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Dynamic Power Allocation using Stackelberg Game in a Wireless Sensor Network

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Dynamic Power Allocation using Stackelberg Game in a
Wireless Sensor Network
Mohit Srinivasan, Ahan Kak, Kaustubh Shivdikar ,Chirag Warty
Intelligent Communications Laboratory, Mumbai, India
E-mail : mohit.s@intelcomlab.com, ahan.kak@intelcomlab.com, kaustubhcs07@gmail.com ,chirag.warty@intelcomlab.com
Abstract—Wireless sensor networks are characterized by a lim-
ited availability of resources such as the power required for data
transmission. Cooperative communication enables transmission
of data without using too much power. The fading of data is
considerably less when the nodes are engaged in a cooperative
communication protocol, rather than a competitive game. The
quintessential concern for each node is the power it needs to allo-
cate in order to relay the other nodes data. In cooperative com-
munication, the nodes need to transmit not only their own data,
but the data of the neighboring nodes too. An efficient solution
to this problem can be determined by employing the Stackelberg
game. From the determined solutions, improvement in the
cooperation among the neighboring nodes can be worked upon.
A cooperation region can be established within which the nodes
work towards transmitting the data more efficiently. A similar
concept can be applied to multi-hop networks and Nrelay
multi-hop networks. Thus, an optimal region of cooperation for
a single node, which permits it to achieve maximum cooperation
amongst all the other nodes at the same time can be determined.
Since we employ a game theoretic approach, we can determine a
trade off between quantities such as power allocated and utility
of the nodes, which results in maximum optimization of the
network. Through this paper, we aim to improve the network
utility factor of the wireless sensor network through dynamic
power allocation using the Stackelberg game.
TABLE OF CONTENTS
1. INTRODUCTION......................................1
2. SYSTEM MODEL .....................................2
3. COOPERATIVE COMMUNICATION ..................3
4. GAME THEORY ......................................5
5. DYNAMIC POWER ALLOCATION ....................6
6. NETWORK UTILITY MANAGEMENT ................6
7. PERFORMANCE EVA L UA T I O N .......................7
8. CONCLUSION ........................................8
ACKNOWLEDGMENTS ..................................9
REFERENCES ...........................................9
BIOGRAPHY ............................................9
1. INTRODUCTION
Wireless sensor networks are being used extensively for
monitoring real time data and processing the data. One of the
main drawbacks of a sensor node is the limited availability
of resources such as power for transmission of data. Once
the node has drained its power, it cannot function efficiently.
Hence, to better sustain a node and to increase its operating
life, the focus is now on cooperative communications. Co-
operative communications works on the principle of nodes
helping each other to transmit their data. Each node acts as a
relay to transmit the neighbor’s data. In this manner, a single
node need not use great amount of power to transmit the data
978-1-4673-7676-1/16/$31.00 c
2016 IEEE
to the destination. Instead, the relaying principle helps in
the transmission with less amount of power. Transmission
diversity requires multiple antennas at the transmitter. But
due to constraints on the design, we sometimes cannot use
multiple antennas. This is where cooperative communica-
tions comes into the picture. A cooperative network creates a
virtual MIMO (Multiple Input Multiple Output) system, thus
allowing transmission diversity or cooperation diversity. Co-
operative diversity is a technique that combats the slow fading
and shadowing effect in wireless communication channel [5].
The author in [1] has analyzed the advantages of using co-
operative communication in satellite communication, which
justifies the ability of cooperative communication protocols
to include a wide range of systems.
Game theory is one of the many tools used to address the
issues concerning wireless sensor networks. The application
of mathematical analysis to wireless networks has met with
limited success, due to the complexity of mobility and traffic
models, coupled with the dynamic topology and the unpre-
dictability of link quality that characterize such networks [2].
The ability to model individual and independent decision
makers whose actions potentially affect all other decision
makers makes game theory particularly attractive to analyze
the performance of ad hoc networks [2]. Majority of the wire-
less systems in modern times are multi agent systems which
have the capability to either help in the overall improvement
in network efficiency and throughput, or act maliciously and
refuse to cooperate. Hence, game theory can be used to an-
alyze the functioning of the network. Some of the important
applications of game theory include resource allocation and
auctions in wireless sensor networks. Power and bandwidth
allocation in such networks can be analyzed using different
game strategies. One may also describe cooperation as a
zero sum game in terms of power and bandwidth of the
mobiles in the network [7]. The premise of cooperation is
that certain (admittedly unconventional) allocation strategies
for the power and bandwidth of mobiles lead to significant
gains in system performance [7]. In the cooperative allocation
of resources, each mobile transmits for multiple mobiles [7].
