Transcript BTP_midsem.ppt

Effect of Power
Control in Forwarding
Strategies for Wireless
Ad-Hoc Networks
Supervisor:Prof. Swades De
Presented By:Aditya Kawatra 2004EE10313
Pratik Pareek 2004EE10336
Problem Statement
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To model the power consumption and effective interference
for forwarding strategies like NFP, LRD, and Random
Transmission in wireless ad-hoc networks
Using the above, evaluate total power consumption for a
unit forward distance, and the no. of retransmissions
required.
Also, to verify in the light of above analysis the best
forwarding strategy, which is NFP as of now (based on onehop Transmission Probability, Interference Factor and
Throughput [1])
Introduction
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In previous work, Interference Zone (IZ) effects have not been
taken into account.
In this zone, nodes can sense the carrier signal from transmitting
nodes, but cannot decode the data. Usually RI=2RT
The solid circle is the transmission zone (of
radius RT) and the dotted circle is the
interference zone boundary (of radius RI)
Introduction (contd.)
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But if particular intended receiving node (Y) receives
simultaneous signals from its interfering nodes  probability of
decoding error (~BER) increases
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Thus, the aim is to predict a probabilistic interference at Y (in
terms of SIR)
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Some basic assumptions are –
The transmission protocol followed is a simple CSMA (Carrier
Sense Multiple Access) instead of the usual slotted ALOHA [2]
and a Poisson process node distribution
Initially, no power control is assumed, i.e. all Txs occur at full
power. Later pdf of a receiving node [1] will be factored in along
with other complexities
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Introduction (contd…)
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Time lag between data transmission and reception at any node is
assumed negligible. So with CSMA, all IZ nodes will instantaneously
sense Tx carrier and keep quiet
Nodes in IZ will also keep quiet if nodes from outside transmit, i.e.
they can fall in the interference zone of some external transmitting
node. This possibility is ignored as we want to conduct a worst-case
analysis.
Analysis
The expression for the expected value of
interference will be –
I n  P1 I 11/( n1)  P2 ( I 21/( n 2 )  I 22 /( n 2 ) )
 P 3 ( I 31/( n 3 )  I 32 /( n 3 )  I 33 /( n 3 ) )  ....
Where,
Pi is the probability of there being total ‘i’ nodes in the total shaded area .
I ij is the probabilistic interference considering that only j nodes are exclusive
interferers (j<=i), given that there are total n nodes in the shaded region
Analysis (Contd..)
I Total  ( P1 I 11/( n1)  P2 I 21/( n 2 )  P3 I 31/( n 3 )  ....)
 ( P2 I 22 /( n 2 )  P3 I 32 /( n 3 )  P4 I 42 /(n4 )  ....)
 ( P3 I 33 /(n 3 )  P4 I 43 /( n4 )  P5 I 53 /(n5 )  ....)  ...
ITotal  Int1  Int 2  Int 3  ...
Interference due to One Effective Transmitting Node
Ap (in Green) is the area common
to the Interference region of N1 and the
total shaded area.
An (in Pink) is the compliment area to Ap
in the total shaded region region.
Pr(r,α)k is the probability of k nodes
present in the Ap region
Prc(r,α)1-k is the probability of (1-k) nodes
present in the An region
1 1
 PT 
c
I 21 ( A)    Pr( r ,  ) k Pr ( r ,  )1 k pt  x rdrd
2 k 0
r 
1 2
P 
I 31 ( A)    Pr( r ,  ) k Pr c ( r ,  ) 2 k pt  Tx rdrd
3 k 0
r 
1 n 1
P 
I n1 ( A)    Pr( r ,  )k Pr c (r ,  )n k 1 pt  Tx rdrd
n k 0
r 
Int1  I11  I 21  I 31  .... I n1  ...
Interference due to two effective transmitting nodes
1
 PT

I 22 ( A)    pt  x  I 11 ( An )rdrd
2
r

1 1
P

I 32 ( A)    Pr( r ,  ) k Pr c ( r ,  ) 2 k pt  Tx  I 2 k ,1 ( An )rdrd
3 k 0
r

1 2
P

I 42 ( A)    Pr( r ,  ) k Pr c ( r ,  ) 3 k p t  Tx  I 3 k ,1 ( An )rdrd
4 k 0
r

1 n 2
 PT

c
I n 2 ( A)    Pr( r ,  )k Pr ( r ,  )n k 1 pt  x  I n k 1,1 ( An )rdrd
n k 0
r

Int 2  I 22  I 32  I 42  .... I n 2  ...
Interference due to three effective transmitting nodes
1 0
 PT

c
I 33 ( A)    Pr (r ,  )2 pt  x  I 2, 2 ( An )rdrd
3 k 0
r

1 1
 PT

c
I 43 ( A)    Pr( r ,  ) k Pr ( r ,  ) 3 k pt  x  I 3 k , 2 ( An )rdrd
4 k 0
r

1 n 3
p P

I n 3 ( A)    Pr( r ,  ) k Pr c ( r ,  ) n k 1  t x T  I n k 1, 2 ( An )rdrd , n  3
n k 0
 r

