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‫دانشکده مهندس ی کامپیوتر‬
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‫مخابرات سیار (‪)40-626‬‬
‫سیستمهای سلولی‬
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‫نیمسال او ‪91-92‬‬
‫افشین ّ‬
‫همتیار‬
Most Widespread Example: GSM
 The total Bandwidth is divided into a number of
narrowband (200KHz) channels.
 8 Users are given time slots in each narrowband
channel.
 So GSM is a combination of FDMA and TDMA.
 Multiple access is orthogonal that means users
within the cell never interfere with each other.
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The GSM Specifications
 Access Method
FDMA/TDMA
 Frequency Band
900MHz and 1800MHz
 No. of Channels
125 radio carriers
 Max No. of user channels
125*8 = 1000 channels
 Channel Bandwidth
200KHz
 Uplink (MS  BS) Freq. BW.
890 to 915MHz
 Downlink (BS -> MS) Freq. BW
935 to 960MHz
 Modulation
Digital GMSK
(Gaussian Minimum Shift Keying)
 Speech Coding
RPE-LTP
(Regular Pulse Excited- Long Term Prediction)
 Speech Bit Rate
13Kbps
 Data bit Rate
12Kbps
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Why We Use Cellular Systems?
 Assume we have S frequency channels available for our
mobile system.
 For GSM, we have 125 frequency channels and 8 time slots
per channel thus S is equal to 1000.
 How many people can speak at the same time in a city with
that many channels?
 If we use 1000 channels for the whole city with one Base
station then obviously 1000 people can talk at the same time.
 Then, how many people are actually speaking simultaneously
with their phones in Tehran?
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Cells and Base Stations
 Divide the area into “Cells” with different “Base Stations”
 Frequencies/Timeslots/Codes reused at spatially-separated
locations.
 Cells should be far enough so that signals do not interfere.
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Mobile Switching Center
 Base Stations/”Mobile Switching Centers” (MSC) coordinate
handoff and control functions.
 Shrinking cell size increases capacity, as well as networking
cost and burden.
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Cell Shape
 Why hexagonal cells?
o They give the maximum distance to center for minimum
number of cells to cover an area.
 Are cells so uniform in reality?
o They are designed based on uniform design.
o In reality base stations are closed to designed locations.
o real Footprints should be simulated or measured in real
deployments.
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Reuse Concept
 S: Total number of channels
 K: Number of channels in each cell
 N: Number of cells that in total use all S
channels
 N cells form a “cluster”
 N is usually 1, 3, 4, 7, or 12
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Cluster Size (1)
Note that choice of cluster size (N) is independent
from actual size of cells, so for fair comparison,
assume identical cell sizes and decide on best value
of N.
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Cluster Size (2)
 If we use M clusters in an area, the total capacity (number
of users that can talk at the same time) will be:
C = M.S = M.K.N
 Assume, number of cells in the area is fixed (cell size is
fixed) thus M.N is fixed.
 Therefore , to maximize C, should maximize K (number of
channels per cell)
 S = K.N thus minimize N for highest capacity
 Decreasing N causes
Higher capacity but higher interference as well
 Therefore, for a given mobile system we should first specify
how much interference we can tolerate.
 Then, choose the smallest value of N that ensures that
amount of interference.
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
Distance between Cells
Same Cells
Adjacent Cells
R
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
No. of Channels per Cell
 For hexagonal cells we have:
N = i2 + i.j + j2  Reuse distance is D = R√(3N)
 Example: AMPS
o Total BW = 25MHz
o Each channel = 30KHz simplex
o For N = 4, 7, 12 we will have
104, 59 and 34 channels per cell
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Interference and System Capacity (1)
 The terminology of capacity for cellular system is not
related to Shannon capacity!
 Here capacity means the number of users a cellular
system can support.
 Co-channel interference inherent in cellular systems
due to frequency reuse .
 Mobile systems are designed to be
interference limited and not noise limited.
 Co-channel interference can not be reduced by
increasing Tx power, only can be reduced by having
enough separation between co-channel sites.
 Therefore, interference computation is the main way of
estimating capacity.
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Interference and System Capacity (2)
 How should we find the best possible N?
 The starting point in mobile system design is the
minimum acceptable Signal to Interference Ratio
(SIRmin ) level at receiver.
 Then, we need to find out the relation between SIRmin
and Nmin.
