Dr. Prapun Suksompongprapun@siit.tu.ac.th

Lecture 14 (Review)

1

Mobile CommunicationsTCS 455

Office Hours:

BKD 3601-7

Tuesday 14:00-16:00

Thursday 9:30-11:30

Announcements

2

Read

Chapter 3: 3.1 – 3.2, 3.5.1, 3.6, 3.7.2

Posted on the web

Appendix A.1 (Erlang B)

Chapter 9: 9.1 – 9.5

Due date for HW3: Dec 18

Course Organization

3

Course Web Site:

http://www.siit.tu.ac.th/prapun/ecs455/

Lectures:

Tuesday 10:40-12:00 BKD 2601

Thursday 13:00-14:20 BKD 3215

Textbook:

Wireless Communications: Principles and Practice

By Theodore S. Rappaport

2nd Edition, Prentice Hall PTR, 2002.

ISBN-13: 978-0130422323.

Call No. TK5103.2 R37 2002

Companion Site:

http://authors.phptr.com/rappaport/

Course Web Site

4

Please check the course

Web site regularly.

Announcement

References

Handouts/Slides

Calendar

Exams

HW due dates

www.siit.tu.ac.th/prapun/ecs455/

Grading System

5

Coursework will be weighted as follows:

Mark your calendars now!

Late HW submission will be rejected.

All quizzes and exams will be closed book.

For grad. student, this is 2/3 of your final score.

Assignments 5%

Class Participation and Quizzes 15%

Midterm Examination•09:00 - 12:00 on Dec 22, 2009

40%

Final Examination (comprehensive)•09:00 - 12:00 on Mar 9, 2010

40%

Midterm Exam

6

Not to torture you!

Most questions are straightforward

A few difficult ones

Worth 1 to 2 points each

Study

HW questions / quiz

Only small parts of HWs are graded.

Please take a careful look at the solution.

Lecture notes

Textbook chapters

Midterm Exam

7

9 pages

9 problems

Start at 9:00 AM

You may start at 9:09 AM if you want to.

99 Points + 1 hidden point

Topics

8

Chapter 1 > 10%

Fourier transform, modulation

Chapter 2 > 50%

Cellular System

Chapter 3 > 30%

Erlang B derivation: Poisson Process and Markov Chain

Chapter 4 < 10%

Duplexing: FDD and TDD

Provided Formula

9

0

0

2

2

2

2

0

2

0

2cos 1 cos 2

2sin 1 cos 2

1 1cos

1 1cos

2

2

2

2

2

2

j f

j ft

j j

c

t

t

c c c

c

f

c

j

x x

x x

g t t e G f

e g t G f f

m t f t M f

G f g t e dt

f

f M f f

t f f e f f e

0

!ErlangB ,

!

m

km

k

A

mm AA

k

10

Chapter 1 Review & Introduction

Office Hours:

BKD 3601-7

Tuesday 14:00-16:00

Thursday 9:30-11:30

Handout #1

11

Fourier Transform

Modulation

More on HW1

Frequency-Domain Analysis

12

Modulation: 1 1

cos 22 2

c c cm t f t M f f M f f

Shifting Properties: 02

0

j ftg t t e G f

02

0

j f te g t G f f

Overview of Mobile Communications

13

Wireless/mobile communications is the fastest growing

segment of the communications industry.

Cellular systems have experienced exponential growth over

the last decade.

Cellular phones have become a critical business tool and part

of everyday life in most developed countries, and are rapidly

replacing wireline systems in many developing countries.

Mobile?

14

The term “mobile” has historically been used to classify all

radio terminal that could be moved during operation.

More recently,

the term mobile is used to describe a radio terminal that is

attached to a high speed mobile platform

e.g., a cellular telephone in a fast moving vehicle

the term portable is used to describes a radio terminal that can

be hand-held and used by someone at walking speed

e.g., a walkie-talkie or cordless telephone inside a home.

802.11?

History of Wireless Communications

15

The first wireless networks

were developed in the Pre-

industrial age.

These systems transmitted

information over line-of-sight

distances (later extended by

telescopes) using smoke signals,

torch signaling, flashing

mirrors, signal flares, or

semaphore flags.

