A Kalman Filter based Adaptive On DemandTransmission Power Control (AODTPC) Algorithm

for Wireless Sensor Networks

M M Y Masood, Ghufran Ahmed and Noor M KhanAcme center of Research in Wireless Communications (ARWiC)

Department of Electronics Engineering

Mohammad Ali Jinnah University

Islamabad, 44000

{mmymasood, gahmad78}@gmail.com, noor@ieee.org

Abstract—Transmission power control (TPC) is a key tech-nique to save the energy of a sensor node in a resource-constrained wireless sensor network (WSN). A variety of algo-rithms have been proposed to enhance the lifetime of the network.Nevertheless, Power-level regulation of a sensor node in time-varying propagation environment still needs deep investigationdue to the uncertain behavior of the wireless fading channel.In order to address this issue, an energy efficient and reliablepower control algorithm that works according to the variationsin the propagation environment is presented in this paper.We propose an adaptive version of a well known algorithm,On Demand Transmission Power Control (ODTPC), named asAdaptive ODTPC or AODTPC. The proposed algorithm is basedon Kalman Filter, which is used to predict the future receivedradio signal strength indicator (RSSI) values by incorporatingthe time-varying fading channel conditions. These values arethen used to regulate the transmission power level with the helpof ODTPC strategy prior to data transmission. Thus, the mainobjective of this work is to capture the time-varying variationsof uncertain environment and adjust the power levels accordingto realistic environment behavior. Simulation results demonstratethat AODTPC performs better in terms of energy efficiency andincreases node lifetime than its predecessor.

I. INTRODUCTION

Wireless sensor networks (WSNs) consist of resource con-

strained sensor nodes that are used for environmental mon-

itoring. Sensor nodes collect the data from the environment

and send towards sink in hop by hop manner. The sink is

a powerful node that transmits the data to control center via

satellite or internet for further processing [1]. Fig.1 shows a

typical WSN. Wireless sensor networks (WSNs) has numerous

applications to monitor the areas where the transmission

through wire is infeasible, some of them are habitat moni-

toring, surveillance system, border monitoring etc [2]. Since,

these applications require a long network lifetime due to

unattended nature of the sensor nodes i.e. once deployed,

therefore, it is extremely difficult to replace the batteries

of these sensor nodes. Extensive research efforts have been

made to design energy efficient systems, thus, Researchers are

focusing to get a solution that help to increase the network

lifetime. Among different strategies that have been evolved,

transmission power control (TPC) is an important technique

Fig. 1. A typical wireless sensor network

to utilize energy in a suitable way. The main benefits of

TPC is the high reliability of wireless links and thus, packet

reception rate (PRR). In [3], advantages of the power control

in wireless multi-hop networks are analyzed. There are many

TPC techniques available in the literature, however, these

suffer from the following major deficiencies:

• Existing TPC techniques do not react to the changes in

time varying channel especially if the channel is subject

to fast fading.

• Existing TPC techniques do not ensure data reliability

closer to 100%, which is very vital to ensure because

energy saving without data reliability is meaningless.

In this paper, we focus to design an adaptive power controller,

which is adaptive to the variations of the channel and provides

data reliability in uncertain fading channel environment. A

signal transmitted through a transmitter suffers by the effect

of fading environment that distort signal both in phase and

amplitude. Such an environment between the two ends of

communication link, creates the fluctuations in the received

signal strength indicator (RSSI) values and thus, reduces the

packet reception rate (PRR). Nevertheless, these fluctuations

in RSSI values create the need of immediate change in power

level, that can compensate the variation occurred at that

978-1-4673-4451-7/12/$31.00 ©2012 IEEE

particular instant. However, power levels regulation on the

basis of existing power control strategies does not provide

power level adjustment by incorporating channel knowledge.

Power level adjustments without the knowledge of channel

environment do not ensure data reliability. Furthermore, these

existing TPC techniques adjust power levels as when the

received signal strength indicator (RSSI) value falls below the

sensitivity level, which is undesirable in many applications.

Therefore, there is a need to adjust power level by getting the

knowledge of fading channel adaptively prior to data packet

transmission. Based on this analysis, we propose a Kalman

Filter based adaptive transmission power control, which is an

extension of a well known transmission power control (TPC)

algorithm, ODTPC [4], named as AODTPC. In this algorithm,

Kalman Filter is used to estimate the channel variations and to

predict the upcoming received signal strength (RSSI) values

based on the knowledge of channel state information (CSI). On

the basis of these predicted RSSI values, transmission power

levels are adjusted according to the transmission power control

ODTPC. The aim of this work is, thus, to adjust best possible

power levels of a sensor node in fading environment providing

data reliability and packet reception rate closer to 100%.

