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    Chapter Three

    The Cellular Concept:

    System DesignFundamentals

    BY : Adisu W.

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    Objectives of the Chapter

    In cellular system, the available radio spectrum is limited

    E.g., because of regulatory issues

    Hence, the number of simultaneous calls supported is limited

    How to achieve high capacity (or support simultaneous calls at

    the same time ) covering very large areas?

    Frequency reuse by using cells

    Overview of system design fundamentals on cellular

    communication

    Cell formation and associated frequency reuse, handoff,

    interference, and power control

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    Lecture Outline

    Introduction

    Cellular Concept and Frequency Reuse

    ChannelAssignment Strategies

    Handoff Strategies

    Interference and System Capacity

    Trunking and Grade of Services

    Summary

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    Used Acronyms• BS: Base station• MS: Mobile station• MSC: Mobile switching center • GOS: Grade of services• CCI : Co-channel interference•

    ACI: Adjacent channel interference

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    Introduction

    Conventional Mobile Radio System and its Limitations

    Single high power transmitter and large antenna towers Large size radios with large batteries

    Provide limited number of channels

    Poor quality of service

    Still in use for some public/private organizations

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    The coverage area called tower footprint of these towers was

    theoretically circular in shape with radius around 50 km.

    As long as cities being covered were far away from each other, no

    interference occurred between the transmissions in different

    cities.6

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    The assigned spectrum (40 MHz) was used in every city being covered.

    • But, full duplex transmission would require a total of 60 kHz per user

    • Thus total number of users who can call or receive calls at the same

    time in any city was around 660 users only.

    • For a large city(for example with 10Million residents ) this is

    extremely low and the system would get congested so easily.

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    Due to the large distance between the MS and the BS (up to 50 km or

    more), mobile phones had to transmit high powers.

    This results in the need of large batteries and therefore phones were

    large in size and inconvenient.

    So what ?

    • Cellular system with frequency reuse is the solution to avoid the

    problem of spectral congestion , capacity and power budget.

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    The Cellular System

    High capacity is achieved by dividing the coverage area of each

    BS to a small geographic region called a cell

    Single, high power transmitter (large cell) are replaced with

    many low power transmitters (small cells)

    A portion of the total number of channels is allocated to each cell

    Available group of channels are assigned to a small number of

    neighbouring BS called cluster

    Near by BS are assigned d/t groups of channels to minimize

    interference

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    Cellular System Architecture10

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    The same channels ( frequencies/timeslots/codes ) are reused by

    spatially separated base stations

    Reuse distance and frequency reuse planning.

    A switching technique called handoff enables a call to proceed

    from one cell to another

    As demand (# of users ) increases, the number of BS may be

    increased to provide additional capacity:

    Use smaller cells: e.g., Microcells, Picocell, Femtocell

    Also cell sites in trucks to replace downed cell towers after

    natural disasters, or to create additional capacity for large

    gatherings(football games, rock concerts)

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    The Cellular ConceptThe Cellular Idea

    Divide the service area into several smaller cells

    Put at least as many towers as the # of cells and reduce the transmitter

    power of each BS

    Reuse the allocated frequency spectrum (channels) as many times as

    possible by controlling interference

    Gains but with Pains

    Greater system capacity with the cost of large infrastructure

    Optimal frequency spectrum utilization attained by making system

    more complicated

    User equipment design made smarter at the cost of circuit complexity

    and processing power 13

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    Frequency Reuse Example14

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    The Cell Shape

    Actual radio coverage area of cell is amorphous(irregular shaped)

    Obtained by field measurements or by using prediction modelsthrough computer simulation

    This is known as footprints

    (a) is theoretical coverage area and (b) measured coverage areawhere red, blue, green, and yellow indicate signal strength in

    decreasing order

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    All cells should have same shape and equal area

    Circular (theoretical): If path loss was a decreasing function

    of distance(say 1/d n) where d is the distance b/n BS & MS

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    When using hexagon to model coverage areas, we may use:

