E Vagnon
email: eric.vagnon@g2elab.grenoble-inp.fr

Y Avenas

J C Crebier

P O Jeannin

I Al Batta

Electrical Characterization of a Pressed Contact Between a Power Chip and a Metal Electrode

Keywords: component; Pressed contact, Electrical contact resistance measurement, power chip. I

This study deals with the power electronics packaging and the needs for additional knowledge about electrical pressed contact behavior. For this, a measure bench has been realized. It is able to characterize the pressed interface between a metal electrode and a power chip as a function of the clamping force (0-8000N) and the temperature (up to 100°C). First measurement results show that the electrical contact resistance is negligible compared to the chip on-state voltage. Second measurement results show that the high value of the chip metallization resistance masks also the contact resistance. Finally, it appears that it is necessary to estimate the chip contact zone influences on the current repartition. Then a method based on both, the use of a chip model and the measurements directly on the chip, has been developed. It is able to look for the steady state current repartition in the chip as a function of the contact zone and the chip metallization physical parameters.

INTRODUCTION

This study is a part of a research work looking for new power electronics packaging [START_REF] Vagnon | Study and Realization of a Low Force 3D Press-Pack Power Module[END_REF] [START_REF] Vagnon | Guepratte: A Busbar Like Power Module Based On 3D Chip On Chip Hybrid Integration[END_REF]. It concerns the electrothermo-mechanical contacts of the vertical power chips.

The packaging of power electronics chips must fulfill some tasks and requirements [START_REF] Murari | Smart Power ICs, technologies and Applications[END_REF]: the electrical interconnections of power and control between the components, the external electrical circuits and the environment; the thermal and mechanical interconnections; the chemical and radiation protections; the correct matching between the cost of production and supply business; and finally the global reliability of the module.

The electro-thermo-mechanical contacts are usually based on backside soldering and front side wire bonding. Widely used for small and medium power levels, back side soldering technique is well known and established. It presents very low thermal and electrical resistances. However the thermomechanical aging of solders causes reliability problems [START_REF] Murari | Smart Power ICs, technologies and Applications[END_REF]. The electrical interconnections on the front side of the chip are usually realized thanks to wire bond technology [START_REF] Ménager | Industrial and lab-scale power module technologies : A review[END_REF]. This technique relaxes the thermo-electrical stresses but the reliability is still a question [START_REF] Hamidi | Reliability and lifetime evaluation of different wire bonding technologies for high power IGBT modules[END_REF]. Besides, the wires introduce some undesired parasitic inductances [START_REF] Xing | Extraction of parasitics within wirebond IGBT modules[END_REF] and they can not be considered for heat exchange or removal. Double sided solder packages with bumps [START_REF] Gillot | Double-Sided Cooling for High Power IGBT Modules Using Flip Chip Technology[END_REF] [START_REF] Rinne | Solder bumping methods for flip chip packaging[END_REF] improve the heat transfers but amplify the thermo-mechanical stress leading to reduced reliability and robustness. Moreover, the temperature limitations of regular soldering techniques and materials prohibit their use for high temperature applications like SiC applications.

From medium up to high and very high power levels, pressed contacts are often considered. Mainly used in the past for chips with large surfaces, products are now available with IGBT in the range of 1cm² and contacted by pressure. The reasons for this technique to remain limited are related to its implementation cost. It presents a good reliability over the time but its implementation is quite difficult: the pressure on the components must be set between 3.10 6 Pa and 10 7 Pa [START_REF] Abb | Recommendations regarding mechanical clamping of Press-pack High Power Semiconductors[END_REF], which corresponds to a clamping force up to 135 kN (for 12cm²) and more as the contact surfaces increase.

In a previous paper [START_REF] Vagnon | Study and Realization of a Low Force 3D Press-Pack Power Module[END_REF] we have evaluated the feasibility of a low force press-pack module for the medium power applications (from hundreds of W to several kW). Now, we need to make the electrical and thermal characterizations of the pressed contact between the chip metallization and the metal electrodes (Fig. 1). In this paper, we show the experimental setup for the electrical contact resistance and direct voltage drop measurements in a chip as a function of pressure and temperature. This work is notably important to find the best metal interface to improve the contact behavior.

Moreover, an experimental method coupled with simulations is developed to anticipate the current repartition in a chip as a function of the contact zones between the electrode and the chip metallization. This method is based on a both use of a chip model and measurements. A measurement bench has been realized (Fig. 2). A chip, diode or IGBT is griped between two copper jaws up to 8000N. The chip surface is around 1cm². A special care has been paid on the mechanical structure design to achieve high clamping forces without chip destruction. A force sensor indicates continuously the clamping force value. Below the inferior copper jaw, there is a heat exchanger to regulate the chip temperature. It is based on heat carrier oil that circulates and regulates the temperature of the device under test. The maximum oil temperature is 150°C. The temperature is measured with a thermocouple close to the chip. The experimental device allows the characterization of two different chip types: diodes and IGBT. For this, two kinds of superior jaws have been designed to be adapted to the chip front side layout (Fig. 3). Moreover, for the IGBT case, the command signal (gate contact) is integrated in the jaw to allow its conduction mode and the current circulation in the device.

Metal electrode

Front side Metallization

Back side Metallization

The electrical contact resistance measurement is based on the four points method. A current is injected in the device and the voltage drop is measured closest to the contact region. As the expected electrical contact resistance value is small, the current must be large enough to guarantee the quality of the measurements. In our case, about 100A/cm² current density was injected. To avoid the temperature rise during the measurements, the current injection is made only for a small time: the pulse duration is 300µs and the period 80ms. Moreover, the experiments have been designed to allow two different types of measurements. The first available measure is the electrical contact resistance between the chip and an electrode made by a solid copper jaw (Fig. 4): ∆V c = ∆V R contact + ∆V solid copper [START_REF] Vagnon | Study and Realization of a Low Force 3D Press-Pack Power Module[END_REF] Knowing the injected current value, we can deduce the electrical resistance with a voltage measure. This measure is possible on both sides of the chip (Fig. 3 and4). The current pulses are created by a Tektronix Sony High Power Curve Tracer (371A). It has been necessary to shield the wires to avoid electromagnetic disturbances on the measuring chain (Fig. 5).

For the voltage measurements, the input signal is amplified by a differential amplifier (AD 622AN) and displayed on the oscilloscope. A 0.05Ohm shunt is used to visualize the current.

A. Global voltage drop

In Fig. 6 we can see the global voltage drop ∆V global of a diode Eupec 3.3kV -50A for a 70A current injection during 300µs and for two different clamping forces: 250N and 5000N at the ambient temperature.

