1(48) An Analysis of the Throughput of Packet Radio Networks André Stranne Licentiate thesis...

1(48)

An Analysis of the Throughput of

Packet Radio Networks

An Analysis of the Throughput of

Packet Radio Networks

André Stranne

Licentiate thesis presentation

Lund, 16/5 – 2003

André Stranne

Licentiate thesis presentation

Lund, 16/5 – 2003

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OutlineOutline

• Introduction and background

• System model

• Packet collision analysis

• Interfering energy analysis

• Approximations

• Summary


• System model



• Approximations

• Summary

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Introduction and backgroundIntroduction and background

An Analysis of the Throughput of Packet Radio Networks


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Data communicationsData communications

WirelineWireline WirelessWireless

RadioRadio

10110100101101011010010110

Fixed phoneADSL

Ethernet

Fixed phoneADSL

EthernetGSM

Bluetooth3G

GSMBluetooth

3G

Internet IRIR SoundSound

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Radio networksRadio networks

Circuit switchedCircuit

switchedPacket

switchedPacket

switched

Phone callsPhone calls

GSM(3G)GSM(3G)

Internet dataInternet data

BluetoothGPRS(3G)

BluetoothGPRS(3G)

10110100101101011010010110 11101110 101101 011011

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00 10110111101110 0101

011011

?OK OK OK

ThroughputThroughput

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- What data rates can be expected in packet radio

networks?

- What data rates can be expected in packet radio

networks?

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Analysis: How to do it?Analysis: How to do it?

• Analyze real packet radio networks– Realistic but not very convenient

• Create mathematical models of packet radio networks

• Analyze real packet radio networks– Realistic but not very convenient

• Create mathematical models of packet radio networks

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OutlineOutline


• System model



• Approximations

• Summary


• System model



• Approximations

• Summary

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Main featuresMain features

• Networks, units

• Packet transmissions

• Packet-based slow frequency hopping

• Different packet lengths

• Networks, units

• Packet transmissions

• Packet-based slow frequency hopping

• Different packet lengths

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System modelSystem model

• System• Networks• Units

• System• Networks• Units

Unit

NetworkInterferenceInterference

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Packet transmissionsPacket transmissions

• Frequency channels• Packet-based frequency hopping

• Frequency channels• Packet-based frequency hopping

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Performance measurePerformance measure

• Throughput = achieved data rate• Throughput = achieved data rate

NetworkTransmitted

data

Lost data

Throughput

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Packet reception modelsPacket reception models

• What is the cause of packet losses in the networks?

– Packet collision analysis:

– Interfering energy analysis:

• What is the cause of packet losses in the networks?

– Packet collision analysis:

– Interfering energy analysis:

CollisionsCollisions

Interferingenergy

Interferingenergy

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OutlineOutline


• System model



• Approximations

• Summary


• System model



• Approximations

• Summary

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Collision analysisCollision analysis

• Packet reception model

– Packet losses from packet collisions



?

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• Probability of collision?

• Probability of successful packet reception?

• Throughput?

• Probability of collision?

• Probability of successful packet reception?

• Throughput?

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Calculation outlineCalculation outline

• Calculate how probable n collisions are with packets transmitted from a single interferer j,

• Calculate how probable n collisions are with packets transmitted from a single interferer j,

( )jp n( )jp n

• Hard to find that expression

• Details in the thesis

• Hard to find that expression

• Details in the thesis

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• Calculate how probable n collisions are with packets transmitted by all interferers

• Calculate how probable n collisions are with packets transmitted by all interferers

Assumption: independent packet transmissionsAssumption: independent packet transmissions

1( ) ( ) ... ( )Np n p n p n 1( ) ( ) ... ( )Np n p n p n

Convolutions of PDFs (probability distribution functions)Convolutions of PDFs (probability distribution functions)

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• Sum the probabilities for the number of collisions that can be tolerated for successful packet reception

• If no collisions can be tolerated:

• Sum the probabilities for the number of collisions that can be tolerated for successful packet reception

• If no collisions can be tolerated:

(success) ( 0)p p n (success) ( 0)p p n

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Bluetooth exampleBluetooth example

• System of Bluetooth ”piconets”

• 79 frequency channels

• System of Bluetooth ”piconets”

• 79 frequency channels

P acket selection probability r = [ 1=3 1=3 1=3 ]Header length h = [ 150 158 158 ] ¹ sG uard interval length d = [ 275 269 271 ] ¹ sP acket duration L = [ 625 1875 3125 ] ¹ sP ayload bit rate D = [ 1 1 1 ] bits/ ¹ s

625 μs

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Single interferer!

