1.
EndtoEnd Channel Capacity Of
A Wireless Sensor Network
Under Reachback
Presented by Shirish Karande @ CISS 2006, Princeton, NJ
For
Muhammad U. Ilyas & Hayder Radha
2.
Objectives
To determine an expression for the
endtoend channel capacity
between a sensor and the base
station of a 2level hierarchy, Wireless
Sensor Network employing SlepianWolf coding.
To determine the effects of cluster
sizes on endtoend capacity.
12/31/13
2
3.
Outline
12/31/13
Network Model
Wireless Networking Standards for WSNs
EndtoEnd Channel
Notation
Cluster Communication Capacity
Overlay Network Communication Capacity
EndtoEnd Capacity
Results
3
4.
Tesselated Wireless Sensor
Networks
Gupta & Kumar † studied the scalability of a
wireless networks with randomly chosen
source destination pairs.
They offer two solutions;
– Design smaller networks
– Localize communication by clustering
nodes.
Assumptions
– Network has a 2level hierarchy.
– (Intra)cluster communication between
nodes and clusterhead (CLH) is 1hop and
proceeds at one frequency.
– Different clusters may or may not use
different frequencies.
– ON communication proceeds at one
frequency.
__________________________________________________________________
†
P. Gupta, and P. R. Kumar, “The Capacity of Wireless Networks,” IEEE Transactions on
Information Theory, Vol. 46, No. 2, March 2000.
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4
5.
Cluster Communication
SlepianWolf Coding for WSNs†
Basic Idea:
–
–
–
Sensors transmit readings to CLH one after the
other.
Successive transmissions in a round will take fewer
bits (figure).
Total number of bits transmitted will approach joint
entropy.
H ( X 1 ) + H ( X 2  X 1 ) + H ( X 3  X 2 , X 1 ) + ... + H ( X n  X n  1,..., X 3, X 2 , X 1 ) = H ( X 1, X 2, X 3,..., X n )
–
–
–
Assumption:
Loss of the kth transmission causes inability of
receiver to reconstruct all following transmissions
k+1 to n.
MAC protocol may be CSMACA or TDMA
___________________________________________________
†
D. Marco, and D. L. Neuhoff, “Reliability vs. Efficiency in Distributed
Source Coding for FieldGathering Sensor Networks,” IEEE
International Conference on Information Processing in Sensor
Networks (IPSN’04), Berkeley, CA, 2004.
12/31/13
5
6.
Overlay Network Communication
In the Overlay Network (ON),
communication between CLHs and
the BS proceeds over multihop routes
(figure).
We are assuming use of a shortest
path routing protocol that
subsequently results a tree topology
for the routes to BS (figure).
Transmissions in the ON are on one
frequency, i.e.
Higher traffic volume near the base
station gives rise to the reachback
problem.
MAC protocol may be CSMACA or
TDMA
__________________________________________________________________
†
J. Barros, S. D. Servetto, “On the Capacity of the Reachback Channel in Wireless Sensor
Networks,” IEEE Workshop on Multimedia Signal Processing, December 2002.
12/31/13
6
7.
IEEE 802 LAN/MAN Standards
Committee
IEEE 802
LAN/ MAN Committee
802.1
Higher Layer
LAN Protocols
Working Group
802.11
Wireless Local
Area Network
Working Group
TG1
WPAN/Bluetooth
Task Group
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802.15
Wireless Personal
Area Network
Working Group
TG2
Coexistence
Task Group
802.20
MBWA
Working Group
TG3
WPAN High Rate
Task Group
7
TG4
WPA Low Rate
Task Group
8.
Wireless Networking
Standards
802.15.4
Frequencies
MAC type
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802.11b
Bluetooth
868  868.6 MHz
902  928 MHz
2.4  2.4835 GHz
2.4  2.4835 GHz
2.4 2.4835 GHz
1.TDMA in beaconmode
2. CSMA/CA in
beaconlessmode
1.CSMA/CA in
DCF
2. Polling in PCF
Polling
8
9.
EndtoEnd Channel Model
Bit Error Rate &
Packet Error Rate
(endtoend)
Bit Error Rate &
Packet Error Rate
(1 hop)
Bit Error Rate
Pathloss Model
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9
10.
Notation
N
Is the total number of sensors.
M
Is the total number of clusters.
Ni
Is the number of sensors in cluster i.
ni ( j )
Is the ith cluster’s jth node.
" i Î {1, 2, 3,..., M }
" j Î {1, 2, 3,..., N i }
n i ( 0)
f ( n i ( 0) )
" i Î {1, 2, 3,..., M }
12/31/13
Is the clusterhead (CLH) of cluster i.