We can observe the same global voltage drop for both clamping forces, so it shows that the electrical contact resistance is negligible compared with the on-state voltage drop of the chip. Moreover, to evaluate the solid copper contribution ∆V solid copper on the global voltage drop ∆V global we have moved the measure point positions on the copper jaws. We noticed that these displacements have no consequences on the results. As a result, it could be stated that the resistance voltage drop of the solid copper is negligible with regards to the voltage drop across the device while it is in the on-state carrying large current levels. That is a very interesting and important conclusion for the packaging manufacturers: the value of the electrical contact resistance between the chip and the metal electrode is negligible in a pressed contact implementation. On the other hand, it is necessary to improve our knowledge of the interface contribution to the chip on-state behavior. That's why we tried to measure the contact resistance of the interface ∆V R contact .

B. Contact resistance measurement

To allow the measurement of the contact resistance we have separated the measures carried out on each face of the chip (Fig. 4). Moreover, on the front side of the chip we have localized four measure points on different places of the chip metallization. That was possible for both IGBT and diode (Fig. 7). Like in III.A we make the verification that ∆V solid copper was negligible. Then (1) can be write ∆V c = ∆V R contact .

Measure points

IGBT Diode

Contact areas The non equipotentiality of the metallization leads us to measure the surface resistance of a chip metallization (Fig. 9). The results are about 3mΩ for the diode and 20mΩ for the IGBT.

V

That shows that the electrical contact resistance between a metal electrode and a chip metallization is hidden by the characteristics of the metal layer deposited at the surface of the power chip. In fact, the metallization resistance masks the contact resistance.

Finally the value of the contact resistance is not the key point; and it becomes necessary to evaluate the interactions between the contact zones location and the metallization physical parameters on the chip current repartition.

IV. THE CURRENT REPARTITION IN A CHIP AS A FUNCTION OF THE CONTACT ZONES.

A non homogeneous current repartition in the chip could create some hot points in the chip [START_REF] Chen | Modeling and Analysis of Metal Interconnect Resistance of Power MOSFETs with Ultra Low On-Resistance[END_REF] [START_REF] Ishiko | Design concept for wire-bonding reliability improvement by optimizing position in power devices[END_REF]. An extreme consequence could be the destruction of the chip. Then it is very important to study the influence of the contact zone on the current repartition.

The resistivity and the thickness of the metallization are not given by the chip manufacturers. Then we developed a measure method for the physical characterization of the chip metallization. After that, using a semiconductor chip model, it was possible to predict the current repartition as a function of the contact zones surface and locations and the physical characteristics of the metallization.

A. Realization of a numerical model of the chip metallization.

With e the metallization thickness and ρ the resistivity.

Finally the Ohm's law applied to the metallization can be written [START_REF] Lagonotte | Réseaux électrocinétiques et algèbre linéaire (notions fondamentales)[END_REF]:

V G e I . . ρ = (4)
with I the nodes current matrix, V the nodes voltage matrix and G the conductance matrix. It is interesting to notice that G is a coefficient matrix depending only on the nodes positions and not on the physical parameters of the metallization (e and ρ).

B. Identification between the model results and the measures to find the physical characteristics of the metallization (electrical resistivity and thickness).

Based on the same measurement principle as depicted Fig. 9, a current is injected in the corner of the metallization. From the surface voltage measures and a comparison with a normalized model it is possible to calculate the ratio ρ/e of the metallization:

e I G I G e V V Model Measure ρ ρ = ⋅ ⋅ ⋅ = - - 1 1 (5)
To guarantee the X,Y locations of the measure points and the injection current points, we have developed a Plexiglas footprint situated on the top of the chip (Fig. 11). The surface metallization is 9*9mm². Then we placed on the footprint a 0.3mm diameter hole each millimeter. These holes create a 64 holes network making possible the current injection or the voltage measure in many different conditions. The current injection and tools used for the measurements are the same as those depicted Fig. 5. The measurement device allows two kinds of measures. The two current electrodes can be first contacted on the front side of the chip; method used to find the physical parameters of the metallization (Fig11). Or one electrode current in the chip front side, and the second one contacted on the back side of the chip by a connection to the Cu plate: method used for the surface voltage observation. This step has been validated by an experimental test with a well known and simple to characterize metal layer, a patterned copper layer on a PCB.

For the diode metallization characterization we obtained a value ρ/e = 3mΩ with measures realized on a Dynex diode 1.7kV-50A Ti/Ni/Ag. In Fig12 we can see the surface voltage distribution measured with the second method for an injected current I=43A in a corner and exit by the chip back side. For the voltage measure, the opposite corner of the current injection is considered as for the voltage reference. The voltage values observed are the difference between this point and all the other meshed points (nodes) of the network. We can see that ∆Vmax is close to 1.5V. It clearly demonstrates that when the power diode is forward biased, its metallization is not an equipotential. Although this experiment is carried out in extreme testing conditions, it seems now interesting to analyze the consequences of this non homogeneous voltage distribution on the chip current repartition inside the power device. As the current measures in different regions of the chip are impossible, it was necessary to fall back to simulation in order to estimate the impact of the metallization and the electrical contact regions on the current distribution inside the power device. Of course, this is an important issue since a non homogeneous current repartition would lead to poor performances but it would also lead to inhomogeneous temperatures and greater current concentrations. Soon, the device may fail due to this phenomenon.

The goal of the simulation is to create a model representing the metallization and the behavior of the power diode by a full descretization of the metal layer but also the vertical device. Reproducing a comparable surface voltage profile could help us understanding and estimating the current distribution inside the power device. The exact comparison between measure and simulation is not possible at the time of this paper due to the differences observed between the semiconductor model and the real chip. However, it can be used to analyze the tendencies of the electrical magnitudes.

C. Current repartition simulations

In Fig. 13 we can see the geometrical structure simulated with R m the metal resistance (defined in IV.1), R ci contact resistance between metal and silicon (10 -4 >R c >10 -6 Ω.cm² [START_REF] Murari | Smart Power ICs, technologies and Applications[END_REF]).

Diode model

The diode model is a VHDL-AMS model taking into account the semi-conductor behavior. Physical parameters and concentrations are those of a classical power diode 600V-100A. The electrical equation of the diode is V d =Vj + R on .I d in which all the parameters depends on the carrier concentration, also dependent on the current density. Vj represents the forward bias of the PN junction and Ron represents the conduction voltage drop as a function of the injected carrier "n" and "p" concentration injected in the drift region of the power diode. This simple model has been derived based on [START_REF] Mohan | Power electronics, Converters, applications and design[END_REF] For example for I d = 100A, R on =0.23mΩ, V j =0.653V and V d =0.677V. The surface of each elementary diode depends on the number of nodes chosen for the simulation. In the model, the lateral conduction and diffusion currents due to the carriers concentrations and voltage gradients are not considered. However, for each simulation, we have estimated the current value neglected by making this approximation.

