ENERGY EFFICIENCY OF MIMO COOPERATIVE NETWORKS WITH ENERGY HARVESTING SENSOR NODES

International Journal of Ad hoc, Sensor & Ubiquitous Computing (IJASUC) Vol.4, No.2, April 2013
DOI : 10.5121/ijasuc.2013.4201 1
ENERGY EFFICIENCY OF MIMO COOPERATIVE
NETWORKS WITH ENERGY HARVESTING SENSOR
NODES
Said El Abdellaoui1
, Youssef Fakhri1,2
, Samir Saoudi3
andDriss Aboutajdine1
1
LRIT, UnitéAssociée au CNRST (URAC 29), Faculty of Sciences University
Mohammed V-Agdal Rabat, Morocco.
elabdellaoui.said@yahoo.fr, aboutaj@fsr.ca.ma
2
Equipe: Réseaux et Télécommunication, Faculty of Sciences, University Ibn
Tofail,Kenitra, Morocco.
fakhri-youssef@univ-ibntofail.ca.ma
3
Institut TELECOM/TELECOM Bretagne, UMR CNRS 3192 Lab-STICC,
Technopôle Brest-Iroise, France.
samir.saoudi@telecombretagne.eu
ABSTRACT
This paper addresses the maximizing network lifetime problem in wireless sensor networks (WSNs) taking
into account the total Symbol Error rate (SER) at destination. Therefore, efficient power management is
needed for extend network lifetime. Our approach consists to provide the optimal transmission power
using the orthogonal multiple access channels between each sensor. In order to deeply study the
properties of our approach, firstly, the simple case is considered; the information sensed by the source
node passes by a single relay before reaching the destination node. Secondly, global case is studied; the
information passes by several relays. We consider, in the previous both cases, that the batteries are non-
rechargeable. Thirdly, we spread our work the case where the batteries are rechargeable with unlimited
storage capacity. In all three cases, we suppose that Maximum Ratio Combining (MRC) is used as a
detector, and Amplify and Forward (AF) as a relaying strategy. Simulation results show the viability of
our approach which the network lifetime is extended of more than 70.72%when the batteries are non
rechargeable and 100.51% when the batteries are rechargeable in comparison with other traditional
method.
KEYWORDS
Energy-Efficiency, MIMO Cooperative, Cooperation Communication, Amplify-and-Forward, Optimal
Power Allocation
1. INTRODUCTION
Wireless sensor networks (WSNs) are an important technology that has been employed in
various applications. This network type is composed of a large number of sensor nodes
distributed on a geographic zone, which can be dropped from an aircraft or helicopter, for
tracking physical phenomena (temperature, sound, vibration…..). Each node equipped with an
embedded processor, sensors and a radio. Maximizing network lifetime is the most important
objective for evolving sensor networks. Network lifetime can be defined according to the used
application. In [1] Network lifetime was defined as the time until the first sensor runs out of
energy, however in [2] was defined as the time until the last sensor runs out of energy.
In this paper, our goal is to find the optimal transmission power in order to maximize the
network lifetime considering different schemes and taking to account the total SER constraint at
destination. We assume that source node transmit their obtained sensing data to relaying nodes
before reaching the destination virtually creating MIMO system [3]. Concerning the

