The Cellular Concept System D Fd l Design Fundamentals

Wireless Information Transmission System Lab.

The Cellular Concept D F d lSystem Design Fundamentals

National Sun Yat-sen UniversityInstitute of Communications Engineering

Table of ContentsTable of Contents

Frequency Reuseq yChannel Assignment StrategiesHandoff StrategiesHandoff Strategies

Prioritizing HandoffsP ti l H d ff C id tiPractical Handoff Considerations

Interference and System CapacityPower ControlTrunking and Grade of ServicegImproving Coverage and Capacity in Cellular SystemsTrunking Theory

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Trunking Theory


Frequency Reuse


Cellular System Design ConsiderationsCellular System Design Considerations

To solve problems of spectral congestion and user p p gcapacity.Replacing a single, high power transmitter with many p g g g p ylow power transmitters.Neighboring base stations are assigned different groups g g g g pof channels so that the interference between base stations is minimized.Available Channels are distributed throughput the geographic region and may be reused as many times as necessary.With fixed number of channels to support an arbitrarily l b f b ib

4

large number of subscribers.

Concepts of Frequency ReuseConcepts of Frequency Reuse

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Cellular Networks and Frequency ReuseCellular Networks and Frequency Reuse

One important characteristic of cellular networks is pthe reuse of frequencies in different cells.By reuse frequencies, a high capacity can be achieved.By reuse frequencies, a high capacity can be achieved.However, the reuse distance has to be high enough, so that the interference caused by subscribers usingso that the interference caused by subscribers using the same frequency (or an adjacent frequency) in another cells is sufficiently lowanother cells is sufficiently low.To guarantee an appropriate speech quality, the

i t i t f ti (CIR) h tcarrier-to-interference-power-ratio (CIR) has to exceed a certain threshold CIRmin which is 9 dB for th GSM t

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the GSM system.

HexagonsHexagons

Hexagonal cell shape has been universally adopted.g p y pThe actual radio coverage of a cell is known as the footprint and is determined from field measurements orfootprint and is determined from field measurements or propagation prediction models.Base stations can be placed at:Base stations can be placed at:

The cell center – center-excited cells – omni-directional antennasantennas.The cell vertices – edge-excited cells – sectored directional antennas.antennas.

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Reuse FactorReuse FactorDue to the fact that the hexagonal geometry has exactly six equidistant neighbors

d th t th li j i i th t f ll d h f it i hband that the lines joining the centers of any cell and each of its neighbors are separated by multiples of 60 degrees, there are only certain cluster sizes and cell layouts which are possible.

R F i2+ij+j2 i j ti i t

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Reuse Factor = i2+ij+j2; i,j are non-negative integers.

Co-channel Neighbor CellsCo channel Neighbor Cells

M i ll lMove i cells along any chain of hexagons.Turn 60o counter-clockwise and move j cells.For example:

N=19: i =3, j =2;, j ;N=12: i =2, j =2;N=7; i =2, j =1;; , j ;

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Channel Assignment Strategies


Channel Assignment StrategiesChannel Assignment Strategies

Fixed Channel Allocation

Dynamic Channel AllocationDynamic Channel Allocation

Hybrid Channel Allocation

Borrowed Channel Allocation

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Fixed Channel AssignmentFixed Channel Assignment

Each cell is allocated a predetermined set of voice pchannels.Any call attempt within the cell can only be served byAny call attempt within the cell can only be served by the unused channels in that particular cell.Probability of blocking is highProbability of blocking is high.

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Dynamic Channel Assignment StrategyDynamic Channel Assignment Strategy

Channels are not allocated to different cells permanentlyChannels are not allocated to different cells permanently.Each time a call request is made, the serving base station requests a channel from the MSC.q SCThe MSC allocates a channel to the requested cell following an algorithm that takes into account the likelihood of future gblocking within the cell, the frequency of use of the candidate channel, the reuse distance of the channel, and other cost f ifunctions.MSC only allocates a given frequency if that frequency is not presently in use in the cell or any other cell which falls withinpresently in use in the cell or any other cell which falls within the minimum restricted distance of frequency reuse to avoid co-channel interference.

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co channel interference.

Dynamic Channel Assignment StrategyDynamic Channel Assignment Strategy

MSC has to collect real-time data on channel occupancy, traffic distribution, and radio signal strength indications (RSSI) of all channels on a continuous basis.Reduce the likelihood of blocking at the expense of increasing the storage and computational load.g g p

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Borrowing StrategyBorrowing Strategy

M difi d f fi d h l i iModified from fixed channel assignment strategies.

A cell is allowed to borrow channels from a neighboring cell if all of its own channels are already

i doccupied.

The MSC supervises such borrowing procedures and ensures that the borrowing of a channel does not di i f i h f h ll i idisrupt or interfere with any of the calls in progress in the donor cell.

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Handoff Strategies


Handoff / HandoverHandoff / Handover

In a cellular network, the process to transfer the ownership of , p pa MS from a BS to another BS.Handoff not only involves identifying a new BS, but also requires that the notice and control signals be allocated to channels associated with the new base station.Usually, priority of handoff requests is higher than call initiation requests when allocating unused channels.H d ff b f d f ll d i f lHandoffs must be performed successfully and as infrequently as possible and be imperceptible to the uses.