R m R ci R ci+1 D i D i+1 I i V i+1 V i I di I di+1
Figure 13. Geometry of the simulated structure

Current sources

An electrical contact between a copper electrode and the chip is represented by a limited number of current sources connected to a comparable number of nodes N i . The number of nodes and their locations depend on the electrode geometry and the contact surface. The total current injected is always the same to simplify the simulation comparisons. Then

∑ = i I 100A.

Simulation conditions

We considered that the power chip simulated is a 1cm² power diode. The surface contact of the chip has been discretized in 20*20 = 400 elementary contacts represented by nodes. The number of nodes is lower than 400 in order to limit the computation time.

A program generates automatically the netlist used to describe the simulation schematic and parameters as a function of the nodes number, the current injection zones and the physical parameters (metallization resistivity, contact resistance between metal and silicon, drift and anode region characteristics, carrier lifetime, diffusion potential…).

Only the steady state forward bias conduction mode is simulated with Simplorer Software. As a result, the power diode model doesn't have to be implemented to represent dynamic behavior.

D. Results and discussion

In Fig. 14 we can see the current repartition in the diode (I di ) and the chip surface voltage (V i ) for three different values of the metallization resistance: 30mΩ, 3mΩ and 0.3mΩ. The chip surface is 1cm² and the injection current zone is 4mm² located in a corner.

As it could be expected, in each case, the voltage gradients of the metallization can be observed and they impact on the current distribution in the power device. As expected, the current density is maximum below the contact zone. When the value of the resistance increases, the difference between the highest and the lowest current increases (Fig. 14): the metallization parasitic resistance impacts on the current repartition and focuses the current way below the contact zone.

About the diode lateral diffusion current

For each simulation we notice that lateral diffusion currents among elementary diodes were lower than 5% of the average current flowing through each of them. The maximum value is obtained for the highest metal resistance. If greater, the diffusion currents would equalize the current distribution among the elementary diodes but it seems that it is a second order phenomena that is not enough important to impact on the current repartition. Then the approximation of the current repartition is still correct. Finally, the influence of the metallization in the chip current repartition is illustrated. A special care to a regular contact zone repartition on the chip surface is necessary to ensure an homogeneous current repartition in the chip. Fig. 15 shows the current repartition with four contact zones correctly spreadon the surface of the chip metallization. We notice that I dmax =1,77.I dmin . V.

CONCLUSION

The need to better know the electrical pressed contact behavior induced us to realize a measure bench able to characterize the pressed interface between a metal electrode and a power chip as a function of the clamping force (0-8000N) and the temperature (up to 100°C). The measures shown that the electrical contact resistance is negligible compared to the chip on-state voltage and that the important value of the chip metallization resistance masks the contact resistance. Finally, it appeared that it was necessary to estimate the chip contact zone influences on the current repartition. Then a method based on both use of a chip model and a specific measurement technique has been developed. It was able to estimate the current repartition in a diode as a function of the contact zone, the metallization physical properties and the semiconductor properties.

Figure 1 .

 1 Figure 1. The chip and the pressed contact zone

Figure 2 .

 2 Figure 2. Electrical contact resistance measurement device

Figure 3 .Figure 4 .

 34 Figure 3. Integration of the command signal in the device for the IGBT characterization

Figure 5 .

 5 Figure 5. Current pulse generation and mesuring chain

Figure 6 .

 6 Figure 6. Global voltage drop for 250N and 5000N clamped force at ambiant temperature

Figure 7 .

 7 Figure 7. Different places for the electrical contact resistance measurements In Fig 8, we can see the evolution of the electrical contact resistance between the copper jaw and a Diode metallization as a function of the clamping force for four measure points (diode Eupec 3.3kV -50A). Even if the global evolution is a decrease of the resistance value for clamping force increase, it is very surprising that the results depend on the measure point position. It means that the chip metallization can not be considered as an equipotential.

Figure 8 .

 8 Figure 8. Electrical contact resistance as a function of the clamping force at 25°C (diode Eupec 3.3kV -50A)

Figure 9 .

 9 Figure 9. Measure of the surface resistance of the chip metallization

Figure 10 .

 10 Figure 10. Numerical model of the metallization Diode metallization is modeled by a resistance network in accordance to Fig.10. R m is the elementary metal resistance:

Figure 11 .

 11 Figure 11. Top view and side view of the measurement bench

Figure 12 .

 12 Figure 12. Surface voltage repartition with I=43A injected in a corner

Figure 14 .

 14 Figure 14. Current diodes (Idi) and voltage surface repartitions (Vi) for different values of the metallization resistance

Figure 15 .

 15 Figure 15. Current repartition with four contact zones. Rm = 3mΩ

ACKNOWLEDGMENT

The authors are very grateful to M. Emmanuel Arnould (G2Elab) for all the advices and the experimental setup and Pearl Lab (Alstom Transport) for funding part of this work.


Ben Elyes

Guillaume Hamida
email: guillaume.chelius@inria.fr

Jean-Marie Chelius
email: jean-marie.gorce@insa-lyon.fr

Gorce

On the Complexity of an Accurate and Precise Performance Evaluation of Wireless Networks Using Simulations

Keywords: I.6.7 [Simulation Support Systems]: Environments; C.2.1 [Network Architecture and Design]: Wireless communication Wireless networks, physical layer modeling, performance analysis

In wireless multi-hop networks, there is a growing need for the performance evaluation of protocols and distributed applications. Due to the high complexity of analytical models and the difficulty of setting up large scale testbeds, simulations are generally considered as the most convenient methodology for evaluating the performance of wireless systems. However, evaluating a protocol can be a tedious task as it depends on several factors including the physical layer modeling and the dimensioning of protocol or environment parameters. As a consequence inferring an overall performance for a protocol is a real issue. In this paper, we highlight some main factors that may affect the accuracy of the performance evaluation of protocols using simulations. First, we focus on the physical layer (PHY) modeling which represent a key point for the sake of realism and confidence. Second, we discuss the impact of some protocol parameters on the behavior of the evaluated protocols.

