# Transmission power adaptation according to the message length for Wireless Sensor Networks

Denis Dessales, Anne-Marie Poussard, Rodolphe Vauzelle, Noël Richard, François Gaudaire, Christophe Martinsons

► To cite this version:

Denis Dessales, Anne-Marie Poussard, Rodolphe Vauzelle, Noël Richard, François Gaudaire, et al. Transmission power adaptation according to the message length for Wireless Sensor Networks. IEEE 22nd International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), 2011, Sep 2011, Toronto, Canada. pp.46-50, 10.1109/PIMRC.2011.6140005. hal-00867219

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<figure><img src="image_1.png" /></figure>
# Transmission Power Adaptation According to the Message Length for Wireless Sensor Networks

D.Dessales*, A-M.Poussard*, R.Vauzelle*, N.Richard*, F.Gaudaire and C.Martinsons

*University of Poitiers, XLIM Laboratory, SIC department, France

Email: {dessales, poussard, vauzelle, richard}@sic.univ-poitiers.fr

‖CSTB, Acoustic & Lighting, Grenoble, France

Email: {francois.gaudaire, christophe.martinsons}@cstb.fr

**Abstract**—The energy efficiency of a wireless sensor depends of three criteria : the transmission power (transmission range), the radio links quality (BER) and finally the message length. In this paper, we propose to reduce the overall consumption of a sensor by adapting the transmission power according to the last two criteria. The originality of our approach is to improve an energy model by the use of a realistic propagation model and a realistic BER estimation. Thus, from this complete model we show the propagation channel influence on the adjustment of the transmission power. The consequences on the energy consumption are illustrated in terms of lifetime on a forwarding sensor. Simulation results demonstrate clearly that significant gains on the lifetime of a sensor are obtained by adjusting the transmission power in function of the frame length.

## I. INTRODUCTION

Many systems based on Wireless Sensor Networks (WSN) are emerging today and a wide range of applications are possible : building monitoring, industrial control, military applications, etc. In many scenarios, each sensor must operate without battery replacement for several years. Energy efficiency is hence the main challenge in the design of a WSN.

Recent advances on energy efficiency for WSN are organized essentially around the optimization of the lower layers of OSI model. Many studies suggest to maximize the network lifetime, the use of routing strategies and the design of low power MAC protocols [1]. However, the energy efficiency of a WSN starts at the physical layer. The energy consumed by radio circuits is the most significant and impact directly the performances of the other layers. Recent works on physical layer concern essentially, in one hand the hardware optimization [2], and in the other hand, to find the good tradeoff between the radio links quality and the energy efficiency. The principle is to improve the Bit Error Rate (BER) by transmission power control mechanisms [3] or cooperative Multiple-Input-Multiple-Output (MIMO) techniques [4]. Moreover, because of the interdependence of various parameters affecting consumption, a "cross-layer" approach [5] is an efficient way to optimize the global consumption by taking into account the conjoint performances of these lower layers.

Nevertheless, propagation models used to assess these optimizations are generally not realistic. In addition, the transmission quality is dependent on both the BER and the message length to transmit [6]. The aim of this paper is hence to propose a cross-layer optimization based on a transmission

power adaptation according to the type of information to transmit (data, acknowledgment, synchronization ...), and more particularly in function of the message length. Moreover, our approach is independent of the network architecture.

This paper is organized as follows : in section II, energy model and realistic BER estimation with a realistic channel model are introduced. Studied configurations and simulations results are presented and analyzed in terms of lifetime in section III. Finally, a short conclusion is drawn in section IV.

## II. OPTIMAL TRANSMISSION POWER

After presenting the general approach, we focus on the analysis of the energy consumption model. Then, we present the BER estimation used and finally how we do in practice the implementation to achieve transmission power adaptation.