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Handoff / HandoverHandoff / HandoverHandover Occasions

Bad signal quality on current channelnoise or interferenceffi l d i llTraffic overload in current cellload balancing

Handover Indicator: The parameters to monitor to determine HO occasiondetermine HO occasion

RSSI, in ensemble average sense.Bit Error Rate (BER)/Packet Error Rate (PER), more accurate.( ) ( ),

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Handoff / HandoverHandoff / Handover

Need to specif an optim m signal le el to initiateNeed to specify an optimum signal level to initiate a handoff.

i i bl i l f bl iMinimum useable signal for acceptable voice quality at the base station receiver is normally

k b 90 d 100 dtaken as between -90 dBm to -100 dBm.useableminimumhandoff PrPr −−=Δ

If Δis too large, unnecessary handoffs may occur.If Δis too small there may be insufficient time toIf Δis too small, there may be insufficient time to complete a handoff.

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Illustration of a handoff scenario at cell boundaryboundary

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Illustration of a Handoff Scenario at Cell BoundaryBoundary

Figure (a) demonstrates the case where a handoff is not g ( )made and the signal drops below the minimum acceptable level to keep the channel active.p pThe dropped call event in figure (a) can happen when there is an excessive delay by the MSC in assigning athere is an excessive delay by the MSC in assigning a handoff or when the threshold Δ is set too small for the handoff time the system.handoff time the system.Excessive delays may occur during high traffic conditions due to computational loading at the MSC orconditions due to computational loading at the MSC or due to the fact that no channels are available on any of the nearby base stations

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the nearby base stations.

Handoff / HandoverHandoff / HandoverDuring handoff, it is important to ensure that the drop in the measured signal level is not due to momentary fading and that the mobile is actually moving away from th i b t tithe serving base station.The base station monitors the signal level for a certain

i d f ti b f h d ff i i iti t dperiod of time before a hand-off is initiated.The time over which a call may be maintained within a

ll ith t h d ff i ll d th d ll icell, without hand-off, is called the dwell time.

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Handoff in 1st Generation Cellular Systemsff y

Signal strength measurements are made by the base g g ystations and supervised by the MSC.Base station monitor the relative location of each userBase station monitor the relative location of each user.Locator receiver is used to determine signal strengths of users in neighboring cells and is controlled by the MSCusers in neighboring cells and is controlled by the MSC.Based on the information from locator receiver, MSC d id if h d ff i tdecides if a handoff is necessary or not.

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Handoff in 2nd Generation TDMA Systems

Handoff decisions are mobile assisted.In mobile assisted handoff (MAHO), every mobile measures the received power from surrounding basemeasures the received power from surrounding base stations and reports the results to the serving base station.MAHO enables the call to be handed over at a muchMAHO enables the call to be handed over at a much faster rate.

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Handoff or HandoverHandoff or Handover

Mobile Assistant Handover – more efficient.GSM:

MS monitors all BSsMS reports the measurements to the BSMSC makes decision

USDC (IS-54/136): BSs monitor all MSs. When a MS is lea ing the cell the BS sends it a meas rement orderWhen a MS is leaving the cell, the BS sends it a measurement orderThe MS begins its measurement and reportsMSC makes the Handover decision.

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Handover Algorithms (IS-95 vs WCDMA)Handover Algorithms (IS-95 vs. WCDMA)

Basic IS-95 handover algorithm uses absolute threshold algorithm.

WCDMA handover algorithm users l ti th h ld l ithrelative threshold algorithm.

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Absolute Threshold HandoverAbsolute Threshold Handover

Eb/No

Th_Add

Th_Drop

TimeTime

NeighborSet

CandidateSet

ActiveSet

NeighborSet

(1) (2) (3) (4) (5) (6)

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Basic IS-95 HO AlgorithmBasic IS 95 HO Algorithm1. Pilot strength exceed T_Add. MS sends a Pilot Strength

M M d f il h C did SMeasurement Message and transfers pilot to the Candidate Set.2. BS sends a Handover Direction Message.

M bil t ti t f il t t th A ti S t d d3. Mobile station transfers pilot to the Active Set and sends a Hanover Completion Message.

4 Pilot strength drops below T Drop. MS starts the handover drop4. Pilot strength drops below T_Drop. MS starts the handover drop timer.

5. Handover drop timer expires. MS sends a Pilot Strength Measurement Message.

6. BS sends a Handover Direction Message. MS moves pilot from the Active Set to the Neighbor Set and sends a Handoverthe Active Set to the Neighbor Set and sends a Handover Completion Message.

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Problems with Absolute Threshold AlgorithmAlgorithm

Some locations in the cell receive only weak il t ( i i l h d th h ld)pilots (requiring a lower handover threshold).

Some locations in the cell receive a few strong an dominant pilots (requiring a higher handover threshold).

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Relative Threshold HORelative Threshold HO

Strongest Pilot in Active SetEc/Io

MS_Ec/Io

Window_Add

_

AS Th Hyst

Window_DropAS_Th

AS_Th_Hyst

AS_Th_Hyst

TimeT_DropT_Add

Time

MS AS MS

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MS AS MS

Active vs Monitored SetActive vs. Monitored Set

Active Set (AS): User information is sent from all ( )these cells and they are simultaneously demodulated and coherently combined.y

Monitored Set (MS): Cells which are not included inMonitored Set (MS): Cells, which are not included in the active set, but are monitored according to a neighboring list assigned by the UTRANneighboring list assigned by the UTRAN.

