Paulette Gavignet

Jean-Luc Barbey

Hisao Nakajima

Thierry Guillossou

SOA-Based Label Extractor for Optical Burst Switching Application

Keywords: Optical Burst Switching (OBS), Semiconductor Optical Amplifiers, Optical signal detection

I. INTRODUCTION

HE increasing traffic in transport networks and its packet nature has pushed the Optical Burst Switching (OBS) solutions emergence. Since more than ten years many implementations have been tested with various architectures and core/edge node options including the label processing. According to the area covered by the label, a read and rewrite process can be necessary. In the case of the Labeled OBS (L-OBS) core node presented in [START_REF] Legrand | Labelled OBS Test Bed for Contention Resolution Study[END_REF] the label is only read and is not rewritten as it is supposed valid in the whole network.

The foundation of the OBS concept is to switch the data in the optical domain, the label/BCP (Burst Control Packet) is the only part of the signal to be processed, hence converted into the electrical domain. In the conventional OBS (C-OBS), the BCP is sent over a proper wavelength prior to the corresponding payload burst with an appropriate offset time for the node elements configuration. It can suffer from BCP loss as well as payload loss. In [START_REF] Legrand | Labelled OBS Test Bed for Contention Resolution Study[END_REF] we have shown that L-OBS P. Gavignet, J.-L. Barbey, H. Nakajima, and T. Guillossou are with Orange Labs Networks, Lannion Cedex 22307, France (e-mail: paulette.gavignet@orange.com; jeanluc.barbey@orange.com; b4na.kaji. mmec1@orange.fr; thierry.guillossou@orange.com). A. Carer is with the Institut National de Recherche en Informatique et en Automatique/Institut de Recherche en Informatique et Systèmes Aléatoires, Université de Rennes 1, Rennes 35065, France (e-mail: arnaud.carer@irisa.fr). Color versions of one or more of the figures in this letter are available online at http://ieeexplore.ieee.org.

with label tied to the payload leads to better burst loss probabilities than C-OBS. In the L-OBS implementation, the label has the same wavelength as the payload, and is transmitted in the optical domain inside the node as it is valid for the entire path into the network (from source to destination). To cope with this implementation a conventional label extraction technique consists in picking up part of the input optical signal through an optical coupler and converts it in the electrical domain [START_REF] Chiaroni | Demonstration of the Interconnection of Two Optical Packet Rings with a Hybrid Optoelectronic Packet Router[END_REF]. Then the label is electronically separated from the payload. Note that the optical power at the output port of the coupler is smaller than at the input one. This is one drawback of this technique for the OBS node application.

The L-OBS demonstrator presented in [START_REF] Legrand | Labelled OBS Test Bed for Contention Resolution Study[END_REF] was built to validate the simulation results showing the interest of the L-OBS compared to C-OBS and assess performances and limitations of the key functions. The label extractor is one key function for asynchronous bursts handling. Prior work [START_REF] Lee | Demonstration of optical label detection and 10 Gbit/s packet routing using 4x4 optical crosspoint switch[END_REF] presents label detection with an optical label operating at a different wavelength than the payload. We present here an original solution of label reading which copes with asynchronous burst arrival while optically transmitting the entire burst (label plus payload) with an optical gain. For this purpose we use the amplifying detection mode of a Semiconductor Optical Amplifier (SOA) [START_REF] Gustavsson | Travelingwave Semiconductor Laser Amplifier Detectors[END_REF][START_REF] Rampone | Semiconductor Optical Amplifier Used as an In-Line Detector with the Signal DC-Component Conservation[END_REF][START_REF] Fortenberry | Up to 16 dB Improvement in Detected Voltage using Two-Section Semiconductor Optical Amplifier Detector[END_REF]. Indeed it optically amplifies the signal going through the SOA and allows obtaining an electrical copy of the signal (for a frequency range of several hundreds of MHz, limited by the stray capacitance and carrier lifetimes of the SOA). The paper assesses the working range of the extractor according to the optical input power and the SOA bias current using burst loss rate measurement results. First part of the paper is a reminder of the L-OBS node architecture; then, the extractor and its electrical circuitry are presented. Finally we show burst loss rate results confirming the utilization range of the device.

II. DESCRIPTION OF THE L-OBS NODE

The global scheme of the L-OBS core node is presented in Fig. 1. The principle of the node is to switch each input burst of each ingress port to the correct egress port according to the information contained in the label. The node makes a burst contention resolution using both wavelength and time domains. The routing inside the node is based on wavelength. The bursts are composed of a label of 16 bits at 155 Mbps and a variable length payload at 10 Gbps making them a total burst length between 1 and 100 µs. The 16 bits of the label have the respective functions of: 1) Delimiter for the 8 first bits 2) Egress port number for the 2 following bits and 3) Burst duration for the last 6 bits.

At each ingress port of the node, a Label Extractor (LExt) makes the extraction of the burst label signal which is sent to the Control Unit (CU). The CU (based on a 100 MHz FPGA) processes the label and configures the switch matrix according to the result of a scheduling algorithm performed to avoid contention using wavelength and time domains. As the labels arrive at an asynchronous rhythm, the inputs of the CU are periodically scanned (every 80 ns) in order to detect the eventual arrival of a new label on a port. The bits of label arriving on the CU are then processed to detect the validity of the label (correct delimiter) and then perform the scheduling.

In case no resources are found (blocking), the burst is discarded and a counter is incremented in the FPGA indicating the reason (lack of processing resources, lack of wavelength or lack of Tunable Delay Line (TDL)). 528 counters and comparators inside the FPGA monitor each transit burst in the system. This massive parallelized processing allows to monitor all the transit bursts and to choose in 2 µs latency a free route for a new burst. A burst number monitoring counter is also incremented for each detected burst of each ingress port of the CU. During the label processing, the optical signal passes through a 2 µs calibrated Fiber Delay Line (FDL) in order to let the CU send the control information to both the Tunable Wavelength Converters (TWC) and eventually a TDL. The bursts are wavelength routed to the egress ports via the demultiplexer on a wavelength basis.

In our L-OBS solution the bursts arrive asynchronously and the labels are recovered at the burst rhythm in less than 2 µs. Optical Amplifier SOA-S-OEC-1550 used in the amplifying detection mode and an electronic circuitry which recovers the label signal from the detected signal.

III. DESCRIPTION OF THE EXTRACTOR

The electrically detected signal is amplified (RF AMP), then filtered using a 150 MHz Low Pass Filter (LPF) in order to keep only the 155 Mbps label signal. A 100 MHz RC High Pass Filter (HPF) acting as a differentiator takes a time derivative of the signal. Then the signal is sent into a high speed comparator with hysteresis (ACDMP 552 from Analog Devices) where the label signal is recovered. Finally it is converted into the LV-PECL format signal to cope with the FPGA board input format. The power consumption of the extractor is about 1.4 W excluding the thermoelectric cooler's one. The RF amplifier itself consumes nearly 1W. Note that feeding the derivative signal to the comparator's input can avoid zero level fluctuations issues that are inherent when handling the signal without the DC component. Fig. 3 shows oscilloscope traces, for an SOA bias current (I SOA ) of 50 mA and an input power (Pi) of -16 dBm at λ=1550 nm, corresponding to the optical burst input (a) and the optical burst output (b) (after O/E conversion). Figs. 3c,3d and 3e are respectively the electrical signals at the bias tee, the RF amplifier and the HPF outputs. Fig. 3f shows the extracted label after the recovery and the LV-PECL adaptation. The bits stream corresponds well to the emitted label sequence. Underdamping trace shown in Fig. 3f stems from an impedance mismatching between the oscilloscope and the LV-PECL output. We can see that the first filtering process is achieved inside the SOA (Fig. 3c) as the detection bandwidth is limited to several hundreds of MHz according to several parameters like input wavelength, optical input power and SOA bias current.

IV. PERFORMANCES OF THE EXTRACTOR

Four extractors were built in order to equip each input port of the L-OBS demonstrator presented in Fig. 1. In order to test the utilization range of the extractor, we have made several tests with various values of optical input power (Pi) and bias current (I SOA ) for the SOA of the extractor. The Anritsu MP1810A bursts generator is configured to work at 9.92 GHz which is an integral multiple (i.e. 64) of 155 MHz; thus each bit of label is coded with 64 bits at 9.92 GHz. Tests were performed with two bursts size: 9920 bits corresponding to the shortest burst duration of 1 µs in the demonstrator and 49600 bits (5 µs bursts). The inter-burst was in both cases equal to 1984 bits during which no signal was transmitted; it corresponds to the shortest inter-burst duration of 200 ns. The goal of the tests was to determine in which conditions of I SOA and/or Pi in the SOA, the bursts were correctly detected. For that purpose we have measured the difference between the theoretical number of bursts emitted by the burst generator (N T ) and the effective number of bursts detected (N D ) by the CU (FPGA) during a time interval of measurement. As indicated in section II, the burst number (N D ) monitoring counter is incremented in the FPGA for each detected burst of each ingress port. We used this counter to deduce the number of undetected bursts. Then we have plotted the ratio (N T -N D )/N T , which gives the undetected bursts ratio of the couple Label Extractor-CU. According to the quality of the signal at the label output (see Fig. 2), the FPGA is capable or not of detecting the input bursts. If I SOA and Pi are not well chosen, the label bits are distorted and the FPGA is unable to identify and count the bursts up.

We consider that the working range of the LExt corresponds to the range of values of optical input power (Pi) and/or bias current (I SOA ) for which the bursts are correctly detected (i.e. the undetected bursts ratio is zero). However due to instabilities in FPGA clock, there is always a small difference when comparing N T to N D . Indeed the clock of the FPGA, which is independent of that of the burst emitter, is not as stable as the bursts emitter's one as there is no temperature compensation. Its stability is about 10 ppm compared to 1 ppm for the burst generator. Thus observing the detected labels (as in Fig. 3f) and the decisions taken by the CU in terms of output wavelength of the TWC we found that bursts are well detected with an absolute value of undetected bursts ratio lower than 10 -5 . -10,2 dBm/1 µs bursts -14,2 dBm/1 µs bursts -17,2 dBm/1 µs bursts -10 dBm/5 µs bursts -14 dBm/5 µs bursts -17 dBm/5 µs bursts Good working Bad working Fig. 4. Undetected bursts ratio versus ISOA for various optical input powers (Pi) in the extractor for short (1 µs) and long (5 µs) bursts.

Fig. 4 shows the undetected bursts ratio versus I SOA for various input powers (Pi) in the extractor and for 1 µs and 5 µs bursts. Pi is measured with a power meter and corrected to take into account the burst duration and the guard band. It is thus representative of the instantaneous power of the burst at the input of the LExt. We observe that curves shift to higher I SOA when decreasing Pi, the "good working" ranges (for the undetected burst ratio ≤ 10 -5 ) widen when decreasing Pi and are larger for 5 µs bursts than for 1 µs ones. These last results can be explained by considering physical mechanisms underlying changes in the terminal voltage of a constant current driven SOA subjected to an optical signal injection.

