T.-H Nguyen

S.-P Gorza

Laurent Bramerie

Mathilde Gay

Marwa Kazdoghli Lagha

Member, IEEE Trung-Hien Nguyen
email: trung-hien.nguyen@ulb.ac.be

Christophe Peucheret

Robin Gerzaguet

Simon-Pierre Gorza

Member, IEEE Jérôme Louveaux

Member, IEEE François Horlin

Experimental Demonstration of the Trade-off between Chromatic Dispersion and Phase Noise Compensation in Optical FBMC/OQAM Communication Systems

Keywords: Filterbank multicarrier, offset-QAM, coherent detection, PN estimation, CD compensation, CFO compensation, long-haul communications. I. INTRODUCTION

Filterbank multicarrier based on offset-quadrature amplitude modulation (FBMC/OQAM) is a promising candidate for optical fiber communication systems, thanks to its better time/frequency confinement compared to other multicarrier modulations. Among linear impairments, the compensation of fiber-induced chromatic dispersion (CD) and laser-induced phase noise (PN) in FBMC/OQAM systems induces a compromise in terms of the number of used subcarriers. Considering a fixed dedicated signal bandwidth, the number of subcarriers is expected to be large enough to allow a better frequency-domain CD compensation. On the other hand, it should be sufficiently small in order for the compensation of common phase error inherent to the PN to work properly. In this paper, we experimentally demonstrate the trade-off between CD and PN compensation that we previously highlighted by simulations. More specifically, considering a 20-GHz FBMC/4--OQAM modulation and an aggregated laser linewidth of about 200 kHz, we show that the maximum transmission distance reaches 3100 km with nearly 512 active subcarriers and 3-tap equalizers, when a maximum 1-dB optical signal-to-noise ratio (OSNR) penalty at a bit-error-rate (BER) of 3.8× ×10 -3 can be tolerated. Moreover, we propose and validate a frame structure and an integrated synchronization/channel equalization architecture to implement a standalone demodulation system.

appeared as a promising multicarrier modulation candidate in optical fiber communication systems [START_REF] Fickers | Multicarrier offset-QAM for long-haul coherent optical communications[END_REF][START_REF] Horlin | Dualpolarization OFDM-OQAM for communications over optical fibers with coherent detection[END_REF][START_REF] Zhao | Dispersion tolerance enhancement using an improved offset-QAM OFDM scheme[END_REF][START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF]. Compared to the commonly used optical orthogonal frequency-division multiplexing (OFDM) modulation, FBMC/OQAM has no cyclic prefix and hence increases the throughput rate. Originally, FBMC/OQAM was introduced assuming a large subcarrier bandwidth, i.e. 2-4 GHz. Thanks to OQAM, the orthogonality between adjacent subcarriers is preserved without requiring any redundant cyclic prefix as for OFDM. However, when the system is implemented with multiple optical sub-channels, phase-coherent lasers are required, leading to an increase of the system cost. We alternatively proposed to increase the number of subcarriers of the FBMC modulation [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF]. In the multiple optical sub-channels case, by deactivating one subcarrier at the spectrum edge of each subchannel, multiple sub-channels can be placed closer to each other at the cost of negligible guard bands (tens of MHz only). The constraint on phase-coherent lasers is also relaxed. This approach is made possible thanks to the good time-frequency confinement of FBMC modulation and a better side-lobe suppression compared to OFDM. Fig. 1 illustrates the multiple sub-channels case with a constraint of a negligible guard band in a wavelength-division-multiplexing (WDM) system.

In contrast to single carrier systems, multicarrier systems leverage the use of a simple 1-tap equalizer on a per-subcarrier basis to compensate for the fiber-induced chromatic dispersion (CD) by using a sufficiently high number of subcarriers. This is made possible by the fact that the channel is nearly flat at the subcarrier level. Several studies aimed at enhancing the transmission distance by using more advanced equalizer structures [START_REF] Zhao | Dispersion tolerance enhancement using an improved offset-QAM OFDM scheme[END_REF][START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF][START_REF] Rottenberg | Advanced chromatic dispersion compensation in optical fiber FBMC-OQAM systems[END_REF], albeit at the price of additional computational complexity. Increasing the number of subcarriers leads to the increase of symbol duration and unfortunately makes the multicarrier systems more prone to the time-varying laserinduced phase noise (PN) effects. PN creates loss of the OQAM orthogonality, resulting in inter-carrier interference (ICI) and inter-symbol interference (ISI). Considering the FBMC symbol level, PN causes both common phase error (CPE) and ICI [START_REF] Kakkavas | FBMC-OQAM with phase noise: Achievable performance and compensation[END_REF]. Similar to OFDM systems, ICI compensation methods often require feedback structures that may be undesirable in real-time implementations. In contrast, CPE compensation methods only need feedforward structures to still deliver a good performance [START_REF] Nguyen | Simple feedforward carrier phase estimation for optical FBMC/OQAM systems[END_REF]. We hence focus on CPE compensation methods. Research on CPE compensation methods is very active in both wireless [START_REF] Kakkavas | FBMC-OQAM with phase noise: Achievable performance and compensation[END_REF][START_REF] Dore | Blind phase tracking algorithm for FBMC receivers[END_REF][START_REF] Zaidi | Evaluation of waveforms for mobile radio communications above 6 GHz[END_REF][START_REF] Moles-Cases | A comparison of OFDM, QAM-FBMC, and OQAM-FBMC waveforms subject to phase noise[END_REF] and optical communications [START_REF] Nguyen | Lowcomplexity blind phase search for filter bank multicarrier offset-QAM optical fiber systems[END_REF][START_REF] Nguyen | Extended Kalman filter for carrier phase recovery in optical filter bank multicarrier offset QAM systems[END_REF][START_REF] Rottenberg | ML and MAP phase noise estimators for optical fiber FBMC-OQAM systems[END_REF]. Although the proposed algorithms for CPE compensation have proved their effectiveness, they provide a limited performance when the number of subcarriers is too high [START_REF] Nguyen | Simple feedforward carrier phase estimation for optical FBMC/OQAM systems[END_REF].

As pointed out in our recent work [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF], there exists therefore a trade-off between CD and PN compensation when designing an FBMC/OQAM system utilizing a dedicated signal modulation bandwidth. However, this result was not validated experimentally. Note that, the trade-off study and system design can be extended quite straightforwardly to other multicarrier systems such as those using OFDM. In this paper, we apply the system-design methodology proposed in [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF] to a particular system specification and experimentally validate it in a system using 20-GHz FBMC/OQAM modulation, a summed laser linewidth of about 200 kHz and 1-or 3-tap equalizers. Moreover, we propose a frame structure and an integrated synchronization/channel equalization architecture to enable the system to work properly.

The paper is organized as follows: in Section II, a mathematical description of an FBMC/OQAM transmission system is introduced. In Section III, we present the transceiver structure. The detailed digital signal processing (DSP) is discussed in Section IV. In Section V, we describe our experimental setup. The results are presented and discussed in Section VI. Section VII discusses the influence of the digitalto-analog converter/ analog-to-digital converter (DAC/ADC) limited resolution. Finally, Section VIII concludes the paper.

