Mobile Communication Slide

download Mobile Communication Slide

of 251

Transcript of Mobile Communication Slide

  • 8/4/2019 Mobile Communication Slide

    1/251

    Abstract of the courseContent of the course

    Course requirements and references

    Mobile Communications

    Instructor: Nguyen Le Hung

    Email: [email protected]; [email protected]

    Department of Electronics & Telecommunications Engineering

    Danang University of Technology, University of Danang

    Mobile Communications Course Information 1

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    2/251

    Abstract of the courseContent of the course

    Course requirements and references

    Abstract of the course

    This undergraduate course helps students to understandmathematical fundamentals and practical transmissiontechniques in 4G mobile communications (i.e., WiMAX,LTE).

    The course lecture notes also provide some possibleresearch directions (in 4G mobile broadbandcommunications) that can be considered for final-yearprojects of undergraduate students.

    Mobile Communications Course Information 2

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    3/251

    Abstract of the courseContent of the course

    Course requirements and references

    Content of the course

    Chapter 1: IntroductionHistory & development of 1G/2G/3G/4G networks.Promises and future trendsCellular mobile communications

    Chapter 2: Mobile wireless channel models.Path lossShadowingMultipath fading channels

    Chapter 3: Physical-layer transmission techniques.Digital modulationsPerformance of digital modulations over fading channelsOrthogonal frequency division multiplexing (OFDM)fundamentals

    Mobile Communications Course Information 3

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    4/251

    Abstract of the courseContent of the course

    Course requirements and references

    Course requirements and references

    Pre-requisite: Basis knowledge of statistics, stochasticprocesses and digital communications systems.

    Class lecture notes: based on the following references:

    Gordan L. Stuber, Principles of Mobile Communication,

    Second Edition, 2002A. Goldsmith, Wireless Communications, Cambridge2005.Recent IEEE journal and conference papers.

    Course assessment:

    Exercises and/or projects: 20%

    Midterm exam: 30%

    Final exam: 50%

    Mobile Communications Course Information 4

    O li

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    5/251

    OutlineIntroduction

    Cellular mobile communications

    Chapter 1: Introduction to Mobile

    Communications

    Nguyen Le Hung

    Mobile Communications Chapter 1: Introduction to Mobile Communications 1

    O tli

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    6/251

    OutlineIntroduction

    Cellular mobile communications

    Outline of Chapter 1

    1 IntroductionDevelopment of mobile communication systemsMobile broadband technology evolution

    Promises and future trends

    2 Cellular mobile communicationsSystem model

    Frequency reuseCellular concept

    Mobile Communications Chapter 1: Introduction to Mobile Communications 2

    Outline Development of mobile communication systems

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    7/251

    OutlineIntroduction

    Cellular mobile communications

    Development of mobile communication systemsMobile broadband technology evolutionPromises and future trends

    Development of mobile communications systems

    time

    code

    frequency

    code

    space

    FDMA (1G)e.g., AMPS ~ 1980s

    TDMA (2G)e.g., GSM ~ 1990s

    OFDM, SDMA (4G)e.g., WiMAX, LTE

    2010s

    CDMA (3G)e.g., W-CDMA ~ 2000s

    frequency

    time

    time

    ~ 1 Gbps (stationary),

    ~ 100 Mbps (mobile)

    frequency

    frequency

    ~ 14 Mbps (downlink),

    ~ 5.8 Mbps (uplink)~ 50 Kbps

    A new signal dimension will be exploited in 5G ?

    Mobile Communications Chapter 1: Introduction to Mobile Communications 3

    Outline Development of mobile communication systems

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    8/251

    OutlineIntroduction

    Cellular mobile communications

    Development of mobile communication systemsMobile broadband technology evolutionPromises and future trends

    OFDM versus FDMA

    Frequency

    Mobile Communications Chapter 1: Introduction to Mobile Communications 4

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    9/251

    Outline Development of mobile communication systems

    http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    10/251

    OutlineIntroduction

    Cellular mobile communications

    Development of mobile communication systemsMobile broadband technology evolutionPromises and future trends

    Promises and future trends

    multimedia services: Voice, Video distribution, Real-time videoconferencing, Data, for both businessand residential customers:

    Explosive traffic growth

    Internet growth, VoIP, VideoIP, IPTV

    Cell phone popularity worldwide

    Ubiquitous communication for people and devices Emerging systems opening new applications

    Unified network: Single distributed network,multiple services, packet architecture

    Extracted from Digital Communication lecture notes, McGill Uni.

    Mobile Communications Chapter 1: Introduction to Mobile Communications 6

    Outline System model

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    11/251

    IntroductionCellular mobile communications

    yFrequency reuseCellular concept

    System model of cellular mobile communications

    BTS

    LTE/LTEAdvanced

    Single Cell

    Multicell

    approach using

    game theory

    Uplink (SCFDMA),

    limited feedback design

    Downlink (OFDMA)

    SingleUserMultiuser

    Precoding(SDMA)

    Multihop

    Relay

    BTS

    BTS

    BTS

    BTS

    Inter

    cellinterferenceIntercellinterference

    Singleuser/Multihop:

    Channel Estimation,

    Synchronization (CFO),

    Channel Coding, ...