Is the frequency used for cluster
communication in the ith cluster.
10
11.
Notation
d ( ni ( j ) ,nk ( l) )
pn k ( l ) ( n i ( j ) )
f ( ni ( j ) )
I f ( ni ( j ) , nk ( l) )
ì 0 if
ï
ï
=ï
í
ï 1 if
ï
ï
î
12/31/13
Is a function returning the spatial distance between ith
cluster’s jth node and kth cluster’s lth node.
Is the probability of nk(l) transmitting at the same time
as ni(j)
Is a function that returns the frequency at which the
node provided as argument is communicating.
f ( ni ( j ) ) ¹ f ( nk ( l ) )
Is the indicator function returning;
f ( ni ( j ) ) = f ( nk ( l ) )
•1 when the two nodes in the argument are
communicating at the same frequency and
there is a potential for interference.
•0 when the two nodes in the argument are
communicating at different frequencies and
there is NO potential for interference.
11
13.
Pathloss Model
We are considering the pathloss (PL) model in the “IEEE 802.15.4a
Channel Model  final report”† published by the IEEE 802.15.4a
channel modeling subgroup that was subsequently adopted for all
further work on this standard.
– Separate channel models for
•
•
•
•
100900 MHz
1000 MHz
2 – 6 GHz
2 – 10 GHz
outdoor)
(indoor office)
(narrowband)
(short range Body Area Networks)
(indoor residential, indoor office, industrial, outdoor, open
All 3 wireless networking standards being considered fall in the 2.4 –
2.4835 GHz freq range.
Most envisioned WSN applications are expected to operate in
environments considered for 2 – 10 GHz PL model.
_________________________________________________________
Andreas F. Molisch, Kannan Balakrishnan, ChiaChin Chong, Shahriar Emami, Andrew
Fort, Johan Karedal, Juergen Kunisch, Hans Schantz, Ulrich Schuster, Kai Siwiak,
“IEEE 802.15.4a channel model  final report”, 2004.
†
12/31/13
13
14.
2 – 10 GHz Pathloss Model
Provides the received signal power at the ith cluster’s jth
node of a transmission from the kth cluster’s lth node
PT X  amp is the transmitter signal power after amplification
hT X  ant
is the transmitter antenna efficiency
hR X  ant
is the receiver antenna efficiency
These are assumed constant for all nodes in a WSN of
homogeneous devices.
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14
15.
Pathloss Model
The pathloss model is accompanied with sets of values for its environmental
parameters for the different environments mentioned previously.
However, some reference parameters remain constant across all environments,
these are;
fc = 5GHz
d 0 = 1m
Reference frequency
Reference distance
Based on these parameters we can determine the different remaining model
paramters;
K 0 K PL 0
PL 0
Pn k ( l ) ( n i ( j )) = I f ( f ( n i ( j )) , f ( n k (l )) ) × 0 × T X  amp × T X  ant × R X  ant ×
K P
h
h
2
æ ( n i ( j ), n k (l )) ö f
d
÷
ç
÷
ç
d 0 ø × fc
÷
ç
è
( )
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15
2K + 2
16.
Physical Layer Model
For the Physical Layer Channel Model we assume an Additive
White Gaussian Noise (AWGN) channel that is characterized by the
SignaltoInterference & NoiseRatio (SINR) at the receiver.
PT X
SINR =
PA + å Pint
PA
is the ambient noise power due to colocated communication networks operating in same
frequency spectrum, or devices (e.g. microwave ovens).
PT X
Is the signal power of the transmitted signal at the receiver
Pint
Is the signal power of interfering nodes at the receiver
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16
17.
Physical Layer Model
To obtain the SINR of the signal transmitted by the ith cluster’s jth
node at its CLH (i.e. CLH of cluster i), we substitute the pathloss
model in the power terms of the SINR equation.
