Development, modelling and control of a micro/nano positioning 2DoF stick-slip device Micky Rakotondrabe, member, IEEE, Yassine Haddab and Philippe Lutz, member, IEEE Abstract-The works presented in this article are motivated by the high performances required in micromanipulation/microassembly tasks. For that, this paper presents the developement, the modelling and the control of a 2 degrees of freedom (in linear and angular motion) micropositioning device. Based on the stick-slip motion principle, the device is characterized by unlimited strokes and submicrometric resolutions. First, experiments were carried out to characterize the performances of the micropositioning device in resolution and in speed. After that, a state-space model was developed for the sub-step functioning. Such functioning is interesting for a highly accurate task like nanopositioning. The model is validated experimentally. Finally, a controller was designed and applied to the micropositioning device. The results show good robustness margins and a response time of the closed-loop system.

Index Terms-Micropositioning device, stick-slip, linear and angular motion, state-space modelling, postioning control.

I. INTRODUCTION

N Owadays, the need of miniaturized systems with com- plex functions is in constant growth. Microfabrication technologies are not always suitable to produce such systems, particularly hybrid systems (i.e. combining several functions: mechanical, electrical, thermal, optical, etc.). For them, microassembly is better adapted. To manipulate and to assemble microproducts, especially MEMS (MicroElectroMechanical Systems), the use of conventional assembly systems leads to major difficulties because of the scale effects (adhesion forces [START_REF] Fearing | Survey of sticking effect for micro parts handling[END_REF], lack of precision ...). In order to take into account these scale effects, a complete study of the actuators, the sensors and the production methods must be made. Also, production systems should have dimensions which are adapted to those of the products. These systems are called microfactories and consist of microssembly and micromanipulation stations.

As the microcomponents of the microproducts (MEMS for example) generally have dimensions between 10µm and 2mm, it is very interesting to use stations that are able to handle such a range of dimensions. However, a very high positioning accuracy is required in microassembly. It is generally micrometric or submicrometric. So the positioning devices should have submicrometric resolution. Finally, to pick, transport and place a component from one location to another, in order to complete the assembly, the devices must have a high stroke motion.

For these reasons, a microgripper device with a large gap, high stroke and high resolution is of interest. Two possibilities may be used.

• First, one can use a high stroke positioning device coupled with a microgripper (Fig. 1-a), examples in [2] [START_REF] Dechev | Development of a 6 Degree of Freedom robotic micromanipulator for use in 3D MEMS microassembly[END_REF]. In order to cover the range of the components sizes, different microgrippers with different gaps are required. The advantage of this solution is that the resolution of the large stroke device does not necessarily have to be very high if the resolution of the microgrippers is. However, a system able to exchange the different microgrippers is required [START_REF] Clévy | A new micro-tools exchange principle for micromanipulation[END_REF]. • The second solution is the use of two or more independant devices with high stroke which collaborate together in order to pick, transport and place the components (Fig. 1b). In this case, the gap of the microgripper is naturally unlimited. The references [5] [6] are two examples of this concept. While microgrippers are not necessarily useful, the concept necessitates positioning devices with a high stroke and a high resolution. As part of our microfactory project, the latter concept was chosen. We describe in this paper the development of a micropositioning device dedicated to a microfactory station. Another important aspect in microassemby is the need of higher dexterity. As the shapes of the MEMS become more and more complex, positioning devices with a higher number of degrees of freedom (DoF) are needed. The microrobots presented in [START_REF] Fatikow | A piezoelectric mobile robot for handling of microobjects[END_REF] [8] [START_REF] Bergander | Mobile cm3-microrobots with tools for nanoscale imaging and micromanipulation[END_REF] are good examples. Each of them has 3DoF (x-y linear motions and z angular motion).

On the other hand, the automation of microassembly stations is interesting because the productivity rate can be increased.

However, the higher the number of DoF is, the higher the complexity of the automation of positioning devices in collaboration is. A compromise has to be found. We propose the kinematic structure of a microassembly and micromanipulation station as shown in Fig. 2. The station consists of two devices each having one 2DoF (linear and angular). One axis supports both the devices in order to increase the ease of their collaboration. This paper reports the development of one 2-DoF micropositioning device based on the stick-slip principle.

When fine positioning is needed in a task, the use of the displacement within a step (sub-step), i.e. within a stick-phase, is prefered. During the fine positioning mode, the disturbances may influence the success of the task. These disturbances may be the variation of the load, the environment (temperature and pressure) and so on. In addition, good performances are often necessary for the tasks. They are the response time, the statical error and the bandpass. To ensure the disturbances rejection and the robustness in performances, a closed loop control of the positioning device is recommended. Two control modes are also possible for that: the coarse mode control and the fine mode control. For the former, a first approach is the use of a basic algorithm (if error > one step, then apply a step) [START_REF] Rakotondrabe | Voltage/frequency proportional control of stick-slip micropositioning systems[END_REF]. Another approach is the control of the amplitude of the periodic input signal [START_REF] Fatikow | Microrobot system for automatic nanohandling inside a scanning electron microscope[END_REF]. Concerning the fine mode, [START_REF] Hung | Dual-stage piezoelectric nano-positioner utilizing a range-extended optical fiber Fabry-Perot interferometer[END_REF] uses a 2 nd order model and an adaptive sliding mode control to perform while [START_REF] Salisbury | Closed-loop control of a complementary clamp piezoworm actuator[END_REF] obtains a 4 th order model and computes a polynomial digital controller to perform the precise positioning. These controllers are dedicated to only one mode. It is also possible to compute one controller which takes into account both the fine and coarse functioning modes [START_REF] Sedghi | Control design of hybrid systems via dehybridization[END_REF] [START_REF] Rakotondrabe | Voltage/frequency proportional control of stick-slip micropositioning systems[END_REF]. Notwithstanding, using dedicated controllers remain the best way to obtain good performances because the specifications can be efficiently taken into account during the synthesis. Motivated by the need of high accuracy in micromanipulation/microassembly tasks, we present in this paper the modelling and control of the sub-step (fine) positioning of the developped micropositioning device.

The paper is organized as follows. First, the development of the micropositiong device is presented. Then, its performances are detailed. After that, a state-space model is developed for the sub-step functioning. The identification of parameters and the validation of the whole model are presented. Finally, the synthesis and the implementation of a P I controller is given. The phase and gain margins of the closed-loop system are high and can ensure the stability and the performances facing the uncertainties on the numerical values of the different parameters of the models.

II. GENERAL DESCRIPTION OF THE MICROPOSITIONING DEVICE

A. Target System

First, we present the wanted characteristics of the microsystem:

• the device has two degrees of freedom: linear and angular motions, • the desired resolution is greater than 1µm, end-effectors 2DoF positioning devices Fig. 2. Principle of the micrompanipulation station.

• in each motion, a very high stroke has to be possible: more than 5cm in the linear motion and 360 • in the angular one, • finally, the device has to have adequate dimensions: a maximum volume of 2cm × 2cm × 2cm.

B. Presentation of the used microactuators

There are different principles to obtain the high stroke and the high resolution characteristics of a micropositioning device. They can be classified into principles with embedded microactuators and principles with non-embedded microactuators. It is obvious that those with embedded actuators may offer a theoretically infinite stroke. Among these principles, the stick-slip one is very interesting for two reasons: the compactness of the used microactuators and the simplicity of the control signal (just the use of a sawtooth signal). Stickslip actuators are generally based on piezoelectric materials. Two modes of motion can be obtained with a micropositioner using stick-slip actuators: the stepping mode and the sub-step mode. The stepping mode consists in applying a sawtooth voltage to the micropositioner and letting it move step by step, in high range and with a high velocity on the workspace (Fig. 3-a, b andc). The resolution in this mode is limited to one step. When the difference between the reference position and the present postion becomes smaller than a step, the legs (piezoelectric actuators) are bent slowly until the final position is reached (Fig. 3-d). This is the sub-step mode and the obtained resolution can be very high.

In [START_REF] Bergander | Monolithic piezoelectric push-pull actuators for inertial drives[END_REF], a stick-slip microactuator called push-pull microactuator is proposed. It offers the possibility to perform several DoF from only one bulk material. Due to its characteristics, we use this microactuator in 2-DoF configuration (Fig. 4-a andb) to move our micropositioning device. The microactuator is based on a piezoelectric layer. There are four electrodes on the upper face and one electrode on the electrical ground in the lower face. They constitute the active parts of the microactuator. A sapphire disk-shaped foot is glued on the latter. When a positive electrical potential is applied to two electrodes while the opposite potential is applied to the other two, one half of the active part contracts while the second one expands. Thus, the foot performs a displacement δ and a rotation (Fig. 4-c). Now, let us place the microactuator on N is high enough, there is no rotation of the foot and the displacement of the microactuator only depends on δ (Fig. 4-d). The stick-slip motion is obtained when applying a saw-tooth voltages to the electrodes. While the foot is in contact with the base, the nonactive surface of the upper face will be glued with the body of the micropositioning device (hatched area in the Fig. 4-a).

∆x body microactuators t [s] U [V] t [s] U [V] t [s] U [V] t [s] U [V]

C. Integration of the microactuators on the 2-DoF device

This part presents the integration of the above microactuator inside the 2-DoF device in order to move it. A cylindrical tube is used to support the device. This is the base on which the microactuator will be placed. The upper face of the microactuator is embedded in the device body while the foot is in contact with the tube. We especially use a glass-tube because the contact between glass and sapphire materials has optimal friction characteristics:

• during the stick-phase, a sufficient adherence is performed so the loss of displacement is minimized, • during the slip phase, the friction is relatively low so the issued overheating is minimized. Such overheating may destroy the microactuators elements (sapphire, etc.). To maintain the axial guidance of the device on the tube, at least two contact points are necessary. However, to maintain the radial guidance, at least three contact points spread out over 360 • are necessary. So we use six contact points to maintain the device on the tube. All the contact points are represented by microactuators in order to obtain a maximal total torque when they are activated simultaneously. The two "axial-guidance" microactuators form a pair of microactuators and glued together on an alumina support in order to facilitate their integration (Fig. 5-a and b). A system for the adjustment of the radial force is introduced for each pair of microactuators (Fig. 5-c andd). It is based on two tilted plates (lower and upper) and a screw. Through the plates, the adjustment of the screw will move the microactuator back-and-forth and then increases or decreases the radial force. It is used to preload (nominal radial force) the microactuators. However, the glass-tube presents a high cylindricity default and the micropositioning device may work imperfectly. To solve that, the third tilted plates system is replaced by an adaptable spring-system (Fig. 5-e). The lateral spring maintains the microactuator pinned against the body while the radial spring compensates the default of the tube. The adaptable springs are built by folding and shearing a thin metallic plate (thickness = 0.05mm) (Fig. 5-f).