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Soft Handover Algorithm(for Active Set limit = 2)(for Active Set limit = 2)

ΔT ΔT ΔT

AS_Th + AS_Th_Hyst

CPICH 1Ec/No

AS_Th -AS_Th_HystAS_Rep_Hyst

CPICH 2

CPICH 3

Time

Cell 1 Connected

Time

Event AAdd Cell 2

Event B

Event CRemove Cell 3

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Event BReplace Cell 1 with Cell

3

Intersystem HandoffIntersystem Handoff

Intersystem handoff happens when a mobile moves from y ppone cellular system to a different cellular system.The MSCs involved in the two cellular systems areThe MSCs involved in the two cellular systems are different.Compatibility between the two MSCs must beCompatibility between the two MSCs must be determined.

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Prioritizing HandoverPrioritizing HandoverGuard Channel Concept : Use reserved guard channel for handover.

Disadvantage: Reducing the total carrier traffic.

Queuing of Handover Requests: To prevent forced i i b i htermination by queuing the request.

Queuing of handoffs is possible due to the fact that there is a finite time interval between the time the received signal levelfinite time interval between the time the received signal level drops below the handoff threshold and the time the call is terminated due to insufficient signal level.

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Practical Handover ConsiderationPractical Handover ConsiderationProblem 1: Simultaneous traffic of high speed and low speed mobiles.

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 coit is possible to provide large and small cells which are co-located at a single location.Small cell for low speed mobileSmall cell for low speed mobileLarge cell for high speed mobileNeed Strength Detection and Handoff control.

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g

The Umbrella Cell ApproachThe Umbrella Cell Approach

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Practical Handover ConsiderationPractical Handover ConsiderationProblem 2: Cell Dragging

Caused by pedestrian users that provide a very strong signal to the base station.Often occurs in an urban environment when there is a line ofOften occurs in an urban environment when there is a line-of-sight (LOS) radio path between the subscriber and the base station.As the user travels away from the base station at a very low speed, the average signal strength does not decay rapidly and the received signal at the BS may be above the handoffthe received signal at the BS may be above the handoff threshold, thus a handoff may not be made.Creates a potential interference and traffic management p gproblem.

Solution: Careful arrangement of handoff threshold and

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radio coverage parameters.

Handoff Control ParametersHandoff Control Parameters

bli ih d ff PrPr −=Δ

Δ≅ 6~12 dB (AMPS) → Δ≅0~6 dB (GSM)

useableminimumhandoff PrPr −Δ

Δ≅ 6 12 dB (AMPS) Δ≅0 6 dB (GSM)

Typical time to make a handoff – once the signal level is blow the handoff threshold : 10 sec (AMPS) → 1~2 sec (GSM)

The faster handoff process supports a much greater f ti f h dli hi h d d l drange of options for handling high speed and low speed

users and provides the MSC with substantial time to ll th t i i d f h d ff

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rescue a call that is in need of handoff.

Handoff MiscellaneousHandoff Miscellaneous

Intra-frequency Handoff: handoffs in the same q ysystem and carrier.Inter-frequency Handoff: handoffs between sameInter frequency Handoff: handoffs between same systems and different carriers.

May be used for handoff between different cell layers ofMay be used for handoff between different cell layers of the multi-layered cellular network, when the cell layers use different carrier frequencies.

Inter-system Handoffs: handoffs between different systems.systems.Inter-frequency and inter-system handoffs may be used for coverage or load balancing reasons

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used for coverage or load balancing reasons.

Frequency Utilization with WCDMAq y

Operator band 15 MHz

Power 4.2-5.0 MHz 4.2-5.0 MHzAnother UMTS

operatorAnother UMTS

operator

5.0-5.4 MHz 5.0-5.4 MHz3 cell layers

FrequencyUplink: 1920-1980 MHzDownlink: 2110-2170 MHz

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Downlink: 2110-2170 MHz

Intra-Frequency HandoffIntra Frequency Handoff

Hard Handoff: assign different radio channels during aHard Handoff: assign different radio channels during a handoff.

Soft Handoff: the ability to select between the instantaneous received signals from a variety of baseinstantaneous received signals from a variety of base stations.

Soft handoff exploits macroscopic space diversity provided by theSoft handoff exploits macroscopic space diversity provided by the different physical locations of the base stations.

Softer Handover: A mobile station is in the overlapping cell coverage area of two adjacent sectors of a base t ti

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station.


Interference and System Capacity


InterferenceInterference

The major source limiting cellular system capacityThe major source limiting cellular system capacity comes from interferences (as oppose to noise).Interference has been recognized as a majorInterference has been recognized as a major bottleneck in increasing capacity and is often responsible for dropped calls.p pp

Major Types of Interference:Major Types of Interference:Co-Channel InterferenceAdjacent Channel InterferenceAdjacent Channel Interference

Intra-Cell TypeInter-Cell Type

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Co-channel Cells and InterferenceCo channel Cells and Interference

In a given coverage area there are several cells that use theIn a given coverage area, there are several cells that use the same set of frequencies. These cells are called co-channel cells.The interference between signals from co-channel cells is called co-channel interference.Unlike thermal noise which can be overcome by increasing the signal-to-noise ratio (SNR), co-channel interference can＇t be overcome by simply increasing the carrier power because an increase in carrier power increases the interference to neighboring co channel cellsto neighboring co-channel cells.To reduce co-channel interference, co-channel cells must be physically separated by a minimum distance

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physically separated by a minimum distance.