II. FBMC/OQAM TRANSMISSION SYSTEM MODEL

In order to assess the trade-off between CD and PN compensation, we consider only one polarization, even if the results can straightforwardly be extended to two polarizations. An equalizer for polarization demultiplexing and polarization mode dispersion (PMD) compensation can, for example, be designed based on the minimum mean-square-error (MMSE) criteria [START_REF] Horlin | Dualpolarization OFDM-OQAM for communications over optical fibers with coherent detection[END_REF]. We denote the number of subcarriers, subcarrier index and QAM symbol duration as 2M, m and T, respectively. At the transmitter, a burst of N S QAM symbols, c m,q , are firstly passed to the OQAM block, where the real and imaginary components of QAM symbols are delayed with respect to each other to form the real-valued symbols, d m,l , at the rate 2/T. These real-valued symbols are then multiplied by a phase rotation factor, θ m,l = j m+l . After that, the samples are up-sampled by M before being filtered by the synthesis filter bank (SFB). Note that we use a poly-phase network (PPN) [START_REF] Bellanger | FBMC physical layer: a primer[END_REF] in order to get an efficient implementation of the SFB. We use the PHYDYAS filter [START_REF] Bellanger | FBMC physical layer: a primer[END_REF] as the prototype filter g[n] of length L g = 2KM, where K is the overlapping factor set to 4. The output FBMC signal at the rate F S = 1/T S = 2M/T is obtained by the summation of all subcarriers and can be written as [START_REF] Siohan | Analysis and design of OFDM/OQAM systems based on filterbank theory[END_REF] s n

[ ] = d m,l ⋅ g m,l n [ ] m=1 2 M ∑ l=1 2 N S ∑ , (1)
where g m,l n

[ ] = θ m,l g n -lM [ ]exp jπ m / M ( ) n -(L g -1) / 2 ( ) ( ) .
After generation and conversion into the analog domain, the electrical signal is then modulated onto the optical domain before propagating over optical fibers. In our studies, we work in the linear transmission region, where CD is the main impairment. The transfer function associated with CD, H f [ ] , can be expressed as [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF] H f

[ ] = e -j π Dλ 2 L c f 2 , ( 2
)
where L, λ and c are the fiber length, the wavelength and the speed of light in vacuum, respectively. The fiber dispersion coefficient is denoted by D, whose typical value is 17 ps/nm/km for a standard single mode fiber (SSMF). Note that, f is the relative frequency with respect to the optical carrier frequency and f ∈ -

F S / 2, F S / 2 [ ] .
At the receiver side, the received signal, r[n], after heterodyne-detection is corrupted by zero-mean additive white Gaussian noise (AWGN) denoted by w[n], the carrier frequency offset (CFO) Δf CFO (originating from the frequency difference between the transmitter and receiver local oscillator lasers) and the PN φ[n] of linewidth Δν. The combined PN coming from transmitter and receiver lasers is modeled as a Wiener process [START_REF] Nguyen | Simple feedforward carrier phase estimation for optical FBMC/OQAM systems[END_REF] φ

n [ ] = φ n -1 [ ]+θ n [ ] , (3)
where θ[n] is a zero mean real Gaussian random variable with variance σ θ 2 = π⋅Δν⋅T/M. The received signal can be expressed as

r n [ ] = S f [ ]H f [ ]e j 2π fT S n f =-F s /2 F s /2 ∑ + w n [ ] ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ e j 2π n⋅ f CFO ⋅T S +φ n [ ] (
) , ( 4)

in which S f [ ] is the Fourier transform of s[n].
Coarse CFO compensation is carried out within the framework of the frame synchronization (see Section IV.A). We denote ! r n

[ ] as the received signal after frame synchronization. In order to build a proper receiver chain, some assumptions are made on the impairments and channel effects encountered by the received signal as follows -We assume that the remaining CFO is small (i.e., smaller than the subcarrier spacing) and constant over the FBMC symbol.

-We assume that the coherence bandwidth of the channel is larger than the subcarrier spacing [START_REF] Rappaport | Wireless communications: Principle and practice[END_REF]. It means that simple single tap equalization can be applied at the receiver stage.

-We assume that the coherence time of the phase noise process is shorter than, or equal to, the FBMC symbol duration. By doing so we can approximate (3) by the so-called CPE term φ .

Based on the aforementioned assumptions 1 , the received signal at the output of the analysis filter bank (AFB), at the subcarrier m 0 and the multicarrier symbol l 0 can be expressed as 1 It is important to note that these hypotheses are made to ease the receiver stage processing. In practice, they are not mandatory to allow a functional chain.

y m 0 ,l 0 = ! r n [ ]g m 0 ,l 0 * n [ ] n=1 L g ∑ ≈ e j πl 0 ⋅Δf l 0 +φ l 0 ( ) H m 0 d m,l g m,l n [ ]g m 0 ,l 0 * n [ ] n=1 L g ∑ m=1 2 M ∑ l=1 2 N S ∑ + ! w m 0 ,l 0 (5)
where H m = H[f m ] with f m being the m-th subcarrier frequency, Δf l 0 and φ l 0 are the CFO and CPE at the multicarrier symbol l 0 , respectively , ! w m 0 ,l 0 denotes the filtered additive noise with zero mean and variance of the complex noise σ w 2 . Note that, the coefficient 2 on the exponential term of the residual CFO disappears due to the fact that the time-frequency spacing product of FBMC is equal to 0.5. Since

Re g m,l n [ ]g m 0 ,l 0 * n [ ] n=1 L g ∑ { } ≈ δ m-
m 0 ,l-l 0 , in which δ is the Kronecker delta function and Re is the real part operator, the received signal in (5) can be reformulated as follows

y m,l ≈ H m d m,l + j ⋅u m,l ( ) e j πl⋅Δf +φ l ( ) + ! w m,l , (6)
where u m 0 ,l 0 is the intrinsic interference coming from the neighboring symbols on the subcarrier of interest. It is assumed to be independent of the transmitted data at the subcarrier and time index of interest.

After channel compensation, residual CFO and PN tracking, the transmitted signal can be recovered by taking the real part of the compensated signal. In the following sections, we discuss in detail the frame structure and the digital signal processing (DSP) procedure.

III. FRAME STRUCTURE AND RECEIVER ARCHITECTURE

The schematic diagram of an optical FBMC/OQAM transceiver is illustrated in Fig. 2. At the transmitter side, the following stages are implemented:

-FBMC/OQAM generation: the QAM symbols are passed to the OQAM pre-processing block. The OQAM data symbols and the training symbols are sent to the SFB in order to construct the time-domain FBMC signal.

-Training sequences for the fine CFO (A) and channel estimation (B): they are implemented before the OQAM data symbols (D), as shown in Fig. 3. Considering the data-bearing training symbols, zeros are alternatively inserted along with pilot symbols, which are binary phase-shift-keying (BPSK) data. The zeros play the role of avoiding interference from the adjacent pilot symbols. Note that, we deactivate the subcarriers at the center (DC subcarrier) and the two edges of the spectrum due to the bandwidth limitation of the digital-toanalog converter.

-FBMC frame construction: the frame synchronization training sequence (P) is appended in front of the generated FBMC signal before being optically modulated and propagated over the optical fiber. For simplicity, we choose this training sequence of BPSK modulation and assume that it is known beforehand at the receiver side.

At the receiver side (Fig. 2), after coherent detection, we carry out the following steps -Time-domain frame synchronization and coarse CFO compensation: the detailed algorithms will be discussed later in Section IV.A.

-Frequency-domain processing: the signal is converted to the frequency-domain by passing through the AFB. The processing consists of the coarse CD compensation, fine CFO estimation (using A), channel equalization (using B) and blind PN tracking. Note that, in order to compensate for the channel response, we use a two-stage compensation, in which the first stage suppresses the static CD based on the method in [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF] and the second stage uses the channel estimation (CE) pilots to compensate for residual CD and other frequency responses inherent to bandwidth-limited devices (see Sections IV.B and C).

-Finally, the OQAM post-processing block transforms the OQAM signals back to QAM signals for bit-error-rate (BER) calculation. In what follows, we describe the algorithms used in each block at the receiver side.