79 channelsLow collision probability!

No collisions

2 collisions1 collision

Prob. of number of collisions

from single interferer

Prob. of number of collisions

from single interferer

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Medium sizepacket type

20 interferers

40 interferers

60 interferers

80 interferers100 interferers

All interferers!

Prob. of total

number of collisions

Prob. of total

number of collisions

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More interferers

More collisions

More lost packets

Reduced data rate

No interferers

26

Network throughput

Network throughput

50 %

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Increasing systemthroughput

Decreasing systemthroughput

Maximum systemthroughput

Total throughputfor all piconets in

the system

System throughput

System throughput

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OutlineOutline


• System model



• Approximations

• Summary


• System model



• Approximations

• Summary

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Energy analysisEnergy analysis

• Collision-based packet reception model• Collision-based packet reception model

no collision

collision

collision

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• New packet reception model

– More detailed

– The collision analysis does not account for• the duration of the packet overlaps in the collisions

• the strength of the received interfering signals

– Interfering energy

• New packet reception model

– More detailed

– The collision analysis does not account for• the duration of the packet overlaps in the collisions

• the strength of the received interfering signals

– Interfering energy

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• Interfering energy• Interfering energy

Time

1

2

3

1 2 3

Single frequency channel

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Time

1

1I

Length of overlap

1g

Signal strength

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Time

1

2

2I

2g

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Time

1

2

3

3g

3I

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3

1I i i

i

E I g

3

1I i i

i

E I g

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• Basically the same as for the collision analysis• Basically the same as for the collision analysis

Variables fornumber of collisions

Variables fornumber of collisions

Variables foramount of interfering energy

Variables foramount of interfering energy

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• Link budget• Link budget

E ¤ective isotropic radiated power E IR P = 8 dBmP ropagation path loss (reference units) L P L ,ref = 4 dBP ropagation path loss ( interfering units) L P L ,i nt er f = [ 4 18 24 ] dBR eceiver loss L r = 2 dBM inimum received SN IR °m in = 20 dB

Noise …gure F sys = 20 dBNoise bandwidth B = 60 dB H zR eference noise power density N 0 = -174 dBm/ H z

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Distance betweeninterferers and

reference nodes

Increasinginterference

Network throughput

Network throughput

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Bluetooth exampleBluetooth exampleSystem

throughput

System throughput

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OutlineOutline


• System model



• Approximations

• Summary


• System model



• Approximations

• Summary

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Complexity issuesComplexity issues

• Exact expressions complicated

• Simple approximations needed

– For the collision-based analysis, we have such an approximation

– Approximation of energy-based analysis is beyond the scope of this thesis

• Exact expressions complicated

• Simple approximations needed

– For the collision-based analysis, we have such an approximation

– Approximation of energy-based analysis is beyond the scope of this thesis

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Full expression / approximationFull expression / approximationR ¹ =

P M ¹

¸ =1 r ¹ ¸D ¹ ¸ l¹ ¸ p (success; ¹ ; ¸ ; nmax )P M ¹

k=1 r ¹ kL ¹ k

p(success; T ¹ ¸ ; nmax ) =nm a xX

n=0

p(n)

p(n) = p1(n) ¤ ::: ¤ pN ¡ 1(n)

pj (n) =1X

m=0

µ1 ¡

1q

¶m¡ nµ1q

¶n µmn

¶pj (m)

pj (m) =1

P M ji=1 r j i L j i

M jX

k=1

r j k £

ÃZL j k¡ dj k

z=0pj ;a (mjk; z)dz+

ZL j k

z=L j k¡ dj k

pj ;g(mjk; z)dz

!

