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Dr. Prapun [email protected]

Lecture 14 (Review)

1

Mobile Communications

TCS 455

Office Hours:BKD 3601-7Tuesday 14:00-16:00Thursday 9:30-11:30
mailto:[email protected]:[email protected]

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Announcements

2

Read Chapter 3: 3.13.2, 3.5.1, 3.6, 3.7.2

Posted on the web

Appendix A.1 (Erlang B)

Chapter 9: 9.19.5

Due date for HW3: Dec 18

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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/
http://www.siit.tu.ac.th/prapun/ecs455/http://authors.phptr.com/rappaport/http://authors.phptr.com/rappaport/http://www.siit.tu.ac.th/prapun/ecs455/

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Course Web Site

4

Please check the courseWeb site regularly.

Announcement

References Handouts/Slides

Calendar

Exams

HW due dates

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

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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 Examination09:00 - 12:00 on Dec 22, 2009

40%

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

40%

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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

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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

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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

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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 A

Ak

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10

Chapter 1

Review Introduction


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Handout #1

11

Fourier Transform Modulation

More on HW1

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Frequency-Domain Analysis

12

Modulation: 1 1

cos 22 2

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

Shifting Properties: 020j ft

g t t e G f 02 0

j f te g t G f f

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Overview of Mobile Communications

13

Wireless/mobile communications is the fastest growingsegment of the communications industry.

Cellular systems have experienced exponential growth overthe last decade.

Cellular phones have become a critical business tool and partof everyday life in most developed countries, and are rapidlyreplacing wireline systems in many developing countries.

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Mobile?

14

The term mobile has historically been used to classify allradio terminal that could be moved during operation.

More recently,

the term mobile is used to describe a radio terminal that isattached 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 canbe hand-held and used by someone at walking speed

e.g., a walkie-talkie or cordless telephone inside a home. 802.11?

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History of Wireless Communications

15

The first wireless networkswere developed in the Pre-industrial age.

These systems transmitted

information over line-of-sightdistances (later extended bytelescopes) using smoke signals,torch signaling, flashing

mirrors, signal flares, orsemaphore flags.

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Semaphore

16

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History of Wireless Comm. (2)

17

Early communication networks were replaced first by thetelegraph network (invented by Samuel Morse in 1838) andlater 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

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18

The first network based on packet radio, ALOHANET, wasdeveloped at the University of Hawaii in 1971.

ALOHANET incorporated the first set of protocols forchannel access and routing in packet radio systems, and many

of the underlying principles in these protocols are still in usetoday.

Lead to Ethernet and eventually wireless local areanetworks

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19

The most successful application of wireless networking has beenthe cellular telephone system. The roots of this system began in 1915, when wireless voice

transmission between New York and San Francisco was firstestablished.

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

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

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

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20

A solution to this capacity problem emerged during the 50sand 60s 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 atspatially-separate locations with minimal interference

between them.

Frequency reuse

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21

The second generation (2G) of cellular systems, first deployed inthe early 1990s, 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 digitalhardware.

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

Unfortunately, the great market potential for cellular phonesled to a proliferation of (incompatible) second generation cellular

standards. As a result of the standards proliferation, many cellular

phones today are multi-mode.

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22

Chapter 2

Cellular System


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Handout #2

23

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Radio-frequency spectrum

24

Commercially exploited bands

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25

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Tessellating Cell Shapes

26

Hexagonal cells: Having largest area for a given

distance between the center of apolygon and its farthest perimeterpoints

Approximating a circular radiation

pattern for an omnidirectional basestation antenna and free spacepropagation

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Frequency Reuse (N = 4, N = 7)

27

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

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

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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.

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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 2

R R R R

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Frequency Reuse

30

Cluster: a group of Ncells using the complete set ofavailable frequencies

4-cell reuse 7-cell reuse12-cell reuse

19-cell reuse

total

cell

A SC

A N

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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.)

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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 reusedistance.

Co-channel reuse ratio

3 .D

Q NR

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Q and N

33

Co-channel reuse ratio3 .

DQ N

R

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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 amobile receiver which monitors a forward channel can beexpressed 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

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SIR

35

The SIR should be greater than a specified threshold for propersignal 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 712 dB, depending on the study

done, is suggested as the appropriate threshold.

Only a relatively small number of nearby interferers need beconsidered, because of the rapidly decreasing received power asthe 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

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SIR: N = 7

36

More accurate calculation

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SIR: N = 3

37

2

R

3

2

R

D1

D2 D3

D4

D5D6

2R

4R 13R

13R 7R

7R

2

2

1 5

22

2 4

3

6

31 4 13

2

5 3 42 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

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Improving Coverage and Capacity

38

As the demand for wireless service increases, the number ofchannels assigned to a cell eventually becomes insufficient tosupport 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 S

C A N

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Sectoring (N = 7)

39

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Sectoring (N = 7)

40

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Sectoring (N = 3, 120)

41

K = 2

1

3S

NI K

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Sectoring (N = 3 , 60)

42

K = 1

1

3S

NI K

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60 Degree Sectoring

43

1S A S

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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

totalcell

A SC

A N

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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 upontermination of the call, the previously occupied channel isimmediately returned to the pool of available channels.

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Common Terms

46

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

of single or multiple channels. Denoted byA.

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

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

Grade of Service (GOS): A measure of congestion which is specified as theprobability 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

.

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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 isexponentially 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

CA

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Erlang B

48

0

! .

!

b kC

k

A

CPA

k

A

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Example

49

How many users can be supported for 0.5% blockingprobability 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.