Semaphore

16

History of Wireless Comm. (2)

17

Early communication networks were replaced first by the

telegraph network (invented by Samuel Morse in 1838) and

later by the telephone.

In 1895, Marconi demonstrated the first radio transmission.

Early radio systems transmitted analog signals.

Today most radio systems transmit digital signals

composed of binary bits.

A digital radio can transmit a continuous bit

stream or it can group the bits into packets.

The latter type of radio is called a packet radio and is

characterized by bursty transmissions

History of Wireless Comm. (3)

18

The first network based on packet radio, ALOHANET, was

developed at the University of Hawaii in 1971.

ALOHANET incorporated the first set of protocols for

channel access and routing in packet radio systems, and many

of the underlying principles in these protocols are still in use

today.

Lead to Ethernet and eventually wireless local area

networks

History of Wireless Comm. (3)

19

The most successful application of wireless networking has been the cellular telephone system.

The roots of this system began in 1915, when wireless voice transmission between New York and San Francisco was first established.

In 1946 public mobile telephone service was introduced in 25 cities across the United States.

These initial systems used a central transmitter to cover an entire metropolitan area. Inefficient!

Thirty years after the introduction of mobile telephone service, the New York system could only support 543 users.

History of Wireless Comm. (4)

20

A solution to this capacity problem emerged during the 50’s

and 60’s when researchers at AT&T Bell Laboratories

developed the cellular concept.

Cellular systems exploit the fact that the power of a

transmitted signal falls off with distance.

Thus, two users can operate on the same frequency at

spatially-separate locations with minimal interference

between them.

Frequency reuse

History of Wireless Comm. (5)

21

The second generation (2G) of cellular systems, first deployed in the early 1990’s, were based on digital communications.

The shift from analog to digital was driven by its higher capacity and the improved cost, speed, and power efficiency of digital hardware.

While second generation cellular systems initially provided mainly voice services, these systems gradually evolved to support data services such as email, Internet access, and short messaging.

Unfortunately, the great market potential for cellular phones led to a proliferation of (incompatible) second generation cellular standards.

As a result of the standards proliferation, many cellular phones today are multi-mode.

22

Chapter 2 Cellular System

Office Hours:

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Tuesday 14:00-16:00

Thursday 9:30-11:30

Handout #2

23

Radio-frequency spectrum

24

Commercially exploited bands

25

Tessellating Cell Shapes

26

Hexagonal cells:

Having largest area for a given distance between the center of a polygon and its farthest perimeter points

Approximating a circular radiation pattern for an omnidirectional base station antenna and free space propagation

Frequency Reuse (N = 4, N = 7)

27

Cluster: a group of N cells use the complete set of available

frequencies

D

B

C

A

D

B

C

A

D

B

C

A

D

B

C

A

D

B

C

A

D

B

C

A

D

B

C

A

Activity 1

28

You have seen N = 3, 4, 7

Find the next five lowest values of N.

In HW2, find the next fifteen lowest values of N.

Hexagon

29

R

R

R

R

R

2

R

R

2R

3R

3

2

R

3

2R

3

2R

3R

2 21 3 1 3 3Area 6 2 2.598

2 2 2 2R R R R

Frequency Reuse

30

Cluster: a group of N cells using the complete set of

available frequencies

4-cell reuse 7-cell reuse12-cell reuse

19-cell reuse

total

cell

A SC

A N

Co-channel Interference (N=19)

Method of locating co-channel cells in a cellular system. In this example, N = 19 (i.e., I = 3, j = 2). (Adapted from [Oet83] © IEEE.)

Center-to-center distance (D)

32

D

3j R 3i R

120

2 2

2 2

3 3 2 3 3 cos 120

3 3

D i R j R i R j R

R i j ij R N

This distance, D,

is called reuse

distance.

Co-channel reuse ratio

3 .D

Q NR

Q and N

33

Co-channel reuse ratio

3 .D

Q NR

SIR

34

Frequency reuse co-channel interference

K = the number of co-channel interfering cells

The signal-to-interference ratio (S/I or SIR) for a

mobile receiver which monitors a forward channel can be

expressed as

S = the desired signal power from the desired base station

Ii = the interference power caused by the ith interfering co-

channel cell base station.