2
mediaaccess, we assume orthogonal channel between each sensor [4]. The channel based on
standard strategy of Time Division multiple accesses (TDMA) [5]. The temporal space is
divided between all the transmitters.
The remainder of the paper is organized as follows. The section II looks at the related work
and background of the approaches and algorithms used. In the section III, we study the
maximizing network lifetime problem considering different schemes where the batteries are
non-rechargeable. Then, we assume the same assumptions quoted before with the exception that
the transmitters are able to harvest energy from nature (rechargeablebatteries). The section VI
summarizes our simulation results and the last section concludes the paper.
2. RELATED WORK
In wireless Sensor Network (WSN), the most important objective is to make the nodes
operational as long as possible. In the literature, there are numerous works that address the
network lifetime problem.
Cooperative communication [6][7] is new class method which mitigates the degradation
effects of fading channels by exploiting the diversity gain achieved via the relay nodes.
Cooperative diversity is realized by different relaying strategies. We mention the most popular
strategy namely amplify-and-forward, demodulate-and-forward, Decode-and-Forward and
Compress-and-Forward strategy. In the Amplify-and-Forward strategy (AF) [8], the relay
simply amplifies the source transmission and retransmits it. The Demodulate-and-Forward
strategy [9] permits to the relay to demodulate individual symbols and to retransmit them. In the
Decode-and-Forward (DF) strategy [10], the relay decodes the entire message, re-encodes it and
re-transmits it to the destination. In [11], the Compress-and-Forward (CF) strategy allows to the
relay to send a quantized version of its received signal. The most popular cooperation strategies
are amplified-and-forward (AF) and decode-and-forward (DF) [12]. Theoretical studies such as
[12] show clearly that the choice of the best strategy is based on Signal-to-Noise Ratio (SNR) of
the different channels, and specify that the AF strategy does not to lose information since there
is no decision at the relay. From a complexity standpoint, the AF strategy appears to be the
simpler of strategies which it used in our work.
Various energy efficient protocols have been proposed to prolong network lifetime. Heinzelman
et al. proposed a Low-Energy Adaptive Clustering Hierarchy protocol (LEACH) in [13] which
the selection strategy of heads nodes is made randomly. Then, in [14], the authors improve the
LEACH protocol [15] and propose an optimized algorithm for the clustering in order to prolong
network lifetime.
In [16][17] optimal solutions are presented for maximizing a static network lifetime through a
graph theoretic approach using a static (multicast/broadcast) tree. In [18][25], the total energy
consumption is minimized using an optimal water-filling solution.
On the other hand, there has been recent research effort on wireless communication using
energy harvesting transmitters [19]-[21]. In [19], energy harvesting transmitters with batteries of
finite energy storage capacity are considered and the problem of throughput maximization by a
deadline is solved in a static channel. Sharma et al. in [20] propose energy management
schemes for a single energy harvesting node. The aim is to maximize the throughput and
minimize the delay. In [21], the dynamic programming framework is used to calculate the
optimal online policy with different energy budgets.
3. OPTIMALPOWER ALLOCATION SCHEMES
3.1 General System Model
We give a background and precisely define the terms used throughout this paper. We know
that the received power at a node varies according to the distance between U-node and V-node
noted d , where αis the path loss (attenuation) factor. The path loss can be formulated
as = 10 ( ) + . We assume a source-node, destination-node and M sensors

3
(relays) randomly distributed in the area of interest. We suppose that each sensor has an initial
energy noted and each one is equipped by only one antenna and has an "Amplify and
Forward" as relaying strategy.
We consider the problem of optimal power allocation for WSNs when using the Orthogonal
Channel Configuration between each sensor. We Note that is the channel coefficient from
the u-node to the v-node assuming that has a Rayleigh distribution and represents the well
known variance where = . In addition, is the additive Gaussian noise between U and
V node with ~ Ɲ (0, ).
In this article, our goal is to maximize the network lifetime expressed by the following equation:
= ∗
Where T is the period measurement of channel condition (T=1 to simplify), N is the number of
transmissions until the network can continuously meet the application requirements. This is
valid for many types of modulation including, quaternary phase shift keying (QPSK), M-pulse
amplitude modulation (M-PAM), and rectangular M-quadrature amplitude modulation (M-
QAM) [22].
3.2 Virtual MIMO with a Single Relay
Firstly, we assume that the source node transmit their obtained sensing data to relaying
station before reaching the destination creating several boughs (Fig. 1). We note that exist two
communication systems: SIMOsystem created between the source-node and the M relay-nodes
and MISO system created between the M relay-nodes and the destination-node which makes a
virtual MIMO with a single relay in each bough.
Figure 1: System Model
We consider that the nodes transmit their data over quasi-static rayleigh fading channel. Our
aim is to find the optimal power transmission taking into account the required SER at the FC.
The average SER at high SNR is formulated as [22][23]:
( ) =
( , )
̅
(
1
̅
+
1
̅
) (1)
Where
( , ) =
∏ 2 − 1
2( + 1)!
is a parameter relating to the modulation type used (see Table 1), ̅ is an average SNR of the
u-node to the v-node, where ̅ = ⁄ and is the average transmission power.