PL 0
K 0 × T X  amp × T X  ant × R X  ant ×
P
h
h
2
æ ( n i ( j ), n i (0)) ÷ f
ö
çd
ç
d 0 ÷ × fc
÷
ç
è
ø
( )
SINR ( n i ( j )) =
Nk
M
PA +
PL 0
I f ( f ( n i ( j )) , f ( n k (l )) ) × n k (l ) ( n i ( j )) × 0 × T X  amp × T X  ant × R X  ant ×
p
K P
h
h
2
æ ( n k (l ), n i (0)) ÷ f
ö
d
l =0
ç
ç
d 0 ÷ × fc
÷
ç
è
ø
åå
k =1
( )
æ
ç
çK ×
h
h
PL
ç 0 PT X  amp × T X  ant × R X  ant × 0
ç
ç
2K + 2
ç
f
ç
ç
fc
ç
è
( )
SINR ( n i ( j )) =
2K + 2
æ
öæ
ç
ç
ç
PA × f f
÷
ç
çK 0 × T X  am p × T X  ant × R X  ant × 0 ÷
P
h
h
PL ÷
ç
ç
c
÷
ç
ç
+
÷
2K + 2
ç
ç
÷K ×
ç
ç
÷ 0 PT X  amp × T X  ant × R X  ant × 0
h
h
PL
f
ç
ç
÷
÷
ç
fc
÷
è
øç
ç
ç
è
( )
( )
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2K + 2
ö
÷
÷
÷
1
÷
÷
×
÷
2
÷ æ ( n ( j ), n (0)) ö
÷ çd i
i
÷
÷ç
÷
÷ç
d0 ø
÷
÷è
ø
2K + 2
ö
÷
÷
÷
÷
1
÷
I f ( f ( n i ( j )) , f ( n k (l )) ) × nk (l ) ( n i ( j )) ×
p
å1 å0
2÷
÷
æ ( n k (l ), n i (0)) ö ÷
k = l=
÷÷
çd
÷÷
ç
d0 ø ø
÷÷
ç
÷
è
÷
M
Nk
17
18.
Physical Layer Model
1
æ ( n i ( j ), n i (0)) ÷
ö
çd
÷
ç
d0 ÷
ç
è
ø
2
SINR ( n i ( j )) =
( )
2K + 2
PA × f f
c
+
K 0 × T X  amp × T X  ant × R X  ant × 0
P
h
h
PL
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Nk
åå
k =1 l =0
1
I f ( f ( n i ( j )) , f ( n k (l )) ) × n k (l ) ( n i ( j )) ×
p
2
æ ( n k (l ), n i (0)) ö
d
÷
ç
÷
ç
d0 ø
÷
ç
è
( )
2K + 2
PA × f f
c
PA ' =
K 0 × T X  amp × T X  ant × R X  ant × 0
P
h
h
PL
If,
SINR ( n i ( j )) =
M
1
×
æ ( n i ( j ), n i (0)) ö
÷ P '+
çd
÷
ç
d0 ø A
÷
ç
è
2
1
M
Nk
1
I f ( f ( n i ( j )) , f ( n k (l )) ) × n k (l ) ( n i ( j )) ×
p
2
æ ( n k (l ), n i (0)) ÷
ö
d
l =0
ç
ç
d0 ÷
÷
ç
è
ø
åå
k =1
18
19.
Bit Error Rate
Next, from our knowledge of a Physical Layer model we compute a Bit
Error Rate (BER). We use the Lognormal Shadow Fading Model†.
1
2p
Q (x) =
If,
Then, PB ER ( n i ( j )) = Q (
¥
òe
u
2
du
x
1
2×
SINR ( n i ( j )) =
2p
)

¥
ò
e

u
2
du
‡
2×
SINR ( n i ( j ))
______________________________________________
†
‡
T.S. Rappaport, “Wireless Communications – Principles and Practice, 2nd ed,” Pearson Education,
Singapore, 2002.
C BSC ( n i ( j ) ) = 1  H b ( PBER ( n i ( j ) ) )
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19
20.
Packet Error Rate
Recall: Failure of ni(0) to receive kth transmission from a
sensor in a round results in an inability to reconstruct/ a
complete loss of all subsequent transmissions k+1 to Ni.
Hence,
PPER ( n i ( j ) ) = 1  ( 1  PBER ( n i ( j ) ) )
h
h + é ( X n i ( j ) X n i ( 1) ,X n i ( 2) ,...,X n i ( j  1) ) ù
H
ê
ú
ê
ú
†
Is the number of header bits.
_______________________________________________
†
j
C PER ( n i ( j ) ) = ( 1  PPER ( n i ( j ) ) ) × ( 1  PPER ( n i ( k ) ) )
Õ
k =1
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20
21.
Overlay Network Communication
Channel Capacity
22.
Options in Overlay Network
We are considering two options for the way CLHs
communicate their packets to the Base Station.
– Option 1: No recoding, simple forwarding of downstream
packets and transmission of own packets.
– Option 2: Additional compression of own packet based on
received downstream packets.
________________________________________
Downstream:
Upstream:
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farther away from base station
closer to base station
22
23.
Pathloss Model (ON)
Remains similar to the one derived for the clusterlevel communication,
R 1( n i ( 0) ) Is a function that returns the upstream neighbor of ni(0).