Besides the dimensions, the weight is the main criteria of the design because of the limited torque that the microactuators can deliver. This is why the optimized shape of the body minimizing the weight is a triangle (Fig. 5-b). The body is made of alumina material. We call the whole device the 'TRING'module (Triangular RING module). Due to the complexity of the shape and the smallness of the dimensions, the body of the TRING-module was fabricated with Electric-Discharge technology. The Fig. 6 shows the TRING-module on its tube.

III. CHARACTERISATION OF THE TRING-MODULE

A. Step characteristics

Here, we evaluate the amplitude of a step of the microsystem in linear and in angular motions.

1) Linear motion: in linear motion, we perform the measurements with an interferometer with a 1.24nm resolution. The Fig. 7-a shows a linear displacement of the microsystem with a sawtooth voltage with 150V of amplitude and 500Hz of frequency. We remark that the step is quasi constant during Decreasing the amplitude will decrease the value of the step and will then increase the resolution of the micropositioning device. As example, with U = 75V the step is approximatively 70nm. However, whatever the amplitude is, the step efficiency is constant. The step efficiency is defined as the ratio between the gained step and the amplitude of the applied voltage [START_REF] Driesen | Energy consumption of piezoelectric actuators for inertial drives[END_REF] :

η step = step ∆amp ≈ 0.7 (1)
2) Angular motion: as we do not have an accurate appropriate sensor to measure the angular motion, we use the linear sensor and apply the measurement principle shown in Fig. 8. Let θ represent the angle of displacement of the microsystem, dl be the tangential displacement and R meas ≈ 2cm be a radius. Around the characterisation point, we have:

θ ≈ dl R meas (2)
The experiments give a step of 0.0025 • with U = 150V , 0.0015 • with U = 100V and 0.001 • with U = 75V . Of course, the radius R meas is not exactly known and the used value is approximative. As its uncertainty is bounded by ±2cm, the uncertainty on θ is bonded by ±10%.

B. High stroke characteristics

Here, the capability of the TRING-module in terms of speed is analyzed. The analysis is done with different values of frequency and amplitude. To measure the displacement, we use an optical sensor with 500nm of resolution and ±4cm of range for the linear motion while an accelerometer with 1 • of accuracy and ±90 • of range for the angular one is used.

1) Linear motion: Fig. 9 summarizes the speed performances of the TRING-module in linear motion. The spectrum (Fig. 9-a) indicates the linearity of speed versus frequency (for a given voltage amplitude). Above 10kHz, saturation and disturbances appear. They are due to the bandpass limit and to the eigen frequencies of the microactuators and of the entire structure. We can also remark the linearity of speed versus amplitude (for a given frequency) (Fig. 9-b). The applied maximal amplitude is 150V in order to avoid destruction or depolarization of the piezo microactuators. Below 35V , the device cannot have a high stroke motion because there is not enough torque to provide the sliding. It only moves back and forth following the microactuators. The maximal speed is about 1.8mm/s and it is obtained when the frequency is 10kHz and the amplitude 150V . A test gives the maximal force that the TRING-module can deliver. For that, we use a spring with a known stiffness and which is pushed by the device. When the speed of the latter becomes null, the maximal force is obtained: 150mN . This is good enough for the manipulation of small parts.

2) Angular motion: To measure angular displacement, we use a capacitive based sensor from FREESCALE: weight < 2g, dimensions 2mm×6mm×6mm. Due to its smallness, it is easily inserted into the TRING-module. It has a measurement stroke of ±90 • and the accuracy depends on the electronic filter and amplifier. As we only take an interest in the high stroke motion, the used accuracy is ±0.5 • . Fig. 10 shows speed performances. The same remarks made about the linear motion can be derived: frequency linearity up to 10kHz and minimal voltage for displacement about 35V . Maximal speed is about 20 • /s, i.e. nearly 18s for one complete rotation.

IV. SUB-STEP MODELLING OF THE TRING-MODULE

Here, we develop a state-space model of the TRING-module working in sub-step. There are two reasons why we want to model it: firstly, to ease the synthesis of a controller, secondly, to help the design of the microactuator from given performances.

A. Main assumptions

The study of the microsystem is reduced to the study of one microactuator with a mass on it. The radial force -→ N applied on each microactuator will be called normal force. The weight of the microsystem is weak in comparison with the result of the normal forces. The manipulation force (load) is not introduced here since it is considered as a disturbance. The adhesion forces between the foot and the spindle are insignificant in relation to the normal force. The base (tube) and the foot are assumed to be rigid and no vibration appears on the tube because we only work in stick-phase. During this phase, the foot and the tube are stuck and then there is no shock causing any vibration.

B. Working equations

Two parts are considered here: the determination of the piezoelectric working equation and the determination of the friction working equation. The former gives the internal states of the piezoelectric microactuator while the latter gives the internal state of the friction. We will apply the fundamental principle of the dynamics to combine them and to obtain the model of the whole device.

1) Piezoelectric working equation: Fig. 11-a shows one microactuator placed on a base. The mass M is composed of: the mass of one piezoelectric actuator, one tilted-plate system and a sixth of the body's mass. Cx 1 z 1 represents the local referential in the symetric plane of the piezoelectric layer. Point C represents the center of the contact surface between the foot and the layer. Point D is the center of the upper surface (Fig. 11-b). A displacement δx D of D generates a displacement δx of the TRING-module body with the same amplitude and direction. The aim of this subsection is to find the displacement of point D relative to point C. When we apply two symetrical voltages (+U and -U ) to the electrodes, the piezoelectric layer warps (Fig. 11-b). We assume that the radial force N is sufficient to maintain all the lower surface of the foot pinned against the base. Let us isolate the piezoelectric layer. We can summarize the following important parameters (Fig. 11-c):

• the resultant force -→ F and the resultant torque -→ Γ relative The resultant force -→ F consists of:

• the normal force -→ N .

-→ N is assumed to be reduced to point D. When δx D = 0, we consider that -→ N still stays coaxial with the principal axis of the foot because δx D is small in relation to the surface.

• the normal reaction --→ N applied on point C by the foot to the piezo layer, • two equivalent forces -→ F e and --→ F e are applied to the half active parts of the piezo layer. They are parallel to the electric field. Each of the forces is applied at an equivalent distance r e from the principal axis. We assume that r e is constant whatever the strain δx D is, the latter being negligible compared with the former, • a lateral force -→ F l is applied to each part of the layer. This force is perpendicular to the electric field and is assumed to be at an equivalent distance r l from the upper surface of the foot. We can consider that r l is constant whatever the deformation of the piezo layer is because δz D is null.

The equivalent forces F e , -F e and F l are due to the fact that the foot is constrained in rotation. Foremost, let us study the equation of the two active parts. For that, Sx indicates the contraction (or expansion) of one active part along the Cx 1 axis. In the case of a parallelepipedal layer characterized by a length L, a width w and a thickness e (Fig. 12-a), the transversal strain equation of the piezo layer can be derived using [START_REF]An American National Standard -IEEE Standard on Piezoelectricity[END_REF]:

Sx = d 31 • L e • U + s 13 • L • σ pa + s 11 • L • σ pp ( 3
)
where:

• d 31 < 0, s 13 > 0 and s 11 > 0 are respectively the transversal piezoelectric constant, the transversal elastic constant and the axial elastic constant, • σ pa and σ pp represent the mechanical stresses respectively parallel and perpendicular to the electrical field, the electrical field being parallel with z 1 axis, • e is the thickness at rest (without strain) and E ≈ U e . Notwithstanding, the shape of one active part of the microactuator is not parallelepipedal but hemicylindrical with a radius R e (Fig. 12-b). It can be considered as a sum of parallelepipeds with a constant width dw and a y 1 dependent length written L(y 1 ). However, to facilitate the equation of the axial strain Sx, we introduce a shape coefficient c oef f inside the (equ 3):

Sx = c oef f . d 31 .
R e e .U + s 13 .R e .σ pa + s 11 .R e .σ pp (4)

The previous equation is related to only one active half part. In spite of this, the displacement δx D can be constructed with the strain of the two half active parts. As the two parts are symmetric, we can use the (equ 4) in introducing a correction coefficient c orr . Considering q = c orrD .c oef f , we obtain:

Sx = q. d 31 .
R e e .U + s 13 .R e .σ pa + s 11 .R e .σ pp [START_REF] Thompson | Automating microassembly with orthotweezers and force sensing[END_REF] Let us now evaluate the stresses σ pa and σ pp . Let A a be the area on which the equivalent force -→ F e is applied and A l the area on which the lateral force -→ F l is applied (Fig. 12-b). We have:

σ pa = F e A a ( 6
)
σ pp = F l A l (7)
On the other hand, if we isolate the foot, we have:

F mp = -2.F l ( 8
)
Γ mp = F mp .h c ( 9
)
where F mp and Γ mp = -Γ are respectively the force and the torque applied to the foot by the piezo layer. The height of the foot is represented by h c . It is reminded that two vertical forces defined by -→ N and --→ -N are also acting on the foot. As their sum equals zero, they will not be considered. Moreover, using a previous assumption stating that -→ N stays co-axial with the foot, the latter force does not influence the torque Γ mp .

Using (equ 5)-(equ 9), and noting that δx = δx D , we infer: The (equ 10) is a static model. To complete this, we assume that the piezo layer has a second order dynamic behaviour. A higher order would complicate the model, a lower order (first order) is not sufficient if the system has a resonance frequency.

δx = q. R e e . [
If a and b respectively represent the inertial and the viscous parameters of the piezo layer, the working equation is:

d δx dt = q. R e a.e . [d 31 .U -e.k.F mp ] - b a . δx - 1 a .δx (12)
2) Equations of the friction: In the previous part, we determined the displacement of mass M in relation to point C (the foot). In this part, we determine the displacement x C of point C in relation to the base and thus to the reference 0 . In fact, during the stick-phase, the pre-displacement due to the deflexion of the asperities may have an amplitude with an order of magnitude equivalent to δ x . In addition, if the state of the friction can be expressed, it will be easy to control the force friction in order to maintain the device working in stickphase. According to the applications there are several models of friction [START_REF] Armstrong-Hélouvry | A survey of models, analysis tools and compensation methods for the control of machines with friction[END_REF] but the one which allows the modelling of the stick-phase is the single-state elastoplastic model [START_REF] Dupont | Single state elastoplastic models[END_REF]. The application of this model to our case (stick-phase and no lubricant) gives:

f f = -N • ρ 0 • x C ( 13
)
where f f indicates the deflexion resistance of the medium asperity, ρ 0 represents the Coulomb parameter.

