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Cellular Systems

Mobile CommunicationsCellular Systems

Wen-Shen Wuen

Trans. Wireless Technology LaboratoryNational Chiao Tung University

Vincent W.-S. Wuen Mobile Communications 1

Outline Cellular Systems

Outline

1 Cellular System Fundamentals

2 Frequency Reuse

3 Interference and System Capacity

4 Trunking and Grade of Services

5 Improving Coverage and Capacity in Cellular Systems

6 Channel Assignment Strategies

7 Handoff Strategies


Cellular System Fundamentals Cellular Systems

Introdcution

Early mobile radio systems:

Cover a large area by using a single, high powered transmitterwith an antenna mounted on a tall tower.

No frequency reuse, no interference

Limited user capacity

Cellular concept:

Based on power fall off with distance of signal propagation andreuse the same channel frequency at spatially separatedlocations

Sovling problem of spectral congestion and user capacity

Replacing a single, high power transmitter (large cell) withmany low power transmitters (small cells)

Available channels can be reused as many times as necessaryso long as the co-channel interference is kept below acceptablelevels



Cellular System

Each cell is assigned to a unique channel set, Cn

Adjacent cells: cells assigned to a different channel sets

Co-channel cells: cells using the same channel sets



Tesselating Cell Shapes

To approximate the contours of constant received poweraround the base station

Hexagonal cells:

Having largest area for a given distance between the center of apolygon and its farthest perimeter pointsApproximating a circular radiation pattern for an omnidirectionalbase station antenna and free space propagation

Diamond cells: better approximating contours of constantpower in modern urban microcells


Frequency Reuse Cellular Systems

Frequency Reuse

S: total number of duplex channels available for use

k: number of channels assigned to a cell (k < S)

N: number of cells sharing the S duplex channels

S = kN (1)

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

C: the total number of duplex channels with frequency reuse

M: number of replica of a cluster

C = MkN = MS (2)

Cluster size: N is typically 4, 7 or 12 for hexagonal cell shape.

Frequency reuse factor: 1/N

For the same cell size at a given area, N ↓⇒ M ↑⇒ C ↑Vincent W.-S. Wuen Mobile Communications 8


Various Cluster Sizes for Hexagonal Cells

Cluster sizes:

4-cell reuse

7-cell reuse

12-cell reuse

19-cell reuse

N-cell reuse



Locating Co-Channel Cells in Hexagonal Cells

Example: N = 19, i = 3, j = 2



Reuse Distance

The distance between co-channel (frequency reuse) cells

Origin: (0,0)

Nearest co-channel locationP: (i, j)

Reuse Distance, D

D = p3R

√i2 + ij+ j2 (3)

= Rp

3N (4)



Number of Cells Per Cluster

Number of cells per cluster, N

N = Acluster

Acell= 3

p3x2/2

3p

3R2/2=

p3D2/2

3p

3R2/2

= 1

3

(D

R

)2

= 1

3

(3R2

(i2 + ij+ j2

)R2

)= i2 + ij+ j2 (5)


Interference and System Capacity Cellular Systems

Interference

Major limiting factor in the performance and major bottleneckin increasing capacity

Sources of interference:

anothr mobile in the same cella call in progress in a neighboring cellother base station operating in the same frequency bandany noncellular system which leaks energy into the cellularfrequency band

Interference effects:

Cross talk: interference on voice channelsMissed and blacked calls: interference on control channels

System-generated cellular interference

Co-channel interferenceAdjacent channel interference



Co-channel Interference

Cannot be combated by simply increasing transmitter power

To reduce, co-channel cells must be separated by a minimumdistance to provide sufficient isolation



Co-channel Interference, cont’d

Assume

the size of each cell is the samebase stations transmit the same power

⇒ co-channel interference ratio is independent of TX power andis a function of the radius of the cell, R, and the distancebetween centers of nearest co-channel cells, D.

Co-channel reuse ratio, Q

Q ,D

R=p

3N (6)

Q ↑⇒ spatial separation of co-channel cells ↑⇒ co-channelinterference ↓Q ↓⇒ N ↓⇒ M ↑⇒ C ↑ channel capacity ↑, but co-channelinterferece ↑



Signal to Interference Ratio, SIR, S/I

S

I= S∑Nco

i=1 Ii

(7)

S: desired signal power from the desired stationIi: the interference power caused by the i-th interfering co-channelcell base stationDi: the distance of the i-th interferer from the mobile.