4
In order to simplify our calculation, we start by writing the average SER at the high SNR in
terms of transmission power:
=
( , ) 1
+
1
(2)
Where (resp. ) is the power of transmission at the source (resp.at the rth
relay).
Based on experimental measurements by Raghunathan et al. [24], the data is very expensive in
terms of energy consumption. Then the energy consumed in processing and reception is
negligible. Consequently, our goal is minimize the transmission power for the M relay. We take
into account the SER estimation being less than or equal to a known target value δ.
Then, our problem formulation is:
≤
≥ 0
We use the method of Lagrange multipliers to find the local maxima of our function, subject to
the constraints quoted before. The Lagrange function defined by:
£( , , ) = − +
( , )
(
1
+
1
) −
The Karush-Kuhn-Tucker (KKT) conditions are as follows:
≥ 0, ≥ 0, = 0
( , )
(
1
+
1
) − = 0
The partial derivative of with respect to is as follows:
£( , , )
= 1 − −
( , ) 1
+
1
= 0
Then, the solution in term of Lagrangian parameters is as follows:
=
1 −
( , ) 1
+
1
(3)
In the first, we must find the parameters of the Lagrangian. The optimal solution is obtained by
solving the KKT conditions: If we consider thatν = 0, using the KKT condition, we obtain
that = 1, which implies that = 0∀ . This result is not acceptable, then, > 0. If we consider
that ≠ 0, we obtain that = 0∀ wich is unacceptable, thus = 0. Solving for > 0 and
= 0 from the precedent equation, the Lagrangian parameter can be written as follows:

5
=
1
( , )
( + )
(4)
In order to find parameters of the Lagrangian, we multiply the previous equation by(1 +
1 ), we obtain:
=
1
+ (5)
Let us note that can be found numerically. Using (5), the solution can be express as follows:
=
( , )
+ − ( , )
(6)
3.3 Single bough with Multi relay (simple case)
Before looking for the case where the information passes through the N relays-nodes, in each
bough, to reach the destination-node, we take the simple case where it has a one bough. The
source-node transmits their obtained sensing data to N relays-nodes before reaching the
destination which virtually creating MIMO system.
Our aim is to provide the optimal transmission power taking into account the SER constraint
at FC while guaranteeing the required performance. Assuming the same assumptions quoted
before, the average SER at high SNR is formulated as:
( ) = ( , )
1
̅ ,
(7)
Where ( , ) = (1, ) = 3 4⁄ . Then, the average SER in terms of transmission power
can be written as:
= (1, )
1
,
(8)
Where is the transmission power to the ith relay (i=1,…, N) and is the transmission
power to the source-node. The formulation of our problem can be written as follows:
≤
≥ 0
Using the Lagrangian method, we obtain:
Figure 2: Single bough with a Multi relay
N relays

6
£( , , ) = − + (1, )
1
,
(9)
≥ 0, ≥ 0, = 0 ∀
(1, )
1
,
= 0
The partial derivative of with respect to is as follows:
£( , , )
= 1 − −
(1, )
,
= 0
Taking into account the KKT conditions, and following the same lines as in the previous
section, we find that > 0 and = 0. Then, The Lagrangian parameter, after multiplying
the both sides by φ , (1, )⁄ , can be formulated as:
,
(1, )
=
,
(1, )
After having reversed the equation, we compute the sum of all the resulting equations, we
obtain:
=
(1, ) 1
,
Then, our optimal transmission power can be express as follows:
=
(1, )
,
1
,
(10)
3.4 Virtual MIMO with a Multi relay (Generalized case)
In this section, we extend the case where multiple relays are used in each bough
(Figure 3). We note that three communication systems exists; SIMOsystem created
between the source-node and first M relay-nodes, SISO system created between the
relay-nodes(r denotes the rth
bough) and MISO system created between the last M relay-
nodes and the destination-node.

7
The average SER at high SNR, in this case, is formulated as:
( ) =
( , )
̅[ , ]
1
̅[ , ]
+
1
̅[ , ]
(11)
Denote that ̅[ , ] is the average SNR at the first relay corresponding to the bough due
to the source-node, and ̅[ , ] is the average SNR of the relay corresponding to the
bough. We consider that we have M boughs and each one contains relays (r denotes
the rth
bough). Then, the average SER at the high SNR is expressed in term of power as
follows:
=
( , )
φ
1
φ[ , ]
+
1
[ , ]φ[ , ]
(12)
Following the same line as the previous section, the formulation of our problem is:
[ , ]
≤
≥ 0
£ [ , ], , = [ , ] − [ , ] [ , ] + [ , ]
( , ) 1
[ , ]
1
[ , ] [ , ]
−
[ , ] ≥ 0, [ , ] ≥ 0, [ , ] [ , ] = 0
[ , ]
( , ) 1
[ , ]
+
1
[ , ] [ , ]
− = 0
The partial derivative of with respect to [ , ] is as follows:
£ [ , ], ,
[ , ]
= 1 − [ , ]
Figure 3: System Model.

