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    Network engineering formobile networks

    Salah Eddine El Ayoubi

    Orange Labs

    [email protected]

    2013

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    outline

    objective: ensuring QoS in mobile networks

    coverage in mobile networks

    dimensioning radio interface for capacity

    2 Salah Eddine Elayoubi Mobile Network Engineering

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    coverage targets

    mobile operators have to ensure complete coverage:

    minimize white zones

    cover villages as well as cities

    cover routes

    3 Salah Eddine Elayoubi Mobile Network Engineering

    limited power

    loss due to propagation

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    cellular networks

    each base station covers a cell / sector

    large cells required to reduce costs, however:

    degraded QoS at cell edge: coverage problems

    many users served: capacity problems

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    What is spectrum ?

    f1 f2 f3

    30 MHz 300 MHz 3 GHz 30 GHz

    radio waves are characterized by their frequency, measured in Hertz (Hz)

    spectrum is the continuous aggregation of these frequencies

    5 Salah Eddine Elayoubi Mobile Network Engineering

    VHF UHF SHF

    the operator buys an amount of frequency from the regulator ofeach country

    a set of contiguous frequencies is called a carrier

    each operator has a limited number of carriers

    each carrier has a limited capacity in terms of number of users thatcan be served, as we will see next

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    Operator dilemma

    coverage is not the only criterion:

    QoS in coverage areas is important

    QoS includes:

    access rate

    good communication probability

    throughput

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    operator target: ensure coverage target and QoS

    with lowest costs

    operator dilemma:

    low cost -> large cells -> more users in each cell -> more

    spectrum needed

    spectrum is limited and too costly

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    example of network deployment

    exercise

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    Challenges related to spectrum

    f1

    f2

    f3

    8 Salah Eddine Elayoubi Mobile Network Engineering

    VHF UHF SHF

    30 z 300 z 3 GHz 30 GHz

    frequency=speed of light / wavelength

    different challenges when using different frequency bands large frequency -> small wavelength -> low penetration of obstacles

    low frequency -> large wavelength -> large antennas needed

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    Main guidelines when managing spectrum

    Frequencies that areFrequencies that areFrequencies that areFrequencies that are

    usable for cellularusable for cellularusable for cellularusable for cellular

    networking are betweennetworking are betweennetworking are betweennetworking are between

    400 MHz and 5 GHz400 MHz and 5 GHz400 MHz and 5 GHz400 MHz and 5 GHz Low frequencies areLow frequencies areLow frequencies areLow frequencies are

    used when there is aused when there is aused when there is aused when there is a

    need for largeneed for largeneed for largeneed for large

    coveragecoveragecoveragecoverage

    9 Salah Eddine Elayoubi Mobile Network Engineering

    , . ., . ., . ., . .

    areas.areas.areas.areas.

    High frequencies areHigh frequencies areHigh frequencies areHigh frequencies are

    used when there is aused when there is aused when there is aused when there is a

    need for large capacity,need for large capacity,need for large capacity,need for large capacity,

    e.g. in urban areas.e.g. in urban areas.e.g. in urban areas.e.g. in urban areas.

    FrequencyFrequencyFrequencyFrequency

    (MHz)(MHz)(MHz)(MHz)400 1000 5000

    Terminal

    too big

    overage

    too smallCoveragefrequencies

    Capacityfrequencies

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    High demand

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    Limited resource

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    How to share spectrum

    f3 f3

    11 Salah Eddine Elayoubi Mobile Network Engineering

    f1 f1

    f2

    f2 f3 f1

    f2

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    objective: ensuring QoS in mobile networks

    coverage in mobile networks

    dimensioning radio interface for capacity

    outline

    12 Salah Eddine Elayoubi Mobile Network Engineering

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    link budget

    link budget objective

    maximum distance between a user and its serving base station while guaranteeing

    a given quality of service

    equipment parameters propagation model cell rangereceived signals SINR

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    equipment parameters

    determine gains and losses due to equipments.

    antenna gain GA: directivity of antenna amplifies the signal in some directions.