    Center excited cell: BS depicted as being in the center of the cell

    • Omni-directional antenna is used

    Edge excited cell: Placed on three of the six cell vertices

    • Sectored directional antenna is used

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    Geometry of Hexagons

    Axes U and V intersect at 60 0

    Assume unit distance is the distance between cell centers

    If cell radius to point of hexagon is R, then

    2Rcos 30 o = 1 or R = 1/3 (Normalized radius of a cell) To find the distance of a point P(U,V) from the origin, use XY to

    UV coordinate transformation as

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    Using this equation, to locate the co-channel cells, start from a

    reference cell and move:

    i-hexagons along the U-axis and

    j- hexagons along the V-axis

    The distance, D, between co-channel cells in adjacent cluster is

    given by

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    The number of cells in a cluster is given by

    where i and j are non-negative integers

    In real system , there are only certain cluster sizes and layouts

    possible.

    Typical values of N are 1, 3, 7, 12, …

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    Locating Co-channel Cells

    Observation: In the geometry of the hexagon, the number of

    cells per cluster can only have values such that

    Hence to find out the nearest co-channel neighbours of a

    particular cell, do the following

    Move i cells in the U direction

    Then turn 60 0 CCW and move j cells in the V direction

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    Example 1 : N=7, i=2,j=1

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    Example 2 : N=28, i=4, j=2

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    Frequency Reuse Principles

    Let us assume a city of 10 Million mobile users

    Let every user is allocated a radio spectrum for analog

    speech of 4kHz bandwidth

    Thus the required bandwidth is 4 kHz * 10 Million users =40 GHz!

    This is clearly impractical!

    No other services possible using a radio transmission

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    Cellular radio systems rely on intelligent allocation and reuse of

    channels through out the coverage area

    Available group of channels are assigned to a cluster

    Same group of frequencies are reused to cover another cell

    separated by a large enough distance

    • Hence a trade-off in the design is required

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    To understand the frequency reuse concept, consider a cellular

    system which has a total of S duplex channels available for use

    If each cell is allocated a group of k channels (k

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    If a cluster is repeated M times within the system, the total number

    of duplex channels can be used as a measure of capacity and is

    given by

    C =MS= MkN

    The factor N is called the cluster size and is typically values are1,3 , 7, 12,...

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    The value N is a function of how much interference a mobile or

    BS can tolerate while maintaining a sufficient quality of

    communication.

    Smallest possible value of N is desirable in order to maximize

    capacity over a given coverage area

    The frequency reuse factor of a cellular system is given by1/N

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    Effect of Cell Size Trade-off

    Advantages of smaller cell size:

    Higher M (more replication of the cluster)

    Higher system capacity

    Lower power requirements for mobiles

    Disadvantage of smaller cell size:

    Additional base stations required

    More frequent handoffs(Burden of MSC)

    Extra possibilities for interference

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    Effect of Cluster Size Trade offs

    Each clusters have unique group of channels which are repeated

    over clusters

    Keeping cell size the same:

    Large N: weak interference but lower capacity

    Small N: higher capacity, more interference, need to maintain

    certain S/I threshold level

    • More clusters are required to cover area of interest,

    • So capacity is directly prop. to replication factor for fixed area

    • Results in larger co-channel interference

    • May result in lower Quality of Service (QoS)31

    S D i E l

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    System Design ExamplesA total of 33 MHZ bandwidth is allocated to a particular FDD cellular phone system. If the simplex

    voice/control channel bandwidth is 25 Khz, find the total # of channels available per cell if the

    system uses (a) 4-cell frequency reuse (b) 7-cell frequency-reuse plan. If 1 MHZ out of the total

    allocated bandwidth is used for control channels, determine an equitable distribution of the control

    and voice channels in each cell in case of each frequency-reuse plan.

