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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

In line with recent research efforts made to conceive energy saving protocols and algorithms and power sensitive network architectures, in this paper we propose a transmission strategy to minimize the energy consumption in a sensor network when using a localization technique based on the measurement of the strength (RSS) or the time of arrival (TOA) of the received signal. In particular, we find the transmission power and the packet transmission rate that jointly minimize the total consumed energy, while ensuring at the same time a desired accuracy in the RSS or TOA measurements. We also propose some corrections to these theoretical results to take into account the effects of shadowing and packet loss in the propagation channel. The proposed strategy is shown to be effective in realistic scenarios providing energy savings with respect to other transmission strategies, and also guaranteeing a given accuracy in the distance estimations, which will serve to guarantee a desired accuracy in the localization result.

Due to environmental concerns and to the limited lifetime of energy resources, an intensive research activity is being carried out in energy-efficient protocols and algorithms for wireless networks, trying to reduce the energy consumption of the different network activities.

One of the activities that should be optimized is the localization of the nodes, as many applications rely on the knowledge of the position of the user or the surrounding objects to provide useful information and services. Furthermore, knowing the position of the nodes can be used to optimize other network aspects, such as routing [

The localization of the nodes in wireless networks is usually based on radio frequency techniques [

The research in localization for wireless sensor and ad hoc networks is very active, and a number of works have considered the energy consumption as a factor in the design of localization techniques and algorithms. This is a critical issue, since wireless devices have limited energy resources (batteries), which should be efficiently managed in order to extend the life of the network as much as possible [

Approaches that include the use of dedicated hardware specially designed for this purpose [

However, energy consumption cannot be considered independently. The accuracy of the localization should be also taken into account, as in general, we could probably allow higher energy consumption if more accurate localization result is needed. In contrast to other works that focus on this trade-off by modifying the frequency of the localization to trade higher energy consumption for better localization accuracy (in terms of update rate) [

The structure of the paper is as follows. Section 2 reviews some related work regarding the consumption-accuracy trade-off in localization systems. Section 3 defines the application scenario and the communication models that have been selected for our analysis. Section 4 analyzes the energy consumption of the localization procedure and proposes a transmission strategy, based on local information at each node, which minimizes the total power consumption of the network and at the same time achieves a given accuracy in the distance estimations. Some modifications to this theoretical strategy are also proposed to achieve the desired performance under real propagation conditions. The performance of the proposed strategy is evaluated in Section 5 and compared with other strategies through a set of simulations based on experimental measurements. Finally, Section 6 extracts some conclusions and proposes some future work.

The trade-off between the energy consumption and the accuracy of localization algorithms was first addressed in [

This idea is followed by some object-tracking systems, as [

In our previous work [

We consider here a typical scenario of a wireless multi-hop network composed of both mobile nodes and nodes that are deployed at fixed positions. In this scenario, the position estimation of the mobile nodes should be updated frequently enough so that the nodes can be tracked as they move. Hence, each localization of these nodes should be performed within a given period _{0}, which depends on the mobility pattern of each node. In this work, we assume that _{0} is known. In fact, there are several methods available in the literature (e.g., [

As explained in Section 1, the position of a node in a wireless network is usually computed from the measurements of a parameter of the radio signal (RSS, TOA,

The measured radio parameters are random variables, so their uncertainty can be reduced, in general, by averaging a number of measurements. In particular, both TOA and RSS measurements are usually described as random Gaussian variables [

Let us suppose that a node will average the RSS or TOA of all packets received during a period _{0}, which depends on how often the localization of the node must be performed, with the objective of achieving a given accuracy in the distance estimations. The number of received packets (_{0}, packets can be sent either with a high transmission power (so that the _{0}, or with a lower transmission power (some packets will be lost) but at a higher rate (_{0}, with _{0}).

The goal is to optimize the transmission strategy at each node with the aim of obtaining a given accuracy in the RSS or TOA measurements, while minimizing the energy consumption in the global network. As the radio system is the most energy demanding part of a node (see Section 1) we will only take into account the energy consumption of the radio system. The transmission strategy will be defined by two parameters: the transmission power (_{TX}_{0}).

We will assume that all nodes in the network are synchronized; hence, one-way TOA measurements can be performed in the network. In addition, given that nodes are synchronized, they can turn off their radio when they are not transmitting or expecting to receive a packet from another node, so idle listening is avoided and the energy consumption of the radio system is only due to transmitting and receiving packets.

In order to evaluate the energy consumption during the localization procedure, some assumptions about the receiver and radio channel behavior must be done. In the following, we propose to use simple models of the receiver and the channel.