    Network Controller STBC with highspeed users

    (large Doppler spread)

    Cognitive radio

    Space Time Block Code: STBC; Peakto

    Average Power Ratio: PAPR; V

    OFDM

    Usercooperation

    (cooperative/multihop

    communications)

    Mobile Communications Chapter 1: Introduction to Mobile Communications 7

    Outline System model

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    12/251

    IntroductionCellular mobile communications

    yFrequency reuseCellular concept

    Frequency reuse

    The available spectrum is partitioned among the base stations(BSs).

    A given frequency band is reused at the closest possibledistance under a certain requirement of co-channelinterference.

    Smaller cells have a shorter distance between reusedfrequencies = an increased spectral efficiency.

    Microcells are of great importance in improving spectralefficiency.

    Under frequency-reuse, users in geographically separated cellssimultaneously employ the same carrier frequency.

    Mobile Communications Chapter 1: Introduction to Mobile Communications 8

    Outline System model

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    13/251

    IntroductionCellular mobile communications

    Frequency reuseCellular concept

    Cellular concept

    The cellular layout of a conventional cellular system is quiteoften described by a uniform grid of hexagonal cells or radiocoverage zones.

    In practice the cells are not regular hexagons, but instead aredistorted and overlapping areas.

    The hexagon is an ideal choice for representing macrocellularcoverage areas, because it closely approximates a circle andoffers a wide range of tessellating reused cluster sizes.

    A tessellating reuse cluster of size N can be constructed if

    = 2 + + 2, (1)

    where and are non-negative integers and . It followsthat the allowable cluster sizes are = 1, 3, 4, 7, 9, 12, . . ..

    Mobile Communications Chapter 1: Introduction to Mobile Communications 9

    Outline System model

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    14/251

    IntroductionCellular mobile communications

    Frequency reuseCellular concept

    Cellular concept: Multicell layout with frequency-reuse

    3-cell 4-cell

    7-cell

    Macrocellular deployment

    with 7-cell clusters

    Macrocellular deployment

    with 3-cell clusters

    Mobile Communications Chapter 1: Introduction to Mobile Communications 10

    Introduction

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    15/251

    Wireless channel modeling

    Chapter 2: Wireless Channel models

    Mobile Communications Chapter 2: Wireless Channel models 1

    IntroductionWi l h l d li

    Multipath wireless propagationP h l h d i d f di

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    16/251

    Wireless channel modeling Path loss, shadowing and fading

    Multipath wireless propagation

    reflection and diffraction

    Extracted from Digital Communication lecture notes, McGill Uni.

    Mobile Communications Chapter 2: Wireless Channel models 2

    IntroductionWi l h l d li

    Multipath wireless propagationP th l h d i d f di

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    17/251

    Wireless channel modeling Path loss, shadowing and fading

    Path loss, shadowing and fading

    The characteristic of (mobile) wireless channel is the variations of

    the channel strength over time and frequency.

    The variations can be divided into two types:Large-scale fading is yielded by:

    path loss of signal as a function of distance andshadowing by large objects such as buildings and hills.

    Small-scale fading is yielded by the constructive and destructiveinterference of the multiple signal paths between transmitter andreceiver.

    Mobile Communications Chapter 2: Wireless Channel models 3

    IntroductionWireless channel modeling

    Multipath wireless propagationPath loss shadowing and fading

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    18/251

    Wireless channel modeling Path loss, shadowing and fading

    An example of path loss, shadowing and fading

    0 50 100 150 200 250 300 350-150

    -140

    -130

    -110

    -100

    -90

    -80

    -70

    -60

    -50

    ReceivedPower[dBm]

    Traveled distance [m]

    Pathloss

    Fading +

    Shadowing +

    Pathloss

    Shadowing +

    Pathloss

    Mobile Communications Chapter 2: Wireless Channel models 4

    IntroductionWireless channel modeling

    Multipath wireless propagationPath loss shadowing and fading

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    19/251

    Wireless channel modeling Path loss, shadowing and fading

    An example of path loss, shadowing and fading (cont.)

    0

    K (dB)

    Pr

    P(dB)

    t

    log (d)

    Path Loss Alone

    Shadowing and Path Loss

    Multipath, Shadowing, and Path Loss

    Mobile Communications Chapter 2: Wireless Channel models 5

    IntroductionWireless channel modeling

    Path loss modelsShadowingF di h l d l

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    20/251

    Wireless channel modelingFading channel model

    Path loss models

    It is well known that the received signal power decays with the

    square of the path length in free space.

    More specifically, the received envelope power is

    = 4

    2, (1)

    where:

    is the transmitted power, and are the transmitter and receiver antenna gains,respectively is the radio path length.

    Mobile Communications Chapter 2: Wireless Channel models 6

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    21/251

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    22/251

    gFading channel model

    Path loss models (cont.)

