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



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
The expression for the expected value of
interference will be –
I n  P1 I11/(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.
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 2
P 
I 31 ( A)    Pr( r ,  ) k Pr c ( r ,  ) 2 k pt  Tx rdrd
3 k 0
r 
1 n 1
 PT 
c
I n1 ( A)    Pr( r ,  )k Pr (r ,  )n k 1 pt  x rdrd ; Int1  I11  I 21  I 31  .... I n1  ...
n k 0
r 
Interference due to three effective transmitting nodes
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
 pt PT

c
I n 3 ( A)    Pr( r ,  ) k Pr ( r ,  ) n k 1  x  I n k 1, 2 ( An )rdrd , n  3
n k 0
 r

Int 3  I 33  I 43  I 53  ....I n3  ...
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

c
n  k 1  PT
I nj ( A)    Pr( r ,  ) k Pr (r ,  ) n  k 1 pt (1  pt )

I
(
A
)
 x
n  k 1, j 1
n 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



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




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.
Other Simulation Results and Plots
I vs d/R
for 2 values of λ



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



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.
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 –
PT ( z ) 
PT ( RT ) x
.z
RTx
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
w  RT
n 1
1
 PT ( z ) 
c
I n1 ( A) 
f
(
w
)
Pr(
r
,

)
Pr
(
r
,

)
p
.
q
.
f
(
z
)
 x dz . .dr .d .dw

r
k
n  k 1 t
r

n w R ff
 r 
k 0
 R ff is the distance for node to be in far field of the transmitter X.
R ff  (2 D2 /  ) 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})
The other expressions are :1
I n 2 ( A) 
n
1
I n 3 ( A) 
n
w  RT

wl
w  RT

wl
n 2
 P (z)

f r ( w )  Pr( r ,  )k Pr c ( r ,  )n k 1 pt f r ( z ) T x  I n k 1,1 ( An )dz . .dr .d .dw , n  2
 r

k 0
n 3
 P (z)

f r ( w )  Pr( r ,  )k Pr c ( r ,  )n k 1 pt f r ( z ) T x  I n k 1, 2 ( An )dz . .dr .d .dw , n  3
 r

k 0
Thus, the general expression is
1
I nj ( A) 
n
w  RT

wl
n j
 P (z)

f r ( w )  Pr( r ,  )k Pr c ( r ,  )n k 1 pt f r ( z ) T x  I n k 1, j 1 ( An )dz . .dr .d .dw , n  2, j  n
 r

k 0
Transmitted Power and Device Power

For Total Transmission Power consumed per unit forward progress, we used the
expression
fr (d ) PT (d ) N ReTx (d )
E (d ) 
d
where PT (d )  PT ( RT )(d / RT )
x
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.
 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
2
fr (d ) I L (d ) N ReTx (d )
E (d ) 
d

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.
NFP Plots
For NFP, the expression for fr would be
f r , ( r0 , 0 ) 
2 r e
2 r 2
1  eN
2
Where N is the average no. of nodes within the transmission circle = RT
Total Device power for Navg = 4 is
3.81*10-4 Watts and for Navg = 8 is
7.3*10-5 Watts.
Total Transmitted power for
Navg = 4 is 6.805*10-5 and for
Navg = 8 is 1.49*10-5.
MVR Plots
2r0 e 2AZ
f r , (r0 , 0 ) 
1  e N
For MVR, the expression for fr would be
0  r0  R
,0   0  2
2
Where
r cos  0
r cos  0
r cos  0
ÀZ  R {cos ( 0
)( 0
1 0
)}
R
R
R
2
1
And,
  2
f r (r0 )  
 0
f r , (r0 , 0 )d
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 Device power for Navg =4 is
1.9*10-3 Watts
Total Transmitted power for Navg =4
is 2.1*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