It is well known that when an optical signal is injected, the SOA amplifies the input signal. Simultaneously the amplified signal stimulates recombination of carriers in the active layer and depletes the conduction and valence bands resulting in a decrease in quasi-Fermi level separation. This appears as a negative change in the terminal voltage. In a single contact SOA -actual case -changes in the terminal voltage have to be proportional to the spatial average of the optical power in the SOA with the opposite sign. Basically, to obtain a good working range of I SOA , the amount of changes in the terminal voltage (∆V) has to be within the input voltage range of the electronics of the extractor. Therefore finding relationships among ∆V, I SOA and Pi would allow explaining the results. Unfortunately it was not possible to directly measure ∆V without perturbing the experiment. Therefore we explain the results resorting to an estimation of the longitudinal average of optical power inside the SOA instead of ∆V. We approximated the SOA by one dimensional amplifier of which the optical power evolves as exp(gz) with g the gain coefficient, supposed to be constant, z the propagation direction. We calculated the longitudinal average of the optical power with Pi, I SOA and the output power (P out ) for good undetected burst ratios. Fig. 5 shows the longitudinal average optical power inside the SOA for various Pi for the minimum (lower limit) and maximum (upper limit) values of I SOA for which the extractor detects correctly the bursts. Uncertainties coming from experimental components (photodiode, bias current and polarization dependence of gain) are estimated to be about +/-0.5 dB. As expected when expressing I SOA in terms of longitudinal average power, the curves are roughly independent of Pi and similar for 1 µs and 5 µs bursts. These show that good working ranges (upper limit -lower limit at given Pi) are determined by the input voltage range of the electronics of the extractor and ∆V. In order to evaluate the behavior of the Label Extractor in actual conditions, we have plotted in Fig. 6 the undetected burst ratio versus Pi for I SOA = 45 mA and for the two burst sizes studied before. Indeed, in actual configuration the bias current of the SOA included in each extractor is set and bursts that can come from different parts of the network arrive at the input of the LExt and so have different input levels. We can observe that the input power range is 4 dB which proves that the designed extractor is compatible with variations of the input power and the bursts duration in an actual implementation. In case of higher variation of the input power at the extractor input, another SOA can be used in a saturated configuration in order to limit the variation of the bursts amplitude. The fiber to fiber gain of the SOA is about 8 dB at 45 mA for Pi = -10 dBm and is higher than 17 dB at 100 mA for Pi = -17 dBm which makes the use of such solution of extraction interesting in terms of data path optical budget to compensate for losses inside the node.

V. CONCLUSION

We have reported experimental results of a label extractor for Labeled-OBS applications. The extractor which uses an SOA in the amplifying detection mode to extract the label part of a burst with attached payload has the advantage of being completely transparent to the entire optical burst (label plus payload). A working range of more than 25 mA has been observed for an optical input power of -14 dBm with two burst sizes. Moreover a tolerance to the input power fluctuations of 4 dB together with a fiber to fiber gain higher than 8 dB has been demonstrated which validates the use of the designed function in a practical environment.

TFig. 1 .

 1 Fig. 1. L-OBS core node internal architecture.

Fig. 2 Fig. 2 .Fig. 3 .

 223 Fig. 2 shows the scheme of both optical and electrical parts of the extractor. It is mainly composed of a CIP Semiconductor

Fig. 5 .

 5 Fig. 5. Longitudinal average optical power inside the SOA versus Pi with upper and lower limit of ISOA for short (1 µs) and long (5 µs) bursts.

Fig. 6 .

 6 Fig.6. Undetected bursts ratio versus optical input power (Pi) in the label extractor for ISOA = 45 mA.


Rim Brahem

Aude Royon-Lebeaud

Dominique Legendre

Effect of length path on valve tray columns: experimental study

Keywords: valve trays hydrodynamics, interfacial area, absorption columns, scale up, path length

Experimental measurements of hydrodynamic and interfacial area parameters are carried out over two rectangular pilot scale valve tray columns. The effect of tray path length on extrapolation between the two columns is studied and phenomenological correlations for hydrodynamic and interfacial area are proposed. Correlations are compared both to literature and to industrial results

showing good agreement and a significant improvement for the prediction of industrial conditions.

Discrepancies preventing an accurate description of industrial trends are highlighted through comparison between typical emulsion height profiles on both columns.

Introduction

Natural gas commercialisation is subject to constraining environmental and operational specifications. Such specifications require treatment of gas stream in order to remove several components like water, heavier hydrocarbons, acid gases (CO 2, H 2 S, organic sulphur compounds, COS, CS 2 , HCN), nitrogen oxides (NOx), sulphur dioxide (SO 2 ), nitrogen compounds, volatile organic compounds (VOCs), volatile chlorine compounds (HCl, Cl 2 …) or volatile fluorine compounds (HF, SiF 4 …) (Kohl & Nielsen, 1997). Depending on initial gas composition and required product specifications, gas stream is processed through several units (dehydration, desulphurisation, acid gas removal …).

For the acid gas removal unit, different kinds of technologies are employed: physical or chemical absorption, physical or chemical adsorption, permeation, redox or cryogenics. Technology choice is mainly based on concentration of acid compounds, partial pressures, selectivity to a specific compound and specifications of final products. Though, the most spread technology is gas liquid absorption using amines solutions.

Valve trays are widely used as contactors for absorption columns because of their relatively low cost and their better performance for specific situations. Within the gas sweetening process context, mass transfer and hydrodynamics having important effects on column effectiveness and operability, absorption columns design depends greatly on the well determination of hydrodynamics and mass transfer parameters related to gas liquid contactors. Actually this design relies on empirical correlations established on pilot scale units. However existence of considerable discrepancy between sets of correlations encountered in literature makes optimisation of column design difficult to achieve. Experimental works have been carried out on hydrodynamics and mass transfer mainly on sieve trays, and little on valve trays [START_REF] Zuiderweg | The influence of surface phenomena on the performance of distillation[END_REF][START_REF] Mc Allister | Perforated -plate performance[END_REF][START_REF] Barker | The evaluation of liquid mixing effects on a sieve plate using unsteady and steady state tracer techniques[END_REF][START_REF] Kister | Entrainment from Sieve Trays in the Froth Regime[END_REF][START_REF] Colwell | Clear height and froth density on sieve trays[END_REF][START_REF] Zuiderweg | Sieve trays : A view on the state of the art[END_REF][START_REF] Bennett | New pressure drop correlation for sieve tray distillation columns[END_REF][START_REF] Scheffe | Mass transfer characteristics of valve trays[END_REF][START_REF] Fasesan | Hydraulic characteristics of sieve and valve trays[END_REF]Poherecki & Moniuk, 1988 ;[START_REF] Peytavy | Interfacial Area and Gas-Side Mass Transfer Coefficient of a Gas-Liquid Absorption Column : Pilot-Scale Comparison of Various Tray Types[END_REF]Liang et al. 2008...).

Still malfunctions on industrial columns are related [START_REF] Kister | WHAT CAUSED TOWER MALFUNCTIONS IN THE LAST 50 YEARS ?[END_REF][START_REF] Kister | Understanding maldistribution in 3-pass trays[END_REF] even for sieve trays which have been more frequently studied. Divergences between literature correlations could be attributed to the great number of influent parameters (geometric, operational and physicochemical). Impacts of considerable number of these influent parameters have not been studied thoroughly. For a given system and an established operational condition, overall hydrodynamic parameters on tray related to absorption effectiveness are mainly clear liquid height h Lc , emulsion height h Fe and mean liquid fraction α L . These parameters are related to each other through the following expression:

Fe L L h h α =
(1)

Correlations for these three parameters reported in literature can be sorted into two groups regarding the phenomenological description adopted for the gas liquid emulsion flow.

The most used description is the one established on the hypothesis of a homogeneous mixture. This postulate justifies the use of Francis equation describing the height over an exit weir of a stationary fluid flow. When considering the gas-liquid emulsion rate in the Francis equation, correlations for the clear liquid height over the tray are proposed in experimental studies under the following form [START_REF] Stichlmair | Dimensionierung des Gas/Flüssigkeit-Kontaktapparates Bodenkolonne, Teil 2[END_REF][START_REF] Hofhuis | Flow regimes on sieve trays for gas/liquid contacting[END_REF][START_REF] Colwell | Clear height and froth density on sieve trays[END_REF][START_REF] Bennett | New pressure drop correlation for sieve tray distillation columns[END_REF][START_REF] El Azrak | Etude des plateaux à clapets caractérisation du transfert de matière et de l'hydrodynamique[END_REF]Liang et al., 2008 …):

3 / 1 2         + = = g L C h h h L w L Fe L Lc α α α (2)
L is the liquid loading defined as

w L L Q L = (3)
where Q L is the liquid rate, L w and h W are the width and the height of exit weir respectively, g is the gravity acceleration and C is a constant taking into account the friction on the tray.