    The path loss is defined by

    () = 10 log10

    = 10 log104

    42

    sin22 (4)

    Several useful empirical models for macrocellular systems have beenobtained by curve fitting experimental data.

    Two of the useful models for 900 MHz cellular systems are:

    Hatas model based on Okumuras prediction method and

    Lees model.

    Hatas empirical model is probably the simplest to use. Theempirical data for this model was collected by Okumura in the cityof Tokyo.

    Mobile Communications Chapter 2: Wireless Channel models 8

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    23/251

    Fading channel model

    Okumura-Hata models

    With Okumura-Hatas model, the path loss between two isotropic

    BS and MS antennas is

    () =

    + log10() for urban area

    + log10() for suburban area + log10()

    for open area

    (5)

    where

    = 69.55 + 26.16log10() 13.82log10() () = 49.9

    6.55 log10()

    = 5.4 + 2 (log10(/28))2

    = 40.94 + 4.78 (log10())2 18.33 log10()

    Mobile Communications Chapter 2: Wireless Channel models 9

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    24/251

    Fading channel model

    Okumura-Hata models (cont.)

    and

    =

    [1.1log10

    () 0.7] 1.56 log10() + 0.8 for medium or small city8.28 [log

    10(1.54)]

    2 1.1 for 200MHz

    3.2 [log10

    (11.75)]2 4.97 for 400MHz

    for large city

    (6)

    Okumura-Hatas model is expressed in terms of:

    the carrier frequency: 150 1000(MHz),

    BS antenna height: 30 200(m),

    the mobile station (MS) height: 1 10(m),

    the distance: 1 20(km).

    Mobile Communications Chapter 2: Wireless Channel models 10

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    25/251

    g

    Numerical results of Okumura-Hata models

    1 5 10 15 20100

    150

    200

    250

    300

    350

    400

    450

    Pathloss(dB)

    Distance d (km) under scale of log10

    urban area

    suburban area

    open area

    Figure 1: Path loss for = 1.5m, = 50m, = 900MHz.

    Mobile Communications Chapter 2: Wireless Channel models 11

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    26/251

    g

    Shadowing

    A signal transmitted through a wireless channel will typically

    experience random variation due to blockage from objects in thesignal path, giving rise to random variations of the received power ata given distance.

    Such variations are also caused by changes in reflecting surfaces andscattering objects.

    Thus, a model for the random attenuation due to these effects isalso needed. Since the location, size, and dielectric properties of theblocking objects as well as the changes in reflecting surfaces andscattering objects that cause the random attenuation are generallyunknown, statistical models must be used to characterize this

    attenuation.The most common model for this additional attenuation islog-normal shadowing.

    Mobile Communications Chapter 2: Wireless Channel models 12

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    27/251

    Shadowing (cont.)

    Empirical studies have shown that has the following log-normal

    distribution:

    () =2

    2exp

    10log10 2 (dBm)

    22

    () =2

    2 exp10log10 (dBm)22

    where:

    and denote the mean envelop and mean squared levels ofreceived signal (where the expectation is taken over the pdf of the

    received envelope). stands for standard deviation. (dBm) = 30 + 10[log10

    2

    ] (dBm) = 30 + 10[log10 ]

    Mobile Communications Chapter 2: Wireless Channel models 13

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    28/251

    Shadowing (cont.)

    Sometimes is called the local mean because it represents the

    mean envelope level where the averaging is performed over adistance of a few wavelengths that represents a locality.

    This model has been confirmed empirically to accurately model thevariation in received power in both outdoor and indoor radiopropagation environments

    Mobile Communications Chapter 2: Wireless Channel models 14

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    29/251

    Fading channel model

    Two MainMultipaths

    LocalScattering

    The complex transmitted signal can be expressed by

    () = Re

    ()2

    . (7)

    Over a multipath ( physical paths) propagation channel, thereceived signal can be obtained by

    () =

    1

    =0()( ()) + (). (8)

    Mobile Communications Chapter 2: Wireless Channel models 15

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    30/251

    Fading channel model (cont.)

    Substituting (7) into (8) yields the following

    () = Re

    1=0

    () ( ()) 2(())

    + ()

    = Re1

    =0

    () (()) 2+ ()

    = Re()2

    + ()

    As a result, the received baseband signal can be determined by

    () =()( ()) + (). (9)

    where () is the receiver (thermal) noise signal.

    Mobile Communications Chapter 2: Wireless Channel models 16

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    31/251

    Wireless channel modeling (cont.)

    The next step in creating a useful channel model is to convert the

    continuous-time channel to a discrete-time channel.We take the usual approach of sampling theorem.

    Assuming that the input waveform is band-limited to , thebaseband equivalent can be represented by

    () =

    sinc( ), (10)

    where = (/) and sinc() sin()

    .