1

K

i

i

S SSIR

II

SIR

35

The SIR should be greater than a specified threshold for proper signal operation. In the first-generation AMPS system, designed for voice calls, the

desired performance threshold is SIR equal to 18 dB. For the second-generation digital AMPS system (D-AMPS or IS-

54/136), a threshold of 14 dB is deemed suitable. For the GSM system, a range of 7–12 dB, depending on the study

done, is suggested as the appropriate threshold.

Only a relatively small number of nearby interferers need be considered, because of the rapidly decreasing received power as the distance increases. In a fully equipped hexagonal-shaped cellular system, there are always

six cochannel interfering cells in the first tier.

Approximation:

1 13

S kR DN

I K R KK kD

SIR: N = 7

36

More accurate calculation…

SIR: N = 3

37

2

R

3

2

R

D1

D2 D3

D4

D5 D6

2R

4R 13R

13R 7R

7R

2

2

1 5

22

2 4

3

6

31 4 13

2

5 34

2 2

2

4

D D R R

D D R R

D R

D R

1

2 7 2 13 2 4

t

t i

i

P RSIR

P D

Even more accurate calculation…

Improving Coverage and Capacity

38

As the demand for wireless service increases, the number of

channels assigned to a cell eventually becomes insufficient to

support the required number of users.

At this point, cellular design techniques are needed to

provide more channels per unit coverage area.

Easy!?

total

cell

A SC

A N

Sectoring (N = 7)

39

Sectoring (N = 7)

40

Sectoring (N = 3, 120)

41

K = 2

1

3S

NI K

Sectoring (N = 3 , 60)

42

K = 1

1

3S

NI K

60 Degree Sectoring

43

Sectoring

44

Advantages

Assuming seven-cell reuse, for the case of 120 sectors, the number of interferers in the first tier is reduced from six to two. This reduction lead to the increase of SIR.

The increase in SIT can be traded with reducing the cluster size which increase the capacity.

Disadvantages

Increase number of antennas at each base station.

Decrease trunking efficiency due to channel sectoring at the base station. The available channels in the cell must be subdivided and dedicated to a

specific antenna.

1

3S

NI K

total

cell

A SC

A N

Estimating the number of users

45

Trunking

Allow a large number of users to share the relatively small

number of channels in a cell by providing access to each user,

on demand, from a pool of available channels.

Exploit the statistical behavior of users

Each user is allocated a channel on a per call basis, and upon

termination of the call, the previously occupied channel is

immediately returned to the pool of available channels.

Common Terms

46

Traffic Intensity: Measure of channel time utilization, which is the average channel occupancy measured in Erlangs. This is a dimensionless quantity and may be used to measure the time utilization

of single or multiple channels.

Denoted by A.

Holding Time: Average duration of a typical call. Denoted by H = 1/.

Blocked Call: Call which cannot be completed at time of request, due to congestion. Also referred to as a lost call.

Grade of Service (GOS): A measure of congestion which is specified as the probability of a call being blocked (for Erlang B). The AMPS cellular system is designed for a GOS of 2% blocking. This implies

that the channel allocations for cell sites are designed so that 2 out of 100 calls will be blocked due to channel occupancy during the busiest hour.

Request Rate: The average number of call requests per unit time. Denoted by .

M/M/m/m Assumption

47

Blocked calls cleared Offers no queuing for call requests.

For every user who requests service, it is assumed there is no setup time and the user is given immediate access to a channel if one is available.

If no channels are available, the requesting user is blocked without access and is free to try again later.

Calls arrive as determined by a Poisson process.

There are memoryless arrivals of requests, implying that all users, including blocked users, may request a channel at any time.

There are an infinite number of users (with finite overall request rate). The finite user results always predict a smaller likelihood of blocking. So,

assuming infinite number of users provides a conservative estimate.

The duration of the time that a user occupies a channel is exponentially distributed, so that longer calls are less likely to occur.