The second phenomenological description used for the gas liquid flow is the trajectory model. In this model the liquid progress toward tray exit is the effect of droplets projection over the exit weir. Such description points out the importance of momentum transfer from the ascending gas to the cross liquid flow. As a consequence the flow parameter FP representing the ratio between the liquid and the gas inertia is used for correlations describing hydrodynamic parameters:

G L G L U U FP ρ ρ = (4)
where U L is the horizontal liquid velocity defined as

w LC L L L h Q U × = (5)
U G is the vertical gas velocity toward the active area A a defined as

a G L A Q U = (6)
and ρ L and ρ G are the liquid and gas densities, respectively. To access the horizontal liquid velocity U L , the knowledge of clear liquid height h Lc is required. Thus for empirical correlations, different authors have used the flow ratio Ψ instead of the flow parameter FP [START_REF] Dhulesia | Operating flow regimes on the valve tray[END_REF]1984 ;Békássy-Molnár &[START_REF] Békássy-Molnár | Clear liquid height on sieve plates in the froth, mixed and spray regimes[END_REF][START_REF] Mustafa | Hydrodynamic Characteristics of Nutter Valve Trays, New Correlations[END_REF]:

G G L Lc U L h FP ρ ρ ψ = × = (7)
The clear liquid height is then written as a power law of Ψ:

α ψ A h Lc = (8)
For the mean liquid fraction α L several studies agree well with the fact α L is mainly dependent on gas inertia [START_REF] Bennett | New pressure drop correlation for sieve tray distillation columns[END_REF]Liang et al., 2008 …). Some efforts have been made to propose dimensional consistent correlations by using the Froude number Fr, comparing gas inertia to liquid weight on the tray [START_REF] Hofhuis | Flow regimes on sieve trays for gas/liquid contacting[END_REF][START_REF] Colwell | Clear height and froth density on sieve trays[END_REF][START_REF] Zuiderweg | Sieve trays : A view on the state of the art[END_REF][START_REF] Chen | Models for liquid head, pressure drop and weeping[END_REF]:

Lc L G G h g U Fr ρ ρ 2 = ( 9
)
The interfacial area and the mass transfer coefficients in both liquid and gas sides are also important parameters for column design. For these parameters less phenomenological descriptions can be found and the reported expressions are mainly put under a power law form [START_REF] Badssi | Influence of Pressure on the Gas-Liquid Interfacial Area and the Gas-side Mass Transfer Coefficient of a Laboratory Column Equipped with Cross-Flow Sieve Trays[END_REF][START_REF] Peytavy | Interfacial Area and Gas-Side Mass Transfer Coefficient of a Gas-Liquid Absorption Column : Pilot-Scale Comparison of Various Tray Types[END_REF][START_REF] Pohorecki | Plate Efficiency in the Process of Absorption with Chemical Reaction -Experiments and Example Calculations[END_REF]. Furthermore little works on the mass transfer parameters have been made on a reasonably large pilot units to account for the hydrodynamic effects [START_REF] Scheffe | Mass transfer characteristics of valve trays[END_REF][START_REF] El Azrak | Etude des plateaux à clapets caractérisation du transfert de matière et de l'hydrodynamique[END_REF]Liang et al., 2008). For these parameters the choice of a characteristic liquid velocity seems more problematic as well. Indeed, depending on the considered study two characteristic liquid velocities are encountered: the liquid loading L or the liquid velocity U La toward the active area Aa:

a L La A Q U = (10)
The effect of column dimensions which impact scalability to larger sizes has been less studied.

Studying hydrodynamics on sieve trays, [START_REF] Hofhuis | Flow regimes on sieve trays for gas/liquid contacting[END_REF] used two different size columns and proposed dimensional coherent correlations for hydrodynamic parameters and regime transitions. Other works have used different sets of experimental data and have indirectly considered the effect of the column size [START_REF] Colwell | Clear height and froth density on sieve trays[END_REF][START_REF] Zuiderweg | Sieve trays : A view on the state of the art[END_REF][START_REF] Bennett | New pressure drop correlation for sieve tray distillation columns[END_REF][START_REF] Chen | Models for liquid head, pressure drop and weeping[END_REF]. Krishna et al. (2003) have carried out a CFD study where the effect of column diameter has been investigated through the modelling of two different columns. In this work the authors showed an important impact of scale effects especially on the mixing characteristics.

In this work the effect of path length L P , the distance travelled by the liquid on a tray between the entrance and the exit weir, is investigated by carrying out hydrodynamic and interfacial area measurements. Two different path lengths are considered: L P =0.36m and L P =0.96m. In literature this geometric parameter has not been studied thoroughly. Table 1 shows some examples of characteristic path lengths L P from literature. As shown in the table, some works have been conducted on relatively small path lengths L P in comparison with industrial units.

Experimental set up

The present experimental study has been realized on two rectangular pilot columns, C2 and C3, having the same geometrical characteristics but a different path lengths L P (See figure 1.a). The total tray pressure drop (ΔP Tray ) and the emulsion pressure drop (ΔP Emulsion ) were measured using Rosemount manometers (see figure 1). ΔP Emulsion was measured at four different positions and a mean value was considered. Assuming that ΔP Emulsion is mainly generated by the liquid weight over the tray, the clear liquid height h Lc was evaluated as:

g P h L Emulsion Lc ρ ∆ = (11)
The emulsion height measurements were made using video records post-processing. For each video a mean emulsion profile is processed and a mean emulsion height h Fe over the tray is measured.

More details on hydrodynamic measurements and image processing can be found in Brahem et al., 2013a. The interfacial area was measured using an indirect reactive absorption method. The reaction of CO 2 absorbed in an aqueous ammonia solution is employed (400ppm CO 2 in air/ 0.1N NaOH in water).

This method has been validated for interfacial area measurements of structured packing by [START_REF] Bibiliography Alix | Mass transfer and hydrodynamic characteristics of new carbon carbon packing : Application to CO 2 post-combustion[END_REF]. The absorption reaction can be described by the following set of equilibriums:

) ( 2 ) ( 2 l g CO CO ↔ - -↔ + 3 ) ( 2 HCO OH CO l O H CO OH HCO 2 2 3 3 + ↔ + - - - (12)
The 1 st reaction represents the physical absorption of CO 2 at the interface. Equilibrium is assumed and represented by the Henry's law:

He P C i G CO i L CO , , 2 2 = (13)
The 3 rd reaction rate is assumed to be much higher than the 2 nd reaction rate (Pinsent et al., 1956[START_REF] Pohorecki | Plate Efficiency in the Process of Absorption with Chemical Reaction -Experiments and Example Calculations[END_REF]. Thus the overall kinetic rate is controlled by the 2 nd reaction [START_REF] Pohorecki | Plate Efficiency in the Process of Absorption with Chemical Reaction -Experiments and Example Calculations[END_REF]:

2 2 CO OH C C k r - = (14)
In the present study the hydroxide concentration is largely higher than the CO 2 concentration, so that the reaction can be considered as pseudo 1 st order:

2 2 ' 0 2 CO CO OH C k C C k r = = - (15)
The double film absorption model is considered. The mass transfer from gas to liquid is considered to take place into two thin layers located on both sides of the interface. Assuming equilibrium at the interface and neglecting the resistance to the mass transfer on the gas side (

b G CO i G CO P P , , 2 2 ≈
), the CO 2 absorbed flux is controlled by the mass transfer processes in the liquid film and by the absorption rate in the liquid:

( )         - ⋅ ⋅ = - ⋅ ⋅ = b L CO i G CO L b L CO i L CO L C He P k E a C C k E a , , , , 2 2 2 2 φ (16)
where Φ is the CO 2 absorbed flux, a the interfacial area, E the enhancement factor taking into account the contribution of the reaction, k L the liquid side mass transfer coefficient, A perfectly agitated flow for the liquid phase and a plug flow for the gas phase are also assumed for the determination of the interfacial area. Two infrared analysers were used at the column entry and exit to measure the CO 2 concentrations. The hydroxide concentration in the liquid was measured by titration with HCl.

Comparison between the two columns

The difference observed between correlations from literature is partially due to the use of different liquid and gas velocities in the experiments. For the liquid velocity two parameters are commonly used, either U La the liquid velocity toward active area [START_REF] Badssi | Influence of Pressure on the Gas-Liquid Interfacial Area and the Gas-side Mass Transfer Coefficient of a Laboratory Column Equipped with Cross-Flow Sieve Trays[END_REF][START_REF] Scheffe | Mass transfer characteristics of valve trays[END_REF] or L the liquid rate per weir length (or liquid loading) [START_REF] El Azrak | Etude des plateaux à clapets caractérisation du transfert de matière et de l'hydrodynamique[END_REF][START_REF] Colwell | Clear height and froth density on sieve trays[END_REF]. The liquid loading divided by the clear liquid height can be considered as a horizontal characteristic liquid velocity in opposition to U La which represents a vertical characteristic velocity.

For the gas velocity, the kinetic factor (the squared root of gas inertia) is usually employed. We consider here two different gas kinetic factors. The first one uses the gas velocity toward the active area A a while the second one considers the gas velocity toward the net area A n = A a + A d where A d is the area of one downcomer. The gas kinetic factor toward A a is

2 Ga G U Fa ρ = (22) with a G Ga A Q U = (23)
The gas kinetic factor toward

A n is 2 Gn G U Fa ρ = (24) with n L Gn A Q U = (25)
In order to identify a pertinent characteristic liquid velocity allowing the comparison between the two columns, the results for the pressure drop, the liquid fraction, the emulsion height and the interfacial area are examined either fixing the liquid velocity toward active area U La or the liquid loading L. Corresponding plot for the total pressure drop and the mean emulsion height toward gas kinetic factor Fa are first presented in Figure 2. The Comparison between these two plots seems to indicate that the liquid loading L is more adapted for extrapolation from the little column to the larger one. Concerning gas velocity, the tray pressure drop is presented in Figure 3 and the mean liquid fraction is shown in Figure 4 for different liquid loading L either for a fixed kinetic factor toward the active area Fa or for a fixed kinetic factor toward the net area Fn. The results suggest that Fa is better suited for the comparison of the selected hydrodynamic parameters (pressure drop, emulsion height, mean liquid fraction) especially for intermediate and high velocities. However considering the interfacial area, the choice of Fn appears to be more pertinent as shown in Figure 5. This could be explained by the fact that the liquid-gas emulsion is not totally disengaged in the downcomer so that the mass transfer also takes place in the downcomer.

As it may be noticed trough the different plots of the present results for the considered gas and liquid velocities, the choice of a characteristic velocity is made difficult by the little sensitivity of the measured parameters to these velocities. In some configurations both proposed velocities can be representative: for instance for pressure drop at low gas and liquid rates any velocity could be considered for extrapolation (Figure 2 (a & b) & Figure 3). In some other conditions such as for mean emulsion heights (Figure 1 c &d), the two characteristic velocities fail to superimpose the results for the two columns for moderate to high liquid loads. Such failure to find a similar evolution suggests that the hydrodynamic behaviour between the two columns is not totally identical. In particular, a sharp increase of the interfacial area is noticed when increasing the gas flow rate for the two columns but a different critical value is found (see [START_REF] Brahem | Experimental hydrodynamic study of valve trays[END_REF][START_REF] Brahem | Experimental hydrodynamic study of valve trays[END_REF] for a detailed description of the hydrodynamic regimes). The limit associated to the increase of interfacial area is related to flooding and lies outside the nominal operating conditions of industrial columns and thus it is of little interest.

A b

Correlations

In order to propose dimensional homogeneous expressions the choice of adapted parameters is discussed in this paragraph. Once the general form of the correlation is settled, the least square method is used to determine the constant parameters by minimizing the deviation to experimental data.