The signal power γ can be modeled by using log-normal

shadowing model along with channel impairments, as stated in

equation(1). Where, d is the transmitter and receiver separation

distance, γ0 is the signal power at a reference distance do, xis the channel state information and σ denotes the uncertainty

in signal power and usually modeled as zero-mean Gaussian

i.i.d process. Fading channel generates abrupt change in the

RSSI values and makes the wireless link uncertain. Such a

situation can be viewed in Fig. 2, where a simulation is done

to illustrate the variations occurred by the means of channel

impairments.

γ = γ0 + 10nlog(d0d) + 20log(x) +Xσ (1)

The RSSI values with the channel impairments have uncertain

behavior and produces sudden fluctuations, which in turn cre-

ates wrong power level adjustments at that particular instant.

Thus, in order to compensate the uncertainty of fading channel,

it is needed to estimate the fading channel behavior and predict

the RSSI values before they are received at the receiver.

The remainder of the paper is organized as follows: In

section II, existing power control strategies is explained briefly.

Section III presents the system model for the proposed power

control and section IV discusses AODTPC. Simulations and

results are shown in Section V. Finally, section VI concludes

the paper.

II. RELATED WORK

There is a lot of published work that provides a detailed

discussion about the requirement of transmission power con-

trol in wireless communications based systems. As discussed

earlier in section I, the main objective of the transmission

power control algorithms is to find an optimal power level

for each sensor node that can provide a good data reliability

0 50 100 150 200 250 300 350 400 450 500-60

-40

-20

0

(a) RSSI without Channel Impairments

dBm

0 50 100 150 200 250 300 350 400 450 500-60

-40

-20

0

(b) RSSI with Channel Impairments

dBm

Fig. 2. RSSI behavior with and without channel impairments.

along with low energy. Hence, power control algorithms try to

switch power levels among different transmission power levels

according to their specified mechanism.

In PCBL (Power Control with Blacklisting) algorithm [5],

the power levels are adjusted according to the notifications

received from the receiver. Receiver will notify with an ac-

knowledgement as when an erroneous packet is encountered,

however, a complete reception of data packet leads to the

decrement of transmission power level by fixed one step.

Furthermore, as when the packet reception rate (PRR) of a

sensor node is lower than some predefined PRR, that act

as a threshold, it will blacklist that specific node and stop

to transmit through that node. Although, such mechanism is

good to ensure data reliability, however, as when propagation

environment is uncertain and produces sudden variations in

signal power, such mechanism leads to increase the number

of blacklist nodes, which in turn reduces the throughput.

Adaptive Transmission Power Control (ATPC) algorithm [6]

uses an initialization phase in which transmitting node sends

a beacon message to all of its neighbors at each power level.

Receiving nodes calculate the RSSI/LQI of each of these

beacons and send these values back to the transmitter along

with acknowledgement. Upon receiving the RSSI/LQI values,

the transmitting node determines the optimal power level. Then

runtime tuning phase starts, in which a transmitter sends the

data packet to a receiver. The receiver notifies the transmitter

only if the particular RSSI/LQI value exceeds or falls below

a predefined threshold region.

Both PCBL [5] and ATPC [6] have initialization phase over-

heads. Additionally, as the channel variations are frequent

in an urban environment, therefore, it creates the need of

initialization phase repeatedly to adjust power levels of nodes

at optimum level. Furthermore, as discussed earlier received

signal strength suffers with the variations of channel environ-

ment, hence, only the RSSI values are not enough to adjust

the power levels optimally in fading channel environment.

In contrast, ODTPC [4] and MODTPC [7] do not utilize

any initialization phase. Whenever a transmitting node needs

to transmit data packet to any of its neighbor, it sends

with maximum power level and the receiver calculates the

corresponding received signal strength indicator (RSSI) value.

If this value exceeds or falls below the threshold region,

receiver notifies the transmitter through a notification message.

Based on this specific notification message, transmitting node

adjusts its power level. In addition MODTPC [7] decrease

power levels by one step as when the RSSI value is within

the specified threshold region, which provides less energy

usage but does not ensure a good reception of data packets.

Although ODTPC [4] and MODTPC [7] do not use any

initialization phase, however, their response to adjust power

levels in a fading environment where channel variations are

sudden, is not as much fast as the channel variations occur in

the environment.

