Basics of Cellular CommunicationsGrade of Service, Interference, & Capacity

© Tallal Elshabrawy 2

The Cellular Concept

Early Mobile Communications Single, high powered transmitter with an antenna mounted on a tall

tower The Cellular Concept

Replace a single high power transmitter (large cell) with many low power transmitters (small cells) each providing coverage to only a small portion of the service area

© Tallal Elshabrawy 3

Frequency Reuse

EDF

AG

BC

EDF

AG

BC

EDF

AG

BC

Each base station is allocated a group radio channels to be used within a small geographic area

Base station in adjacent cells are assigned channel groups which contain completely different channels than neighboring cells

Cluster

Cluster

Cluster

A Cluster: A Group of N cells that which collectively use the complete set of available frequencies

Total Number of Channels in the System:

C=MkN=MS

M: Number of clusters within the systemK: Number of channels per cellN: Cluster SizeS: Number of available physical channels

© Tallal Elshabrawy 4

Locating Co-channel Cells Number of Cells per Cluster N = i2+ij+j2, i, j are non-negative integers To find nearest co-channel neighbor of a given cell

Move i cells along any chain of hexagons Turn 600 counter clockwise and move j cells

i=3, j=2, N=19

Grade of Service and Capacity (i.e., Blocking Probability)

© Tallal Elshabrawy 6

Trunking & Grade of Service

Trunked Radio System:

Each user is allocated a channel on per call basis, and upon termination of the call, the previously occupied channel is immediately returned to the pool of available channels.

Grade of Service:

A measure of the ability of a user to access the trunked system

GOS measures in cellular networks Probability that a call is blocked Probability a call experiences a delay greater than a certain queuing

time

© Tallal Elshabrawy 7

Traffic Intensity

Traffic intensity generated by each user: Au Erlangs Au = H

H : average duration of the callλ : average number of call requests per unit time

For a system containing U users and unspecified number of channels, Total offered traffic intensity: A Erlangs

A = UAu

In C channel trunked system, if the traffic is equally distributed among the channels, Traffic intensity per channel : Ac Erlangs

Ac = UAu/C

© Tallal Elshabrawy 8

Types of Trunked SystemsCalls Blocked Cleared Trunking SystemNo queuing provided for call requests and calls are blocked if no available channels

Calls Blocked Delayed Trunking SystemQueuing is provided to hold call requests. Calls are blocked if no available channels for a certain delay

Assumptions: Calls arrive as determined by Poisson distribution Infinite number of users Memoryless arrivals of requests : all users can request

channel at any time Probability of user occupying a channel is exponentially

distributed Finite number of channels available in the trunking pool

© Tallal Elshabrawy 9

Erlang B FormulaC

kC

k 1

AC!Pr blocking GOS (Calls Blocked Cleared)Ak!

M/M/C/C Queuing System

Exponential Interarrival Time(Poisson Arrival Process)

C Servers and Exponential Service Times

Service time distribution

Inter-arrival time distribution

Number of Servers

Queue Size

© Tallal Elshabrawy 10

Erlang B Curves

© Tallal Elshabrawy 11

Erlang C Formula

C

kC 1C

k 0

C-A t-

H

APr delay 0

A AA C! 1

C k!

Pr delay t =Pr delay 0 Pr delay t delay 0

Pr delay t =Pr delay 0 e =GOS (Calls Blocked Delayed)

Average Delay for Calls in Queued System

D=Pr dela

Hy 0

C A

© Tallal Elshabrawy 12

Erlang C Curves

Pr[delay>0]

Interference and Capacity in Cellular Systems

© Tallal Elshabrawy 14

The wireless environment constitutes a shared medium

Interference is the major limiting factor in performance of wireless systems in general

Types of Interference: Co-channel interference Adjacent channel interference

Interference & System Capacity

© Tallal Elshabrawy 15

EDF

AG

BC

EDF

AG

BC

EDF

AG

BC

EDF

AG

BC

EDF

AG

BC

EDF

AG

BC

EDF

AG

BC

Frequency reuse = 7Co-channel interfering cells for cell allocated with channel group A

Frequency reuse implies that several cells use the same set of channels

Co-channel Interference

© Tallal Elshabrawy 16

Co-channel Interference, SIR & System Capacity

Improving SIR1 by increasing P1 would result in a decrease in SIR2

Co-channel Interfering Cells

R

DR

BS 1

BS 2

MT 1

MT 2

P1

P2

H12

H11

H22

H21

BS: Base StationMT: Mobile TerminalPx: Transmitter power by base station xHxy: Small-scale & Large-scale channel between base station x and mobile terminal ySIRy: Signal-to-Interference Ratio at mobile terminal y

1 111

2 21

2 222

1 12

P HSIR

P H

P HSIR

P H

Improving BOTH SIR1 & SIR2 is possible by increasing the distance separation between BS1 and BS2

© Tallal Elshabrawy 17

D

i(2R’)j(2R’)

3R ' R

2where R is the Cell Radius

Q: Co-channel reuse Ratio

Distance Separation between Base Stations

© Tallal Elshabrawy 18

SIR Computations

XR

D

D

D

D

D

D

Assume interference from first tier (ring) of co-channel interferers

n

r 00

dP P

d

B

n n0 0

k Nn n

0 i 0 ii 1 i 1

P R d RSIR

P D d D

Di: interfering distance from ith co-channel interferenceNB No. of co-channel interfering sites

nn

B B

3N QSIR

N N

© Tallal Elshabrawy 19

n

n n n

RSIR

2 D R 2 D R 2 D

SIR Computations

X

R

D

D+R

D+R

D

D-R

D-R

Assume interference from first tier (ring) of co-channel interferers

n

r 00

dP P

d

B

n n0 0

k Nn n

0 i 0 ii 1 i 1

P R d RSIR

P D d D

n n n

1SIR

2 Q 1 2 Q 1 2 Q

Worst Case SIR

Di: interfering distance from ith co-channel interferenceNB No. of co-channel interfering sites

© Tallal Elshabrawy 20

nSIR Q , Q=D R 3N

Improving SIR means increasing cluster size, which corresponds to a decrease in system capacity

Decreasing the cell size does not affect the SIR as Q=D/R remains constant. A decrease in cell size corresponds to an increase in system capacity

SIR & System Capacity

© Tallal Elshabrawy 21

Example

N=7Q=4.6. Worst Case SIR = 49.56 (17 dB)

n n n

1SIR

2 Q 1 2 Q 1 2 Q

To design cellular system with worst performance better than 18 dB, N=9

Capacity reduction = 7/9

In First Generation cellular systems, sufficient voice quality is achieved when SIR = 18 dB

© Tallal Elshabrawy 22

Adjacent Channel Interference

Adjacent channel interference results from imperfect receiver which allows nearby frequencies to leak into the passband

Adjacent channel interference can be minimized through careful filtering and channel assignments

© Tallal Elshabrawy 23

Improving Coverage and Capacity in Cellular Systems: Cell Splitting

Subdividing a congested cell into smaller cells, each with its own base station and a corresponding reduction in antenna height and transmitter power Cell splitting Increasing system capacity by increasing the number of clusters in a given area

nSIR Q , Q=D R 3N

Decreasing Transmitter Power

The SIR is independent of transmitted power as long as it is the same for all base stations

rSNR P Noise The SNR must be a above a minimum threshold controlled by Pr

Why not make Transmitter Power as low as possible?