Mean liquid fraction

The Froude number has been considered by some authors to describe the evolution of the liquid fraction [START_REF] Colwell | Clear height and froth density on sieve trays[END_REF][START_REF] Hofhuis | Flow regimes on sieve trays for gas/liquid contacting[END_REF][START_REF] Chen | Models for liquid head, pressure drop and weeping[END_REF]. This choice is also adopted here and the corresponding correlation is expressed as follow:

1 1 1 1 β α Fr a L + = (26)
Such expression has also been suggested in previous studies [START_REF] Azbel | The hydrodynamics of bubbler processes[END_REF][START_REF] Kim | Theoretical study of vapour-liquid hold up on a perforated plate[END_REF][START_REF] Kawagoe | Flow pattern and gas hold up conditions in gas sparged contactors[END_REF][START_REF] Colwell | Clear height and froth density on sieve trays[END_REF]. From the present experimental results, the values are fixed to a 1 =11.3 and β 1 =0.54 and the following correlation is proposed:

Clear liquid height

Several authors have reported that the clear liquid height depends on the hydrodynamic regime [START_REF] Dhulesia | Clear liquid height on sieve and valve trays[END_REF][START_REF] El Azrak | Etude des plateaux à clapets caractérisation du transfert de matière et de l'hydrodynamique[END_REF]Mustafa & Békàssy-Molnar, 1991 & 1997…). Correlations for the clear liquid height for each hydrodynamic regime are proposed by [START_REF] Hofhuis | Flow regimes on sieve trays for gas/liquid contacting[END_REF] and Mustapha & Békàssy-Molnar (1997). Hofhuis suggests a transition between the emulsion and the spray regimes for a critical value of the flow parameter FP (squared root of liquid to gas inertia) between FP=3 and FP=4. Mustafa & Bekassy (1991) proposed correlations depending on the flow ratio Ψ (=FP*h Lc ) in which the dependence to this parameter depends on the hydrodynamic regime.

Taking these studies into account, our results for the clear liquid height are represented toward the flow ratio Ψ (see Figure 7). The transition limit is observed for a flow parameter FP=4 which is coherent with previous studies [START_REF] Hofhuis | Flow regimes on sieve trays for gas/liquid contacting[END_REF]Zuiderwerg, 1982). For both main hydrodynamic regimes, a correlation for the clear liquid height is determined.

Emulsion regime

For the emulsion regime, the two phase flow over the exit weir is commonly described as homogeneous. This description leads to express the clear liquid height under the following form:

3 / 1 2 2         + = g L a h h L w L L α α (28)
This form arises from the well-known Francis equation traducing mass conservation of a stationary fluid flow over a weir. Fitting our results in the emulsion regime we found a 2 =1.315 so that the following correlation is proposed:

3 / 1 2 315 . 1         × + = g L h h L w L Lc α α (29)

Spray regime

For the spray regime, the trajectory model is usually used to describe the flow on the tray. No explicit form can be easily obtained from this description. In literature (Mustafa & Békassy-Molnar, 1997;[START_REF] Dhulesia | Clear liquid height on sieve and valve trays[END_REF] the flow ratio ψ is commonly used as main correlating parameter. In this work we propose a correlation based on the two main parameters controlling the flow over the tray, namely the flow parameter FP and the Froude number Fr:

2 3 β ψ ψ Fr a FP h Lc = = (30)
From our experiments we deduced a 2 =1.315 and β 2 =1.18 and the following correlation is proposed for the spray regime:

Mean emulsion height

The evolution of mean emulsion height can now be easily deduced from the mean liquid fraction and the clear liquid height by using relation (1):

L L Fe h h α =
The corresponding results are reported in Figure 9 where a satisfactory agreement with experimental results is shown. A deviation similar to the one noticed for both mean liquid fraction and clear liquid height is observed.

Interfacial area

In order to propose a dimensionally homogeneous correlation for the interfacial area, we consider the rate of interfacial area. This rate represents the specific interfacial area per unity of emulsion volume. The results obtained for the two columns show that the interfacial area divided by the net area An is more adapted for the description of the hole experimental points. To estimate a total emulsion volume, the mean emulsion height is considered. Thus the rate of interfacial area is expressed as follows:

Fe Fe i h a h An a a ' = × = (32)
Several works on bubbling flows [START_REF] Bouaifi | A comparative study of gas hold-up, bubble size, interfacial area and mass transfer coefficients in stirred gas-liquid reactors and bubble columns[END_REF][START_REF] Majumder | Bubble size distribution and gas-liquid interfacial area in a modified downflow bubble column[END_REF][START_REF] Muroyama | Mass transfer properties in a bubble column associated with micro-bubble dispersions[END_REF] express this rate of interfacial area as a function of the gas fraction and the maximum bubble size as:

max B G i d C a α = (33)
The maximum bubble size is determined by a critical Weber number We Critical comparing the effect of the surface tension to the inertia that tends to break the interface:

max 2 ' B L Critical d U C We σ ρ = (34)
For the present system of gas injection, we can reasonably consider that the gas inertia controls the bubble size so that we can write:

2 max n B F C d σ = (35)
The consideration of gas fraction for interfacial rate correlation under a power law form showed no relevant dependency for this reason liquid fraction was considered instead of gas fraction which leads to the final correlation form for interfacial area:

3 2 4 ' β α σ L n Fe F a h An a a × = = (36)
From our experiments we obtain a 4 =6454 and β 3 =4.65 so that the evolution of the interfacial area per net tray area can be described using:

65 . 4 2 6354 ' L Fe Fn h a α σ ×         × × = (37)
The comparison between this correlation and the experiments is reported in Figure 10. For the larger column C3, the results are quite satisfying, but for the smaller column C2, the correlation underestimates considerably the experimental results. This highlights the fact that the proposed correlation (37) does not reflect the phenomenological mechanism responsible of the production of gas liquid interface. In fact the form proposed is inspired from works done for bubbling regimes while two phase flow on the tray is considerably different because of the gas jets observed near the valves exit and the presence of an emulsion zone above. It is possible that both gas jet dynamics and emulsion behaviour are different between the two columns.

A b

Comparison to correlations from literature

Several empirical correlations have been proposed in previous works [START_REF] Dhulesia | Clear liquid height on sieve and valve trays[END_REF][START_REF] El Azrak | Etude des plateaux à clapets caractérisation du transfert de matière et de l'hydrodynamique[END_REF]Mustafa & Molnár-Bekassy 1997 ;Liang et al, 2008 ;[START_REF] Scheffe | Mass transfer characteristics of valve trays[END_REF][START_REF] Peytavy | Interfacial Area and Gas-Side Mass Transfer Coefficient of a Gas-Liquid Absorption Column : Pilot-Scale Comparison of Various Tray Types[END_REF]. In order to compare these correlations to the relation obtained in our study, we first select some of the most used ones and compare them to our experiments (Figure 11a & Figure 12a). Then we compare our correlations with experimental points issued from other studies (Figure 11b In order to evaluate the accuracy of the correlation for the interfacial area, and in particular its extrapolability, some expressions from literature [START_REF] El Azrak | Etude des plateaux à clapets caractérisation du transfert de matière et de l'hydrodynamique[END_REF][START_REF] Scheffe | Mass transfer characteristics of valve trays[END_REF]Liang et al, 2008) and from present work are compared to experimental points acquired on industrial columns. The corresponding comparison is presented in Figure 13. A scale effect has been noticed when comparing results between the two columns. A perfect similitude can not be shown even when considering different liquid and gas velocities.

Mean emulsion height h Fe

In Figure 14 a similar behaviour for h Lc is noticeable with two recognisable zones when the gas velocity increases. The first zone corresponding to the increase of h Lc is characterised by an important amount of weeping. In the second zone, increasing the gas velocity results in a drop of the clear liquid height [START_REF] Brahem | Experimental hydrodynamic study of valve trays[END_REF]. The differences lie in a lower dependence to the liquid load on the smaller column C2 and a higher dependence to the gas kinetic factor especially for the second zone. To better understand these discrepancies, typical emulsion profiles are compared between the two columns in Figure 15. Considering the large column, it is shown that for a fixed liquid loading and an increasing gas kinetic factor four different behaviors can be identified (Brahem et al 2013a) while for the small column only three behaviors are observed (Brahem et al 2013b). For the low gas velocities a dumping regime with a highly oscillating profile but rather homogeneous along the tray is noticed for both columns. When increasing the gas velocity for C3 a channeling regime followed by a homogeneous regime are observed while for the column C2 only a regime with a bell-shaped emulsion profile is noticed. Approaching flooding (high gas velocities) a channeling phenomenon is noticed for C3 while profiles for C2 are transformed into a more parabolic form. Moreover the profiles for C2 are less dependent to the gas and the liquid flow rates. As shown in Figure 15.b and Figure 15.c, the profiles for the two columns seem to be similar at both the entrance and the exit of the tray. This is due to the fact the profile is fully controlled by the border conditions imposed on the tray extremities. However, at the middle of the tray, the emulsion profiles do differ between the two columns. For the larger column, the path length L P is large enough for the profile to become stable and independent from the border conditions. However for the small column L P is rather short and the profile is totally controlled by border conditions. This could provide the explanation for the lower dependence of emulsion height to gas and liquid velocities observed in the column C2.

These observations highlight an intrinsic scale effect on hydrodynamic behavior of the two phases flow. Such change in behavior between small and large columns could help to explain the differences noticed between proposed correlations and industrial results.

In addition to geometric scaling effects (dead zone for example), the effects of physicochemical properties and their dependence to operating conditions (pressure and temperature) as well as to the gas and liquid compositions have not been investigated through this work. They are expected to influence hydrodynamic and mass transfer behaviours and could also be at the origin of the differences noticed between proposed correlations and industrial results.

Conclusions

Experiments have been carried out on two different path length columns to provide a wide data base for hydrodynamic parameters and interfacial area on valve trays. Correlations for liquid fraction, clear liquid and emulsion heights and interfacial area have been proposed based on phenomenological descriptions. These correlations allow representing present experimental data with a maximum error of 40% for hydrodynamic parameters and 50% for interfacial area for the two columns considered. Moreover the proposed correlation for the interfacial area improves representativeness for available data from both literature and industrial tests compared to previous correlations (Liang et al 2008[START_REF] Scheffe | Mass transfer characteristics of valve trays[END_REF][START_REF] El Azrak | Etude des plateaux à clapets caractérisation du transfert de matière et de l'hydrodynamique[END_REF].

However the new relation proposed for the description of the interfacial area fails to take into account the scale effect because of a non-negligible impact of the boundary conditions for the small path length column. This dependence due to the impact of the border conditions leads to different emulsion profiles and different regime transitions between the two columns. Moreover other parameters of influence such as physicochemical parameters have not been considered. Their effect is expected to be important and thus has to be quantified in the future.