IV. DIGITAL SIGNAL PROCESSING (DSP) ALGORITHMS

A. Frame Synchronization

The training sequence for the frame synchronization, p[n], is used for start of frame (SoF) identification and coarse CFO compensation. Before doing coarse CFO compensation, we need to identify the SoF. In case the received signal r[n] suffers mainly from the influences of the CFO and the laser PN, a good correlation property of the training sequence can be maintained. Instead of using a timing metric that requires a specific structure of the training sequence, i.e., Schmidl-Cox timing metric [START_REF] Schmidl | Robust frequency and timing synchronization for OFDM[END_REF], we propose to use only a known random sequence and to identify the SoF by the following differential cross-correlation

D k n [ ] = 1 N -k r * n + l [ ] p l [ ] ( ) r * n + l -k [ ] p l -k [ ] ( ) * l=k N -1 ∑ , ( 7
)
where k is the cross-correlation window index, 1 ≤ k ≤ W, W is the cross-correlation averaging window and N is the length of the considered received signal. It is worth noticing that in transmission systems, the CD effect in the fiber cannot be neglected. Fortunately, a coarse estimate of the CD accumulated over a link is normally known beforehand. Instead of applying a coarse CD compensation to the received signal, we propose here to pre-distort the training sequence p[n] with the known CD using (2) and then apply [START_REF] Nguyen | Simple feedforward carrier phase estimation for optical FBMC/OQAM systems[END_REF] for the SoF identification. It is worth mentioning that this predistortion can be applied once for all, at a rate that is negligible compared to that of the received signal. The complexity is hence low because of the short sequence and low rate refreshing calculation. In order to derive a closedform expression of the cross-correlation, which allows the coarse CFO estimation, we neglect the additive noise term in (4). Eq. ( 7) can be re-written as

D k n [ ] ≈ 1 N -k e -j 2π ⋅ f CFO ⋅kT S z * n + l [ ]z n + l -k [ ] ( ) ⋅ p l [ ] p l -k [ ] * ( ) l=k N -1 ∑ ( 8
)
where z is the received signal without AWGN, different from r in the CFO component, thus enabling to estimate the CFO.

The SoF can then be estimated by

n ! = arg max n D k n [ ] k=1 W ∑ . ( 9
)
Based on (8), the coarse CFO can be estimated as follows

f ! CFO = - 1 W ∠D k n [ ] 2π kT S k=1 W ∑ . ( 10
)
where ∠ is the angle operator. In our experiments, we set the training sequence length to 512 and the cross-correlation averaging window is 2. Fig. 4 presents experimental realizations of identification of the SoF in the back-to-back (B2B) and 1200 km transmission cases. In both cases, the peak corresponding to the SoF is clearly visible. After detecting the SoF, coarse CFO estimation is carried out using [START_REF] Moles-Cases | A comparison of OFDM, QAM-FBMC, and OQAM-FBMC waveforms subject to phase noise[END_REF] with an estimation range of [-1/(2WT S ), 1/(2WT S )]. Note that, by using a periodogram, which can provide a better spectral resolution [START_REF] Nguyen | Feedforward weighted-samples based carrier frequency offset compensation in optical coherent M-QAM systems[END_REF], the coarse CFO estimation accuracy can be further increased. As our purpose is to show the tradeoff between the CD and PN compensation, a detailed comparison of the proposed frame synchronization method with others is skipped in this paper.

B. Chromatic Dispersion Compensation

After frame synchronization, which is carried out in the time-domain, the received signal is passed through the AFB block in order to process the signal in the frequency-domain.

The CD compensation method used here is similar to the one in [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF][START_REF] Ihalainen | Channel equalization for multi-antenna FBMC/OQAM receivers[END_REF] that consists in using a finite impulse response (FIR) filter applied per subcarrier. The core idea of the filter design is based on the frequency sampling technique that is thoroughly analyzed in [START_REF] Ihalainen | Channel equalization for multi-antenna FBMC/OQAM receivers[END_REF]. In principle, the equalizer coefficients are set so that the equalizer frequency response is forced to pass through some desired frequency points in the subchannel of interest. Based on the zero-forcing criterion, the equalizer frequency response can be derived at the corresponding points in frequency. Finally, we can deduce a FIR equalizer h m [n] by applying the inverse Fourier transform. Although there are several CD compensation methods, as mentioned in [START_REF] Rottenberg | Advanced chromatic dispersion compensation in optical fiber FBMC-OQAM systems[END_REF], we choose this method as it provides a good performance at a moderate complexity. The equalizer is implemented based on the knowledge of the CD. As already stated, this is a reasonable assumption for many transmission systems, where a coarse estimate of the CD is known. Therefore, this stage acts as a coarse CD compensation. Any residual CD can be compensated at the channel equalizer stage.

C. Fine CFO Compensation and Channel Equalizer

Due to the fact that, after coarse CFO compensation, there remains a residual CFO, which is normally in the range of the subcarrier frequency spacing, i.e., less than 86 MHz (as detailed later in Section V), the phase noise tracking can only guarantee to compensate for laser phase noise, whose linewidth is less than 10 MHz [START_REF] Nguyen | Simple feedforward carrier phase estimation for optical FBMC/OQAM systems[END_REF]. In order to successfully demodulate the signal, we design the training sequences for fine CFO compensation in order to get the residual CFO in the operational range of the phase noise tracking.

Based on the design of the frame structure (Fig. 2), the second and the fourth FBMC symbols are used for fine CFO estimation. Note that, the third symbol is null to avoid any ISI. The two active symbols contain the same training symbol values on each sub-carrier m, for example, a m,2 is equal to a m,4 . Note that, the pilots are protected against ICI from adjacent symbols by inserting zeros surrounding it. Assuming that the PN φ in ( 6) is much smaller than the residual CFO, neglecting the additive noise term in [START_REF] Kakkavas | FBMC-OQAM with phase noise: Achievable performance and compensation[END_REF] ( )

2 e j 2πΔf (11)
The estimated residual CFO at the subcarrier level can be deduced by

Δ ! f m = 1 2π
( )∠y ! m . In order to reduce the effect of the additive white noise, we average the estimated residual CFO overall active pilot positions as follows

Δ ! f = 1 2πQ
∠y "

q 0 +2(m-1) m=1 Q ∑ ( 12
)
where Q is the number of active training symbols in one FBMC symbol (Q < M) and q 0 is the first subcarrier index containing the training symbol. The estimation range is

Δ ! f ∈ -F s 4M , F s 4M [ ) .
Once the residual CFO is estimated and compensated in the time-domain (see Fig. 2), the channel estimation (CE) is carried out. Indeed, the CE can re-use the training symbols aiming at the fine CFO estimation. However, in order to clearly separate each stage of the signal processing, we assign the sixth FBMC symbol as the CE training symbols, whose value at the m-th subcarrier is b m,6 (Fig. 3). Similar to the fine CFO training symbols, the CE training symbols are also alternated with the zero-symbols in order to reduce the ISI/ICI from adjacent symbols. From ( 6), the estimated channel (originating from the residual CD and other unknown response of the system) can be derived by

H ! m = y " m,6 b m,6 (13)
where y ! m,6 is the received symbol of the CE block after the fine CFO compensation and m = q 0 +2(t-1) for t ∈ [1; Q-1]. The estimated channel value between two consecutive CE training symbols is linearly interpolated based on two adjacent derived estimated channel values. It should be noted that more zero-symbols could be inserted between the training symbols and the data symbols (instead of only one zero-FBMC symbol as in Fig. 3) in order to further remove the ICI between the pilots and the data. It is worth noticing that the channel equalization also compensates for the residual CD, which explains (as seen later in the experimental results) why with 1tap equalizer we can propagate the signal for a longer distance than what was reported in [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF].

D. Phase Noise Tracking

Several PN tracking methods have been proposed in the literature [START_REF] Kakkavas | FBMC-OQAM with phase noise: Achievable performance and compensation[END_REF][START_REF] Nguyen | Simple feedforward carrier phase estimation for optical FBMC/OQAM systems[END_REF][START_REF] Dore | Blind phase tracking algorithm for FBMC receivers[END_REF][START_REF] Zaidi | Evaluation of waveforms for mobile radio communications above 6 GHz[END_REF][START_REF] Moles-Cases | A comparison of OFDM, QAM-FBMC, and OQAM-FBMC waveforms subject to phase noise[END_REF][START_REF] Nguyen | Lowcomplexity blind phase search for filter bank multicarrier offset-QAM optical fiber systems[END_REF][START_REF] Nguyen | Extended Kalman filter for carrier phase recovery in optical filter bank multicarrier offset QAM systems[END_REF][START_REF] Rottenberg | ML and MAP phase noise estimators for optical fiber FBMC-OQAM systems[END_REF]. We are interested in blind feedforward PN compensation, as it does not require pilots that cause a reduction in spectral efficiency. Among blind PN compensation algorithms, despite its high computational effort, the modified-blind phase search (M-BPS) algorithm has been shown to provide a better performance than the others [START_REF] Nguyen | Simple feedforward carrier phase estimation for optical FBMC/OQAM systems[END_REF], especially when the number of subcarriers is high. Even though the complexity of the M-BPS scales with the order of the modulation, it does not significantly influence the overall system complexity since the CD compensation block is by far the most complex DSP stage [START_REF] Kuschnerov | Energy efficient digital signal processing[END_REF]. Therefore, we use the M-BPS method for our investigation. More details about this algorithm can be found in [START_REF] Nguyen | Simple feedforward carrier phase estimation for optical FBMC/OQAM systems[END_REF]. Note that, the phase noise tracking also compensates for the tiny remaining CFO.