There are m channels available in the trunking pool. For us, m = the number of channels for a cell (C) or for a sector

Erlang B

48

0

! .

!

C

b kC

k

A

CPA

k

A

Example

49

How many users can be supported for 0.5% blocking

probability for the following number of trunked channels in a

blocked calls cleared system?

(a) 5

(b) 10

Assume each user generates 0.1 Erlangs of traffic.

Erlang B

50

0

! .

!

C

b kC

k

A

CPA

k

A

Example

51

Consider a cellular system in which

an average call lasts two minutes

the probability of blocking is to be no more than 1%.

If there are a total of 395 traffic channels for a seven-cell

reuse system, there will be about 57 traffic channels per cell.

From the Erlang B formula, the may handle 44.2 Erlangs or

1326 calls per hour.

Erlang B

52

0

! .

!

C

b kC

k

A

CPA

k

A

Example

53

Now employing 120° sectoring, there are only 19 channels

per antenna sector (57/3 antennas).

For the same probability of blocking and average call length,

each sector can handle 11.2 Erlangs or 336 calls per hour.

Since each cell consists of three sectors, this provides a cell

capacity of 3 × 336 = 1008 calls per hour, which amounts

to a 24% decrease when compared to the unsectored case.

Thus, sectoring decreases the trunking efficiency while

improving the S/I for each user in the system.

Erlang B

54

0

! .

!

C

b kC

k

A

CPA

k

A

Erlang B Trunking Efficiency

55

Big Picture

56 0

! .

!

i

m

b

i

m

A

mPA

i

total

cell

A SC

A N

1 13

S kR DN

I K R KK kD

S = total # available duplex radio channels for the system

Frequency reuse with cluster size N

Tradeoff

m = # channels allocated to

each cell.

Omni-directional: K = 6

120 Sectoring: K = 2

60 Sectoring: K = 1

“Capacity”

Trunking

Call blocking

probability

Erlang-B formula

or ltra oadffic i [Erlantens ngs] ty =iA

= Average # call attempts/requests per unit time

1Average call lengthH

57

Chapter 3 Poisson process and Markov chain

Office Hours:

BKD 3601-7

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Thursday 9:30-11:30

M/M/m/m Assumption

58

Blocked calls cleared Offers no queuing for call requests.

For every user who requests service, it is assumed there is no setup time and the user is given immediate access to a channel if one is available.

If no channels are available, the requesting user is blocked without access and is free to try again later.

Calls arrive as determined by a Poisson process.

There are memoryless arrivals of requests, implying that all users, including blocked users, may request a channel at any time.

There are an infinite number of users (with finite overall request rate). The finite user results always predict a smaller likelihood of blocking. So,

assuming infinite number of users provides a conservative estimate.

The duration of the time that a user occupies a channel is exponentially distributed, so that longer calls are less likely to occur.

There are m channels available in the trunking pool. For us, m = the number of channels for a cell (C) or for a sector

Assumption (con’t)

59

t

t

K(t)

K(t) = “state” of the system = the number of used channel at time t

3 2 1

The call request process is Poisson with rate

The duration of calls are i.i.d. exponential r.v. with rate .

If m = 3, this call will be blocked

We want to find out what proportion of time the system has K = m.

m =

Poisson Process?

60

One of these is a realization of a two-dimensional Poisson point process and the other contains correlations between the points. One therefore has a real pattern to it, and one is a realization of a completely unstructured random process.

Poisson Process

61

All the structure that is

visually apparent is

imposed by our own

sensory apparatus, which

has evolved to be so

good at discerning

patterns that it finds

them when they’re not

even there!

Example

62

Examples that are well-modeled as Poisson processes include

radioactive decay of atoms,

telephone calls arriving at a switchboard,

page view requests to a website,

rainfall.

Handout #3: Poisson Process

63

Poisson Process

64

Time

1 2 3

N1 = 1 N2 = 2 N3 = 1

The number of arrivals N1, N2 and N3 during non-overlapping time intervals

are independent Poisson random variables with mean = the length of the

corresponding interval.

The lengths of time between adjacent arrivals W1, W2, W3 … are i.i.d.

exponential random variables with mean 1/.

