telecoms funda freq reuse erlangs
TRANSCRIPT
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Fundamentals of CellularFundamentals of Cellular
NetworksNetworks
David TipperAssociate ProfessorAssociate Professor
Graduate Program in Telecommunicationsand Networking
University of PittsburghSlides 4Slides 4
TelcomTelcom 27202720
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Cellular ConceptProposed by Bell Labs 1971Geographic Service divided intosmaller cells
Neighboring cells do not use sameset of frequencies to preventinterference
Often approximate coverage
area of a cell by a idealizedhexagon
Increase system capacityby frequency reuse.
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Cellular Networks
Propagation models represent cell as a circular area Approximate cell coverage with a hexagon - allows easier
analysis
Frequency assignment of F MHz for the system
The multiple access techniques translates F to T traffic channels
Cluster of cells K = group of adjacent cells which use all of thesystems frequency assignment
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Cellular Concept Why not a large radio tower and large service area?
Number of simultaneous users would be very limited(to total number of traffic channels T)
Mobile handset would have greater powerrequirement
Cellular concept - small cells with frequency reuse
Advantages lower power handsets
Increases system capacity with frequency reuse
Drawbacks: Cost of cells
Handoffs between cells must be supported
Need to track user to route incoming call/message
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Cellular Concept (cont)
Let T = total number of duplex channels
K cells = size of cell cluster (typically 4, 7,12, 21)
N = T/K = number of channels per cell
For a specific geographic area, if clusters arereplicated M times, then total number ofchannels
system capacity = M xT
Choice of K determines distance between cells using
the same frequencies termed co-channel cells K depends on how much interference can be
tolerated by mobile stations and path loss
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Cell Design - Reuse Pattern
Example: cell cluster size K = 7, frequencyreuse factor = 1/7, assume T = 490 totalchannels, N = T/K = 70 channels per cell
B
A
E
C
D
G
F
B
A
E
C
D
G
F
B
A
E
C
D
G
F
Assume T = 490 total channels,
K = 7, N = 70 channels/cell
Clusters are replicated M=3times
System capacity = 3x490 = 1470
total channels
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Cluster Size
132
4
3 1 4
21
23
41
31
42
6 75
1
1
11
1
1
K = 4 (i =2, j=0)
K = 7 (i =2, j =1)2
98
6
71
3
1011
124
5
65
8
6
7
9
8
124
5
3
1011
124
910
11 K = 12 (i=2, j=2)
From geometry of grid of hexagons only
certain values of K are possible if replicatingcluster with out gaps
K = i2 + ij + j2 where i and j are non-negativeintegers
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Cellular Concepts
To find co-channel neighbors of a cell, move i cells along anychain of hexagons, turn 60 degrees counterclockwise, and move jcells (example: i=2, j=2, K=12)
K = i2 + ij + j2
r = cell radius
Area of hexagon = 2.61 r2
d = distance to co-channel cell
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Cellular Concepts
From hexagonal geometry The quantity d/r is called the co-channel reuse ratio
K = i2 + ij + j2
r = cell radiusArea of hexagon = 2.61 r2
d = distance to co-channelcell
Krd 3=Krd 3/ =
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Frequency ReuseSITE A SITE B
RSSI, dBm
C/I
Distance
r
d
-60
-90
-120
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Frequency Reuse
A
B
B
A
B
A
B
AA
B
A
B
A
B
K = 19
Relate cluster size to carrier to co-channel interference ratio C/Iat the
edge of a cell
propagation model of the form
Pr= PtLd-
L = constant depending on frequency,
d = distance in meters, = path loss coefficient,Then at edge of a cell in center of
network the C/I is given by
=
== d
r
LdP
LrP
I
C
t
ij
t
6
16
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Frequency ReuseSolving for d/r results in
Remember ,
which results in
/16
=I
C
r
d
Example: Consider cellular
system with a C/I requirementof C/I = 18 dB and a suburban
propagation environment with
= 4 , determine the minimumcluster size.
18 dB => 63.0957,
K = 1/3 x (6 x 63.0957)0.5 =
6.4857 ,
Since K must be an integerround up to nearest feasiblecluster size => K = 7
/26
3
1
=
I
CK
Krd 3/ =
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Frequency Reuse
Note one can relate C/I to K for various path lossgradients
Remember
=d
r
I
C
6
1
=d
rdb
I
C10log107815.7
( )KdbIC 10log576.1 +=
Krd 3/ =
3 4 7 12 13 190
5
10
15
20
25
30
cluster size N
Sr
indB
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Frequency Planning
Typical C/I values used in practice are 13-18 dB.