### A. General approach

The energy consumed by a wireless sensor is mainly due to the generation of the RF signal. The total average power consumption can be divided into two main components : the power consumption of the power amplifier $P_{PA}$ and the power consumption $P_c$ of all other electronic circuits (heterodyne architecture). $P_{PA}$ depends on the transmission power $P_{out}$ and can be approximated as in [2] :

$$P_{PA} = (1 + \alpha)P_{out} \quad (1)$$

where $\alpha = (\xi/\eta) - 1$ with $\eta$ the drain efficiency of the RF power amplifier and $\xi$ the peak-to-average ratio (PAR). By reducing the transmission power $P_{out}$, it is therefore possible to reduce significantly the consumption induced by the power amplifier $P_{PA}$ and hence, the overall consumption of a sensor.

In addition, the energy efficiency of a wireless sensor is also dependent of the quality of radio transmissions. Due to spatio-temporal fluctuations of the radio propagation channel, errors can be introduced into binary messages at the reception. These errors cause retransmissions which increases the energy consumption. The Frame Error Rate (FER) express the probability to have an error into the binary message :

$$FER = 1 - (1 - BER)^{fl} \quad (2)$$

with $fl$ the frame length and $BER$ the bit error rate. So for a constant BER, the probability to have an error into the message is lower if the message is short than if the message is large.
The energy consumption of a sensor is hence also dependent of the message length.

To resume, the energy efficiency of a wireless sensor depends of three criteria : the transmission power (transmission distance), the radio links quality (BER) and finally the message length. Our strategy to reduce the overall consumption of a sensor is to adapt the transmission power according to the last two criteria. The energy consumption model per correct received bit in [7] allows to find this optimal transmission power. Moreover, we propose to improve this model by taking into account the realistic wave propagation conditions.

## B. Energy consumption model analysis

Energy models in the literature like in [8] are generally a simple description of the radio use and do not take into account enough significant parameters from the physical and MAC layers. The energy consumption model proposed in [7] is from this point of view an interesting model. It describes the energy per bit transmitted successfully $E_b$ as follows :

$$E_b = \frac{P}{\text{rate}(1 - \text{BER})^{fl}} \quad (3)$$

where P is the total power consumed which depends on the transmission power, rate is the bit rate transmission, fl is the frame length and BER is the bit error rate. By expressing the energy per bit transmitted successfully according to the BER, this model takes into account the transmission chain and the channel characteristics, but also consumptions induced by frames retransmissions. It allows us to find the good tradeoff between energy efficiency and robustness of communications.

Fig.1.a illustrates the evolution of the energy per bit transmitted successfully according to the transmission power and the frame length. This curves network is obtained for an indoor transmission distance equal to 20 meters in NLOS configuration and with an ASK modulation at 433 MHz. Each curve represents the energy per bit for a particular frame length (90 to 1000 bits). The frame lengths chosen are inspired by the IEEE 802.15.4 standard. A frame length of 90 bits is used as acknowledgment frame (ACK) and the maximum frame length for data is fixed to 1000 bits. All the curves have the same evolution according to the transmission power and present all a minimum. It is therefore possible to determine the optimal transmission power in order to obtain the minimum energy per bit (red triangles on each curve in Fig.1.a). For example, the green curve represents the evolution of the energy per bit for a frame length equal to 90 bits. For low transmission power, the energy per bit increases with the number of retransmissions; for high transmission power, the energy per bit increases because the power amplifier must deliver more power. Thus, the optimal transmission power is located on the minimum of the curve and is equal to -5 dBm. In contrast, the red curve represents the energy per bit for a frame length of 1000 bits and the optimal transmission power is equal to 3 dBm.

From the red triangles obtained in Fig.1.a, we can deduce the Fig.1.b, where optimal energy per bit in function of the frame length are plotted. As expected, the figure shows that the

<figure><img src="image_2.png" /><figcaption>Fig. 1. (a) Energy per bit successfully transmitted according to the transmission power and the frame length (ASK modulation, 433 MHz, transmission distance equal to 20 meters), (b) Energy per bit and transmission power adjusted to the minimum according to the frame length</figcaption></figure>

minimum energy per bit transmitted increases with the frame length. In addition, the transmission power adjusted in order to obtain this energy per bit minimum is plotted (black curve in Fig.1.b). It is relevant to observe that the energy per bit is not entirely proportional to the transmission power. In fact the model expresses the energy per bit transmitted successfully and thus takes into account the possible retransmissions according to the BER. So, for a same transmission power, the energy necessary to transmit one bit successfully can be different according to the frame length.

