2011 International Conference on Telecommunication Technology and Applications
Proc .of CSIT vol.5 (2011) © (2011) IACSIT Press, Singapore
Underwater Acoustic Communications: Optimizing Data Packet Size
With Respect to Throughput Efficiency, BER, and Energy Efficiency
Low Tang Jung 1+ and Azween Abdullah 2
1,2
Computer and Information Sciences Department, Universiti Teknologi PETRONAS, Malaysia
Abstract. The authors of this paper embarked on a research to investigate the relationships between the
data packet size and the three important performance metrics namely, bit error rate (BER), throughput
efficiency, and energy efficiency in underwater acoustic (UWA) communications. The investigations were
conducted via simulations on the ns2 simulator with its MIRACLE (Multi-InteRfAce Cross-Layer Extension
library) package. Based on the results of the simulation the authors have proposed an algorithm/framework to
determine the optimal packet size for UWA data transmission. Each of the three metrics are dealt with
separately in the context of packet size to produce a data set or a look-up graph that can be indexed/consulted
by the algorithm to compute an optimal packet size.
Keywords: throughput efficiency, bit error rate, energy efficiency, optimal packet size, UWA data
transmission.
1. Introduction
Research in underwater acoustic (UWA) communications has always been a challenge to many
researchers. Various papers on the recent advances and challenges in UWA communications and networking
can be found in [1]-[6]. This paper presents the findings of the relationships between data packet size and
these metrics: bit error rate (BER), throughput efficiency, and energy efficiency with other related qualifiers
such as the distance between a source-sink pair, the bit rate, and the packet header length. The findings are
aimed for communications between a source-sink pair only i.e. a one hop data transmission. This work was
accomplished by simulation via the underwater channel model in the network simulator ns2 version 2.34,
with its MIRACLE (Multi-InteRfAce Cross-Layer Extension) library package [7] due to the package
modularity, code portability, re-usability, and extensibility[8]. The CSMA MAC protocol was used in our
simulation works with stop-and-wait automatic request (ARQ) handshaking protocol at PHY layer
implemented between any source-sink pair of nodes. The ns2 runs on Ubuntu platform.
The remainder of the paper is organized as follow. Section 2 describes the simulation setup. Section 3 is
the discussions on the results. Section 4 highlights the outcomes of our findings and Section 5 concludes the
paper.
2. Simulation Setup
2.1. General scenario
The general scenario of the underwater environment set up is shown in Fig 1. A cluster of 100 nodes is
placed somewhere in the middle of a body (cuboid) of water with dimension of 2km x 2km x 200m. By
placing the cluster in the middle of the cuboid is to avoid the complications of acoustic wave reflection near
the water surface and the reflection near the bottom surface. A maximum depth of 200m was chosen as a
+
Corresponding author: Low Tang Jung. Tel.: +6053687421; Fax: +6053656180
E-mail address: lowtanjung@petronas.com.my
7
commonly acceptable shallow wateer depth. Som
mewhere at the
t middle of
o the clusterr is a sink to collect dataa
packets from
m other sourrce nodes. It is
i assumed here
h that all source
s
nodess know the exxistence of th
he sink nodee.
The maxim
mum distance between thee sink and a source nodee is set to 1km
m. Thus dim
mensions of 2km
2
by 2km
m
are deemedd sufficient. The distancee between thhe sink and the various source nodees in the clu
uster will bee
varied from
m a minimum
m of 10m to a maximum of
o 1km in thee course of thhe simulationns.
F 1: The geeneral underwater scenario used
Fig.
u
in the sim
mulation workk.
2.2. The simulationn setup
The esssential comm
munication linnk setup in our
o simulatio
on comprisedd of two nodees i.e. a sourrce-sink pair..
The link is created for a one hop daata packets reelay with constant bit ratte (CBR) moodule per lay
yer. A singlee
k node. The layers invollved in both nodes for a
CBR packeet flow is staarted from a source nodee to the sink
packet flow
w under the nss2 MIRACL
LE layered fraamework is shown
s
in Figg. 2.