∵ Pr = P0

(d

d0

)−n

∴ Ii ∝ D−ni (8)

Assume transmit power of each base station is equal and thepath loss exponent is the same, the S

I of for a mobile at cellboundary:

S

I= R−n∑Nco

i=1 D−ni

= R−n

NcoD−n =(p

3N)n

Nco(9)



Co-channel Interference For N=7

Consider first tier ofco-channel cells:

S

I≈ R−4

2(D−R)−4 +2(D+R)−4 +2D−4

(10)S

I≈ 1

2(Q−1)−4 +2(Q+1)−4 +2Q−4

(11)where Q = D/R and assume n = 4.



Example 1

If signal-to-interference ratio of 15 dB is required for satisfactoryforward channel performance of a cellular system, what is theco-channel reuse factor and cluster size that should be used formaximum capacity if the path loss exponent is (a) n=4, (b)n=3?Assume there are six co-channel cells in the first tier and all of themare at the same distance from the mobile.Solution:(a) Consider 7-cell reuse pattern: Q = D/R =p

3N = 4.583,S/I = (

p3N)n/Nco = 4.5834/6 = 75.3 = 18.66 dB ⇒ N = 7 can be used.

(b) Consider 7-cell reuse pattern: S/I = 4.5833/6 = 16.04 = 12.05 dB< 15 dB, therefore a larger N should be used.N = 12 ⇒ D/R = 6,S/I = 63/6 = 36 = 15.56 dB > 15 dB, therefore N = 12should be used.



Channel Planning of Wireless Systems

Typically 5% of the entire mobile spectrum is devoted to controlchannels and 95% of the spectrum is dedicated to voicechannels.

Air interface standards ensure a distinction between voice andcontrol channels and control channels are not allowed to beused as voice channels and vice versa.

Different frequency reuse strategy is applied to controlchannels to ensure greater S/I protection in control channels.

For propagation consideration, most practical CDMA systemslimits frequency reuse with f 1/f 2 cell planning.

CDMA system has a dynamic, time-varying coverage regiondepending on the instantaneous number of users on the radiochannel. ⇒ breathing cell ⇒ dynamic control of power levelsand thresholds assigned to control channels, voice channels forchanging traffic intensity



Adjacent Channel Interference

results from imperfect receiver filters which allows nearbyfrequency to leak into the passband.

causes near-far effect, a nearby TX captures the receiver of thesubscriber.

ACI can be minimized through careful filtering and channelassignments.

Keeping frequency separation between each channel as large aspossibleAvoiding the use of adjacent channels in neighboring cell sites

For a close-in mobile (MS1) is X times as close to the BS asanother mobile (MS2) and has energy leaks to the passband,the S/I at the BS for the weak mobile (MS2) before receiverfiltering is approximately

S

I= X−n

for n = 4 ⇒ SI ≈−40 dB


Trunking and Grade of Services Cellular Systems

Definition of Common Terms in Trunking Theory

Set-up Time: The time required to allocated a trunked radiochannel to a requesting user.

Blocked Call (Lost Call): Call which cannot be completed at timeof request, due to congestion.

Holding Time: Average duration of a typical call. Denoted by H(in seconds).

Traffic Intensity: Measure of channel time utilization, which isthe average channel occupancy measured in Erlangs.

Load: Traffic intensity across the entire trunked radio system,measured in Erlangs.

Grade of Service (GOS): A measure of congestion specified asthe probability of a call being blocked (for Erlang B), or theprobability of a call being delayed beyond a certain amount oftime (for Erlang C).

Request Rate: The average number of call requests per unittime. Denoted by λ second−1.



Trunking Theory

Each user generates a traffic intensity of Au Erlangs:

Au =λH

The total offered traffic intensity A for a system containing Uusers:

A = UAu

In a C channel trunked system, if the traffic is equallydistributed, the traffic i ntensity per channel, Ac:

Ac = UAu/C

Erlang: the amount of traffic intensity carried by a channel thatis completely occupied (1 Erlang = 1 call-hour / hour).

Busy hour traffic, Ab = call/busy hour × mean call holding time.



Example 2

Call established at 2 am between a central computer and a dataterminal. Assuming a continuous connection and data transferred at34 kbit/s what is the traffic if the call is terminated at 2:45am?Solution:Traffic=(1 call)×(45 min)×(1 hour / 60 min) =0.75 Erlangs

Example 3

A group of 20 subscribers generate 50 calls with an average holdingtime of 3 minutes, what is the average traffic per subscriber?Solution:Traffic=(50 calls)×(3min)×(1 hour/60 min)=2.5 Erlangs2.5/20=0.125 Erlangs per subscriber.



Erlang B: Blocked Calls Cleared

p [blocked] =AC

C!∑Ck=0

Ak

k!

=GOS

where C: the number of trunked channels offered by a trunked radiosystem; A: the total offered traffic.Assumptions of Erlang B:

There are memoryless arrivals of requests.

The probability of a user occupying a channel is exponentiallydistributed.