Game theory has been an emerging tool used in wireless
sensor networks in recent times. Modern systems involve
agents which try to act selfishly or try to maximize their
own benefits/utilities. Hence, game theory acts as the best
tool to formulate and analyze how a system involving such
multi agents works. Stackelberg games and other games
have been used for the purpose of power and bandwidth
allocation in wireless sensor networks. Power allocation
using the Stackelberg game is analyzed in [2] and the authors
have explored the situation where the nodes of the model are
assumed to be moving. The paper then goes on to prove
that when the nodes are closest to each other, they achieve
maximum cooperation. The work carried out in [4] assumes
that the nodes of the network are selfish and want to maximize
their own benefits. It approaches the game strictly from an
economic perspective, assuming the source as a buyer and
1
the relay nodes as the seller. Work done in [5] focusses on
the Karush-Kuhn Tucker (KTT) algorithm for optimal power
allocation and best partner choice. The authors of [6] focus
on using coalition game theory for the purpose of grouping
the nodes, that is, to decide whether a mobile node should
join a particular group or not depending on how beneficial
the power consumption is.
This paper works towards employing the Stackelberg game
for dynamic power allocation in a bidirectional wireless sen-
sor network. The Stackelberg game is a model which consists
of a leader and a follower. The leader first performs an action
which the follower observes. The follower then performs
his action and decides his output. The main challenge as
stated earlier is to determine how much power a node needs to
allocate in order to transmit the neighboring nodes data. This
is a very important issue which needs to be addressed since
a single node in a bidirectional network needs to transmit its
own data as well as relay the other nodes data. This issue
is addressed in this paper. By employing the Stackelberg
game, we determine the cooperation region between two
nodes. This is the region in which the two nodes cooperate
to transmit and relay data. Once this is achieved for a single
relay model, a similar concept can be applied to N relay single
hop network and N relay multi hop networks. Through this
paper, we aim to achieve an improvement in the network
utility factor of the wireless sensor network.
This paper performs a unique analysis of nodes which are
stationary. The system is a bidirectional cooperative com-
munications network. Using the Stackelberg game, we de-
termine the region where the nodes cooperate, known as the
cooperation region. Within this region, we can determine at
which points the utilities of the nodes are maximum. We
then observe that a certain trade off can be made between
parameters of the system such as power allocation and the
utility of the nodes. Ultimately, this paper works towards
improving the network utility factor of the wireless sensor
network.
2. SYSTEM MODEL
We consider a simple model, which consists of two nodes
involved in a bi-directional cooperative communication. We
apply the Stackelberg game to this model and determine the
cooperation region. In a similar way, we can apply the same
concept to an Nnode system. In this model, we consider two
source nodes. The system is as shown in fig(1). In addition
to being source nodes, they also act as relays to transmit the
other nodes data. The main issue which is to be addressed is
how much power a node needs to allocate in order to transmit
the other nodes data. Let the two nodes be denoted by node
2.
The received signals at the destination and node2 are as
follows,
y1,d(t)=P11 G1,dx1(t)+n1d(t)(1)
y1,2(t)=P11G1,2x1(t)+n12 (t)(2)
In the above equations, P11 represents the amount of power
used by node1 in order to transmit its own data, G1,d rep-
resents the path gain for the channel between node1 and the
destination, G1,2represents the path gain for the channel be-
tween node1 and node2, x1(t)represents the data transmitted
by node1, n1,d (t)represents the noise in the path between
node1 and the destination and n1,2(t)represents the noise
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Figure 1.Two relay bi-directional communication.
in the channel between node1 and node2. The noise in the
channels can be AWGN noise, Rician noise, etc.
The signal received from the relay node2 at the destination is
as follows,
y2,d(t)=P21 G2,dx21(t)+n2d(t)(3)
In the above equation, P21 represents the amount of power
used by node2 in order to transmit the data of node1, G2,d
represents the path gain for the channel between node2 and
the destination, x21 (t)represents the data transmitted by
node1, n2,d(t)represents the noise in the path between node2
and the destination. The noise in the channels can be AWGN
noise, Rician noise, etc.
The signal to noise ratio (SNR) for the direct and relay paths
are as given below,
SNR2d=G2dP22
σ2(4)
SNR1d=G1dP11
σ2(5)
SNR12d=G12G2dP11 P12
σ2(G12P11 +G2dP21 +σ2)(6)
SNR21d=G21G1dP22 P12
σ2(G21P22 +G1dP12 +σ2)(7)
Where, P22 represents the power used by node2 in order to
transmit its own data and σ2represents the noise power.
In order to employ the Stackelberg game, we define the utility
function for both the nodes as given below,
U1=kR12d(cP11 +P12)(8)
U2=kR21d(cP22 +P21)(9)
Where, k is the gain per unit of achieved rate at the receiver
and c is the constant which determines the extent of coopera-
tion.