W1 W2 W3 W4

Small Slot Analysis (Poisson Process)

65

Aka discrete time approximation

Time

1 2 3

N1 = 1 N2 = 2 N3 = 1

W1 W2 W3 W4

Time

In the limit, there is at most one arrival in any slot. The numbers of arrivals on the slots are

i.i.d. Bernoulli random variables with probability p1 of exactly one arrivals = where is the

width of individual slot.

The total number of arrivals on n slots is a

binomial random variable with parameter

(n,p1)

D1The number of slots between adjacent

arrivals is a geometric random variable.

In the limit, as the slot length gets smaller, geometric exponential

binomial Poisson

Poisson Process (Recap)

66

We spent a few lectures now studying Poisson process.

This is used to model call arrivals in M/M/m/m queue (which gives Erlang B formula).

Along the way, we review many facts from probability theory.

pmf – Binomial, Poisson, Geometric

pdf - Exponential

Independence

Expectation, characteristic function

Sum of independent random variables and how to analyze it by characteristic functions

You have seen that Poisson process connects many concepts that you learned from introductory probability class.

Handout #4: Erlang B & Markov Chain

67

Small Slot Analysis (Erlang B)

68

Consider the ith small slot.

Let Ki = k be the value of K at the beginning of this time slot.

k = 2 in the above figure.

Then, Ki+1 is the value of K at the end of this slot which is the same as the value of K at the beginning of the next slot.

P[0 new call request] ≈ 1 -

P[1 new call request] ≈

P[0 old-call end] ≈ 1 1k

k

P[1 old-call end] ≈ 1

1k

k k

Suppose each slot duration is .

How do these events affect Ki+1 ?

Small slot Analysis (2)

69

Ki+1 = Ki + (# new call request) – (# old-call end)

P[0 new call request] ≈ 1 -

P[1 new call request] ≈

P[0 old-call end] ≈ 1 - k

P[1 old-call end] ≈ k

k+1kk-1

1 k k 1 k

1 1 1k k k

The labels on the arrows are

probabilities.

Small slot Analysis: Markov Chain

70

Case: m = 2

210

1

2

1 2

1

Markov Chain

71

Markov chains model many phenomena of interest.

We will see one important property: Memoryless

It retains no memory of where it has been in the past.

Only the current state of the process can influence where it goes next.

Very similar to the state transition diagram in digital circuits.

In digital circuit, the labels on the arrows indicate the input/control signal.

Here, the labels on the arrows indicate transition probabilities. (If the system is currently at a particular state, where would it go next on the next time slot? )

We will focus on discrete time Markov chain.

Example: The Land of Oz

72

Land of Oz is blessed by many things, but not by good

weather.

They never have two nice days in a row.

If they have a nice day, they are just as likely to have snow as rain

the next day.

If they have snow or rain, they have an even chance of having the

same the next day.

If there is change from snow or rain, only half of the time is this

a change to a nice day.

If you visit the land of Oz next year for one day, what is the

chance that it will be a nice day?

State Transition Diagram

73

SNR1/2

1/2

1/2

1/2

1/4

1/4

1/4

1/4

R = Rain

N = Nice

S = Snow

Markov Chain (2)

74

Let Ki be the weather status for the ith day (from today).

Suppose we know that it is snowing in the land of Oz today. Then

K0 = S

where S means snow.

Goal: We want to know whether K365 = N where N means nice.

Of course, the weather are controlled probabilistically; so we can only

find P[K365 = N].

From the specification (or from the state transition diagram), we know

that

Define vector

Then,

1 1 1

1 1 1R , N , S

4 4 2P K P K P K

R N Si i ip i P K P K P K

1 1 1

0 0 0 1 and 14 4 2

p p

The Land of Oz: Transition Matrix

75

1 1 1

2 4 4

1 10

2 2

1 1 1

4 4 2

P

R N S

R

N

S

1 R Ni iP K K

1p i p i P

0 np n p P

0.3750 0.1875 0.4375

0.3906 0.2031 0.4063

0.3994 0.2002 0.

