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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
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• Approximations
• Summary
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Introduction and backgroundIntroduction and background
An Analysis of the Throughput of Packet Radio Networks
An Analysis of the Throughput of Packet Radio Networks
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An Analysis of the Throughput of Packet Radio Networks
An Analysis of the Throughput of Packet Radio Networks
Data communicationsData communications
WirelineWireline WirelessWireless
RadioRadio
10110100101101011010010110
Fixed phoneADSL
Ethernet
Fixed phoneADSL
EthernetGSM
Bluetooth3G
GSMBluetooth
3G
Internet IRIR SoundSound
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An Analysis of the Throughput of Packet Radio Networks
An Analysis of the Throughput of Packet Radio Networks
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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An Analysis of the Throughput of Packet Radio Networks
An Analysis of the Throughput of Packet Radio Networks
00 10110111101110 0101
011011
?OK OK OK
ThroughputThroughput
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An Analysis of the Throughput of Packet Radio Networks
An Analysis of the Throughput of Packet Radio Networks
- 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
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• Approximations
• Summary
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• 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
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• Approximations
• Summary
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• Approximations
• Summary
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Collision analysisCollision analysis
• Packet reception model
– Packet losses from packet collisions
• Packet reception model
– Packet losses from packet collisions
?
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Collision analysisCollision analysis
• Packet reception model
– Packet losses from packet collisions
• Packet reception model
– Packet losses from packet collisions
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Collision analysisCollision analysis
• 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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Calculation outlineCalculation outline
• 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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Calculation outlineCalculation outline
• 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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Bluetooth exampleBluetooth example
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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Bluetooth exampleBluetooth example
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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Bluetooth exampleBluetooth example
More interferers
More collisions
More lost packets
Reduced data rate
No interferers
26
Network throughput
Network throughput
50 %
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Bluetooth exampleBluetooth example
Increasing systemthroughput
Decreasing systemthroughput
Maximum systemthroughput
Total throughputfor all piconets in
the system
System throughput
System throughput
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OutlineOutline
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• Approximations
• Summary
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• 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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Energy analysisEnergy analysis
• 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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Energy analysisEnergy analysis
• Interfering energy• Interfering energy
Time
1
2
3
1 2 3
Single frequency channel
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Energy analysisEnergy analysis
• Interfering energy• Interfering energy
Time
1
1I
Length of overlap
1g
Signal strength
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Energy analysisEnergy analysis
• Interfering energy• Interfering energy
Time
1
2
2I
2g
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Energy analysisEnergy analysis
• Interfering energy• Interfering energy
Time
1
2
3
3g
3I
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Energy analysisEnergy analysis
• Interfering energy• Interfering energy
3
1I i i
i
E I g
3
1I i i
i
E I g
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Calculation outlineCalculation outline
• 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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Bluetooth exampleBluetooth example
• 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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Bluetooth exampleBluetooth example
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
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• Approximations
• Summary
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• 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
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• Approximations
• Summary
• Introduction and background
• System model
• Packet collision analysis
• Interfering energy analysis
• 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