There are a finite number of channels available in the trunkingpool.



GOS of an Erlang B System

Trunking efficiency: a meaure of the number of users which can beoffered a particular GOS with a particular configuration of fixedchannels.



Erlang B Chart



Erlang C: Blocked Calls Delayed

Probability of a call not having immediate access to a channeland being queued:

p [delay> 0] =AC

C!

AC +C!(1− A

C

)∑C−1k=0

Ak

k!

=GOS

The probability that the delayed call is forced to wait more thant second:

p [delay> t] = p [delay> 0]p [delay> t|delay> 0]

= p [delay> 0]exp

(− (C −A)t

H

)(12)

Average delay D for all calls in a queued system

D = p [delay> 0]H

C −A



Erlang C Chart



Example 4

How many users can be supported for 0.5% blocking probability forthe following number of trunked channels in a blocked calls clearsystem? (a) 1, (b) 5, (c) 10, (d) 20, (e) 100. Assume each usergenerate 0.1 Erlangs of traffic.Solution:(a) C = 1,Au = 0.1,GOS = 0.005, from the chart,A = 0.005 ⇒ U = A/Au = 0.005/0.1 = 0.05 users(b) C = 5,Au = 0.1,GOS = 0.005, from the chart,A = 1.13 ⇒ U = A/Au = 1.13/0.1 ' 11 users(c) C = 10,Au = 0.1,GOS = 0.005, from the chart,A = 3.96 ⇒ U = A/Au = 3.96/0.1 ' 39 users(d) C = 20,Au = 0.1,GOS = 0.005, from the chart,A = 11.1 ⇒ U = A/Au = 11.1/0.1 ' 111 users(e) C = 100,Au = 0.1,GOS = 0.005, from the chart,A = 80.9 ⇒ U = A/Au = 80.9/0.1 ' 809 users



Example 5

Trunked mobile networks A, B, and C provide cellular services in an urbanarea with 2 million residents. The (no. of cells, no. channels/cell) for thethree providers are (394,19), (98,57) and (49,100). Find the number ofusers that can be supported at 2% blocking if each user averages twocalls/hour at an average call duration of 3 min. Find the percentage marketpenetration for each provider.Solution:System A: GOS = 0.02,C = 19, Au =λH = 2(3/60) = 0.1 Erlangs. For GOS = 0.02and C = 19 ⇒ A = 12 Erlangs U = A/Au = 12/0.1 = 120 ⇒total number of subscribers is 120×394 = 47289System B: GOS = 0.02,C = 57, Au =λH = 2(3/60) = 0.1 Erlangs. For GOS = 0.02and C = 57 ⇒ A = 45 Erlangs U = A/Au = 45/0.1 = 450 ⇒total number of subscribers is 450×98 = 44100System C: GOS = 0.02,C = 100, Au =λH = 2(3/60) = 0.1 Erlangs. For GOS = 0.02and C = 100 ⇒ A = 88 Erlangs U = A/Au = 88/0.1 = 880 ⇒total number of subscribers is 880×49 = 43120Market penetration: A: 47280/2,000,000=2.36%; B:44100/2,000,000=2.205%;C: 43120/2,000,000=2.156%



Example 6

Given a city area: 1300 mile2, with 7-cell reuse pattern, cell radius=4 milesand frequency spectrum: 40MHz with 60KHz channel bandwidth. AssumeGOS=2% for an Erlang B system, if the offered traffic per user is 0.03Erlangs, compute (a) the no. of cells in the service area (b) the no. ofchannels per cell (c) traffic intensity of each cell (d) the maximum carriedtraffic (e) the total no. of users can be served for the GOS (f) the no. ofmobiles per unique channel (g) the theoretical maximum no. of users thatcould be served at one time by the system.Solution:(a) Acell = 1.5

p3R2 = 2.5981×42 = 41.57 square mile. Total no. of cells

Nc = 1300/41.57 = 31 cells.(b) Total no. of channels per cell C = 40MHz/(60kHz×7) = 95 channels/cell.(c) C = 95,GOS = 0.02 ⇒ traffic intensity per cell A = 84 Erlangs/cell.(d) Maximum carried traffic=no. of cells × traffic intensity per cell =31×84 = 2604 Erlangs.(e) Traffic/user=0.03 Erlangs ⇒ Total no. of users = 2604/0.03=86800 users(f) no. of mobiles per channel= no. of users/no. of channels =86800/(40MHz/60 kHz)=130 mobiles/channel.(e) The theoretical maximum no. of served mobiles (all channels areoccupied)= C ×Nc = 95×31 = 2945 users