In [8], authors used Markov chain to adjust the transmission

power levels of a transmitting node. A systematic model to

calculate latency and energy utilization in wireless sensor

networks (WSNs) that are effected by the transmission power

has been discussed in [9]. Ammari et al. [9] focused to an

important factor and concluded that by increasing the number

of hops in a network, the energy consumption of each sensor

node decreases while the latency increases and vice versa.

In [10], Ares et al. proposed two power control algo-

rithms: Multiplicative-increase Additive-Decrease power con-

trol (MIAD-PC) and Packet Error Rate Power Control (PER-

PC). PER-PC is based on signal to interference plus noise ratio

(SINR), while MIAD-PC sets the transmission power level on

the basis of packet reception rate (PRR). A systematical model

of the wireless channel has been developed to approximate

signal to interference plus noise Ratio (SINR) in PER-PC

power control algorithm.

The power control strategies discussed above, adjust power

levels without the involvement of channel variations, however,

the channel variations are embedded inherently in signal

which causes a sudden change in signal power and results

in the loss of data packet. Hence, the above discussed power

controllers do not have a realistic behavior, because they are

not incorporating the channel variations. In order to overcome

the channel variations over the signal strength, there is a need

to get the knowledge of channel states through estimation and

then track the channel states variations during the transmission

of data packets. To overcome this situation, there is a need of

such a filter which is capable of estimating and tracking the

channel behavior optimally in fast fading channel environment.

In order to estimate and track the channel variations, a well

known filter Kalman filter [11] is used to estimate and track

channel variations optimally. A complete system model is

explained in next section.

III. SYSTEM MODEL

In this section, a complete system model of AODTPC is

discussed in detail. Kalman filter is used to predict the future

received signal strength indicator (RSSI) values.

A. System Process Equation

The system process equation can be formulated as:

xk+1 = Fxk + wk (2)

Where

F ε �N×N

xk = [x1,k x2,k x3,k . . . xN,k]ε�N

N = No of channel multipaths

The state transition matrix included in equation(2) is given

by

F =

⎛⎜⎜⎜⎝

α1 0 . . . 00 α2 . . . 0...

.... . .

...

0 0 . . . αi

⎞⎟⎟⎟⎠

iεN

The αi are the channel attenuation factors. It carries the time

varying nature of the channel and modeled as αiεJ0(2πfdT )[12]. Where fd is the maximum doppler shift, J0 is the zeroth

order Bessel function of first kind and T is the time duration

between two consecutive symbols. wk is the system’s process

noise i.e.

wk ∼ N(0, Q)

E[wi.wTj ] = Qδ(i− j)

B. System Discrete Measurement Equation

The observation equation included in the system model

along with channel is given by

γ(k) = g(xk, vk) (3)

where g(.) is a non-linear function of received signal strength

indicator in terms of xk as stated in equation(1) and vk is the

system’s measurement noise i.e.

v(k) ∼ N(0,�)E[vi.v

Tj ] = �δ(i− j)

The system’s process and measurement noises are independent

of each other. The process noise and measurement noise

covariances might vary during each time step or during

each measurement, however, here we assumed they are time-

invariant.

C. Extended Kalman Filter

The processes in real-life are usually non-linear. In order to

apply Kalman Filter on a non-linear system, the linearization

process is needed. Since, the measurement equation(3) is non-

linear in xk, therefore, we can apply Kalman Filter after

linearizing it, the details of Kalman filter can be found in [11].

Linearization procedure of the measurement equation can be

written as follows,

g(xk) ≈ g(x̂k/k−1) + H(x̂k/k−1)xk−H(x̂k/k−1)x̂k/k−1

≈ g(x̂k/k−1) + H(x̂k/k−1)

.[xk − x̂k/k−1]

Where H is Jacobian matrix and it is given by

H(k/k − 1) = H(x̂k/k−1)

=∂g(xk)

∂xTkTherefore the process and measurement equations can be

written as follows

xk+1 = Fxk + wk

γ(k) ≈ g(x̂k/k−1)

+H(x̂k/k−1)[xk − x̂k/k−1]

D. Extended Kalman Filter Recursion

Kalman Filter recursions for the system defined by

equations(2) and(3) can be formulated as

1) Next state prediction before measurement is taken:

x̂k = Fx̂k−1 + wk−1

Pk/k−1 = FPk−1/k−1FT +Q

2) Updating of state after measurement is taken:

x̂k/k = Fx̂k−1 +Kk[γk −H(x̂k/k−1)]

Kk =Pk/k−1HH

k/k

[HHk Pk/k−1HH

k +RIN ]

Pk/k = [1−KkHHk ]Pk/k−1

IV. THE AODTPC PROTOCOL

A. Assumption

In designing of AODTPC, we assume the following:

• Sensor nodes are distributed randomly.