Figure 1

 1 Figure 1 : a. Sketch of the experimental set up with the pressure drop connections. b. Geometrical parameters of the two columns C2 and C3

-.

  liquid at the liquid/gas interface, b L CO C , 2 the CO 2 concentration in the liquid bulk and He the interfacial equilibrium constant (Henry's law). The enhancement factor depends on 3 parameters: -The Hatta number Ha : enhancement factor, also known as a concentration-diffusion factor The ratio between the liquid volume per interfacial area and the liquid film thickness of a fast reaction for which Ha>3 and Z D >>1, the enhancement factor can be approximated by the Hatta number Ha E ≈ and the CO 2 concentration in the liquid bulk is Consequently the absorbed flux is written as: constant D L , the Henry's constant He and the kinetic constant k 2 (constants taken from Pohoericki & Moniuk 1988), the measurement of the CO 2 absorbed flux, the CO 2 pressure in the gas bulk and the hydroxide concentration allow an indirect determination of the interfacial area

Figure 2 :

 2 Figure 2: Comparison of tray pressure drop (a and b) and mean emulsion height (c and d) at a fixed U La (a and c) or at a fixed L (b and d)

Figure 3 :Figure 4 :Figure 5 :

 345 Figure 3: Comparison of tray pressure drop results. a) At a fixed Fn . b) At a fixed Fa

Figure 6 :

 6 Figure 6: Liquid fraction. a. Comparison with correlation (27) for the column C3 for different liquid loadings. b. Parity diagram between experiments and correlation (27)

Figure 7 :

 7 Figure 7: Identification of the transition between the emulsion and the spray regimes

Figure 8 :

 8 Figure 8 compares the above correlations in both hydrodynamic regimes to the experiments. Good agreement is encountered for the two columns.

Figure 9 :

 9 Figure 9: Mean emulsion height a. Comparison between correlations and experiments for the column C3 for different liquid loadings. b. Parity diagram for the two columns.

Figure 10 :

 10 Figure 10: Interfacial area. a. Comparison between experiments and correlation (37) for column C3 for different liquid loadings. b. Corresponding parity diagram.

Figure 11 :Figure 12 :

 1112 Figure 11: Clear liquid height a. Correlations from literature compared to present data b. Present correlation (31) applied to literature dataConsidering the interfacial area, the correlations from literature allow to estimate our experiments with an error of 60% while our correlation (37) permits to reduce the error on the full data base of the same literature to 50%. This dispersion is highly dependent on the indirect method used to measure this parameter and the important uncertainties related to the choice of the kinetic and the thermodynamic constants.

Figure 13 :

 13 Figure 13: interfacial area from industrial columns compared to correlation (37) and correlations from literature.

Figure 13

 13 Figure 13 clearly shows that the proposed correlation allows significantly decreasing the dispersion toward industrial points in comparison with previous expressions. However none of the correlations

Figure 14 Figure 14 :

 1414 Figure 14 reports the clear liquid height and the mean emulsion height for the two columns.

Figure 14 b

 14 Figure 14 b reports the mean emulsion height. The results for the smaller column show a small dependence with both gas and liquid velocities. Comparable values for the larger column C3 are only observable at low gas kinetic factors.

Figure 15 :

 15 Figure 15: Emulsion profiles for the two columns. a) As a function of the distance from the liquid entry normalised by the path length Lp. b) As a function of the distance from the liquid entry. c) As a function of the distance from the exit weir.

Table 1 : Examples of L P (m) values in literature versus industrial units

 1

	Piqueur &	Bennett et	Mustafa &	Fasesan,	Uys et	Liang et	H. Dhulesia,	Industrial units
	Verhoeye,	al., 1983	Békássy-	1987	al., 2012	al., 2008	1984
	1976		Molnár, 1997
	0.15	0.15	0.28	0.43	0.475	0.53	0.89	0.5/0.8
	The two columns considered in this work are presented in section 2. Section 3 is dedicated to the
	comparison of hydrodynamic and interfacial area measurements. In section 4, some attempts are
	made in order to propose phenomenological and dimensionally coherent correlations for clear liquid
	height h Lc , mean emulsion height h Fe, mean liquid fraction α L and interfacial area per net area a'. The
	proposed correlations are compared to correlations from the literature in section 5. Section 6
	discusses the application of the proposed correlation to industrial cases and present some future
	works.


Lotfi Zaouche

Ait Sofiane

Arab

Anfel Khireddine
email: khireddine.anfel@gmail.com

Enrico Natalizio

A reputation-based approach using collaborative indictment/exculpation for detecting and isolating selfish nodes in MANETs

Keywords: MANET, selfish behavior, reputation system, I

Abdelmadjid Bouabdallah (1)

INTRODUCTION

In Wireless Sensor Networks (WSN), collaboration between nodes is essential. If a source and destination of data flow are not in line of sight, the information should be transmitted along intermediate nodes, along a path established and maintained by the network. Routing in such conditions becomes a complex task, especially as energy resources are limited, and nodes can legitimately become selfish and refuse to route other nodes' packets to preserve their energy. The need for cooperation between nodes to ensure the functioning of the network conflicts with the individual interest of each node to spend its energy solely for data for which they are the source or the destination. We can identify two types of non-cooperative nodes: faulty/malicious nodes and selfish nodes. Faulty/malicious nodes belong to the class of nodes that are either defective and therefore cannot follow a well-defined protocol, or intentionally malicious, thus trying to attack the system [START_REF] Marti | Mitigating routing misbehavior in mobile ad hoc networks[END_REF].

Although the problem of selfishness is a form of passive attack, it still causing a negative impact on network's performances. Numerous studies have been performed to evaluate the impact of the presence of selfish nodes in an ad hoc network [START_REF] Vuppala | A Simulation Analysis of Node Selfishness in MANET using NS-3[END_REF][START_REF] Shailender Gupta | Impact of selfish node concentration in manets[END_REF][START_REF] Sundararajan | Modeling the Behavior of Selfish Forwarding Nodes to Stimulate Cooperation in MANET[END_REF]. The non-cooperation of a node implies that packets passing through this node will be lost. The mentioned problem calls for solutions that force the selfish nodes to cooperate in the network and if necessary, excluding them. Such solutions would greatly increase the network performance. In this work, we are interested in the study of the proposed problem of selfishness in mobile ad hoc networks.

Our contribution is summarized in the following points: We propose an improvement of the TWOACK scheme [START_REF] Kash Yap Balakrishnan | TWOACK: Preventing Selfishness in Mobile Ad Hoc Networks[END_REF], aimed at considerably decreasing the number of control packets. Also, the TWOACK scheme is only able to detect a selfish link, whereas our solution detects the selfish node. We propose reward/punishment model for cooperative/selfish nodes by taking into consideration all nodes that participate in the deliverance of a packet.

The rest of the paper is organized in four sections. In Section II, we present the state of the art of solutions for the problem of selfishness. In Section III we present our solution approach. Section IV is devoted to the presentation of the simulation results. Section V concludes the paper.

II. RELATED WORK

Since the transmission of a message imposes a cost (energy and other resources) to the nodes, a selfish node will need an inducement or reward for transmitting messages from others [START_REF] Zhong | Sprite: A Simple, Cheat-Proof, Credit-Based System for Mobile Ad-Hoc Networks[END_REF]. There are two types of solutions to encourage selfish nodes in ad hoc mobile network to cooperate: credit-based systems and reputation-based system.

A. Credit-based system

Systems based on credit provide incentives to nodes to ensure network functionality. To achieve this virtual goal, a payment system may be implemented. Nodes are paid to rely other nodes' packets. This kind of system can be implemented using two models: the Packet Purse Model (PPM), and Packet Trade Model (PTM) [START_REF] Khatawkar | Detection of Routing Misbehavior in MANETs[END_REF].

In [START_REF] Zhong | Sprite: A Simple, Cheat-Proof, Credit-Based System for Mobile Ad-Hoc Networks[END_REF], the authors proposed an interesting solution called SPRITE. When a node receives a message, it keeps a receipt of this message, then when it has a fast connection to the Credit Clearance Service (CCS) it reports its receipts of the messages it received/transmitted. CCS then determines the charge and the credit of each node involved in the transmission of the message.

In this type of solution, we are facing new problems such as the centralization/decentralization of the paying authority, false receipts and sometimes the solution needs to address not only software issues but also hardware ones.

B. Reputation-based System

A reputation-based system relies on the observations of nodes to other nodes. Since one observation does not allow a direct and objective measure of malicious nodes, it is necessary that each node maintains a degree of confidence in respect of all the nodes it has observed. The value of this confidence is influenced by observations on the behavior of nodes. In this type of system, the reputation calculation is either performed locally at each node, or by the distribution of reputations stored in the nodes within the network.

TWOACK scheme [START_REF] Kash Yap Balakrishnan | TWOACK: Preventing Selfishness in Mobile Ad Hoc Networks[END_REF] is based on reputation. A node that transmits/broadcasts a message, is informed that the following node has completed its task by forwarding the message at his turn, by receiving from the two hops next node a special acknowledgment called TWOACK packet. Each node that receives a message must send an acknowledgment to the node two hops back in the message path. The message path is the path that has been given by the routing protocol. To detect a misbehaving node, the source maintains a list of IDs of messages that he has not received TWOACK packet yet, and each node maintains a unique list of data structure for each transmission link that it uses. S-TWOACK (Selective-TWOACK) [START_REF] Kash Yap Balakrishnan | TWOACK: Preventing Selfishness in Mobile Ad Hoc Networks[END_REF] and 2ACK [START_REF] Liu | An Acknowledgment-based Approach for the Detection of Routing Misbehavior in MANETs[END_REF] schemes aims at reducing network congestion caused by the large number of TWOACK packets sent. The first is inspired by the principle of the sliding window, acknowledging a certain number of well received messages. The second one acknowledges only a part of them, and includes a certification mechanism for the security of its packets.

In respect of the presented solutions, our proposal consists in optimizing the control packets. We do not generate control packet until something does not work in the message delivery, whereas TWOACK generates control packet during all transmissions. Consequently, the more selfish nodes are discovered, the less control packets are generated.

III. PROPOSED APPROACH

Since it is the less constraining in the architectural design, and there is no need to have special hardware, we choose to work on Credit-based systems to force the nodes to participate with other nodes, in order to keep a good reputation and keep being well served by others.

A good solution should: (i) guarantee the detection of selfish nodes, (ii) penalize the selfish nodes, and avoid, in the routing phase, those excluded because they do not cooperate anymore (iii) be able to know if it is necessary to give a second chance to a node who wants to repent.

A. Assumptions

We assume that the links are bidirectional. We also assume that a certification service public key is set up and used to encrypt the messages circulating in the network, including messages that are unique to our system, and guarantee data integrity.

B. Operating details of our approach

The principle of our approach is quite simple, and relies on multi-hop acknowledgment. Several studies justify and prove that two hops is an efficient number of hops for the acknowledgments [START_REF] Kash Yap Balakrishnan | TWOACK: Preventing Selfishness in Mobile Ad Hoc Networks[END_REF][START_REF] Liu | An Acknowledgment-based Approach for the Detection of Routing Misbehavior in MANETs[END_REF]. Based on these studies, we choose to make two hops acknowledgment, because it will make the indictment of a node more precise than in the case with higher number of hops. Messages used by the system are described in Table I. Knowing that we have made the assumption that a certification service is implemented in the network, 2HopAck and SelfExculpation messages will be encrypted to ensure their integrity and authenticity.

