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, MVR, and Random Transmission in wireless ad-hoc networks

Using the above, evaluate total transmission and device power consumption for a unit forward distance, taking into account no. of retransmissions required.

Also, to compare the strategies on the above parameters for different node densities and single out the best forwarding strategy (ies), 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 total interference and SIR)

The shaded region is the effective interference region for Y

Basic Assumptions

Some basic assumptions are –

The transmission protocol for the network can be taken to be slotted ALOHA (as in [1] and [2]) with Carrier Sense Multiple Access (CSMA without collision detection). The antennas used in the network are isotropic and the nodes are distributed according to the Poisson point process.

We allow backward transmissions in case of all the power control strategies. This is necessary for calculating the interference from the interfering nodes, since their individual directions of transmissions can be random and it would be unviable to consider all possible directions

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

Basic Assumptions (contd…)

Time lag between a data transmission and a neighboring node sensing it is assumed to be lesser than fixed time slot of the protocol i.e. both the receiver node and the interference zone nodes will sense the transmission within the same time slot as that of data transmission and the transmission and interference nodes will keep quiet from the next slot onwards.

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.

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

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

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

ijIiP

The expression for the expected value of interference will be –

.......)( )5/(535)4/(434)3/(333 nnn IPIPIP....)( )4/(424)3/(323)2/(222 nnn IPIPIP

...321 IntIntIntITotal

Interference due to One Effective Transmitting Node

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

2

0231 ),(Pr),Pr(

3

1)(

kxT

tkc

k rdrdr

PprrAI

....... 13121111 nIIIIInt;

Interference due to three effective transmitting nodes

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,

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

)(0

1,11

1

jjn

rdrdAIr

Ppprr

nAI

jn

knjknx

Tknttkn

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 appropriate 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 and Analysis 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 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

Other Simulation Results and Plots

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

Analysis (Power Control)

Only difference with respect to non-power control equations comes in actual interference amount. Instead of full power PT , it will be PT (z), where z distance from interfering node under consideration and its intended receiver. It is given by –

It will interfere with Y only if z > r/2, where r is its distance from Y. Obviously z ≤ RT . Thus the integral for In1 (say) can be modified as follows

is the distance for node to be in far field of the transmitter X. where D is maximum dimension of the antenna

The q factor cannot be computed and can only be estimated from the respective brute force simulations. For In1, q is 1-Pr(probability that Inj {j>1} occurs / one node at least is interfering) ≈1-(Total number of occurrences for Inj {j>1}/Total number of occurrences for Inj {j>=1})

xxT

TTT z

R

RPzP .

)()(

T

ff

Rw

Rw

n

kx

Trtkn

ckrn dwddrdz

r

zPzfqprrwf

nAI

1

011 ....

)()(..),(Pr),Pr()(

1)(

ffR

)/2( 2 DR ff

The other expressions are :-

Thus, the general expression is

2,....)()(

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

)(2

01,112

ndwddrdzAI

r

zPzfprrwf

nAI

TRw

lw

n

knknx

Trtkn

ckrn

3,....)()(

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

)(3

02,113

ndwddrdzAI

r

zPzfprrwf

nAI

TRw

lw

n

knknx

Trtkn

ckrn

njndwddrdzAIr

zPzfprrwf

nAI

TRw

lw

jn

knjknx

Trtkn

ckrnj

,2,....)(

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

1)(

01,11

Transmitted Power and Device Power

For Total Transmission Power consumed per unit forward progress, we used the expression

where

Here, PT(RT) is the full range transmission power, x is the path loss factor and NReTr(d) is the expected number of retransmissions given d.

d

dNdPdfrdE TxT )()()()( Re

xTTTT RdRPdP )/)(()(

The number of retransmissions, need the BER vs SINR plot. Referring to [4] and assuming that the load factor 8, we extract the BER from this curve

For calculation of actual Device Power we use the expression

Here IL, the current that flows through the load, is obtained from the Transmitted Power vs Current Table for CC2420 Transceiver

For calculation of Device Power, we assume the load resistance to be 1 Ω.

d

dNdIdfrdE TxL )()()()( Re

2

NFP Plots

Where N is the average no. of nodes within the transmission circle = 2

TR

N

r

r e

errf

1

2),(

22

00,

For NFP, the expression for fr would be

Total Transmitted power for Navg = 4 is 6.805*10-5 and for Navg = 8 is 1.49*10-5.

Total Device power for Navg = 4 is 3.81*10-4 Watts and for Navg = 8 is 7.3*10-5 Watts.

MVR Plots

For MVR, the expression for fr would be

Where And,

N

A

r e

errf

Z

1

2),(

20

00,

Rr 00 20, 0

)}cos

1cos

()cos

({cos

2

00000012

R

r

R

r

R

rRÀZ

drfrf rr ),()( 00,

2

00

Total Transmitted power for Navg =4 is 3.6*10-3 Watts and for Navg = 8 is 4.7*10- 3 Watts.

Total Device power for Navg = 4 is 1.7*10-3 Watts and for Navg = 8 is 2.2*10-3 Watts.

Random Selection Plots

Total Transmitted power for Navg =4 is 2.1*10-3 Watts

Total Device power for Navg =4 is 1.9*10-3 Watts

Comparison of MVR and NFP in terms of the Device Power Consumed

We can see that for higher values of Neighboring nodes, Device Power for MVR is much higher than that of NFP.

But the situation changes when Navg gets smaller, i.e node density is sparser OR the transmission radius involved is very large (of the order of 50m).

As per our results, there seems to occur a critical value of λ or Navg, for which the Device power consumed is the same for both, and below this critical value, MVR exhibits better performance.

Contd..

And according to this plot, the critical value of Navg

comes out to be 0.3., or λcritical = 9.55 * 10-4 m-2

If we do a Spline Curve Fit, this Critical Navg is 0.55

λ = Navg /π RT2 N

For this value of λcricitcal , the Device Power Consumed, obtained from the analysis equations were

PwNFP = 0.1436*10-3 Watts

PwMVR = 0.1441*10-3 Watts

Extension : Energy Scavenging Energy Scavenged is the

scalar sum of the Received Intended Signal Power and the Power from the interfering nodes.

As is clear from our results, for scavenging purposes, MVR is quite better than NFP for higher values of Navg.

But, same as for Device Power, here also after a critical value of Navg OR λ, the behavior changes.

For Navg = 0.16 PScvng, NFP = 0.1013*10-5 Watts PScvng, MVR = 0.1007*10-5Watts Thus, we can say that Navg

critical for energy scavenging is close to 0.16 , λcritical = 5.09 * 10-4 m-2

Conclusion

Device Power utilization for NFP and MVR has a λcritical = 5.09 * 10-4

m-2 . Above this value, NFP has much lesser Device Power Utilization. And below this, MVR, shows less Utilization.

Thus, if the network is very wide area, MVR is the better transmission strategy as opposed to the proposed NFP strategy in [1].

For Navg = 4,It is also seen that, Random Forwarding Strategy, is almost equal to MVR in terms of Device Power Utilization. But, shows a poorer performance than NFP

In extension to the desired goals, we also touched upon the Energy Scavenging Problem. We observed that it also has a λcritical .

This λcritical is approx equal to 5.09 * 10-4 m-2

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