• Sensor nodes are deployed in a large number, to avoid

the network partitioning.

• At the beginning, transmission power level of all the

sensor nodes is set at maximum available power level.

• Wireless links are uniform in both the directions.

• All sensor nodes are identical in terms of computational

capability and battery power.

• Sensor nodes have a standard hardware like CC2420 [13].

B. Overview of AODTPC strategy

Adaptive on demand transmission power control (AODTPC)

is a transmission power control strategy that adapts the time

varying nature of the channel and tries to adjust its power

levels at an optimum stage. Since, the existing power control

strategies incorporate only the RSSI value and regulate power

levels only when the RSSI value falls below the sensitivity

level, however, this mechanism is not desirable because at that

particular instant the data packet will be lost. Thus, they try

to increase power level after the loss of data packet, which

is meaningless. The main objective of transmission power

control is to save the energy, however, the first priority is data

reliability. To overcome this situation, upcoming RSSI values

are needed, which can be obtained with the help of Kalman

filter [14]. Kalman filter is an optimal filter and is well known

in the field of tracking and estimation [15]. As the computa-

tional load of Kalman filter is not very high, therefore, it is

well suited for resource constrained wireless sensor nodes [16].

After estimating channel states and predicting RSSI values, the

predicted RSSI values are then used to adjust power levels,

which can be done along with ODTPC power control. By

the means of such mechanism, AODTPC adjust power levels

predictively and ensures the data and link reliability in fast

fading channel conditions.A major enhancement of AODTPC

over other existing power control strategies is that it is adaptive

to the channel variations and performs action before the fall of

RSSI values below the sensitivity level. Furthermore, it does

not rely on the constant feedback from the receiver and it

works optimally in a conditions when the feedback from the

receiver is not available.

C. Transmission Power Control (TPC) Module

In this section, the main procedure of transmission power

control module used in AODTPC, is explained briefly. The

proposed system first uses Kalman filter [14] to estimate

the received signal strength indicator (RSSI) value for future

transmissions, by utilizing the effects of fading environment

present in the surroundings of a sensor node. The predicted

RSSI value is then, used to adjust power level for future data

packets. This adjustment is done on the basis of well known

transmission power controller, on demand transmission power

control (ODTPC) [4]. The power levels are regulated only

when the RSSI values are below RSSITH−Low or above

RSSITH−High, this threshold boundary can be adjusted ac-

cording to the needs of the applications. Upon receiving data

packet, receiver node measures the RSSI value and notifies

transmitter about it. The transmitting node then calculates

the difference between estimated and measured RSSI values,

which is then used to track and correct the channel states. By

utilizing this mechanism, transmitter chooses a power level

adaptively with respect to the changes in time varying channel

and thus, there is no need of frequent acknowledgement (ACK)

packets. This is due to the fact that Kalman filter can track

Tx Rx

Kaman Filter Based RSSI Estimation

TPC Module

Data

Acknowledgement

Channel

Fig. 3. AODTPC system model

�

0 10 20 30 40 50 60 70 80 90 100-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Packet or Block

Cha

nnel

Sta

te In

form

atio

n (C

SI)

ActualEstimate

Fig. 4. Channel state estimation

the channel states without constant availability of measurement

values. Fig. 3 shows a complete system model of AODTPC.

V. SIMULATIONS AND RESULTS

A. Simulation Setup

The performance of the proposed power controller

AODTPC is evaluated by comparing it with ODTPC and

ATPC. The algorithms are implemented in Matlab R©7.3. The

simulation parameters are listed in table I. Since, AODTPC

TABLE ISIMULATION PARAMETERS

Simulation parameters ValuesTransmission Power Levels 31 to 3 (0 to -25 dBm)Simulation time 100 unitsDistance between Tx and Rx 100 mNoise Variance 16Path loss Exponent 3.5Carrier frequency 2.4 GHz

utilizes the information of channel, therefore, it is needed to

estimate the channel states optimally. Thus, Kalman filter is

used to track the channel variations in time-varying fading

propagation environment. Fig.4 shows the channel states esti-

mation. It is noticeable that Kalman filter tracks the variations

of the channel properly, however, there may occur some situa-

tions where the estimation error increases, that happens by the

means of sudden variations in the propagation environment.