    Solution:Total allocated bandwidth = 33 MHz, Duplex channel bandwidth = 25x2=50 K

    Total # of Available(Voice/Control) Channels = 33,000/50 = 660 Channels.(a) N= 4, so total # of Channels/Cell = 660/4 = 165 Channels(b) N=7, so total # of Channels/Cell = 660/7 = 95 Channels

    In case of 1 MHz bandwidth allocated for control channels, total # of control channels =1000/50=20 channels per systems. Out of 660 channels, 20 are used as control and remaining

    640 as voice channels.(A)n=4, each cell can have 20/4=5 control channels and 640/4=160 voice channels. But, each cell

    needs only one control channel, so, each cell will be assigned one control channel and 160 voicechannel.

    (B)n = 7, each cell can have 20/7 = 3 control channels and 640/7=91 voice channels[plus 3 extra], but it needs only 1 control channel, so, we can assign 4 cells with 91 voice channels and one

    control channels, and 3 cells with 92 voice channels and one control channels.

    Hz

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    The Channel Assignment Strategies Objective: maximize the system capacity while minimizing theinterference

    A constrained optimization problem Classification:Fixed ChannelAllocationDynamic ChannelAllocation

    Hybrid ChannelAllocationBorrowed ChannelAllocation Choice has impact on system

    performance Handoff

    Call InitiationMSC Processing Load

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    Fixed Channel Assignment (FCA)

    Each cell is allocated a predetermined set of voice channels.

    Any call attempt within the cell can only be served by the unused

    channels in that particular cell.

    Any request for handoff , if all channels of this candidate cell are

    in use, will not be treated.

    MS may have to wait, call can drop even

    Probability of blocking is high .

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    Simple, but a busy cell will run out of channels before a neighbouring

    cell

    Service variations of fixed assignment strategy exit

    System performance will be limited by the most crowded cell

    Several solution to solve the problem:

    Borrowing strategy Reserve some channels for handoff

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    Borrowing channel assignment strategies

    Modified from fixed channel assignment strategies.

    A cell is allowed to borrow channels from a neighbouring cell if

    all of its own channels are already occupied.

    MSC supervises such borrowing procedures and ensures that

    the borrowing of a channel does not disturb or interfere with

    any of the calls in progress in the donor cell.

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    The MSC allocates a channel to the requested cell following an

    algorithm that takes into account :

    The likelihood of future blocking within the cell

    The frequency use of the candidate channel

    The reuse distance of the channel, and Other cost functions.

    DCA requires the MSC to collect real-time data on channel

    occupancy, traffic distribution, and radio signal strength

    indications (RSSI) of all channels on a continuous basis.

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    Hence DCA

    Reduces the call blocking probability and call drop

    probability during hand off

    Improves system Trunking capacity (traffic intensity/channel):

    all channels are accessible by all cells

    But adds the costs of storage and computational load on

    MSC because

    MSC must collect real-time channel occupancy data• Traffic distribution information

    • Radio signal strength indications (RSSI) of all the channels

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    The Handoff Strategies

    In cellular network, the process to transfer the ownership of MS

    from BS to another BS is termed as Handoff or Handover . MSC facilitates the transfer

    In general, handoff involves

    Identifying the new BS

    Allocation of voice and control signals to channels on new BS

    Usually, priority of handoff requests is higher than call

    initiation requests when allocating unused channels.

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    Handoffs must be performed

    Successfully

    As infrequently as possible, and

    Must be imperceptible to the user

    To meet these requirements, we must specify a minimum usable

    signal level for acceptable voice quality at the base station

    If the received power drops too low prior to handoff, the call

    will be dropped.

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    Handover Indicator : The parameters to determine HO occasion

    RSSI: in ensemble average sense.

    Bit Error Rate (BER)/Packet Error Rate (PER), more accurate.

    By looking at the variation of signal strength from either base

    station, it is possible to decide on the optimum area where handoff

    can take place.

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    Once a particular signal level is specified as the minimum usable

    signal for acceptable voice quality at BS receiver (normally b/n

    - 90 dBm and -100 dBm), a slightly stronger signal level is used asthreshold at which a handoff is made.

    If Δ is too large: unnecessary handoffs may occur, burden on MSC

    If Δ is too small: there may be insufficient time to complete a handoff,

    calls may be loss or dropped.