C. State equations

Here, we write the state-equations of the micropositioning device in linear and in angular motions. The voltage U is considered as the input variable.

First, let us study the case of linear motion. Fig. 13-a represents the system when a voltage U is applied. As we only consider the stick-phase, we can assume that the reference 0 has an origin at the contact between the base and the tip of the medium asperity. In this figure, -→ R is the reaction of the base and is composed of the normal force --→ N and the tangential force -→ T . This latter is the friction. The real system (Fig. 13a) can be approximated by Fig. 13-b where m p is the mass of the foot and m incorporates the mass M and the mass of the piezo layer. We assume that the point D coincides with the center of the mass m. We also assume that there are no rotation components either for m p or for m. If we isolate the mass m, from the precedent remarks and the accelerations law, we have: composed of: 1) the force F pm = -F mp applied by the foot, 2) and the manipulation force applied by the manipulated component. This latter is assumed to be negligible. If not, it may be considered as an external disturbance. Applying the dynamics law to m and using the (equ 14), we can write:

ẍ = ẍC + δx (14)
ẍC + δx = -F mp m ( 15
)
On the other hand, isolating the foot lead us to the following dynamics expression:

ẍC = 1 m p . (F mp -N.ρ 0 .x as ) (16)
From the piezo working equation (equ 12), the dynamics of m in (equ 15) and the dynamics of the foot (equ 16), we have the following expressions:

d δx dt = 1 m equ . q. R e e .d 31 .U -k 1 .x C -b. δx -δx ( 17
)
d ẋC dt = k m m equ . -q.
R e e .d 31 .U + k 2 .x C + b. δx + δx [START_REF] Armstrong-Hélouvry | A survey of models, analysis tools and compensation methods for the control of machines with friction[END_REF] with:

       k m = m (mp+m) m equ = a -m p .k m .q. R e .k k 1 = k m .q. R e .k.N.ρ 0 k 2 = k 1 - N.ρ0.mequ m (19)
1) State equation of the linear mode: Using the equations (equ 17) and (equ 18), we infer the state-space model of the TRING-module:

d dt     δx δx x C ẋC     =     0 1 0 0 -1 mequ -b mequ -k1 mequ 0 0 0 0 1 km mequ b•km mequ k2•km mequ 0     .     δx δx x C ẋC     +      0 q•Re •d31 e•mequ 0 -km•q•Re •d31 e•mequ      .U (20)
2) State equation of the angular mode: Let us notice δs and s C respectively the internal state of the piezo layer and the internal state of the medium asperity during the angular mode. As the displacement δs and s C are very small in relation to the radius of the tube, we can consider that there are no rotation components in the angular mode. The state equation of the two modes are then similar. We have:

d dt     δs δs s C ṡC     =     0 1 0 0 -1 mequ -b mequ -k1 mequ 0 0 0 0 1 km mequ b•km mequ k2•km mequ 0     .     δs δs s C ṡC     +      0 q•Re •d31 e•mequ 0 -km•q•Re •d31 e•mequ      .U (21)

D. Output equations

The output vector has two variables during the stick-phase: the total friction T and the displacement x (for the linear motion) or the angle θ (for the angular motion). Indeed, while the displacement is the main interest of the model, in some applications it is important to estimate or control the friction. For example, if one wants to always ensure the sub-step functioning mode, the friction T is controlled to be lower than a limit friction such as the stick-mode is always guaranteed. If we isolate the foot, we can easily infer that the friction T = F pm . To determine this, we use the (equ 16).

1) Output equation of the linear mode:

We have:

T x = -m•(1-km) mequ -m•b•(1-km) mequ -m•(k1-k2•km) mequ 0 1 0 1 0 .     δx δx x C ẋC     + m•q•Re •d31•(1-km) e•mequ 0 .U (22)
2) Output equation of the angular mode: Fig. 14 Thus, the output equation in the angular mode is:

T θ = -m•(1-km) mequ -m•b•(1-km) mequ -m•(k1-k2•km) mequ 0 1 RD 0 1 RD 0 .     δs δs s C ṡC     + m•q•Re •d31•(1-km) e•mequ 0 .U (23)

V. PARAMETERS IDENTIFICATION AND VALIDATION OF THE SUB-STEP MODEL

In this section, we identify the unknown parameters of the above sub-step modelling. They are the coefficient q, the inertial and the viscous parameters a and b. After identification, we will validate the whole model both for the statical and the dynamical modes. The rest of the parameters are presented in the Table I.

Due to the lack of an accurate angular sensor, we only process the linear motion mode. This does not allow a loss of generality because the angular motion model has the same parameters as the linear motion model except the radius of the tube. We use an interferometer of 1.24nm resolution for the experiments.

Using the state-space equation [START_REF] Rakotondrabe | Design, devbelopment and experiments of a high stroke-precision 2DoF (linear-angular) microsystem[END_REF] and the output equation ( 22), we derive the transfer function relating the sub-step displacement x and the voltage U : with:

G xU = x(s) U (s) = q. Re .
                                                 b num 2 = m equ k m . (k 1 -k 2 ) a den 4 = m 2 equ k m . (k 1 -k 2 ) a den 3 = b.m equ k m . (k 1 -k 2 ) a den 2 = m equ . (1 -k 2 .k m ) k m . (k 1 -k 2 ) a den 1 = b (25)
In addition to the parameters identification, the transfer function described in (24) will be used to synthesize a controller in the next section.

A. Identification of the parameter q

The steady-state form of the transfer function ( 24) is:

q = x.e d 31 . R e .U ( 26
)
On the other hand, when the steady-state is reached, the deflection of the medium asperity becomes null. Thus, To determine q, a statical analysis with a piezoelectric actuator can be performed. Considering the smallness of the piezo layer, it is impossible to isolate it and to carry out experiments. A statical analysis with a FEM method (with ANSYS) was then performed. We apply a voltage of 150V . The corresponding displacement is x = 142nm. Thus, we have q = 0.7515.

B. Validation of the steady-state model

To validate the structure of the steady-state equation (26) and the determined value of q, we compare the corresponding simulation with an experimental result for different values of U . Fig. 15 shows that the curves align well.

C. Identification of the parameters a and b

Considering the smallness of the piezo layer, it is impossible to isolate them and determine the parameters a and b. Thus, we perform a harmonic analysis of one microactuator with a FEM method (with ANSYS). We obtain a = 9.77 × 10 -10 [s 2 ] and b = 200 × 10 -6 [s].

D. Validation of the whole model

To validate the whole model ( 24) with the different identified parameters, we use a harmonic experimental analysis of the TRING-module. The chosen amplitude of the sine voltage is 75V instead of 150V . Indeed, with a high amplitude, the minimum frequency from which the drift starts is low. In the example of Fig. 16, a frequency of 2250Hz already derives a drift when the amplitude is 150V while a frequency of 5000Hz does not when it is 75V . The higher the amplitude is, the higher the acceleration is and consequently the higher the risk of sliding (drift) is. When the TRING-module slides, the sub-step model is no longer valid. Fig. 17 presents the magnitude of the simulation of the equation (24) and the experimental result. It shows that the structure of the model and the identified parameters are befitting.

VI. CONTROL OF THE SUB-STEP FUNCTIONING

The aim of the sub-step control is to improve the performances of the TRING-module during a high accurate task and to reject the disturbances (manipulation force, adhesion forces, environment). Indeed, when positioning a microcomponent, the manipulation force can disturb the positioning task and modify its accuracy. In addition, the numerical values of the parameters (physical and geometrical) are uncertain. Thus, we want to introduce high stability margins in the closed-loop system.

The sub-step functioning necessitates that the derivate of the voltage dU dt should be inferior to a maximum slope Umax . A rate-limiter is then introduced in the closed-loop scheme in order to limit the slope of U (Fig. 18-a).

A proportional controller was first applied. Due to the nonnegligible statical error, an integrator was afterwards added. For the closed-loop system, we want to have a phase-margin of 60 • . To calculate the corresponding proportional gain K p and integrator gain K i = 1 Ti (T i is the integrator time parameter), chosen point should have a phase which is more than 240 • . We take (-184dB, 310 • ) (Fig. 19). This point is obtained with a frequency of ω 0 = 2.89×10 3 rad/s. After that, two are applied:

• addition of a gain of 184dB. The corresponding ratio is g K = 1122018454, • application of the phase delay due to the integrator: ϕ i = 310 • -240 • = 70 • . From this data, we have:

T i = 1 ω 0 . tan(ϕ i ) = 125.94 × 10 -6 (27) γ = T i.ω 0 1 + (T i.ω 0 ) 2 = 0.3420 ( 28
)
Where γ is the gain at high frequency. We directly infer:

K p = γ.g K = 383749529 ( 29
)
K i = 1 T i = 7940 (30)
The controller was implemented following the principlescheme in Fig. 18. The reference displacement is a step input signal x ref erence = 100nm. Because the voltage generated by the controller is rate-limited, the settling-time relative to the step input is no more of great interest. Hence, we are more interested by the static precision. Fig. 20-a shows the experimental response of the TRING-module. The accuracy is about ±5nm and the vibrations are due to the high sensitivity of the measurement to the environment. Such performances are of great interest for micromanipulation/microassembly. The Fig. 20-b shows the Black-Nichols diagram of the closedloop system and indicates the margin phase. According to the figure, the margin gain is 50dB. These robustness margins are widely sufficient to ensure the stability of the closedloop system regarding the incertainty of the parameters and of the structure of the developed model. Finally, the interest of the closed-loop control is to ensure these performances when external disturbances will appear during the micromanipulation/microassembly tasks. It may concern the environmental disturbance (temperature variation, etc.) or the manipulation disturbance (manipulation force).

VII. CONCLUSION

In this paper, we have presented the development, the sub-step modelling and control of a 2DoF (linear angular) micropositioning device, named TRING-module.

The device is based on the stick-slip principle which enables it to have submicrometric resolution and large strokes. The performance analysis show that the TRING-module is well suited for the automated microassembly stations. These performances concern the strokes, the high accuracy and the speeds. Moreover, in order to improve the performances in nanopositioning, we have developped a state-space model of the sub-step of the device working within a step. The model has been experimentally validated. Finally, we have implemented a P I controller making the sub-step mode have good performances for micromanipulation and microassembly use and a good robustness facing an eventual uncertainty of the parameters of the model.

Fig. 1 .

 1 Fig. 1. a: a high stroke positioning device coupled with a microgripper. b: several high stroke and high resolution positioning devices in collaboration.

Fig. 3 .

 3 Fig. 3. Stick-slip principle. a, b and c : stepping mode. d : sub-step mode.

Fig. 4 .

