Effect of Power Control in Forwarding Strategies for Wireless

Ad-Hoc Networks Supervisor:-

Prof. Swades DePresented By:-

Aditya Kawatra 2004EE10313Pratik Pareek 2004EE10336

Problem Statement

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 one-hop Transmission Probability, Interference Factor and Throughput [1])

Introduction

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.)

But if particular intended receiving node (Y) receives simultaneous signals from its interfering nodes probability of decoding error (~BER) increases

Thus, the aim is to predict a probabilistic interference at Y (in terms of SIR)

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

Introduction (contd…)

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

Where,

is the probability of there being total ‘i’ nodes in the total shaded area .

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

)( )2/(22)2/(212)1/(111 nnnn IIPIPI

....)( )3/(33)3/(32)3/(313 nnn IIIP

ijI

iP

The expression for the expected value of interference will be –

Analysis (Contd..)

.......)( )5/(535)4/(434)3/(333 nnn IPIPIP

....)( )3/(313)2/(212)1/(111 nnnTotal IPIPIPI

....)( )4/(424)3/(323)2/(222 nnn IPIPIP

...321 IntIntIntITotal

Interference due to One Effective Transmitting Node

1

0121 ),(Pr),Pr(

2

1)(

kxT

tkc

k rdrdr

PprrAI

Ap (in Green) is the area commonto 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

011 ),(Pr),Pr(

1)(

n

kxT

tknc

kn rdrdr

Pprr

nAI

....... 13121111 nIIIIInt

2

0231 ),(Pr),Pr(

3

1)(

kxT

tkc

k rdrdr

PprrAI

Interference due to two effective transmitting nodes

rdrdAIr

PpAI nx

Tt )(

2

1)( 1122

1

01,2232 )(),(Pr),Pr(

3

1)(

knkx

Ttk

ck rdrdAI

r

PprrAI

....... 24232222 nIIIIInt

2

01,112 )(),(Pr),Pr(

1)(

n

knknx

Ttkn

ckn rdrdAI

r

Pprr

nAI

2

01,3342 )(),(Pr),Pr(

4

1)(

knkx

Ttk

ck rdrdAI

r

PprrAI

Interference due to three effective transmitting nodes

0

02,2233 )(),(Pr

3

1)(

knx

Tt

c rdrdAIr

PprAI

1

02,3343 )(),(Pr),Pr(

4

1)(

knkx

Ttk

ck rdrdAI

r

PprrAI

3

02,113 3,)(),(Pr),Pr(

1)(

n

knknx

Ttkn

ckn nrdrdAI

r

Pprr

nAI

....... 35343333 nIIIIInt

General Result So the general result of interference due to j nodes, when n nodes

are present in the crescent is given by :-

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 A

p region

Pr c(r,α)1-k

is the probability of (1-k) nodes present in the An region

2,

)(),(Pr),Pr(1

)(0

1,11

jjn

rdrdAIr

Pprr

nAI

jn

knjknx

Ttkn

cknj

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, I

n1 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 I

n1 towards left.

Simulation Results and Plots

“Brute force” algorithm

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

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.

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

Other Simulation Results and Plots

I vs d/R

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.

I vs d/Rfor 2 values of λ

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.

SIR vs 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 :-

2,

,))((),(Pr),Pr(1

)(0

1,1

2

1

jjn

rdrddDAIr

Pfprr

nAI

jn

knjknx

TRD

RD

Ptknc

knj

I

T

References

[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