 Pr=P0(d/d0)-n
 S=P0(R/d0)-n (R is radius of the cell)
and Ii=P0(Di/d0)-n (Di is distance between co-channel cells)
 Ii is ith co-channel interference thus Di is the same for
all co-channel cells (Di=D).
 SIR=S/∑Ii=R-n/∑Di-n
=(D/R)n/NC (NC is the number of co-channel cells)
 For hexagonal cells NC=6 thus SIR=(D/R)n/6
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Interference and System Capacity (3)
 Q=D/R is Co-channel Reuse Ratio
 For Hexagonal cells Q=D/R=R√(3N)/R=√(3N)
 SIR=(√(3N))n/6  N=10(2log(6SIR)/n)/3
 Example1: AMPS  SIRmin=18dB=63.1
Assuming n=4  Nmin=7
 Example2: GSM  SIRmin=12dB=15.8
Assuming n=4  Nmin=4
 Example3: SIRmin=15dB=31.6
Assuming n=4  Nmin=7
Assuming n=3  Nmin=12
 So better propagation will lead to larger values of N,
which will decrease capacity.
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Channel Assignment (1)
 Fixed Assignment
o can also use borrowing in advances system
 Dynamic assignment
o Measure RSSI (Radio Signal Strength Indicator),
Traffic distribution, and channel occupancy
 Mostly fixed assignment used in practice.
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Channel Assignment (2)
 In reality, channel planning is a complex optimization
problem, that need to use special program.
 Part of mobile channels are devoted to signaling. Thus
we should to use better reuse ratio (for example 12
instead of 7)
 In CDMA systems in theory, reuse ratio “1” can be
used.
 In practice, we don’t assign co-channel frequencies to
neighboring cells to control interference levels.
 Also an “equivalent reuse ratio” can be defined for
CDMA systems.
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Adjacent Channel Interference (1)
 If Rx filters were ideal then “Adjacent Channel
Interference” was not important.
 But in reality filters are not ideal and so adjacent
channel signals may also enter the receiver.
 Highest Adjacent Channel Interference when desired
user at cell boundaries.
 In practice Adjacent channels are not used in the
same cell or even in neighboring cells.
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Adjacent Channel Interference (2)
 Example:
o In same cell scenario, if another user is much closer
to the base than the desired user, its adjacent
channel signal can cause significant interference.
o Assume the ratio of distance from the two sources
to the base (D1/D2), is equal to 20, then SIR =20-n
which for n=4 is equal to -52dB.
o If Rx filter slope is 20dB/oct, at least 6 channel
separation (each 200KHz) between users is
required.
 In practice some sort of “power control” is used (more
important in CDMA)
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Handoff (1)
 Need to change base stations as we cross cell
boundaries
 Sounds easy, but is not!
 Handoff (or Handover) mechanism should be such
that:
o Least number of handoffs
o More successful handoffs
 Threshold Setting:
o Lower threshold -> More call cutoff probability
o Higher Threshold  More Handoffs.
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Handoff (2)
 Signals should also be averaged over time, otherwise
signals get disconnected due to fading.
 Should also consider velocity in Handoff process.
 Should monitor other Base Station signals as well.
 Channel Reservation for Handoff
 Soft Handoff in CDMA systems.
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Trunking Theory (1)
 Lets assume we have to cover a city with our mobile
system.
 Simple question:
For a given number of subscribers,
how many channels should we assign to that area?
 In practice, for a telephony system when you want to
cover N subscribers, you do not assign N channel to
them. This is due to the fact that subscribers connect
to network only occasionally.
 For example, in an office with N employees, the
number of lines that talk at the same time is only a
fraction of N.
 Obviously we need to define an acceptable quality
level that based on that we can find required number
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of channels for a given N.
Trunking Theory (2)
 Trunking concept:
Allowing large number of users to share
relatively small number of channels based on the fact
users use the channel statistically over time
 Based on a quantitative measure of acceptable
service, N can be found.
 Acceptable service quality in trunking theory is defined
based on the measureable “Grade of Service” (GoS)_
parameter.
 GoS is usually defined based on the following two
parameters:
o “Blocking Rate” which is the probability of getting
a busy tone when trying to dial a number.
o “Waiting Period” to get the number through (for
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queued systems).
