I. J. Communications, Network and System Sciences. 2008; 1: 1-103
Published Online February 2008 in SciRes (http://www.SRPublishing.org/journal/ijcns/).
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
Abstract
Energy efficiency and enhanced backbone capacity is obtained by exploiting the geometric orientation of cooperative
nodes in wireless sensor network. The cooperative communication in wireless sensor networks (WSN) gives us leverage
to get the inherent advantages of its random node’s locations and the direction of the data flow. Depending on the channel
conditions and the transmission distance, the number of cooperative nodes is selected, that participate in an energy
efficient transmission/reception. Simulation results show that increasing the cooperative receive diversity, decreases the
energy consumption per bit in cooperative communications. It has also been shown that the network backbone capacity
can be increased by controlled displacement of antennas at base station at the expense of energy per bit.
Keywords: Cooperative Communication, Energy Efficiency, Capacity, Receive Diversity Sensor Network.
1. Introduction
Wireless sensor network consists of hundred or
thousand of small, inexpensive wireless nodes responsible
for monitoring a physical activity and reporting to the base
station (BS), where end user can access the reported data.
Cooperative communication has gain an obdurate place in
wireless networks. It has been shown [1] that
multiple-input multiple-output (MIMO) systems require
less transmission energy than the single-input
single-output systems. It’s still intricate to build multiple
antennas on low-cost, small-sized sensor nodes; therefore
MIMO techniques cannot be applied directly on wireless
sensor networks. However it is possible to implement
MIMO techniques in WSN without physically having
multiple antennas at the sensor nodes via cooperative
communication techniques [2][3], such distributed MIMO
techniques can offer considerable energy saving even after
allowing some extra circuit power, communication and
training overheads.
The use of cooperative communications in wireless
sensor networks allows for energy savings through spatial
diversity gains [2]. Traditional MIMO utilizes fixed
antenna arrays in transmitter/receiver. These arrays are of
definite geometric shapes, e.g., one dimensional array,
circular array, rectangular array etc, but in cooperative
MIMO communications there is no pre-defined array of
antennas, the cooperative nodes cooperate with each other
at run time to send/receive data.
There is already a lot of works related to cluster
formation [4-7], capacity improvement [8] and energy
efficient cooperative communication [2][3][9] in WSN,
but little attention has been given to cooperative nodes
selection on the basis of their location in clusters to
improve the energy efficiency and reliability.
Most of the recent research work in wireless sensor
networks, modeled the wireless channel with rich scattered
or Rayleigh fading channel model [2][3][10], which is
suitable channel model for wireless communications in
urban areas where dense and large man made buildings act
as rich scatterers. Sensor networks are usually deployed in
the areas far away from human population, e.g., in plain
desert areas for surveillance, on volcano hills for early
alerts and near sea-shore for storm alerts etc. In all these
situations, Ricean fading channel model works well,
because it contains both non line-of-sight (NLOS) and
line-of-sight (LOS) components.
In this paper, we have divided the WSN into two
functional model parts, i) whole sensor network except the
backbone link is modeled with Ricean fading channel and
ii) the backbone link (the link between base station and the
Exploiting Geometric Advantages of Cooperative
Communications for Energy Efficient Wireless
Sensor Networks
Irfan AHMED1, Mugen PENG2, Wenbo WANG2
Wireless Signal Processing and Network Lab
Beijing University of Posts and Telecommunications, Beijing, P.R.China
E-mail: 1irfanahmed44@gmail.com, 2{pmg, wbwang}@bupt.edu.cn
56 I. AHMED ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
cooperative nodes near the base station) is modeled by
pure deterministic channel.
Remainder of this paper is organized as follows. System
model is presented in section 2. Section 3 exploits the
inherent advantages of wireless sensor network.
Performance analysis in terms of energy efficiency and
capacity of sensor network is presented in section 4. We
show simulation results in Section 5, and conclude in
Section 6.
2. System Model
The system model shown in figure 1, it consists of a
cluster based sensor network. Sensor nodes are grouped
for cooperative communications. The selection of group
nodes is described in next section. In typical wireless
sensor network scenarios as narrated above, large number
of nodes are randomly deployed in an unattended area.