 4 Fig. 4. a (upside view) and b (underside view): the push-pull microactuator with 2-DoF configuration [15]. c: displacement and rotation of the foot. d: displacement of the microactuator on a base.

Fig. 5

 5 Fig.5. a: a pair of microactuators is glued onto a support. b and c: three pairs of microactuators are spread out inside the device. d: a tilted-plate system is used to adjust the nominal radial force. e and f: an adaptable spring-system is used to compensate the cylindricity defect of the tube.

Fig. 6 .

 6 Fig. 6. A photograph of the TRING-module on the glass-tube.

Fig. 7 .

 7 Fig. 7. Linear displacement measurement of the TRING-module using an interferometer. a: a series of stick-slip obtained with U = 150V and f = 500Hz. b: vibrations inside a step obtained with U = 150V and f = 60Hz.

Fig. 8 .

 8 Fig. 8. The principle of measurement during angular motion.

Fig. 9 .

 9 Fig. 9. Speed performances in linear motion.

Fig. 10 .

 10 Fig. 10. Speed spectrum in angular motion.

Fig. 11

 11 Fig. 11. a: the mass M is glued on the non-active area of the microactuator. b and c: strain of the microactuator.

Fig. 12 .

 12 Fig. 12. a: a parallelepiped piezo layer. b: a hemicylindrical piezo layer.

Fig. 13 .

 13 Fig.[START_REF] Salisbury | Closed-loop control of a complementary clamp piezoworm actuator[END_REF]. Scheme of the stick-phase. The dimension of asperity is blown up in order to see its deflexion.

Fig. 14 .

 14 Fig. 14. The angle θ is one of the output variables in the angular mode of the stick-phase.

Fig. 15 .

 15 Fig. 15. Validation of the static regime and the identified parameter q.

Fig. 16 .

 16 Fig.[START_REF] Driesen | Energy consumption of piezoelectric actuators for inertial drives[END_REF]. The outbreak of a drift of the TRING-module happens at low frequency when the amplitude is high.

Fig. 17 .Fig. 18

 1718 Fig. 17. Validation of the complete model.

Fig. 19 .

 19 Fig. 19. Black-Nichols diagram of G xU .

ig. 20 .

 20 P I control of the TRING-module in sub-step functioning.

  d 31 .Ue.k.F mp ]

								(10)
	with:	k =	h c .s 13 2.r e .A a	+	s 11 2.A l	-	r l .s 13 2.r e .A a	(11)

TABLE I

 I Physical and geometrical parameters.

		Dimensions:
	e	0.5mm
	hc	0.5mm
	re	0.5mm
	r l	0.25mm
	Re	3mm
	gap	0, 2mm
	A l Aa	5mm 2 0.367mm 2
		Other parameters:
	d 31 s 11 s 13	-210 × 10 -12 m/V 19 × 10 -12 m 2 /N 15 × 10 -12 m 2 /N
	m	1g
	me	1.562mg
	ρ 0	1.583 × 10 9 m -1
	N	1N

ACKNOWLEDGMENT

Particular thanks to Dr. Jean-Marc Breguet, from the 'Laboratoire des Systèmes Robotiques' of the Swiss Federal Institute of Technology Lausanne (LSRO-EPFL), for providing us the microatuators, sensors and many precious advises. This project is partially supported by the EUPASS-project (Evolvable Ultra-Precision Assembly SystemS : http://eupass.org/).


G Villemaud

G De La Roche

J M Gorce

Accuracy Enhancement of a Multi-Resolution Indoor Propagation Simulation Tool by Radiation Pattern Synthesis

Introduction

Regarding the strong development of wireless LAN systems melting various technologies in the same area, coverage prediction tools appeared necessary for fast and effective deployments. Numerous methods have been studied in this framework, almost based on asymptotic theories (e.g. ray-tracing) [START_REF] Mcknown | Ray tracing as design tool for radio networks[END_REF][START_REF] Seidel | 914 mhz path loss prediction models for indoor wireless communications in multifloored buildings[END_REF][START_REF] Fortune | Wise design of indoor wireless systems : practical computation and optimization[END_REF][START_REF] Wolfle | Dominant path prediction model for indoor scenarios[END_REF][START_REF] Neskovic | Modern approaches in modeling of mobile radio systems propagation environment[END_REF]. Actually, in a complex environment with multiple reflections and diffractions resulting in a large angular spread, a ray-tracing approach provides fast results only if few rays or reflexions are taken into account, resulting in a lack of accuracy. Ref. [START_REF] Gorce | An adaptative multi-resolution algorithm for 2D simulations of indoor propagation[END_REF] proposes a new alternative to these techniques derived from classical TLM (Transmission Lines Matrix) methods [START_REF] Hoefer | The transmission line matrix method -theory and applications[END_REF] and calculating flows exchanged between cells corresponding to a spatial discretization of the environment. This innovative approach offers both a precise modeling of the propagation environment and a reduced computational load taking advantage of a multi-resolution algorithm. In this approach, radiating sources are simulated as point sources and are thus obviously omnidirectional leading to an important limit of the method. This paper tackles this problem by introducing multi-point sources. A regularized radiation pattern synthesis is then proposed for modeling particular radiation patterns. This approach enhances the accuracy of the predictions while preserving fast calculation times.

MR-FDPF method limits

The Multi-Resolution Frequency Domain ParFlow (MR-FDPF) algorithm has already demonstrated fast and accurate prediction results for indoor propagation [START_REF] Gorce | The Adaptive Multi-Resolution Frequency-Domain ParFlow (AR-MDPF) Method for Indoor Radio Wave Propagation Simulation. Part I : theory and algorithms[END_REF][START_REF] Gorce | A Deterministic Approach for Fast Simulations of Indoor Radio Wave Propagation[END_REF]. In the ParFlow model [START_REF] Chopard | A lattice boltzmann method for wave propagation in urban microcells[END_REF] a source is simulated as an elementary pixel delivering four equivalent flows. By the way a radiating source simulated with this method is naturally omnidirectional. However, in a deployment-oriented point of view, a more complete definition of the radiating sources is needed : any kind of access point (AP) should be modeled, taking into account the antenna directivity. We propose herein a method to form a desired radiation pattern based on the principles of beamforming techniques. In wireless systems omnidirectional antennas like dipole or whip are widely used, but directive antennas are also more and more often preferred, either to increase range or to efficiently customize the deployment. In 802.11 networks, 6 or 8 dBi gain antennas (e.g. patchs) are often integrated in access points. Representing the radiation of such nonuniform pattern with only four simple flows is intrinsically unfeasible. The use of several sources with appropriate weighting is then needed. Thus, the radiated function can be controlled by adjusting magnitude and phase of each source:

(1) where x n is the complex weight of each source, d the distance between two sources and θ the angle of the considered direction for a linear array of N elements. This approach is

( ) ∑ = - = N n d j n e x F 1 cos θ β θ 1-4244-0123-2/06/$20.00 ©2006 IEEE
nothing else than a well-known array synthesis technique. To properly create a complex radiation pattern, a block of NxN elementary sources is used.

Radiation Pattern Synthesis

Radiation pattern synthesis is a well-known problem in the field of array antennas. A classical approach [START_REF] Svantesson | Antennas and propagation from a signal processing perspective[END_REF] considers the expression (1) as a discrete Fourier transform (DFT) and then extracts the source weights by an inverse DFT. This method is simple and efficient for basic beamsteering applications where only few criteria are needed (maximum gain and half-power beamwidth for example). Due to the spatial sampling, the resolution of this technique depends directly on the number of sources used. Unfortunately oversampling is actually not efficient, to undesired additional sidelobes in the radiation pattern.

Our aim is there to propose a method offering a good approximation of a given radiation pattern with a fixed number of uniformly spaced sources. In this way, our choice focused on a formulation with independence between the number of constraints and the number of weights searched. Calling z r a vector representation of the desired radiation for each direction and x r the weighting vector, we can build:

(2) with [START_REF] Fortune | Wise design of indoor wireless systems : practical computation and optimization[END_REF] for a NxM array of sources with n fixed directions.

In these expressions, the number of fixed points in the radiation pattern appears adaptable, impacting the size of H. Then, computing the generalized inverse of H reveals the weights to impose to our NxM sources to correctly approximate the pattern according to: [START_REF] Wolfle | Dominant path prediction model for indoor scenarios[END_REF] To prevent important oscillations between fixed reference points, two regularization terms are introduced:

(5) with [START_REF] Gorce | An adaptative multi-resolution algorithm for 2D simulations of indoor propagation[END_REF] and I the identity matrix. The terms µ0 and µ1 are adjusted to control the smoothness of the radiation pattern.

x H z r r = ( ) ( ) ( ) ( ) ( ) ( )           = - + - - + - n n M N j M N j e e H θ θ π θ θ π sin 1 cos 1 2 sin 1 cos 1 2 1 1 1 1 L M O M L z H H H x r † † ˆ= z H I D D H H x T r † 1 0 † 1 ˆµ µ + + = O O O O O O O O O O O 0 0 0 1 1 0 0 0 1 1 0 0 0 1 1 - - - = D 2154
The reference radiation pattern used to evaluate and adjust our solution is a simple sinus function with no backward radiation, assuming that it is a good approximation of classical patch-like antennas. To properly simulate AP the study focuses on the front-toback ratio. This reference pattern produces a theoretical power map as represented in Fig. 1 (left) in free-space. An array of 3*3 elements spaced from λ/6 with weights estimated by ( 5) yields power predictions illustrated in Fig. 1 (right). It appears that the estimated radiation fits well with the theoretical one. Although some backward radiated lobes are observed, the resulting front-to-back ratio remains good with 34 dB which is greatly sufficient to accurately model directive access points. It should be noticed that increasing the number of sources can increase the accuracy. Based on these results this algorithm was implemented in our MR-FDPF based wave propagation simulator.

Radiated power (dBm) Figure 2 shows a comparison of two coverage predictions of the same environment (71 by 17 meters with a 5 cm resolution at 2.45 GHz). This illustrates the impact of the radiation pattern of a 120° beamwidth antenna used instead of an omnidirectional one (with the same EIRP). The directive antenna is simulated with a 6x6 array with λ/6 spacing. In both cases the pre-processing time of the environment is 5.6 s (on a P4 3.2 GHz with 2 Go memory). Taking advantage of the multi-resolution principle, a propagation time of only 0.8s is achieved for the 6x6 sources (instead of 0.2 s for the omnidirectional one). So the computational cost of this approach remains very low, even with 36 point sources.

