Cell Capacity And Reuse

8/7/2019 Cell Capacity And Reuse

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Cell Capacity And Reuse


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Outline..

Recapitulation

Cell capacity and reuse

Trunking Traffic

Examples


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Recap

If coverage of each base station is limited to asmall geographical region, we can achieve highcapacity.

Same frequencies/time slots/codes are reusedby spatially separated base stations.

A switching technique called handoffenables acall to proceed uninterrupted from one cell toanother.

The hexagonal model of cells is universallyaccepted. For hexagonal cells the reuse distance is D =

3N R

The reuse factor is given by q=D/R= 3N


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Cell Capacity and Reuse

Consider a cellular system with S duplexchannels.

We allocate k channels to each cell.

If these S channels be divided among N cells(cluster), we haveS=kN

If a cluster of N cells is replicated M times in thesystem, the total number of duplex channels, C,

can be used as a measure of the systemcapacityC = MkN = MS


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Contd

If the cluster size N is reduced keeping thecell size fixed, more clusters are required

to cover the entire area of interest, i.e.M C .

Smaller N (higher capacity) implies largercochannel interference, which may result

in a lower quality of service.


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Example

A 33 MHz BW is allocated to a FDD cellulartelephone system which uses two 25 kHzsimplex channels to provide full duplex voice

and control channels, compute the no. ofchannels available per cell if a system uses a. 4-cell reuse b. 7-cell reuse c. 12-cell reuse. If 1MHz of allocated spectrum is dedicated to

control channels, determine the distribution ofcontrol channels and voice channels in each cellfor each of the three systems.


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Solution Given: Total BW = 33 MHz

Channel BW kHz =25 x 2 simplex channels=50 kHz/duplex channel

Total available channels = 33000/50 = 660 channels (a). For N = 4

total no. of channels available per cell = 660/4= 165channels

(b). For N = 7total no. of channels available per cell = 660/7= 95channels

For N = 12total no. of channels available per cell = 660/12= 55

channels


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Solution contd..

Spectrum for control channels = 1 MHz No. of control channels =1000/50=20 (out of

660)

Voice channels = 660-20=640 640 channels would be allocated with 1 control

channel per cell i. For N = 4, we can have 5 control channels and

160 voice channels per cell. Thus 1 controlchannel and 160 voice channels would beassigned to each cell.


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ii. For N = 7, we can have 3 control channelsand 92 voice channels, two cells with threecontrol channels and 90 voice channels and onecell with two control channels and 92 voicechannels. In practice, however, each cell would

have one control channel, four cells would have91 voice channels and three cells would have 92voice channels.

iii. For N = 12, we can have eight cells with twocontrol channels and 53 voice channels and fourcells with one control channel and 54 voicechannels each. In an actual system, each cellwould have 53 voice channels, and four cellswould have 54 voice channels.


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Trunking and grade of service Available channels are much less than the no. ofusers. Users do not make a request for a channel

allocation at the same time.

Used to accommodate a large number of users. Users share the relatively small no. of channelsin a cell

Each user is allocated a channel on a per callbasis.

Upon termination of call, occupied channel isreturned to the pool of available channels.

Grade of Service : a measure of the congestionwhich is specified as a probability.


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Trunked systems: Blocked calls cleared No queuing, If no channels are available, the requesting user is blocked

without access

Free to try again Assumed that calls arrive as determined by a Poissondistribution.

Probability that a call is blocked, Erlangs B (GOS)

Blocked calls Delayed Queuing is provided. If a channel is not available, the request is delayed until a

channel becomes available. Probability that a call is not having an immediate access,

Erlangs C (GOS)


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Terms used

Setup Time : the time required to allocate a radiochannel to a requesting user.

Blocked call : a call that can not be completed at the timeof request due to congestion (lost call)

Holding Time : average duration of a typical call. Request Rate : The average number of calls per unit

time (). Traffic Intensity : Measure of channel time utilization

(Erlangs). Load : Traffic Intensity across the entire radio system. A channel kept busy for one hour is defined as having a

load of one Erlang.