Let consider that a node N s wants to send a message to N d . N s builds a path to N d by using any routing protocol, but avoiding the known selfish nodes. By sending this packet, all nodes that are on its path will wait for an acknowledgement of the destination for an Ack_Delay time. Upon the reception of the acknowledgment is received, each node increases the reputation of following nodes in the path. If the timeout Ack_Delay expires and no acknowledgment is received, each node N i involved in the message transfer, send a 2HopAck message, to the node N i-2 , who was two hops back in the message path to prove that the node N i-1 who was the intermediate is innocent. When the node N i-2 receives this message, it will increase the reputation of the nodes N i-1 and N i . When after a delay, Exculpation_Delay, the node N i sees that the node N i+1 did not send the 2HopAck packet to node N i-1 , it exculpates itself by sending the previous nodes a package SelfExculpation and hold N i+1 responsible for the failure of the transmission of the message, and decreases its reputation. Nodes receiving this message start increasing the reputation of nodes that transmitted the message to the node N i , and since they do not know which node caused the problem, they will penalize the two nodes N i and N i+1 , by decreasing the reputation of the node that seems most selfish. If after a delay, a node N i does not receive the 2HopAck packet from node N i+2 , and the node N i+1 does not proclaim its innocence, then it will be indicted by the node N i , and will be signaled to the source node. All nodes in the path receiving this indictment will reduce the reputation of node N i+1 , and increase the reputation of other intermediate nodes. In addition, when a node receives a packet, it will check the message path, and will increase the reputation of all intermediate nodes from the source to him.

Each node holds a table named TrustTable that stores the values of reputation he has for other nodes. Whenever a node obtains an observation about a node, it updates the value of its reputation if it has an entry in the table for this node, if no entry in the table corresponds to this node, then it will create a new entry for this node and save the value inside. Initially, each node gives an initial reputation to neighboring nodes. In addition, each node holds a data table called PostTable, which stores the identifier of the messages it transmits, and the path it takes. When the destination sends an acknowledgment to the source to confirm the receipt of a message, all nodes that receive this acknowledgment, in their PostTable checks if there is a message that matches the packet acknowledged, then deletes the corresponding line. And nodes do the same when they receive SelfExculpation or SelfishDetection packets. If a timeout after no acknowledgment is received for a message, the line for this message will be deleted after it has sent the message to the node 2HopAck two hops back, as explained above to exonerate one hop rear's node.

In order to more quickly detect selfish nodes, it is preferable that the network nodes collaborate by exchanging knowledge on the behavior of other nodes. In order not to clutter the network messages, the nodes transmit the values of the reputation of a node only if it changes by a certain threshold. The value of the threshold should be well studied; a value too small will make the collaboration stronger and therefore more effective, but will increase the load on the network, and will be a waste of energy to the nodes. Also, taking a bigger value will reduce the network load, but it will also reduce nodes collaboration, making the detection of selfish nodes slower.

C. Reward and punishment computation

Formulas' parameters and functions are detailed in Table II. The required rate of nodes accusing a node to be selfish, to be considered as such throughout the network.

MPS(i, j)

A function that returns 1 if the reputation of the node j is greater than those of node i, and returns 0 otherwise.

Trust i (j)

A function that returns a reputation of node j that holds node i, which is stored in the TrustTable.

Upon receipt of a reputation value of a node, a new reputation value is calculated for this node, taking into account the value received and the value we already had. To avoid defamatory values that distort the reputation of the nodes, we can take into account the values received with a low impact factor. We apply the following formula to calculate a new value of reputation taking into account the values received:

= * + ∑ ! "# $ $%& ' + #
Where ( is the factor that is given to the reputation we have already calculated previously, receivedReputaion is the value of reputation received from any node.

When a node detects that the reputation of another node has fallen below a certain threshold, it broadcasts a packet named SelfishAlert, containing its identity and the identity of the accused node. Each node receiving this message will save it. If at a certain time you get a number of accusation for a given node, equal to WitnessRate, then this node will be considered selfish by all network nodes. This technique speeds up the process of detecting selfish nodes in the network.

The WitnessRate parameter is very important. Indeed, high levels reduce the rate of false accusations caused by defamatory information sent by malicious nodes, but the detection of selfish nodes becomes longer. A smaller rate ensures that the detection of selfish nodes is faster, but false positive rate could increase. N i rewards N i+1 for sending the message to N i+2 as follow:

) *& = ) *& + +, (1)
And rewards N i+2 for confirming it as follow:

) *-= ) *-+ + (2)
When N i receives a message from N i-1 , it applies:

) $ ' = ) $ ' + +,, ∀ 0 1 ∈ {0 4 , 0 6 , … , 0 894 } (3)
A node penalizes his successor after it did not send 2HopAck packet, using the following formula:

) *-= ) *--<)+, (4)
When a node receives a SelfExculpation packet of a node k, it executes:

) $ ' = ) $ ' + +,, ∀ 0 1 ∈ {0 8*6 , 0 8*= , … , 0 >94 } (5)
) ? = ) ? -1 - ) ? ' * <)+, - B<+ ) ? , ) ?*& * C<)+, + B<+ ) ?*& , ) ? * +B ( 6
)

) ?*& = ) ?*& -1 - ) ?*& ' * <)+, -B<+ ) ?*& , ) ? * C<)+, (7)
If we receive an acknowledgment of the destination these will be applied to each node N i path:

) $ ' = ) $ ' + +,, ∀ 0 1 ∈ {0 8*4 , 0 8*6 , … , 0 D94 } (8) ) *-= ) *-+ + (9)
If no exoneration is sent neither by the node N k itself nor by the node that follows it, a Selfish_Detection packet is sent, and the reputation of node N k will be reduced by all nodes in the path receiving this message by applying formula (4).

IV. PERFORMANCE EVALUATION

In this section we will describe the simulation environment and we will show the simulation results.

A. The simulation environment

For our simulation campaigns, we implemented TWOACK and our protocol on Java. We simulated an ad hoc network with 50 mobile nodes. Selfish nodes are randomly selected from these 50 nodes with a percentage ranging from 0 to 40% in steps of 5%. These nodes move according to the Random Waypoint model. The maximum speed of a node is 15 m/s and the maximum idle time is 3 s. Network nodes have the same range that is equal to 150 meters. The deployment surface of nodes is 1000 * 1000 m². Each node sends a message according to Poisson distribution with parameter E=10 ms. Finally, the simulation time is 300 seconds, and we repeat it 50 times each time we increment the selfish nodes rate in the network. To show that we are tolerant to collisions, we assume that the packets loss rate is 5%. As shown in [START_REF] Dovrolis | Proportional differentiated services, part II: loss rate differentiation and packet dropping[END_REF], this packet loss rate is sufficient. Table III. summarizes these parameters. The important thing to show here as an input, is the rate of selfish nodes in the network, and the time to. Concerning the output, first, we will show the delivery ration of messages. Right after, we will present the overhead caused by the control packet generated by our protocol.

B. Results and discussion

Impact of selfish nodes on message delivery

As shown in Fig. 1, our approach gives excellent results; indeed the lower bound of the success rate of message delivery exceeds 86%. Initially, in the absence of selfish nodes in the network, the rate of rescues message reaches 97%, then increasing the rate of selfish nodes in the network, the delivery rate decreases to 86% when the selfish node rate reaches 40%. And we can see that TWOACK degrades significantly when the selfish rate increases. This is due to the fact that they do not discover the selfish note, but the failing link. So whenever a selfish node moves and create a new link with another node, it can behave as it likes.

When we fix the selfish rate to 40% as shown in Fig. 2, we have at the beginning a message delivery rate of 86% because we have not yet detected the selfish nodes, and as and as these nodes are selfish and discovers that avoids, we the message delivery rate increases till 95%, and it corresponds exactly to the 5% of assumed collision. Meanwhile, TWOACK stabilizes between 40 to 45%.

Control packets overhead on the network

The Fig. 3 shows the evolution of the protocol overhead over time. This is important to show to argue if our solution is too heavy to be interesting or not. Unfortunately, we did not see this kind of figure in the studied work. We can see that our solution is a very light one comparing to TWOACK. We do not exceed 4% of the network traffic, and we can do less than 1% in favorable condition. In fact, what makes control packets in our solution does not reach 0% is only caused by failing links, false detections, and collisions. Concerning TWOACK, we see that the control packet decreases, but this is only because the packets do not reach them destination and therefore no control packets are generated. In the Fig. 4, we can see that the two protocols have stabilized over time. Our solution stabilizes in 1.3% and TWOACK in 8.7%. Another time, as we said before, we do not 0% only because of false detections, collisions and link failing.

V. CONCLUSION AND FUTURE WORK

In this paper, we proposed a new approach for detecting selfish nodes. The simulation results that we obtained were largely sufficient, and have proven the effectiveness and robustness of our approach. As noted in the previous section, our approach goes beyond 90% regarding the detection rate of selfish nodes, which avoids these and offer a delivery rate high enough messages (more than 91%). The evaluation of our approach with respect to time clearly demonstrates its advantages. In fact as the time passes, the rate of successful delivery of messages increases, and the message loss decreases. When 40 of network nodes are selfish, the initial packet delivery ratio is 86% of all the sent packets, which increases to 95% over time.

Fig. 1 :Fig. 2 :

 12 Fig.1: Packet delivery ratio

Fig. 3 :Fig. 4 :

 34 Fig.3: Routing overhead

TABLE I .

 I

	SelfExculpation	Packet sent to the source by the last node that tried to
		transmit the message to report the refusal of a node to
		transmit the message,
	Selfish_Detection Packet sent by a node that does not receive the
		exculpation of his successor, thus accusing him of
		being selfish. It must be said here that if for example
		the message is sent by a node Ni, then the node Ni-1
		will not accept to transmit that packet only if Ni+1 has
		exculpated Ni by sending a 2HopAck packet to him.
	SelfishAlert	Packet sent in order to report the detection of a selfish
		node.

MESSAGES LIST

Message Definition 2HopAck

Message sent by a node Ni to Ni-2 node.

TABLE II .