Radiated power (dBm)

Experimental results

Then to validate this method a comparison of the results obtained for 100 reference measurements in the same environment was performed with a 180° beamwidth AP. In terms of Root Mean Square Error (RMSE) between predicted and measured signal, the classical approach (omnidirectional source) leads to a precision of 5.8 dB. With the radiation pattern synthesis the RMSE falls to 4.4 dB, providing a 1.4 dB increase in the prediction quality. More tests have to be done and even better improvement could be expected with AP having a higher directivity.

Conclusion

The proposed approach to model a desired radiation pattern in a TLM based fast propagation engine appears relevant without notable increase of the computational cost.

A promising forthcoming work now concerns the evaluation of smart antennas or MIMO systems in indoor environments. Our simulator is indeed a good candidate for such simulations due to the natural high spatial resolution.

Figure 1 .

 1 Figure 1. Radiated power in a 500x500 cells free space (5 cm step) for a 20 dBm EIRP Left : desired, Right : 3x3 weighted sources (λ/6 spacing).

Figure 2 .

 2 Figure 2. Coverage predictions (dBm) for an omnidirectional access point (upper) and a directive one (lower) pointed in the right direction with same 17 dBm EIRP.


hysteretic, creeped and oscillating piezoelectric cantilevers

Complete open loop control of

Micky Rakotondrabe, member, IEEE, Cédric Clévy and Philippe Lutz, member, IEEE Abstract-The feedforward compensation of nonlinearities, i.e. hysteresis and creep, and unwanted vibrations in micromanipulators is presented in this paper. The aim is to improve the general performances of piezocantilevers dedicated to micromanipulation/microassembly tasks. While hysteresis is attenuated using the Prandtl-Ishlinskii inverse model, a new method is proposed to decrease the creep phenomenon. As no model inversion is used, the proposed method is simple and easy to implement. Finally, we employ an input shaping technique to reduce the vibration of the piezocantilevers. The experimental results show the efficiency of the feedforward techniques and their convenience to the micromanipulation/microassembly requirements.

Note to Practitioners-The works presented in this article are motivated by the high performances required in micromanipulation and microassembly tasks. Such a domain requires high accuracy, sometimes submicrometric, and stability of the micromanipulators. While piezoelectric cantilever structures are very widespread in this domain, their nonlinearities and vibrations undeniably limit their performances such as accuracy and overshoots. This may be detrimental for the micromanipulation/microassembly tasks. Feedback control techniques could easily improve their performances but the sizes of accurate and large bandwidth sensors do not make them easily embarkable for micromanipulation/microassembly systems. Thus, controllers without sensors are of great interest. In this paper, we show that open loop control techniques (also called feedforward techniques) can improve the general performance of piezocantilevers dedicated to micromanipulation/microassembly tasks. We notice that the techniques can also be applied to other nonlinear and oscillating systems. One of the main characteristics of micromanipulation/microassembly systems is the high accuracy that they must have to perform tasks. According to the sizes of the manipulated microparts, the required accuracy may be submicrometric. For instance, fixing a micro lens at the tip of an optical fiber with 1µm of relative positioning error or 0.4µrad of orientation error may cause a loss of 50 % of the light flux [8]. In order to reach the required accuracy, microrobots, micromanipulators and gripping tools are designed differently from classical robots and manipulators. Depending on the nature of the micromanipulation/microassembly tasks, and notably on the shape of the manipulated microparts, several gripping tools can be used: microgrippers, needles, vacuum grippers, ice grippers, etc. For flexibility and accuracy reasons, microgrippers are very efficient [7]. Most of positioning and gripping systems are often based on active materials in order to avoid mechanical clearances and then to increase the accuracy. Among active materials, piezoelelectric ones are widespread and their use continues to grow due to their fast response time, high resolution and sensor capabilities. Piezoelectric materials are notably appreciated and very common in piezotube scanners for AFM microscopes, in piezocantilevers and microgrippers for micromanipulation/microassembly and in actuators for step-by-step microrobots. In the case of micromanipulation/microassembly, piezocantilevers and piezoelectric microgrippers (composed of two piezocantilevers) especially offer the possibility to estimate and to control the force at the same time as the positioning control [9] [10].

Unfortunately, like other active materials, performances of piezocantilevers (and piezoelectric materials in general) are strongly affected by nonlinearities. These nonlinearities, which are the hysteresis and the creep, appear in the voltage-strain transfer [11]. While piezoelectric materials present nonlinearities with large electric fields, bending structures (cantilevers) suffer from poorly damped vibrations.

Hysteresis and the creep indeniably influence on the positioning repeatability and the accuracy of the micromanipulation/microassembly systems. It also decreases the accuracy of the force estimation if such a technique is used in the systems. In addition, the vibration critically influences overshoot of micromanipulation forces and may cause damages of manipulated fragile microparts (biological parts, optical parts, etc.) or conversely a rigid micropart may cause the damage of a micromanipulator. Finally, controlling the force may make a release task successful in the presence of adhesion forces.

  compensation, input shaping. I. INTRODUCTION Nowadays, miniaturized systems which integrate more intelligence and functionalities are required more and more. These systems are either micromechanisms (micro ball bearings, microgears, micromotors), micro-optical systems (switches, lasers) or hybrid Micro-Opto-Electro-Mechanical-Systems (MOEMS) like micro-scanners, microspectrometers, or micro-coils [1] [2] [3] [4] [5]. To produce them, monolithic FEMTO-ST Institute, UMR CNRS 6174 -UFC / ENSMM / UTBM Automatic Control and Micro-Mechatronic Systems depart., AS2M 24, rue Alain Savary 25000 Besançon -France {mrakoton,cclevy,plutz}@femto-st.fr Paper type: regular paper. First submission: June 2008. microfabrication can be used but new perspectives are opened with micromanipulation/microassembly techniques, such as hybrid microassembly [6] [7].


G Villemaud

C Decroze

C Dall'omo

T Monediere

B Jecko

DUAL-BAND PRINTED DIPOLE ANTENNA ARRAY FOR AN EMERGENCY RESCUE SYSTEM BASED ON CELLULAR-PHONE LOCALIZATION

Keywords: multiband antenna, direction finding, folded dipole, directive antenna, hybrid array

This paper describes our contribution in the RNRT project called LUTECE, dedicated to the emergency localisation of cellular phones. This contribution takes place in the field of antennas, with the development of two biband systems : a directive array for the emission part, and a circular array of five elements with separated outputs for the receiving part. Different evolutions of these antennas are presented starting from the same basic element, finally optimised on a dielectric substrate to offer good mechanical characteristics. All antennas are studied using our FDTD code.

INTRODUCTION

Emergency rescue in case of avalanches statistics reveal for snow-flooded persons that 92% survive after 15 minutes, but only 30% survive after 45 minutes. Detection of GSM phones appears to be an easy efficient way to accelerate the localisation of these victims. Numerous examples are well known of people rescued by this way, but only when the phone was in base stations range. For the uncovered areas, no solutions are yet studied.

The project LUTECE, managed by the THALES Communications company, proposes to develop a detection system that can be used on board in an helicopter. This project is labelled by the RNRT (Réseau National de Recherche en Télécommunications) and then funded by the French Ministry of Industry. Such a system may allowed fast life saving in desert zones with no need of an important rescue team. Moreover no particular equipment is needed for GSM owners, they only have to put their cellular on wait mode.

To achieve this detection, two different antenna systems are needed, both covering the GSM and DCS bands, while presenting good mechanical characteristics. This paper describes the directive antenna developed for the emission part, and a circular array for the receiving part.

BASIC CONCEPT

System principle

The LUTECE system mainly consists in a Base Station Simulator connected to a directive antenna, used to awake the cellular phone, and a circular array of five antennas, receiving the uplink signal and allowing a DOA (Direction of Arrival) determination (figure 1). Then the helicopter's pilot can be constantly informed of the target's direction.

Antenna needs for the emission part

To achieve a good compromise between a large enough footprint and a sufficient level of gain, an emitting antenna with a halfpower beamwidth of about 45° is required (horizontally polarised).

This antenna also needs to present good matching characteristics (VSWR<2) for all GSM and DCS bands. Furthermore, a mechanical beamsteering will be provided by a tilted platform, in order to cover an area forward the helicopter.

Receiving antennas

Five antennas are needed to operate a good goniometry of the uplink signal. Moreover, these antennas has to form a circular array with separated outputs. Phase and magnitude of the received signal on each antenna are then analysed with a MUSIC-type algorithm to calculate the DOA.

These elements only have to cover the uplink bands for GSM and DCS standards. Large enough apertures are required for each antenna (about 80°), with an horizontal polarisation. Coupling coefficients between those elements also have to be studied and minimised.

BASIC ANTENNA ELEMENT

Working principle

The basic element consists in a folded dipole associated to a limited groundplane [1]. This limitation of the ground allows to obtain large bandwidths, acting as a load when the last part of the dipole is widened [2]. Then to achieve a directive radiation pattern, this structure is placed above a larger ground plane used as a reflector [3]. Afterwards the whole structure is modelled and simulated using a FDTD code, including the rigid coaxial cable jointing the upper and the lower groundplane. The height between the two grounds is then adjusted to optimise the bandwidths while conserving a relatively low profile.

Experimental results

The first topology developed and fabricated is presented on figure 2. The lower ground plane used is a 35 by 35 cm one, and the overall height represents 48 mm. Foam pieces are added to strengthened the structure.

Measurements results show a very good agreement between predicted and effective performances of this element. Large bandwidths are obtained (figure 3) together with good radiated characteristics. A maximum gain of 10 dBi is achieved in the GSM band with halfpower beamwidths of about 70° and a maximum gain of 7 dBi for the DCS band with 100° apertures.

EMITTING ANTENNA RESULTS

On air substrate

Considering the good performances of this basic element, a four elements array based on this topology has been developed to achieve the desired aperture. Due to the biband working of this array, an optimal distance between the elements has to be found to offer the best compromise relatively to the different wavelengths. The proposed structure after FDTD study is shown on figure 4.

As previously, the measurements are in very good agreement with the calculations. The GSM and DCS bandwidths are then largely covered (figure 5).

The obtained radiation patterns are also similar to the predicted ones. Figure 6 presents normalised radiation patterns at GSM and DCS frequencies for the vertical plane corresponding to the larger dimensions of the array.

The measured maximum gain is 13.5 dBi for the GSM band, for an average halfpower beamwidth of 54°, and 13.7 dBi for the DCS band, with an average aperture of 43°.

By the way, this array offers good matching and radiating characteristics, unfortunately along with relatively poor mechanical characteristics, even if foam reinforcements are used.

On dielectric substrate

To prevent mechanical problems, a new solution using a dielectric substrate was explored. The idea is then to print directly the dipoles and the upper grounds on each faces of a 3.175 mm height substrate (permittivity 2.33).