R ¯ ( n i ( 0) ) Is a function that returns the set of all downstream neighbors of ni(0).
PL 0
K 0 × ON  T X  amp × T X  ant × R X  ant ×
P
h
h
2
2K + 2
æ ( n (0), R 1( n ( 0) ) ) ö
d i
÷× f
i
ç
÷
ç
ç
d0 ÷
fc
÷
ç
è
ø
M
PL 0
+ å pn k (0) ( n i (0)) × 0 × ON  T X  amp × T X  ant × R X  ant ×
K P
h
h
2
æ ( n i (0), n k (0)) ÷ f
ö
d
k =1
ç
k¹ i
ç
÷
d 0 ÷ × fc
ç
è
ø
( )
SINRON ( n i (0)) =
PON  A
If,
SINRON ( n i (0)) =
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( )
PON  A ' =
PON  A
( f)
×f
2K + 2
c
K 0 × ON  T X  amp × T X  ant × R X  ant × 0
P
h
h
PL
1
×
æ ( n (0), R 1( n (0)) ) ö
÷ P
i
çd i
'+
÷
ç
ç
d 0 ÷ ON  A
÷
ç
è
ø
2
M
å
k =1
k¹ i
1
pn k (0) ( n i (0))
æ ( n i (0), n k (0)) ö
÷
çd
÷
ç
d0 ø
÷
ç
è
2
23
2K + 2
24.
1Hop Bit Error Rate (ON)
Similar to clusterlevel BER model, the BER of the
channel between ni(0) and its upstream neighbor is,
PON  BER ( n i ( 0) ) = Q
(
2×
SINRON
1
n i ( 0) ) =
(
2p
)
¥
ò
e

u
2
du
2×
SINRON ( n i ( 0) )
The expressions obtained up to this point hold true for ONs
irrespective of whether or not CLHs are doing SlepianWolf
recoding on their own packets based on packets received
from downstream CLHs.
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24
25.
CLHtoBase Station
Bit Error Rate
The BER of the channel formed between a CLH
and the base station can be treated as a cascade
of BSCs.
The BER is defined by a recursive expression
which models the channel as two BSCs (i) a BSC
between the CLH and its upstream neighbor, and
(ii) another BSC between the upstream neighbor
and the Base station.
é
é
PON  BER  E 2E ( n i ( 0) ) = PON  BER ( n i ( 0) ) ×1  PON  BER  E 2E ( R 1( n i ( 0) ) ) ù+ PON  BER  E 2E ( R 1( n i ( 0) ) ) ×1  PON  BER ( n i ( 0) ) ù
ê
ú
ë
û
ë
û
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25
26.
1Hop Packet Error Rate
PON  PER  n k ( 0) ( n i ( 0) ) Is the packet error rate for the link between nk(0) and
R1↑(nk(0) for a packet originated at ni(0).
For an ON without SlepianWolf coding.
PON  PER  n k ( 0) ( n i ( 0) ) = 1  ( 1  PON  BER ( n k ( 0) ) )
h + é X ni ( 1) ,X n i ( 2) ,..., X ni ( N i ) ù
H
ê
ú
ê
ú
(
)
For an ON with SlepianWolf coding.
PON  PER  n k ( 0) ( n i ( 0) ) =
é
ù
é
h + ê ( X ni ( 1) , X ni ( 2) ,..., X ni ( N i )  X n ( 1) , X n ( 2) ,..., X n ( N i ) ) úù
H
l
l
ê
úú
l
1  ê1  PON  BER ( n i ( 0) ) )
´
(
ê
ú
ë
û
12/31/13
é
ù
ê
Õ ( 1  PON  PER  nk ( 0) ( n j ( 0) ) ) ú
ê Õ
ú
n
êk ( 0) Î R ¯ ( n i ( 0) ) n j ( 0) Î R ¯ ( n i ( 0) )
ú
ë
û
26
27.
CLHtoBase Station
Packet Error Rate
PON  PER  E 2E ( n i ( 0) ) Is the endtoend packet error model for the channel between CLH
ni(0) and the base station.
R ( n i ( 0) ) Is a function that returns the set of all downstream neighbors of ni(0).
M
PON  PER  E 2E ( n i ( 0) ) = 1 
Õ
k =1
n k ( 0) Î R ( n i ( 0) )
( 1 † P
ON  PER  n k ( 0)
( n i ( 0) ) )
___________________________________________________________________________
†
C ON  PER  E 2E ( n i ( 0) ) = 1  PON  PER  E 2E ( n i ( 0) )
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27
28.
SensortoBase Station
Channel Capacity
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28
29.