pj ;a (mjk; z) =½

±(m ¡ 1) z · L j k ¡ Tpj (m ¡ 1jz + T ¡ L j k) z > L j k ¡ T

pj ;g (mjk; z) =½

±(m) z · L j k ¡ Tpj (mjz + T ¡ L j k ) z > L j k ¡ T

y = z + T ¡ L j k

pj (mjy) =M jX

º=1

r j º pj (mjy; º )

pj (mjy; º ) =½

±(m ¡ 1) y · L j ºpj (m ¡ 1jy ¡ L j º ) y > L j º

eR =

P Mi=1D i r i li

³1 ¡ 1

q

(́N ¡ 1)L i ¡ di +

Pkrk(L k¡ dk)P

krkL k

P Mk=1 rkL k

ApproximationApproximation

Accurate enough?Accurate enough?

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Approximation error (Bluetooth example)Approximation error (Bluetooth example)

Bluetooth79 channels

10 channels

30 channels

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OutlineOutline


• System model



• Approximations

• Summary


• System model



• Approximations

• Summary

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ContributionsContributions

• Probabilistic framework for analysis of PRNs that transmit packets of different lengths

• Exact expressions for the throughput

• Approximate expression which can be used for strongly interfering networks

• Probabilistic framework for analysis of PRNs that transmit packets of different lengths

• Exact expressions for the throughput

• Approximate expression which can be used for strongly interfering networks

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PublicationsPublications

• F. Florén, A. Stranne and O. Edfors, Analysis of Slow Frequency Hopping Networks, NRS 01, Sweden, 2001

• F. Florén, A. Stranne, O. Edfors and B.-A. Molin, Throughput Analysis of Strongly Interfering Slow Frequency-Hopping Wireless Networks, VTC Spring 2001, Greece, 2001

• A. Stranne, F. Florén and O. Edfors, Evaluating a Performance Analysis of Slow FH Systems by Simulations, RVK 02, Sweden, 2002

• A. Stranne, F. Florén, O. Edfors and B.-A. Molin, Throughput of IEEE 802.11 FHSS Networks in the Presence of Strongly Interfering Bluetooth Networks, PIMRC 2002, Portugal, 2002

• F. Florén, A. Stranne and O. Edfors, Analysis of Slow Frequency Hopping Networks, NRS 01, Sweden, 2001

• F. Florén, A. Stranne, O. Edfors and B.-A. Molin, Throughput Analysis of Strongly Interfering Slow Frequency-Hopping Wireless Networks, VTC Spring 2001, Greece, 2001

• A. Stranne, F. Florén and O. Edfors, Evaluating a Performance Analysis of Slow FH Systems by Simulations, RVK 02, Sweden, 2002

• A. Stranne, F. Florén, O. Edfors and B.-A. Molin, Throughput of IEEE 802.11 FHSS Networks in the Presence of Strongly Interfering Bluetooth Networks, PIMRC 2002, Portugal, 2002

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PublicationsPublications

• A. Stranne, F. Florén, O. Edfors and B.-A. Molin, Throughput of Strongly Interfering Slow Frequency-Hopping Networks, submitted to IEEE Transactions on Communications, 2003

• A. Stranne, F. Florén, O. Edfors and B.-A. Molin, Analysis of Strongly Interfering Slow Frequency-Hopping Systems, Technical Report, Department of Electroscience, Lund University, 2003

• A. Stranne, F. Florén, O. Edfors and B.-A. Molin, Throughput of Strongly Interfering Slow Frequency-Hopping Networks, submitted to IEEE Transactions on Communications, 2003

• A. Stranne, F. Florén, O. Edfors and B.-A. Molin, Analysis of Strongly Interfering Slow Frequency-Hopping Systems, Technical Report, Department of Electroscience, Lund University, 2003

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Future workFuture work

• Approximations

• Development of system model

• Applications of the results

• Approximations

• Development of system model

• Applications of the results

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Special thanks toSpecial thanks to

1(48) An Analysis of the Throughput of Packet Radio Networks André Stranne Licentiate thesis...

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