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    Example 1: Improper Handoff Situation

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    Example 2: Proper Handoff Situation

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    How to Prioritize Handoff

    Guard Channel Method

    A fraction of the total available channels is reserved for handoff

    In case of fixed channel assignment, it affects system capacity.

    But good in case of dynamic channel assignment

    Queuing Handoff Request Method

    Any handoff request, if can not be tackled immediately, it will be

    placed in queue for sometime and answered before the signallevel goes below the minimum acceptable level.

    Does not guarantee 100% success for all handoff requests46

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    Handoff Styles

    1. Network Controlled Handoff (NCHO)

    Used in the 1G mobile cellular systemsHere each BS constantly monitors signal strength from MS in its

    cell.

    Based on the measurements, MSC decides if handoff is necessary

    or not.

    MS plays passive role in the process

    Creates heavy burden on MSC

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    2. Mobile Assisted Handoff (MAHO)

    Used in 2 nd and above generation systems

    MS measures received power from surrounding BS and report to

    serving BS

    Handoff is initiated when power received from neighboring cell

    exceeds current value by a certain level or for a certain period of

    time

    Faster since measurements made by MS

    MSC doesn ’t need to monitor the signal strength

    • Simple burden on MSC

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    3. Hard Handoff: Break before make

    FDMA, TDMA (1G and 2G Systems)

    The mobile has a radio link with only one BS at anytime.

    Old BS connection is terminated before new BS connection is

    made

    4. Soft Handoff: Make before break

    The mobile has simultaneous radio link with more than one BS at

    any time (example CDMA systems ).

    New BS connection is made before old BS connection is broken.

    Mobile unit remains in this state until one BS clearly

    predominates.

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    5. Intersystem Handoff:

    Used for MS found the border of the system(home service

    provider ’s service area)MSC of the serving cell talks to the MSC of the neighboring

    system or vice versa to transfer the call.

    Several issues should be resolved before handoff can take place• Call type• Roaming is allowed or not•

    Compatibility issues or standards• User authenticity and call charges issues

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    Practical Handoff Problems

    Problem 1: Simultaneous traffic of high speed and low speedmobiles.Small cell → high speed mobile → frequent handoff large cell → Reduce capacity

    Solution: Umbrella Cell - cell split or hierarchical cell structure

    By using different antenna heights and different power levels ,

    it is possible to provide large and small cells which are co-

    located at single location.

    Small cell for low speed mobileLarge cell for high speed mobile

    Need strong detection and handoff control.

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    This concept minimizes the number of handoffs for high speed

    users and provides additional micro cell channels for pedestrian

    users.

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    P bl 2 C ll D i

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    Problem 2: Cell Dragging

    Caused by pedestrian users that provide very strong signal to the

    BS.

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    Often occurs in an urban environment when there is line-of-sight

    (LOS) radio path between the subscriber and the base station.

    As the user travels away from the BS at very low speed, theaverage signal strength does not decay rapidly and the received

    signal at the BS may be above the handoff threshold, thus handoff

    may not be made.

    Creates potential interference and traffic management problem .

    Solution: Careful arrangement of handoff threshold and radio coverage

    parameters.

    Interference and System Capacity

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    Interference and System Capacity

    What is Interference : unwanted signal which affects the speech

    quality and system capacity

    Sources of interference includes:

    Another mobile in the same cell

    A call in progress in the neighboring cellOther BS operating in vicinity using the same frequency band

    Some non cellular device/system leaking energy in the cellular

    frequency band.

    Two major types of interferences are:

    Co-Channel Interference ( CCI )

    Adjacent-Channel Interference( ACI )54

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    It is a major Bottle Neck in system capacity : a trade off has to be

    made between system capacity and information quality.

    Interference in the voice channels causes crosstalk

    A subscriber hears interference in the background due to an

    undesired transmission

    Interference in the control channels causes error in digital

    signalling which causes

    Missed calls

    Blocked calls

    Dropped calls

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    To reduce co-channel interference , co-channel cells must be

    physically separated by minimum distance to provide sufficient

    isolation due to propagation .