SensortoBase Station/
EndtoEnd BER & PER
PBER − S 2 BS ( ni ( j ) )
Is the packet error rate for the channel from ni(j) to ni(0)
to base station.
†
PBER − S 2 BS ( ni ( j ) ) = PON − BER − E 2 E ( ni ( 0 ) ) × 1 − PBER ( ni ( j ) ) + PBER ( ni ( j ) ) × 1 − PON −BER −E 2 E ( ni ( 0 ) )
PPER − S 2 BS ( ni ( j ) )
Is the packet error rate for the channel from ni(j) to ni(0)
to base station.
‡
PPER − S 2 BS ( ni ( j ) ) = 1 − 1 − PPER ( ni ( j ) ) ×1 − PON − PER − E 2 E ( ni ( 0 ) )
_________________________________________________________________________
†
CBER − S 2 BS ( ni ( j ) ) = 1 − H b PBER − S 2 BS ( ni ( j ) )
‡
CPER − S 2 BS ( ni ( j ) ) = 1 − PPER − S 2 BS ( ni ( j ) ) = 1 − PPER ( ni ( j ) ) ×1 − PON − PER − E 2 E ( ni ( 0 ) )
(
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)
29
30.
Results
Physical Layout & Network Topology of WSN
10
Physical layout and routing
topology of a wireless sensor
network consisting of 50
sensors in a square shaped
plane of size 10 x 10.
8
7
6
Y
Configured with 5 CLHs.
9
5
Base station is located at
coordintate (0,0).
4
We assume an IEEE 802.15.4
frame structure.
2
3
1
0
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0
1
2
3
4
5
X
6
30
7
8
9
10
31.
EndtoEnd Channel Capacity
and Probability
SensortoBase Station: P BERS2BS vs P PERS2BS
0.4
Probability of Error
Figure 1  Bit and packet error
probability of the endtoend
channel.
P
0.3
BERS2BS
PERS2BS
0.2
0.1
0
0
10
20
30
40
50
60
Sensor Node ID
70
80
90
100
SensortoBase Station: CBERS2BS vs CPERS2BS
1
CBERS2BS
CPERS2BS
0.9
Capacity
Figure 2 – Bit and packet level
capacity of the endtoend
channel.
P
0.8
0.7
0.6
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0
10
20
30
40
50
60
Sensor Node ID
31
70
80
90
100
32.
Effect of Clustering on
Capacity
Av
eraged PBE S2BS v PP RS2BS
s E
R
0.8
BE S2BS
R
Probability of Error
Figure 1  Bit and packet error
probability of the endtoend
channel with varying number of
clusterheads.
P
P
PR
E S2BS
0.6
0.4
0.2
0
0
5
10
15
20
25
Number of CLHs
Av
eraged C
BE S2BS
R
v C
s
PR
E S2BS
1
0.9
0.8
Capacity
Figure 2  Bit and packet level
capacity of the endtoend
channel with varying number of
clusterheads.
0.7
0.6
C
BE S2BS
R
0.5
0.4
0
CP RS2BS
E
5
10
15
Number of CLHs
12/31/13
32
20
25
34.
References
12/31/13
P. Gupta, and P. R. Kumar, “The Capacity of Wireless Networks,” IEEE Transactions
on Information Theory, Vol. 46, No. 2, March 2000.
J. Barros, S. D. Servetto, “On the Capacity of the Reachback Channel in Wireless
Sensor Networks,” IEEE Workshop on Multimedia Signal Processing, December 2002.
“IEEE P802.15.4/D18, Draft Standard: Low Rate Wireless Personal Area Networks,”
February 2003.
Soo Young Shin, Hong Seong Park, Sunhyun Choi, Wook Hyun Kwon, "Packet Error
Rate Analysis of IEEE 802.15.4 under IEEE 802.11b Interference," 3rd International
Conference on Wired/ Wireless Internet Communications 2005 (WWIC'05), Xanthi,
Greece, May 1113, 2005.
Andreas F. Molisch, Kannan Balakrishnan, ChiaChin Chong, Shahriar Emami, Andrew
Fort, Johan Karedal, Juergen Kunisch, Hans Schantz, Ulrich Schuster, Kai Siwiak,
“IEEE 802.15.4a channel model  final report,” 2004.
D. Marco, and D. L. Neuhoff, “Reliability vs. Efficiency in Distributed Source Coding for
FieldGathering Sensor Networks,” IEEE International Conference on Information
Processing in Sensor Networks (IPSN’04), Berkeley, CA, 2004.
T.S. Rappaport, “Wireless Communications – Principles and Practice, 2 nd ed,” Pearson
Education, Singapore, 2002.
34
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