End-to-End Channel Capacity Of End-to-End Channel Capacity Of A Wireless Sensor Network A Wireless Sensor Network

Under ReachbackUnder Reachback

Presented by Shirish Karande @ CISS 2006, Princeton, NJ

For Muhammad U. Ilyas & Hayder Radha

04/13/23 2

ObjectivesObjectives

To determine an expression for the end-to-end channel capacity between a sensor and the base station of a 2-level hierarchy, Wireless Sensor Network employing Slepian-Wolf coding.

To determine the effects of cluster sizes on end-to-end capacity.

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OutlineOutline

Network Model Wireless Networking Standards for WSNs End-to-End Channel Notation Cluster Communication Capacity Overlay Network Communication Capacity End-to-End Capacity Results

04/13/23 4

Tesselated Wireless Sensor Tesselated Wireless Sensor NetworksNetworks

__________________________________________________________________† P. Gupta, and P. R. Kumar, “The Capacity of Wireless Networks,” IEEE Transactions

on Information Theory, Vol. 46, No. 2, March 2000.

Cell/ Cluster Boundary

Clusterhead

Base Station

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 2-level hierarchy.– (Intra-)cluster communication between

nodes and clusterhead (CLH) is 1-hop and proceeds at one frequency.

– Different clusters may or may not use different frequencies.

– ON communication proceeds at one frequency.

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Cluster CommunicationCluster Communication

Slepian-Wolf 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.

– Assumption:– Loss of the k-th transmission causes inability of

receiver to reconstruct all following transmissions k+1 to n.

– MAC protocol may be CSMA-CA or TDMA___________________________________________________

† D. Marco, and D. L. Neuhoff, “Reliability vs. Efficiency in Distributed Source Coding for Field-Gathering Sensor Networks,” IEEE International Conference on Information Processing in Sensor Networks (IPSN’04), Berkeley, CA, 2004.

H(X1) H(X1|X2) H(X3|X2, X1) H(Xn|Xn-1, … , X1)

( ) ( ) ( ) ( ) ( )1 2 1 3 2 1 1 3 2 1 1 2 3| | , ... | ,..., , , , , ,...,n n nH X H X X H X X X H X X X X X H X X X X-+ + + + =

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Overlay Network CommunicationOverlay 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 CSMA-CA or TDMACell/ Cluster Boundary

Active Links

Clusterhead (CLH)

Base Station__________________________________________________________________† J. Barros, S. D. Servetto, “On the Capacity of the Reachback Channel in Wireless Sensor

Networks,” IEEE Workshop on Multimedia Signal Processing, December 2002.

04/13/23 7

IEEE 802 LAN/MAN Standards IEEE 802 LAN/MAN Standards CommitteeCommittee

IEEE 802 LAN/ MAN Committee

802.1Higher Layer

LAN ProtocolsWorking Group

802.11Wireless Local Area Network

Working Group

802.15Wireless Personal

Area NetworkWorking Group

802.20MBWA

Working Group

TG1WPAN/Bluetooth

Task Group

TG2Coexistence Task Group

TG3WPAN High Rate

Task Group

TG4WPA Low Rate

Task Group

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Wireless Networking Wireless Networking StandardsStandards

802.15.4 802.11b Bluetooth

Frequencies868 - 868.6 MHz

902 - 928 MHz

2.4 - 2.4835 GHz

2.4 - 2.4835 GHz 2.4 -2.4835 GHz

MAC type

1.TDMA in beacon- mode

2. CSMA/CA in beaconless-mode

1.CSMA/CA in DCF

2. Polling in PCFPolling

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End-to-End Channel ModelEnd-to-End Channel Model

Higher Layers(Application

+ Presentation +Session)

Transport

Network

Data Link (MAC)

Physical (PHY)

Wireless Channel

Transmitter

Higher Layers(Application

+ Presentation +Session)

Transport

Network

Data Link (MAC)

Physical (PHY)

Receiver

Pathloss Model

Bit Error Rate

Bit Error Rate & Packet Error Rate (1 hop)

Bit Error Rate & Packet Error Rate (end-to-end)

04/13/23 10

NotationNotation

Is the total number of sensors.