 II

	RST	Positive value to add to the reputation of a
		node as a bonus for sending 2HopAck
		packet.
	lastBroadcastedTrust i (j)	The last value of reputation had broadcast the node i about the node j.
	Ack_Delay	The time that a node has to wait for
		acknowledgment of the message he
		collaborated to transmit. After that, the node
		Ni launches Exculpation_Delay.
	Exculpation_Delay	The time node Ni must wait for the
		2HopAck packet from Ni+1 toward Ni-1.
		Beyond this period, the node Ni sends a
		packet SelfExculpation.
	Others_Exculpation_Delay The time a node Ni must wait 2HopAck
		packet from node Ni+2 exculpating the node.
		Ni+1.
		The initial reputation of each node.
		Change threshold that must wait before
		broadcasting the new reputation of a node.
	Threshold	The threshold for which a node is
		considered selfish if it goes below it.
	WitnessRate
			PARAMETER LIST
		Parameter/function	Definition
		RSD	Positive value to add to the reputation of a
			node having transmitted a message.
		PNSD	Positive value to subtract of the reputation
			of a node as a punishment for failing to
			transmit a message.
		APNSD	Positive to subtract also the node that seems
			to be the selfish node value.
		RSM	Positive value to add to the reputation of a
			node as a reward for reporting the bad
			behavior of a node.

TABLE III .

 III

	SIMULATION PARAMETERS
	Parameter	Value
	Number of nodes	50
	Rate selfish nodes	0-40 % (step 5%)
	Maximum Speed	15 m/s
	Maximum idle time	3 s
	Radius increased	150 m
	Width of the area	1000 m
	Length of the area	1000 m
	Simulation time	300 s
		0.75
	Threshold	0.25
	RSD	0.1
	PNSD	0.15
	APNSD	0.05
	RST	0.05
	RSM	0.03
		0,2
	WitnessRate	5 %


Mokrane Dahoumane
email: m.dahoumane@ipnl.in2p3.fr

D Dauvergne

J Krimmer

J.-L Ley

E Testa

Y Zoccarato

A Low Noise and High Dynamic Range CMOS Integrated Electronics associated with Double Sided Silicon Strip Detectors for a Compton Camera gamma-ray Detecting System

I. INTRODUCTION

everal techniques to be used in hadrontherapy for cancer treatment worldwide are under study and development. The treatment consists in irradiating the tumorous cells with protons or ions. During irradiation, part of the incident projectiles undergoes nuclear fragmentation. Since excited fragments emit γ-rays almost instantaneously (below the ns range), the detection of prompt-gamma rays can be used to monitor online the ion range [START_REF] Min | Prompt gamma measurements for locating the dose falloff region in the proton therapy[END_REF], [START_REF] Testa | Monitoring the Bragg peak location of 73 MeV⁄u carbon ions by means of prompt γ-ray measurements[END_REF]. A Compton camera device has been proposed [START_REF] Richard | Design Guidelines for a Double Scattering Compton Camera for Prompt-gamma imaging During Ion Beam Therapy: A Monte Carlo Simulation Study[END_REF], [START_REF] Roellinghoff | Design of a Compton camera for 3D prompt-gamma imaging during ion beam therapy[END_REF], and is nowadays being one of the most attractive techniques thanks to its very high efficiency and fastness for the online dose control and high resolved 3D image reconstruction. In the proposed system shown in Fig. 1 The detectors have been bonded and mounted on a PCB test board for characterization. First measurements of the leakage current as a function of temperature have already been done successfully. The scatter detector provides the spatial and temporal coordinates (x, y, z, t) and the energy deposited during the interaction of γ-rays. The DSSD detector will be S coupled with a multi-channel readout electronics fulfilling the particular requirements imposed by the application, such as:

• Low Equivalent Noise Charge (ENC) about 120 electrons rms (FWHM = 1 keV), • Large dynamic range for both P&N polarities (from 3000 to 3000,000 electrons -N side), • High occupancy rate: 10 5 hits/s per strip. This requires a fast switched system to avoid pile-up. For this aim, a dedicated Front End Electronics (FEE) is designed and fabricated using the AMS CMOS 0.35 µm process. Hereafter will follow design details and test results of the realized circuit prototype. II. DESIGN ARCHITECTURE Fig. 2 shows a block diagram of a single channel of the circuit which is AC-coupled with a double sided DSSD detector. According to signal-to-noise ratio, and number of integrated functionalities, this circuit is an improved version and a complete system in comparison with the results of a previous version [START_REF] Dahoumane | A Low Noise and High Dynamic Charge Sensitive Amplifier-Shaper associated with Silicon Strip Detector for Compton Camera in hadrontherapy[END_REF]. Each channel includes a Charge Sensitive Amplifier (CSA) followed by two parallel shapers. Slow and fast shapers, with 1 μs and 15 ns shaping time are used to measure the energy and time stamping, respectively. In order to increase the detection efficiency, a 3 bit multi-gain configuration is chosen to implement the fast shaper. The output of the latter is sent to a voltage comparator which provides a digital signal used as event time stamp and resetting signal of the CSA feedback capacitor to avoid pileup or circuit saturation. During the reset phase, the outputs of the two shapers are fixed to a reference value. A 5 bit DAC is integrated to compensate any comparator offset dispersion between channels. A programmable digital circuit is also integrated in this design to adjust the delay and the width of the reset signal with 3 and 5 bit control signals, respectively. All configuration settings are controlled by an I2C interface circuit which is integrated in the circuit. The present design provides the readout of the two sides of the DSSD thanks to a hole or electron configurable system. Indeed, a DC shift level diode was inserted between the source of the IN-NMOS transistor and the ground as shown in Fig. 3.

In order to determine the DSSD signal profile and thus the depth of interaction point in the silicon, the CSA output can be directly accessed.

The detector, with a capacitance C d , produces charge pulses that are integrated on the CSA feedback capacitor C f [START_REF] Dahoumane | A Low Noise and High Dynamic Charge Sensitive Amplifier-Shaper associated with Silicon Strip Detector for Compton Camera in hadrontherapy[END_REF], [START_REF] Paul | Prospects for charge sensitive amplifiers in scaled CMOS[END_REF], [START_REF] Hofmann | Development of readout electronics for monolithic integration with diode strip detectors[END_REF].

A. The Charge Sensitive Amplifier (CSA) description

Classical cascode architecture has been chosen to implement the CSA stage of the readout [START_REF] Dahoumane | A Low Noise and High Dynamic Charge Sensitive Amplifier-Shaper associated with Silicon Strip Detector for Compton Camera in hadrontherapy[END_REF], [START_REF] Radeka | Design of a charge sensitive preamplifier on high resistivity silicon[END_REF]. The geometry of each component is optimized for the foreseen performances. The first order transfer function of the CSA in response to a pulse charge stimulus is given by:

f d in out C G C j Zf I V 0 0 1 ) ( ω ω ω + - = , (1)
where, Z f is the equivalent feedback impedance composed by R off (very large) of the MOS switch in parallel with C f . and C d the detector capacitance. The value of C f (250 fF) is fixed by the maximum signal of the dynamic range and the power supply voltage value which is 3.3 V in 0.35 µm CMOS process we used. An NMOS input transistor has been chosen to get a better power supply rejection ratio and higher speed than the PMOS one (more details were reported in the previous version of this design [START_REF] Dahoumane | A Low Noise and High Dynamic Charge Sensitive Amplifier-Shaper associated with Silicon Strip Detector for Compton Camera in hadrontherapy[END_REF]). In order to minimize the ballistic deficit, G 0 C f has to be very superior to C d (G 0 C f >>C d ), where G 0 is the open loop gain of the CSA, C f the feedback capacitance and C d the detector capacitance. To ensure up to 99 % of signal charge transfer, G 0 should be around 67 dB according to the following formula which gives the charge transfer rate α:

f d C G C 0 1 1 + = α . ( 2
)
The rise time of the CSA output for a pulse charge stimulus is determined by the amplifier time constant τ CSA as:

in d f d CSA R C C G f C = = 0 0 2π τ , (3)
where,

0 0 2 G f c π ω = (4)
is the Gain Bandwidth Product. A pole-zero R and C feed forward compensation technique is used to improve stability without affecting the speed of the CSA [START_REF] Sansen | Feedforward Compensation techniques for High Frequency CMOS amplifier[END_REF].

The authorized output dynamic range maintaining all transistors in the saturation mode is given by the approximate following formula:

V fF fC C Q V f out 92 . 1 250 480 max 0 - = - = - = , ( 5
)
where Q 0 is the injected charge. The total dynamic range corresponding to both polarities equals ±1.92 V. So, a DC level shifting is needed in the case of P polarity (Cf. Fig. 3).

The CSA includes a source follower witch is needed to increase the driving capability.

B. The shaper implementation

A CR-RC signal shaping has been chosen to implement the two shapers (Cf. Fig. 3). Active shaping is performed by using a two stage compensated Miller OTA (Operational Transconductance Amplifier) [START_REF] Dahoumane | A Low Noise and High Dynamic Charge Sensitive Amplifier-Shaper associated with Silicon Strip Detector for Compton Camera in hadrontherapy[END_REF]. The shaping stages perform a pulse shaping primarily to optimize the signal-to-noise ratio (SNR) of the system and also to measure the energy and the time with the slow shaper around 1 µs shaping time and the fast one with a shaping time of 15 ns, respectively.

CR-RC shaper transfer function in the frequency domain is given by:

( ) 2 1 ) ( s s s H τ τ + = , (6)
where, τ is the shaping time. Here, we chose the derivation and the integration time constants to be equal (Cf. Fig. 3):

R C shaping × = τ . (7)

III. NOISE STUDY

A. Noise calculation

The most critical issue in this design is the noise. The desired energy resolution of the Compton camera which gives an acceptable spatial resolution of the whole hadrontherapy system must be below 1 keV FWHM. This corresponds to an input ENC (Equivalent Noise Charge) of 120 electrons rms.

Generally, there are two main sources of noise in a CSA: a parallel and a series noise. The parallel noise is generated by the thermal noise of the feedback resistor and the detector leakage current fluctuations. The input referred power spectral density (PSD) of the parallel noise is given by:

2 4 2 ) ( n f G i i R kT qI S = + = ω , (8)
where, q is the electron elementary charge, I G is the detector leakage current, k is the Boltzmann constant and T is the temperature.

In this design, the feedback resistor was removed and replaced by a MOS switch. Therefore, this source of noise which represented 75% of the total noise in the previous design related in [START_REF] Dahoumane | A Low Noise and High Dynamic Charge Sensitive Amplifier-Shaper associated with Silicon Strip Detector for Compton Camera in hadrontherapy[END_REF] has been canceled. The noise input voltage spectrum (series noise PSD) of a MOS transistor in saturation is given by:

f A e WLf C K g kT S n ox f m v + = + = 2 3 8 ) (ω . ( 9
)
The first term is the channel thermal noise and the second term is the 1/f or Flicker noise [START_REF] Sansen | Limits of low noise performance of detector readout front ends in CMOS technology[END_REF]. Optimal noise matching is found by varying input transistor dimensions. Total (series and parallel) noise output voltage spectrum is given by:

2 2 2 2 2 1 ) ( f n n f d out C i f A e C C S ω ω + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = . ( 10
)
This formula is obtained through the following approximations: infinite open loop gain of CSA and considering an ideal integrator (i.e. no feedback resistance). The output noise voltage of the complete chain is performed by integrating the product of CSA's output PSD by the shaper's Transfer function as in:

π ω ω ω 2 ) ( ) ( 2 0 2 d j H S V out out ∫ ∞ = . (11)
Total input referred noise after shaping is given by: π τ τ where, C t is the total input capacitance composed mainly by C d and grid-source C gs capacitance of the CSA input transistor, τ is the filtering time constant (shaping time). In this design, calculations were done to find the optimal value of W/L of the input transistor leading to the best trade-off between minimizing series and 1/f noise and maintaining low value of Ct.