For relating P12 and P21 we define a parameter γsuch that,
P12 =γP21 (10)
Hence, ultimately, we arrive at the following two equations
for the utility of the nodes,
U1=kR12d(cP11 +γP21)(11)
2
U2=kR21d(cP22 +P21)(12)
Node 1 will tell node 2 to consume P21 Watts of power to
transmit its data, while node 2 will tell node 1 to consume
γmultiples of P21 Watts of power to transmit its data.
Determining P11 and P22 is an optimization problem. For
node 1 which is assumed to be the follower in the Stackelberg
game, determining P21 is a game problem. For node 2 which
is assumed to be the leader, determining γis again a game
problem.
For the optimization problem, we differentiate equation (7)
w.r. t P11 and equate it to zero (for maximization of utility).
We therefore arrive at the following equation,
P11 =w
cσ2
G1d
(13)
Similarly, we optimize the utility function of node 2 and
equate it to zero to get,
P22 =w
cσ2
G2d
(14)
where,
w
=kbW
ln2(15)
where, b is known as the bandwidth factor and W is the
transmission bandwidth. We now use the Stackelberg game
to determine to maximize the utilities of the two nodes. We
consider node 2 to be the follower and node 1 to be the leader.
For the follower side solution, we assume that node 2 pro-
vides the value of γto node 1. The game problem is therefore
to choose P21 in such a way that it maximizes the utility of
the follower that is, node 1. Hence, differentiating the utility
of node 1 w.r.t P21, we get,
P21 =γA1B1+(γA1B1)2+4γA1B1w(1 + A1)
2γ(1 + A1)B1
(16)
where,
A1=G12P11
σ2+G1dP11
(17)
B1=σ2+G12P11
G2d
(18)
This power is the power used by node 2 to transmit the data
of node 1. Hence, upto a certain point, the power will remain
positive. Beyond that point, the power becomes negative
which is not possible. Hence, we denote this point by γ2.
This is the boundary of the cooperation region which we are
trying to determine. In order to determine γ2, we substitute
P21 = 0 in the above equation. Hence, we get,
γ2=2K2
K2
31(19)
where,
K2=2w(1 + A1)
A1B1
(20)
For the leader side solution, we need to first determine
whether R21dis a concave function of γ. By taking the double
derivative of P12 with respect to γ, we observe that it is nega-
tive for all values of γ. Hence, R21dis a concave function of
γ. There will be a value of γat which R21dachieves a local
maximum. This is the value of γ1. Differentiating P12 with
respect to γ, we get the value of γ1as follows,
γ1=K2K3
K2
31K2(21)
where,
K3=2+A1
A1
(22)
The value of γ2will always be more than the value of γ1.
The cooperation region is defined by the following case wise
representation,
f(x)=(γ1
2); Nodes will cooperate
else ; Nodes will not cooperate (23)
This is the region within which the nodes cooperate. The Per-
formance Evaluation Section explains the simulation results
and the cooperation region in more detail.
3. COOPERATIVE COMMUNICATION
Cooperative communications helps single antenna nodes to
reap the benefits of a virtual MIMO system. This improves
transmission diversity and thus leads to an overall improve-
ment in the throughput and the efficiency of the system.
There are three main protocols which are used in cooperative
communications, namely Detect and Forward, Amplify and
Forward (A.F) and Decode and Forward (D.F).
Amplitude and Forward Scheme
In the A.F scheme, the relay receives a signal from the source
and simply amplifies or pumps up the signal and transmits
it to the destination. The destination node therefore receives
two signals one directly from the source and the other which
was amplified by the relay. The destination node compares
the signal to noise (SNR) ratio of the two signals and chooses
the optimal signal. It has been shown that for the two-user
case, this method achieves diversity order of two, which is
the best possible outcome at high SNR [7]. In amplify-and-
forward it is assumed that the base station knows the interuser
channel coefficients to do optimal decoding, so some mech-
anism of exchanging or estimating this information must be
incorporated into any implementation [7]. The AF scheme re-
quires the storage of a large amount of analog data and hence
it is not a feasible scheme for TDMA (Time Division Multiple
Access) systems. AF also suffers from the noise amplification
problem which can degrade the signal quality (since even
noise can get amplified), particularly at low SNR values.
Another potential challenge is that sampling, amplifying,
and retransmitting analog values is technologically nontrivial.
Nevertheless, amplify-and-forward is a simple method that
lends itself to analysis, and thus has been very useful in
furthering our understanding of cooperative communication
systems [7].
