Wireless Sensor Network, 2010, 2, 905-909
doi:10.4236/wsn.2010.212108 Published Online December 2010 (http://www.scirp.org/journal/wsn)
Lifetime Optimization via Network Sectoring in
Cooperative Wireless Sensor Networks
Hadi Jamali Rad1, Bahman Abolhassani1, Mohammad Abdizadeh2
1School of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran
2School of Electrical Engineering, Sharif University of Technology, Tehran, Iran
Received October 3, 2010; revised October 12, 2010; accepted October 14, 2010
Abstract
Employing cooperative communication in multihop wireless sensor networks provides the network with sig-
nificant energy efficiency. However, the lifetime of such a network is directly dependant upon the lifetime of
each of its individual sections (or clusters). Ignoring the fact that those sections close to sink have to forward
more data (their own data plus the data received from the previous sections) and hence die sooner with con-
sidering equal section sizes, leads to a sub-optimal lifetime. In this paper, we optimize the section sizes of a
multihop cooperative WSN so that it maximizes the network lifetime. Simulation results demonstrate a sig-
nificant lifetime enhancement for the proposed optimal sectoring.
Keywords: Wireless Sensor Network (WSN), Cooperative Communications,
Virtual Multi-Input-Multi-Output (V-MIMO), Energy Efficiency
1. Introduction
Wireless sensor networks (WSNs) consist of a large num-
ber of tiny sensor nodes deployed over a large area. Such
wireless nodes typically operate with small batteries for
which replacement, when possible is very difficult and
expensive. Thus, in many practical scenarios, the wireless
nodes should operate for many years without any battery
replacement or recharge. Hence, minimizing the power
consumption in different functional layers of wireless
nodes is a very challenging design consideration. Fur-
thermore, affected by channel impairments, energy con-
straints of the sensor nodes are the main limiting factors of
the system performance of WSNs and therefore power
efficiency is of special importance in such networks.
Diversity techniques have been proposed to provide
a wireless network with reliable and power efficient
communications [1,2]. However, tiny sensor nodes
cannot accommodate multiple antennas and hence the
implementation of MIMO-based communications in a
wireless sensor network (WSN) requires cooperation
among sensor nodes [3,4]. These sensor nodes can be
considered as a virtual MIMO (V-MIMO) unit.
Moreover, in large WSNs, multihop communications
are used instead of long-haul transmission to reduce
high energy consumption due to exponentially increase
in path-loss with the distance between source and sink
of information. In multihop networks, there are several
sections (also can be called clusters) between the source
and the sink nodes. Thus, the multihop sections closer to
the sink should not only transmit their own information
but also relay the information of other sections. So, the
closer the section to the sink is, the higher energy it con-
sumes and hence the sooner it dies [5]. Therefore, mini-
mizing the total energy consumption of these multihop
networks results in dying of closer sections to the sink,
which itself reduces the lifetime of the network. This
motivated us to mathematically derive the optimum sec-
toring (section sizes) of a multihop cooperative WSN to
maximize its lifetime.
2. Network Model
In a typical multihop cooperative WSN, the network will
be triggered by an event whose information should be
collected by a local V-MIMO unit and then be transmit-
ted by that unit to a sink. If the sink is far from th e event,
the information should be forwarded to the sink by a
multihop-based routing manner [3].
To facilitate the analysis, we consider a linear network
topology for such cooperative WSNs. The network with
a node density β (nodes/m) can be divided into m sec-
tions (the same clusters for a general configuration) each
with one information collecting/forwarding V-MIMO
unit containing NT sensor nodes. The network length is
D and a section length di (distance between i-th section

906 H. JAMALI RAD ET AL.
Figure 1. Network sectoring. (a) uniform sectoring; (b) optimal sectoring.
boundaries) is considered for each section (as depicted
in Figure 1(a)).
Total energy consumption for transmitting L bits in a
MIMO system over a Rayleigh fading channel can be
expressed as [3]
 

0
=1+ k
bctcrb
ELEGdLP PR   (1)
where α is a parameter describing the efficiency of radio
frequenc y p o wer amplifier. b
E is the average energy per
bit at the receiver for a gi ven bit error rate requirement. G0
is the power attenuation factor at unit distance (d = 1 m)
and k is the path-loss exponent. Pct and Pcr are the circui-
try power consumption at the transmitter and receiver
sides, respectively. Rb is the bit rate [3-5]. Simply, if the
sensor nodes are uniformly distributed in the network,
the average number of bits generated in each section will
be equal L1 = L2= Lm = L. The scenario for informa-
tion transmission to the sink in this network can be ex-
plained in the following three phases.
Phase 1: In each section, the local information is col-
lected by a V-MIMO unit (a group of NT nodes). Con-
sider that generalization for multiple V-MIMO units in
each section is straight forward.
Phase 2 (non-cooperative communication): In each
section, the NT nodes broadcast their information to all
the other V-MIMO nodes using different time slots with
uncoded M-QAM [3]. Meanwhile, these NT nodes are
placed beside each other with a maximum separation of
lm = T N

meters. For these trans missions, we consider
a Rayleigh fading channel with square-law path-loss plus
additive white Gaussian noise (AWGN). Energy con-
sumption of the i-th section for the non-cooperative
phase can be expressed as [5]
   