INTRODUCTION

Due to the technological advances in miniaturization, low-power circuit design and efficient wireless capability, mobile ad hoc networks (MANET) have emerged as a promising technology with numerous military and civil applications, such as emergency operations, disaster recoveries, tactical surveillance, etc. Such networks are composed by a collection of wireless nodes that can dynamically self-organize to form a network without using any pre-existing infrastructure. More recently, there have been growing research interest in large-scale and autonomous wireless sensor networks (WSN), where a hundreds or a thousands of energyconstrained sensors are deployed over an area of interest to provide connectivity and monitor ambient conditions in the surrounding environment. Numerous applications are envisaged for wireless sensor networks such as, weather monitoring, fire detection, target tracking, etc. In wireless multi-hop networks, there is a growing need for the performance evaluation of networking protocols. Contrarily to the reliable physical medium of wired networks, wireless systems rely on a radio medium which is prone to failure. In such a context, the medium is shared by several nodes increasing packet loss due to collision and interference. In particular, interference is a major limiting factor for wireless communication. This issue makes it harder the performance evaluation of wireless networking protocols.

Three main approaches are generally adopted for the performance evaluation of networking protocols: analytical analysis, experimentation and simulation. Due to the high complexity of wireless communications, analytical analysis are often based on unrealistic assumptions (e.g., node synchronisation, ideal MAC layer, homogeneous location model, symmetric radio links, etc.) and inaccurate physical layer (PHY) models. An example of inaccurate PHY modeling is the famous disk model which has been widely used to model the radio range of wireless nodes where the interference is generally not taken into account. In addition, theoretical analysis always focuses on a given layer, ignoring the other network layers. Concerning the experimentation approach, it can provide valuable insight into the behavior of protocols in wireless environments. However, setting up large scale testbeds is a tedious task and is not always feasible. Moreover, the obtained results are strongly correlated to the surrounding environment and are not easily reproducible.

For these reasons, the use of simulations is generally considered as the most convenient methodology to analyse the performance of protocols and distributed applications. Nonetheless, the complexity of the physical phenomena constituting the radio medium introduces a tradeoff between accuracy and computational cost in wireless network simulation. Several wireless network simulators have been proposed in the last years. Examples are NS-2, Glo-MoSim [START_REF] Bajaj | Simulation of large-scale heterogeneous communication systems[END_REF], JiST/SWANS [START_REF] Barr | Scalable Wireless Ad hoc Network Simulation[END_REF], GTSNetS [START_REF] Ould-Ahmed-Vall | Simulation of large-scale sensor networks using gtsnets[END_REF], OMNeT++, OP-NET, etc. They all provide an advanced and complete simulation environment to investigate and evaluate networking protocols and wireless systems. However, the complexity of the wireless physical layer (PHY) leads to implementation choices during the simulators design. As a consequence, the PHY simulation accuracy varies drastically from one simulator to another. In particular, interference management is probably the point where current simulators differ the most largely. The reason that generally justifies a low accuracy is performance. Moreover, some protocol and environment parameters are generally tuned arbitrarily during the performance evaluation of high level protocols. In this context, it is hard to obtain a representative and an overall performance evaluation of protocols. In fact, several previous publications have shown that the behavior of wireless networking protocols may radically differ from a simulation environment to another one [START_REF] Cavin | On the accuracy of manet simulators[END_REF][START_REF] Heidemann | Effects of detail in wireless network simulation[END_REF][START_REF] Takai | Effects of wireless physical layer modeling in mobile ad hoc networks[END_REF].

In this paper, we highlight the main factors that may affect the accuracy of the simulation results. First, we focus on the physical layer modeling which represents a key point for the sake of realism and confidence. The question we raise is: what is the real impact of the physical layer modeling on the behavior of the evaluated high level protocols ?. To analyse this question, we present the main physical modeling issues, including the radio range modeling, the radio link modeling and the interference modeling. Then, we review the PHY models implemented in common simulators and we use the WSNet [START_REF] Chelius | Worldsens: development and prototyping tools for application specific wireless sensors networks[END_REF] simulation environment to analyse the impact of the PHY modeling on the accuracy of the performance evaluation of high level protocols. Finally, we investigate the impact of some protocol and environment parameters on the performance evaluation of application-layer protocols. The second question we raise is: what is the impact of the dimensioning of these protocols on the global performance accuracy ?. We focus on the dimensioning of a hello protocol and the battery parameters.

The remainder of this paper is organized as follows. In Section 2 we discuss the related work in modeling of wireless systems using simulation model. In Section 3, we describe the main physical layer modeling issues and we review the PHY models of common simulators. Then, in Section 4, we analyze qualitatively the impact of the PHY modeling on the behavior of a layer-3 protocol. Next, in Section 5, we investigate the impact of some protocol and environment parameters on the global performance of protocols. Finally, we conclude in Section 6.

BACKGROUND

Wireless network simulators. Numerous wireless network simulators have been developed and are concurrently used in the academic research world. The NS-2 network simulator is one of the most popular environment for wired and wireless network simulations. NS-2 is developed in C++ and uses OTcl for scripting and configuration, however it suffers from a limited scalability though some recent optimizations have been proposed to support simulations of a few thousand nodes [START_REF] Naoumov | Simulation of large ad hoc networks[END_REF]. GloMoSim [START_REF] Bajaj | Simulation of large-scale heterogeneous communication systems[END_REF] is a simulation environment based on a C-derived language, called Parsec, which supports the sequential and parallel execution of discreteevent simulations. Thanks to parallelization, GloMoSim was shown to scale up to 10, 000 nodes. The JiST/SWANS [START_REF] Barr | Scalable Wireless Ad hoc Network Simulation[END_REF] is a scalable java-based discrete event simulation for wireless networks. It was shown that JiST/SWANS outperforms NS-2 and GloMoSim in terms of scalability and memory usage. The Georgia Tech Network Simulator, GTNeTS [START_REF] Ould-Ahmed-Vall | Simulation of large-scale sensor networks using gtsnets[END_REF], is a C++ object-oriented simulation environment dedicated to the simulation of wireless sensor networks. GTSNeTS claims to scale to networks of several hundred thousands of nodes.

More recently, we have proposed the WSNet [START_REF] Chelius | Worldsens: development and prototyping tools for application specific wireless sensors networks[END_REF] simulation framework. The main goal of WSNet is to provide a modular architecture which eases the development and the addition of new simulation models. Moreover, WSNet offers a wide range of PHY layer modeling, starting from a basic perfect PHY layer to a very precise one.

In this paper, we choose to use WSNet1 for our performance evaluation analysis as none of the existing simulator offer a sufficient diversity in PHY models.