The equations which govern a two relay system employing
the A.F scheme is as follows,
y1,d(t)=P11 G1,dx1(t)+n1d(t)(24)
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Figure 2.Coded Cooperation
The amplification factor which amplifies the the signal re-
ceived by the relay is given by,
β=P
PG
12 +N0
(25)
where P is the received power from node 1 and N0is the
variance of the noise in the channel. The signal received at
the destination is given by,
y2,d =βPG
12G2dG1dx(t)+βG2dn12 +n2d(26)
The maximum ratio combiner (MRC) output receives two
input signal - y1dand y2d. The output of the MRC is as
follows,
y=my1d+ny2d(27)
where m and n are the combining factors. Thus, this is how
the A.F scheme is designed. We employ a similar scheme in
the bi-directional model used in this paper.
Decode and Forward Scheme
The decode-and-forward relay protocol is a protocol defined
for wireless cooperative communications. In the D.F scheme,
the source sends the data in an encoded form to the relay.
The relay then decodes this data and again encodes using
either the same or a different scheme and transmits it to the
destination. The relay does not include any information about
the level of reliability of the source-relay link. Hence, this
processing of the signal at the relay is also know as a make
hard decision. When uncoded modulation is used, this pro-
tocol is also know as Detect-and-Forward as the processing
of the relay is detection of the signal. There are two types of
decode and forward techniques - Fixed Decode and Forward,
and Adaptive Decode and Forward. This scheme removes the
noise by decoding the received signals and then regenerating
and re-encoding the signal to be forwarded to the destina-
tion. Sometimes, the relay can incorrectly decode/relay the
received message from the source and send this incorrect
information to the destination. Hence, the DF scheme suffers
from the error propagation problem. In Adaptive Decode
and Forward scheme, the relay forwards the signal to the
destination only if it is able to decode the signal correctly. The
correct decoding can be checked using some error detection
check or SNR threshold. A special case is that when the
relay detects the signal but does not decode it. In this case
the scheme is called detect-and-forward.
Figure 3.N Relay A.F scheme.
Coded Cooperation Scheme
Coded cooperation is a method that integrates cooperation
into channel coding [7]. Coded cooperation works by sending
different portions of each users code word via two indepen-
dent fading paths [7]. The basic idea is that each user tries to
transmit incremental redundancy to its partner [7]. Whenever
that is not possible, the users automatically revert to a non co-
operative mode [7]. All this is managed through code design
and and there is no feedback between the users. Hence, the
efficiency of coded cooperation is high and is more improved.
The efficiency of different protocols depends on the quality
of the channels and more importantly on the position of the
nodes. This paper focusses on the A.F technique owing to its
simplicity and ease of implementation.
Multi-Node Amplify and Forward Protocol
The multi-node system model consists of n nodes which
forward the data to the destination individually. We consider a
source only amplify and forward strategy in which the relays
forward the information from the source and the cooperation
takes place in two phases. In phase 1, the data is sent
from the source node to the destination and the Nrelays.
In phase 2, the relays amplify the received data from the
source and transmit it to the destination. By determining the
received signals from the relays and the original signal from
the source, the destination will determine the best possible
signal using maximum receiver combining technique.
The system model for N relay is as shown below, The
governing equations for phase 1 of transmission as well as
the received signals at the destination and the ith relay are
as follows,
ys,d =Pohs,dx+ns,d (28)
ys,ri=Pohs,rix+ns,ri(29)
The signal received at the destination from the ith relay
after it has amplified and forwarded the data is as follows,
yri,d =Pi
Poh2
s,ri+N0
hri,dys,ri+nri,d (30)
The concept of cooperation region and dynamic power al-
location can be applied to the above Nrelay model, thus
improving the network utility factor of the system. By using
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Figure 4.Multi-node Cooperation. The (k+1)th relay
combines information from the source as well as all other
relays.
the same concept as in case of the two relay model, we can
determine the cooperation regions between each relays and
the source. The source can then determine which relay can
cooperate with it the most, and which node will result in
maximum utility and least power consumption for the deter-
mined cooperation region. Further work can be employed in
the domain of Nrelay multihop networks.
Multi-Node Decode and Forward Protocol
As in the previous case, the link between any two nodes in
the network is modeled as a Rayleigh Fading Channel with
AWGN. The network model is based on the assumption that
the channel coefficients for each link are independent of each
other. A fixed DF strategy is not feasible in a multi-node
environment, and, thus, a selective DF scheme is employed.
Such a scheme works well because the probability of error
increases with distance from the source, due to poor SNR. In
general, each relay decodes the information after combining
the source signal as well as signals from each of the previous
relay. Cooperation occurs in (N+1)phases, as opposed to
2 phases for the single relay model. In phase 1, when the
source transmits, the expressions for information received by
the destination and the ith relay are
ysd =Pt
sdx+nsd (31)
ysri=Pt
sri+nsri(32)
The notations used above follow from the single relay model.