    So, when the size of each cell is approximately the same , and the

    BS transmit the same power , the co-channel interference ratio is

    independent of the transmitted power and becomes a function of

    the radius of the cell (R) and the distance between centres of the

    nearest co-channel cells (D)

    By increasing the ratio of D/R , the spatial separation between co-

    channel cells relative to the coverage distance of the cell is

    increased.

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    Thus interference is reduced from improved isolation of RF

    energy from the co-channel cell

    Co-channel Reuse Ratio (Q) : The spatial separation between co-

    channel cells relative to the coverage distance of a cell .

    For hexagonal geometry, it is related to the cluster size N

    Small value of Q provides larger capacity since the cluster size is

    small, whereas large value of Q improves the transmission

    quality , due to smaller level of co-channel interference

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    h l f l f

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    Co-channel reuse ratio for some values of N

    Hence there is capacity versus interference trade off

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    h l l f

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    Co-Channel Signal to Interference Ratio

    Let i 0 be the number of co-channel interfering cells , then the

    signal-to- interference ratio (SIR) for a mobile receiver whichmonitors a forward channel can be expressed as

    Where S is the desired signal power from the desired BS

    I i is the interference power caused by the i th interfering

    co-channel cell BS

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    Propagation measurements in mobile radio channel show that the

    average received signal strength at any point decays as a power

    law of the distance between transmitter and receiver

    The average received power P r at a distance d from the

    transmitting antenna is then

    Where P o is the received power at close reference distance in thefar-field and n is the path-loss exponent (mostly between 2 to 6)

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    Now consider the forward link where the desired signal is the

    serving BS and the interference is due to co-channel BS.

    If D i is the distance of the i th interferer from the mobile, the

    received power at given mobile due to the i th interfering cell will be

    proportional to (D i)-n.

    When the transmit power of each BS is equal and n is the same

    throughout the coverage area, S/I for a mobile can be approximated

    as

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    For hexagonal cluster of cells with the MS situated at the edge of

    the cell

    Hence, as long as all cells are of the same size, S/I is

    independent of the cell radius, R

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    E l

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    Example

    If a signal to interference ratio of 15dB is required for satisfactory

    forward channel performance of a cellular system, what is thefrequency reuse factor and the appropriate cluster size that

    should be used for maximum capacity if the path loss exponent is

    (a) n = 4 , (b) n = 3? Assume that there are 6 co-channels cells inthe first tier, and all of them are at the same distance from the

    mobile. ( Hint: First consider 7 cell reuse pattern and decide the

    practical cluster size.

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    This is referred to as the near-far effect , where nearby

    transmitter (which may or may not be of the same type as that

    used by the cellular system) captures the receiver of the

    subscriber.

    Alternatively, the near-far effect occurs when mobile close to BS

    transmits on channel close to one being used by weak mobile.

    The BS may have difficulty in discriminating the desired

    mobile user from close adjacent channel mobile.

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    Near-far effect: This occurs when an interferer close to the BS

    radiates in adjacent channel, while the subscriber is far away from

    the BS

    The BS may not discriminate the desired mobile user from the

    “bleed ove r” caused by the close adjacent channel mobile

    Or, an interferer which is in close range to the subscriber ’s

    receiver is transmitting while the receiver receives from the

    BS.

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    In practice, power levels transmitted by every subscriber are under

    constant control by the serving BS

    Each MS transmits with the smallest power necessary

    In power control

    Reduces the transmit power level of MS close to the BS since

    high T X power is not necessary in this case.

    MS located far away must transmit with larger power than

    those nearby

    Power control reduces o ut-of-band interference , prolongs

    battery life , and generally reduces even co-channel interference

    on the reverse channel

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    ACI can be minimized through careful filtering and channel

    assignments .

    By keeping the frequency separation between each channel in

    given cell as large as possible , the adjacent channel interference

    may be reduced considerably

    Channels are allocated such that the frequency separation between

    channels in a given cell is maximized.