    14 Salah Eddine Elayoubi Mobile Network Engineering

    feeder loss LF: due to the cable between amplifier and antenna.

    for an emitted power Pmax:

    F

    Amax

    L

    GPpoweruseful

    =

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    propagation model

    link budget objective

    maximum distance between a user and its serving base station while guaranteeing

    a given quality of service

    equipment parameters propagation model cell rangereceived signals SINR

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    use of propagation models

    Ptxpathloss

    C

    pathloss

    Ptx

    I

    16 Salah Eddine Elayoubi Mobile Network Engineering

    propagation models allow to compute:

    The received signal power ( coverage maps)

    The interfering power ( QoS maps) a propagation model is the first building block of (almost) any radio

    planning tool

    Serving BS Interfering BS

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    path loss models

    free space propagation

    only valid for line of sight, without multiwithout multiwithout multiwithout multi----pathpathpathpath

    22

    44

    =

    =

    cDfDPathloss

    D

    17 Salah Eddine Elayoubi Mobile Network Engineering

    these conditions are not met in cellular networks

    statistical models (e.g. Okumura-Hata)

    simple models with A & B statistically tunedfor typical environments (urban, etc.)

    no geographical data required

    useful for dimensioning

    ( ) 4020withlog][ += BDBAdBPathlosse.g. urban environment

    D

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    received signals

    link budget objective

    maximum distance between a user and its serving base station while guaranteeing

    a given quality of service

    equipment parameters propagation model cell rangereceived signals SINR

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    received signals

    for a user situated at distance d from a base station:

    )(dPLL

    GP

    powerreceivedF

    Amax

    =

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    PL(d)=path loss at distance d

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    SINR

    link budget objective

    maximum distance between a user and its serving base station while guaranteeing

    a given quality of service

    equipment parameters propagation model cell rangereceived signals SINR

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    interference in the dowlink

    interference is received by the mobile

    from the base stations:

    it depends on the position of the

    mobile in the cell cell-edge users are subject to

    higher interference because they

    are closer to interferers.

    21 Salah Eddine Elayoubi Mobile Network Engineering

    observations: the origin of interference is well

    defined.

    the intensity of this interference

    is to be calculated.

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    interference in the uplink

    interference is received by the base

    station from the mobiles in adjacent

    cells:

    it is independent from theposition of the mobile in the cell.

    it depends on the distribution of

    mobiles in interfering cells.

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    observations: the average interference is

    uniform for all mobiles.

    the position of interferers is

    unknown.

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    SINR calculations

    collisions decrease the Signal to Interference Ratio (SINR):

    noiseceinterferenreceived

    powerreceivedSINR

    +=

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    a lower SINR means a larger Bit Error Rate (BER):

    degraded QoS

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    cell range

    link budget objective

    maximum distance between a user and its serving base station while guaranteeing

    a given quality of service

    equipment parameters propagation model cell rangereceived signals SINR

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    maximal cell range

    for a good reception, the SINR must be larger than a target:

    SINR>SINRtarget

    for a given cell range R, calculate the SINR at cell edge:

    SINR(R)

    for a larger R, SINR degrades as received power becomes

    lower compared to noise

    25 Salah Eddine Elayoubi Mobile Network Engineering

    the optimal cell range is the largest R so that SINR(R)>SINRtarget

    in general, the limiting link for coverage is the uplink as mobiles

    have low emitted powers.

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    example coverage of a cell

    exercise

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    outline

    objective: ensuring QoS in mobile networks

    coverage in mobile networks

    dimensioning radio interface for capacity

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    Erlang-like capacity

    need to install resources:

    that insures a Quality of Service (QoS) for users

    example: number of frequency carriers per cell user perceived QoS includes:

    blocking rates for real-time calls

    -

    28 Salah Eddine Elayoubi Mobile Network Engineering

    -

    this is called Erlang-like capacity:

    reference to mathematician Agner Krarup Erlang

    example Erlang-B law.

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    Erlang-B law

    probability of call loss:

    B=blockin rate 5055606570758085

    9095

    1000.0001 0.001 0.01

    c

    Erlang tableB

    29 Salah Eddine Elayoubi Mobile Network Engineering

    E=traffic intensity C= number of circuits

    Each call uses one

    circuit 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 805

    101520253035

    40

    85

    A simple Erlang calculator can be found at:

    http://perso.rd.francetelecom.fr/bonald/Applets/erlang.html

    E

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    the race for bit rates in mobile networks

    Wide Area

    Mobility

    1995 2000 2005 2012

    GSMGPRS 4G?