By the way, a new design of the basic element is performed, offering smaller dimensions of only 80x64 mm. This new structure presents narrower bandwidths, but still large enough to cover the desired frequencies.

A four elements array based on this new element was modelled and optimised, finally much more compact than the previous one (194x170 mm). This array has good matching characteristics, but presents an inappropriate halfpower beamwidth of 62° for the GSM frequencies and also some important sidelobes.

Therefore, in order to obtain better performances, an innovative structure was developed, composed of a four biband elements array with a DCS-only element inserted at the center (figure 7). We have then achieved a four elements array for GSM frequencies associated to a five elements array for the DCS band. The spacing between elements can now be more easily adjusted, allowing narrower apertures and lower sidelobes (figure 8).

Regarding these encouraging results, a specific feeding circuit has been studied. This circuit will be placed under the lower ground plane and will provide a feeding of each element with the same phase.

RECEIVING ANTENNAS RESULTS

Nearly the same basic element on dielectric substrate is also intended to be used to receive the uplink signal.

Five separated antennas are needed, with a circular disposition (figure 9). Numerical studies have shown that to consider the coupling coefficients between elements negligible (minor than -30 dB), a very large diameter of the circle is required. Considering the limited space allowed under an helicopter, a close disposition of the elements has been chosen, along with coupling matrix implementation in the DOA algorithm.

Even with such close spacing (approximately 140 mm between two antennas), good matching characteristics are kept, with predicted maximum gains of about 6 dBi

CONCLUSION

Different kinds of antenna systems have been presented in this paper, all based on the same basic element : a folded dipole presenting large bandwidths.

In the field of the LUTECE RNRT project, a directive hybrid five elements array on dielectric substrate allows an efficient emission for cellular phones awaking.

Moreover, five identical antennas disposed in circle can offer good performances to determine the direction of the uplink signal.

ACKNOWLEDGEMENT

We wish like to thanks all partners of the LUTECE project, particularly to the RNRT.

  . Villemaud, C. Decroze, F. Torres, T. Mone´die`re, B. Jecko, Multiband antenna for mobile communication standards, Int Conf Antenna Technol Appl Electromagn, Montre´al, 2002, pp. 533-536. 2. S.S. Sandler and R.W.P. King, Compact conical antennas for wideband coverage, IEEE Trans Antennas Propagat 42 (1994), 436-439.

  3. H.C. Tung, S.T. Fang, and K.L. Wong, Printed dual-band monopole antenna for 2.4/5.2-GHz WLAN access point, Microwave Opt Techonol Lett 35 (2002), 286-288. 4. T.Y. Wu, S.T. Fang, and K.L. Wong, Printed monopole array antenna for WLAN operation in the 2.4/5.8-GHz band, Microwave Opt Techonol Lett 37 (2003), 370-372.5. J.D. Kraus, Antennas, 2nd ed.,McGraw-Hill, New York, 1988, pp. 462-464.

Fig. 1 :

 1 Fig. 1 : LUTECE system structure

Fig. 3 :

 3 Fig. 3 : Comparative return losses

Fig. 6 :

 6 Fig. 6 : Comparative radiation patterns


Guillaume Villemaud
email: guillaume.villemaud@insa-lyon.fr

Pierre-François Morlat

Jacques Verdier

Jean-Marie M Gorce

Marylin Arndt

Coupled Simulation-Measurements Platform for the Evaluation of Frequency-Reuse in the 2.45 GHz ISM band for Multi-mode Nodes with Multiple Antennas

Introduction

It is obvious to say that properly evaluating performance of an entire wireless network is a very hard task. There is for example a deep gap to fill between purely theoretical approaches of radio link capacity and effective QoS results on an exploited network. Moreover, the increasing complexity of RF systems conduces to numerous hard issues such as antenna coupling, RF impairments influence, interference mitigation capability, etc... Large efforts are made to offer more and more precise simulation of large scale wireless networks (e.g. wireless sensor networks WSN) with enhanced modelling of radio link performance. [START_REF] Ben Hamida | Impact of the Physical Layer Modeling on the Accuracy and Scalability of Wireless Network Simulation[END_REF] discusses the accuracy of radio link modelling needed to ensure efficient network simulators. Authors had proposed an event-driven network simulator with a particular attention paid to PHY layer modelling, whereas only based on analytical formulation transforming SINR (signal to interference plus noise ratio) information in terms of BER (bit error rate) or PER (packet error rate). This relation between SINR and BER, whatever its formulation, is required to render the very complex behaviour of the radio link, far away from the often used spherical or omnidirectional models for nodes coverage. A radio link suffers from additional effects of pathloss, shadowing and fading. To overcome the limitation of only defining a static threshold depending on distance (i.e. mainly pathloss exponent), it is important to take into account the temporal and spatial variability of the link. Thus the real capacity of a link is not only depending on an average value of the received power, but also on the temporal behaviour of this power. Most of capacity studies are based on statistical laws such as Rice, Rayleigh or Nakagami-m ones, allowing extracting some theoretical boundaries for example in terms of packet error outage [START_REF] Mary | M-ary Symbol Error Outage Over Nakagami-m Fading Channels in Shadowing Environments[END_REF]. These statistical laws were developed to fit intensive measurement campaigns. These campaigns try to represent all kinds of environments and topologies which is very difficult considering the very large number of possibilities. Indeed, numerous solutions are also proposed to replace empirical approaches based on measurements by wave propagation simulations. For example [START_REF] De La Roche | On predicting Fast Fading Strength from indoor 802.11 Simulations, ICEAA 2007[END_REF] and [START_REF] Pereira | Sensitivity of the MIMO Channel Characterization to the Modeling of the Environment[END_REF] propose some solutions to add statistical analysis upon a deterministic wave propagation tool. This kind of analysis allows a better prediction of wireless link capacity than a pure average power consideration. Hence, a good evaluation of wireless network performance could be based on associating precise wireless link models with a network simulator. A very interesting study of extracting radio link behaviour from measurements to feed GloMoSim simulator [START_REF] Zeng | GloMoSim: A Library for Parallel Simulation of Large-ScaleWireless Networks[END_REF]6] could be find in [START_REF] Zhou | Models and solutions for radio irregularity in wireless sensor networks[END_REF]. Also [START_REF] Kashyap | A Measurement-Based Approach to Modeling Link Capacity in 802.11-based Wireless Networks[END_REF] investigates 802.11 links through measurement values used to drive a Markov chains model of the considered network. [START_REF] Stepanov | On the impact of a more realistic physical layer on MANET simulations results[END_REF][START_REF] Dricot | High-accuracy physical layer model for wireless network simulations in NS-2[END_REF] propose interconnection of NS2 [11] with raytracing wave propagation tools to offer more realism in each link. But even if the use of concurrent communications in different standards is a hot topic, it still remains an important need for a complete system evaluation of radio transmission scheme with enhanced realism both for radio channel and terminal's architecture. Particularly, as far as we know, the influence of strongly overlapping interfering channel with a different communication standard is never considered. As we will present in the next section, trying to model performance in such a context without taking into account actual capabilities of terminal architectures often conduces to strong constrains on frequency reuse in dense areas. To tend to a realistic evaluation of a complete complex transmission scheme with concurrent signals, it is necessary to use some dedicated hardware connected to system-level simulator. System-level simulators are able to really create a radiofrequency signal based on the used communication standard that will be used in a measurement platform, and the measured received signal will be re-injected in the simulator to emulate the receiver part of the link. In this paper, we propose the use of such a simulation-hardware connected solution to evaluate the capability of using overlapping channels in the 2.45 GHz ISM band with different PHY standards with an emphasis on a realistic multiple antenna architecture at the receiver. From our point of view, this approach is greatly necessary to address the whole complexity of such a system and to offer a good evaluation of expectable performance, possibly to extract better models for large scale simulation. Moreover, adding a complete modelling of the receiver architecture with non-ideal RF components to a real radio channel measurement will offer a reduced development cycle of future terminals with enhanced capacity. This paper is organized as follows. Section 2 explains the context of overlapped channels and offered possibilities if a terminal can manage correctly two overlapped channels. Section 3 presents simulation and measurement tools used to precisely evaluate allowed performance in this study case. Detailed results comparing simulations and experiments are given in Section 4 showing the wide area of possible studies with this approach. Section 6 includes discussion and conclusion.

Study Case and Possible Scenarios

2.1 Context. The 2.45 GHz ISM band is well known to host lots of competitive radio standards. Even if we only consider IEEE 802.11 standards, channels are defined with only 5 MHz separation while occupying at least a 20 MHz bandwidth. So adjacent channels are strongly overlapping, therefore interfering. Then it is commonly admitted for WiFi system deployment that a frequency allocation panel (FAP) may use only 3 non-interfering channels in the whole band, otherwise it leads to complex optimization problems [START_REF] De La Roche | A QoS-based FAP criterion for Indoor 802[END_REF]. Moreover, additional technologies such as Bluetooth or ZigBee are sharing this band, producing a large amount of possible interference.

Study

Case. The study case we depict here is one of a terminal able to receive a 40 MHz bandwidth signal (i.e. possibly containing up to 5 overlapped channels). Considering that this receiver has multimode capabilities (by the way of multiple dedicated chips or ideally software defined radio structure), we would like to appreciate possible performance while receiving information on two overlapped channels with different standards. Several approaches could be considered to mitigate or suppress interference. One way is to use interference cancellation techniques like multi-user detection as presented in [START_REF] Mary | Performance Analysis of Mitigated Asynchronous Spectrally-Overlapping WLAN Interference[END_REF][START_REF] Mary | Reduced Complexity MUD-MLSE Receiver for Partially-Overlapping WLAN-Like Interference in Heterogeneous Multipath Channels[END_REF]. This way becomes harder (i.e. resource-consuming) in the case of interference from various standards. Another way is to use multipleantenna techniques, enabling spatial rejection of the interfering signal. That is the way we here focus on, considering that more and more terminals tend to be equipped of two or more antennas in order to be compatible with new MIMO standards. MIMO systems require multiple antennas, hence multiple RF chains and digital processing capabilities, but all devices are not always using MIMO modes, depending on the network architecture and the radio channel conditions. However, multiple-antenna resources could be used to perform effective interference mitigation for the simpler radio modes, by the way operating a real multi-mode interference mitigation which is not dependent on the chosen standards. For the sake of understanding, we will here present only results with non-MIMO standards, i.e. without space-time coding, but results are not limited to mono-antenna standards.