HexagonHexagon

Rr ⋅=23

Rr ⋅=3

R2

Rr ⋅=2 r

R

2 2( ) 3 3Cell Area 6 2 32 2

r R R r⋅= ⋅ = ⋅ =

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HexagonHexagon

A ll d ( )A cell centered at (u,v)

rjrivu = )2,2(),(

uux o ⋅=⋅=23)30cos(

vuvuy o +=+⋅=2

)30sin(

2i=3

2

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Hexagon Distance

Distance between (ua, va) and (ub, vb)

Hexagon D stance

2 2 2

2 2

( ) ( )ab a b a bD x x y y= − + −

⎛ ⎞ ⎛ ⎞23 3

2 2 2 2a b

a b a bu uu u v v

⎛ ⎞ ⎛ ⎞= − + − + −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

( ) ( ) ( ) ( )2 2

2 2 2

(2 ) ( ) ( ) ( )( )a b a b a b a b

b b b b

u u v v u u v v

r i i j j i i j j

= − + − + − ⋅ −

⎡ ⎤= ⋅ − + − + − −⎣ ⎦

For special case (distance from origin)

(2 ) ( ) ( ) ( )( )a b a b a b a br i i j j i i j j⎡ ⎤+ +⎣ ⎦

p ( g )

2 22D r i j ij= ⋅ + +

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Hexagonal ClusterHexagonal Cluster

Hexagonal ClusterEach cluster is surrounded by six similar clusters with the same orientationEach cluster has a total area equivalent to what can be

ll d “ h ＂called a “super-hexagon＂view a cluster as a “hexagon＂

2 22D r i j ij= ⋅ + +

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j j

Super-Hexagon ConceptSuper Hexagon Concept

D=Frequency Reuse Distanceq y

'2DR =D 2

Super HexagonAN

A−=

( )22 3 'CellA

R=R’( )2

2 2

2 3r

i j i j

=

= + + ⋅

R

Cluster Size

i j i j= + + ⋅=

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Co-Channel Reuse RatioCo Channel Reuse Ratio

The signal to co-channel interference ratio is independent of theThe signal to 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 centers of the nearest co-channel cells (D). Co-channel Reuse Ratio Q : The spatial separation between co-channel cells relative to the coverage distance of a cell.

jijirD 2 22 ⋅++⋅⋅= 3

NR

Nr

3

2

⋅=

⋅⋅=Rr ⋅=

23

NR 3=

NRDQ 3==

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RQ

CO-Channel Reuse RatioCO Channel Reuse Ratio

Small Q Small N Large Capacity

Large Q Large N Small Level of Co-Channel Interference

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Large Q Large N Small Level of Co-Channel Interference

Co Channel Signal to Interference Ratio (SIR)Co-Channel Signal to Interference Ratio (SIR)

SIR: Signal to Interference Ratio.gConsider only first tier interference.Assuming all interfering BS＇s are equal-distance.ssu g a e e g S s a e equa d s a ce.

∑=

0i

I

SIS

NR 3⋅

n

r ddPP

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

00

∑=1i

iI

( 3 )Worst Case SIR=n n n

tPR R N− −

≈ =

⎠⎝

00 0

1

Worst Case SIR= i nn

t ii

i D iPd−

−

=

≈ =

∑(Mobile)

Example: i0=6, n=4N=3 ⇒ SIR=11.3 dB

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N=7 ⇒ SIR=18.7 dB

7-Cell Co-channel Signal to Interference RatioRatio

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An approximation of the exact geometry.

7-Cell Co-Channel Signal to Interference Ratio An ApproximationRatio – An Approximation

2( ) 2( ) 2

n

n n n

S RI D R D R D

−

− − −=− + + +( ) ( )

( ) ( )4 4 4

1S=

( ) ( )4 4 42 1 2 1 2I Q Q Q− − −− + + +

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Adjacent Channel InterferenceAdjacent Channel Interference

Adjacent channel interference results from imperfect j preceiver filters which allow nearby frequencies to leak into the passband.pAdjacent channel interference can be minimized through careful filtering and channel assignmentscareful filtering and channel assignments.Channels are allocated such that the frequency separation between channels in a given cell isseparation between channels in a given cell is maximized.

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Near-Far EffectNear Far Effect

A nearby transmitter (which may or may not be ofA 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.captures the receiver of the subscriber.Alternatively, the near-far effect occurs when a mobile close to a base station transmits on a channelmobile close to a base station transmits on a channel close to one being used by a weak mobile. The base station may have difficulty in discriminating thestation may have difficulty in discriminating the desired mobile user from the close adjacent channel mobilemobile.

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Power Control


Power Control for 2G Cellular SystemsPower Control for 2G Cellular Systems

Power levels transmitted by subscriber unit are under ycontrol by the serving base stations.Power control is to ensure that each mobile transmits thePower control is to ensure that each mobile transmits the smallest power necessary to maintain a good quality link on the reverse channelon the reverse channel.Power control not only helps prolong battery life for the subscriber unit but also dramatically reduces the reversesubscriber unit, but also dramatically reduces the reverse channel S/I in the system.

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Power Control in 3G (WCDMA)Power Control in 3G (WCDMA)

Tight and fast power control is perhaps the most g p p pimportant aspect in WCDMA in particular on the uplink. Without it, a single overpowered mobile

ld bl k h l llcould block a whole cell.Near-Far problem of CDMA: A MS close to the base

i b d d bl k l fstation may be overpowered and block a large part of the cell.P l i WCDMAPower control in WCDMA:

Open-loop power controlCl l lClose-loop power control

Inner-loop power controlOuter-loop power control

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Outer loop power control

Open Loop Power Control in WCDMAOpen Loop Power Control in WCDMAAttempt to make a rough estimation of path loss by measuring downlink beacon signal.Disadvantage: Far too inaccurate, because fast fading is essentially uncorrelated between uplink and downlink, due to the large frequency separation of uplink and d li k b d f th WCDMA FDD ddownlink band of the WCDMA FDD mode.Open-loop power control is used in WCDMA to provide

i iti l tti f th MS t th b i ia coarse initial power setting of the MS at the beginning of a connection.

