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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

c−σ2

G1d

(13)

Similarly, we optimize the utility function of node 2 and

equate it to zero to get,

P22 =w

c−σ2

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

3−1(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

3−1−K2(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,γ

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 =β√PG

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 i−th 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 i−th 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

4

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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 i−th 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=√Pt∗srlysrl+

l−1

i=max(1,l−m)

Pit∗rirlyrirl(33)

Provided, the l−th 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=√Pt∗sdysd +

N

i=1

Pit∗ridyrid(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,σ

2=10

−8,c =1.2,a =

10−7,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.

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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.

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