Is the total number of clusters.

Is the number of sensors in cluster i.

Is the i-th cluster’s j-th node.

Is the clusterhead (CLH) of cluster i.

Is the frequency used for cluster

communication in the i-th cluster.

( )

{1,2,3,..., }

{1,2,3,..., }

i

i

n j

i M

j N

" Î

" Î

N

M

( )( )0

{1,2,3,..., }

if n

i M" Î

iN

( )0in

Cell/ Cluster Boundary

Active Links

Clusterhead (CLH)

Base Station

04/13/23 11

NotationNotation

( ) ( )( ),i kd n j n l Is a function returning the spatial distance between i-thcluster’s j-th node and k-th cluster’s l-th node.

Is the probability of nk(l) transmitting at the same timeas ni(j)

Is a function that returns the frequency at which thenode provided as argument is communicating.

( ) ( )( )( )( ) ( )( )

( )( ) ( )( )

0,

1

i k

fi k

i k

iff n j f n lI n j n l

iff n j f n l

ìï ¹ïï= íï =ïïî

Is the indicator function returning;•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.

( )( )if n j

( ) ( )( )k in lp n j

Cluster Communication Cluster Communication Channel CapacityChannel Capacity

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Pathloss ModelPathloss 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• 100-900 MHz (indoor office)• 1000 MHz (narrowband)• 2 – 6 GHz (short range Body Area Networks)• 2 – 10 GHz (indoor residential, indoor office, industrial, outdoor,

open outdoor)

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, Chia-Chin Chong, Shahriar Emami, Andrew Fort, Johan Karedal, Juergen Kunisch, Hans Schantz, Ulrich Schuster, Kai Siwiak, “IEEE 802.15.4a channel model - final report”, 2004.

04/13/23 14

2 – 10 GHz Pathloss Model2 – 10 GHz Pathloss Model

Provides the received signal power at the i-th cluster’s j-th node of a transmission from the k-th cluster’s l-th node

TX ampP - is the transmitter signal power after amplification

is the transmitter antenna efficiency

is the receiver antenna efficiency

These are assumed constant for all nodes in a WSN of homogeneous devices.

TX anth -

RX anth -

04/13/23 15

Pathloss ModelPathloss 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;

Reference frequency

Reference distance

Based on these parameters we can determine the different remaining model paramters;

5cf GHz=

0 1d m=

0K K

( ) ( ) ( ) ( )( )( ) ( )

00 2 2 2

0

( ) ( ) , ( )( ), ( )k i fi k TX amp TX ant RX antn l

i k

c

PLP n j I f n j f n l K P

d n j n l fd f

h h- - - K+= × × × × ×

æ ö÷ç ×÷ç ÷÷çè ø

0PL

04/13/23 16

Physical Layer ModelPhysical Layer Model

For the Physical Layer Channel Model we assume an Additive White Gaussian Noise (AWGN) channel that is characterized by the Signal-to-Interference & Noise-Ratio (SINR) at the receiver.

int

TX

A

PSINR

P P=

+å

APis the ambient noise power due to co-located communication networks operating in samefrequency spectrum, or devices (e.g. microwave ovens).

Is the signal power of the transmitted signal at the receiver

Is the signal power of interfering nodes at the receiver

TXP

intP

04/13/23 17

Physical Layer ModelPhysical Layer Model

To obtain the SINR of the signal transmitted by the i-th cluster’s j-th node at its CLH (i.e. CLH of cluster i), we substitute the pathloss model in the power terms of the SINR equation.