In phase 2, the first relay, on correct decoding, forwards the
information with power P1to the destination. The signals
from the source and previous relays are combined using MRC
at any relay l
yri=Ptsrlysrl+
l1
i=max(1,lm)
Pitrirlyrirl(33)
Provided, the lth relay decodes correctly, it transmits with
power Plin Phase (l+1), otherwise it remains idle. Finally,
the destination combines all received signals in the (N+1)
Table 1.Utility Table for Prisoners Dilemma
Action Cooperate Defect
Cooperate (2,2) (0,3)
Defect (3,0) (1,1)
phase using MRC as follows
yd=Ptsdysd +
N
i=1
Pitridyrid(34)
4. GAME THEORY
Game theory is the branch of mathematics which deals with
intelligent agents which are capable of making decisions
which are either conflicting with others, or in tandem with
the interest of the other agents. This is particularly useful
for applications in wireless sensor networks since cooperative
communication depends on nodes interacting and cooperat-
ing with each other. There are two types of games which can
be played- cooperative game and non-cooperative game [8].
As the name suggests, in cooperative games, the players take
decisions which depend on the outcomes of the neighboring
players. In non-cooperative games, the agents or the players
of the games are selfish and have conflicting interests. It is
assumed that each player acts without communicating with
the other players. John Nashs identification of the Nash
equilibrium has perhaps had the biggest impact on game
theory [8]. Simply put, in a Nash equilibrium, no player has
an incentive to unilaterally deviate from its current strategy
[8]. Put another way, if each player plays a best response to
the strategies of all other players, we have a Nash equilibrium.
One of the features of a Nash equilibrium (NE) is that in
general it does not correspond to a socially optimal outcome
[8]. That is, for a given game it is possible for all the players
to improve their costs (payoffs) by collectively agreeing to
choose a strategy different from the NE [8]. A Pareto optimal
equilibrium describes a social optimum in the sense that no
individual player can improve his payoff (or lower his cost)
without making at least one other player worse off [8]. Pareto
optimality is not a solution concept, but it can be an important
attribute in determining what solution the players should play
(or learn to play) [8]. Loosely, a Pareto optimal (also called
Pareto efficient) solution is a solution for which there exists
no other solution that gives every player in the game a higher
payoff (lower cost) [8].
Prisoner’s Dilemma
An example of a game problem is the Prisoner’s dilemma.
It is analyzed as a non-zero sum game. The game is based
on an imaginary situation which consists of two people who
have committed crimes. The prisoners are given two choices
- either to cooperate or defect. If the prisoners cooperate
and provide evidence against the other, then they make a
gain. If they defect, then they get a punishment. There
are multiple cases which are possible. If both the prisoners
defect, then the law authorities will not have any evidence
against both of them and hence, they won’t be charged. The
prisoners therefore escape without any punishment. If they
both cooperate, then they are let off with a light punishment.
If one defects and the other cooperates, then the prisoner who
cooperates will get a lesser punishment and the other gets a
harsh punishment. The state of the game in which both the
prisoners defect is the best strategy for the players, but the
5
Figure 5.The Dynamic Power Allocation Algorithm
prisoners are isolated and hence are not aware of each others
strategies. The utility table for the prisoners dilemma is as
shown in table 1.
Stackelberg Game
Bandwidth allocation and power allocation are two major
areas of application of game theory in sensor networks. A
plethora of games can be applied to such networks, common
among them being the Stackelberg game. The Stackelberg
game is an extensive game which is centered around two
agents- the leader and the follower. First, the leader per-
forms his action. The follower then observes the leader
and performs his action. Situations can arise where there
are multiple leaders or followers. The game used in this
paper is the Stackelberg game, which helps in determining
the cooperation region between various nodes in a wireless
network. Thus, game theory acts as an effective tool in the
analysis of resource allocation in wireless sensor networks.
5. DYNAMIC POWER ALLOCATION
Power allocation and bandwidth allocation are two key areas
where game theory plays an important role in wireless sensor
networks. In wireless communication, the nodes share a
single spectrum and hence, bandwidth allocation is impor-
tant. At the same time, the nodes in a wireless network are
characterized by a limited availability of power. Periodic
charging of the nodes is not a viable option, especially if
the wireless sensor network is situated in mountainous or
inaccessible regions. Hence, dynamic power allocation is of
quintessential importance.
In this paper, we explore the possibility of a time varying
channel. Because the channel is time varying, all the param-
eters such as the channel gains will keep on varying. Hence,
at every instant the SNR values of the channels will vary. If
the SNR value is very high, then not much power needs to be
used up to transmit the data from the nodes. However, if the
SNR value is low, then we need to pump up or amplify the
power to increase the signal power. An algorithm based on
this concept is employed in this paper. As mentioned earlier,
we also address the issue of how much power a node needs to
use in order to transmit the neighboring nodes data. We also
determine the region of cooperation which facilitates relaying
of data between the nodes.