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Contd..

Grade of Service : a measure of thecongestion which is specified as aprobability. The probability of a call being blocked

(Erlang B).

The probability of a call being delayed

beyond a certain amount of time (Erlang C).


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Traffic Theory

Average no. of MSs requesting service (request/time)average arrival time =

Average time for which MS requires serviceaverage hold time = T

Offered load a = T (Erlangs) E.g. in a cell with 100 MSs, on an average 30 requests

are generated during an hour(3600 s) with averageholding time T = 360 sec.

The arrival rate = 30/3600 requests. A channel kept busy for one hour is defined as oneErlang.

Offered load a = (30 calls/3600 sec)x(360 sec / call) = 3Erlangs


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Contd..

Average arrival rate during a short interval t is given by t. Assuming Poisson Distribution of service requests, the

probability P(n,t) for n calls to arrive in an interval oflength t is given by

Assuming to be the service rate, probability of eachcall to terminate during interval t is given by t.

Thus, probability of a given call requires service for time tor less is given by

tn

en

tnP PP !!!),(

tetS Q! 1)(


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Contd.. Probability of an arriving call being blocked is

Where S is the number of channels in a group

Probability of an arriving call being delayed is

where C(S,a) is the probability of an arriving call being delayedwith a load and S channels.

GOS

k

aS

aaSB

S

k

k

S

!!

!0 !

1

!),(

Erlangs B formula

Erlangs C formula

!

!

1

0 !1

1),(

s

k

ks

s

k

a

ass

a

aSS

a

aSC


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Contd..

capacity

nonblockedtrafficefficiency !

)(. channelstrunksofno

trafficnonroutedofportionsErlangsv!


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Traffic theory : Example 1

Consider a cell with S= 2 channels 100 Mobile Stations

Generating on an average 30 requests/hour Average holding T= 360 seconds (6 minutes) Efficiency?

Load a = T= (30 x 6)/60 = 3 Erlangs

Blocking probability, B(S,a) = 0.53 Total number of rerouted calls =30 x 0.53=16 Efficiency=3(1-0.53)/2= 0.7


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Traffic theory : Example 2 Consider a system with:

100 cells Each cell has S = 20 channels The users average = 2 calls/hour

The average duration of each call T is 3 min How many no. of users can be supported if the allowedprobability of blocking is 2%?

From Erlangs B chart, total carried traffic = 13Erlangs

Traffic intensity per usera = T = 0.1 Erlangs Total no. of users that can be supported per cell =

13/0.1= 130 users per cell Total no. of users that can be supported = 13,000


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Traffic theory : Example2 (contd..) Consider another system with:

100 cells Each cell has S = 20 channels The users average =2 calls/hour The average duration of each call (T) is 3 min How many numbers of users can be supported if the allowed

probability of blocking is 0.2%?

From Erlang B chart total carried traffic= 10 Erlangs Traffic intensity per user = T= 0.1 Erlang

Total no. of users that can be supported per cell=10/0.1=100 users/cell Total no. of users that can be supported = 10,000


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Traffic theory : Example 3 Consider another system with: Total no. of channels = 20

Probability of blocking constraint = 1%

Approach 1: Divide 20 channels in 4 trunks of 5 channels. Traffic capacity for one trunk (5 channels) = 1.36 Erlangs

Traffic capacity for four trunks (20 channels) = 5.44 Erlangs Approach 2: Divide 20 channels in 2 trunks of 10

channels. Traffic capacity for one trunk (10 channels) = 4.46 Erlangs Traffic capacity for 2 trunks (10 channels) = 8.92 Erlangs

Approach 3: Use 20 channels as such Traffic capacity for one trunk (20 channels) = 12.00 Erlangs


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Source:

1. Wireless Communications Principles and

practice by T. S. Rappaport, PearsonEducation

2. Internet

Documents

Cell Capacity And Reuse