institute for Infocomm Research 74 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

essentially via a system re-scaling of the <strong>cellular</strong><br />

geometry without any changes in frequency planning.<br />

• Small cells lead to more cells/area which in turn leads<br />

to increased traffic capacity.<br />

• For new cells to be smaller in size, the transmit power<br />

must be reduced. If n=4, then with a reduction of cell<br />

radius by a factor of 2, the transmit power should be<br />

reduced by a factor of 2 4 (why?)<br />

• In theory, cell splitting could be repeated indefinitely.<br />

In practice it is limited<br />

1. by the cost of base stations<br />

2. handover (fast and low speed traffic)<br />

3. not all cells are split at the same time : practical<br />

problems of BS sites, such as co-channel<br />

interference exist<br />

<br />

4. Innovative channel assignment schemes must<br />

be developed to address this problem for<br />

practical systems.<br />

Sectorization<br />

• Keep the cell radius but decrease the D/R ratio. In<br />

order to do this, we must reduce the relative<br />

interference without increasing the transmit power.<br />

• Sectorization relies on antenna placement and<br />

directivity to reduce co-channel interference. Beams<br />

are kept within either a 60° or a 120° sector.<br />

Institute for Infocomm Research 75 National University of Singapore<br />

Institute for Infocomm Research 76 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

• If we partition a cell into three 120° sectors, the<br />

number of co-channel cells are reduced from 6 to 2 in<br />

the first tier.<br />

• Using six sectors of 60°, we have only one co-channel<br />

cell in the first tier.<br />

• Each sector is limited to only using 1/3 or 1/6 of the<br />

available channels. We therefore have a decrease in<br />

trunking efficiency and an increase in the number of<br />

required antennas.<br />

• But how can the increase in system capacity be<br />

achieved?<br />

Institute for Infocomm Research 77 National University of Singapore<br />

Institute for Infocomm Research 78 National University of Singapore


EE5401 <strong>Cellular</strong> Mobile Communications<br />

EE5401 <strong>Cellular</strong> Mobile Communications<br />

<br />

Micro cells<br />

• Micro cells can be introduced to alleviate capacity<br />

problems caused by “hotspots”.<br />

• By clever channel assignment, the reuse factor is<br />

unchanged. As for cell splitting, there will occur<br />

interference problems when macro and micro cells<br />

must co-exist.<br />

Institute for Infocomm Research 79 National University of Singapore<br />

Institute for Infocomm Research 80 National University of Singapore

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