8
− [ , ]
( , ) 1
[ , ] [ , ]
1
[ , ]
+
1
[ , ] [ , ]
(13)
Following the same instructions quoted before, we obtains that [ , ] > 0 and [ , ] = 0. In
order to find the optimal solution, we must start by finding the Lagrangian parameters.
According to the previous equation, we have:
[ , ] =
1
( , )
[ , ] [ , ] [ , ]
+
[ , ] [ , ]
(14)
We multiply the (13) by
[ , ]
+
[ , ] [ , ]
, we obtain:
[ , ] =
[ , ] [ , ] 1
[ , ]
+
1
[ , ] [ , ]
Let us note that can be found numerically. Finally, the optimal transmission power for
the node in the lth
bough and jth
hop is given by:
[ , ] = [ , ]
[ , ]
[ , ]
+
[ , ] [ , ]
(15)
3.5 Energy harvesting in Virtual MIMO with a Single relay
Our goal is to maximize the network lifetime. In this section, we consider the same
case in the first part (single relay in each bough), with the exception that the transmitters
are able to harvest energy from nature. Figure 4 shows that the transmitter has an energy
queue (battery) where the arriving (harvested) energy is stored.In addition, we consider
that the energy harvesting times and energy harvesting amount are known before the
transmission starts.
Noted that
( )
is the energy arrivals at jth period for the rth sensor and
( )
is the unit
of energy is available at time 0.
( )
is the fading channel coefficients for the rth sensor
at jth period where j=1,…..,N and r= 1,……, M. For simplify, we note that epoch ( )
is
time interval between the two previous consecutive events.
Figure 4: System Model

9
Assuming that the transmission power is constant in each epoch ( )
, the constraint of
causality on the power management policy can be formulated as:
( ) ( )
≤
( )
(16)
Where
( )
is the transmission power at the jth period for the rthsensor.
Our aim is to provide an optimal transmission power in order to maximize the network
lifetime taking into account a Symbol Error Rate (SER) constraint and a causality
constraint on the harvested energy. We consider that the battery capacity is unlimited
( = ∞ ).
Then, the formulation of our problem is:
( )
.
( , )
( ) ( )
1
( ) ( )
+
1
( ) ( )
≥ = 1, … ,
( )
≥ 0 ∀ ,
( ) ( )
≤
( )
= 1, … . ,
£( , , , ) =
( )
−
( )
+
( , )
( ) ( )
1
( ) ( )
+
1
( ) ( )
−
+
( ) ( ) ( )
−
( )
Since the objective function and the constraints are convex, has a unique maximizer.
Using the Karush-Kuhn-Tucker (KKT) condition, we obtain:
£( , , , )
( )
= 1 − −
( , )
( ) ( ) ( ) ( )
1
( ) ( )
+
1
( ) ( )
+
( )
= 0
Satisfying the KKT condition, we obtain: = 0, then,
=
( )
( , )
( ) ( ) ( ) ( ) ( ) ( )
+
( ) ( )
We multiply the numerator and denominator by
( ) ( )
+
( ) ( )
, then, we obtain:

10
=
( ) ( ) ( )
=
( ) ( )
( ) ( )
+
( )
(17)
Let us note that cannot be found easily, that why we assume a solution geometrical.
In solution geometrical we can present all target solutions in a region in which all the
constraints are satisfied.
The figure 9 shows the feasible region where all feasible solutions must lie in. The
figure has upper wall which presents the cumulative energy harvested∑
( )
. In
other hand, this wall presents the total emission energy that can be spent. The required
power consumption ∗
must be full located inside this region. In our algorithm, we use
the equation (6) to calculate the optimal power ensuring that this power is not greater
to
( )
where
( )
=
( )
( )
(18)
We recalculate our optimal power once a new energy amount arrives, or if there is a
change in channels status in order to be adapted to these changes. To simplify, we
consider that the conditions of channel are measured every one second (
( )
−
( )
=
1 ∀ , ) (see algorithm 1).
Algorithm 1
INITIALIZATION
0
( )
 Find (equ.6) for i={1,…,M}
START
 ++
( )
 Find (equ. 18)
If
( )
≠
( )
( )
 Find (equ.6)
If
( )
≠ 0
( )
Find (equ.6)
If
( )
≥
( )
( )
 0 (don’t transmit)
END
4. SIMULATIONS AND RESULTS
We study the average network lifetime. We compare our novel method to EP
method when varying same parameters, in order to show the relevance and the
robustness of our proposal. The simulations parameters are generated randomly such
that each parameter belongs to an uniform distribution between and , ∈ [ ; ].