    This representation follows from the sampling theorem, which says

    that any waveform band-limited to /2 can be expanded in termsof the orthogonal basis functions sinc( ) with coefficients bysamples (taken uniformly at integer multiples of 1/)

    Mobile Communications Chapter 2: Wireless Channel models 17

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    32/251

    Wireless channel modeling (cont.)

    As a result, the baseband received signal can be determined by

    () =

    ()

    sinc (( ()) ) + ()

    =

    ()sinc (( ()) ) + ().

    The sampled outputs at multiples of 1/ is (/) then

    =

    (/)sinc ( (/)) + (/).

    (11)

    Mobile Communications Chapter 2: Wireless Channel models 18

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    33/251

    Wireless channel modeling (cont.)

    Let

    then one can have

    =

    (/)sinc ( (/)) + (/)

    Then, the discrete-time channel model can be given by

    =

    , + (/) (12)

    where , =

    (/)sinc ( (/))This simple discrete-time signal model is widely used inphysical-layer transmission techniques in OFDM systems (e.g., WiFi,

    WiMAX, LTE)

    Mobile Communications Chapter 2: Wireless Channel models 19

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    34/251

    Examples of transmitted baseband signal

    01

    00 10

    11

    I+11

    1

    +1

    Q b0b1

    0 1

    I+11

    1

    +1

    Q

    b011 10

    11 11 10 11

    10 10

    I+11

    1

    +1

    Qb

    0

    b1

    b2

    b3

    +3

    11 01

    11 00 10 00

    10 01+3

    00 10

    00 11 01 11

    01 10

    00 01

    00 00 01 00

    01 013

    3

    BPSK

    QPSK

    16-QAM

    Over multipath channels, the received signal at MS is:

    =

    , + (/) (13)

    It is noted that multipath fading gains , (channel impulseresponse) is time-variant (depend on time index ).

    Mobile Communications Chapter 2: Wireless Channel models 20

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    35/251

    Channel estimation in mobile communications

    Source

    encoder

    Channel

    encoder

    Digital

    modulation

    Channel

    Source

    decoder

    Channel

    decoder

    Digital

    demodulation

    S

    h

    r= Sh + n

    Pilot

    S

    Data

    S

    Data

    S

    Pilot

    S

    Data

    S

    Data

    S

    Pilot

    S

    h h h h h h

    Mobile Communications Chapter 2: Wireless Channel models 21

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    C

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    36/251

    Literature Review of Channel Estimation in Wireless

    Communications

    Detection/decoding

    in communicationsRx signal

    vectorTx signal

    matrixCIR

    vectorRx noise

    vector

    Noncoherent Coherentwithout using CSI- per ormance

    loss

    use CSI

    re uire Channel Estimation CE

    (CSI)

    r= Sh + n

    with channel parameters as:

    Deterministic unknowns Random variables

    Fisher approaches: Bayesian approaches:

    , , , ,

    Multipath fading channel (freq. selective) in multi-carriertransmissions (e.g.,OFDM)

    Time-invariant (quasi-static) Time-variant (Time-selective)

    Perfect

    Synch.

    Imperfect

    Synch.

    Channel Estimation (CE)

    Blind Pilot Semi-blind

    Joint CE and Synch.

    Semi-blind

    Perfect

    Synch.Imperfect

    Synch.

    Channel Estimation (CE)

    PilotJoint CE and Synch.

    Semi-blindPilot

    Pilot design to minimize:

    MSE CRLB

    Pilot design to minimize: Pilot design to minimize:

    MSE BCRLB

    Turbo-based

    Decision-direct.

    Mobile Communications Chapter 2: Wireless Channel models 22

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    Ti i h i d bil d f k /h

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    37/251

    Time-variant path gain , under mobile speed of 5 km/h

    0 1 2 3 4 5 6 7 8 9 10 11 12 13 141

    1.1

    1.2

    1.3

    1.4

    1.5

    1.6

    1.7

    1.8

    1.9

    2

    Time (in OFDM symbol duration)

    Absolutevalueofamplitudeo

    fonepathgainhl Mobile user speed = 5 km/h,

    fc

    = 2 GHz,

    128FFT, CP length = 10,fs

    = 1.92 MHz,

    2 time slots in LTE are considered,Jakes model is considered.

    pilot OFDM symbol

    for channel estimation

    Mobile Communications Chapter 2: Wireless Channel models 23

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    d bil d f 50 k /h

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    38/251

    , under mobile speed of 50 km/h

    0 1 2 3 4 5 6 7 8 9 10 11 12 13 140.95

    1

    1.05

    1.1

    1.15

    Time (in OFDM symbol duration)

    Abso

    lutevalueofamplitudeo

    fonepathgainhl

    Mobile user speed = 50 km/h,fc

    = 2 GHz,

    128FFT, CP length = 10,fs

    = 1.92 MHz,

    2 time slots in LTE are considered,Jakes model is considered

    Data OFDM symbol

    Mobile Communications Chapter 2: Wireless Channel models 24

    IntroductionWireless channel modeling

    Path loss modelsShadowingFading channel model

    d bil d f 300 k /h

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    39/251

    , under mobile speed of 300 km/h

    0 1 2 3 4 5 6 7 8 9 10 11 12 13 140.8

    0.9

    1

    1.1

    1.2

    1.3

    Time (in OFDM symbol duration)

    Absolutevalueofamplitudeofonefadinggainhl Mobile user speed = 300 km/h,

    fc

    = 2 Ghz, 128FFT, CP length = 10, fs

    = 1.92 Mhz,

    2 time slots in LTE are considered,Jakes model is considered.