The probability of a successful reception of a packet is the probability of successfully receiving all its bits, assuming that there is no error correction. It is well known that the probability of bit error depends on the encoding and modulation of the radio signal, thus, the packet reception probability will also depend on them. For example, for QPSK and BPSK modulation schemes, the packet reception probability in presence of additive white Gaussian noise and in absence of interferers is given by [_{b}/N_{0} is the signal to noise ratio per bit, _{b}

More complete models have been proposed [

On the other hand, a model of the channel that relates the transmission power to the received power is needed, as it will provide a relation between transmission power _{TX}_{RX}_{TX}^{2}) is a zero-mean Gaussian random variable with standard deviation _{0}, and has to be experimentally determined. On the other hand, the path loss exponent

As previously said, this channel model provides a relation between the transmitted power (_{TX}_{RX}

As explained in Section 3, our goal is to optimize the transmission strategy for the localization process with the aim of obtaining certain accuracy in the distance estimations while minimizing the energy consumption. In this section, we first include a theoretical analysis of the energy consumption during the localization procedure in terms of the transmission strategy parameters (transmission power and packet transmission rate) and the channel behavior (characterized through the

Let us consider a certain link of a network like the one described in Section 3, consisting of a transmitter node, which will periodically send packets, and a receiver node, which will measure the RSS or the TOA of all received packets. The receiver will average all the measurements (_{0}, so that the standard deviation of the measurements can be reduced by a factor of
_{obj}

On the other hand, when _{0}. As shown in Section 3.1, the

The consumed energy at transmission during _{0} is given by:
_{0}, _{p}_{tx}_{p}_{0}, this consumed energy is an appropriate parameter to analyze the energy efficiency.

If we assume that the receiver is awake and listening to possible receptions only at given periods (previously negotiated with the transmitter), the consumed energy at reception during _{0} is given by:
_{r}_{rx}_{RX}_{rx}

Using _{TX}_{rx}_{RX}_{χ}_{χ}

It can be obviously noticed that, for a given distance, the greater the required accuracy (described by _{TX}_{E}_{χ}

Deriving

In conclusion, if we manage to achieve the

To provide some illustrative results, _{0} = 1 s, and uses 8-bytes packets, with _{p}_{RX}

On the other hand, note that the desired accuracy imposed a relationship between

In conclusion, among the pairs _{TX}_{TX}

Note (from _{b}

Let us also remark that the value of the localization period _{0} does not have any influence on the applicability of our strategy as long as it is big enough to send the required number of packets, which is usually the case in practice. Furthermore, the value of _{0} does not need to be constant in time. In fact, it can be optimized to adapt to the mobility characteristics of the mobile node [

Note that as we have assumed that there is a synchronization schedule known by all the nodes, the localization messages should be sent within the assigned periods. In principle, this does not affect the localization accuracy or the proposed strategy, as long as the required number of packets can be transmitted.

Finally, we would like to point out that in practice, the synchronization of the network may not be perfect. In this case, the nodes should be listening to possible transmissions also during the idle periods in order not to lose packets, so the energy consumption in reception mode would increase. The proposed strategy is not directly affected, as it optimizes the energy consumption in transmission mode, but the energy savings, relative to the total energy consumption, would not be as high as in the ideal synchronization case. Another effect of an imperfect synchronization is that TOA measurements will not be so accurate, so its standard deviation will increase and the distance estimation errors will be higher. This does not affect the performance of the proposed strategy, as it was formulated in terms of the desired number of packets. But clearly, the desired number of packets to achieve a certain accuracy will increase with respect to the ideal case (see _{t}

In a real environment, the random nature of the propagation channel will have some effects on the proposed strategy that should be overcome. In particular, both the transmission power and the packet transmission rate need to be modified in order to maintain the desired accuracy when real propagation conditions are considered. In the rest of this section, we explain how and why these two parameters of the transmission strategy have to be corrected.

On one hand, the proposed strategy relies on the calculation of the transmission power that is necessary to reach the receiver with the optimum

According to _{snr}

If one of the received packets is used to estimate the distance, the difference between the transmission power necessary to reach the receiver with the desired _{TX}

As a consequence, the estimated transmission power has to be corrected by adding a margin equal to the mean value of _{b}

On the other hand, even when the optimum transmission power is used, the final _{snr}_{b}^{−1} (1 − ^{1/}^{8l}_{obj}_{obj}_{b}_{b}

Although the energy consumption will increase when these two corrections are included in the transmission strategy, they are necessary to achieve the desired number of received packets in real environments and, therefore, to achieve the desired accuracy; otherwise, the accuracy would not be guaranteed. Nevertheless, the final energy consumption is very small and still entails significant savings with respect to other transmission strategies.