( )

( ) ( )( ) ( )( ) ( )

( ) ( )

020 2 2

0

02( ) 0 2 2

1 0

0

( ), (0)

( )( ) , ( ) ( )

( ), (0)

k

k

TX amp TX ant RX ant

i i

c

i NM

A fi k n l i TX amp TX ant RX antk l k i

c

PLK P

d n j n fd f

SINR n jPL

P I f n j f n l p n j K Pd n l n f

d f

h h

h h

- - - K+

- - - K+= =

× × × ×æ ö÷ç ×÷ç ÷÷çè ø

=+ × × × × × ×

æ ö÷ç ×÷ç ÷÷çè ø

å å

( )( )

0 02 2

( )

TX amp TX ant RX ant

c

i

K P PL

ff

SINR n j

h h- - -K+

× × × ×

=

( )

( )

2

0

0 02 2

1

( ), (0)i i

TX amp TX ant RX ant

c

d n j nd

K P PL

ff

h h- - -K+

æ ö÷ç ÷ç ÷ç ÷ç ÷×ç ÷ç ÷æ öç ÷ ÷ç÷ç ÷÷çç ÷ç ÷÷ç÷è ø è ø

æ ö÷ç ÷ç × × × × ÷ç ÷ç ÷ç ÷ç ÷ç ÷÷ç ÷ç ÷è ø

( )( ) ( )( ) ( )

( )

2 2

2( )1 00 0

0

1( ) , ( ) ( )

( ), (0)

k

k

NMAc

fi k n l ik lTX amp TX ant RX ant k i

fP fI f n j f n l p n j

K P PL d n l nd

h h

K+

= =- - -

æ ö÷ç ÷ç ÷×ç ÷ç ÷ç ÷+ × ×ç ÷ç ÷æ ö× × × × ÷ç ÷ç ÷ç ÷ç ÷ç ÷÷ç ÷ç ÷è øçè ø÷

å å

04/13/23 18

Physical Layer ModelPhysical Layer Model

( )

( )

( )( ) ( )( ) ( )

( )

2

0

2 2

2( )1 00 0

0

1

( ), (0)

( )

1( ) , ( ) ( )

( ), (0)

k

k

i i

i

NMAc

fi k n l ik lTX amp TX ant RX ant k i

d n j nd

SINR n jfP f

I f n j f n l p n jK P PL d n l n

dh h

K+

= =- - -

æ ö÷ç ÷ç ÷÷çè ø=

×+ × ×

æ ö× × × × ÷ç ÷ç ÷÷çè ø

å å

( )2 2

0 0

'A

cA

TX amp TX ant RX ant

fP fP

K P PLh h

K+

- - -

×=

× × × ×

( )( ) ( ) ( )( ) ( )

( )

2

2( )0 1 0

0

1 1( )

1( ), (0) ' ( ) , ( ) ( )( ), (0)

k

k

i NM

i iA fi k n l i

k l k i

SINR n jd n j n P I f n j f n l p n j

d d n l nd

= =

= ×æ ö÷ç + × ×÷ç ÷÷ç æ öè ø ÷ç ÷ç ÷÷çè ø

å å

If,

04/13/23 19

Bit Error RateBit 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†.

If,

Then, ‡

______________________________________________† T.S. Rappaport, “Wireless Communications – Principles and Practice, 2nd ed,” Pearson Education,

Singapore, 2002.‡

( ) 212

u

x

Q x e dup

¥-

= ò

( ) ( )( )( )

2

2 ( )

1( ) 2 ( )

2i

u

BER i i

SINR n j

P n j Q SINR n j e dup

¥-

×

= × = ò

( )( ) ( )( )( )1BSC i b BER iC n j H P n j= -

04/13/23 20

Packet Error RatePacket Error Rate

Recall: Failure of ni(0) to receive k-th 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,

†

Is the number of header bits.

_______________________________________________†

( )( ) ( )( )( ) ( ) ( ) ( ) ( )( )1 2 1| , ,...,1 1 n nn j n ji ii i

h H X X X X

PER i BER iP n j P n j -é ù+ê úê ú= - -

h

( )( ) ( )( )( ) ( )( )( )1

1 1j

PER i PER i PER ik

C n j P n j P n k=

= - × -Õ

Overlay Network Communication Overlay Network Communication Channel CapacityChannel Capacity

04/13/23 22

Options in Overlay NetworkOptions 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: farther away from base station Upstream: closer to base station

04/13/23 23

Pathloss Model (ON)Pathloss Model (ON)

Remains similar to the one derived for the cluster-level communication,

Is a function that returns the upstream neighbor of ni(0).

Is a function that returns the set of all downstream neighbors of ni(0).

If,

( )2 2

0 0

'ON A

cON A

ON TX amp TX ant RX ant

fP fP

K P PLh h

K+

-

-- - - -

×=

× × × ×

( )( )( ) ( )

( )

21(0)

20 1

0

1 1(0)

(0)(0), (0) '(0), (0)k

ON i Mn ii i

ON Ak i kk i

SINR np nd n R n P

d d n nd

­

-=¹

= ×æ ö÷ç +÷ç ÷ç æ ö÷÷çè ø ÷ç ÷ç ÷÷çè ø

å

( )( )1 0iR n­

( )( )0iR n¯

( )

( )( )( ) ( )( )

( ) ( )

00 21 2 2

0

0(0) 0 2 2 2

1

0

(0), 0

(0)(0)

(0), (0)k

ON TX amp TX ant RX ant

i i

c

ON i M

ON A n i ON TX amp TX ant RX antk i kk i

c

PLK P

d n R n fd f

SINR nPL

P p n K Pd n n f

d f

h h

h h

- - - - ­ K+

- - - - - K+=¹

× × × ×æ ö÷ç ÷ç ×÷ç ÷÷ççè ø

=+ × × × × ×

æ ö÷ç ×÷ç ÷÷çè ø

å

04/13/23 24

1-Hop Bit Error Rate (ON)1-Hop Bit Error Rate (ON)

Similar to cluster-level BER model, the BER of the channel between ni(0) and its upstream neighbor is,

( )( ) ( )( )( )( )( )

2

2 0

10 2 0

2ON i

u

ON BER i ON i

SINR n

P n Q SINR n e dup

¥-

-

×

= × = ò

The expressions obtained up to this point hold true for ONs irrespective of whether or not CLHs are doing Slepian-Wolf recoding on their own packets based on packets received from downstream CLHs.

04/13/23 25

CLH-to-Base Station CLH-to-Base Station Bit Error RateBit 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.

( )( ) ( )( ) ( )( )( ) ( )( )( ) ( )( )1 12 2 20 0 1 0 0 1 0ON BER E E i ON BER i ON BER E E i ON BER E E i ON BER iP n P n P R n P R n P n­ ­

- - - - - - - -é ù é ù= × - + × -ê ú ë ûë û

04/13/23 26

1-Hop Packet Error Rate1-Hop Packet Error Rate

Is the packet error rate for the link between nk(0) and

R1↑(nk(0) for a packet originated at ni(0).

( ) ( )( ) ( )( )( ) ( ) ( ) ( )( )1 2, ,...,

0 0 1 1 0 n n n Ni i i i

k

h H X X X

ON PER n i ON BER kP n P né ù+ê úê ú

- - -= - -

( ) ( )( )0 0kON PER n iP n- -

For an ON without Slepian-Wolf coding.

For an ON with Slepian-Wolf coding.

( ) ( )( )

( )( )( ) ( ) ( ) ( ) ( ) ( ) ( )( )( ) ( )( )( )

( ) ( )( )( ) ( )( )

1 2 1 2

0

, ,..., | , ,...,

00 0 0 0

0

1 1 0 1 0

k

n n n nn N n Ni i i i il l l

k

k i j i

ON PER n i

h H X X X X X X

ON BER i ON PER n jn R n n R n

P n

P n P n¯ ¯

- -

é ù+ê úê úê ú- - -

Î Î

=

é ùé ù ê úê ú- - ´ -ê úê úë û ê úë ûÕ Õ

04/13/23 27

CLH-to-Base Station CLH-to-Base Station Packet Error RatePacket Error Rate

Is the end-to-end packet error model for the channel between CLH

ni(0) and the base station.

Is a function that returns the set of all downstream neighbors of n i(0).

†

( )( )2 0ON PER E E iP n- -

( )( ) ( )( )2 20 1 0ON PER E E i ON PER E E iC n P n- - - -= -

___________________________________________________________________________

†

( )( )0iR n­

( )( ) ( ) ( )( )( )( ) ( )( )

2 01

0 0

0 1 1 0k

k i

M

ON PER E E i ON PER n ik

n R n

P n P n

­

- - - -=

Î

= - -Õ

04/13/23 28

Sensor-to-Base Station Sensor-to-Base Station Channel CapacityChannel Capacity

04/13/23 29

Sensor-to-Base Station/ Sensor-to-Base Station/ End-to-End BER & PEREnd-to-End BER & PER

Is the packet error rate for the channel from ni(j) to ni(0) to base station.

†

Is the packet error rate for the channel from ni(j) to ni(0) to base station.

‡

2 21 1 1 0PER S BS i PER i ON PER E E iP n j P n j P n

2PER S BS iP n j

_________________________________________________________________________

†

‡ 2 2 21 1 1 0PER S BS i PER S BS i PER i ON PER E E iC n j P n j P n j P n

2 2 20 1 1 0BER S BS i ON BER E E i BER i BER i ON BER E E iP n j P n P n j P n j P n

2BER S BS iP n j

2 21BER S BS i b BER S BS iC n j H P n j

04/13/23 30

ResultsResults

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10Physical Layout & Network Topology of WSN

X

Y

Physical layout and routing topology of a wireless sensor network consisting of 50 sensors in a square shaped plane of size 10 x 10.

Configured with 5 CLHs.

Base station is located at coordintate (0,0).

We assume an IEEE 802.15.4 frame structure.

04/13/23 31

End-to-End Channel Capacity End-to-End Channel Capacity and Probability and Probability

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

Sensor-to-Base Station: PBER-S2BS

vs PPER-S2BS

Sensor Node ID

Pro

babi

lity

of E

rror

PBER-S2BS

PPER-S2BS

0 10 20 30 40 50 60 70 80 90 1000.6

0.7

0.8

0.9

1

Sensor-to-Base Station: CBER-S2BS

vs CPER-S2BS

Sensor Node ID

Cap

acity

CBER-S2BS

CPER-S2BS

Figure 1 - Bit and packet error probability of the end-to-end channel.

Figure 2 – Bit and packet level capacity of the end-to-end channel.

04/13/23 32

Effect of Clustering on Effect of Clustering on CapacityCapacity

0 5 10 15 20 250

0.2

0.4

0.6

0.8

Averaged PBER-S2BS

vs PPER-S2BS

Number of CLHs

Pro

babi

lity

of E

rror

PBER-S2BS

PPER-S2BS

0 5 10 15 20 250.4

0.5

0.6

0.7

0.8

0.9

1

Averaged CBER-S2BS

vs CPER-S2BS

Number of CLHs

Cap

acity

CBER-S2BS

CPER-S2BS

Figure 1 - Bit and packet error probability of the end-to-end channel with varying number of clusterheads.

Figure 2 - Bit and packet level capacity of the end-to-end channel with varying number of clusterheads.

Thank You!Thank You!

??????

04/13/23 34

ReferencesReferences

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 11-13, 2005.

Andreas F. Molisch, Kannan Balakrishnan, Chia-Chin 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 Field-Gathering Sensor Networks,” IEEE International Conference on Information Processing in Sensor Networks (IPSN’04), Berkeley, CA, 2004.

T.S. Rappaport, “Wireless Communications – Principles and Practice, 2nd ed,” Pearson Education, Singapore, 2002.