    Data OFDM symbol

    Mobile Communications Chapter 2: Wireless Channel models 25

    Digital modulation techniquesSignal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union Bound

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    40/251

    y yPassband modulation

    Chapter 3: Physical-layer transmission techniques

    Section 3.1: Digital modulations

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 1

    Digital modulation techniquesSignal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union Bound

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    41/251

    Passband modulation

    Outline of the lecture notes

    1 Digital modulation techniquesAdvantages over analog modulationMain considerations in digital modulation techniquesTypical types of digital modulation techniques

    2 Signal Space AnalysisRationalSignal and system modelGeometric representation of signals

    Practical examplesSignal space representation

    3 Receiver Structure and Sufficient StatisticsGeneral resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    4 Error Probability Analysis and the Union Bound

    Error probabilityThe union bound on error probability

    5 Passband modulationGeneral principlesAmplitude and phase modulationPulse amplitude modulation (MPAM)Phase shift keying (MPSK)Quadrature amplitude modulation (MQAM)

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 2

    Digital modulation techniquesSignal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union Bound

    Advantages over analog modulationMain considerations in digital modulation techniquesTypical types of digital modulation techniques

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    42/251

    Passband modulation

    Advantages over analog modulation

    The advances over the last several decades in hardware anddigital signal processing have made digital transceivers muchcheaper, faster, and more power-efficient than analogtransceivers.

    More importantly, digital modulation offers a number of otheradvantages over analog modulation, including:

    higher data rates,powerful error correction techniques,resistance to channel impairments,

    more efficient multiple access strategies, andbetter security and privacy.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 3

    Digital modulation techniquesSignal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundP b d d l i

    Advantages over analog modulationMain considerations in digital modulation techniquesTypical types of digital modulation techniques

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    43/251

    Passband modulation

    Advantages over analog modulation (cont.)

    Digital transmissions consist of transferring information in theform of bits over a communications channel.

    The bits are binary digits taking on the values of either 1 or 0.These information bits are derived from the information

    source, which may be a digital source or an analog source thathas been passed through an A/D converter.

    Both digital and A/D converted analog sources may becompressed to obtain the information bit sequence.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 4

    Digital modulation techniquesSignal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundP b d d l ti

    Advantages over analog modulationMain considerations in digital modulation techniquesTypical types of digital modulation techniques

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    44/251

    Passband modulation

    Main considerations in digital modulation techniques

    Digital modulation consists of mapping the information bitsinto an analog signal for transmission over the channel.

    Detection consists of determining the original bit sequencebased on the signal received over the channel.

    The main considerations in choosing a particular digitalmodulation technique are:

    high data ratehigh spectral efficiency (minimum bandwidth occupancy)high power efficiency (minimum required transmit power)

    robustness to channel impairments (minimum probability of biterror)low power/cost implementation

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 5

    Digital modulation techniquesSignal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Advantages over analog modulationMain considerations in digital modulation techniquesTypical types of digital modulation techniques

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    45/251

    Passband modulation

    Typical types of digital modulation techniques

    Often the previous ones are conflicting requirements, and thechoice of modulation is based on finding the technique thatachieves the best tradeoff between these requirements.

    There are two main categories of digital modulation:

    amplitude/phase modulationfrequency modulation

    Frequency modulation typically has a constant signal envelopeand is generated using nonlinear techniques, this modulationis also called constant envelope modulation or nonlinear

    modulation

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 6

    Digital modulation techniquesSignal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Advantages over analog modulationMain considerations in digital modulation techniquesTypical types of digital modulation techniques

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    46/251

    Passband modulation

    Typical types of digital modulation techniques (cont.)

    Amplitude/phase modulation is also called linear modulation.

    Linear modulation generally has better spectral propertiesthan nonlinear modulation, since nonlinear processing leads tospectral broadening.

    However, amplitude and phase modulation embeds theinformation bits into the amplitude or phase of thetransmitted signal, which is more susceptible to variationsfrom fading and interference.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 7

    Digital modulation techniquesSignal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Advantages over analog modulationMain considerations in digital modulation techniquesTypical types of digital modulation techniques

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    47/251

    Passband modulation

    Typical types of digital modulation techniques (cont.)

    In addition, amplitude and phase modulation techniquestypically require linear amplifiers, which are more expensiveand less power efficient than the nonlinear amplifiers that canbe used with nonlinear modulation.