    EDGE UMTS LTEHSPA

    +

    HSDPA

    Mobile TV

    HSUPA

    Wide Area

    Mobility

    Mobility

    1995 2000 2005

    4G?EDGEUMTS LTE

    HSPA

    +

    HSDPA

    DVB-x

    30 Salah Eddine Elayoubi Mobile Network Engineering

    Short range

    Mobility

    Data Rate

    10kbps 100kbps

    Fixed

    WLAN

    Fix

    1Mbps 10Mbps 100Mbps

    .

    Data Rate

    10kbps 100kbps

    Fixed

    WLAN

    Fixed

    Wimax

    1Mbps 10Mbps

    .

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    objective: ensuring QoS in mobile networks

    coverage in mobile networks

    dimensioning radio interface for capacity

    outline

    31 Salah Eddine Elayoubi Mobile Network Engineering

    GSM

    UMTS

    LTE

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    GSM operation

    the spectrum assigned to GSM is divided into sub-bands of

    200 KHZ each.

    the subbands cannot be used in adjacent cells

    due to inter-cell interference

    a frequency reuse map is necessary

    32 Salah Eddine Elayoubi Mobile Network Engineering

    1/3 of sub-bands used in each cell 1/7 of sub-bands used in each cell

    a transmitter (a dedicated amplifier) is necessary for each sub-

    band in the cell.

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    Time Division Multiple Access operation

    several frequency sub-bands of 200 KHZ each

    each sub-band is allocated for different users at different times

    the time frame of 4.62 ms is divided into 8 time slots

    but the transmitter serves up to 7 users (one TS for signalling)

    33 Salah Eddine Elayoubi Mobile Network Engineering

    Transmitters

    Time slots

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    example capacity of a GSM cell

    exercise

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    objective: ensuring QoS in mobile networks

    coverage in mobile networks

    dimensioning radio interface for capacity

    outline

    35 Salah Eddine Elayoubi Mobile Network Engineering

    GSM

    UMTS

    physical layer

    capacity calculations LTE

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    Code Division Multiple Access

    everybody transmits at the same

    time-frequency resources.

    each transmitter has its own code

    the receiver decodes the signal and

    views the others' signals as residual

    interference.

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    spreading process

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    downlink spreading codes

    Walsh code:

    W(0,1) = 1

    W(0,2) = 1, 1

    W(1,2) = 1,-1

    W(0,4) = 1, 1, 1, 1

    W(1,4) = 1,-1, 1,-1

    W(2,4) = 1, 1,-1,-1

    W(3,4) = 1,-1,-1, 1

    W(0,8) = 1, 1, 1, 1, 1, 1, 1, 1

    W(1,8) = 1,-1, 1,-1, 1,-1, 1,-1

    W(2,8) = 1, 1,-1,-1, 1, 1,-1,-1

    W(3,8) = 1,-1,-1, 1, 1,-1,-1, 1

    38 Salah Eddine Elayoubi Mobile Network Engineering

    W(4,8) = 1, 1, 1, 1,-1,-1,-1,-1

    W(5,8) = 1,-1, 1,-1,-1, 1,-1, 1W(6,8) = 1, 1,-1,-1,-1,-1, 1, 1

    W(7,8) = 1,-1,-1, 1,-1, 1, 1,-1

    orthogonal codes, as synchronous transmissions

    problem: multipath propagation that introduces delays

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    UMTS capacity constraint

    power of base station limited by Pmax

    admission control constraint:

    Com

    n

    i

    iii PPMqNFPP ++=

    max

    1

    0maxmax )(

    39 Salah Eddine Elayoubi Mobile Network Engineering

    intra-cell interference

    intra-cell interference

    noise

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    capacity calculations

    Exercise

    40 Salah Eddine Elayoubi Mobile Network Engineering

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    general capacity calculation

    admission control constraint indicates that there is a resource

    (power) shared by users of different demands

    (position+service).

    traffic c,i (Erlang) in zone i for class c.

    41 Salah Eddine Elayoubi Mobile Network Engineering

    -

    = =

    =C

    c

    n

    i ic

    Mic

    nCMG

    MMic

    1 1 ,

    ,,1,1

    !