CA

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Erlang B

50

0

! .

!

b kC

k

A

CPA

k

A

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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 or1326 calls per hour.

CA

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Erlang B

52

0

! .

!

b kC

k

A

CPA

k

A

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Example

53

Now employing 120 sectoring, there are only 19 channelsper 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 cellcapacity of 3 336 = 1008 calls per hour, which amountsto a 24% decrease when compared to the unsectored case.

Thus, sectoring decreases the trunking efficiency whileimproving the S/I for each user in the system.

CA

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Erlang B

54

0

! .

!

b kC

k

A

CPA

k

A

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Erlang B Trunking Efficiency

55

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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 toeach cell.

Omni-directional: K = 6120 Sectoring: K = 260 Sectoring: K = 1

Capacity

Trunking

Call blockingprobability

Erlang-B formula

or ltra oadffic i [Erlantens ngs]ty =iA

= Average # call attempts/requests per unit time

1Average call lengthH

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57

Chapter 3

Poisson process and Markov chain


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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 isexponentially 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

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Assumption (cont)

59

t

t

K(t)

K(t) = stateof the system

= the number of used channel at time t

3

2

1

The call request process isPoissonwith rate

The duration of calls are i.i.d. exponentialr.v. with rate .

If m = 3, this call will beblocked

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

m =

Poisson Process?

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Poisson Process?

60

One of these is a realization of a two-dimensional Poisson pointprocess and the other contains correlations between the points.

One therefore has a real pattern to it, and one is a realization ofa completely unstructured random process.

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Poisson Process

61

All the structure that isvisually apparent isimposed by our ownsensory apparatus, which

has evolved to be sogood at discerningpatterns that it findsthem when theyre not

even there!

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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.

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Handout #3: Poisson Process

63

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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 intervalsare independent Poisson random variables with mean = the length of thecorresponding 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)

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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 arei.i.d. Bernoulli random variables with probability p1 of exactly one arrivals = where is thewidth of individual slot.

The total number of arrivals on n slots is abinomial random variable with parameter(n,p1)

D1The number of slots between adjacentarrivals is a geometric random variable.

In the limit, as the slot length gets smaller, geometric exponentialbinomial Poisson

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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. pmfBinomial, 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.

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Handout #4: Erlang B & Markov Chain

67

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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 - kP[1 old-call end] k

k+1kk-1

1 k k 1 k

1 1 1k k k

The labels on the arrows areprobabilities.

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Small slot Analysis: Markov Chain

70

Case: m = 2

210

1

2

1 2

1

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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 goesnext.

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 thesystem is currently at a particular state, where would it go next onthe next time slot? )

We will focus on discrete time Markov chain.

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Example: The Land of Oz

72

Land of Oz is blessed by many things, but not by goodweather.

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?

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State Transition Diagram

73

SNR1/2

1/2

1/2

1/2

1/4

1/4

1/4

1/4

R = RainN = NiceS = Snow

Markov Chain (2)

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Markov Chain (2)

74

Let Kibe 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 onlyfind P[K365 = N].

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

Define vector

Then,

1 1 11 1 1

R , N , S4 4 2

P 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 1

4 4 2

p p

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The Land of Oz: Transition Matrix

75

1 1 1

2 4 4

1 102 2

1 1 1

4 4 2

P

R N S

R

N

S

1

R Ni i

P 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

SNR

1/2

1/2

1/2

1/2

1/4

1/4

1/4

1/4

Fi di P f l

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Finding Pn for large n

76

1 1 1

2 4 41 1

02 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 0.40630.3906 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

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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]

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Global Balance Equations

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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

Letpkbe the long-termprobability that K = k.

3 1

5 2A Bp p

M/M/m/m Queuing Model

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Small slot Analysis: Markov Chain

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Case: m = 2

210

1

2

1 2

1 Letpkbe the long-termprobability 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

Global Balance equations

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Truncated birth-and-death process

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Continuous-time Markov chain More general than M/M/m/m

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Chapter 4

Multiple Access


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Duplexing

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Allow the subscriber to send simultaneously information to thebase 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 communicationfrom the infrastructure to the users/stations

Reverse channel or uplink (UL) is used for communication fromusers/stations back to the infrastructure.

Two techniques

1. Frequency division duplexing (FDD)

2. Time division duplexing (TDD)

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Frequency Division Duplexing (FDD)

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Provide two distinct bands of frequencies (simplex channels)for every user.

The forward band provides traffic from the base station tothe mobile.

The reverse band provides traffic from the mobile to thebase station.

Used in cellular

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Time Division Duplexing (TDD)

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

Each duplex channel has both a forward time slot and areverse 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 appearssimultaneous 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 thesame frequency

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Problems of FDD

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Because each transceiver simultaneously transmits andreceives radio signals which can vary by more than100 dB,the frequency allocation used for the forward and reversechannels must be carefully coordinated within its own system

and with out-of-band users that occupy spectrum betweenthese two bands.

The frequency separation must be coordinated to permit theuse of inexpensive RF and oscillator technology.

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Advantages of FDD

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TDD frames need to incorporate guard periods equal to themax 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.

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Advantages of TDD

Enable adjustment of the downlink/uplink ratio to efficientlysupport 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 linkadaptation, MIMO and other closed loop advanced antennatechnologies.

Ability to implement in nonpaired spectrum FDD requires a pair of channels

TDD only requires a single channel for both DL and ULproviding greater flexibility for adaptation to varied globalspectrum allocations.

ECS455 - Lecture 14.pdf

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