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    If a subscriber is at distance d 1 and the interferer is d 2 from the

    base station, then SIR (prior to filtering) is

    Example:

    Suppose a subscriber is at d 1 = 1000m from the BS and an

    adjacent channel interferer is at d 2 = 100m from the BS

    Assume: Path loss exponent is n = 3

    The signal-to-interference ratio prior to filtering is then

    Hence we should use careful filtering to avoid this .

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    Trunking and Grade of Services

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    Trunking and Grade of Services

    Trunking System : A mechanism to allow many users to share

    fewer number of channels. Not every user calls at the same time.

    Penalty: Blocking Effect.

    If traffic is too heavy, call is blocked!!

    Small blocking probability is desired.

    There is trade-off between the number of available circuits and

    blocking probability.

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    T U d i T ki g Th

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    Terms Used in Trunking Theory

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    Setup time: The time required to allocate a radio channel to a requesting

    user. Users request may be blocked or have to wait

    Blocked Call: A call that cannot be completed at the time of request due

    to congestion

    Also called lost call => lost revenue( e.g., pick hours, holidays)

    Holding Time(H): Average call duration in seconds

    Depends on users and operator's tariff

    Request (or call) Rate ( λ ): Average number of calls per unit time

    Typically taken to be at the busiest time of day

    Depends on type of users community: Office, residential, call center

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    Erlang : The amount of traffic intensity carried by a channel that

    is completely occupied.

    For example, a radio channel that is occupied for 30 minutes

    during an hour carries 0.5 Erlangs of traffic.

    Grade of Service (GOS): is a measure of the ability of a user to

    access a trunked system during the busiest hour.

    GOS is typically given as the likelihood that a call is blocked ,

    or the likelihood of a call experiencing a delay greater than acertain queuing time.

    T ffi I i (A) M f h l i ili i hi h

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    Traffic Intensity(A) : Measure of channel time utilization, which

    is the average channel occupancy measured in Erlangs. This is a

    dimensionless quantity and may be used to measure the time

    utilization of single or multiple channels.

    Load: Traffic intensity across the entire trunked radio system,

    measured in Erlangs.

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

    specified as the probability of a call being blocked (Erlang B),

    or the probability of a call being delayed beyond a certain

    amount of time (Erlang C).

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    Trunking Efficiency: is a measure of the number of users which

    can be offered a particular GOS with a particular configuration of

    fixed channels.

    The way in which channels are grouped can substantially alter the

    number of users handled by a trunked system.

    From Table 3.4, for GOS=0.01

    10 trunked channels can support 4.46 Erlangs.

    Two 5 trunked channels can support 2x1.36=2.72 Erlang.

    10 trunked channels support 64% more traffic than two 5

    channel trunks do.

    Computation of GOS

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    Computation of GOS

    Analysis

    Average arrival rate( λ ): Average number of MSs requesting

    service (call request/time)

    82

    h ld i ( ) A d i f ll ( i f

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    Average hold time(H): Average duration of a call (or time for

    which MS requires service)

    An average traffic intensity offered (generated) by each user

    Example 1: If a user makes on average two calls per hour, and

    that a call lasts an average of 3 minutes

    83

    Then the total offered traffic intensity for U users are

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    Then the total offered traffic intensity for U users are

    In a C channel trunked system, if traffic is distributed equally among

    channels, then traffic intensity per channel

    In Example 1 , assume that there are 100 users and 20 channels

    Then A = 100(0.1)= 10 andA c = 10/20 = 0.5

    Note: Ac is a measure of the efficiency of channels utilization

    Offered traffic is not necessarily the traffic carried by the trunked

    system, only that is offered to the system

    The maximum possible carried traffic is the total number of channels, C, in Erlangs

    Example AMPS system is designed for a GOS of 2% blocking

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    Example, AMPS system is designed for a GOS of 2% blocking

    Channel allocations for cells are designed so that 2 out of 100 calls

    will be blocked due to channel occupancy during the busiest hour

    What do we do when a call is offered (requested) but all

    channels are full?