V. EXPERIMENTAL SETUP

The goal is to assess the trade-off between the CD and PN compensation. Hence, in our experiments, we consider only one polarization in order to simplify our setup. Fig. 5 shows the overall experimental setup. The recirculating fiber loop is further detailed in Fig. 6. At the transmitter side, a random binary sequence is generated offline to build the FBMC/OQAM signal. A training sequence is appended in front of the frame. These signals are loaded into a high speed arbitrary waveform generator (AWG), which contains four 88 GS/s 6-bit digital-to-analog converters (DACs) [START_REF] Schmidt | High-speed digital-to-analog converter concepts[END_REF].

The DACs impose to fix the sampling rate at 88 GS/s for the signal generation. The 88 GHz bandwidth is divided into many FBMC sub-carriers. In order to keep the pre-emphasis simple, we vary the subcarrier spacing (corresponding to a change of the number of subcarriers) and only activate the necessary number of subcarriers such that the signal bandwidth always occupies 20 GHz. For instance, the total DAC bandwidth is divided into 1024 sub-channels, such that the subcarrier spacing is about 86 MHz. We activate only 243 subcarriers surrounding the center frequency in order to create a 20.88 GHz FBMC/4-OQAM signal (equivalent 41.76 Gb/s signal). Note that, in order to facilitate reading in the following text and figure legends, we use a number of active subcarriers of the form 2 N , which is close to the real number of active subcarriers, i.e., when 243 subcarriers of the FBMC signal are activated, we mention it as 256-subcarrier FBMC signal.

The digital signals modulate the optical carrier, originating from a continuous wave (CW) laser, by using an inphase/quadrature (IQ) modulator. The laser wavelength is set to 1550 nm. Note that, the IQ modulator operates at the minimum bias point and the electrical signal amplitudes are adjusted so that the modulator is operated in the linear region of its transfer function. The modulated FBMC signal at the output of the IQ modulator is boosted by an optical erbiumdoped fiber amplifier (EDFA), denoted by Amp. Tx. The output power is then attenuated using a variable optical attenuator (VOA), namely Att.3, in order to get the desired launching power. We are only interested in linear transmission impairments to evaluate the trade-off between CD and PN compensation. To this aim, we (without showing the results here) scan over several launching powers and search for the one with lowest bit-error-rate (BER). Finally, we select the launching power to be -4 dBm as the working value. The optical signal is launched into a recirculating fiber loop, consisting of two spans of 100 km of standard single mode fiber (SSMF), two inline EDFAs and an optical band-pass filter (OBF) of 1.6-nm bandwidth. The noise figure of each inline EDFA is about 6 dB. The attenuator Att.4 is tuned to keep the optical power equal after each loop. After passing the fiber loop, the signal is passed to another VOA (Att.1), followed by an EDFA (Amp.2) to adjust the optical signal-tonoise ratio (OSNR), which is measured in a 0.1 nm noise bandwidth. Another OBF is used to reject the out-of-band amplified spontaneous emission (ASE) noise. The polarization controller at the receiver input is used to maximize the received signal on one polarization.

At the receiver side, the optical signal (S) is mixed with the local oscillator (LO) which is another CW laser of 10 dBm output power. Note that, the gain of the EDFA Amp.2 was adjusted in such a manner that the signal power at the input of the coherent receiver is held constant at -5 dBm. Both transmitter and receiver lasers have linewidths of about 100 kHz. The outputs of the 90° optical hybrid are detected by four balanced photodetectors. The output photocurrents are digitized using a 4-channel real-time digital sampling oscilloscope (DSO) of 100 GS/s sampling rate and 5-bit resolution [START_REF] Tektronix | Scalable performance oscilloscopes: DPO70000SX series datasheet[END_REF]. Finally, the acquired digital signals are resampled back to the DACs rate (88 GS/s), and processed offline for the digital receiver implementation. Note that, each FBMC frame contains about 20 000 data bit used for BER calculation and the BER is averaged over 5 acquisition frames.

VI. RESULTS AND DISCUSSION

The design of a 20-GHz FBMC transmission system based on 4-OQAM modulation is assessed in the presence of both CD and PN. The summed laser linewidth is about 200 kHz. Note that, this aggregated laser linewidth is utilized in our simulations in Section VII and the PN model is based on the Wiener process [START_REF] Vanin | Analytical estimation of laser phase noise induced BER floor in coherent receiver with digital signal processing[END_REF]. The CD equalizers have 1 or 3 taps. We investigate the suitable number of active subcarriers for the system. This number is varied in order to find the best tradeoff between CD and PN compensation. It is worth noticing that the CD equalizers considered here with different number of taps are the static ones (the first block of the frequency processing in Fig. 2), which is different to the dynamic 1-tap channel equalization (the third block of the frequency processing in Fig. 2). Note that higher order OQAM constellations could be used. For instance, 16-OQAM modulation has been numerically investigated in [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF] to assess the system performance in the presence of both CD and PN.

However, since we wish to validate the trade-off between PN and CD compensation, we limit ourselves to 4-OQAM modulation in the present experimental work. Indeed, for higher modulation orders, the limitation inherent to PN may be hidden by other effects, such as the limited resolution of the DAC/ADC.

In order to make a benchmark of the experimental results in the absence of optical channel impairments, we first analyze the back-to-back (B2B) performance. Fig. 7 presents measured BERs as a function of the OSNR for different values of the number of subcarriers i.e., 64, 256 and 1024. At low OSNRs, a small number of subcarriers leads to poor BER performance, as the additive noise is dominant and the averaging operation of the M-BPS based PN compensation is less accurate. This explains why the BER when 64 subcarriers are used is higher than that when 256 and 1024 subcarriers are used. On the contrary at high SNRs, a larger number of subcarriers results in a longer FBMC symbol duration and the PN compensation is hence less effective, because the PN algorithm compensates only for the common phase error over an entire FBMC symbol. A likely origin of the error-floor observed when 1024 subcarriers are used could be the residual PN-induced intersubcarrier interference. At moderate SNRs, all the considered numbers of subcarriers provide a similar BER performance.

In the next step, we consider only the 256-subcarrier FBMC transmission system using 1-tap and 3-tap CD equalizers. We investigate the OSNR penalty (compared to the B2B case) as a function of the transmission distance for maintaining the BER to 3.8×10 -3 (corresponding to a hard-decision forward error correction (FEC) limit [START_REF] Leven | Estimation of soft FEC performance in optical transmission experiments[END_REF]) in Fig. 8. As expected, the OSNR penalties increase with the propagation distance. We estimate the maximum transmission distance at 1 dB OSNR penalty, by the interpolation between the two points around the 1 dB penalty value. We find that the maximum transmission distances of 1-tap and 3-tap equalizers are 1300 km and 2900 km, respectively. This confirms the effectiveness of using a 3-tap CD equalizer over a 1-tap CD equalizer, at the cost of increasing the complexity [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF]. Compared to our previous simulation results for 1-tap equalizer [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF], it can be seen from Fig. 8 that in this experimental work we can transmit the signal further away, i.e., about two times extension of the transmission distance subject to 1-dB OSNR penalty at a BER of 3.8×10 -3 . This is due to the fact that, in the present case, the pilot-aided channel compensation (Section III.C) much probably helps to compensate for the residual channel effect left from the static CD equalizer step.