Digital systems have lower C/I (13-15 dB)
Once the frequency reuse cluster size and frequencyallocation determined frequencies must be assigned tocells
Must maintain C/I pattern between clusters.
Within a cluster seek to minimize adjacent channelinterference
Adjacent channel interference is interference fromfrequency adjacent in the spectrum
f2f1
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Frequency Assignment
Typical C/I values used inpractice are 13-18 dB.
Once the frequency reuse
cluster size and frequencyallocation determined
frequencies must be assigned tocells
Must maintain C/I patternbetween clusters.
Within a cluster seek to
minimize adjacent channelinterference
Adjacent channel interference isinterference from frequencyadjacent in the spectrum
Example: You are operating a cellularnetwork with 25KHz NMT trafficchannels 1 through 12. Labeling the
traffic channels as {f1, f2, f3, f4, f5, f6, f7,f8, f9, f10, f11, f12}
Place the traffic channels in the cellsbelow such that a frequency reuse
cluster size of 4 is used and adjacent
channel interference is minimized
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Sectoring1
23
21
3
120 sectoring
Sectoring
used to improve the C/I ratio
make cluster size K smaller
Use directional antennas rather than omni-directional
cell divided into 3 (120o sectoring) or 6 (60o sectoring) equallysized sectors
Frequencies/traffic channels assigned to cells must partitioned
into 3 or 6 disjoint sets
Reduces the number of co-channel cells causing interference
Disadvantages: need intra-cellhandoff, increases complexity
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Sectoring
43
52
1
67
55
5
55
5
12
32
1
3
120 sectoring
120o sectoring reduces number of interferersfrom 6 to 2
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Sectored Frequency Planning
Example: Allocatefrequencies for a GSMoperator in U.S. PCS B-block who uses a 7 cellfrequency reuse pattern with3 sectors per cell
Use a Frequency Chart available from FCC web site
Groups frequencies into 21categories Cells A-G andsectors 1-3 in each cell
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Sectored Frequency Planning
Example: Allocate frequencies for a AMPS operator in cellular
B-block who uses a 7 cell frequency reuse pattern with 3 sectorsper cell
Use a Frequency Chart available from FCC web site
Groups frequencies into 21 categories Cells 1-7 and sectors A-B ineach cell
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Traffic Engineering
Given or N = T/K traffic channels per cell what is GoS or how many users can besupported for a specific GoS
Required grade of service? Usually 2% blocking probability during busy hour Busy hour may be
1. busy hour at busiest cell
2. system busy hour3. system average over all hours
Basic analysis called Traffic Engineering orTrunking same as circuit switched telephony, use Erlang B
and Erlang C Models
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Traffic Engineering
Estimate traffic distribution? Traffic intensity is measured in Erlangs
(mathematician AK Erlang)
One Erlang = completely occupied channel,e.g., a radio channel occupied for 30 min.per hour carries 0.5 Erlangs
Traffic intensity per user AuAu = average call request rate x average holding
time H
Total traffic intensity = traffic intensityper user x number of users = Au x nu
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Traffic Engineering
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Erlang B Model M/M/C/C queue
To estimate the performance of a trunked system use the ErlangB queueing model
C identical servers process customers in parallel.
Customers arrive according to a Poisson process Customer service times exponentially distributed
The system has a finite capacity of size C, customers arrivingwhen all servers busy are dropped
Blocked calls cleared model (BCC)
Analyze using Markov Process of n(t) number of customers inthe system at time t
)1( be P
bP
e
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M/M/C/C
32 C)1(C
Cj111 )1()( jjj jj
10 0j
Cj1)( ccC
Let i denote the steady state probability of icustomers in thesystem, then the state transition diagram for n(t) is given by
Flow balance equations
Solve determining i in terms of 0 , then sum of probabilities = 1
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M/M/C/C
c
n
n
c
c
n
a
c
a
acB
0!
!),(
Probability of a customer being blocked B(c,a) =i
B(c,a) Erlangs Bformula, Erlangs blocking formulaErlang B formula can be computed from the recursive formula
Valid for M/G/c/c queue
),1(
),1(),(
acBac
acBaacB
Usually determined from table or charts
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Traffic Engineering
Erlang B blocking probabilities
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Erlang B Charts
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Traffic Engineering Erlang B table
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Traffic Engineering Erlang B Table
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M/M/C/C
)),(1( acBe
)),(1( acBc
ae
)),(1( acBa
L
Other performance metrics can be related to Erlang B formula B(c,a)The carried load
Effective throughput of the system
Mean server utilization
Mean number in the system
Average delay in the system
1W
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Traffic Engineering Example
Consider a single analog cell tower with 56 traffic channels, when allchannels are busy calls are blocked. Calls arrive according to aPoisson process at a rate of 1 call per active user an hour. During thebusy hour 3/4 the users are active. The call holding time isexponentially distributed with a mean of 120 seconds.