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Outer Loop Power Control in WCDMAOuter Loop Power Control in WCDMA

To adjusts the target SIR setpoint in the BS according j g p gto the individual radio link quality requirements, usually defined as BER or FER.The required SIR for FER depends on the mobile speed, multipath profile, and data rate.Should the transmission quality is decreasing, the Radio Network Controller (RNC) will command the Node B to increase the target SIR.Outer loop power control is implemented in RNC because there might be soft handover combining.

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Inner-loop Power Control in WCDMA Uplink

Base station performs frequent estimates of the

UplinkBase station performs frequent estimates of the received Signal-to-Interference Ratio (SIR) and compares it to a target SIRcompares it to a target SIR.

If the measured SIR is higher than the target SIR, the base station will command the MS to lower the power.station will command the MS to lower the power.If SIR is too low, it will command the MS to increase its power.p

The power control is operated at a rate of 1500 times per second.per second.

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Inner-loop Power Control in WCDMA DownlinkDownlink

Adopt same techniques as those used in uplinkAdopt same techniques as those used in uplink.Operate at a rate of 1500 times per second.

There is no near-far problem in downlink. Purposes for downlink closed loop power are:Purposes for downlink closed-loop power are:

Provide a marginal amount of additional power to MS at the cell edge as they suffer from increased other-cellthe cell edge as they suffer from increased other-cell interference.Enhancing weak signals caused by Rayleigh fading at lowEnhancing weak signals caused by Rayleigh fading at low speeds when other error-correcting methods (interleaving and error correcting codes) doesn＇t work effectively.

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Trunking and Grade of Service


Trunking SystemTrunking System

Trunking system: A mechanism to allow many user toTrunking system: A mechanism to allow many user to share fewer number of channels.

Not every user calls at the same timeNot 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 a trade-off between the number of available circuits and blocking probability.

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Grade of Service (GOS)Grade of Service (GOS)

Erlang: The amount of traffic intensity carried by a g ff y ychannel that is completely occupied.For example a radio channel that is occupied for 30For 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 aGrade of Service (GOS) is a measure of the ability of a user to access a trunked system during the busiest hour.GOS i t i ll i th lik lih d th t ll iGOS is typically given as the likelihood that a call is blocked, or the likelihood of a call experiencing a delay

t th t i i tigreater than a certain queuing time.

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Definitions of Terms Used in Trunking TheoryTheory

Set-up Time: The time required to allocate a radio p qchannel to a user.Blocked Call: Call which can＇t be completed at ptime of request, due to congestion.Holding Time: Average duration of a typical call. g g ypDenoted by H (in second).Traffic Intensity: Measure of channel time utilization, ff y ,which is the average channel occupancy measured in Erlangs. This is a dimensionless quantity and may be used to measure the time utilization of single or multiple channels. Denoted by A.

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Definitions of Terms Used in Trunking TheoryTheory

L d T ffi i i h i k d diLoad: 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).Request Rate: The average number of call requests per unit time. Denoted by μ second-1.p y μ

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Computation of GOSComputation of GOS

A =λHAu λHAu : each user generate a traffic intensity of Au Erlangλ : average number of call request per unit time for eachλ : average number of call request per unit time for each user.H : average duration of a call.

A=UAuA: Total offered traffic intensity.U: Total users in a system.

Ac=UAu/CC : # of channels in a truncking systemAc: traffic intensity per channel

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Computation of GOSComputation of GOSThere are two types of trunked systems:

No queueing for call requests:for every user who requests service, it is assumed there is no setup time

d th i i i di t t h l if i il bland the user is given immediate access to a channel if one is available.If no channels are available, the requesting user is blocked without access and is free to try again later.y gCalled blocked calls cleared.GOS: Erlang B formula determines the probability that a call is blocked.

A queue is provided to hold calls which are blocked.If a channel is not available immediately, the call request may be delayed until a channel becomes availabledelayed until a channel becomes available.Called blocked calls delayed.GOS: Erlang C formula gives the likelihood that a call is initially

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g g ydenied access to the system.

Trunked Systems with no Queuing for Call Requests – blocked calls cleared

Blocking Probability -- Erlang B Formula:

Call Requests blocked calls cleared

Blocking Probability Erlang B Formula:

GOSCA

blocking

C

!]Pr[AMPS cellular system is designed

GOS

kA

Cblocking C

k

k ==

∑=0 !

!]Pr[ for a GOS of 2% blocking.

There are infinite number of users.Call requests are memoryless; both new and blocked users may request a channel at any time.Service time of a user is exponentially distributedT ffi t d ib d b P i d lTraffic requests are described by Poisson model.Inter-arrival times of call requests are independent and exponentially distributed

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exponentially distributed.

Trunked Systems with Queuing for Call Requests – Blocked Calls Delayed

Erlang C Formula – the likelihood of a call is initially

Requests Blocked Calls Delayed

g ydenied to access a channel:

−⎞⎛=> 1]0Pr[ C k

C

AAAdelay

∑=

⎟⎠⎞

⎜⎝⎛ −+

1

0 !1!