CBR
CBR
MMAC
MMAC
MPH
HY/BPSK/Underwaater
MPH
HY/BPSK/Underwaater
U
Underwater
Channell
Figg. 2: The ns2 MIRACLE
M
lay
yered framework.
The trannsmitter CBR
R module, as
a an agent, generates
g
datta packet of the requiredd size. The CSMA
C
MAC
C
protocol is deployed inn the MMAC
C layer for media
m
accesss. BPSK moodulation is used in thee MIRACLE
E
physical layyer (MPHY) to send thhe data packkets. The un
nderwater chhannel is coonfigured wiith Shannonn
characteristics.
nged from 10 bits to 10000. There weere situationss
For ourr simulations, for the mosst part the paacket size ran
where a paccket size of more than 1000
1
bits waas necessary. The distancce between the source node
n
and thee
sink node varied
v
from 10m to 10000m with vaarious increm
ment steps depending onn situations needed.
n
Thee
transmittingg node is set to a frequenccy of 8.2KH
Hz with the signal bandwiidth of 6KHzz. The link haas a capacityy
of 100kbps with a DroopTail queuee. The basic throughput definition from
f
[9] was adopted ex
xcept wheree
explicitly sttated in the description
d
off the various simulations.
3. Resullts and Diiscussionss
Three sets
s of simullation were conducted.
c
A the simullation resultss discuss in this section are with thee
All
aim to veriify directly or indirectlyy the feasibbility to find
d optimal daata packet ssize based on
o the BER,,
throughput efficiency, and
a the energgy efficiencyy metrics. Th
he outcomes of the simulaations were consolidated
c
d
wever only three
t
sets wo
ould be usedd as look-upp graphs (or data sets) inn
to constructt four sets of graph. How
implementinng the propoosed algorithhm for findinng the optim
mal packet sizze. First set of graphs reelates packett
sizes to BE
ERs with diff
fferent headeer length. Second set relates optimall packet sizees to range-rrate productss
qualified byy various BE
ERs. Third seet relates paccket sizes to throughput efficiency
e
quualified by vaarious BERss
and range-rrate products. The final seet is on enerrgy efficiency
y with respecct to packet size qualified by variouss
BERs with implicit relaation to energgy per usefull bit metric. All these setts of graphs (or data sets) formed thee
o
n process.
integral partt of the data packet size optimization
8
3.1. Data packet size and BER
When ARQ protocol is used in the relatively high BER links the communication performance is sensitive
to the packet size. This implied that there is a need in choosing a suitable packet size based on BER. In our
simulation we used the kopt equation (1) below, which was adopted from [10,11].
(1)
This equation shows that the optimal packet size kopt is the function of BER, ρ and packet header length,
h. Some of the crucial parameters used in this simulation include:
Packet Size
Header length
Distance
: 10 – 14,000 bits
: 10, 40, 160 bits
: 10m – 1000m
Fig. 3 shows a set of graphs relating packet size to different BERs with different header length, h. This is
one of the set of graphs to be used in the proposed optimization algorithm. Do take note that a header length
of 160 bits is the standard length used in the RTS data packet for stop-and-wait ARQ protocol. In the
proposed algorithm this RTS packet will double its function as a test data packet for the source node to
compute the quality of the link thus obtaining the BER of the link. All these graphs would be used by the
proposed algorithm in finding the optimal data packet size. These graphs may be used for comparative study
purpose too.
A simplified data set can be obtained from Fig. 3 or from equation (1). For example, with a header length
of 40 bits, the simplified data set is obtained as in TABLE I. This simplified data set stores BERs in an
incremental step of a decade. These increment steps make BER computation practically faster. For practical
implementation the packet size to be composed in actual transmission can be the truncated value or a roundup value if truncation is not preferred.
Table I: Sample of a simplified data set.
BER
10-2
10-3
10-4
10-5
10-6
kopt
39.86605
178.9482
612.1234
1979.8950
6304.5221
Truncate
39
178
612
1979
6304
14000
Packet Size (bits)
12000
10000
h = 160
8000
6000
h = 40
4000
h = 10
2000
0
10-6
10-5
10-4
10-3
10-2
10-1
BER
Fig. 3: Data packet size plotted against different BERs.