Due to the presence of scatterers as well as line-of-sight
component in those areas, Ricean fading channel model
has been used to modeled the WSN, Ricean fading channel
has both LOS and NLOS components [1]
() ()
/1 1/1H= HHw
KK K++ + (1)
where
()
/1 HKK+ is LOS or deterministic component of
the channel,
()
1/ 1Hw
K+ is NLOS or scattered component
Figure 1. System Model
of the channel and K is the Ricean factor, it is the ratio of
the LOS power to the scattered power. 0K
=
in the
presence of rich scattered or pure Rayleigh fading, and
K→∞ in case of non-fading channel.
We restrict our analysis to the case of frequency-flat
fading. The elements of Hw are zero-mean circularly
symmetric complex Gaussian (ZMCSCG) random
variable with unit variance [1]. We have assumed binary
phase shift keying (BPSK) modulation with Alamouti
scheme [11] for cooperative MIMO communications. We
have furthermore assumed that the channel is unknown to
the transmit nodes and is perfectly known to the nodes at
receive side.
3. Advantages of Cooperative
Communications in WSN
3.1. Exploiting the WSN Architecture
1) WSN is deployed with hundred or thousand of
structural or randomly placed nodes making it
ideal for cooperative communications.
Selections of nodes in a cooperative group which
are approximately at same distance from the
intended receive nodes, results in equal energy
consumption per bit in cooperative
communications.
2) By selecting closest nodes within a cooperative
group, we can decrease energy consumption per
bit in intra-cooperative node communications.
3) In WSN the data flow direction is from sensor
network to BS i.e., most of the time BS act as a
receiver (neglecting small amount of signaling
data from BS to network). By increasing the
number of antennas at BS, we can take
advantages of receive diversity at BS, because
BS has no energy constraint.
4) Usually the base station is located at some height
in order to get reliable communication with the
network, which results in a dominant LOS
component. By exploiting this LOS
communications we try to get maximum capacity
in this backbone link.
3.2. Selection of Cooperative Nodes in a Network
Cooperative communications in WSN can be more
beneficial if transmit cooperative nodes are at equal
distance from the intended receive nodes. This strategy
evenly distributes the transmission energy in LOS
component because in LOS component the power loss is
inversely proportional to the square of the distance
between the transmitter and receiver. In addition to this the
cooperative nodes should be at minimum distance from
each other to save energy in local communication within
the cooperative nodes group. These measures reduce the
required bit energy for desired BER. How these measures
can be taken?
3.2.1. Algorithm
After the cluster formation [5] and selection of
cluster-heads in each cluster, following steps ensure the
energy efficient selection of cooperative nodes:
Step I: BS broadcasts RSSI (Receive Signal Strength
Indication) beacon signal to neighbor cluster nodes.
EXPLOITING GEOMETRIC ADVANTAGES OF COOPERATIVE COMMUNICATIONS FOR ENERGY 57
EFFICIENT WIRELESS SENSOR NETW
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
Step II: Each node
()
i
χ
measures receive signal
strength, calculate
(
)
di
χ
and send back an ACK beacon
signal to BS, where
()
di
χ
is the distance between
node
()
i
χ
and BS.
Step III: Upon receiving the ACK beacons from all
nodes, BS calculates their distances from itself
(
)
BS
di
.
Final estimate
()
_BS
di
χ
is obtained by averaging
()
di
χ
and
()
BS
di.
Please note that
()
diis not an actual physical distance,
it is equal-power-distance.
Step IV: Based on these estimates BS allocates an
equal-power group identity to those nodes which lies
within a certain range
()
()
_
min BS
di
χ
+ℵ∆Ξ, where
is
an integer and ∆Ξ is small distance depends upon
()
()
_
min BS
di
χ
and
()
()
_
max BS
di
χ
.
Step V: Each node in equal-power group
P
multicasts
a RSSI beacon signal within its group. It will know its
distance from other nodes in the group with the help of
ACK receives.
Finally the cooperative communications group
,
CC P
  . Nodes selection preference order in C
is
Proximity > Residual node energy
Node within a cooperative communication group with
highest residual energy becomes the
cooperative-group-head, it responsible for data
aggregation and the communication within the cooperative
group.
In the same way cooperative-group-head plays the role
of BS for neighbor clusters and follows from Step I to V.