2
20 2
=1+
i
intrabmct cr
ELEGlLPPbBW   (2)
where b2 represents the modulation constellation size,
2b
E denotes b E for constellation size b2 and BW is the
transmission bandwidth of each sensor node.
Phase 3 (cooperative communication): When the to-
tal information is collected by a V-MIMO unit, it will be
encoded and transmitted using practical orthogonal
STBC code design explained in [6] to the V-MIMO unit
of the next section. This code design allows us to obtain
the energy consumption with best accuracy. It is notable
that each of these V-MIMO units should relay the infor-
mation of previous units as well. For these transmissions,
we consider a Rayleigh fading channel with k-th order

H. JAMALI RAD ET AL. 907
path-loss plus AWGN.
In order to take the effect of training overheads for
channel estimation into account, suppose that the infor-
mation block size of the STBC code is equal to F sym-
bols and in each block we include N training symbols.
Hence, if R is the transmission rate [4,5], the effective bit
rate of the MIMO transmission is given by

1eff
FN
RRbBW
F

 (3)
where b1 represents the modulation constellation size for
the cooperative communications. Hence, by considering
(1) and (3), energy consumption of each section for mul-
tihop transmissions (cooperative communications) can be
given by
 






1
10
1
=1+ kTct Tct
i
interb i
eff effeff
iLNPi LNP
bBW
EiLαEG dRR R

 
(4)
where 1b
E denotes b E for constellation size b1. In the
above equation, the first term denotes the energy con-
sumption for transmitting iL bits (L bits collected by the
i-th V-MIM O pl us (i – 1)L bits received from (i – 1) pre-
vious sections), the second and the third terms denote the
circuitry energy consumption for transmitting iL and
receiving (i – 1)L bits. Therefore, the total energy con-
sumption of each sectio n by considering bot h c oo pe rative
and non-cooperative communications can be expressed as
Ei = ii
intra inter
EE.
3. Optimal Networ k S ec t o r i n g
As mentioned earlier, maximizing the lifetime of the
network is our main goal. In the explained cooperative
network model, the lifetime of the network is directly
dependent upon the existence of each section. It means
that if one section dies because of its high workload, the
network connectivity will be broken and the network will
become useless. Hence, the effective lifetime of the net-
work is inversely proportional to the maximum energy
consumption (workload) among the network sections as
1,1,,.
max( )
i
Lifetimei m
E
 (5)
Consid er Figure 1(a) where the network has a uni-
form sectoring. In this case, the energy consumption for
the non-cooperative communication (as in (2)) is ap-
proximately equal for all sections. Therefore, knowing
the fact that each section should not only transmit its
own information but also forward the information of
previous sections, the workload of the sections closer to
the sink is much higher. Thus, with equal-size sections,
the network lifetime is limited to the lifetime of the m-th
section (the last section), whose lifetime is much shorter
than other sections. Obviously, this is not the optimal
performance for this network.
In order to maximiz e the network lifetime, we propose
to modify the section sizes as illustrated in Figure 1(b).
To find the optimal network sectoring, the following
optimization problem should be solved for the linear
network unde r con sideratio n
1
min max(),
..
i
m
i
i
E
s
tdD

 (6)
Lemma: Instead of solving the above optimization
problem, we solve the following equivalent optimization
problem problem


2
2
11
1
11
min( ),
..
mm
ii i
ii
m
i
i
Var EEE
mm
std D






(7)
For the simplicity, by considering (2) and (4), we re-
write Ei asCiBiAdE k
ii  , where

 
1
10
1,
,.
b
eff
TctTcrTcr
eff effeff
bBW
AL EGR
LNPLNPLNP
BC
RR R
 
 
(8)
Hence, we will have


2
2
11
1
11
min ,
..
mm
kk
ii
ii
m
i
i
iAdiB CiAdiB C
mm
std D


 



(9)
To solve the above problem, we define the Lagrangian
(J) [7] associated with the problem (9) as