We now investigate the maximum transmission distance for 1-tap and 3-tap equalizers versus the number of subcarriers under the constraint of a 1-dB OSNR penalty at a BER of 3.8×10 -3 (Fig. 9). The same approach than in Fig. 8 was used to extract the maximum distance at 1 dB OSNR penalty for each number of subcarriers and number tap, as reported in Fig. 9. When the number of subcarriers is small, the compensation of CD is not fully efficient since the channel response is not flat enough at the subcarrier level. In this case, the 3-tap equalizer can help, increasing more than 2 times the transmission distance compared to the 1-tap equalizer for a number of subcarriers smaller than or equal to 256. The CD compensation is more effective when a higher number of subcarriers is used and the maximum transmission distance is hence increased; the distance is indeed improved by a factor of 10 from 64 to 1024 subcarriers in the 1-tap case. Finally, we observe that, in the current system configuration, with 1-tap equalizer, the transmission distance increases constantly with the number of subcarriers, whereas when applying 3-tap CD equalizers, the maximum transmission distance of 3100 km is achieved by using a 512-subcarrier FBMC system and slightly decreases with larger numbers of subcarriers. This can be explained by the fact that, in this case, PN becomes the dominant limitation. Consequently, with the considered link configuration, the optimum number of subcarriers are 1024 and 512 when using the 1-tap and 3-tap equalizers, respectively.

Relaxing the constraint about the FEC limit, we investigate the BER as a function of transmission distance when fixing the received signal power at -10 dBm in Fig. 10. The numbers of considered subcarriers are 64, 256 and 1024. The same observation as in Fig. 9 regarding the use of a larger number of taps in the equalizer depending on the number of subcarriers can be made. It can indeed be observed that a clear gain on the transmission distance can be achieved when increasing the number of equalizer taps from 1 to 7 for the 64-subcarrier FBMC system. While the 256-subcarrier FBMC system provides a moderate increase in the transmission distance when the number of equalizer taps varies from 1 to 3, no additional significant performance gain can be obtained in such a system by further increasing the number of equalizer taps from 3 to 7 (not shown in the plot). It can be observed that a 1-tap equalizer seems to be sufficient for the 1024subcarrier FBMC system.

The slope difference for each number of subcarriers is worth to be noted. Interestingly, at short distance (for a BER of 2×10 -4 typically), the 1024-subcarrier FBMC system shows a maximum transmission distance much lower than the 256subcarrier FBMC system and even the 64-subcarrier FBMC system with 3-tap and 7-tap equalizers. It is explained by the fact that the PN effect at this short distance becomes dominant over the CD effect and a large number of subcarriers is not advantageous anymore. This confirms again the trade-off between the CD and PN compensation found in our previous work [START_REF] Nguyen | Efficient chromatic dispersion compensation and phase noise tracking for optical fiber FBMC/OQAM systems[END_REF]. The methodology gives us indications on how to optimize the transmission system based on the input parameters of laser linewidth, the number of equalizer taps (linked to the system complexity). Although our verification was carried out with FBMC/4-OQAM modulation within 20 GHz bandwidth, the same methodology can be applied to systems of higher bandwidth and higher modulation orders.

VII. DISCUSSION ON DAC/ADC LIMITED RESOLUTION

In our experiment, we optimize the generated and received signals over the full-dynamic ranges of the DAC and ADC (the same approach has been followed by many previous works, for instance [START_REF] Zhao | Dispersion tolerance enhancement using an improved offset-QAM OFDM scheme[END_REF] and [START_REF] Poggiolini | Analytical and experimental results on system maximum reach increase through symbol rate optimization[END_REF]). Furthermore, we modulate the electrical signal in the linear region of the IQ modulator transfer curve. Therefore, the impact of peak-to-averagepower-ratio (PAPR) on the system performance is translated into the limitation of the DAC and ADC resolution.

We numerically evaluate the limitation inherent to the PN and to the limited DAC/ADC resolution. Fig. 11 shows the BER as a function of the SNR in four cases: [START_REF] Fickers | Multicarrier offset-QAM for long-haul coherent optical communications[END_REF] No impairments (no PN and unlimited DAC/ADC resolution); (2) With only limited DAC/ADC resolution and no PN; (3) With PN of 200 kHz and no limited DAC/ADC resolution; (4) With both impairments. Note that, the number of bits of the DAC and ADC are set to 6 and 5 bits, respectively [START_REF] Schmidt | High-speed digital-to-analog converter concepts[END_REF][START_REF] Tektronix | Scalable performance oscilloscopes: DPO70000SX series datasheet[END_REF]. The number of subcarriers is set to 256. It can be seen that, at high SNRs, the BER of case ( 2) is lower than that of case (3), implying that the effect of PN is stronger than that originating from the limited DAC/ADC resolution. When the two impairments are present, the BER becomes worse. Note that, the same conclusions can be drawn for other numbers of subcarriers, but it is skipped here due to space constraint. The numerical results confirm again that the previously observed error floors obtained for measured BERs with a high number of subcarriers come mainly from the PN effect.

VIII. CONCLUSION

We have experimentally demonstrated the trade-off between CD and PN compensation in optical FBMC/OQAM systems. The previously proposed methodology for the transmission system design has been experimentally verified for a FBMC/4-OQAM signal occupying a 20-GHz bandwidth, about 200-kHz summed laser linewidth and 1-or 3-tap equalizers. The results showed that we could propagate the signal over a distance of 3100 km using 512 subcarriers and a 3-tap equalizer, subject to 1 dB OSNR penalty at a BER of 3.8×10 -3 . A frame structure and an integrated synchronization/channel equalization architecture have also been proposed and validated to ensure the system works properly.

FFig. 1 .

 1 Fig. 1. Examples of multiple sub-channels multiplexing in WDM systems. a) Coherent-phase lasers required; b) Coherent-phase lasers relaxed with a negligible guard band.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Block diagram of an equivalent FBMC/OQAM transmission system.

Fig. 4 .

 4 Fig. 4. Cross-correlation functions of the frame synchronization in the backto-back configuration and after 1200 km transmission. The SoF corresponds to the peak maxima.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Experimental setup. CW: continuous wave laser; Amp.: optical amplifier; AWG: arbitrary waveform generator; IQ mod.: in-phase/quadrature modulator; Att.: optical attenuator; DSO: digital sampling oscilloscope; OBF: optical band-pass filter; PC: polarization controller.

Fig. 7 .

 7 Fig. 7. Back-to-back BER versus OSNR for FBMC/4-OQAM signal with different number of subcarriers.

Fig. 8 .

 8 Fig.8. OSNR penalty at a BER of 3.8×10 -3 as a function of the transmission distance using 1-tap and 3-tap equalizers for CD compensation when 256 subcarriers are considered.

Fig. 9 .

 9 Fig.9. Maximum transmission distance versus number of subcarriers subjected to 1-dB OSNR penalty at a BER of 3.8×10 -3 using 1-tap and 3-tap equalizers for CD compensation.

Fig. 10 .

 10 Fig. 10. BER as a function of the transmission distance when the numbers of subcarriers are 64, 256 and 1024.

Fig. 11 .

 11 Fig. 11. BER as a function of SNR with impairments originating from PN and 5-bit DAC/ 6-bit ADC. The number of subcarriers is 256.

  and multiplying the fourth symbol to the conjugate version of the second one, we can get

	y !	m = y m,2 * y m,4 ≈ H m * a m,2 + ju m,2 ( (	) *	e -jπ 2 Δf	) H m a m,4 + ju m,4 ( (	) e jπ 4 Δf	)
		= H m a m,2 + ju m,2

> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

ILTERBANK MULTICARRIER (FBMC) based on offsetquadrature amplitude modulation (OQAM) has currently

This work is supported by the Belgian Fonds National de la Recherche Scientifique (FNRS) under Grant PDR T.1039.15.