Example 7

A hexagonal cell within a four-cell system has a radius of 1.387 km. A totalof 60 channels are used within the entire system. If the load per user is0.029 Erlangs and λ= 1 call/hour, compute the following for an Erlang Csystem which has a 5% probability of delayed call: (a) how many user persquare kilometer will the system support? (b) the probability that a delayedcall will have to wait for more than 10 seconds? (c) the probability that acall will be delayed for more than 10 seconds?Solution:Cell area=2.598× (1.387)2 = 5km2. no. of channel per cell C = 60/4 = 15channels.(a) For Erlang C of 5% probability of delay with C = 15, the trafficintensity=9.0 Erlangs.no. of users=total traffic intensity/traffic per user = 9/0.029=310 users for5 km2 or 62 users/km2

(b) H = Au/λ= 0.029hour = 104.4 second.p[delay> 10|delay] = exp(−(C −A)t/H) = exp(−(15−9)10/104.4) = 56.29% (c)p[delay> 0] = 5% = 0.05p[delay> 10] = p[delay> 0]p[delay> 10|delay] = 0.05×0.5629 = 2.81%


Improving Coverage and Capacity Cellular Systems

Cell Splitting

Let R ↓ and keeps D/Runchanged

Pr[at old cell boundary] ∝ Pt1R−n

Pr[at new cell boundary] ∝ Pt2(R/2)−n

for n = 4

Pt2 = Pt1

16



Cell Splitting

Example 8

Assume each BS uses 60channels and large cell radius of 1km and microcell radius of 0.5km. Find the number of channelsin a 3 km by 3 km square aroundA when (a) without the use ofmicrocells (b) the labeledmicrocells are used (c) all originalBS are replaced by microcells.Solution:(a) 5×60 = 300 (b) (5+6)×60 = 660(2.2x) (c) (5+12)×60 = 1020 (3.4x)



Sectoring

Increasing S/I ratio, keeping cell radius R the same anddecreasing D/R ⇒ D ↓⇒ N ↓⇒ frequency reuse ↑ ⇒ cluster sizeN can be reduced because of S/I is improved.



Sectoring, cont’d



Microcell Zone



Microcell Zone


Channel Assignment Strategies Cellular Systems

Channel Assignment Strategies

Fixed channel assignment

each cell is allocated to a predetermined set of voice channels ⇒the call is blocked is all the channels are occupied.borrowing strategy: a cell is allowed to borrow channels from aneighboring cell if all of its own channels are occupied.MSC supervises the borrowing procedure to ensure no disruptingcalls or interference with any of the calls in progress in the donorcell.

Dynamic channel assignment

the serving BS request a channel from MSC whenever a callrequest is made.following an algorithm considering the likelihood of futureblocking in the cell, the frequency of use of the candidate cell, thereuse distance of the channel and other cost functions.MSC needs to collect real-time data on channel occupancy, trafficdistribution, and radio signal strength indicator (RSSI) of allchannels on a continuous basis. ⇒ increasing storage andcomputational load on the system.


Handoff Strategies Cellular Systems

Handoff

When a mobile moves into a different cell when a conversationis in progress, the MSC automatically transfer the call to a newchannel belonging to a new BS.

Many handoff strategy prioritize handoff requests over callinitiation requests when allocating an unused channel.

Handoff threshold: a signal level slightly stronger than theminimum usable signal for acceptable voice quality.

∆= Pr,handoff −Pr,min.usable

∆ too large ⇒ unnecessary handoffs burden MSC

∆ too small ⇒ may be insufficient time to complete a handoffbefore a call is lost



Handoff Scenario at Cell Boundary



Handoff Decision

Monitor the signal level of MS for a period of time

to ensures MS is actually moving away from the serving BS.

Dwell time

The time over which a call may be maintained within a cell,without handoff, depending on propagation, interference,distance between the MS and BS, and other time varyingeffects

Monitor RSSI

BS monitors the signal strengths of all its reverse voicechannels to determined the relative location of each MS.

Locator receivers monitor the signal strength of users inneighboring cells need of handoff and report RSSI to MSC.

Mobile assisted handoff (MAHO)

MS measures the received power from the surrounding BS’sand continuously reports to the serving BS.

Faster handoff time than first generation analog system

Suited for microcellular environmentsVincent W.-S. Wuen Mobile Communications 47


Handoff Considerations

Prioritizing Handoffs

Guard channel concept: reserves a fractional of total availablechannels exclusively for handoff ⇒ reducing total carried traffic⇒ combining with dynamic channel assignment to offerefficient spectrum utilization

Queuing of handoff requests: using the finite time intervalbetween the time the received signal levels drops below thehandoff threshold and the time the call is terminated ⇒ notguarantee a zero probability of forced termination



Handoff Considerations

Umbrella cells

Cell dragging

Hard handoff

Soft handoff


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