Hence, considered communication standards will be IEEE 802.11b and IEEE 802.11g. Obviously these standards are not new, but offer the advantage of a large background of theoretical study and complementarities of used waveforms. 802.11b uses a spread spectrum technique (DSSS) while 802.11g uses orthogonal frequency division multiplexing (OFDM) signals. Those two kinds of waveforms do not have the same sensitivity to interference, and we of course suppose here that there is no coordination between concurrent signals, that is no common MAC layer. Moreover, DSSS and OFDM are basis of lots of standards intended to be used for wireless personal area networks (WPAN), wireless sensor networks (WSN) or even body area networks (BAN). We could refer to ZigBee or Bluetooth 3.0 as examples, but also lots of customized technologies. Subsequently results will be presented on two concurrent communications on 20 MHz bandwidth each, possibly overlapping in the whole 40 MHz bandwidth of the receiver.

Scenarios.

We could think about various topologies open to improvement with through approach. The main point is that the studied node has multi-mode (802.11b and 802.11g), multi-channel (40 MHz instantaneous received bandwidth) and multiantenna (2 or more branches). We refer at this kind of terminal as a multi-* node. Figures 1 to 3 present examples of possible usage enabling a more efficient reuse of frequencies. Figure 1 depicts the case of a multi* node receiving signals from two access points (AP) using overlapped channels. If this terminal is able to efficiently separate those two incoming signals, it could receive twice the throughput of a classical system without the need of using two widely spaced channels. It emphasizes that not only the FAP is simplified, but also that multiroute approaches or network coding could be used rather than collaborative schemes or distributed MIMO, more difficult to implement (i.e. supposing modifying PHY or MAC layers). This scenario also offers the possibility for a multi-* node to get access to two different networks at the same time for two different applications without requiring two different hardware. On Figure 2, we consider a case of a multi-* node receiving information from an AP and another mobile user at the same time. This could be in the case of a mesh network, where multi-* node could act as a relay for the MU in bad receiving conditions. This also could be, as in the first scenario, to maintain two different connections simultaneously, for example a laptop connected to Internet through the AP and to a wireless peripheral at the same time. Finally, Figure 3 shows a case of a distributed network, ad hoc or WSN for example. Several neighbours could try to send data to the multi-* node at the same time on different channels. For the sake of comprehensiveness, in this figure we represent two non-overlapped channels, which could occur in the 40 MHz studied band, but one can understand that any combination of used channels is interesting to compare. Of course, those presented scenarios are here to illustrate so possible network architectures where presented results offer interesting perspectives. Following results will be only discussed in terms of radio link behaviour and could be applied in any of those topologies.

From this point it is important to underline that we only consider in this paper the receiver part of the problem. One reason is that, as said before, we do not want to analyze natively MIMO modes. Here is the point: our approach does not necessarily require that all nodes have multi-* ability and no pre-coding at the emitter is needed. The other reason is that our aim is to mutualise information from concurrent networks, that is to say received signals are never synchronized. The hard point is here clearly in the receiver part, aiming that the multi-* node could easily coordinate its emitted signals, and moreover could eventually use beamforming to emit signals simultaneously without interfering.

We will present in the next section the Agilent Platform used and the associated tools enabling to precisely evaluate the behaviour of such concurrent communications, and effective results are exposed in Section 4. We can use this platform to generate any kind of complex waveforms, connect any kind of antenna (omnidirectional or directional, simple or dualpolarized). The two ESG could be finely synchronized in the case of a real MIMO system, but of course in the present study case could also be completely de-synchronized and then emit different standards.

Simulation and Measurement Tools

The two RF inputs of the VSA could also be connected to any kind of antennas, and the VSA chassis is mobile, enabling to test different radio channel conditions. In each of these cases, this interaction with software analysis could bring a lot of information: power level, frequency domain spectrum, time domain received frames, Error Vector Magnitude (EVM), constellation, and finally the more representative one for performance evaluation: bit-error-rate (BER). With the connected solution, received signals could be directly analyzed through VSA software tool, or could be re-injected in an ADS simulation to feed simulated receiver structures.

It is important to understand that each block on Figure 4 is a high-level representation, Ptolemy offering the possibility to finely describe the content of each part of the system down to discrete RF or digital components. Moreover, a great interest of this solution is co-simulation possibilities. For example, the dataflow simulator can be linked to a frequency domain simulator called harmonic balance in order to accurately take into account the influence of RF components spectral behaviour. Furthermore, cosimulation with Matlab is also helpfull, enabling to easily implement signal processing algorithms in the receiver structure (e.g. multi-antenna processing).

Radio channel analysis.

To be sure that further performance evaluation in the context of concurrent communications is significant, first validation of our platform is there presented. Further, an analysis of a realistic indoor radio channel is exposed.

AWGN validation.

At first, in order to validate the structure of our radio platform, first tests were realized in a Single-Input Single-Output (SISO) configuration under Average White Gaussian Noise (AWGN) condition, i.e. a single path between emitter and receiver without shadowing or fading. Figure 5 presents results we obtained for an 11 Mbps AWGN 802.11b transmission.

For each Eb/No, 10 000 frames of 100 bytes are emitted and demodulated to accurately estimate the corresponding BER. The theoretical 11 Mbps 802.11b BER variation was computed according to (1) [START_REF] Borgo | Analysis of the hidden terminal effect in multi-rate IEEE 802.11b networks[END_REF]:

dv v dy y BER N X X v X v         - ⋅                 - - = - ∞ - + - - ∫ ∫ 2 1 2 2 2 exp 2 exp 2 1 1 π (1)
Where No Eb X ⋅ = 2 and N=8 in the case of an 11

Mbps transmission.

Whereas those measurements were not obtained in an anechoic chamber but in a close and static line-ofsight working condition, one can see a very good agreement between theory, pure simulation and measurements.

Other tests were done for an uncoded 36 Mbps 802.11g SISO transmission, under an AWGN propagation channel. For such a data rate, a 16-QAM modulation scheme is used. The theoretical Symbol Error Probability P s for a M-QAM is computed considering two independent M PAM modulations on both I-and Q-channels [START_REF] Proakis | Digital Communications[END_REF]:

(

with :

( )

        -       - = b M M M Q M P γ 1 log 3 1 1 2 2 (3)
where b γ denotes the energy per bit to noise ratio (Eb/No) and Q the Gaussian function.

The relationship between the Signal to Noise Ratio (SNR), the transmission data rate, the coding rate Rc, the signal bandwidth (BW) and b γ is given by:

b c BW R rate data SNR γ ⋅ ⋅ = _ (4)
Where BW = 20 MHz, and Rc=3/4 in the case of a 802.11g transmission [START_REF]Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: Further Higher Data Rate Extension in the 2.4 GHz Band[END_REF].

In the end, the theoretical Bit Error Probability (BER) is:

Realistic indoor channel analysis.

While we could be confident in our connected solution to model AWGN conditions, we can then try to analyze the mian characteristics of the indoor radio channel we will use in our scenarios. Our aim is to study SIMO performance under realistic working conditions. In this context, antenna coupling, channel correlation, and also different propagation conditions must be introduced in the measurement system. Depending on the current capabilities of our platform only 1x2 SIMO configuration is possible for each concurrent link. Correlation of received signals and antenna coupling introduce loss of information diversity, and then a reduction of SIMO performance. Envelope correlation ρ between two signals x and y is computed according to (6) [START_REF] Dietze | Analysis of a two-branches maximal ratio an selection diversity system with inequal SNRs and correlated Inputs for a Rayleigh Fading Channel[END_REF]:

[ ] ( ) ( ) 2 2 ) ( ) ( ) ( ) ( y y E x x E y y x x E - ⋅ - - ⋅ - = ρ (6)
where E(.) denotes the expected value and A very low envelope correlation (ρ<0.5) is observed. Obviously, a quite constant BER is also obtained, proving that for all distance between the two antennas, correlation has no influence on system's performance. For different antenna spacing, coupling between the two arms (S12 parameter) is computed and the maximum value, obtained for a distance of 0.3 λ is equal to -20 dB. That is why, coupling effect between receiving antennas could be considered as negligible.

Another point is studying polarization behaviour. This point is often omitted in wireless link studies, whereas polarization diversity could be as rich as spatial one. By the use of dual-polarized patch antennas, we also have tested received power on each polarization (with only vertical or horizontal polarization at the emitter) and correlation between cross polarizations. Results shown in Figure 7 emphasize the power balance between vertical and horizontal polarization at the receiver for a vertically polarized emitter. This power balance reveals that in short range LOS conditions, the emitted polarization could be 7.5 dB above the perpendicular one, but till NLOS conditions are established, the power is equally divided between horizontal and vertical polarizations at the receiver. Moreover, correlation factor between orthogonal polarizations was always found lower than 0.35. Therefore we could consider that resorting to dually polarized antennas offers the high degree of diversity needed for interference rejection.

Finally, fine characterization of the propagation channel was realized. To be able to describe multipath behaviour of indoor channels, we use the emission of repetitive pseudo-noise sequences (PN9). At the receiver, recorded received signals are correlated with the reference PN9 sequence in order to separate all delayed paths. This approach allows to extract the Power Delay Profile (PDP) of the measured channel, and also to analyze the temporal evolution of this PDP on a long-term point of view. One example of measured PDP in indoor multi-path environment is given on Figure 8. The measured NLOS channel used has a delay spread much less important (about 76 ns, τrms = 35 ns) than the often used channel model ETSI-A for office environment (delay spread = 390 ns, τrms = 50ns) [START_REF]Channels Models of Hiperlan/2 in different indoor Scenarios[END_REF]. Amplitude distribution fits a Rayleigh law, which increases the interest of spatial diversity, and the coherence bandwidth of the considered multi-path channel is 5.2 MHz, signifying that also frequency diversity has to be considered for 802.11g OFDM signals.

Therefore, some feedback in our connected solution was performed. Actually, in order to ensure an easier comparison between simulation and measurements, a customized multipath channel block is defined in Ptolemy schemes fed with measurements data. This approach is twofold: used channel model is a better representation of our measurement conditions than ETSI-A models, and also this also a reduction of the number of simulated paths, i.e. reduction of simulation time. Consequently, we have a finely tuned connected solution, permitting a quick comparison between simulated and measured performance. This platform will then be used in the next section to analyze possible performance with multi-* devices.