C

k

kC

kA

CACA

]0|Pr[]0Pr[]Pr[ delaytdelaydelaytdelay >>>=>))(exp(]0Pr[ HtACdelay −−>=

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Trunked Systems with Queuing for Call Requests – Blocked Calls Delayed

The average delay D for all calls in a queued system is

Requests Blocked Calls Delayed

g y q ygiven by:

HAC

HdelayD−

>= ]0Pr[

The average delay for those calls which are queued is given by:given by:

HAC −

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Erlang B ChartErlang B Chart

74

Erlang C ChartErlang C Chart

75

Trunking EfficiencyTrunking EfficiencyTrunking 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 t k d ttrunked system.

F T bl 3 4 f GOS 0 01From Table 3.4, for GOS=0.0110 trunked channels can support 4.46 Erlangs.T 5 t k d h l t 2 1 36 2 72 E lTwo 5 trunked channels can support 2x1.36=2.72 Erlang.10 trunked channels support 64% more traffic than two 5 channel trunks do

76

channel trunks do.


Improving Capacity in Cellular Systems


System Expansion TechniquesSystem Expansion Techniques

Adding New ChannelsgFrequency borrowingCell SplittingCell SplittingSectoring / SectorizationChange of Cell PatternCoverage zoneg

78

Cell SplittingCell Splitting

Cell splitting is the process of subdividing a congested p g p g gcell into smaller cells, each with its own base station and a corresponding reduction in antenna height and p g gtransmitter power.

Cell splitting increases the capacity of a cellular system since it increases the number of times that channels aresince it increases the number of times that channels are reused.

79


Cell splitting⇒ small cells (microcells)p g ( )

SameSame service area

More cells in the service area, more capacity.

80


Cell Splitting(Hot Spot)

81

Transmit Power for Split cellTransmit Power for Split cell

The transmit power of the split cell must be reduced.p p

For example if new cell radius is half of that of old cellFor example, if new cell radius is half of that of old cell and the path loss exponent n = 4:

ntr RPP −∝ 1boundary] cell oldat [

ntr RPP −∝ )2(boundary] cell newat [ 2

boundary]celloldat[boundary]cellnewat[ PP = boundary]celloldat [boundary]cellnewat [ rr PP

161

2t

tPP =

82

SectoringSectoringThe technique for decreasing co-channel interference and thus increasing system capacity by using directional antennas is called sectoring.

The factor by which the co-channel interference is reduced depends on the amount of sectoring used.

# of antenna ↑ , # of handover ↑ , trunking efficiency ↓

83

SectoringSectoring

84

SectoringSectoring

85

Chang of cell PatternChang of cell Pattern

N=7, ⇒ CT/7 channels per cell N=3, ⇒ CT/3 channels per cell

86high SIR low SIR (⇐ by-product)

A Novel Microcell Zone ConceptA Novel Microcell Zone Concept

87

A Novel Microcell Zone ConceptA Novel Microcell Zone Concept

Any channel may be assigned to any zone.y y g yWhen a mobile travels from one zone to another, there is no handoverno handover.A given channel is active only in a particular zone. Thus interference is reduced and capacity is increasedThus interference is reduced and capacity is increased.Without the degradation in trunking efficiency.

88

Summaries of Improving Capacity in Cellular SystemsCellular Systems

While cell splitting increases the number of base stations in order to increase capacity, sectoring and zone microcells rely on base station antenna placements to i it b d i h l i t fimprove capacity by reducing co-channel interference.Cell splitting and zone microcell techniques do not

ff th t ki i ffi i i i d bsuffer the trunking inefficiencies experienced by sectored cells, and enable the base station to oversee all handoff chores related to the microcells thus reducinghandoff chores related to the microcells, thus reducing the computational load at the MSC.

89


Trunking Theory


IntroductionIntroductionThere are two major classes of trunked radio systems:

Lost Call Cleared (LCC)Lost Call Delayed (LCD)

Lost Call Cleared systemQueueing is not provided for call requests.When a user requests service, the user is given immediate access to a channel if one is available.If h l il bl th ll i bl k d ith tIf no new channels are available, the call is blocked without access to the system. The user is free to try the call again later.Calls are assumed to arrive with a Poisson distributionCalls are assumed to arrive with a Poisson distribution.The time between successive calls is exponentially distributed.The Erlang B formula describes the grade of service (GOS) as

91

g g ( )the probability that an user will experience a blocked call.

IntroductionIntroductionAssumed that there are infinite number of users.Assume that all blocked calls are instantly returned to an infinite user pool, and may be retried at any time in the future.

L t C ll D l d tLost Call Delayed system:Queues are used to hold call requests that are initially blocked.Wh h l i t i di t l il bl th ll tWhen a channel is not immediately available, the call request may be delayed until a channel becomes available.The Erlang C formula gives the likelihood that all channels areThe Erlang C formula gives the likelihood that all channels are in use. It is also necessary to know the probability of how long the cal must be delayed before a channel is available.The GOS is measured by the probability that calls will have delayed greater than t seconds.Assume that all calls in the queue are eventually serviced

92

Assume that all calls in the queue are eventually serviced.


Erlang B Formula


Basic AssumptionsBasic AssumptionsCall requests are memoryless, implying that all users, including blocked users, may request a channel at any time.The probability of a user occupying a channel (call the service time) is exponentially distributed.Traffic requests are described by a Poisson distributionwhich implies exponentially distributed call inter-arrival titimes.Inter-arrival times of call requests are independent of

h theach other.There infinite number of users and there are finite

b f h l il bl i th t k d l94

number of channels available in the trunked pool.