    1],...,Pr[

    ,

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    objective: ensuring QoS in mobile networks

    coverage in mobile networks

    dimensioning radio interface for capacity

    outline

    42 Salah Eddine Elayoubi Mobile Network Engineering

    GSM

    UMTS

    LTE

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    outline: LTE

    physical layer

    capacity calculations use case: mobile TV

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    LTE context and E-UTRAN requirements

    1 Tx antenna, 2 Rx antennas16 QAM modulation, code rate 5/6

    56 Mbit/s

    (71 Mbit/s for 64QAM)

    Peak rate (Uplink)(in 20 MHz, FDD)

    2 Tx and 2 Rx antennas- -

    0.7 b/s/Hz/cell

    Average cell spectrum

    2 Tx and 2 Rx antennasMIMO transmission with linear

    receiver

    1.72 b/s/Hz/cell

    (8.6 Mbit/s in 5 MHz)

    Average cell spectrumefficiency (downlink)

    2 Tx and 2 Rx antennas,64 QAM modulation, code rate 5/6

    144 Mbit/sPeak rate (Downlink)(in 20 MHz, FDD)

    Expected performance (based on analysis and simulations)

    1 Tx antenna, 2 Rx antennas16 QAM modulation, code rate 5/6

    56 Mbit/s

    (71 Mbit/s for 64QAM)

    Peak rate (Uplink)(in 20 MHz, FDD)

    2 Tx and 2 Rx antennas- -

    0.7 b/s/Hz/cell

    Average cell spectrum

    2 Tx and 2 Rx antennasMIMO transmission with linear

    receiver

    1.72 b/s/Hz/cell

    (8.6 Mbit/s in 5 MHz)

    Average cell spectrumefficiency (downlink)

    2 Tx and 2 Rx antennas,64 QAM modulation, code rate 5/6

    144 Mbit/sPeak rate (Downlink)(in 20 MHz, FDD)

    Expected performance (based on analysis and simulations)

    44 Salah Eddine Elayoubi Mobile Network Engineering

    Assumptions:FDD, 30% retransmissions

    ~ 10 msUser plane latency(two way radio delay)

    .

    < 50 msecs (dormant->active)

    < 100 msecs (idle ->active)

    Connection setuplatency

    Assumptions:FDD, 30% retransmissions

    ~ 10 msUser plane latency(two way radio delay)

    .

    < 50 msecs (dormant->active)

    < 100 msecs (idle ->active)

    Connection setuplatency

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    the 3M of LTE

    Multi-carrier Frequency dimension

    Allow for spectrum flexibility and higher bandwidths.

    Data rate = Bandwidth [Hz] x Spectrum efficiency [bps/Hz]

    Multi-antenna (MIMO) Spatial dimension

    45 Salah Eddine Elayoubi Mobile Network Engineering

    Information Theory:Max. spectrum efficiency increases linearly with the number ofantennas.

    Multi-Layer Cross-layer optimization (PHY, MAC, RLC)

    Packet oriented radio interface Low latencies and higher spectrum efficiencies.

    l i i h f di i

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    multi-carrier the frequency dimension

    Orthogonal Frequency Division Multiplexing (OFDM)

    Facilitates equalization at the receiver

    Divides bandwidth in narrowband sub-carriers

    46 Salah Eddine Elayoubi Mobile Network Engineering

    Time-frequency resources can be allocatedto data and control channels

    TimeFrequency

    Spectrumallocation1.25 - 20 MHz

    1ms sub-frame (LTE DL)

    L1/L2Control User A User B

    TimeFrequency

    Spectrumallocation1.25 - 20 MHz

    1ms sub-frame (LTE DL)

    L1/L2Control User A User B

    M lti t th ti l di i (1/2)

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    Multi-antenna the spatial dimension (1/2)

    MIMO increases spectrum efficiency

    NTX NRX

    47 Salah Eddine Elayoubi Mobile Network Engineering

    Theoretical Maximum: Spectrum Eff. = min(NTX, NRX) x Single antenna Eff.

    Yes but

    Additional antenna branches are costly especially on the terminal side

    Achievable rates highly depend on propagation conditions

    Mobile feedback required for high rates -> limitation of supported speeds

    Different and adaptive solutions required depending on thedeployment scenario (coverage vs. rate trade-off).

    M lti t th ti l di i (2/2)

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    Multi-antenna the spatial dimension (2/2)

    multi-antenna mechanisms in E-UTRAN downlink

    Space diversitySpace diversitySpace diversitySpace diversity for improved robustness

    of common control channels and

    for users with high speed and/or low rate

    BeamformingBeamformingBeamformingBeamforming for coverage

    limited deployments

    Spatial multiplexingSpatial multiplexingSpatial multiplexingSpatial multiplexing for high rates near

    A) Transmit diversity-> Increased robustness

    B) Beamforming-> Increased coverage

    48 Salah Eddine Elayoubi Mobile Network Engineering

    Adaptive selection of number of layers.