## C. Realistic BER estimation

As we could see in section B, the energy to transmit one bit successfully is largely dependent of the BER. In order to improve the accuracy of his estimation and to compute the energy per bit, we propose to perform a realistic BER estimation by taking into account a realistic propagation model based on a 3D ray-tracing approach. Moreover, a typical transmission chain in WSN is modeled. It is based on elements already implemented into the radio chip chosen for a future experiment [9]. It is composed of three main blocks: a transmission block with an ASK modulator; a block corresponding to the transmission channel; and finally a reception block which performs the inversed process of the transmission block and provides the received binary message.

The channel model used to perform the BER estimation is a semi-deterministic model composed of a 3D radio wave prop-
agation model and a spatio-temporal variability model. The 3D radio wave propagation simulator based on an optimized ray-tracing and developed in the XLIM-SIC laboratory [10] is used to determine all the paths between two nodes of a sensor network. It takes into account all the characteristics (electric, geometric) of a 3D environment, the characteristics of antennas and provides information of each radio path : magnitude, phase, delay, polarization. However, an indoor radio channel is nonstationary in time [11]. In our case, even if the nodes of the network don't move, the channel presents temporal fluctuations due to the motion of people. To take into account these temporal variations in the channel modeling, a statistical law describing the small-scale fading of the channel is added to the impulse response. The complex coefficient $\tilde{a}_k$ for the path k is correlated with a Rayleigh distribution for NLOS radio link, or with a Rice distribution for LOS link. Thus, the received signal $\tilde{r}(t)$ can be expressed by:

$$ \tilde{r}(t) = \sum_{k=1}^{N} (\tilde{a}_k c_k) \times \tilde{s}(t - \tau_k) + n(t) \quad (4) $$

where $\tilde{s}(t)$ is the transmitted signal, $\tau_k$ is the delay for the $k^{th}$ path, $\tilde{a}_k$ is the complex coefficient of the path k and N the number of paths. $c_k$ represents the complex Rayleigh or Rice coefficient (parametrized with measurements performed in typical configurations) and $n(t)$ the Gaussian noise. Finally, a complete transmission system is modeled according to the real characteristics of the environment.

### D. Practical implementation

<figure><img src="image_3.png" /><figcaption>Fig. 2. Transmission power adaptation principle</figcaption></figure>

The transmission power adaptation principle is resumed on Fig.2. The final goal is to adjust the transmission power according to the frame length with the energy model described in section II-B. In this paper, we consider that the transmission power is defined in advance before installing the system. For this, a preliminary analysis of the transmission conditions is need to assess the optimal transmission powers in function of the quality of service requested (BER). After the installation completed, the physical layer of each sensor takes into account the frame length provided by the MAC layer and chooses his transmission power (beforehand defined with the preliminary analysis). In the case where transmission conditions are invariant in time, this method reduces significantly the protocol overhead. In contrast, if the transmission conditions vary, it is preferable to adjust the transmission power while the network is in operation by using the energy model in an adaptive way like TPC mechanisms [3] or ARF [12].

### III. SIMULATION AND RESULTS

The aim of this section is to assess the energy performances of the proposed approach in a representative indoor

environment. The transmission power adaptation according to the frame length (90 to 1000 bits) is computed for different transmission distances and for different positions of sensors in order to show the channel influence on the adaptation. The transmission power adaptation is also performed to guarantee a BER of $10^{-3}$. Finally, the consequences in terms of lifetime of this adaptation are illustrated.