Trunking Theory (3)
 Basic definition:
 Blocked Call: A call that can not get through
 Holding Time: Average duration of a call (H in sec)
 Request Rate: Average number of requested calls
in unit of time for each user (λ in 1/sec)
 Erlang: One Erlang is the amount of traffic that will
completely occupy the channel for the given period
of time.
Example: If a channel in one hour is only occupied for
30 minutes then the traffic of that channel is 0.5 Erlangs.
 Traffic Intensity: Average occupancy of one or more
channel (A in Erlangs)
 GoS:
o Possibility of blockage of a call (Erlang B formula)
o Possibility of a connection with a delay more than a
specific value (Erlang C formula)
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Trunking Theory (4)
 Traffic parameters:
 Au: Average traffic offered by each user
 A: Offered traffic by U users
 AC: Average traffic of each channel
 C: Number of available channels
Au=λ.H  A=U.Au  AC=A/C
 Note that if too much traffic is offered to a system,
than the actual traffic supported will at most be C
Erlangs if C channels are available.
 The Gos defined for wireless system is different from
wired values:
 For wired system GoS is about 0.5%
 For wireless systems GoS of 2-5% is usually specified.
 For example for 2% GoS at peak hours, 2 out of 100
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calls attempted by subscribers will be blocked.
 You can guess what is the current GoS we have in Tehran!
Trunking Theory (5)
GoS Equations (Case 1: No queue)
 Users try to call; if get busy signal, try at a later time.
 Call requests are independent and have a Poisson
distribution:
λ=mean call arrival rate for all users=average of t1, t2, . . .
 Call duration (holding times) have exponential
distribution: 1/μ = average of τ1, τ2, . . .
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Trunking Theory (6)
GoS Equations (Case 1: No queue)
 Then, for C channels in the system, it can be shown
that the probability of blocking is given by:
A=λ.H=λ./μ is the total traffic offered to the system
 The above equation is called the Erlang B formula.
(Bad) 1 ≥ GoS ≥ 0 (Good)
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Trunking Theory (7)
Capacity of an Erlang B System
Number of
channels
Capacity (Erlangs) for GoS
=0.01
=0.005
=0.002
=0.001
2
0.153
0.105
0.065
0.046
4
0.869
0.701
0.535
0.439
5
1.360
1.130
0.900
0.762
10
4.46
3.96
3.43
3.09
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12.0
11.1
10.1
9.41
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15.3
14.2
13.0
12.2
40
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27.3
25.7
24.5
70
56.1
53.7
51.0
49.2
100
84.1
80.9
77.4
75.2
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Trunking Theory (8)
Example 1
 How many users, assuming 0.1 Erlang traffic for
each user, can be supported for 0.5% blocking
probability for the following number of trunked
channels: 5, 10, 100 channels
 C=5
 1.13 Erlang traffic  11 users
 C=10  3.96 Erlang traffic  39 users
 C=100  80.9 Erlang traffic  809 users
 Quick observation: for smaller number of channels,
the ratio of users to channels is around 2 but for
higher C, the ratio is around 8
 having larger pool of channels creates more
efficient trunking.
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Trunking Theory (9)
Example 2
 Assume one million residents in a city.
 Assume 49 cells with 100 channels per cell assigned
 For 1% GoS and average calls of two 3 minutes calls
per hour, find percentage of market penetration.
 Au=λ.H=2(3/60)=0.1 Erlang
 C=100  A=84.1 Erlang (total traffic)
  U=A/Au=84.1/0.1=841 user/cell
 Total subscribers = 49x841= 41209
 Penetration =41209/1000000 x 100% = 4.12%
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Truncing Theory (10)
Example 3




City Area = 1300Km2
Hexagonal cells radius = 4Km , and N = 7
Total BW = 49MHz, and full duplex BW = 100KHz
GoS = 1%, and Offered traffic/user = 30 mErlang
 Find:
a) Number of cells
b) Number of channels/cell
c) Traffic of each cell
d) Maximum carried traffic
e) Total number of users that can be served
f) Maximum number of serves users that can talk
at the same time
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Truncing Theory (11)
Example 3
a) Cell area = 3√3/2 R2 ≈ 2.6R2 = 41.6Km2
 number of cells = 1300/41.6 ≈ 31 cells
b) Total number of channels/cell = 49MHz/100KHz/7 =
70 channels
c) C = 70, GoS = 1%  A = 56.1 Erlang/cell
d) Maximum carried traffic = 56.1x31 = 1739.1
e) Total number of users = 1739.1/0.03 = 57970 user
f) Maximum number of simultaneous calls = number
of all channels = 70x31 = 2170 calls
So, about 2170/57970 x100% = 3.7% of users in
the same area can talk at the same time.