Simulated and Experimental results for multi-* nodes

4.1 Mono-mode performance. Let us remind here that studied multi-* nodes have a receive bandwidth of 40 MHz (hence multi-channel, see Figure 9), multi-mode capability (802.11b or 802.11g received frames) and multi-antenna structure. A first point is to verify available performance with multi-antenna processing in this kind of architecture. [START_REF] Godara | Application of antenna arrays to mobile communications, part II: beam forming and direction of arrival considerations[END_REF]. In our case, we consider mobile receivers mostly used in indoor environments, with large angular spread, so it is very difficult to calculate the Direction of Arrival of Signal of Interest with algorithms such as ESPRIT or MUSIC [START_REF] Sarkar | Smart Antennas[END_REF] which also have an important computational complexity. Therefore we prefer to take advantage of the training sequence used in 802.11 receivers [START_REF]Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: Further Higher Data Rate Extension in the 2.4 GHz Band[END_REF] and to compute the optimal combination (Figure 10) of different signals with the help of an adaptive algorithm with a Minimum Mean Square Error (MMSE) criterion. A simple adaptive algorithm is the Least Mean Square (LMS) which has a low complexity of O(N), but this algorithm has a very slow convergence.

Taking into account that the training sequence time of an 802.11g burst is small, it is preferable to use SMI which offers a faster convergence, even if SMI has a greater complexity of ) ( 3 N O . We apply the Sample Matrix Inversion (SMI) algorithm [START_REF] Gupta | SMI adaptive antenna arrays for weak interfering signals[END_REF] in the temporal domain, directly after downconversion on an N elements array. The array element spacing is λ/2 with λ the wavelength. We define the signals at the element inputs by ) ( ),..., ( 1 i s i s N and the input signal vector by:

S(i) = [ ] T N i s i s ) ( ),..., ( 1 (7)
where T denotes the transpose operation. The covariance matrix R and the cross covariance vector r are estimated with K samples of the signal vector (K is the number of sample of the training sequence d):

∑ = ⋅ = K n H i S i S K R 1 ) ( ) ( 1 ( 8
)
where H denotes the transpose and conjugate operation. Of course, results presented in this paper using connected solution will only use two branches of diversity but results could be extended to larger cases. Dedicated Matlab codes were developed for ADS cosimulation for two purposes. The first one is the detection of received signals on each RF inputs of the VSA, the second one to apply SMI algorithm to signals after all steps of synchronization performed by ADS blocks.

∑ = ⋅ = K n H i d i S K r 1 ) ( ) ( 1
As first results of our multi-antenna testbed, we can see on figures 11 and 12 the bit-error-rate performance of 1x2 SIMO transmissions (i.e. one emitting antenna and two receiving antennas) compared to a classical SISO case for both standards in a simple AWGN channel. In both case, we retrieve the well-known consideration that in an AWGN channel, a diversity structure of order 2 produces a 3 dB decrease of required SNR for a targeted BER. Another point presented in Figure 13 is the available diversity depending of channel characteristics. As previously discussed in section 3.3.2, studied multipath channel with our radio platform is shorter than ETSI-A model. Consequently, BER performance appears better for an equivalent SNR, while diversity degree is quite the same, offering the same rejection capacity. 4.2 Multi-* performance. In multi-* operating mode, we would like to evaluate performance when two overlapped channels with different modes are received. The first scenario presented corresponds to two emitters, one on 802.11b mode, the other one on 802.11g mode. We analyze here results in a multipath environment, hence non-line-of-sight (NLOS) conditions. Nevertheless received SNR for both channels are kept constant, corresponding in each case of the required SNR to reach a 5.10 -3 BER without any concurrent communication in a SISO configuration (only one received antenna). This supposes that the radio link would be quite good with only one of those two links. But in our configuration, both links are maintained at the same time and moreover on overlapped channels (see Figure 14). The separation between centre frequency of each channel, also called channel spacing ∆ is then varied from 0 (co-channel interference) to 15 MHz. Table 2 summarizes mean measured values obtained with our radio platform. We compare BER obtained with or without SIMO processing at receiver. Obviously, with co-channel interference in SISO configuration, radio links are unusable, BER reaches 0.5. In this co-channel configuration, SIMO processing does not bring a sufficient performance enhancement to expect channel reuse. But it can be observe a quick decrease of BER till a 5 MHz channel spacing with the use of multi-antenna processing. This supposes that multi-* devices allow a better frequency reuse and can support simultaneous connections with different modes on strongly overlapped channels.

Of course, obtained BER values depend directly on exact operating conditions (emitters positions, received power, channel type…). But in every tested condition we found the same global behaviour meaning that till a 10 MHz channel spacing parallel communications could be maintained.

Another test is presented on Figure 15. On that case, channel spacing is fixed at 10 MHz. The 802.11b link (in red channel) is maintained as previously at the SNR level corresponding to a 5.10 -3 BER without any concurrent communication in a SISO. Then the power of the 802.11g channel is progressively increased. BER curves are shown on Figure 16. We can observe that in a SISO case, 802.11b link is rapidly degraded when the 802.11g interferer increases in power, thus none of those two links appear exploitable. But with antenna processing (blue lines), we can see that an interesting trade-off could be found to ensure two parallel available radio links.

Discussion and Conclusion

Of course multi-antenna processing is not a novelty and already often considered in large-scale wireless networks studies. Hybrid multi-mode terminal use is also a largely studied item. But as far as we know combining multiple modes with multiple antennas in multiple overlapped channels was never considered, whereas it here appears to be an interesting way of enhancing spectral usage. This way of considering simultaneous connections could be compared to distributed or collaborative MIMO techniques, where several nodes transmit at the same time on common channels. But here we have shown that without any precoding and even with different standards we could reach interesting performance and ensure a better frequency reuse.

Our approach was to establish a complete connected solution with simulation-measurement coupling for a complete and fast analysis of complex radio links.

This solution allows a great realism of node architectures and can be studied further on. We are now focusing on enhancing the simulation of RF architecture in order to design efficient terminal structures for multi-* nodes. One first step is a better simulation of realistic RF components, particularly of RF impairments. A study of the impact of such impairments on effective radio link performance could be found in [START_REF] Morlat | On the compensation of RF Impairments with Multiple Antennas in SIMO-OFDM Systems[END_REF]. Another important point is to found efficient way of creating multi-* nodes without notably increasing complexity and consumption. Some possible ideas are proposed in [START_REF] Gautier | IQ imbalance reduction in a SMI multi-antenna receiver by using a code multiplexing front-end[END_REF], but this aspect greatly depends on targeted networks.

From this point we can emphasize some observations. Multiplying degrees of freedom surely offers promising possibilities at the PHY layer in order to increase spectral efficiency of networks. Nevertheless, it remains that the number of available parallel channels is directly related to the number of antennas.

To overcome this limitation, our approach needs to be combined with interference cancellation algorithms. Furthermore, to be efficient in a mesh or ad hoc configuration, this approach needs to be studied in a cross-layer point-of-view, supposing that a common MAC layer could use two different simultaneous PHY links.

Therefore, this coupled system-level simulation and measurement platform could bring some efficient evaluation of realistic radio links and could be used to feed network-level simulators with precise values. This platform could also be used to calibrate wave propagation prediction tools, or also to implement natively MIMO standards like WiMax or LTE. First results with this connected solution of frequency-agile RF architectures proposed for LTE-Advanced multiband operation are very promising. Only this kind of high quality hardware could offer the possibility of studying future possible architectures at a reasonable cost with trustable results.

FIGURE 1 :

 1 FIGURE 1: One multiband terminal receiving signals from two access points on overlapped channels.

FIGURE 2 :

 2 FIGURE 2: One multiband terminal receiving signals from one access point and one other mobile unit (MU) on overlapped channels.

FIGURE 3 :

 3 FIGURE 3: One multiband terminal receiving signals from two over mobile units on non-overlapped channels.

FIGURE 4 :

 4 FIGURE 4: 2x2 MIMO radio platform with connected solution with ADS software.

FIGURE 5 :

 5 FIGURE 5: 802.11b AWGN compared results. Eb/No -dB

Figure 6

 6 Figure 6 compares simulated, measured and theoretical BER for an uncoded 36 Mbps 802.11g (16-QAM) transmission. In order to obtain a targeted BER value estimation (variance of 10 -2 ), 10 000 frames of 200 bytes are transmitted in measure and simulation tests for each SNR value. A good matching between the different data can be observed (deviation is around only 1 dB).

FIGURE 8 :

 8 FIGURE 8: Power Delay Profile

FIGURE 9 :

 9 FIGURE 9: Example of received 40 MHz signal on one antenna and obtained signals after channel filtering.

FIGURE 7 :

 7 FIGURE 7: Map of indoor polarization measurements and average power balance (in dB) between vertical en horizontal polarizations at receiving points.

FIGURE 10 :

 10 FIGURE 10: Diversity combining structure Lots of different algorithms exist to take advantage of spatial diversity and to combine different signals arriving at the same receiver[START_REF] Godara | Application of antenna arrays to mobile communications, part II: beam forming and direction of arrival considerations[END_REF]. In our case, we consider mobile receivers mostly used in indoor environments, with large angular spread, so it is very difficult to calculate the Direction of Arrival of Signal of Interest with algorithms such as ESPRIT or MUSIC[START_REF] Sarkar | Smart Antennas[END_REF] which also have an important computational complexity. Therefore we prefer to take advantage of the training sequence used in 802.11 receivers[START_REF]Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications: Further Higher Data Rate Extension in the 2.4 GHz Band[END_REF] and to compute the optimal combination (Figure10) of different signals with the help of an adaptive algorithm with a Minimum Mean Square Error (MMSE) criterion. A simple adaptive algorithm is the Least Mean Square (LMS) which has a low complexity of O(N), but this algorithm has a very slow convergence.

  to apply to different signals, an approximate solution to the MMSE problem is calculated as:

FIGURE 11 :FIGURE 12 :

 1112 FIGURE 11: BER versus Eb/No for an 802.11b transmission with one or two received antennas in an AWGN channel.

FIGURE 13 :

 13 FIGURE 13: BER versus Eb/No for an 802.11g transmission with two received antennas in different channels.

FIGURE 16 :

 16 FIGURE 16: BER depending on 802.11g received power for a channel spacing of 10 MHz in a multipath environment.

TABLE 1 :

 1 Correlation value as a function of antenna spacing.

	x =	E	(x	)	.
	Table 1 presents correlation value in function of the
	antenna spacing d (a fraction of wave length λ) in the
	case of a NLOS (Non Line of Sight) transmission
	configuration. For each distance value, we also give

TABLE 2 :

 2 Obtained BER with measured channels depending on channel spacing and antenna configuration.

	SISO AWGN simulation
	SISO AWGN measure
	SIMO AWGN simulation
	SIMO AWGN measure
	SIMO ETSI-A
	SIMO Multi-path measured
	SIMO Multi-path simulated
	SIMO AWGN measure

FIGURE 15: Definition of study case with overlapping channels and variable power of 802.11g signal. 802.11g received power (dBm)

Acknowledgements

Authors wish to thank Orange Labs for supporting this work and Agilent technologies for collaborating on connecting solution development.