Modeling and simulation of wireless networks. The literature in the context of modeling of wireless systems provides a lot of papers analyzing the accuracy of the simulation results. In [START_REF] Cavin | On the accuracy of manet simulators[END_REF], the authors investigate the accuracy of three popular simulators (NS2, GloMoSim and OPNET). Through the simulation of a basic flooding algorithm, they show a significant divergence in the obtained results between the simulators. The major reason for this issue is the PHY layer modeling which is implemented differently from a simulator to another. Indeed, in [START_REF] Takai | Effects of wireless physical layer modeling in mobile ad hoc networks[END_REF], the physical layer models of these three simulators is presented in detail, and the authors discuss some PHY layer factors which are relevant to the performance evaluation of protocols. In [START_REF] Heidemann | Effects of detail in wireless network simulation[END_REF], the authors discuss the effects of detail in wireless simulation. They show how the performance evaluation of protocols can vary when tuning the level of detail. They suggest to adapt the level of detail required by a given question. In [START_REF] Varshney | Detailed models for sensor network simulations and their impact on network performance[END_REF], the authors describe the impact of using detailed models for battery, processor power consumption and traffic models on the behavior of protocols.

Contribution. Our contribution is twofold. First, we provide an in-depth analysis of the PHY layer modeling and we show, through extensive simulations, its impact on the accuracy of the performance evaluation of high level protocols. Second, we investigate the impact of the dimensioning of some protocol and environment parameters on the global performance of the protocol.

PHYSICAL LAYER MODELING ISSUES

For the sake of realism and confidence in simulation results, an accurate PHY modeling is a key point. In analytical studies as in simulations, the disk model has long prevailed. It relies on a set of strong assumptions: time stationarity :

lij (t) = lij (1) independence : lij = f (xi, xj) (2) switched link (on/off) : lij ∈ {0, 1} (3) symmetry
: lij = lji (4) isotropy : lij = f (xi, dij) (5) homogeneity
: lij = f (dij) (6)
where lij refers to the radio link between nodes i and j and dij to the geometric distance between i and j.. The disk model provides the radio network with three axioms: the radio range is constant, the radio link is switched, and the network is interference free. If the asset of this model holds in its simplicity for both theoretical studies and simulations, the resulting simulations are far from realistic. Nonetheless, improving this model is not a trivial task as a hard tradeoff between complexity and realism holds. Basically, this model can be improved by relaxing either of the three previously stated axioms, as discussed below.

Radio range modeling

The range of a radio system is based upon the definition of a signal to noise ratio (SNR) threshold noted γlim . If the system is interference free, the range is a constant and the radio link is defined by:

lij : Ω 2 → B = {0, 1} (xi, xj) → l(xi, xj) = ( 1 if γij ≥ γlim 0 else (7)
where the SNR γij is given by: γij = hij • P i N j , where hij is the path-loss and Pi and Nj are the transmission power and the noise level respectively.

The transceiver properties. They are the transmission power Pi, the noise level Ni, the antenna gain and its radiation pattern gi(θ, φ). Variations of Pi, Ni or antenna gains affect the spatial homogeneity assumption (and so far the symmetry), which means that all nodes not further have the same range. Note that a non-uniform noise level Nj is highly probable for low cost small radio systems. The isotropy which is not statistically affected by these parameters does not further hold if the radiation patterns of the antennas are introduced according to:

hij = g(xi, xj) • gi(θij , φij) • gj(θji, φji),
where g(xi, xj) is the propagation path-loss. It should be noted that 3D radiation pattern and 3D distribution of radio systems is pertinent for the simulation of small indoor environments for example.

Propagation models. The simplest model refers to the line of sight (LOS) scenario but in urban and indoor environments, more complicated scenarios occur due to shadowing and multiple paths. Two complementary approaches can be used to deal with propagation. The former approach relies on a deterministic modeling of the wave propagation and provides fine simulations of any environment. The most usual algorithms are ray-tracing based [START_REF] Almers | Survey of channel and radio propagation models for wirelessmimo systems[END_REF] but discrete methods have been also proposed [START_REF] Gorce | A deterministic approach for fast simulations of indoor radio wave propagation[END_REF]. The high accuracy of these methods is definitely balanced by their high computational cost. Another limitation of purely deterministic models is that simulating one real environment is often too specific. Thus, the later approach relies on a statistical description complementing the deterministic model. A stochastic variable sij is then introduced in the propagation path-loss to handle shadowing:

gij = gij • sij.
The most usual model is the log-normal shadowing. A very challenging issue with shadowing is to introduce a spatial correlation between radio links which is not found in current simulators. Thus, sij should be a spatial correlated stochastic process constant in time; it is not the case in some works as shadowing is often confused with fading. Fading refers to SNR time variations due to multi-path interference. It has a leading role in wireless communications and is introduced also as a stochastic variable fij:

gij (t) = gij • sij • fij (t)
This late variable is not spatially correlated as it relies on small scale phenomenon. Meanwhile, it is a time variant parameter. Considering its temporal correlation may be highly relevant [START_REF] Pham | New cross-layer design approach to ad hoc networks under Rayleigh fading[END_REF] and represents another challenge for wireless simulators.

Radio link modeling

A frame error rate (FER) as a function of the mean SNR can substitutes for the SNR threshold of Equation 7. It derives from the bit error rate (BER) function which itself relies on the radio interface properties. lij then relates to the probability of a successful transmission. Some theoretical asymptotic expressions are well-known for various modulation techniques [START_REF] Wang | A simple and general parametrization quantifying performance in fading channels[END_REF]. However, the exact derivation at low SNR is sometimes not straightforward more specifically in the case of fading channels, which can be introduced at this level with:

Ps (E|γ) = Z ∞ 0 Ps (E|γ) • fγ (γ|γ) • dγs. ( 8
)
where fγ (γ|γ) stands for the instantaneous SNR distribution due to fading. It can be also of great importance to considering channel coding. For instance, bloc coding can be introduced thanks to bounding the code word error probability. Last but not least, the radio link can be more complex if the pulse time-spreading due to multi-path lies beyond the symbol period. In this case, the impulse response should be considered.

Interference modeling

Interference disturbs the packet reception at the physical layer. It appears as a crucial point in PHY simulations as final results can be strongly influenced by the interference model. As we will see in SubSection 3.4, interference management is probably the point where current simulators differ the most largely. Sources of interference include nodes operating in the same frequency band or in different frequencies. The first type of interference is known as co-channel interference, while the latter is termed adjacent channel interference.

The most efficient approach for introducing interference consists in replacing the SNR by a signal to interference plus noise ratio, SINR, which can be derived according to:

γij = hij • Pi Nj + P k =i,j h kj • P k (9)
The proper derivation of the SINR requires the knowledge, at a given time, of all the signals which are concurrently received at a given receiver. To be exhaustive, it should be noted that non linear receivers (with multi-user detection for instance) can outperform classical receivers in the presence of interference. In this case, it would be necessary to compute the FER not from the general SINR, but rather from the vector of received powers at each node.

