# for Power Control in Wireless

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21 Νοε 2013 (πριν από 4 χρόνια και 5 μήνες)

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A Game Theoretic Framework
for Power Control in Wireless
Sensor Networks

Shamik Sengupta, Mainak Chatterjee, and
Kevin A. Kwiat

IEEE TRANSACTIONS ON COMPUTERS,
2010

Outline

Introduction

Interference

Game

Nash Equilibrium

Numerical results

Conclusions

2

Introduction

Transmission at the optimal transmit power
level

High power level

High success probability

Energy is depleted faster

Increase the interference

-

3

Game theory have been used for solving
resource management problems

Network bandwidth allocation

Distributed database query optimization

Allocating resources in distributed systems such
as clusters, grids, and peer
-
to
-
peer networks

Achieve efficient energy usage through
optimal selection of the transmit power level

4

Interference

Randomly distributed nodes

Not contention
-
based protocol

But use code division multiplexing

Nonzero cross
-
correlation

The number of simultaneously active nodes
in the vicinity of a receiver is limited

5

Interference

Interference at node
w

from a local neighbor
node
u
.

6

Interference area is

Poisson distribution with node density as

The maximum number of interferers is

7

Game

Incomplete noncooperative game

Transmit at higher power will lead to a
noncooperative situation

Devise an equilibrium game strategy to
impose constraints on the nodes

strategy profile

space of strategy profiles

8

utility of node
i

is

utility vector

a node’s available information

its own power level

channel condition

expected SINR of neighboring receiver nodes

9

utility (node
i

transmit to node
j
)

efficiency function

P
e
: bit error rate (BER).

for example,

noncoherent FSK,

DPSK,

γ
j

:
the expected SINR of node
j

10

Nash Equilibrium

Net utility

cost function is a convex function of
s
i
.

Transmitting probability

is the probability density function of
s
i

11

The probability that any
l

nodes out of
N

nodes are active is given by

The expected net utility of
i
th node (if the
node is transmitting) is given by

12

Achievable gain (net utility considering both
modes: transmitting with
0 <
s
i

<
P
t
, and not
transmitting) obtained by node
i

is

Nash equilibrium point, the expected net
utility for transmitting and for being silent
should be equal at the threshold, i.e.,
s
i

=
P
t
.

13

Assume
T
1

be the solution

Suppose that a node unilaterally changes its
strategy and changes the threshold value to
T
2

Find that

14

Numerical results

15

16

17

DPSK

18

noncoherent PSK

19

20

21

22

23

Conclusions

Game
-
theoretic approach

Power control problem encountered in sensor
networks

Noncooperative games with incomplete
information

Existence of Nash equilibrium

if assume a minimum and maximum threshold for
channel condition and power level

24

Without simulation

Without comparison with other approach

How to know
γ
j
?

How to find out the transmit power thresholds

Optimal power control

25