2

3

5

7

4004

0.4000 0.2000 0.4000

p

p

p

p

8 9 10 365p p p p

SNR1/2

1/2

1/2

1/2

1/4

1/4

1/4

1/4

Finding Pn for “large” n

76

1 1 1

2 4 4

1 10

2 2

1 1 1

4 4 2

P

2

0.4375 0.1875 0.3750

0.3750 0.2500 0.3750

0.3750 0.1875 0.4375

P

3

0.4063 0.2031 0.3906

0.4063 0.1875 0.4063

0.3906 0.2031 0.4063

P

5

0.4004 0.2002 0.3994

0.4004 0.1992 0.4004

0.3994 0.2002 0.4004

P

7

0.4000 0.2000 0.4000

0.4000 0.2000 0.4000

0.4000 0.2000 0.4000

P

8 9 10P P P

Land of Oz: Answer

77

Recall that

So,

Note that the above result is true regardless of the initial

0 np n p P

77 0 0.4 0.2 0.4p p P

0p

365365 0 0.4 0.2 0.4p p P

P[K365 = N]

Global Balance Equations

78

Easier approach for finding the long-term probabilities

A B

3/5

1/2

2/5 1/2

2 / 5 3 / 5

1/ 2 1/ 2P

Let pk be the long-term

probability that K = k.

3 1

5 2A Bp p

Small slot Analysis: Markov Chain

79

Case: m = 2

210

1

2

1 2

1 Let pk be the long-term

probability that K = k.

0 1p p 1 22p p

0 1 2 1p p p

2

0 1 0 2 02

1 1, ,

21

2

p p Ap p A pA

A

b mp p

M/M/m/m Queuing Model

Global Balance equations

Truncated birth-and-death process

80

Continuous-time Markov chain

More general than M/M/m/m

81

Chapter 4 Multiple Access

Office Hours:

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Thursday 9:30-11:30

82

Duplexing

83

Allow the subscriber to send “simultaneously” information to the

base station while receiving information from the base station.

Talk and listen simultaneously.

We define forward and reverse channels as followed:

Forward channel or downlink (DL) is used for communication

from the infrastructure to the users/stations

Reverse channel or uplink (UL) is used for communication from

users/stations back to the infrastructure.

Two techniques

1. Frequency division duplexing (FDD)

2. Time division duplexing (TDD)

Frequency Division Duplexing (FDD)

84

Provide two distinct bands of frequencies (simplex channels)

for every user.

The forward band provides traffic from the base station to

the mobile.

The reverse band provides traffic from the mobile to the

base station.

Used in cellular

Time Division Duplexing (TDD)

85

Use time instead of frequency to provide both a forward and reverse link.

Each duplex channel has both a forward time slot and a reverse time slot.

The UL and DL data are transmitted on the same carrier frequency at different times.

If the time separation between the forward and reverse lime slot is small, then the transmission and reception of data appears simultaneous to the users at both the subscriber unit and on the base station side.

Used in Bluetooth and Mobile WiMAX

Each transceiver operates as either a transmitter or receiver on the same frequency

Problems of FDD

86

Because each transceiver simultaneously transmits and

receives radio signals which can vary by more than100 dB,

the frequency allocation used for the forward and reverse

channels must be carefully coordinated within its own system

and with out-of-band users that occupy spectrum between

these two bands.

The frequency separation must be coordinated to permit the

use of inexpensive RF and oscillator technology.

Advantages of FDD

87

TDD frames need to incorporate guard periods equal to the

max round trip propagation delay to avoid interference

between uplink and downlink under worst-case conditions.

There is a time latency created by TDD due to the fact that

communications is not full duplex in the truest sense.

This latency creates inherent sensitivities to propagation delays

of individual users.

Advantages of TDD

88

Enable adjustment of the downlink/uplink ratio to efficiently support asymmetric DL/UL traffic.

With FDD, DL and UL always have fixed and generally, equal DL and UL bandwidths.

Assure channel reciprocity for better support of link adaptation, MIMO and other closed loop advanced antenna technologies.

Ability to implement in nonpaired spectrum

FDD requires a pair of channels

TDD only requires a single channel for both DL and UL providing greater flexibility for adaptation to varied global spectrum allocations.