11
4.1 Virtual MIMO with a Single Relay
In order to show the viability and the performance of the novel algorithms, we compare
it to the equal power method (EP) [25]. We fixed the transmission power corresponding
to the source node for10dB and we vary the modulation of the transmit information.
The modulations used are M-Phase Shift Keying (M-PSK) and M-Quadrature
Amplitude Modulation (M-QAM), then, the k parameter can be formulated differently
in each modulation case (table 1). We suppose that the direct link between the source
and the destination node is assumed normalized by 1. We considerer four significant
figures where all of the digits present are non-zero.
Table 1:Modulation parameters
Modulation k
M-PSK 2sin ( )
M-QAM 3
− 1
Figure 5 depicts the lifetime network while increasing the number of boughs. The
curves show that the network lifetime is clearly extended when the number of bough
exceeds 5. While between 1 and 5 bough, the improvement is less important in terms of
network lifetime. In general, the proposed approach improves the EP method
concerning the average network lifetime which is extended by an average of 78.01%
respectively 70.85%) using 16QAM (respectively 8PSK). Table 2 shows the parameters
used for simulations.
In the second, we fixed the used modulation (16QAM) and we vary the transmission
power corresponding to the source.
Figure 5: Comparison between the optimal power and equal power allocation.

12
Figure 6 shows the average network lifetime increasing the number of bough where
varying the transmission power corresponding to the source . As it can be seen, the
network lifetime, in the both methods, increases as the value of . However, the curves
show that our approach provides a meaningful improvement relative to the EP Method
which the lifetime network is extended by an average of 92.23%, 70.72% and 64.31%
respectively for P = 16db, 10db and 7db. Therefore, the simulation results prove that the
transmission power and the modulation used play a significant factor in extending the
network lifetime. Obviously, with high we can reach farther relay of the source.
Table 2:Simulations parameters
Estimate Parameters
10 : The threshold of SER
10dB P : Power corresponding to the source node
U[0.5,1] d ∶ Distance between u and v node ( = 2)
U[100, 400] E :The initial energy
4.2 Virtual MIMO with a Multi relay
Figure 7 represents the average network lifetime while increasing the number of relays
N in each bough ( = ∀ ). The figure shows that our new method is more effective
than the EP method concerning the average network lifetime which is extended by an
average of 80.98%. We assume the same Simulations parameters (see Table 3).
Estimate Parameters

13
4.3 Energy harvesting in Virtual MIMO with a Single relay
To evaluate the performance of our new algorithm, we compare our Optimal Power
Allocation algorithm where the batteries are Rechargeable (OPAR) with two other
methods, namely the Equal Power (EP) method and Optimal Power Allocation where
the batteries are Non-Rechargeable (OPANR). We assume an unlimited battery
capacity, and generate the Quantity of energy arrivals with a Gaussian distribution [50,
100].The 16-QAM modulation is used. Table 4 shows the parameters used for
simulations.
Estimate Parameters
U[50, 100] Quantity of energy arrivals

14
Figure 8 shows the network lifetime increasing the number of relays. As it can be
seen, our proposed OPAR algorithm improves the EP and OPANR method concerning
the average network lifetime. For the range [1,9], the improvement is less important in
terms of network lifetime. As expected, for more than 9 boughs, the total average
lifetime is substantially increased to about 100.51% and 247.78% using OPAR method
compared to respectively EP and OPANR method. Table 4 shows the parameters used
for simulations.
5. Conclusion
This paper presents a new algorithm which aims to maximize the network lifetime
under Orthogonal Channel configuration using several cases. We take into account the
estimation of overall Symbol Error Rate(SER) constraint at the FC and we suppose, in
addition, that a MaximumRatio Combining(MRC) is used at the receiver as a detector
and amplify-and-forward as relaying strategy. We have showed that the proposed
optimal power allocation methods maximize the average network lifetime better than
the EP method in all the studied cases. The network lifetime is extended by an average
that can reach 100.51% when the batteries are rechargeable.
Figure 9: Feasible Region.

15
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ENERGY EFFICIENCY OF MIMO COOPERATIVE NETWORKS WITH ENERGY HARVESTING SENSOR NODES

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