3.2. Data packet size and throughput efficiency
9
In stop-and-wait ARQ protocol, its throughput efficiency is defined as the ratio of time for a useful
packet and the total time spent on the average for a successful packet transmission. The average time is taken
over the number of retransmissions. With a probability of packet error given as ρ the average time needed to
transmit 1 packet successfully is given by [12] as,
1
(2)
With this, the efficiency for transmitting a group of g successful packets can be expressed as,
1
(3)
where Nl is the payload length, and T is the bit duration. So, with a given a set of physical layer parameters
(ρ, R, d) where ρ is the probability of packet error, R is the bit rate, and d is the distance between transmitter
and the receiver, the throughput efficiency can be written in the form of,
1
(4)
(5)
where,
and TW is the total waiting time in the stop-and-wait protocol, c is the nominal underwater acoustic sound
speed of 1500 m/s, and h is the header length.
The optimal packet size can now be evaluated by differentiating η with respect to Nl and equate it to
zero. From which the optimal packet size, kopt is given by,
1
1
(6)
From (4), the optimal throughput efficiency can be written as,
1
(7)
Take note that μ is related to dR (range × rate) product where d denotes the distance in meter between a
source-sink pair and R is the data transmission rate in bps. It is explicit that kopt is a function of dR and the
BER (ρ) of the communication link. Some of the crucial parameters used in our simulation include:
Link delay
: 0.01s
BER (ρ)
: 10-3 , 10-4
Distance (d)
: 10m to 5km
Rate (R)
: 100 bps to 1000 bps
Header (h)
: 160 bits
No. of group (g) : 1
The simulation of this kopt resulted in a set of graphs shown in Fig. 4. These plots depict the
relationship between optimal packet size and dR products qualified by different ρ. It can be seen here that
10
low quality link does not permit large packet size. By keeping the distance d between the source-sink pair
constant e.g. static nodes deployment, and for a certain BER, the packet size seems to be increasing fairly
linearly with an increasing R. However the packet size increases at a faster rate if the link ρ is low.
2500
Optimal packet Size (bits)
2000
1500
ρ = 10-4
1000
500
0
ρ = 10-3
0
0.5
1
1.5
2
2.5
3
dR (m-bps)
3.5
4
4.5
5
x10 5
Fig. 4: Data packet size against dR (range×rate) products with different BERs.
By substituting the kopt variable in (7) with values from Fig. 4 a set of throughput efficiency graphs are
thus obtained as in Fig. 5.
1
0.9
ρ = 10-4 ; dR = 5x102
1
0.8
Throughput Efficiency
0.7
ρ = 10-4 ; dR = 5x103
0.6
0.5
ρ = 10-3 ; dR = 5x102
0.4
0.3
ρ = 10-3 ; dR = 5x103
2
ρ = 10-4 ; dR = 5x104
0.2
0.1
0
0
ρ = 10-3 ; dR = 5x104
500
1000
1500
Packet Size (bits)
2000
2500
Fig. 5: Throughput efficiency against kopt under different ρ and dR
As expected, link with high BER will have lower peak throughput efficiency than link with low BER.
This is mainly due to the smaller optimal packet size that is allowed in low quality link. For instance, with
constant dR product of 5x102 but different ρ of 10-4 (line 1) and 10-3 (line 2), the peak throughput efficiency
for ρ of 10-4 is approximately 1.5 times better than ρ of 10-3. Moreover at this peak efficiency the optimal
packet size for ρ of 10-4 is doubled that for ρ of 10-3. The reason for this phenomena is that the high BER is
certainly to produce more packets lost in the course of transmission thus pulling down the throughput
efficiency peak performance.