    Thus, the general tradeoff of linear versus nonlinearmodulation is one of better spectral efficiency for the formertechnique and better power efficiency and resistance tochannel impairments for the latter technique.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 8

    Digital modulation techniquesSignal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    48/251

    Passband modulation Signal space representation

    Rational

    Digital modulation encodes a bit stream of finite length intoone of several possible transmitted signals.

    Intuitively, the receiver minimizes the probability of detectionerror by decoding the received signal as the signal in the set of

    possible transmitted signals that is closest to the one received.Determining the distance between the transmitted andreceived signals requires a metric for the distance betweensignals.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 9

    Digital modulation techniquesSignal Space Analysis

    Receiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    49/251

    g p p

    Rational (cont.)

    By representing signals as projections onto a set of basisfunctions, we obtain a one-to-one correspondence between theset of transmitted signals and their vector representations.

    Thus, we can analyze signals in finite-dimensional vector

    space instead of infinite-dimensional function space, usingclassical notions of distance for vector spaces.

    In this section we show:

    how digitally modulated signals can be represented as vectorsin an appropriately-defined vector space, and

    how optimal demodulation methods can be obtained from thisvector space representation.

    This general analysis will then be applied to specificmodulation techniques in later sections.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 10

    Digital modulation techniquesSignal Space Analysis

    Receiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    50/251

    g p p

    Transmitted signal

    Transmitter Receiver +

    n(t)

    AWGN Channel

    s(t)i 1 K

    m ={b ,...,b } ^1 K

    m ={b ,...,b }^ ^r(t)

    Figure 1: Communication system model over AWGN channel (i.e., aspecial case of wireless channel).

    Consider a communication system model as shown in theabove figure.

    Every seconds, the sytem sends = log2 bits ofinformation through the channel for a data rate of = /bits per second (bps).

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 11

    Digital modulation techniquesSignal Space Analysis

    Receiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    51/251

    Transmitted signal (cont.)

    There are = 2 possible sequences of bits and each bitsequence of length comprises a message = {1,...,} , where = {1,...,} is the set ofall such messages.

    The message has probability of being selected fortransmission, where

    =1 = 1.

    Suppose that message is to be transmitted over theAWGN channel during the time interval [0, ). Since thechannel is analog, the message must be embedded into ananalog signal for channel transmission.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 12

    Digital modulation techniquesSignal Space Analysis

    Receiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    52/251

    Transmitted signal (cont.)

    Therefore, each message is mapped to a uniqueanalog signal () = {1(),...,()} where () isdefined on the time interval [0, ) and has energy

    = 0

    2 (), = 1,...,. (1)

    When messages are sent sequentially, the transmittedsignal becomes a sequence of the corresponding analog signalsas follows

    () =

    ( ). (2)

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 13

    Digital modulation techniquesSignal Space Analysis

    Receiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    53/251

    Transmitted and received signals

    In the aforementioned model, the transmitted signal is sentthrough an AWGN channel where a white Gaussian noiseprocess () of power spectral density /2 is added to formthe received signal

    () = () + (). (3)

    T0 2T 3T 4T

    s (t)1 1 1

    2s (tT)

    s (t2T) s (t3T)

    s(t)

    ...

    m1

    m1

    m1

    m2

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 14

    Digital modulation techniquesSignal Space Analysis

    Receiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    54/251

    Received signal

    Given (), the receiver must determine the best estimate ofwhich () was transmitted during each transmissioninterval [0, ).

    This best estimate of () is mapped to a best estimate of

    the message () and the receiver produces this bestestimate = 1,..., of the transmitted bit sequence.The goal of the receiver design in estimating the transmittedmessage is to minimize the probability of message error

    ==1

    ( = sent) ( sent) (4)over each time interval [0, ).

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 15

    Digital modulation techniquesSignal Space Analysis

    Receiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    55/251

    Introduction

    By representing the signals {(), = 1,...,} geometrically,one can solve for the optimal receiver design in AWGNchannels based on a minimum distance criterion.

    Note that, wireless channels typically have a time-varying

    impulse response in addition to AWGN. We will consider theeffect of an arbitrary channel impulse response on digitalmodulation performance in the next sections.

    The basic premise behind a geometrical representation ofsignals is the notion of a basis set.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 16

    Digital modulation techniquesSignal Space Analysis

    Receiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    56/251

    Basis function representation of signals

    Specifically, using a Gram-Schmidt orthogonalizationprocedure, it can be shown that any set of real energysignals = {1(),...,()} defined on [0, ) can berepresented as a linear combination of real

    orthogonal basis functions {1(),...,()}.We say that these basis functions span the set .Each signal {() } can be represented by

    () =

    =1 ,(), 0 < , (5)where

    , =

    0

    ()() (6)

    is a real coefficient representing the projection.Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 17

    Digital modulation techniquesSignal Space Analysis

    Receiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    RationalSignal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    57/251

    Basis function representation of signals (cont.)