Rachid Boudhan

Aurélie Joubert

Danielle Venditti

Sylvain Durecu

Kamal Gueraoui

Laurence Le Coq

INFLUENCE OF OPERATING CONDITIONS ON BAG FILTER PERFORMANCES FOR INCINERATION FUMES TREATMENT

Keywords: Filtration, Bag Filter, Efficiency, Pressure Drop, Clogging/Unclogging Cycle, Incineration

Filtration performances of a bag filter implemented for the flue gas treatment of waste incineration plant were studied at laboratory scale in order to evaluate the influence of filtration cycles (clogging/unclogging). The filtration performances were evaluated during clogging with a submicronic aerosol with nano-size fraction, at a filtration velocity of 1.9 cm.s -1 . Investigations of the influence of filter washing and filtration velocity on the filtration performances were performed with the same filtering media in flat configuration. Experimental results showed an influence of filtration velocity on fractional filtration efficiency in particular for particle diameter close to the Most Penetrating Particle Size of the filter. Moreover, results indicated that new filters were significantly less efficient than washed filters at the beginning of the clogging. Finally the influence of clogging/unclogging cycles on bag filter performances was demonstrated both for pressure drop and filtration efficiency evolutions during clogging.

Introduction

Nanoparticle research is currently an area of intense scientific interest in order to understand their behavior and transport. ISO (2008) defines a nanoparticle as nanoobject with all three external dimensions at the nanoscale which, the size range is approximately from 1 to 100 nanometers (nm). According to toxicology studies, nanoparticles are responsible for health problems (Ostiguy et al., 2006).

There is a huge interest in nanoparticle filtration as one of the simplest methods to reduce efficiently the exposure to such particles. The bag filters have been successfully used for this purpose and allow to reach high performances depending on fibrous media used. So bag filters are usuely used for particulate matter removal in incineration fumes treatment. The pressure drop across the filter and filter efficiency permit to quantify the filtration performances during the operation. But a tradeoff between filter efficiency and pressure drop is often necessary to achieve high filtration efficiency while limiting economical costs due to pressure drop (Brown et al.,1993).

The filtration operation using bag filters is simple. The gas is fed at the bottom of a filter chamber that contains several filter bags. The air is filtered through the various bags (from the outside surface to the inside one) that are usually in vertical position. The filtered air exits through the top of the filtration device. The filter media that retains particles is unclogged periodically by pulse jet method (the injection of compressed air from inlet to the outlet of the bag filter produces a pulse-jet gas flow removing the particles collected on the outside surface of the filter bag) and the particles are recovered at the bottom of the system. During each cycle (clogging/unclogging) the particle collection efficiency increases rapidly due to the formation of a cake formed at the surface of the media until reaching values close to 100%. At the beginning of each cycle, the accumulation of a residual cake on filter surface may influence the filtration time and makes the formation of particles cake faster, while the maximum pressure drop may be reached faster (Park et al., 2012).

This study focused on filtration performances of bag filters used for the flue gas treatment of waste incineration. The study aimed to quantify the filtration performances of a bag filter regarding submicronic particles with nano-size fraction during clogging/unclogging cycles. The influence of filter washing and filtration velocity was also investigated, in particular to assist the development of technical recommendations.

Materials and methods

General Methodology

The filtration performances of bag filter were evaluated at laboratory for 10 cycles of clogging/unclogging. The particles used for the clogging were representative to those found in incineration fumes at the outlet of the boiler. The experiments were conducted at ambient conditions of temperature and humidity and for a filtration velocity of 1.9 cm.s -1 representative of that encountered in incineration plants. The results were presented as evolution of filter pressure drop and fractional efficiency (particle collection efficiency versus particle diamter) during the 10 cycles of clogging/unglogging.

The influence of 2 maintenance and operating conditions were also investigated from experiments with the same filtering media but implemented in flat geometry, resepctively bag cleaning and filtration velocity. First, the influence of filter was studied. Indeed, in addition to on-line unclogging, the bag filters are periodically washed off-line to remove remaining pollutants. In order to assess the influence of filter washing, two kinds of flat filters were clogged in the same operating conditions and particle concentration: new (blanck) and washed (used) filters. Note that, in waste incineration plants, in order to benefit from the increase of filtration efficiency of the particulate cake, the bag filters are often pre-coated with sorbent (eg sodium bicarbonate used in flue gas treatment for acid gas absorption) before operation in the system. Regarding the experiments with the bag filter geometry, the media was washed. Secondly, the influence of filtration velocity was also investigated. Flat fabric filters were clogged at two filtration velocities, namely 1.4 and 1.9 cm.s -1 .

Experimental set-up

Two laboratory-scale filtration units were used to perform clogging tests of filter in flat and bag configurations. The experimental set-up for single bag filter (reduced height to 0.44 m) was described by Tran et al. (2014). It had been developed in order to operate up to 150°C and in presence of humidity (conditions encountered by the bag filters in flue gas treatment of waste incineration). Laboratory air is previously filtered by an HEPA filter and is fed to filtration device througth a tube with a sufficient length (1 m) to provide an established flow path and comprising the injection of particles. The bag filter module is equipped with upstream and downstream sampling probes for particle counting (SMPS, Grimm) and air is finally exhausted to the atmosphere after filtration of residual particles. The on-line unclogging of bag filter was provided by pulse jet method (compressed air at 6-7 bar). A removable tank allowed dust recovering at the bottom of the bag filter module. The experimental set-up dedicated to flat filters was a simple filtration conduct with the same equipment as the previous set-up (filtration of the ambient air, particle injection, sampling up and downstream of the filter) without on-line unclogging device.

In both experimental set up, the aerosol used for clogging was a condensation aerosol from graphite monoliths (generator DNP 2000, Palas). Filtration efficiency was quantify from isokinetic sampling up-and downstream of the filters and particle counting with a mobility diameter particle counter (SMPS, Grimm) in the range 16-315 nm. Each test with flat filter was repeated three times with different filter samples. For all clogging tests, the maximum pressure drop was set to 120 Pa.

Filter characteristics

Flat and bag filters, constituted of the same filtering media, were used to perform clogging tests. The flat filters were sampled from a commercial bag filter provided by the company TREDI. Structural properties of the filtering media are presented in Table 1. The media is a non-woven structure composed of Teflon fibers (Polytetrafluoroethylene PTFE). The size distribution of fiber media was determined by Scanning electron microscope and picture analyses. More than 100 fibers were analyzed from 3 different sampling.

Results and discussion

Bag filter performances during clogging/unclogging cycles

Figure 1 shows the increase of pressure drop as a function of time during 10 cycles of bag filter clogging/unclogging. The maximum pressure drop was set to 120 Pa for all filtration cycles, once reached the filter is unclogged thanks to pulse jet. In accordance with literature (Park et al., 2012), the experimental results confirm that the clogging time period of the filtration cycles decreases from the first cycle (1090 min) to the last one (62 min). In terms of minimum pressure drop, the baseline which corresponds to the measured pressure drop ΔP just after cleaning increases with filtration cycles. This increasing (from around 20 to 80 Pa) is due to the residual cake from previous filtration cycles. The evolution of bag filter efficiency versus particle diameter for different level of clogging (ratios ΔP/ΔP0 with ΔP0 the initial filter pressure drop of cycle 1) during the first clogging cycle is presented in Figure 2. The results indicate that the minimum particle collection efficiency in size range studied was 91%. The results also reveal, in accordance with filtration theory, an increase in particle collection efficiency with the filter clogging. The Most Penetrating Particle Size (MPPS) value, is not observable for the size range at ΔP/ΔP0=2.7, but decreases from 90 nm for ΔP/ΔP0=5.6 to 60 nm for ΔP/ΔP0=7, for higher level of clogging (ie from ΔP/ΔP0=9) particle collection efficiency reaches almost 100% wathever particle diameter is. MPPS area (around 50-200 nm) the fractional efficiency decreases from the first to the last clogging cycle with a maximum efficiency close to 100% and a minimum of 98.5 %. The fractional efficiency for particles with diameter less than 50 nm and above 200 nm is less influenced by the sequence of clogging/unclogging cycles.