Another interesting observation in Fig.5 is that with a constant BER, the peak throughput efficiency will
drop when the dR product increases. For example, comparing lines with ρ of 10-4 but with different dR of
5x102, 5x103, and 5x104 respectively the peak efficiency drops from 0.8 to 0.6 and down to 0.2! This issue
can be explained by the fact that as the distance d increases and/or the transmission rate R is getting higher
the chances for data packets being dropped will also increase thus bring along a poorer peak throughput
11
efficiency. Also noticed in Fig. 5 that for a good quality link, e.g. lines for ρ of 10-4, the high throughput
efficiency seems to be sustained way passed the peak value. In other words the throughput efficiency is
maintained almost at its peak even though the optimal packet size is increasing. This may induce a fact that
data packets with large size can be transmitted in a high quality link to attain a high throughput efficiency.
3.3. Data packet size and energy efficiency
Energy efficiency is defined as the ratio of the amount of data transmitted and the energy consumed for
that operation. The underwater wireless channel, being time-varying and noisy in nature, dictates the
possibility of data corruption causing packet losses (discarded) at the sink which demands retransmissions of
the packets resulting in a waste of valuable energy. A well known primary cause of energy wastage is in the
retransmissions of data packets.
It is a known fact in wireless data communications, that the rate of packet errors is sensitive to the packet
size. In other words, if the data packet size (thus the amount of data bits) can be adjusted or optimized
according to the communication link quality (the error rate) there exist a possibility of reducing
retransmissions thus improving the energy efficiency. In a nut shell, the packet size is reduced when the link
is noisy to reduce the chances of packet errors therefore reducing retransmissions i.e. energy conservation.
Our investigation focused on the physical layer (PHY) and it is assumed that nodes is able to discover
each other and self-organize into a communication network with peer-to-peer communication between any
pair of neighbouring nodes. In this context, the energy efficiency equation by [13] is adopted as below (8)
and would be the main reference for the simulation works on finding the relationship between energy
efficiency and packet sizes. This equation is a function of packet length l and the link BER ρ. c1 and c2 are
transmitter/receiver equipment constant with h denotes the header length. Implicitly it involves the energy
per useful bit (EPUB) element.
1
(8)
In our simulation it is assumed that the source and the sink are of homogeneous type therefore they have
the same equipment constants i.e. c1 = c2. So the energy efficiency term in the ηe equation i.e. the term:
can be approximated to l/(l + h) for (l + h) >> 1. This is acceptable since in most of the practical applications
packet length is more than hundreds of bits. This is also in line with the basic definition of energy efficiency.
In this energy efficiency simulation, some of the essential parameters used were:
Link delay
BER( )
Header (α)
Length (l)
:
:
:
:
0.01s
10-2 , 10-3 , 10-4
160 bits
0 – 1000 bits
The simulation output is shown in Fig. 6. The graph strongly depicts high energy efficiency for low BER.
The energy efficiency for link with BER of 10-4 is almost two folds than those with BER of 10-2. The
efficiency drops very sharply for high BER when the packet length is increased beyond the peak energy
efficiency. This is practically true because the probability of packets being corrupted is high and therefore
the demand for retransmission increases and more energy is thus wasted. Therefore it is not surprise to
observe that the energy efficiency tapered off more gently beyond the peak performance for links with low
BERs. The consequence is large packet length/size in good quality link is able to attain higher energy
efficiency than links with poor quality.
12
1
ρ = 0.0001
0.9
Energy Efficiency
0.8
ρ = 0.001
0.7
0.6
0.5
0.4
ρ = 0.01
0.3
0.2
0.1
0
0
100
200
300
400
500
600
700
Packet Size (bits)
800
900
1000
Fig. 6: Energy efficiency against packet size under different BERs.
4. The Outcomes
The main outcome of the simulations described in the preceding sections lead the authors into finding a
possible solution to determine the optimal packet size qualified collectively by the three metrics of:
throughput efficiency, BER, and energy efficiency. We proposed an algorithm framework as follow.