4. Performance Analysis
4.1. Network Performance in Ricean Fading
Channel
We have modeled the sensor network with Ricean
fading channel model. In the particular arrangement of
cooperative nodes shown in figure 1, where all nodes
(antennas) are at same distance from the intended receivers,
we use following equation [2] for total energy required per
bit per hop,
()()
2
__
02
4
1tx electrx elect
bitl fTR
bbtr
PP
d
NMNn n
RR
GG
π
αρ λ
=++ + (2)
where
α
is depends upon the drain efficiency of power
amplifier in transmitter circuitry,
ρ
is the signal power
(from nT transmit nodes) to noise ratio at each of the
receive node, 0
N is AWGN power spectral density, dis
the distance between transmitter and receiver,
λ
is the
carrier wavelength, ,
tr
GG are antenna gains of transmitter
and receiver respectively, l
M
is the link margin
compensating hardware process variations and other noise
or interference, f
N is the receiver noise figure,b
Ris
transmission rate and _tx elect
P,_rx elect
P are power dissipated
in transmitter and receiver circuits, respectively. The
system parameters related to above equation are taken
from [2, Table I], and the power consumption values of
transmitter and receiver circuits (_tx elect
P=38mW,
_rx elect
P=41mW) are of TelosB mote1 [12]. Expression for
BER as a function of SNR in Ricean fading channel is
given as [1]
22
min
2
min
4
14
2
min
1
1/4
HF
T
TR
TR
T
dK
n
nn
nn d
Kn
b
T
K
Pe
Kd n
ρ
ρ
ρ
⎛⎞
⎜⎟
⎜⎟
−×⎜⎟
×⎜⎟
++
⎜⎟
⎝⎠
⎛⎞
+
⎜⎟
++
⎝⎠ (3)
where min
d is the minimum distance of separation of
underlying scalar constellation and H
F
is the Frobenius
norm of channel matrix H. Using upper bound in above
expression, we obtain table I, which has been used for
evaluation of energy per bit in equation (2).
4.1.1. Discussion
From equation (2) and (3), we can see that the
transmission energy per bit for a desired BER is functions
of the number of transmit/receive nodes, underlying
constellation size and the channel condition. Table I
shows the values of
ρ
for different combinations of
transmit and receive nodes at 3
10
b
P
=. It can be seen that
required SNR at receiver nodes decreases with increasing
number of cooperative nodes for a fixed BER.
4.2. Backbone Link Performance in Deterministic
or LOS Channel
4.2.1. Energy Consumption
The backbone link is modeled by LOS channel, for
which the total energy required per bit is given by equation
(2). The SNR (
ρ
) per receive node in equation (2) is given
as [1, equation 5.60]
(
)
2
exp 4/H
bT
F
Pn
ρ
=− (4)
then the equation (2) becomes
1 With very low power TelosB mote and power loss exponent of two,
we can neglect the inter-node cooperation overhead [14].
58 I. AHMED ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
() ()
2
0
22
__
ln 1/4
1
4H
b
T
bitl f
tr
F
tx electrx elect
TR
bb
nPN
d
E
MN
GG
PP
nn
RR
π
αλ
=+
++
(5)
4.2.2. Capacity
The instantaneous capacity (in bps/Hz) for T
n transmit
and R
n receive cooperative nodes under an average
transmit power constraint is given by [1]
2
logdetIHH
R
H
n
T
Cn
ρ
⎡⎤
⎛⎞
=+
⎢⎥
⎜⎟
⎢⎥
⎝⎠
⎣⎦
(6)
where I
R
nis
R
R
nn× identity matrix, His
R
T
nn× channel
matrix and H
H
is the Hermitian transpose of H.
For LOS propagation, and a narrow-band channel at
fixed carrier frequency/
c
f
c
λ
=, ray tracing from
transmitter to receiver gives following channel matrix H
with complex scalar entries
()
,,
,,
exp 2/
nodejnode k
jk
nodejnode k
jT R
HTR
π
λ
−−
= (7)
where ,,nodejnode k
TR is the distance between jth
transmit node and kth receive node.
Let RT
nnn== be the number of nodes participating
in cooperative communication on either side. With
,
rt
ddd in figure 2, the path lengths between any pair
of transmit and receive nodes are approximately the same
to within the array size i.e.,,,nodejnodek
dT R≈− , and the
complex scalars
j
k
H
all have same magnitude but
different phases
j
k
θ
. Mathematical example of this
particular type of normalized His given as [13]
(
)
exp
jk jk
Hj
θ
= (8)
where
()( )
2
00jk ii kk
n
π
θ
=−−−
⎡⎤
⎣⎦
, 00
,ik are arbitrary
integers.