    Spatial multiplexing of usersSpatial multiplexing of usersSpatial multiplexing of usersSpatial multiplexing of users in scenarios

    with high user density and low rate traffic

    C) Spatial multiplexing-> Increased throughput

    D) Multi-user beamforming (SDMA)-> Increased capacity

    M lti la er Fast packet sched ling

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    Multi-layer Fast packet scheduling

    Cross-layer design (Layer 1 Layer 2)

    Time

    Fast fading

    ~~~~Achievable

    Throughput

    User 1User 1User 1User 1

    User 2User 2User 2User 2

    Fixed ressource

    allocation

    userthroughputTransmission time

    Time

    Fast fading

    ~~~~Achievable

    Throughput

    User 1User 1User 1User 1

    User 2User 2User 2User 2

    Fixed ressource

    allocation

    Fixed ressource

    allocation

    userthroughputTransmission time

    Circuit oriented andlayered design

    49 Salah Eddine Elayoubi Mobile Network Engineering

    Usage of terminal feedback for resource allocation and phy-layer configuration

    Cross-layer mechanisms already implemented in HSDPA.

    Extension to frequency adaptive scheduling and adaptive MIMO transmission

    Time

    Fast fading

    ~~~~AchievableThroughput

    User 1User 1User 1User 1

    User 2User 2User 2User 2

    Intelligentschedulingwith feedback

    globalthroughput

    Multi-userdiversity gain

    bad

    good

    Time

    Fast fading

    ~~~~AchievableThroughput

    User 1User 1User 1User 1

    User 2User 2User 2User 2

    Intelligentschedulingwith feedback

    globalthroughput

    Multi-userdiversity gain

    bad

    good

    Packet oriented andcross layer design

    no intra cell interference but inter cell interference

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    no intra-cell interference, but inter-cell interference

    remains an issue

    no intra-cell

    50 Salah Eddine Elayoubi Mobile Network Engineering

    n er erence as

    chunks areorthogonal

    inter-cell interference

    is due to collisions

    between chunks

    used in different cells

    link budget for throughput calculations

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    link budget for throughput calculations

    link budget objective

    maximum distance between a user and its serving base station while guaranteeing

    a given quality of service

    equipment parameters propagation model throughputreceived signals SINR

    51 Salah Eddine EL AYOUBI June 2010

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    link level curves

    provide throughput vs SNR

    curves according to:

    multiple antenna use

    (SISO, MIMO) channel model (AWGN,

    Vehicular A, ..)

    52 Salah Eddine Elayoubi Mobile Network Engineering

    main output is the throughput versus distance

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    main output is the throughput versus distance

    stand-alone user throughput as a function of the distance to the base station

    DL Cell Throughput versus Distance

    18000

    Max throughput

    53 Salah Eddine Elayoubi Mobile Network Engineering

    0

    2000

    4000

    6000

    8000

    10000

    12000

    14000

    16000

    0,000 0,050 0,100 0,150 0,200 0,250

    Distance (Km)

    DL

    CellThroughput(Kb

    ps)

    Throughput @ cell edge

    interference calculations

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    interference calculations

    Exercise

    54 Salah Eddine Elayoubi Mobile Network Engineering

    outline: LTE

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    outline: LTE

    physical layer

    capacity calculations use case: mobile TV

    55 Salah Eddine Elayoubi Mobile Network Engineering

    how can link budget help capacity analysis?

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    how can link budget help capacity analysis?

    link budget gives the throughput vs distance:

    throughput depends on position

    cell can be decomposed into rings:

    To simplify analysis

    Homogeneous throughput in each ring

    56 Salah Eddine Elayoubi Mobile Network Engineering

    DL Cell Throughput versus Distance

    0

    2000

    4000

    6000

    8000

    10000

    12000

    14000

    16000

    18000

    0,000 0,050 0,100 0,150 0,200 0,250

    Distance (Km)

    DLCellThroughput(Kbps)

    voice traffic: multi-Erlang analysis

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    voice traffic: multi Erlang analysis

    Consider voice traffic

    Calls arrive with Poisson rate

    Stay in communication for an average time T=3min

    Require each 20 Kbps, or are blocked otherwise.