B. Noise simulations

To simulate the noise of a switched system, a transient noise simulation method is recommended, the drawback of this method is its high simulation time. Fig. 4 shows the transient noise response of the CSA to the same injected charge using Cadence tool: 75 sweeps are used. The CSA was configured in the electron functioning mode. There is different ways to calculate the noise on the Fig. 4. Best noise results are obtained by combining a CDS (Correlated Double Sampling) and averaging techniques. First an interval on the curve is selected and an average of the values is calculated by choosing number of samples. Then, the signal amplitude is the difference between the hit signal and its base line (Cf. Fig. 4). The standard deviation σ of the amplitudes is then calculated. The noise is given by: ( )

q gain ENC × = σ , ( 13
)
where, gain is the CSA conversion gain given in mV/fC and q is the elementary charge. More statistics increase obviously the result, but at the expense of the counting rate. So, a compromise is to be found between counting rate and noise. This method gave an ENC noise of 105 electrons (rms), with CSA conversion gain = 3.5 mV/fC andσ=59.2 µV.

The same method has been used to measure the noise (electrically) in the test.

IV. LAYOUT DESIGN

The multi-channel nature of the design which will fit the form of the strips of the DSSD detector (crosstalk issue), low noise and high speed are parameters that require a special care when drawing the layout of the input stage (CSA). Therefore, the R in must be minimized by splitting the input transistor into a matrix of small transistors perfectly identical. The size of each channel has exactly the width of a pad (100 µm). This makes the channel multiplication easier and minimizes the mismatch between channels.

Fig. 5 shows the layout of the ASIC, an emphasis of the input transistor of the CSA is carried out.

V. EXPERIMENTAL RESULTS

A prototype has been fabricated in a CMOS 0.35μm process from Austria Micro System. It includes 8 channels of the described FEE readout of the Compton camera. A photography of the chip is shown in Fig. 6. The circuit dissipates a power of 23 mW per channel from 3.3 V supply voltage and occupies an area of 2×4.5 mm 2 , including pads.

A. Test setup

A test board was designed to characterize the prototype experimentally. Fig. 7 shows a photography of the test board and a synoptic of its modules. A charge injection circuit is used to simulate the detector charge which will be generated by the stopping of a Compton recoil electron in the DSSD. This circuit is composed of a fast pulse generator terminated by a 50 Ω resistor, a 1 pF injection capacitor and a 10 pF capacitor to simulate the detector capacitance. The response of the ASIC to an input pulse is sent to a 50 Ω fully differential buffering stage to drive different signal processing devices (e.g. scope, external amplifiers, ADCs…).

B. Test results and circuit performances

The circuit has been successfully tested. The test results are in good agreement with analytic and simulation calculations. All the functionalities have been validated. Fig. 8 shows output waveforms of the circuit for both negative and positive signal polarities. The measured shaping time of the slow shaper is 0.9 µs. The measured rise time of the CSA is 30 ns in response to a fast pulse injected charge. The CSA is fast enough to follow the incoming charge signal without modifying its shape. The circuit achieves a high linearity even over the needed dynamic range, mostly less than 1 % of INL with a conversion gain of 3.6 mV/fC, which is very close to the simulation one. The noise evaluation has been performed according to the measurement standards. Noise and signal were measured in the same conditions (temperature and electromagnetic environment).

An ENC of 290 electrons rms was measured for electron configuration on the output of the CSA. The ENC measured on the slow shaper output is about 390 electrons rms (electron configuration). The performances obtained for the hole configuration are slightly lower than those achieved for the electron one. This is due to the DC shift level diode used in case of P polarity (Cf. Fig. 3). The parallel disposition and neighborhood of channels gives a cross talk of 0.6 %, mostly (>90%) coming from the supply voltage disturbance.

C. Time measurements and digital part testing

The time measurement is performed on the fast shaper's branch of a readout channel. As said above, the fast shaper is followed by a fast comparator. The latter provides a digital signal used for time stamping and reset signal. A digital part is integrated in the chip to control the width of the reset signal and its occurrence delay. In order to bypass the comparator offset dispersion problems, a 5bit DAC has been integrated. It tunes the reference voltage of the comparator of each channel individually. All these parameters are controllable thanks to I2C interface witch is integrated in this prototype.

The tests of all these modules have been successfully performed. Among them: comparator S-curves, DAC linearity, I2C writing and reading frames, fast shaper gain. The digital part is thoroughly tested, because it is very important to control the instant of the reset separately for the CSA and the shaper. The width of the shaper reset must be larger than the CSA one. This was verified and validated in the tests.

D. Detector readout system

After electrical characterization, the ASIC was coupled to a 64-strip double-sided SSD detector to measure the energy spectrum of radioactive sources (e.g. 133 Ba providing photon lines at 30.9, 53, 80.9, 276, 303, 356 and 383 keV). Fig. 10 shows a photography of the PCB card designed to support mechanically and to bias the detector. This mezzanine card will be mounted on a data acquisition (DAQ) mother card in the way shown in Fig. 1-b. The DAQ card is being manufactured.

VI. CONCLUSION AND OUTLOOK

An 8-channel front end readout electronics has been designed and fabricated in 0.35 µm CMOS process from AMS. It will readout the signals delivered by the Silicon Strip Detectors constituting the Compton camera for promptgamma monitoring of hadrontherapy. The test of this prototype has given very satisfactory results and has validated all the functionalities and features of the circuit. By using a switch-reset technique, parallel noise that could be generated by a feedback resistance is removed. In contrast, the complexity of the design is increased. Noise measurement setup is being optimized in order to get better results. In the final design of a plane composing the scatter detector the analog signal of the ASIC will be directly sent to an ADC. So, the scope and the setup noise will be canceled. Production of 180 additional chips is scheduled for February 2015, to equip all the scatter detectors.

Abstract-An 8 -

 8 channel Front End integrated Electronics (FEE) circuit is designed and fabricated using the AMS-CMOS 0.35 µm process to equip a Compton camera system for quality control in Hadrontherapy. The circuit provides the energy deposited by prompt γ rays interacting in a 2 mm thick Double sided Silicon Strip Detector (DSSD), the (x,y,z) space coordinates and the time of the interaction. Each channel includes a Charge Sensitive Amplifier (CSA) followed by two parallel shapers. Slow and fast shapers, with 1 μs and 15 ns shaping time are used to measure the energy and time stamping, respectively. In order to increase the detection efficiency, a 3 bit multi-gain configuration is chosen to implement the fast shaper. The output of the latter is sent to a voltage comparator which provides a digital signal used as event time stamp and resetting signal of the CSA feedback capacitor to avoid pileup or circuit saturation. A 5 bit DAC is integrated to compensate any comparator offset dispersion between channels. A programmable digital circuit is also integrated in this design to adjust the delay and the width of the reset signal. All configuration settings are controlled by an I2C interface circuit which is integrated in the circuit. The present design provides the readout of the two sides of the DSSD thanks to a hole or electron configurable system. All the functionalities of the design have been successfully tested and validated. The test results are in good agreement with analytical and simulation calculations. A high linearity over a range of 3×10 3 to 3×10 6 electrons is reached with a conversion gain of 3.6 mV/fC. The circuit (CSA output) achieves an ENC (Equivalent Noise Charge) of 290 electrons rms. The circuit dissipates 23 mW/channel and occupies an area of 2×4.5 mm 2 , including pads.

Fig. 1 .

 1 Fig. 1. Compton Camera device. (a): monitoring configuration system: the prompt γ-ray emission points are reconstructed by intersecting the ion trajectory, given by the hodoscope and the Compton cone, reconstructed with the Compton camera [4]. (b): zoom on the scatter detector composed of 10 planes of DSSD mounted on PCB EFF&DAQ card.

Fig. 2 .

 2 Fig. 2. Block diagram of a single channel of the readout electronics to be coupled with a double sided DSSD detector. The P and N strips are read with two different selectable configurations.

Fig. 3 .

 3 Fig. 3. CMOS switched reset feedback : illustration of a hole configuration by inserting a well dimensioned DC shift level Diode on the source of the input transistor of the CSA.

Fig. 4 .

 4 Fig. 4. Transient noise response of the CSA (75 simulation iterations), configured in electron functioning mode.

Fig. 5 .

 5 Fig. 5. Layout of the full chip fabricated in CMOS 0.35 µm process of AMS: a zoom on the CSAs' input transistor is shown.

Fig. 6 .

 6 Fig. 6. Photography of the chip showing its various blocks: 8 parallel complete channels, bias blocks and individual testing blocks.

Fig. 7 .

 7 Fig. 7. Test set up and photo of the test board supporting the ASIC (device under test). On the top, is shown a synoptic of the test board.

8 .

 8 Screenshot of the response of the circuit to P and N polarities. In (a) is shown the CSA output and in (b) the CSA+slow shaper output. Linearity measurement was also performed and shown in Fig. 9. The top of the figure shows the measured and simulated CSA outputs as a function of the input charge (in fC). The bottom of this figure shows the measured and simulated output of the chain including CSA and slow shaper. On the left side is shown the electron mode and on the right the hole mode functioning of the circuit.

Fig. 9 .

 9 Fig. 9. Output vs. injected charge (Qinj) response of the CSA for N and P polarities on the top side. Output vs Qinj response of a complete chain (CSA followed by slow shaper) for N and P polarities on the bottom of the figure.

Fig. 10 .

 10 Fig. 10. Photography of the silicon detector bonded on a PCB mezzanine card. The P and N strip are ac-coupled with the readout ASICs. Bias resistors are also mounted on this card. TABLE I gives a summary of the circuit performances. The measured parameters are close to schematic simulation ones. The values of the measured noise include the setup and the

TABLE I .

 I PERFORMANCE SUMMARY

This work is supported by the FP7-ENVISION program (grant agreement n°241851), the ANR Gamhadron project (ANR-09-BLAN-0106), the Rhône-Alpes Regional Program for Hadrontherapy Research, and the LabEx PRIMES (ANR-11-LABX-0063).