The power controllers adjust their power levels on the basis

of RSSI values. RSSI values with the channel impairments

for AODTPC, ODTPC and ATPC are shown in Fig.5. The

RSSI values are observed at different lower threshold levels

while the upper threshold is kept constant at 0 dBm. It is

noticeable from the figure that RSSI values behaves mostly in

a similar manner, however, at some places there is difference

in the RSSI values. That is due to the fact that AODTPC

utilizes channel estimates to get the RSSI values and then

adjusts its power levels, hence, the values that are used by

the power controller AODTPC are more reliable than those

of ODTPC and ATPC. In fading environment, the channel

severely degrades the strength of signal and creates variations

in RSSI values, therefore, if the variations in RSSI values are

not observed then this situation leads to wrong power level

adjustment and that results in loss of data packet at the receiver

side. This situation can be envisioned in Fig.5(b) more clearly,

where RSSI value falls below the lower threshold and therefore

at this stage the power level should be increased, however, the

ATPC and ODTPC does not account this particular situation.

Furthermore, AODTPC utilizes upcoming RSSI values all the

time that ensures the reliability of data packets. The power

�

0 10 20 30 40 50 60 70 80 90 100-80

-60

-40

-20

0

20

40

Packet or Block

RS

SI(d

Bm

)

AODTPCODTPCATPC

(a) RSSITH−low=-50 dBm,RSSITH−High=0 dBm

�

10 20 30 40 50 60 70 80 90 100

-80

-60

-40

-20

0

20

Packet or Block

RS

SI(d

Bm

)

AODTPCODTPCATPC

(b) RSSITH−low=-70 dBm,RSSITH−High=0 dBm

Fig. 5. Plots of RSSI values for AODTPC, ODTPC and ATPC. RSSI lowerthreshold is kept at (a)-50 dBm (b)-70 dBm; while RSSI upper threshold isfixed at 0dBm.

level adjustment is the main objective of the power controllers

and that should be reliable. After obtaining the RSSI values

the power controllers adjust power levels according to their

specified mechanism. Fig.6 shows the power level adjustment

for AODTPC, ODTPC and ATPC on the basis of RSSI values

as shown in Fig.5. The simulation is done with different lower

thresholds while the upper threshold is constant at 0 dBm.

Since, the RSSI values that are used in AODTPC are reliable

to adjust the power levels, therefore, the power levels that

are adjusted with the help of AODTPC will be more secure

and optimum. As explained earlier, at some places RSSI value

falls below the sensitivity level and at that place the power

level should be increase, AODTPC encounters this situation

predictively, however, other two power controllers ATPC and

ODTPC unable to handle such a situation. In order to compare

the performance of power controllers in terms of overall

energy consumption, Fig. 7(a) and 7(b) show the cumulative

energy consumed by sensor nodes using ODTPC, ATPC and

AODTPC for different scenarios as discussed previously. It is

thus clear from the plots that AODTPC consumes less energy

�

0 10 20 30 40 50 60 70 80 90 100-25

-20

-15

-10

-5

0

Packet or Block

Pow

er L

evel

s (d

Bm

)

AODTPCODTPCATPC

(a) RSSITH−low=-50 dBm,RSSITH−High=0 dBm

�

0 10 20 30 40 50 60 70 80 90 100-25

-20

-15

-10

-5

0

Packet or Block

Pow

er L

evel

s (d

Bm

)

Adaptive ODTPCODTPCATPC

(b) RSSITH−low=-70 dBm,RSSITH−High=0 dBm

Fig. 6. Plots of power levels for AODTPC, ODTPC and ATPC. RSSI lowerthreshold is kept at (a)-50 dBm and (b)-70 dBm; while RSSI upper thresholdis fixed at 0dBm.

�

�

(a) RSSITH−low=-50 dBm,RSSITH−High=0 dBm

�

�

(b) RSSITH−low=-70 dBm,RSSITH−High=0 dBm

Fig. 7. Energy consumption in Percentage for ATPC, ODTPC and AODTPC.RSSI lower threshold is kept at (a)-50 dBm and (b)-70 dBm; while RSSI upperthreshold is fixed at 0dBm

as compared to ODTPC and ATPC.

VI. CONCLUSION

Adjusting the optimum power level of a sensor node in

uncertain fading propagation environment is a challenging

task. Uncertain variations in propagation environment distortthe signal strength and as a result initiate severe packet loss.

In order to capture the time-varying nature of the environment

and to predict the received signal strength value, Kalman

Filter is used. In this paper, the proposed algorithm behaves

according to the time-varying nature of the environment and

adjusts its power levels optimally, hence provides high data

reliability. Simulation results show that the proposed algorithm

performs better as compared to existing transmission power

control strategies like ODTPC [4] and ATPC [6].

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