Figure 3: Evolution of fractional efficiency as a function of equivalent diameter in electrical mobility at the upper pressure drop for different filtration cycles

Influence of filter washing and filtration velocity on filtration performances

In order to investigate the influence of filter washing on the filtration efficiency, washed and new filters implemented in flat geometry were clogged in the same operating conditions. Figure 4 presents the fractional efficiency for 3 levels of clogging (ratios ΔP/ΔP0). The results indicate that at lower pressure drop (ΔP/ΔP0=2), the washed filter compare to the new filter at the same level of clogging, presents a significantly higher efficiency in the MPPS area. As expected this gap in efficiency decreases with increasing the level of clogging until reaching particle collection efficiency of almost 100% for ΔP/ΔP0=6.

Influence of filtration velocity on filtration performances

Figure 5 compares the fractional collection efficiency for flat filters clogged at 2 different filtration velocities of 1.4 and 1.9 cm.s -1 and for different level of clogging (ratios ΔP/ΔP0). As seen previously in Figure 4 and in accordance with filtration theory, there is an increase of efficiency with the increase of pressure drop ratio for the both filtration velocities. For the begining of clogging (ΔP/ΔP0=2, Figure 5), the efficiency is significantly higher at filtration velocity of 1.4 cm.s -1 than at 1.9 cm.s -1 for particle size ranging from 50 to140 nm (ie below the MPPS). This result is consistent with filtration theory: for particle size smaller than the MPPS, the Brownian diffusion is the dominant particle collection mechanism whose efficiency increases with decreasing the filtration velocity. The influence of filtration velocity is not significant for higher level of clogging, when filtration efficiency becomes close to 100% whatever particle size is. Efficiency(-)

Equivalent diameter in electrical mobility (nm)

V=1.4 cm.s-1, Δp/Δp0=2 V=1.4 cm.s-1, Δp/Δp0=4 V=1.4 cm.s-1, Δp/Δp0=5 V=1.9 cm.s-1, Δp/Δp0=2 V=1.9 cm.s-1, Δp/Δp0=4 V=1.9 cm.s-1, Δp/Δp0=4.5

Figure 1 :

 1 Figure 1: Pressure drop across bag filter versus time for 10 clogging/unclogging cycles

Figure 2 :

 2 Figure 2: Evolution of fractional efficiency as a function of equivalent diameter in electrical mobility, for the first filtration cycle (C1) at different values of ΔP/ΔP0 Figure 3 shows the fractional efficiency evolution at the upper pressure drop (120 Pa) for different clogging cycles. The results indicate that for particle size close to the

Figure 4 :

 4 Figure 4: Evolution of fractional efficiency as a function of equivalent diameter in electrical mobility for washed and new flat filters for different values of ΔP/ΔP0 at 1.4 cm.s -1 filtration velocity

Figure 5 :

 5 Figure 5: Evolution of fractional efficiency, as a function of equivalent diameter in electrical mobility, of washed and new flat filters at two filtration velocities (1.4 and 1.9 cm.s -1 ) and at different values of ΔP/ΔP0ConclusionThe filtration efficiency and pressure drop of bag and flat filters were evaluated for particle size range of 16-315 nm. The main conclusions obtained experimentally are:(1) the efficiency of bag filter increases with increase of pressure drop during clogging until reaching efficiency of almost 100%.(2) Filtration efficiency decreases with increase of velocity, especialy for particles diameters ranging between 50-140 nm. (3) New filters are significantly less efficient than washed filters in the beginning of clogging at low ΔP/ΔP0 ratios.ReferenceBrown, R.C., Air filtration: An Integrated Approach to the theory and Application of Fibrous Filters. Chap. 8. Pergamon. Oxford (1993) ISO (2008). Nanotechnologies, terminology and definitions for nano-objects, nanoparticle, nanofibre and nanoplate. ISO/TS 27687. International Organization for Standardization; (2008) Ostiguy, C. et al., Les effets à la santé reliés aux nanoparticules. Rapport IRSST. Montréal. (2006) Park, B.H. et al., Filtration Characteristics of Fine Particulate Matters in a PTFE/Glass Composite Bag Filter. Aerosol and Air Quality Research. 12: 1030-1036. (2012) Tran., D.T. et al., Evaluation des performances d'un filtre à manche en conditions de laboratoire représentatives du traitement des fumées d'incinération -application aux déchets contenant des nanomatériaux. Proceedings of the 29ème Congrès Français sur les Aérosols, Paris, (2014)

Table 1 :

 1 Main structural parameters of the filtering media

	Parameters	Value	Method
	Thickness (µm)	1256 ± 31	Scanning electron microscope
	Fiber median diameter (µm)	19.5	Scanning electron microscope
	Total porosity (-)	0.64	Mercury porosimetry
	Basis weight (g/m 2 )	750	NF EN 12 127


Gaëtane Plassart
email: gaetane.plassart@cea.fr

Didier Picart

Michel Gratton

Arnaud Frachon

Michael Caliez

Michael Caliez Mechanical

Michaël Caliez

Mechanical behaviour of a high explosive: multiaxial loading and straininduced anisotropy

Introduction

2.

Modern numerical tools enable simulating operational life conditions of pyrotechnic structures but an improved and accurate mechanical constitutive law of the explosive composition is required. The main difficulty comes from the complexity of the behaviour of such a material. The aim of this study is to determine the behaviour law of a TATB-based PBX, denoted "M2".

M2 is an energetic material made of a large majority of TATB crystals. Explosive crystals are coated with a thin layer of a thermoplastic binder, millimetric metagrains being then obtained by granulation. Granules are vacuum-packed in a tight elastomer bag, before being submitted to isostatic compaction cycles at approximately 150°C and 200 MPa. The temperature is chosen to soften the binder. The pressure applied to densify the material is higher than the one experienced during the life cycle of the pyrotechnic structure (p max about 10 MPa). After cooling, the part of compacted material can be machined. This compaction process eliminates most of the initial porosity, resulting in a quasibrittle material with a polycrystalline microstructure of characteristic size around 50 µm.

TATB crystals being strongly anisotropic, optical microscopy (figure 1) reveals a variation of colours. Grain orientations and binder locations being random by distribution, the material is initially isotropic on the macroscopic scale.

Thermomechanically speaking, experiments (compressive and tensile tests, triaxial compressions and dynamic mechanical analysis) have shown that M2 is a viscoelastic material with temperature-, pressure-and strain rate-dependencies. Moreover, M2 develops irreversible strains during a compressive loading.

Few years ago, the CEA and the Gabriel LaMé mechanical laboratory proposed a first constitutive law. This law deals with a generalised Kelvin-Voigt viscoelastic model combined with an isotropic damage, a viscoplasticity flow rule with isotropic hardening, and a yield stress depending on the confinement. Failure (which is considered here to be at the maximal stress) is treated by two uncoupled equations: one linking the maximum positive principal strain to pressure, when the other one is based on the maximum positive effective principal stress.

Parameters have been determined from DMA measurements and compressive tests with cyclic loading at 20°C and 50°C, and at 20°C under a 10 MPa triaxial pressure. Comparisons between model and experimental data have shown an under-estimation of the transversal strains. Straininduced anisotropy could be the reason of such differences. Strain-induced anisotropy in some aggregate or granular materials 3.

Because of its microstructure and its quasi-brittle behaviour, the material M2 can be compared to concretes and geomaterials. Literature reports several experiments showing strain-induced anisotropy in these materials.