#### A. Studied configuration

The presented results correspond to a representative indoor environment (Fig.3). To assess the channel influence on the transmission power adjustment, a sensor node is placed every 0.5 meter into the environment. The maximum transmission range is hence equal to 25 meters. The numerical transmission chain is composed of an ASK modulation at 433 MHz. The data rate is equal to 250 Kbps. This choices results of a previous study [13] on the definition of an energy efficient physical layer. Finally, the noise power is fixed around the threshold of chip sensitivity, ie -105 dBm. In this study we are particularly interested by NLOS links. In LOS configurations, only the transmission power adjustment according to the BER is relevant. The influence of the frame length is not significant because the transmission power is already greatly reduced.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Studied indoor environment</figcaption></figure>

#### B. Numerical results

<figure><img src="image_5.png" /><figcaption>Fig. 4. Evolution of the transmission power according to transmission distance and for different frame lengths (90 to 1000 bits as in Fig.1.a), at 433 MHz with an ASK modulation</figcaption></figure>

Fig.4 illustrates the average transmission power obtained after adjustment according to the transmission distance and for
different frame lengths (90 to 1000 bits). It appears clearly that the transmission power obtained is proportional to the distance of transmission. For distance less than 3 meters (first vertical dotted line), the transmission powers are low and very similar. For distance between 3 and 13 meters (second vertical dotted line), transmission powers increase sharply. We can note a gap of nearly 10 dB between a frame length of 1000 and 90 bits. The differences between transmission powers becomes significant. Finally, after a transmission distance greater than 13 meters, transmission powers are fairly stable. The blue curve represents the average transmission power obtained to ensure a BER less or equal to $10^{-3}$, without to take into account the frame length. Before a distance of 10 meters, the transmission power obtained is less than transmission powers obtained according to the frame length. For distances greater than 10 meters, the transmission power with pure BER adjustment is more low except for a frame length of 90 and 100 bits. In reality, this adjustment is less energy efficient because it does not take into account the frame length and the possible retransmissions due to the BER. For example, with a frame length of 1000 bits and a BER equal to $10^{-3}$, it is necessary to retransmit one frame at each time. The consumptions induced by these retransmissions are significant. It is therefore better to increase a little more the transmission power and to reduce the number of retransmissions. The adaptation performed according to the frame length is the result of this optimal tradeoff between the energy cost of the transmission power and the energy cost of retransmissions.

<figure><img src="image_6.png" /><figcaption>Fig. 5. Cumulative distribution functions of transmission power gaps between an ACK frame of 90 bits and different frame lengths (100 and 1000 bits), at 433 MHz with an ASK modulation</figcaption></figure>

Cumulative distribution functions plotted on the Fig.5 express the differences of transmission power adjustment between different length of data frames and an ACK frame of 90 bits. For 50% of positions, the mean gap between a data frame of 1000 bits and an ACK frame of 90 bits is equal to 10 dB. In contrast, the mean gap between a frame of 100 bits and a frame of 90 bits is less than 1 dB.

### C. Impact on sensor lifetime

The aim of this section is to assess the interest to adapt the transmission power according to the frame length. In a first

step, we estimate the sensor lifetime when the transmission power is adjusted with the most larger frame (data frame) and we show the difference when the adjustment is only performed with a BER criterion by taking into account the retransmissions. In a second step, we show the lifetime gain when the transmission power is not only adapted to the data frame length but also to the ACK frame length.

To estimate the lifetime of a sensor, we use the battery model developed in [14]. It takes into account the self-discharge effect by considering a leakage power equal to 10% of the full energy $E$ during one year $P_{leak} = (0.1 \cdot E)/(24 \cdot 365)$. The time $T_{empty}$ where the battery is considered empty is hence given by the following equation:

$$T_{empty} = \frac{E}{P + P_{leak}} = \frac{E}{24 \cdot 365 \cdot P + 0.1 \cdot E} [years] \quad (5)$$

where $P$ is the average power consumption ($P = U \cdot I_{avg}$ with $U = 3V$ the power supply and $I_{avg}$ the average current consumed), $E$ is the total energy of battery in Wh. For lifetime estimation we consider $E = 2.1$ Wh.