Physical modeling in common simulators

Several wireless network simulators have been proposed in the last years. They all provide an advanced and complete simulation environment to investigate and evaluate networking protocols and wireless systems. However, the complexity of the wireless physical layer (PHY) leads to implementation choices during the simulators design. As a consequence, the PHY simulation accuracy varies drastically from one simulator to another, as shown on Table 1. Interference modeling, which is one of the most crucial aspects for cross-layer and protocol studies, is probably the point where current simulators differ the most largely. The first step toward interference evaluation is to identify which signals are interfering with each other in order to assess the terms in the denominator of eq. 9, on the basis of timing considerations only. This set of interfering signals can be very large for large scale simulations. As a consequence, various simulators rather limit the range at which any signal can propagate and thus can interfere. In other words, disregarding the radio range model effectively used for the Regarding the SINR computation, several strategies have been investigated and implemented in existing simulators, as shown on Table 1. They are all variations of eq. 9 regarding timing granularity. They induce a varying level of realism, precision but also complexity. Three main approaches, for the SINR computation, are adopted: (i) strongest signal: the noise value considered for the SINR computation is the power of the strongest interfering signal (i.e., N 3 on Figure 1); (ii) cumulative: the noise value considered for the SINR computation is the cumulative power of the signals that interfere with the considered signal at reception time (i.e., N 5 on Figure 1); and (ii) adaptive: several SINR values are computed for the packet; whenever the set of interfering signals changes, a new SINR value is computed. The noise value considered for each SINR computation is the cumulative power of all concurrent interfering signals (i.e., from N 1 to N 5 on Figure 1).

It is obvious that these interference models offer different levels of complexity, accuracy or realism. In the next section, we evaluate, using the WSNet simulation framework, the impact of these on the behavior of high level protocols.

IMPACT OF THE PHY MODELING ON LAYER-3 PROTOCOLS

This section quantifies the impact of the physical modeling on the behavior of a high level protocol. First, we present the simulation environment and the assumptions. Then, we investigate the impact of the radio range modeling as well as the radio link and the interference modeling on a hello protocol using WSNet. We choose to study a hello protocol as it represents an important network service on which several protocols are based, e.g., routing and self-organizing protocols.

Assumptions

We consider 500 static nodes, randomly deployed in a 200 × 200 area, running a basic hello protocol. Using this protocol, each node can be in two states: listening or talking. These states occur inside a timeframe of duration w. In each occurrence of w (a.k.a., in each round or timeframe of the hello protocol), a node picks randomly an offset ti, such that ti ∈ [0, w -τ ]. The hello packet is then transmitted at ti during τ . The hello packet transmission is performed without any carrier sensing nor clear channel assessment. Each node transmits only one hello packet per timeframe and keeps listening to the medium during the rest of the frame. Upon the reception of a hello packet, the transmitter is said to be discovered by the receiver which adds an entry in its neighbor table. This entry contains, in general, the neighbor identifier and a timeout to remove old entries associated to mobile or dead nodes. The neighbor table is then used by layer-3 protocols for determining, for example, the next hop during the routing process.

For our analysis, we assume a timeframe, w, of duration 500ms, and that each node emits one hello packet per round (100B/s) through an IEEE 802.15.4 868Mhz compliant radio with a transmission power of 0dBm and a radio sensitivity threshold of -92 dBm. The hello protocol is then evaluated according to the following four metrics: (i) the number of discovered neighbors: which is the average number of discovered neighbors at each round of the hello protocol; (ii) the distance from the farthest discovered neighbor: which is the maximal distance from which a node have been discovered; (iii) the number of connex components: which reflects the network connectivity. The more the number of connex components increases, the more network connectivity is reduced; and (iv) the link success probability: which is the probability of successful transmission according to the distance between the transmitter and the receiver. These metrics are evaluated at the end of each round, and for a node located at the center of the simulation area in order to avoid the edge effects. We performed the same set of simulations with various PHY models. The simulation results are averaged over 30 runs with a 95% confidence interval.

Effects of the radio range modeling

We first start by evaluating the impact of the radio range modeling on the behavior of the hello protocol. The interference modeling is not yet taken into account. We consider (i) a free-space propagation model with a pathloss of 2; (ii) a log-normal shadowing model with a standard deviation of 4dB and a close-in reference distance of 1m; and (iii) a rayleigh block-fading model. At this time the shadowing model does not include spatial correlation and the fading is uncorrelated between two frames. These radio range models are compared according to the above metrics. The average number of discovered neighbors, the distance from the farthest discovered neighbor and the number of connex components are shown on Figure 2 in function of the time, while the distribution of the link success probability is drawn on Figure 3. This probability represents the probability that a link exists between a transmitter and a receiver in function of the distance between them.

We notice on Figure 2-(a), that the average number of discovered neighbors, at each round, is almost the same for the three models; however, we observe that the average number of connex components is slightly different, as shown on Figure 2-(c). Indeed, the pathloss model induces a network which is less connected (i.e., a higher number of connex components) than the one obtained with the fading and the shadowing models. This fact can be explained by the log-normal random variable, introduced in the shadowing and fading models, which allows longer communication range than the pathloss model, as shown on Figure 2-(b), and thus the network connectivity is improved.

Considering the link success probability, shown on Figure 3, we observe that the link probability decreases in function of the distance between the emitter and the receiver, and that the shadowing and fading models present a higher link success probability for higher distance. These results show that the radio range modeling impacts strongly the network connectivity as well as the link success probability. As most of layer-3 protocols exploit the graph of connectivity, obtained by the hello protocol, it is thus important to use an adequate radio range model for the performance evaluation of networking protocols.

Effects of the radio link modeling

We now evaluate the impact of the radio link modeling on the behavior of the hello protocol. Two radio link models are considered: the threshold-based and the BER-based models. In the thresholdbased model, a packet is correctly received iff the signal to noise ratio (SNR) is higher than a given threshold. This model is used, for example, in NS-2, GTSNetS [START_REF] Ould-Ahmed-Vall | Simulation of large-scale sensor networks using gtsnets[END_REF], etc. In the BER-based model, the packet reception depends on the frame error rate (FER) which itself depends on the bit error rate (BER). The BER is computed according to the SNR and the technique of modulation (e.g., BPSK, FSK, OQPSK, etc.). Such radio link model is used, for example, in GloMoSim [START_REF] Bajaj | Simulation of large-scale heterogeneous communication systems[END_REF], WSNet [START_REF] Chelius | Worldsens: development and prototyping tools for application specific wireless sensors networks[END_REF], etc.