4.1. Prerequisities
A database consists of three data sets belonging to the three look-up graphs similar to Fig. 3, Fig. 4, and
Fig.6 is constructed. The data sets could be constructed by simulation means or by performing actual
measurements at the body of water where the sensor nodes are to be deployed. The database constructed
shall be loaded into the memory of the underwater nodes as the “knowledge acquired” from the
communication link measurements. It is worth mentioning here that for UW nodes with memory constraint
perhaps only a simplified data sets shall be loaded into it but, of course, on the expense of lesser
communication effectiveness.
4.2. The algorithm
/*three data sets are denoted as F3, F4, and F6 to represent Fig.3, Fig.4, and Fig.6 respectively */
/* Source node and sink node are of homogeneous type */
/*test packet is essentially the RTS packet format with header length (h) of 160 bits */
{Source node: send(test_packet) to the sink with predefined bit rate (R);
Sink: ack_and_return(test_packet);
Source: with returned packet computes:
{
BER (ρ);
distance (d);
with ρ indexed into F3 to acquire Nopt1;
with dR product indexed into F4 to acquire Nopt2;
Nopt := average(Nopt1 , Nopt2 );
with Nopt indexed into F6 to acquire the energy efficiency (η);
check: difference between η and ηopt from F6;
if (difference) < (5%) then
packetsize := Nopt
else
{
with ρ indexed into F6 to obtain packet size (N) corresponds to max η ;
packetsize := average(N, Nopt);
} end_if
}
Source: assemble data_packet with packetsize ;
13
Source: send(data_packet);
}
5. Conclusions
The authors presented in this paper their simulation works in finding the relationship between optimal
data packet size and three important UWA communications performance metrics of BER, throughput
efficiency, and the energy efficiency. In fact this is the extension to the previous work by the same authors
found in [14]. The outcomes of the simulation has lead the authors to propose an algorithm that may be
implemented in underwater sensor nodes to determine the optimal packets size qualified by the three
performance metrics for an effective and efficient data transmission. The proposed algorithm shall be
verified and tested in more depth in the authors’ next course of research.
6. References
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Engineering, vol.121, No.2, April 1996, pp.125-136.
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Journal of Ad Hoc Networks 3, May 2005, pp 257-279.
[3] J. Heidemann, W. Ye, J. Willis, A.A. Syed, Y. Li. Research Challenges and Applications for Underwater Sensor
Networking. Proc. of IEEE Wireless Communications and Networking Conference, Apr. 2006, pp 229-235.
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Advances and Future Challenges. Marine Technology Society Journal, vol.42, No.1, Spring 2008, pp.103-116.
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& Networking. Invited paper, Proc. IEEE Oceans'08 Conference, September 2008.
[6] M. Stojanovic. Underwater Wireless Communications: Current Achievements and Research Challenges. IEEE
Oceanic Engineering Society Newsletter, Spring 2006.
[7] Regents of the SIGNET lab, University of Padova, 2007.
[8] N. Baldo, F. Maguolo, M. Miozzo, M. Rossi, M. Zorzi. ns2-MIRACLE: A Modular Framework for Multitechnology and Cross-layer Support in Network Simulator 2. 2nd international conference on Performance
evaluation methodologies and tools, 2007.
[9] M.C. Vuran, I.F. Akyildiz. Cross-layer Packet Size Optimization for Wireless Terrestrial, Undewater, and
Underground Sensor Networks. Proc. IEEE INFOCOM ’08, April 2008.
[10] E. Modiano. Data Link Protocols for LDR MILSTAR Communications. Lincoln Laboratory, Communications
Division Internal Memorandum, October 1994.
[11] M. Schwartz. Telecommunication Networks: Protocols; Modeling and Analysis. Addison-Wesley, New York , pp.
125-156, 1987.
[12] M. Schwartz. Telecommunication Networks. Adison Wesley, 1988.
[13] Y. Sankarasubramaniam, I.F. Akyildiz, S.W. McLaughlin. Energy Efficiency Based Packet Size Optimization in
Wireless Sensor Networks. Proc. 1st IEEE Int. Workshop on Sensor Network Protocols and Applications
(SNPA'03), May 2003.
[14] T.J. Low, A. Azween. Underwater Acoustic Communications: Relationship Between Data Packet Size,
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Dec 2010.
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