    These basis functions have the following property0

    ()() =

    1 = ,

    0 = . (7)

    The basis set consists of the sine and cosine functions

    1() =

    2

    cos (2) (8)

    and2() =

    2

    sin(2) . (9)

    where

    2 is used to obtain

    0

    2 () = 1, = 1, 2.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 18

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Rational

    Signal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    58/251

    Basis functions in linear passband modulation techniques

    With these basis functions, one only obtain an approximationto (7), since

    0

    21() =2

    0

    0.5 [1 + cos (4)] = 1+sin (4)

    4(10)

    The numerator in the second term of (10) is bounded by 1,and for 1 the denominator of this term is very large.As a result, this second term can be neglected.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 19

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Rational

    Signal and system modelGeometric representation of signalsPractical examplesSignal space representation

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    59/251

    Basis functions in linear passband modulation (cont.)

    With these basis functions, one can have0

    1()2() =2

    0

    0.5sin(4) = cos(4)

    4 0

    (11)

    where the approximation is taken as an equality as 1.With the basis set 1() =

    2/ cos (2) and

    2() =

    2/ sin (2), the basis function representation(5) corresponds to the complex representation of () interms of its in-phase and quadrature components with anextra factor of2/ as follows

    () = ,1

    2

    cos (2) + ,2

    2

    sin(2) . (12)

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 20

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Rational

    Signal and system modelGeometric representation of signalsPractical examplesSignal space representation

    ( )

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    60/251

    Basis functions in linear passband modulation (cont.)

    In practice, the basis set may include a baseband pulse-shapingfilter () to improve the spectral characteristics of the transmittedsignal:

    () = ,1() cos (2) + ,2() sin (2) (13)

    where the simplest pulse shape that satisfy (7) is the rectangularpulse shape () =

    2/ , 0 < .

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 21

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Rational

    Signal and system modelGeometric representation of signalsPractical examplesSignal space representation

    D fi i i d i i l i

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    61/251

    Definitions used in signal space representation

    We denote the coefficients {,} as a vectors = [,1,...,,] which is called the signalconstellation point corresponding to the signal ().

    The signal constellation consists of all constellation points

    {s1, ..., s}.Given the basis functions {1(),...,()} there is aone-to-one correspondence between the transmitted signal() and its constellation point s.

    The representation of () in terms of its constellation points is called:

    its signal space representation andthe vector space containing the constellation is called thesignal space.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 22

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    62/251

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Rational

    Signal and system modelGeometric representation of signalsPractical examplesSignal space representation

    D fi iti d i i l t ti ( t )

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    63/251

    Definitions used in signal space representation (cont.)

    With this signal space representation we can analyze theinfinite-dimensional functions () as vectors s infinite-dimensional vector space 2.This greatly simplifies the analysis of the system performance

    as well as the derivation of the optimal receiver design.Signal space representations for common modulationtechniques like MPSK and MQAM are two-dimensional(corresponding to the in-phase and quadrature basisfunctions).

    In order to analyze signals via a signal space representation,we need to use some definitions for the vector characterizationin the vector space .

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 24

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Rational

    Signal and system modelGeometric representation of signalsPractical examplesSignal space representation

    D fi iti d i i l t ti ( t )

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    64/251

    Definitions used in signal space representation (cont.)

    In particular, the length of a vector in is defined as

    s =

    =12,. (14)

    The distance between two signal constellation points s and sis thus

    s s =

    =1

    (, ,)2

    = 0 (() ())2 .(15)

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 25

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    Rational

    Signal and system modelGeometric representation of signalsPractical examplesSignal space representation

    D fi iti d i i l t ti ( t )

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    65/251

    Definitions used in signal space representation (cont.)

    Finally, the inner product (), () between two realsignals () and () on the interval [0, ) is defined as

    (), () =

    0()(). (16)

    Similarly, the inner product s, s between two real vectors is

    s, s = ss =

    0()() = (), (). (17)

    It is noted that two signals are orthogonal if their innerproduct is zero.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 26

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Receiver structure and sufficient statistics

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    66/251

    Receiver structure and sufficient statistics

    Given the channel output () = () + (), 0 < , wenow investigate the receiver structure to determine whichconstellation point s or, equivalently, which message , wassent over the time interval [0, ).

    A similar procedure is done for each time interval[ , ( + 1)).

    We would like to convert the received signal () over eachtime interval into a vector, since it allows us to work infinite-dimensional vector space to estimate the transmitted

    signal.

    However, this conversion should not compromise theestimation accuracy. For this conversion, consider the receiverstructure shown in the next figure.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 27

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Receiver structure and sufficient statistics (cont )

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    67/251

    Receiver structure and sufficient statistics (cont.)

    )()()( tntstri

    T

    dt0()

    T

    dt0

    ()

    111, rnsi

    )(1 tI

    )(tN

    I

    NNNirns ,

    Find ii

    mm

    As shown in the above figure, the components of signal andnoise vectors are determined by

    , = 0

    ()(), (18)

    and

    =

    0

    ()(). (19)

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 28

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Receiver structure and sufficient statistics (cont )

    http://-/?-http://-/?-http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    68/251

    Receiver structure and sufficient statistics (cont.)