Consider the case of 2n=and 00
,0ik=, the small path
length difference
,1 ,1,1,2/4
node nodenode node
TR TR
δ
λ
=−−− = (9)
guaranteed that the channel matrix is orthogonal and of full
rank, 2 in this case. Practically this can be realized by the
slight movement of antennas at base station. Since base
station is mostly act as a receiver in the wireless sensor
network, positioning of antennas based on received RSSI
at base station can be easily achieved.
With these values orthogonal channel matrix become
1
1
Horthognal
j
j
⎛⎞
=⎜⎟
⎝⎠
(10)
and the capacity from equation (6)
[
]
2
log 1Cn
ρ
=
+ (11)
Advantage of cooperative MIMO in terms of capacity
can be obtained if the channel matrix H is orthogonal.
4.2.3. Discussion
Interestingly, from equation (5) we see that the distance
dependant part of above equation is inversely proportional
to the square of Frobenius norm of channel matrix, and, it
linearly dependent on the number of transmit nodes.
Therefore the receive diversity techniques provide more
energy efficient communication.
In clear LOS environment, capacity of wireless channel
depends upon the rank of channel matrixHas depicted by
equation (6). Capacity becomes maximum, when the
channel matrix is of full rank (or orthogonal).
5. Simulation Results
We determine the impact of the selection of cooperative
nodes and the physical orientation of antennas of BS on the
total energy required per bit transmission in WSN and the
capacity of the backbone link. The simulations are
performed using MATLAB® by The MathWorks.
Figure 3 shows an amount of extra energy consumption
per bit compared to our selection algorithm. The
transmission distance ratio along x-axis is the ratio of the
distance of intra cooperative group nodes without our node
selection algorithm and with our algorithm. Since intra
cooperative group communication is non-cooperative 1 to
1 communication, therefore more energy consumption per
bit is observed in the case of severe fading, K=1, it rises
with square of the distance and consumes 33% more
energy when the nodes separation is 3.5 time to that of
closest nodes of our algorithm. With increasing values of K
(i.e., less fading) the slope of extra energy consumption
decreases. Therefore in fading channels our algorithm
saves a sufficient amount of energy.
In figure 4 we have total energy consumption per bit as
a function of long-hual distance in a rich scattering
environment i.e., K=1. Among different combinations of
transmit and receive cooperative nodes, the largest receive
diversity combination (1, 4
TR
nn
=
=) gives lower energy
consumption per bit in a wide range of transmission
distance (from 60m to onwards).
Figure 5 shows an improvement in all energy curves as
compared to the energy curves in figure 4, this is due to
EXPLOITING GEOMETRIC ADVANTAGES OF COOPERATIVE COMMUNICATIONS FOR ENERGY 59
EFFICIENT WIRELESS SENSOR NETW
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
less severe fading environment, K=2.
When the deterministic or LOS component is dominant
K=10, (i.e., the channel is more close to AWGN channel)
as shown in figure 6 the lowest energy consumption per bit
is given by the case when there is one transmit node and
two receive cooperative nodes, it remains with lowest
energy per bit up to the transmission range of 100m., after
that (1,4
TR
nn==) combination becomes the lowest
energy. This confirms the effectiveness of large receive
diversity in long haul transmissions because at large
distances the 1st term (which depends upon d, nT, and nR) in
equation (2) becomes more dominant than 2nd and 3rd
terms.
In pure deterministic or LOS communications with BS,
we have neglected the receive circuit energy consumption
in the BS, because BS has no energy constraint. Figure 7,
shows that the receive diversity case (1,4
TR
nn==)
renders the least energy consumption per bit in the entire
transmission range. Due to the LOS BS antennas
orientation the energy consumption per bit is smallest
among all other Ricean cases. But the cost we have given
for this, is the degradation in spectral efficiency (bps/Hz).
Figure 8 shows a comparison of LOS orthogonal
channel capacity (2,2
TR
nn==) with (1, 4
TR
nn==).
We can see that there is a trade off between energy
consumed per bit and the capacity. In most of the cases
capacity is not the main issue, and we are more concerned
about the energy consumption.
Finally, figure 9 shows how cooperative energy
consumption depends on the constellation sizebfor
various cooperative MIMO schemes. It is clear from
Figure 9 that there is an optimal constellation size for each
cooperative MIMO scheme for which the total
transmission energy per bit is minimized. It again
strengthens our argument that receive diversity give more
energy efficient cooperative communication. We have
used following approx. expression to obtain relation
between BER and SER in (3) for K=1,
2
,2
log b
M
b
P
PM
M
≈= (12)
Table 1.