It is interesting to analyze how much energy will be consumed if the best transmission strategy is not perfectly achieved, due to an error in the estimated transmission power. As it has been mentioned above, the error in the estimated transmission power is due to an error in the distance estimation, which depends itself on the RSS or TOA measurement errors and on the number of packets that are averaged at the receiver. In this section, we first evaluate how the energy consumption is affected by the errors in the estimated transmission power and then we study how the distance estimation errors propagate to errors in the estimated transmission power, and therefore affect the energy consumption.

Let us suppose a transmitter node X that has to send packets to another node Y, so that Y receives in average _{obj}_{0}. As the optimum _{min}_{obj}

_{min}_{obj}_{b}_{obj}_{obj}_{b}

As shown in _{min}_{min}_{min}_{min}_{obj}_{obj}

The behavior shown in these figures is valid for both TOA-based and RSS-based localization schemes, but as the probability distribution of the distance estimation is different for the two localization schemes (see

This error in the transmission power can be calculated as:

_{min}_{min}

_{obj}

In conclusion, for both TOA and RSS-based localization methods, a greater variance in the measurements will produce a greater variance in the optimum transmission power estimation and thus, more energy consumption and a higher probability of losing packets.

The proposed strategy has been derived from the assumption that the power consumption of the transmitter is equal to the transmitted power. However, for real devices, this assumption may not be true due to the inefficiencies of the hardware. In this case, the theoretical strategy previously proposed has to be slightly modified, by substituting the transmission power _{tx}_{T}_{tx}_{T}_{tx}_{tx}

Similarly to the ideal case, we can minimize this energy consumption with respect to the

The value of

As an illustration, we next apply this method for two common radio chips used in wireless sensor networks devices: the ChipCon chips CC1000 and CC2420. Clearly, real devices also include other components apart from the radio chip, which will also affect the energy consumption. However, this example illustrates how to proceed in a general case where there is a nonlinear relationship between transmission power and consumption. Several values of _{T}_{tx}_{tx}

Introducing this expression and its derivative in

Thus, if we manage to achieve at the receiver the corresponding value of signal to noise ratio _{b}

In conclusion, the general receipt to apply the proposed method for a specific device is:

Characterize the energy consumption of the device as a function of the transmission power

Approximate this behavior with an analytical expression for _{tx}_{T}_{tx}

Introduce this expression in

Calculate the corresponding values of

Calculate correction factors numerically as explained in Section 4.2

In this section, we first describe a set of experiments that were carried out to characterize a real propagation environment in order to obtain realistic models to simulate the performance of the proposed strategy. Next, we include a numerical evaluation of the proposed transmission strategy that compares its performance with the performance of other transmission strategies in several scenarios.

In order to simulate a realistic situation, we carried out some experiments to characterize the propagation environment of our laboratory using Memsic's MICAz motes [

The first set of experiments were carried out to determine the _{RX}

We also made some experiments to characterize our radio channel, that is, to establish a relation between transmission and received power in terms of the distance. In these experiments, two MICAz motes were used again, with the same configuration as in the _{TX}_{0} = 1 m, _{TX}

We have run a set of simulations to evaluate the energy consumption of the proposed strategy in several scenarios. In these simulations, the performance of the proposed strategy is also compared with other two strategies: (1) sending _{TX}_{0} + _{RX}

In these simulations, we considered networks composed of reference nodes and mobile nodes. In order to estimate the position of the mobile nodes, each reference node transmits packets to them. These nodes measure the RSS of the received packets and calculate their distance to each of the reference nodes. With these range estimations and the known positions of the reference nodes, the mobile nodes are able to calculate their own positions. As soon as they have an estimated value of their physical position, they can send packets to other nodes with the information about their estimated position and act themselves as reference nodes. Consequently, every node of the network will transmit packets to and receive packets from every other node within its communications range. Considering the transmission strategy proposed in the previous section for a single link, we applied it to the whole network by finding at each node the optimum transmission strategy
_{TX}

First, we simulated a network composed of four reference nodes deployed randomly in a 15 × 15 m^{2} room and one mobile node that stays in the center of the room during 20 seconds. The localization is done every second (_{0} = 1 s) and the desired accuracy is such that _{0} = 1 m and _{b}

Next, to simulate a more realistic scenario, we added shadowing with

As explained before, the number of received packets at the furthest neighbor determines the accuracy of the distance estimation at these nodes. The accuracy of the distance estimations in closer neighbors will be at least as good as the one at the furthest neighbor. In order to better understand the behavior of the proposed transmission strategy, we have represented in _{t}_{RSS}_{RSS}_{RSS}

Finally, we have evaluated the performance of the proposed strategy for a case in which the power consumption is not equal to the transmitted power (which is usually the case for real devices). To this end, we repeated the previous simulation experiments considering the energy model for the CC2420 radio chip described in Section 4.4 and following the steps described in that section to adjust the proposed strategy.