Derivation of Erlang BDerivation of Erlang BConsider a system with C channels and U users.Let λ be the total mean call arrival rate per unit time for the entire trunked system (average number of call requests per unit time over all channels and all users).Let H be the average call holding time (average call duration).If A is the offered load for the trunked system, A=λH.The probability that a call requested by a user will be blocked is i bgiven by:

Pr[Blocking]=Pr[None of the C channels are free]ll i di h d bCalls arrive according to the Poisson distribution:

( ) ( ){ } ( )Pr for = 0, 1, 2...!

nea t a t n nn

λτ

τ λτ−

+ − = =

95

!n

Derivation of Erlang BDerivation of Erlang Ba(t) is the number of call requests (arrivals) that have occurred i 0since t = 0.

The Poisson process implies that the time of the nth call arrival and the i t i l ti between successive call requests areand the interarrival times between successive call requests are mutually independent.The interarrival times between call requests are exponentiallyThe interarrival times between call requests are exponentially distributed and mutually independent, and the probability that the interarrival time will be less than some time s is given by g yPr(τn≤s)=1-e-λs, s≥0 where τn is the interarrival time of the nth arrival and τn=tn+1-tn, where tn is the time at which the nth call

i drequest arrived.The probability density function forτn is:

( ) 0np e λττ λ τ−= ≥

96

( ) , 0.n np eτ λ τ= ≥

Derivation of Erlang BDerivation of Erlang BFor every t ≥0 andδ≥0

( ) ( ){ } ( )( ) ( ){ } ( )

Pr 0 1

Pr 1

a t a t O

a t a t O

δ λδ δ

δ λδ δ

+ − = = − +

+ − = = + (A)( ) ( ){ } ( )( ) ( ){ } ( )

Pr 1

Pr 2

a t a t O

a t a t O

δ λδ δ

δ δ

+ = = +

+ − ≥ =

(A)

where O(δ) is the probability of more than one call request arriving over the time interval δ and is a function ofδ such that

( )⎧ ⎫( )0

lim 0O

δ

δδ→

⎧ ⎫=⎨ ⎬

⎩ ⎭The probability of n arrivals in δseconds is given by:

( ) ( ){ } ( )Pr nea t a t nλδ

δ λδ−

+ − = =

97

( ) ( ){ } ( )Pr!

a t a t nn

δ λδ+ − = =

Derivation of Erlang BDerivation of Erlang BThe user service time is the duration of a particular call that has

f ll d h k dsuccessfully accessed the trunked system.Service times are assumed to be exponentially distributed with mean call duration H where μ 1/H is the mean i tmean call duration H, where μ=1/H is the mean service rate.The probability density function of the service time is

( ) nsμ−

where sn is the service time of the nth call.Thi t ki t i ll d M/M/C/C i Th

( ) nsnp s e μμ=

This trunking system is called an M/M/C/C queueing system. The first M denotes a memoryless Poisson process for call arrivals, the 2nd M denotes an exponentially distributed service time thethe 2nd M denotes an exponentially distributed service time, the first C denotes the number of channels available, and the last Cindicates a hard limit on the number of simultaneous users that

98

are served.

Derivation of Erlang BDerivation of Erlang BConsider a discrete time stochastic process {Xn|n=0, 1, 2,…} that takes values from the set of nonnegative integers, so that the possible states of the process are i=0,1, 2, …. The process is

id t b M k h i if it t iti f th t t t isaid to be a Markov chain if its transition from the present state ito the next i+1 depends solely on the state i and not on previous states.states.At time kδ, the number of calls (occupied channels) Nk in the system may be represented as Nk = N(kδ), where N is a discrete y y p k ( ),random process representing the number of occupied channels.The transition probability Pi,j, which describes the probability of ,jchannel occupancies over a small observation interval, is given by { }, 1Pr |i j k kP N j N i+= = =

99

{ }, 1 |i j k kj+

Derivation of Erlang BDerivation of Erlang BUsing Equation (A) and letting δ→0, we obtain:

( )( )

1

1 1oo

ii

P O

P O i

λδ δ

λδ μδ δ

= − +

= − − + ≥( )( )( )

, 1 0

1

ii

i iP O i

P O i

μ

λδ δ

μδ δ+ = + ≥

= + ≥( )( )

, 1

,

1

, 1, 1i i

i j

P O i

P O j i j i j i

μδ δ

δ− = + ≥

= ≠ ≠ + ≠ −

100

Derivation of Erlang BDerivation of Erlang BAt steady state, we have the Global Balance Equation:

As a result, we have:1 , n nP n P n Cλδ μδ− = ≤

1C

P =∑1

21 1

n nP P n

P

λ μ

λ λ λ

− =

⎛ ⎞0

1nn

P=

=∑01 2 1 0

1 1 2 2

n in C C

PP P P Pλ λ λμ μ μ

λ λ

⎛ ⎞= = = ⎜ ⎟

⎝ ⎠

⎛ ⎞ ⎛ ⎞⎛ ⎞0 0 0

1 1

1 1 ! 1 1! !

n in C C

n n ii i

P P P P n P Pn i

λ μ λμ λ μ= =

⎛ ⎞ ⎛ ⎞⎛ ⎞= ⇒ = = − = −⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠

∑ ∑

01

1nC

Pλ

=⎛ ⎞⎜ ⎟∑

101

0 !n nμ=⎜ ⎟⎝ ⎠

∑

Derivation of Erlang BDerivation of Erlang BThe probability of blocking for C trunked channels is:

1!1

C

CCP P

λμλ

⎛ ⎞⎜ ⎟⎛ ⎞ ⎝ ⎠

⎜ ⎟0

0

! 1!