    Blocked calls cleared; Offers no queuing for call requests, ErlangB

    Blocked calls delayed; Erlang C

    85

    Types of trunked systems:

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    yp y

    1. Blocked Calls Cleared

    No queuing for call requests: For every user who requests service, it is assumed there is no

    setup time and the user is given immediate access to a channel if

    channel is available.

    If no channels are available, the requesting user is blocked

    without access and is free to try again later.

    GOS: Erlang B formula determines the probability that a call is

    blocked.

    86

    Erlang B is a measure of the GOS for a trunked system which

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    Erlang B is a measure of the GOS for a trunked system which

    provides no queuing for blocked calls

    Setting the desired GOS, one can derive

    Number of channels needed

    The maximum number of users we can support as A = UAU

    or

    The maximum A U we can support (and set the number of

    minutes on our calling plans accordingly)

    Since C is very high, it is easier to use table or graph form

    Blocking Probability: Erlang B Formula :

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    Where C number of trunked channels andA total offered traffic

    Assumption to the model

    There are infinite number of users.

    Call requests are memory less; both new and blocked users may request a

    channel at any time.

    Service time of a user is exponentially distributed

    Traffic requests are described by Poisson model.

    Inter-arrival times of call requests are independent and exponentially

    distributed.88

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    2. Blocked Calls Delayed

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    A queue is provided to hold calls which are blocked.

    Instead of clearing a call, put it in a queue and have it wait until achannel is available

    First-in, first-out line; Calls will be processed in the order

    received

    If a channel is not available immediately, the call request may be

    delayed until a channel becomes available.

    GOS: Erlang C formula gives the likelihood that a call is

    initially denied access to the system

    There are two things to determine here

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    g

    The probability a call will be delayed (enter the queue), and

    The probability that the delay will be longer than t seconds

    The first time is no longer the same as Erlang B

    It goes up, because blocked calls aren ’t cleared, they “stick

    around” and wait for the first open channel

    Meaning of GOS

    The probability that a call will be forced into the queueAND it

    will wait longer than t seconds before being served (for some

    given t)

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    Once it enters the queue, the probability that the delay is greater

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    q , p y y g

    than t (for t > 0) is given as

    The marginal (overall) probability that a call will be delayedAND

    experience a delay greater than t is then

    The average delay for all calls in a queued system

    94

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    The Erlang C chart showing the probability of a call being delayed as a

    function of the number of channels and traffic intensities in Erlangs

    95

    Examples

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    Consider a system with

    • 100 cells• Each cell has C = 20 channels• Each user generates on average = 2 calls/hour • The average duration of each call (H) = 3 Minutes

    How many number of users can be supported if the allowed

    probability of blocking is

    a . 2% b. 0.2%

    Solution:

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    a. From Erlang B Chart, total carried traffic = 13 Erlangs Traffic intensity per userA U = Hλ = 0.1 Erlangs The total number of users that can be supported by a cell = 13/0.1 =130 Users/cell

    Therefore, the total number of users in the system is 13,000

    b. Again from Erlang B Chart, total carried traffic = 10 Erlangs Traffic intensity per user A U = Hλ = 0.1 Erlangs The total number of users that can be supported by a cell = 10/0.1 =

    100 Users/cell Therefore, the total number of users in the system is 10,000

    We support less number of users here

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    More Examples…

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    1. How many users can be supported for 0.5% blockingprobability for the following number of trunked channelsin a blocked calls cleared system? Assume Au=0.1E

    a) 1, b) 5, c) 10,d) 20, e) 1002. An urban area has a population of 2 million residents.three competing trunked mobile networks (system A, B

    and C) provide cellular crevice in this area. System A has394 cells with 19 channels each, system B has 98 cellswith 57 channels each, and system C has 49 cells eachwith 100 channels.

    Find the number of users that can be supported at 2%

    Summary

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    Concepts such as handoff, frequency reuse, Trunking

    efficiency, and frequency planning are covered

    Capacity of cellular system is a function of many things,

    E.g: S/I that limits frequency reuse , which intern limits the

    number of channels within the coverage area

    Trunking efficiency limits the number of users that can access a

    trunked radio system.

    We may have a block call cleared or block call delayed

    trunked system