At the beginning of the 1990s, Mazars, Berthaud and Ramtani [1] made some alternated tensile/compressive tests on a concrete. They observed a stiffness recovery at the beginning of the compression. This phenomenon, called unilateral effect, is interpreted considering a network of cracks in the material. When cracks open in traction and increase in density, there is a stiffness loss and so a decrease of the elastic modulus. At the opposite, when cracks are compressed and closed, a stiffness recovery is obtained. With this interpretation, the influence of cracks on the behaviour depends on their orientation. It implies an anisotropy due to damage. Shortly after, Gotuwka and co-workers [2][3] characterized three different concretes. To do so, they carried out some compressive cyclic loadings. Each cycle was composed by three steps: loading, stress relaxation at fixed strain and partial unloading of 40 MPa. They considered the secant modulus, between the relaxation-end and the unload-end, as elastic. They showed a higher decrease of the transversal modulus than of the longitudinal one. This observation was interpreted as anisotropy on the elastic moduli evolutions. Gotuwka and co-workers concluded to an anisotropic damage for these concretes, cracks preferentially spreading along the loading direction.

At the same time, efforts were made to characterize geomaterials, particularly in France at the Mechanical Institute of Grenoble. Cambou, Lanier and colleagues studied the induced anisotropy of a dense Hostun sand [4] and a dry one [START_REF] Lanier | -Etude expérimentale et analyse théorique de l'anisotropie induite du sable d'Hostun[END_REF]. For these sands, they emphasized a strain-induced anisotropy making two successive loads with intermediate unload. Samples were submitted to the same first compressive loading, the direction of the second loading changing depending on the samples. The aim was to see the first loading influence on the second one. Data showed an increase of the sample stiffness in the direction initially compressed, whereas the ductility increased in the initial expansion directions. According to the authors, the load-induced anisotropy observed can be modelled by an elastoplastic law with kinematic hardening.

Le and co-workers [6] characterized the CEA explosive composition "M1" in the quasistatic domain. This material is a HMX-based PBX whose fabrication process is likely the same than M2, the two materials morphology being similar. Analysing the experimental results, they noticed that the ratio of elastic strain evolves during loading and that the transversal modulus decreases faster than the longitudinal one. A dilatancy mechanism being not able to explain this phenomenon, an anisotropic evolution of the damage was assumed.

Benelfellah and co-workers [START_REF] Frachon A | Anisotropic damage model with unilateral effect and sliding friction for brittle materials[END_REF] made an in-depth study of the induced anisotropy of M1. Elastic secant moduli degradation in the longitudinal and transversal directions was compared from compressive cyclic loadings. Making alternated tensile/compressive tests, the unilateral effect due to damage was highlighted.

Thus, experimental tests made on concretes, on sand and on the M1 PBX emphasize a straininduced anisotropy. Two models were proposed in the literature to interpret data: (1) a constitutive law based on an anisotropic damage by microcracking (used for concretes and M1) or (2) an anisotropy linked to a kinematic hardening for sands.

We want to characterize the strain-induced anisotropy of M2 and if this anisotropy could be modelled as a consequence of damage or plasticity. Optical microscopy analysis being hardly tractable for small strain, we carry out macroscopic experimental testings inspired by those described above.

Experimental study of the strain-induced anisotropy 4.

An experimental campaign of alternated tensile/compressive tests, inspired by Mazars and coworkers [1] and by Benelfellah and co-workers [7], has been carried out on M2. Two tests were done:

(1) a compression up to 30 MPa (~ 0.95 σ max , where σ max is the maximal compressive stress) followed by a tensile loading to failure and (2) a traction up to 7 MPa (~ 0.95 σ max , where σ max is the maximal tensile stress) followed by a compressive loading to failure. Dog-bone-shape samples with a central volume of 10 mm in diameter and 20 mm in height were used. Glue helped to stick the samples to the horizontal platens of the machine. Two longitudinal gauges and two transversal ones measured strains. The strain rate of 10 -5 s -1 was applied on one of the longitudinal strain gauge.

The curves are given on figures 2 and 3. ε L (respectively ε T ) is the mean of the two longitudinal (respectively transversal) strains. σ is the longitudinal stress, positive in traction and negative in compression, measured by the machine strength cellule.

Experimental data don't reveal a stiffness recovery (no unilateral effect) when stress sign changes. However, viscosity of the material may smooth the curves and hide the phenomenon. Therefore, M2 stiffness recovery would be low to negligible. made four steps: loading, stress relaxation, unloading and strain recovery. We followed this last process. Experiments were carried out without lateral confinement or under a 10 MPa pressure. Cylindrical samples of 10 mm in diameter and 20 mm in height were used. They were put between two compressive platens without lubrication. Two longitudinal gauges and two transversal ones measured the strains. The strain rate of 10 -5 s -1 was controlled on one of the longitudinal strain gauge.

Comparisons between cyclic compressive test curves and the corresponding monotonic curve are presented on figures 4 and 5. Monotonic tests were made using the same experimental conditions. ε L (respectively ε T ) is the mean of the two longitudinal (respectively transversal) strains. σ is the longitudinal stress, here taken positive in compression. According to the graphs, the envelop curves of tests with cycles are similar to the monotonic curves. So cycles don't influence the envelop behaviour of M2 in compression.

Adding cycles gives a lot of information on the mechanical behaviour. Relaxation and recovery stages help to cancel the viscous effects. Furthermore, strains at recovery end correspond to the irreversible strains and give information about plasticity.

Let's now suppose there is no plasticity when unloading. Consequently, for each cycle, the secant modulus between the relaxation-end and the recovery-end is elastic (green lines on figures 6 and 7). Thus loading cycles enable estimating the evolution of the elastic moduli and quantifying the material damage.

We can also estimate elastic tangent apparent moduli. Let's assume stress state goes back inside the elastic domain when loading direction is reversing. Elastic tangent moduli are calculated at load (blue lines on figures 6 and 7) and unload (red lines) beginnings by linear regression with a 0.05% longitudinal strain window.

Tangent and secant moduli are compared on figure 6 (unconfined test) and figure 7 (confined test). The two methods give very different results. The tangent moduli (blue and red) are equal to the initial Young's modulus. Thus, we claim that they still represent elasticity and, as a consequence, damage can be neglected. That implies that secant moduli (green) are not elastic and that some plasticity may develop during unloading.

Let us now detail another experimental campaign which will help to understand the causes of the strain-induced anisotropy of M2. an experimental campaign of double compressions on cubic samples was done on M2. The aim was to see the influence of a first load on a second one. First, the samples, which were 20 mm-side cube, were compressed up to 30 MPa (95% of the maximal stress). After unloading and a recovery phase of several hours, samples were subjected to another compressive test, either in the same direction than the first one (« 0°-0° compression », see figure 8), or in an orthogonal direction (« 0°-90° compression», see figure 9). The strain rate was controlled by the cross head speed at 10 -2 mm.s -1 (equivalent to 10 -5 s -1 on the sample). Strains were measured by only one longitudinal and one transversal gauges. To avoid a "barrel effect" on samples because of friction at interfaces, lubricated Teflon was placed between the samples and the compressive platens. Displacement homogeneity was checked by digital image correlation (figure 10-b).

Curves of two representative tests are reported on figure 11. The first part of the curves is similar since it corresponds to the same initial load. Next, the blue curve (respectively the green curve) shows the behaviour of M2 when submitted to a compression in the same direction (respectively in an orthogonal direction). The two samples failed at the same strain-stress values so the failure criterion seems to be independent of load history.

As Cambou and Lanier [4],

we have compared on figure 12 the loading curves reinitialising strains at the beginning of each loading. We have added also the "returned" unload curves. Coloured areas represent the results dispersion of the three tests realized for each operating procedure. So, figure 12 shows: initial loading in red, corresponding to the first load to 30 MPa of figure 11, reloading at 0° in blue, corresponding to the second part of the blue curve of figure 11, reloading at 90° in green, corresponding to the second part of the green curve of figure 11, all unloadings (returned) in grey.

Looking at figure 12, one can see different reloading curves in blue and in green. The anisotropy induced by the first load is evident. The direction of the sample which had seen an expansion (90° direction, green curve) is more ductile than initially. Conversely, the direction submitted to a compression (0° direction, blue curve) increases in rigidity. These experimental results are qualitatively the same as Cambou and Lanier [4] on Hostun sand. