Thesis Title Impact of Signal Length in Cross-

Correlation Based Underwater Network

Size Estimation

December 26, 2015

Presented by Supervised by

Samir Ahmed Shah Ariful Hoque Chowdhury

Roll No: 104018 Assistant Professor

Dept. of ETE, RUET.

1 Of 26

Contents

• Introduction

• Importance of node estimation

• Importance of signal length

• Underwater environment

• Literature review

• Impact of signal length in node estimation

• Corresponding works

• Comparison

• Future work

• Conclusion

December 26, 2015

2 of 26

Introduction

• Node - communication endpoint, terminal equipment.

• Sensor- receiving node, capable of performing some

processing, gathering sensory information and communicating

with other connected nodes.

• Cross-correlation- a measure of similarity between

two waveforms

• Underwater wireless acoustic sensor network (UWASN)

• Signal length – Energy related term

• TS case – triangular sensors case, sensors placed in triangular

shape

December 26, 2015

3 of 26

Importance of node estimation

• To ensure proper network operation

• Successful data collection

• Network maintenance

• To maintain communication quality

• Background noise calculation

December 26, 2015

4 of 26

Importance of Signal Length

• Signal length possesses a very important role in size

estimation of underwater wireless sensor network (UWSN)

• The greater the signal length the greater energy is required

for estimation

• Ideally the signal length is infinity (we consider 106

samples)

• It plays a great role in estimating number of nodes

• Accurate node estimation is being observed and discussed

in this thesis

December 26, 2015

5 0f 26

Underwater environment

• Long propagation delay

• High path loss

• Strong background noise

• Non-negligible capture effect

• Multipath signal propagation

December 26, 2015

6 of 26

Cross-correlation based node

estimation using two sensors [1]

• Basic theory: cross-correlation of two Gaussian signals results a delta.

• Estimation parameter: ratio of standard deviation to the mean, R of the cross-correlation function (CCF).

• Low protocol complexity

• Delay insensitive

• Not affected by capture effect

• Less time required

• Applicable to any environment network

December 26, 2015

7 0f 26

Cross-correlation based node

estimation using two sensors [1]

Figure. Distribution of underwater network nodes and sensors.

December 26, 2015

0 Distance between sensors, dDBS

0

y-axis

z-axis

0

x-axis

D D

D

Distribution of nodes and sensors

Nodes

Sensors

8 of 26

Cross-correlation based node

estimation using two sensors [1]

Figure. Bins, b in the cross-correlation process.

December 26, 2015

-1.0 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1.0

0

20

40

60

80

100

Distance (m)

Coeffic

ient valu

e o

f C

CF

Bins, b

9 of 26

Cross-correlation based node

estimation using two sensors [1] • Estimation parameter, R :

𝑅 =𝜎

𝜇=

𝑁×1

𝑏 × 1−

1

𝑏

𝑁×1

𝑏

=𝑏−1

𝑁

so, 𝑁 =𝑏−1

𝑅2

where b is the number of bins, which is twice the number of samples between the sensors (NSBS), m minus one and can be expressed as:

𝑏 =2×𝑑𝐷𝐵𝑆×𝑆𝑅

𝑆𝑝 ̶̶ 1

December 26, 2015

10 0f 26

Cross-correlation based node

estimation using two sensors [1]

Figure. R versus N for b = 19 with dDBS = 0.5m and SR = 30kSa/s.

December 26, 2015

0 20 40 60 80 1000

1

2

3

4

5

6

7

8

Number of nodes, N

R o

f C

CF

Theoretical

Simulated

11 of 26

Cross-correlation based node estimation

using three sensors (SL) case[2]

Figure. Distribution of underwater network nodes for sensors in line (SL) case

with N transmitting nodes (left) and only one node N1 (right). December 26, 2015

0

0

0

y-axis

z-axis

x-axis

D D

D

Sensors

Node

H3 H1 H2

N1

d11 d12

d13

dDBS 12

0

0

y-axis

z-axis

0

x-axis

D D

D

Distribution of nodes and sensors

Sensors

Nodes

dDBS 23

12 of 26

Cross-correlation based node estimation

using three sensors (TS) case [3]

Figure. Distribution of underwater network nodes for triangular sensors (TS)

case with N transmitting nodes (left) and only one node N1 (right).

December 26, 2015

d11 d12

d13

dDBS 12

dDBS 23

0

Nodes

0

y-axis

z-axis

0

x-axis

D D

D

Distribution of nodes and sensors

Sensors

0

z-axis

D

0 0

y-axis x-axis

D D

Sensors

Node H3

N1

H1 H2

dDBS 31

13 0f 26

Block diagram for TS case

December 26, 2015

d11 d12

d13

dDBS 12

dDBS 23

(t) Sr c1

(t) Sr c2

(t) Sr c3

C12 (τ)

C23 (τ)

σ12

σ23

μ23

μ12 R12

R23

Raverage 3CCF

⁞ ⁞ ⁞

Ratio

σ31 / μ31

Average Ratio

σ12 / μ12

Ratio

σ23 / μ23

Mean

Mean

Standard deviation

Mean

Standard deviation

Sensors

Gaussian

signals Composite

Gaussian

signals

Cross-correlation

Cross-correlation

Nodes

N1

N2

N3

NN

H3

H2

H1

Cross-correlation

Standard deviation

C31 (τ) μ31

σ31 R31

dDBS 31

14 of 26

Cross-correlation based node estimation

using three sensors (TS) case [3]

For TS case, estimation parameter, 𝑅average3CCF can be expressed as:

𝑅average3CCF =

𝑅12 + 𝑅23 + 𝑅31

3

=

𝑏12 − 1𝑁 +

𝑏23 − 1𝑁 +

𝑏31 − 1𝑁

3

For efficient estimation,b12=b23=b31=b,

so, 𝑁𝑒𝑠𝑡 = 𝑏−1

(𝑅average3CCF )2

December 26, 2015

15 of 26

Cross-correlation based node estimation

using three sensors[]

Figure: versus N for SL case (left) and versus N for TS case

(right) with b = 19. [dDBS = 0.5m and SR = 30kSa/s]

December 26, 2015

0 20 40 60 80 1000

1

2

3

4

5

6

7

8

Number of nodes, N

R2

CC

F

ave

rag

e o

f C

CF

s

Theoretical

Simulated

0 20 40 60 80 1000

1

2

3

4

5

6

7

8

Number of nodes, N

R3

CC

F

ave

rag

e o

f C

CF

s

Theoretical

Simulated

2CCFaverageR 3CCF

averageR

16 of 26

December 26, 2015

Effect of signal length in estimation

process, (SL case) [4]

102

103

104

105

106

0

5

10

15

20

25

30

35

Signal length in Number of samples (Ns)

Nu

mb

er o

f n

od

es,

N

Nest

vs Ns plot for SL case

Nest

vs Ns plot for Two sensor case

Exact 32 Nodes

Figure. Estimated N versus Ns plot (x-log, y-normal scale) for two & three

sensor (SL case) method with fixed value of b = 119 using exact 32 nodes

17 of 26

December 26, 2015

Impact of signal length in cross-

correlation based estimation (TS case)

• The channel is considered as ideal

• Receivers are assumed to be ideal

• No multipath effect is considered

• No Doppler shift is considered

• Network dimension — 3D spherical

• Transmitted Signal — White Gaussian

• Signal power — Equal received powers from all nodes

Some initial assumption

18 of 26

Nominal simulation parameters

• Dimension of the sphere, D = 2000m

• Speed of acoustic wave propagation, SP = 1500m/s

• Signal length, Ns = 106 samples (varied for comparison)

• Absorption coefficient, a = 1

• Dispersion factor, k = 1.5

• Distance between equidistance sensors = 1m (can be varied)

Estimation parameter

𝑁𝑒𝑠𝑡 = 𝑏−1

(𝑅average3CCF )2

December 26, 2015

19 of 26

Corresponding Result

December 26, 2015

102

103

104

105

106

100

101

102

signal Length, Ns

num

ber o

f nodes,

N

N vs Ns plot for exact 32 nodes

Estimated N vs Ns plot for b=119

Estimated N vs Ns plot for b=39

Estimated N vs Ns plot for b=19

Figure. Estimated N versus Ns plot (x-log, y-log scale) three sensor (TS case)

method with value of b = 19, b=39 and b=119 using exact 32 nodes

20 of 26

Corresponding Result

December 26, 2015

102

103

104

105

106

100

101

102

signalLength, Ns

num

ber o

f nodes,

N

Estimated N vs Ns plot for 64 nodes,b=39

N vs Ns plot for exact 64 nodes

Estimated N vs Ns plot for 32 nodes,b=39

N vs Ns plot for exact 32 nodes

Figure. Estimated N versus Ns plot (x-log, y-log scale) three sensor (TS case)

method with fixed value of b = 39 using 32 nodes and 64 nodes.

21 of 26

Comparison between TS case and SL case

December 26, 2015

102

103

104

105

106

100

101

102

signalLength, Ns

num

ber

of

nodes,

N

N vs Ns plot for exact 64 nodes

Estimated N vs Ns plot for TS case,b=19

Estimated N vs Ns plot for SL case,b=19

Figure. Estimated N versus Ns plot (x-log, y-log scale) three sensor (TS and SL

case) method with fixed value of b = 19 using exact 64 nodes

22 of 26

Future work

• Estimation with unequal distances between the sensors

• Estimation with non-uniform distribution of nodes

• Estimation with different shape of network

• Estimation with random placement of the sensors

• Estimation with variable propagation delay

• Use of Non-Gaussian signals for estimation

• Estimation with M number of sensors

• This thesis consider only ERP case, so ETP, RTRP cases

requires further work

December 26, 2015

23 of 26

Conclusion

• Using three sensors method, TS case, we can estimate the

number of nodes easily with reduced signal length for which

the required energy will be less than the SL case, three sensors

method

• In this thesis we use smaller signal length than two sensor

technique and provide better performance in estimation

process

• TS case, three sensors techniques provide better performance

than any other techniques in small area

December 26, 2015

24 of 26

References

[1] M. S. Anower, M. R. Frater, and M. J. Ryan, ―Estimation by cross-correlation of the number of

nodes in underwater networks,‖ In Proceedings of Australasian Telecommunication Networks

and Applications Conference (ATNAC), 10–12 November, 2009, pp. 1–6. doi:

10.1109/ATNAC.2009.5464716.

[2] S. A. H. Chowdhury, M. S. Anower, and J. E. Giti (2014), ―A signal processing approach of

underwater network node estimation,‖ In Proc. International Conference on Electrical

Engineering and Information Communication Technology (ICEEICT) 2014, Dhaka, 10−12

April, 2014.

[3] S. A. H. Chowdhury, M. S. Anower, and J. E. Giti (2014), ―Effect of sensor number and location

in cross-correlation based node estimation technique for underwater communications network,‖ in

Proceedings of 3rd International Conference on Informatics, Electronics & Vision (ICIEV 2014),

23–24 May, 2014, Dhaka, Bangladesh

[4] M.A. Hossen, S.A.H. Chowdhury, M. S. Anower (2015), ―Effect of signal length in cross-

correlation based underwater network size estimation‖ Paper id 528_ICEEICT 2015

December 26, 2015

25 of 26

Thank you

December 26, 2015

26 of 26