for Power Control in Wireless

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21 Νοε 2013 (πριν από 4 χρόνια και 1 μήνα)

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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


Comments


2

Introduction


Transmission at the optimal transmit power
level


High power level


High success probability


Energy is depleted faster


Increase the interference

-

“cascade” effect

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

Comments


Without simulation


Without comparison with other approach


How to know
γ
j
?


How to find out the transmit power thresholds


Optimal power control

25