c nC

n

P PC

nμ λ

μ=

⎝ ⎠= =⎜ ⎟⎝ ⎠ ⎛ ⎞

⎜ ⎟⎝ ⎠

∑

The total offered traffic is A=λH=λ/μ. The Erlang B formulawhich gives the probability of blocking can be obtained by:

0n μ⎝ ⎠

which gives the probability of blocking can be obtained by:1

!CA

C

0

!1!

c Cn

n

CPA

n=

=

∑

102

0n=


Erlang C FormulaErlang C Formula


Derivation of Erlang CDerivation of Erlang CAssumption: if an offered call can＇t be assigned a channel, it is placed in a queue which has an infinite length.The Erlang C formula is derived by assuming that the trunked system is a M/M/C/D queue, where C denotes the maximum number of simultaneous users and D is the maximum number of calls that may be held in the queue for serviceof calls that may be held in the queue for service.

104

Derivation of Erlang CDerivation of Erlang CFrom the state diagram:

1 1 1 for for k k k kP k P k C P P k Ck

λλδ μδμ− −

⎛ ⎞= ≤ ⇒ = ≤⎜ ⎟

⎝ ⎠

1 1 1 for for k k k kP C P k C P P k CC

λλδ μδμ− −

⎛ ⎞= ≥ ⇒ = ≥⎜ ⎟

⎝ ⎠

01 !

k

P k Ck

λμ

⎝ ⎠⎧⎛ ⎞

≤⎪⎜ ⎟⎪⎝ ⎠

0

!

1 1 !

k k

k C

kP

P k CC C

μ

λ

⎪⎝ ⎠⇒ = ⎨⎛ ⎞⎪

≥⎜ ⎟⎪⎝ ⎠

0! k CC Cμ −⎜ ⎟⎪⎝ ⎠⎩

105

Derivation of Erlang CDerivation of Erlang C

Since =1, we have:kP∞

∑0

1

Since 1, we have:

1 11 1

kk

C

P

P λ λ

=

+⎡ ⎤⎛ ⎞ ⎛ ⎞⎢ ⎥⎜ ⎟ ⎜ ⎟

∑

( )0 11 ...... .... 1! C C

k k

PC Cμ μ + −

⎛ ⎞ ⎛ ⎞+ + + + =⎢ ⎥⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦⎡ ⎤⎛ ⎞ ⎛ ⎞1

01

1 1 1 1 1! !

k kC

k Ck k c

Pk C C

λ λμ μ

− ∞

−= =

⎡ ⎤⎛ ⎞ ⎛ ⎞⇒ + + =⎢ ⎥⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦∑ ∑

0 1

1 1 1 1

k CCP

λ λ−⇒ =

⎛ ⎞ ⎛ ⎞∑1

1 1 1! ! 1k k k

C

λ λμ μ λ

μ=

⎛ ⎞ ⎛ ⎞+⎜ ⎟ ⎜ ⎟ ⎛ ⎞⎝ ⎠ ⎝ ⎠ −⎜ ⎟

⎝ ⎠

∑

106

Cμ⎝ ⎠

Derivation of Erlang CDerivation of Erlang C

[ ]h l bP C P∞

∑[ ] channels are busy

1 1

r kk C

k

P C P

λ

=

∞

=

⎛ ⎞

∑

01 1

! k Ck C

C k C

PC C

λμ −

=

−

⎛ ⎞= ⎜ ⎟

⎝ ⎠

⎛ ⎞ ⎛ ⎞

∑

01 1

!

C k C

k Ck C

PC C

λ λμ μ

∞

−=

⎛ ⎞ ⎛ ⎞= ⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠∑

01 1 1

! 1

C

PC C

λ λμ μλ

⎛ ⎞= <⎜ ⎟ ⎛ ⎞⎝ ⎠

⎜ ⎟1Cμ

⎝ ⎠ −⎜ ⎟⎝ ⎠

107

Derivation of Erlang CDerivation of Erlang CSubstituting for P0 C

⎛ ⎞

[ ]

1! 1channels are busy

C

rCP C

λμ

⎛ ⎞⎜ ⎟⎝ ⎠=

⎛ ⎞ ⎡ ⎤[ ]

1

y1

1 1 1

r

k CCCλμ λ λ−

⎛ ⎞ ⎡ ⎤−⎜ ⎟ ⎢ ⎥⎛ ⎞ ⎛ ⎞⎝ ⎠ ⎢ ⎥+⎜ ⎟ ⎜ ⎟⎢ ⎥⎛ ⎞∑

0 ! ! 1k k kC

μ μ λμ

=

+⎜ ⎟ ⎜ ⎟⎢ ⎥⎛ ⎞⎝ ⎠ ⎝ ⎠ −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

∑

Cλμ

⎛ ⎞⎜ ⎟⎝ ⎠

1

0

1! 1!

C kC

k

CC k

μ

λ λ λμ μ μ

−

⎝ ⎠=⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ −⎢ ⎥⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦

∑

108

0 !kC kμ μ μ= ⎝ ⎠⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎢ ⎥⎣ ⎦

Derivation of Erlang CDerivation of Erlang CWith A=λ/μ=λH, the Erlang C formula is given by:

[ ] 1Pr channels are busyC

kC

AC =⎛ ⎞

[ ] 1

0

c a e s a e busy! 1

!

kCC

k

CA AA CC k

−

=

⎛ ⎞+ −⎜ ⎟⎝ ⎠

∑

109

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