Int 3  I 33  I 43  I 53  .... I n 3  ...
General Result
So the general result of interference due to j nodes, when n nodes
are present in the crescent is given by :-
1 n j
 PT

c
I nj ( A)    Pr( r ,  ) k Pr ( r ,  ) n k 1 pt  x  I n k 1, j 1 ( An )rdrd
n k 0
r

n  j, j  2
Here,
Inj is the Interference due to j nodes, when there are a total of n nodes
in the shaded region.
Pr (r,α)k is the probability of k nodes present in the Ap region
Pr c(r,α)1-k is the probability of (1-k) nodes present in the An region
Simulation Results and Plots
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As the probability of occurrence of nodes in the region is governed by the
Poisson process, the graph of the total interference peaks at the average
value, ie. λA.
Similarly, In3 and In2 also peak at the same value.
But, In1 shows a unique characteristic. It peaks at a value less than the
average value,(λA). This is because, the no. of effective one node
interference cases decreases as the total no. of nodes increase. This
decrease shifts the peak of In1 towards left.
“Brute force” algorithm
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To simulate the Poisson distribution of nodes a large square
area (dimensions >> RI) was taken and the average number of
nodes (= λ*square area) were randomly positioned.
A list is created of all the nodes located in the total shaded
region (= n) and a transmitting nodes only sub-list is randomly
assigned based on probability of transmission.
Then a random order within the transmitting nodes is selected
and finally after isolating the nodes which are exclusive of each
others’ interference zones, the final effective interfering nodes
are determined (= j).
The approriate Inj is updated and finally each of these is divided
by the total number of iterations.
Comparison between Analysis and Brute Force
Results
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Results obtained from Brute
Force simulation andAnalysis
show a significant match.
This match increases on
increasing the no. of iterations in
the Brute Force Simulation.
The shape of the two results are
also consistent, i.e they peak at
the same value.
This value is very close to the
average no. of nodes in the
shaded region i.e. λA.
Other Simulation Results and Plots
I vs d/R
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The value of I2 and I3 increases as d/R is increased, while I1
decreases for the same.
As d/R increases the total no. of nodes in the total shaded region
(possible interferers) increases thus decreasing the probability of one
effective interfering node
I vs d/R
for 2 values of λ
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The Interference value increases as the receiver moves away (i.e.
d/R increases).
This can be explained by the increased number of nodes in the
shaded region, when d/R is increased.
This graph suggests that by varying λ, we do not see a significant
change in total interference.
SIR vs d/R
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The signal to interference ratio (SIR) decreases as d/R is increased.
When d/R is very small, the power received is large and also the
interference is low. So, the SIR value is very high.
As Interference also monotonically increases with d/R, the SIR curve
continues to show a decrease with increasing d/R.
Future Work
 Incorporate the Power Control Strategy (i.e. NFP, LRD and
the Random Txn) in the analysis and the simulations for
calculating the excepted Interference.
 Use these results to obtain for each strategy ,the
Energy per unit forward progress (single hop).
Average no. of retransmissions
 The equation derived as of now is : D RI
P
1 n j
c
I nj ( A)    Pr( r ,  ) k Pr ( r ,  ) n k 1 pt   f PT ( Tx  I n k 1, j 1 ( An )dD
n k 0
r
 2 D R
n  j, j  2

)rdrd ,

References
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[1] Ting-Chao Hou and Victor O.K. Li, “Transmission Range
Control in Multihop Packet Radio Networks”, in IEEE Trans.
Commun., vol. COM-34, January 1986
[2] Eun-Sun Jung and Nitin H. Vaidya, “A Power Control MAC
Protocol for Ad Hoc Networks”, in MOBICOM’02, September
23-28 2002
Swades De, Chunming Qiao, Dimitri A. Pados, Mainak
Chatterjee and Sumesh J. Philip, “An Integrated Cross-Layer
Study of Wireless CDMA Sensor Networks”, in IEEE Journal
on Selected Areas in Communications, Vol. 22, No.7,
September 2004