6. Conclusion
Geometric orientation based selection of cooperative
nodes and the specific placement of antennas at BS, greatly
impact the total transmission energy consumption per bit
and the capacity of the backbone link. Simulation results
show that, using the geometric advantages in selecting the
cooperative nodes, we come across an energy efficient
transmission for different transmission ranges. Since the
sensor network is data centric and most of the time there is
unidirectional data flow (from network to BS), therefore
cooperative communication with minimum number of
transmit nodes and maximum optimal number of receive
nodes result in low energy per bit transmission. An optimal
constellation size for various cooperative schemes also
reveals that receive cooperative diversity is near optimal.
A trade off exists between energy consumption per bit and
the capacity. Since sensor networks are usually a low data
rate networks, therefore we usually opt low energy
cooperative communication.
7. Acknowledgement
This work was supported by National advanced
technologies researching and developing programs. (China
863 programming, NO.: 2006AA01Z257).
Figure 2. nT transmit and nR receive cooperative nodes LOS
channel model
11.5 22.5 33.5 4
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4x 10-7
Transmission distance ratio
Extra energy consumption per bit (J)
Extra Energy Consumption compared to our Algorithm
K=1
K=2
K=10
K->infinity
Figure 3. Energy consumption as compared to our algorithm
3
10
b
P
=
ρ
2,
1
T
R
n
n
=
=
1,
2
T
R
n
n
=
=
2,
2
T
R
n
n
=
=
1,
4
T
R
n
n
=
=
2,
4
T
R
n
n
=
=
K=1 16.6 13.6 8.8 5.8 4
K=2 14.7 11.7 7.9 4.9 3.5
K=10 9.9 6.9 6 3 2.7
60 I. AHMED ET AL.
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
20 30 4050 6070 80 90100110120
0
0.5
1
1.5
2
2.5
3
3.5
4x 10
-6
Trasmission distance (meters)
Total energy consumption per bit (J)
Network in rich scattering environment, K=1
nT=2,nR=1
nT=1,nR=2
nT=2,nR=2
nT=1,nR=4
nT=2,nR=4
Figure 4. Total energy per bit in Rayleigh fading, K=1
20 40 60 80100 120 140 160
0
0. 5
1
1. 5
2
2. 5
3
3. 5
4x 10
-6
Trasmission distance (meters)
Total energy consumption per bit (J)
Network in less scaterring environment, K=2
nT=2,nR= 1
nT=1,nR= 2
nT=2,nR= 2
nT=1,nR= 4
nT=2,nR= 4
Figure 5. Total energy per bit with K=2
20 40 6080100120 140 160
0. 5
1
1. 5
2
2. 5
3x 10
-6
Trasmission distance (meters)
Total energy consumption per bit (J)
Network with dominant LOS environment, K=10
nT=2,nR= 1
nT=1,nR= 2
nT=2,nR= 2
nT=1,nR= 4
nT=2,nR= 4
Figure 6. Total energy per bit with K=10
20 40 6080100120 140 160
1. 5
2
2. 5
3
3. 5
4
4. 5
5
5. 5
6x 10
-7
Transmission distance (meters)
Transmission energy per bit (J)
Network in clear LOS environment
nT=1,nR=1
nT=1,nR=2
nT=2,nR=2
nT=1,nR=4
Figure 7. Total energy consumption in backbone link
-2 0246810 12
1
1. 5
2
2. 5
3
3. 5
4
4. 5
5
5. 5
6
SNR (dB)
Capacity (bps/Hz)
Backbone Link Capacity
nT=1,nR=4
nT=nR=2
Figure 8. Capacity of backbone link Vs SNR
11.5 22.5 33.5 44.5 55.5 6
0
0. 2
0. 4
0. 6
0. 8
1
1. 2
1. 4
1. 6
1. 8
2x 10-5
Constellation size b
Total transmission energy per bit in J
Cooperative MIMO
1x2
2x1
3x1
3x2
3x3
1x3
2x3
Figure 9. Total transmission energy consumption over b
EXPLOITING GEOMETRIC ADVANTAGES OF COOPERATIVE COMMUNICATIONS FOR ENERGY 61
EFFICIENT WIRELESS SENSOR NETW
Copyright © 2008 SciRes. I. J. Communications, Network and System Sciences. 2008; 1:1-103
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