(a) What is the maximum load the cell can support while providing 2%call blocking?
From the Erlang B table with c= 56 channels and 2% call blocking themaximum load = 45.9 Erlangs
(b) What is the maximum number of users supported by the cell duringthe busy hour?
Load per active user = 1 call x 120 sec/call x 1/3600 sec = 33.3 mErlangs
Number active users = 45.9/(0.0333) = 1377
Total number users = 4/3 number active users = 1836
Determine the utilization of the cell tower = /c = 45.9/56 = 81.96%
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Erlang C M/M/C Model C identical servers processes customers in parallel.
Customers arrive according to a Poisson process
Customer service times exponentially distributed
Infinite system capacity.
Blocked calls delayed model (BCD)
Analyze using Markov Process of n(t) number ofcustomers in the system at time t
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M/M/C
a
C
The server utilization ()
The traffic intensity (a) offered load (Erlangs)
The stability requirement
Ca
C
a1
With traffic intensity aErlangs, Cis the minimum number of servers requirement.
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M/M/C
3 CC)1(C
2
Cj111 )1()( jjj jj
10 0j
Cj11)( jjj CC
Let i denote the steady state probability of icustomers in thesystem, then the state transition diagram for n(t) is given by
Flow Balance equations
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M/M/C
1jjk
Cj
Cj1jj
C
Solve determining i in terms of 0 , then sum of probabilities = 1
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M/M/C (5)
Ci
i
ii
a1;0
!
1
0
0
)()!1(!
1C
n
cn
acc
a
n
a
Cici
i
icc
a;0
!
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M/M/C (6)
1
0)()!1(!
)()!1(),(
c
n
cn
c
cj
j
acc
a
n
a
acc
a
acC
Probability of a customer being delayed C(c,a)
C(c,a) Erlangs Cformula, Erlangs delay formulaErlangs second formula
In the telephone system, C(c,a) represents a blocked call delayed (BCD).
Can compute C(c,a ) from Erlang B value
)),(1(
),(),(
acBac
acBcacC
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M/M/C (7)
1
),(1
),(
q
qq
q
q
WW
ac
acCL
W
aLL
acCac
aL
Other performance measures expressed in terms of C(c,a)
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M/M/C (8)
)1(
),(
1ln
c
acC
p
tp
Distribution of the waiting time in the queue
The pth percentile of the time spent waiting in the queue tp
tcq eacCtwP
)1(),(1
Note: p> 1 - C(c,a)
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Traffic Engineering Example 2
A service provider receives unsuccessful call attempts to wirelesssubscribers at a rate of 5 call per minute in a given geographic
service area. The unsuccessful calls are processed by voice mail andhave an average mean holding time of 1 minute. When all voice mail
servers are busy customers are placed on hold until a serverbecomes free.
Determine the minimum number of servers to keep the percentage of
customers placed on hold < or equal to 1%The offered load is a = 5 call per minute x 1 minute/call = 5 Erlangs
From the Erlang C tables 13 servers are needed.
Determine the .995% of the delay in access the voice servers
With p = .995, C(c,a) = .01, c = 13, and = 1
)1(
),(
1ln
=c
acC
p
t p
yields tp= .0866 minute = 5.2 secs
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Fix Channel Assignment Scheme
Market Study Demographics
Assume
Calls/subs during
Peak one hour with
Average holding time
Number of Subscribers
Per cell
Erlangs/cell
Assume GOS
( % call blocking
< 2 %)
Apply:
Erlang B
Number of Channels per cell and Number of channels per system
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Cell splitting
Cell Spitting
How can one increase capacitywhen hot spot occurs?
One approach insert lowpower microcell reusefrequencies A
Must be careful to not violate
cochannel interferencerequirements
Expensive!
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Frequency Reuse Partitioning
Split channels into two or more groups one
with lower power and smaller reuse cluster size
to increase capacity.
Requires handoffs within a cell.Must be careful to not violate cochannel
interference requirements
Frequency reuse partitioning
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Summary
Cellular Concept
Sectoring
Frequency Planning
Traffic Engineering
Frequency Reuse Partitioning