    We can rewrite () as

    () ==1

    (, + ) () + () ==1

    () + (),

    (20)where = , + and () = () =1 ()denotes the remainder noise.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 29

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Proofs of sufficient statistics for optimal detection

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    69/251

    Proofs of sufficient statistics for optimal detection

    If we can show that the optimal detection of the transmittedsignal constellation point s given received signal () does notmake use of the remainder noise (), then the receiver canmake its estimate of the transmitted message as afunction ofr = (1,...,) alone.In other words, r = (1,...,) is a sufficient statistic for ()in the optimal detection of the transmitted messages.

    Let exam the distribution of r. Since () is a Gaussian

    random process, if we condition on the transmitted signal() then the channel output () = () + () is also aGaussian random process and r = [1,...,] is a Gaussianrandom vector.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 30

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    70/251

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Proofs of sufficient statistics for optimal detection (cont )

    http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    71/251

    Proofs of sufficient statistics for optimal detection (cont.)

    Thus, conditioned on the transmitted constellation s, the sare uncorrelated and, since they are Gaussian and also

    independent. Moreover,

    2

    = 0/2.

    We have shown that, conditioned on the transmitted

    constellation s, is a Gauss-distributed random variable thatis independent of , = and has mean , and variance0/2.

    Thus, the conditional distribution of r is given by

    (rs sent) ==1

    ( ) = 1(0)

    /2exp

    10

    =1

    ( ,)2 .(24)

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 32

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient Statistics

    Error Probability Analysis and the Union BoundPassband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Proofs of sufficient statistics for optimal detection (cont )

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    72/251

    Proofs of sufficient statistics for optimal detection (cont.)

    It is also straightforward to show that [()s] = 0 forany , 0 < . Thus, since conditioned on s and ()are Gaussian and uncorrelated, they are independent.

    Also, since the transmitted signal is independent of the noise,

    , is independent of the process ().We now discuss the receiver design criterion and show it is notaffected by discarding ().

    The goal of the receiver design is to minimize the probability

    of error in detecting the transmitted message givenreceived signal ().

    To minimize = ( = ()) = 1 ( = ()), wemaximize (

    = ()).

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 33

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Proofs of sufficient statistics for optimal detection (cont )

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    73/251

    Proofs of sufficient statistics for optimal detection (cont.)

    Therefore, the receiver output

    given received signal ()

    should correspond to the message that maximizes

    ( sent()).Since there is a one-to-one mapping between messages andsignal constellation points, this is equivalent to maximizing ( sent()).

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 34

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Proofs of sufficient statistics for optimal detection (cont.)

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    74/251

    Proofs of sufficient statistics for optimal detection (cont.)

    Recalling that () is completely described by = (1,...,)and (), we have

    (s sent()) = ((,1,...,,) sent(1,...,, ()))= ((,1,...,,) sent, (1,...,), ())

    ((1,...,), ())

    = ((,1,...,,) sent, (1,...,)) (())

    ((1,...,)) (())

    = ((,1,...,,) sent(1,...,)) . (25)where the third equality follows from the fact that the () isindependent of both (1,...,) and of (,1,...,,).

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 35

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Proofs of sufficient statistics for optimal detection (cont.)

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    75/251

    oo s o su c e t stat st cs o opt a detect o (co t )

    This analysis shows that (1,...,) is a sufficient statistic for() in detecting , in the sense that the probability of error

    is minimized by using only this sufficient statistic to estimatethe transmitted signal and discarding the remainder noise.

    Since r is a sufficient statistic for the received signal (), wecall r the received vector associated with ().

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 36

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Decision regions

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    76/251

    g

    As aforementioned, the optimal receiver minimizes errorprobability by selecting the detector output

    that maximizes

    the probability of correct detection1

    = ( sentr received).In other words, given a received vector r, the optimal receiverselects = corresponding to the constellation s thatsatisfies

    (s

    r) > (s

    r) ,

    = (26)

    where (sr) (s sentr received) for the sake ofnotational simplicity.

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 37

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    Decision regions(cont.)

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    77/251

    g ( )

    Thus, the decision regions (1,...,) corresponding to(s1, ...,s) are the subsets of the signal space anddefined by

    = (r : (sr) > (sr) , = ) . (27)Once the signal space has been partitioned by decisionregions, for a received vector r , the optimal receiveroutputs the message estimate = The receiver processing consists of ) computing the receivedvector r from (), ) finding which decision region contains r, and ) outputting the corresponding message .

    Mobile communications-Chapter 3: Physical-layer transmissions Section 3.1: Digital modulations 38

    Digital modulation techniques

    Signal Space AnalysisReceiver Structure and Sufficient StatisticsError Probability Analysis and the Union Bound

    Passband modulation

    General resultsProofs of sufficient statistics for optimal detectionDecision regions and criterion

    An example on decision regions

    http://-/?-http://-/?-http://find/http://goback/http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-
  • 8/4/2019 Mobile Communication Slide

    78/251

    p g

    This p