It can be seen in

As it can be noticed, for a given energy consumption, the proposed strategy achieves better accuracy than strategy #2, and for a given accuracy, the proposed strategy has lower energy consumption. Our proposed method shows still a gain, but of lower entity with respect to the ideal case shown in

To sum up, the proposed strategy always guarantees a desired accuracy in the distance estimation and, at the same time, yields energy savings, especially when the optimum value of the

In this paper, we have presented an analysis of the energy consumption during the localization process of a wireless sensor network. We have optimized the transmission strategy (in terms of transmission power and packet transmission rate) at each node with the aim of obtaining certain accuracy in the RSS or TOA measurements (expressed by the number of packets that the receiver node should average) while minimizing the energy consumption in the network. We have shown that the optimum transmission strategy consists in sending packets with such a transmission power

We have also proposed some modifications to the theoretical optimal strategy in order to correct the effects of the propagation channel when applying this strategy in a real scenario. In particular, we have proposed how to correct these effects in the case of RSS-based localization, by adding a correction margin to the estimated transmission power and correcting the number of transmitted packets by a factor that depends on the packet length and the value of _{b}

In further work we are planning to evaluate the performance of the proposed strategy using real-field deployments. In particular, we are implementing the embedded versions of the strategy in MICAz motes (under TinyOS 2.1), to experimentally measure and evaluate the energy consumption during the localization when the proposed strategy is executed in these resource-constrained devices.

Future work on studying the effects that the accuracy of the radio measurement has on the distance estimation for TOA-based and RSS-based localization techniques will allow extracting some guidelines for the calculation of the required average number of received packets, depending on the localization accuracy requirements and on the geometric configuration of the network. Further work would also include the analysis of other channel and receiver models and the evaluation of variant channels. Furthermore, the value of the localization period _{0}, which we have considered as constant, may change in order to adapt to the mobility characteristics of the mobile node. The combination of the proposed optimization with the optimization of the localization period may lead to further energy savings and could be a promising line of future work.

This work has been supported by the Government of Madrid under grant S2009TIC-1485 (CONTEXTS) and by the Spanish Ministry of Science and Innovation under grant TIN2011-28620-C02-02.

We assume that the measurement of the time

On the other hand, the distance

For one-way TOA measurements:

For two-way TOA measurements:

It can be noticed that the error (or variance) in the distance estimation does not depend on the actual distance between transmitter and receiver. From these expressions, we can obtain the number of packets that we need to receive in order to achieve a given accuracy in the distance estimation.

Assuming that the measurement of the received signal strength _{RX}

Note that this variance
^{2} if the environment is dynamic or the nodes are moving, whereas in a completely static situation, it will be lower than ^{2}, as explained in Section 3.2.

On the other hand, the distance

In order to calculate the variance of this distance estimation, _{x}_{x}

The variance of a log-normal distribution with parameters _{x}_{x}

It can be noticed that, in this case, the error in the distance estimation does depend on the actual distance between transmitter and receiver. The greater the distance is, the greater the variance of the distance estimator becomes. From this expression, we can obtain the number of packets that we need to receive in order to achieve a given accuracy in the distance estimation.

Energy consumption (in joules) as a function of the

Correction margin for the transmission power calculated from estimated distances in RSS-based localization.

Ratio between the desired number of received packets and the mean value of

Effect of the error in the transmission power on the energy consumption and on the number of received packets.

Probability density function of _{min}

Probability density function of _{obj}

Relation between

Experimental RSS measurements for different distances between two MICAz nodes. The log-normal channel model curve fitting is also represented.

Average energy consumption and average number of received packets at the furthest node of the three strategies for each localization interval for an environment with shadowing.

Relation between the average energy consumption per localization and the TOA-based distance estimation accuracy for the three strategies. (

Relation between the average energy consumption per localization and the RSS-based distance estimation accuracy for the three strategies. (

Average energy consumption and average number of received packets at the furthest node of the three strategies for the CC2420 consumption model.

Relation between the average energy consumption per localization and the distance estimation accuracy for the three strategies for

Fitting of
_{tx}_{T}_{tx}

36.8596 | 48.8470 | |

−0.8256 | −0.8728 | |

^{2} |
0.9945 | 0.9986 |

Average energy consumption (in

Highest _{TX} |
3.20 | 8.00 | 16.00 | 32.00 |

_{TX} |
1.26 | 2.98 | 5.87 | 11.58 |

Proposed strategy | 0.60 | 1.79 | 4.24 | 9.19 |

Energy consumption of the proposed strategy expressed in % with respect to strategy #2.

54% | 73% | 92% | 110% |

Average number of received packets at the furthest neighbor.

Highest _{TX} |
4.98 | 4.96 | 4.93 | 4.90 |

_{TX} |
4.89 | 4.76 | 4.58 | 4.32 |

Proposed strategy | 5.28 | 5.31 | 5.33 | 5.37 |