We consider a free-space pathloss model, a log-normal shadowing model and a rayleigh fading model with the same parameters described above. These models are evaluated according to three radio link models: (i) a threshold-based model; (ii) a BER-based model with a BPSK modulation; and (iii) a BER-based model with a OQPSK modulation. The obtained average number of connex components is shown on Figure 4. From the results, shown on Figure 4, we can make two observations. First, we notice, quite obviously, that the radio range models impact the obtained average number of connex components. The shadowing and fading models induce a better network connectivity than the pathloss radio range model. Second, we observe that the radio link model impact also the network connectivity. Using a simple radio link model, such as the threshold-based model, yields better signal reception rates and thus a better network connectivity (i.e., a lower number of connex components). However, using more accurate models, such as the BER-based model, increases the packet loss and thus we get a lower network connectivity.

From these results it is clear that the radio link model have to be correctly chosen for an accurate performance evaluation of wireless systems. The use of simplistic radio link models is generally motivated by the scalability issue, however such models may leads to a better estimation of the channel conditions than more complex radio link models, and thus impacting the behavior of high level protocols. The use of accurate and precise radio link models is then a key point for the sake of realism and confidence in the simulation results.

Effects of the interference modeling

The previous subsections analyzed the impact of the radio range and the radio link modeling on a hello protocol without interference consideration. As interference is a major limiting factor for wireless communication systems, we investigate in what follows the impact of the interference modeling on the same above metrics. We consider the three radio range models introduced previously with a BER-based link model using a BPSK modulation scheme and a full interference model with an adaptive SINR computation.

The Figure 5 depicts the obtained average number of discovered neighbors, the distance from the farthest discovered neighbor number of connex components, in function of the time. We notice on Figure 5 that the interference impacts strongly the obtained simulation results compared to the results shown on Figure 2. Hence, the average number of discovered neighbors decreases from 25, for the case without interference, to 5, with interference modeling. Moreover, we notice on Figure 5-(b) that the maximal distance from which a node may be discovered is also reduced. This fact is also verified on Figure 6. Finally, regarding the average number of connex components shown on Figure 5-(c), the introduction of the interference modeling makes the network less connected, specially for the pathloss radio range model. Interference modeling is thus important during the evaluation of high level protocols as the behavior and the performance of these protocols depends on the PHY layer modeling accuracy. Evaluating the performance of protocols using inaccurate PHY layer modeling may affect the confidence of the simulation results.

We now investigate the interference modeling accuracy, focusing on the SINR computation methodology and the interference model. We perform the same set of simulations and we vary the interference modeling complexity. We consider a limited interference model with a maximal propagation range of 80m and a full interference model. For both models, we use an adaptive and a cumulative SINR computation methodology. The impact of these models on the number of connex components is shown on Figure 8, and the graphs of connectivity obtained for the full interference model are shown on Figure 7.

Quite obviously, a better accuracy in the interference modeling induces a loss of the network connectivity, or an increase of the number of connex components. As shown on Figure 8, the SINR computation methodology as well as the interference model induces a varying level of accuracy. If the limited interference model is generally motivated by the scalability issue, the use of the full interference model allows more accuracy and confidence in the simulation results, despite an increase of the computation overhead. The validity of the performance evaluation of high level protocols depends thus on the choices made for the PHY modeling, specially for the interference modeling.

DESIGN ISSUES IN WIRELESS NETWORKS

In this section, we analyze the effect of the hello protocol dimensioning and the battery power consumption on the behavior of application-layer protocols. These two issues are important, partic- ularly in the context of wireless sensor networks (WSN) where the energy is a major constraint and where most of the layer-3 protocols are based on a hello protocol. First, we present the assumptions as well as the application-layer protocols used for the analysis.Then we investigate the impact of the hello protocols and the battery model on the network lifetime and the behavior of some application-layer protocols.

Assumptions

We consider three application-layer data dissemination protocols: GHT [START_REF] Ratnasamy | Ght: A geographic hash table for data-centric storage in sensornets[END_REF], XY [START_REF] Das | Performance comparison of scalable location services for geographic ad hoc routing[END_REF] and LBDD [START_REF] Hamida | A line-based data dissemination protocol for wireless sensor networks with mobile sink[END_REF]. These protocols are used in the context of wireless sensor networks with mobile sinks for disseminating data reports from the sensors towards the base station (i.e., the sink). These protocols implements a rendez-vous area for storing the data reports generated by a source node. To collect the generated data, the sink sends its queries towards the rendezvous area and the corresponding data reports are sent back to the sink by geographic routing. The rendez-vous area can be a hashed location, as in GHT [START_REF] Ratnasamy | Ght: A geographic hash table for data-centric storage in sensornets[END_REF], or a central strip as in LBDD [START_REF] Hamida | A line-based data dissemination protocol for wireless sensor networks with mobile sink[END_REF].

All these application-layer protocols are used on top of a greedy geographic routing which implements the basic hello protocol described in SubSection 4.1. Through a periodic exchange of hello packets, each node builds a neighbors table which is used during the routing process to forward messages from the sensor nodes to the sink. We consider 2000 static nodes deployed randomly over a 400 × 400 area, and a mobile sink moving according to a billiard mobility model. Each node runs a IEEE 802.15.4 868Mhz compliant radio with a transmission power of 0dBm and a radio sensitivity threshold of -92dBm, a IEEE 802.11 DCF MAC protocol, and a basic linear-decrease battery model. More realistic battery models can be considered [START_REF] Staehle | Impact of energy models on energy efficient sensor network routing[END_REF] and yet have to be implemented.

We consider two metrics: (i) the success ratio: defined as the ratio of the total number of data packets received by the sink to the total number of packets generated by the sensors; and (ii) the number of active nodes: defined as the total number of active nodes in function of time. The first metric analyzes the performance of the application-layer protocols, while the latter reflects the network lifetime, as the number of active nodes decreases in function of time due to battery depletion.