The algorithm is as shown in fig(5). The algorithm checks
for the SNR value at each instant of the simulation time. If
the SNR value is increasing, then there is no need to allocate
much power for the relaying of the data. This is because the
signal power is increasing and is more than the noise power.
Similarly, if the SNR value decreases, then we need to pump
up the power. This is how we dynamically allocate power
for the nodes. The results of the algorithm which leads to
dynamic power allocation is shown in fig(11).
6. NETWORK UTILITY MANAGEMENT
Network Utility Management can be defined as the process
of managing, monitoring and controlling the important pa-
rameters of the wireless sensor network (WSN) such as the
power utilized by each node, connectivity between the nodes
and environmental obstacles. The main concern, as stated
earlier, in a WSN is to minimize the energy consumption by
the nodes. Hence, we cannot employ the traditional network
management protocols since they only improve the response
time and improve information feedback. In addition, WSNs
are more prone to abnormal or fault conditions. We need to
ensure that we create a system which is perpetual in nature i.e
the nodes do not in any way become energy deficient.
The dynamic power allocation algorithm and determination
of the cooperation region achieved in this paper will lead to
an overall reduction in the power consumed by the nodes
to transmit the data. This leads to an improvement in the
network utility factor. In this paper, we have used a game
theoretic approach for dynamic power allocation. With this
approach, we determine an optimum region of cooperation
between the nodes which results in maximum utility of the
nodes and also results in transmission or relaying of data with
the least amount of power. The improvement in the network
utility of the nodes can be seen from fig(13). By employ-
ing the proposed game theoretic dynamic power allocation
algorithm, we have increased the utility of the nodes. Also
by achieving a trade off between the power allocated by the
nodes to transmit data and the utility functions, important
parameters of the network such as energy consumption and
life of the network can be carefully managed. Employing a
proactive monitoring management system which will deter-
mine the cooperation region and at the same time, determine
how much power should be allocated dynamically, will main-
tain the performance of the network. This can be infused with
a Reactive Monitoring System and a Fault detection system
to maintain and stabilize the parameters of the network such
6
Figure 6.Utilities of the nodes in the two relay model.
Figure 7.Power allocation for Node 2
as energy consumption and power allocation. Thus, with
the concepts mentioned in this paper, we can obtain an
optimization of the network resources and employ an efficient
network utility management strategy.
7. PERFORMANCE EVALUATION
We perform the simulation of the above environment in MAT-
LAB, by assuming the following values of the parameters
which are taken as constants in the environment of the above
system,
Figure 8.Region of Cooperation between the nodes of
the two relay model
Figure 9.Power used by node 2 to relay node 1 data
Figure 10.Region of Cooperation for node 2
Figure 11.Region of Cooperation for node 1
G1d=G21d=G12 =G21 =1
2=10
8,c =1.2,a =
107,W =10
7,b=0.5
With the above assumed values, we determine the coop-
eration region and the power which the nodes utilize to
transfer each others data. The cooperation region, as per the
above simulation is between (0.2912, 1.2000). This region
is highlighted in fig(10) and fig(11). Fig(9) is the curve
which indicates the power used by node 2 in order to relay
node 1 data. Fig(14) is the curve which represents the power
used by node 1 to relay node 2 data. Fig(15) represents the
utility function of node 1 while fig(12) represents the utility
function of node 2. In fig(8), the blue curve indicates the
power used by node 2 to transmit node 1 data i.e P21 while
the red curve indicates the amount of power used by node 1
to transmit node 2 data i.e P12. As can be observed from
fig(6), the utilities of both the nodes are much higher than
their initial values at the end of the cooperation region and
hence, this would be a preferred region of operation for both
the nodes. The purple curve in fig(6) represents the utility
of node 1 and the green curve represents the utility of node
2. However, if one observes fig(8), then the power allocated
by the two nodes for transmitting the others data is high only
in the initial part of the cooperation region. This leads to
one of the main conclusions of this paper. It is quintessential
to strike a balance between the utility of the nodes and the
power they allocate to relay the other node’s data. Hence, a
trade off must be made between the utility of the nodes and
the power allocated by them for relaying data. This can be
done by choosing a value of gamma, such that we get near
optimal values of utility and power allocation.
Ideally, the nodes should relay the neighboring node’s data
with the least amount of power. At the same time,the utility
of the two nodes should be as high as possible. As we can
observe from fig(6) and fig(8), we observe that the power
allocated is the least and the utility is maximum at the far
end of the cooperation region. Hence, the operation of the
nodes of the system for values of γbeyond 0.8 would lead
to an improvement in the network utility factor. The same
can be observed from fig(13). The utility of node 2 in a
7
Figure 12.Utility function of Node 2
Figure 13.Improvement in the utility of Node 2 by using
Game Theoretic Dynamic Power Allocation
game theoretic dynamic model is higher than a passive model
when it operates in a region beyond γ=0.8. For example,
at γ=1, the utility of node 2 has increased from 0.3899
to 0.4025. This is the main conclusions of this paper. The
power allocated by the nodes to transmit each others data at
γ=1is nearly the same at 0.0805Wand 0.0809Wfor node
1 and node 2. For example, the trade off between utility and
the power allocated by the nodes can be done by choosing the
value of γbeyond 0.8. At this value of γ, the power allocated
by the nodes are low and the utilities of both the nodes are
also very close to their maximum values and therefore near to
the maximum. Thus, the most optimum area in the region of
cooperation is the region between γ= 0.8 to γ= 1.2. Thus,
an intelligent, logical decision such as the one above needs to
be taken by the nodes to ensure that the trade off is done in a
fair way to ensure that both the parameters are optimized to
an extent to result in an overall improvement in the network
utility factor.
In the dynamic power allocation scheme, we employ an
algorithm which compares the SNR value of the channel at
each instant of time. The flowchart of the algorithm is as
shown in fig(5). We have assumed a time varying channel,
which means that the parameters of the channel such as gain
coefficient keep varying at each instant of time. Under such
situations, we perform the simulation of the model from t
= 0.1 seconds to t = 1 seconds. The channel coefficients
Figure 14.Power used by node 1 to relay node 2 data
Figure 15.Utility function of Node 1
are considered to be the time varying quantities. The other
parameters of the system such as bandwidth shared by the
nodes, noise power, etc are the same as the previous values
and are considered to be static. During this time interval, we
observe that the SNR values of the channel increases. Hence,
at each instant of time, we need to reduce the power since
the signal power is increasing during propagation through the
channel. This power allocation result by node 2 is shown
in fig(7). We can see that at every instant of time, the
power allocated by node 2 to relay node 1 data is reduced
by half, since the SNR value of the channels during the time
interval is an increasing function. The amount by which the
power is reduced or pumped up depends on the user or the
controller. We have simply taken a factor of 0.5 to explain
the algorithm. From fig(13), we observe that the utility of
node 2 has increased after we employ the game theoretic
power allocation algorithm. Fig(13) compares the utility of
node 2 when it is working in a system which is passive
and when it is working in a system which employs a game
theoretic dynamic power allocation algorithm. This improves
the overall network utility factor of the system.
8. CONCLUSION
Thus, with the above analysis, we have successfully deter-
mined the cooperation region for a two relay model. With the
identification of this region, we have identified the amount
of power used by each node to transmit the data of its
neighboring node. A trade off must be made which will
allow both optimal utility of the nodes as well as power
allocation by them for relaying the data. This paper also uses
a dynamic power allocation algorithm, which appropriately
boosts the power allocated by each node depending on the
SNR value of the channel. For this analysis, we assumed a
time varying channel in which the channel coefficients are
varying with time. By comparing the utility of the nodes and
the power allocated by them to relay each others data, we
observe that a trade off must be made in order to account
for good performance both in terms of power allocation and
utility. With this trade off, we achieve an overall improvement
in the network utility factor.
Further research in this domain can be applied to Nrelay
single hop networks and Nrelay multi-hop networks. Also,
in real life applications, the nodes may be mobile and the
destination may also communicate with the nodes. Hence,
the complexity of the entire system increases to a great ex-
tent. Practical situations will require nodes to cooperate with
each and every node in the system, and hence this concept
can applied to a large scale wireless sensor network. To
summarize, with the dynamic power allocation algorithm and
the determination of the ’Cooperation Region’ , the network
utility factor of a wireless sensor network can be improved.
8
ACKNOWLEDGMENTS
The authors would like to thank Vinayak Kamble, Vikram
Singh, Intelligent Communications Lab and the entire team
for their constant support, valuable inputs and encouragement
throughout the work carried out during the project.
REFERENCES
[1] Chirag Warty, ” Cooperative Communication for Mul-
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tion in bidirectional cooperative communications, IEEE
WCNC proceedings, 2010.
[3] Allen B. MacKenzie, Luiz A. DaSilva, ”Game Theory for
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[4] Beibei Wang, Zhu Han, K.J. Ray Liu, Stackelberg Game
for Distributed Resource Allocation over Multiuser Co-
operative Communications Networks, IEEE GLOBE-
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[5] Hadi Goudarzi, Mohamad Reza Pakravan, Optimal Part-
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ward Cooperative Diversity, Personal, Indoor and Mobile
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[6] Fatemeh Kazemeyni, Einar Broch Johnsen, Olaf Owe1,
Ilangko Balasingham, Grouping Nodes in Wireless Sen-
sor Networks using Coalition Game Theory.
[7] Aria Nosratinia, Todd E. Hunter, Cooperative Commu-
nications in Wireless Netoworks, IEEE Communications
Magazine, October 2004.
[8] Pavel L, ”Game Theory for Control of Optical Net-
works”, 2012, XIII, 261 pp.
[9] K. Liu, Cooperative Communications and Networking.
Cambridge, UK: Cambridge University Press, 2009.
[10] Beibein Wang, Zhu Han, K.J Ray Liu, ”Stackelberg
Game for Distributed Resource Allocation over Mul-
tiuser Cooperative Communication Networks”, IEEE
GLOOBECOM 2006.
[11] S. Mehta and K. S. Kwak (2010). Application of
Game Theory to Wireless Networks, Convergence
and Hybrid Information Technologies, Marius Crisan
(Ed.), ISBN: 978-953-307-068-1, InTech, Available
from: http://www.intechopen.com/books/convergence-
and-hybrid-information-technologies/application-of-
gametheory- to-wireless-networks
[12] Yi Zhao, Raviraj Adve, Teng Joon Lim, ”Improv-
ing Amplify-and-Forward Relay Networks: Optimal
Power Allocation versus Selection”, IEEE Transactions
on Wireless Communications, Vol. 6, No. 8, August 2007
[13] Dejun Yang, Xi Fang, Guoliang Xue, ”Game Theory in
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nications April 2012.
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BIOGRAPHY[
Mohit Srinivasan is currently pursuing
his Bachelor of Technology in Electri-
cal Engineering from Veermata Jijabai
Technological Institute (V.J.T.I), Mum-
bai, India. He received a scholarship
from the Maharashtra Government for
being in the top one percent of outstand-
ing students in the state, and has also re-
ceived several scholarships in his board
exams. He was a project trainee at the
Department of Robotics and Remote Handling at Bhabha
Atomic Research Centre (B.A.R.C), Mumbai, India. He is
currently working as a research fellow at Intelligent Com-
munications Lab, Mumbai. His current research interests
include cooperative communications, game theory, control
systems, robotics, Linear Control Theory, heterogeneous net-
works, microgrids.
Ahan Kak is pursuing his Bachelor
of technology in Electrical Engineering
from Veermata Jijabai Technological In-
stitute (VJTI), Mumbai, India. He is cur-
rently working at the Intelligent Commu-
nication Lab as a research fellow, and
has interned at Ericsson and Larsen and
Toubro in the past. He is a recipient
of the Sir Ratan Tata Trust Scholarship
for excellence in education for the years
2014 and 2015. His current research interests include co-
operative communication, cooperative relaying, game theory
and LTE-A networks.
Kaustubh Shivdikar is currently re-
search fellow from the MIT Media Lab
India Initiative, Kaustubh Shivdikar spe-
cializes in the field of Artificial Neu-
ral Nets and Deep Learning Algorithms.
Pursuing Electrical Engineering from
Veermata Jijabai Technological Institute
(VJTI), he currently conducts research
at the internship program by Intelligent
Communications Lab on Wireless Sen-
sor Networks. He has worked on multiple projects ranging
from Magic Pillow in the field of AR to E-Bag consisting of
analog circuits and power modules. Winner of the AngelHack
Hackathon he is also the youngest speaker from his college to
present his project at TEDx BITS Hyderabad.
Chirag Warty is currently the CEO of
Quantspire. He is also the chief scientist
at Intelligent Communication Labs. He
manages extensive network of research
teams in US, Italy and India. He re-
ceived his Bachelor of Science in Elec-
trical Engineering from University of
Mississippi, USA, Masters of Engineer-
ing from University of IllinoisChicago,
USA. His other alma maters include
Stanford, Cornell, Univ. of Illinois Urbana Champagne
(UIUC), UCLA, UC Berkeley, UC San Diego, USC. He
also has several academic accolades in communications and
signal processing from several IEEE societies. He is a
visiting faculty for University of Mumbai, VJTI, and SNDT
university for management, IT and engineering programs.
He currently manages several projects and is responsible for
9
technology related global strategic decisions. His research
interest include Software Defined Networking (SDN), 4G/5G
wireless technologies and Cyber Physical Systems, Big data
in Mobile Cloud Computing, Physical Layer Security. He
has organized several panels and hosted forums on various
technical subjects. He is a well published author with several
international publications and is a well renowned speaker
for future technologies. He holds several key and executive
positions on IEEE societies. He is currently the guest editor
for Elsievers Special Issue on Big Data Inspired Data Sens-
ing, Processing and Networking Technologies. He serves on
the editorial boards of both IEEE and non-IEEE ventures.
He has also served as chair, co-chair (general or TPC) and
international advisor in various IEEE conferences around the
globe.
10
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