    Example: 2 rings

    57 Salah Eddine Elayoubi Mobile Network Engineering

    ,

    One cell center (edge) user occupies 2% (4%) of the resources Admission control constraint: 2*Kcenter+4*Kedge

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    g g p

    Consider best effort traffic

    Calls arrive with Poisson rate

    Stay connected until transmitting a file of average size 1 Mbits

    Example: 2 rings

    1 Mbps for cell center, 500 Kbps for cell edge

    58 Salah Eddine Elayoubi Mobile Network Engineering

    in the cell until transmitting its file

    the time necessary for the two users to transmit their files is 1+2=3

    seconds

    Within these three seconds, the volume of data transferred is equal

    to 2 files= 2 Mbit.

    The average throughput of the cell is then:

    T=2 Mbit/3 second=667 Kbps

    best effort traffic: Arithmetic versus harmonic mean

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    The arithmetic mean of the throughput is:

    Tarith=(1 Mbps+0.5 Mbps)/2=750 Kbps

    This is different from the average throughput calculated

    previously.

    However, this corresponds to the harmonic mean:

    59 Salah Eddine Elayoubi Mobile Network Engineering

    harm= ps- + . ps - - = ps

    This harmonic mean gives larger weights for cell edge users asthey stay longer in the cell

    The harmonic mean is convenient to measure the cell

    throughput

    best effort traffic: Harmonic mean calculations

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    DL Cell Throughput versus Distance

    2000

    4000

    6000

    8000

    10000

    12000

    14000

    16000

    18000

    DLCellThroughput(Kbps)

    60 Salah Eddine Elayoubi Mobile Network Engineering

    Represents the maximal traffic that can be carried by the cell.

    Used since the paper of Bonald el al., 2003.

    0

    0,000 0,050 0,100 0,150 0,200 0,250

    Distance (Km)

    best effort traffic: Processor sharing

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    Objective:

    Estimate QoS for a given traffic

    Data users share the remaing resources

    not used by streaming and voice ones (priority to

    streaming/voice)

    Fair in time but not fair in throu h ut

    61 Salah Eddine Elayoubi Mobile Network Engineering

    Processor sharing analysis can be used to assess capacity: Several classes corresponding to the number of rings

    Gives average individual throughput at each position of the cell.

    general model with a service mix

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    predict the QoS based on marketing traffic forecasts.

    determine the number of resources needed to ensure a target

    QoS.

    streaming traffic

    multi-Erlanstreaming QoS

    62 Salah Eddine Elayoubi Mobile Network Engineering

    PS

    data traffic

    data QoS

    categorydistribution

    throughput pdf(link budget)

    outline: LTE

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    physical layer

    capacity calculations use case: mobile TV

    63 Salah Eddine Elayoubi Mobile Network Engineering

    Use case: TV traffic

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    mobile TV traffic expected to explode

    TV traffic evolution

    5

    6

    7

    8

    unicast too greedy in resources:

    spectrum resources

    4

    5

    6

    MHz

    64 Salah Eddine Elayoubi Mobile Network Engineering

    0

    1

    2

    3

    4

    2009 2010 2011 2012 2013

    E

    rlang

    0

    1

    2

    3

    2009 2010 2011 2012 2013

    carriersof5

    15

    broadcast solution

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    Point to Multipoint is the solution adapt to radio conditions

    QPSK 1/2

    16QAM 1/216QAM 3/4

    64QAM 3/4

    65 Salah Eddine Elayoubi Mobile Network Engineering

    transmit with QPSK

    advantage: simple

    drawback: suboptimal

    transmit with 16QAM

    advantage: optimal

    drawback: needs

    feedback

    total broadcast: Single Frequency Network

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    if every body is watching TV

    why not cooperating all base stations?

    66 Salah Eddine Elayoubi Mobile Network Engineering

    Interference is seen as a multipath propagation

    drawback: tight synchronization between cells is needed

    Delay and multipath impact

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    Weight function for the constructive portion of a received SFN signal:

    ( ) 1 0

    ( )

    ( ) 0

    CP

    CP uCP CP u

    u

    CP u

    w delay if delay T

    T T delayw delay if T delay T T

    T

    w delay if T T delay

    =

    + = < < +

    = +