Effects of the Hello protocol dimensioning

We first start by evaluating the impact of the hello protocol dimensioning on the behavior of GHT [START_REF] Ratnasamy | Ght: A geographic hash table for data-centric storage in sensornets[END_REF], XY [START_REF] Das | Performance comparison of scalable location services for geographic ad hoc routing[END_REF] and LBDD [START_REF] Hamida | A line-based data dissemination protocol for wireless sensor networks with mobile sink[END_REF]. We consider three hello protocol dimensioning: 1 hello packet transmission every 1, 5 and 10 seconds. The impact of this tuning on the network lifetime is shown on Figure 10, and the impact on the success ratio obtained by the application-layer protocols is shown on Figure 9. We observe, on Figure 10, that the hello protocol impacts significantly the network lifetime. In fact, the more the frequency of the hello packet transmission increases, the more the number of active nodes decreases in function of time. This is mainly due to the batteries depletion. This result highlights a clear tradeoff between the network lifetime and the effectiveness of protocols. If the use of a high frequency of hello-packet transmission reduces the network lifetime, it allows the application-layer protocols to be more effective in dynamic and lossy environments. A tuning of the hello protocol parameters if then important as it may impact the global performance of the network.

Regarding the behavior of the application-layer protocols, we notice on Figure 9 that the obtained success ratio vary in function of the hello protocol parameters. Indeed, we notice a high sensitivity of the application-layer protocols to the layer-3 parameters. For example, using a frequency of 1 hello packet per 1s, we notice that the success ratio of GHT decreases quickly compared to the other approaches. However, when using a frequency of 1 hello packet per 10s, we observe that the success ratio of GHT remains higher, compared to LBDD and XY. This raises again the importance of the dimensioning of layer-3 protocols during the performance evaluation of application-layer protocols.

Effects of battery power consumption

We now investigate the impact of the battery power consumption on the global performance evaluation. A correct dimensioning of the battery parameters is of great importance specially in the context of wireless sensor networks.

In the literature, this dimensioning is generally performed according to a given equipment standard, or simply randomly. Hence, the transmission power is considered sometimes higher than the reception power, whereas in some simulation scenario it is considered equal or lower than the reception power. To better assess the impact of the battery power consumption on the global performance evaluation, we simulated the GHT protocol while varying the transmission power compared to the reception power. The impact of this dimensioning on the network lifetime and the obtained success ratio is depicted on Table 2. The results show that the dimensioning of the battery impact directly the global network lifetime as well as the performance of the application-layer protocol. Thus, if a protocol performs well with a given battery model, it can provides bad results with another battery model. Again, this highlights the importance of using detailed and accurate models for a precise performance evaluation of wireless systems.

CONCLUSIONS

Due to the complexity of wireless communication, simulation is generally the most convenient methodology for the performance evaluation of protocols. However, several factors may affect the confidence and the accuracy of the simulation results. These factors, which include the physical layer modeling and the dimensioning of protocol and environment parameters, increase the complexity of the performance evaluation.

Regarding the physical layer modeling, we have presented the PHY models implemented in five common simulators. Interference management, which is the main limiting factor for wireless systems, is probably the point where current simulators differ the most largely. Through intensive simulations, we have found that the physical layer, in particular interference management, impacts strongly the network connectivity as well as the behavior of networking protocols. For the sake of realism and confidence in simulation results, using accurate and detailed PHY models is thus a key point, despite an increase of the computation overhead. Moreover, we have found that the dimensioning of some protocol and environment parameters (i.e., the hello protocol and the battery model) is also important as it impacts the global performance of protocols. Thus, the question that arises is which parameters should we use when evaluating the performance of a protocol ? and what simulation results must be considered as representative when comparing the performance of several protocols ?. Since it is not possible to simulate a protocol with all the possible values of its parameters, we must either find the "good" values through a step of dimensioning, or by studying the possible existence of bounds for these parameters that would limit the performance of protocols and thus having a representative idea of its effectiveness. In general, it is a problem of representativeness of the obtained simulation results.

Figure 1 :

 1 Figure 1: Strategies for the SINR computation.

  Number of discovered neighbors. (b) Distance from the farthest neighbor. (c) Number of connex components.

Figure 2 :

 2 Figure 2: Impact of the radio range modeling on the behavior of a hello protocol (without interference modeling).

Figure 3 :

 3 Figure 3: Impact of the radio range modeling on the link success probability.

Figure 4 :

 4 Figure 4: Impact of the radio link modeling on the average number of connex components.

  Number of discovered neighbors. (b) Distance from the farthest neighbor. (c) Number of connex components.

Figure 5 :

 5 Figure 5: Impact of the radio range modeling on the behavior of a hello protocol (with interference modeling).

Figure 6 :

 6 Figure 6: Impact of the radio range and the interference modeling on the link success probability.

6 Figure 7 :

 67 Figure 7: The graphs of connectivity obtained with: (a) no interference consideration; (b) full interference model, BER+BPSK, cumulative SINR computation; and (c) full interference model, BER+BPSK, adaptive SINR computation.

Figure 8 :

 8 Figure 8: Impact of the SINR computation methodology on the number of connex components.

1 Figure 9 :

 19 Figure 9: Impact of the hello protocol dimensioning on the behavior of high level protocols.

Figure 10 :

 10 Figure 10: Impact of the hello periodicity on the network lifetime.

Table 1 :

 1 PHY layer modeling in common simulation environments: NS 2.31, JiST/SWANS 1.06, GloMoSim 2.03, GTSNetS and WSNet 2.0. received signal strength computation, the simulator does not generate receptions at nodes further than a given range from the source. Consequently, the considered source cannot induce interference at nodes further than this range. This optimization is called Limited interference model as opposed to the Full interference model. It privileges scalability at the cost of accuracy. This optimization is implemented in NS-2, JiST/SWANS, GloMoSim, etc.

	Simulation	Radio range modeling	Radio link modeling	Interference modeling
	environments	pathloss	shadowing	fading	link model	modulation	model	SINR computation
	NS-2	free space, two-ray	log-normal rician, rayleigh	threshold	-	limited	strongest signal
	GloMoSim [2]	free-space, two-ray	log-normal rician, rayleigh	threshold, BER	BPSK, QPSK	limited	adaptive
	JiST/SWANS [3]	free-space, two-ray	-	rician, rayleigh	threshold, BER	BPSK	limited	cumulative
	GTSNetS [10]	free-space, two-ray	-	-	threshold	-	limited	strongest signal
	WSNet [5]	free-space, two-ray log-normal rician, rayleigh	threshold, BER	BPSK, STEP, OQPSK, FSCK	limited, full	adaptive, cumulative

Table 2 :

 2 TX/RX ratio Network lifetime (s) Success ratio (%) Impact of the battery power consumption on the global performance.

	0.5	480.168	0.185 ± 0.06
	0.75	557.811	0.248 ± 0.07
	1	617.277	0.273 ± 0.07
	1.5	399.811	0.292 ± 0.07
	2	272.877	0.368 ± 0.1

WSNet is available at: http://wsnet.gforge.inria.fr.