<figure><img src="image_7.png" /><figcaption>Fig. 6. Operation of a sensor</figcaption></figure>

Then, we consider the principle illustrated in Fig.6 and we assume sensors perfectly synchronized although in reality, synchronization errors impact directly the coordination of wake/sleep cycles of sensors or again the preambule's length of the frame and finally lead to increase energy consumption [15]. First, the sensor receives the packet to forward (during $T_{DATA} = fl/rate$). After, it transmits an ACK frame (during $T_{ACK} = 90$ bits/rate) to confirm the good reception of the data. Then, it forwards it before to switch into reception mode to receive the ACK frame. Once the transmission is completed, it goes into standby mode during $T_{Sleep}$ and consumes a current equal to $I_{stby} = 0.5\mu A$. To simplify computations, the periods when the node is switching $T_{set-Tx} = T_{set-Rx}$ are considered insignificant compared to the periods of transmission. Moreover, the current consumed during a transmission is assumed equal to the current consumed in reception : $I_{Radio} = (E_b \cdot rate)/U$. The average current consumed $I_{avg}$ is hence given by the following equation :

$$I_{avg} = \frac{2 \cdot (I_{radio} \cdot T_{DATA} + I_{radio} \cdot T_{ACK}) + I_{stby} \cdot T_{Sleep}}{T} \quad (6)$$

In Fig.7 we have plotted the sensor lifetime according to the forwarding interval $T$. In this configuration, the transmission power adaptation is only performed by taking into account the data frame length. In other words, the power to transmit a data frame is equal to the power to transmit an ACK frame. Results are given for a transmission distance of 20 meters
<figure><img src="image_8.png" /><figcaption>Fig. 7. Lifetime vs. forwarding interval T and different frame lengths (90 to 1000 bits) and a transmission distance of 20 meters</figcaption></figure>

(when the average transmission power obtained is stable) and
several data frame lengths (100 to 1000 bits). As we can see,
more the forwarding interval is high and more the lifetime is
large. Moreover, the sensor lifetime is larger for short frame
lengths. For a forwarding interval *T* equal to 10 seconds, the
sensor lifetime obtained is 7 years for a frame length of 100
bits against 3 years for a frame of 1000 bits. Finally, for a
frame length of 1000 bits we can observe that the lifetime is
better when our approach is performed compared to a basic
approach with only a BER adjustment. We note a lifetime gain
of nearly one year whatever the forwarding interval.

<figure><img src="image_9.png" /><figcaption>Fig. 8. Lifetime gain vs. forwarding interval T after transmission power adaptation for a transmission distance of 20 meters</figcaption></figure>

In Fig.8, we have plotted the lifetime gain obtained when
the transmission power is both adapted to the data frame length
and to the ACK frame length. In this case, the power to
transmit a data frame is not equal to the power to transmit an
ACK frame. Now, we deal about the impact of the forwarding
intervals to the lifetime gain obtained. First, the maximal
lifetime gain depends on the forwarding interval *T*. More the
frame length is large, and more the maximal lifetime gain
is obtained for large forwarding intervals. It appears logic
because more the frame is large and less time the node is
into sleep mode. Secondly, by considering only the maximal
lifetime gain of each curve (each frame length), we can
observe that its evolution, according to the data frame length,

is not strictly increasing. In fact, the maximal lifetime gain is
obtained for a data frame equal to 400 bits (mauve curve) and
is equal to nearly 35 days. Before this maximum, the lifetime
gain is increasing. After, for data frame lengths superior
to 400 bits, the lifetime gain is decreasing. In this case,
the consumption is dominated by the transmission duration
*T<sub>DATA</sub>* and not by the current consumed value *I<sub>radio</sub>*.

IV. CONCLUSION

In this paper, we propose an extension of the energy
model proposed by [7] in order to reduce the overall energy
consumption of a WSN. The approach adopted is to take into
account both the radio link quality and the message length, and
then to perform a transmission power adaptation according
to these two criteria. This paper shows the influence of the
channel on transmission power adjustment and the energy
consumption. Simulation results demonstrate that transmission
power adaptation according to the frame length is better than
a basic approach and has a real impact on the sensor lifetime.
In a following work, we integrate an other important factor of
energy consumption, the synchronization step.

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