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Trunking Theory (12)
GoS Equations (Case 2: Blocked users queued)
 In this scenario, blocked users will enter a queue.
 The new model for such scenario is called Elrang C
formula.
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Trunking Theory (13)
Channel Distribution
 For example, if we have 10 channels, what happens if
we divide the set to two 5 channel sets?
 Using bigger channel pools is better in statistical access
scenarios.
 For the above example:
 for 10 channels  4.46 Erlang
 for 5 channels  1.36 Erlang
 1.36x2 = 2.72 < 4.46 Erlang
 A set of 10 channels about 60% more traffic than two 5
channel sets.
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Trunking Theory (14)
Trunking Efficiency
 A measure of efficiency of trunking systems is:
η = Traffic (Erlang)/Number of channels x 100%
 For smaller number of channels, the efficiency is
smaller.
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Capacity Increase (1)
 If we want to have more subscribers in an area, what
can we do?
 Some common approaches:
 Cell Splitting
 Interference Reduction
o Sectoring
o Antenna Adjustment
o Voice Activity Monitoring
o Frequency Hopping
o Smart Antennas
o Interference Cancellation
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Capacity Increase (2)
Cell Splitting
 Diving cells into smaller cells.
 More BTSs required with smaller height and smaller
power.
 Use smaller cells (micro-cells and pico-cells) in more
crowded areas.
 Frequency assignment more complex in various-size
cells, but no other choice.
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Capacity Increase (3)
Sectoring
 Using directional antenna vs. omni-directional antennas
 Why using directional antenna reduces interference?
 Use of 120° antenna:
 for N=3  number of co-channels down from 6 to 3
 SIR: 17dB  20dB
 for N=7  number of co-channels down from 6 to 2
 SIR: 17dB  21.7dB
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Capacity Increase (4)
Sectoring
SIR=(√(3N))n/NC
Omni Antenna  NC= 6
120° Antenna  NC= 2
60° Antenna  NC= 1
 So, by sectoring can get higher SIR and so can use
smaller N.
 Disadvantages:
o More equipment at BTS sites
o More handoffs
o Smaller trunking efficiency due to dividing channels
in each cell into three groups (Erlang B formula)
 In general, sectoring is widely used in practical mobile
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deployments.
Capacity Increase (5)
Sectoring Example
 Assume GoS=1%, Avg. call duration=2minutes,
Avg. 1 call per hour, total number of channels =395,
and N=7
 For omni antenna:
395/7 channel  44.2 Erlang traffic  1326 call/hour
 For 120° antenna:
SIR increases by a factor of 3 for 7-reuse
395/7/3 channels/sector  11.2 Erlang/sector  33.6 Erlang
 1008 call/hour
So, if we don’t change N, we improve SIR, but lose capacity.
 For 60° antenna:
SIR increases by a factor of 6  can reduce N from 7 to 4
395/4/6 channels/sector  9 Erlang/sector  54 Erlang
 1620 call/hour
So, if we can reduce N, by using sectored antenna, we may
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regain the lost trunking efficiency.
Capacity Increase (6)
Other Means
 Antenna height and tilt adjustment
 Voice Activity
 Every user is only talking at about 40% of time
 V.A. is efficiency used in CDMA
 Also incorporated in GSM as DTX (discontinuous transmission)
 Frequency Hopping
 Use a set of frequencies that can be swapped randomly
over time, instead of one fixed channel.
 Hop rate around 200KHz (slow rate hopping)
 Since all channels are not used all the time statistically
reduces the interference (~2dB lower SIR requirement)
 In theory, can marginally achieve N=1 (full reuse)
 In practice, N=3 and N=4 are common
 Widely used in GSM  also improves resistance to fading
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 Two modes in GSM: Baseband and Synthesized
Summary
 In a cellular design always pay attention to the
roles of two main factors:
 Interference
 Cluster size, Trunking Efficiency and Capacity
 A change in system may improve one but degrade
another one.
 In general, mobile planning and optimization is
a quite complicated and time consuming task
relying mainly on lots of experience.
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