1
() .
m
ii
i
J
Var EDd 


 (10)
By setting the first derivative of J with respect to each
of its variables equal to zero, we have
1
2
220,1,, ,
m
jj j i
i
jj j
EE E E
Jjm
dmd d m



 
 

(11)
1
1
2
22.
m
jj i
i
j
EE E
md m









 (12)
To extract Ej, we take a summation over j from both
sides of (12), which results in
1
111
22 , mmm
j
ji
jij
j
E
EE
mm d










 (13)
1
1
0.
mj
j
j
E
d



 




 (14)

908 H. JAMALI RAD ET AL.
From (2) and (4), (Ej is strictly ascending function of
dj) and hence λ = 0. By substituting λ = 0 into (12), we
have
1
12 .
m
i
i
m
E
EE EE
m

 

 (15)
As is expected, Equation (15) means that to maximize
the lifetime of the network, all of the sections should
have equal workload and therefore all die together. From
summation of (2) and (4) and considering (15), the op-
timal section size can be expressed as
1,, .
k
i
ECiB
dim
iA

 (16)
As is clear form (16), the optimal network sectoring
problem has a waterfilling form solution (di) with para-
meter E given by (15), which is determined by network
length constraint D.
Proof of the Lemma: We prove that (6) and (7) have the
same solutions. Assume that these problems have different
solutions

66
,
ii
dE and

77
,
ii
dE for i respectively.
Note that E7
i values are equal i as discussed in (15).
Since the network length constraint should hold for both
solutions, we cannot say 67
ii
dd

i. So, there should
be an i so that 67
ii
dd (unless 67
ii
dd) and 67
ii
EE.
This means that

77
,
ii
dE is a better solution for prob-
lem (6); in other words,

66
,
ii
dE is not the optimal
solution for (6). Hence, our initial assu mption was wrong
and therefore (6) and (7) have the same solution.
4. Performance Evaluation
We consider the explained network model in Section 2
and evaluate the effect of the proposed network sectoring
for a linear m-section WSN using computer simulations.
We consider the case where m = 8, NT = 4, b1 = 2 and b2
= 8. The path-loss exponent is considered to be k = 2 for
non-cooperative transmissions and k = 3 for cooperative
transmissions. As described earlier, the lifetime of the
network is inversely proportional to maximum energy
consumption of individual sections as in (5). Thus, to
represent the results, we define 1/max(Ei), i = 1, 2, , m
as lifetime coefficient.
Figure 2 compares the total energy consumption of
different sections of the multihop network for the case of
uniform and the proposed optimal sectoring for D = 1000 m.
The x-axis represents the boundaries of different sec-
tions from the first section that is located at x = 0. From
the figure, the proposed optimal sectoring (section sizes)
results in equal total energy consumption for different
sections of the network, which in turn leads to maximiz-
ing of the total network lifetime. Meanwhile, in the uni-
form sectoring the closest section to the sink consumes
100200 300400 500600 700800 90010001100
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
-3
Distance of each section from the first section (meters), m = 8
Total energy consump. per section (Joules/bit)
Uniform sectoring of network sections
Optimal sectoring of network sections
Figure 2. Total energy consumption of different sections.
much more energy compared to that of the optimal sec-
toring, and hence the uniformly sectored network will die
sooner. As is expected from our previous analysis,
to achieve even energy distribution in the explained net-
work, the sections which are closer to the sink have
smaller sizes.
Figure 3 illustrates the lifetime coefficient of uniform
and the proposed optimal sectoring. As well, relative
lifetime (R = Lifetime coeff. of optimal/Lifetime coeff.
of uniform) for both schemes is depicted for different
network sizes (D). From the figure, the proposed optimal
sectoring enhances the lifetime of the network by about
130% (2.3 times) for large network sizes (D) compared
to that of the uniform sectoring.
5. Conclusions
In this paper, we investigated the effect of section (clus-
ter) size on the total power consumption of multihop
cooperative WSNs. We proposed an optimal network
sectoring for linear multihop networks so that it mini-
mizes the total power consumption of the network by
evenly distributing the power in such a network. The
simulation results illustrate that the proposed optimal
8001000 1200 1400 16001800 2000 2200 2400 2600
0
0.5
1
1.5
2
2.5
Network length, D (meters)
Lifeime coefficient of uniform sectoring
Lifeime coefficient of optimal sectoring
Relative lifetim e improvement (R)
Figure 3. Lifetime of ne twork versus network size, D.

H. JAMALI RAD ET AL. 909
sectoring scheme leads to equal power con sumption in all
the sections and increases the lifetime of the network up
to 2.3 times compared to the equal sectoring.
6. Acknowledgements
The authors would like to acknowledge Mr. Mehran
Mashreghi for his insightful comments and helpful dis-
cussions.
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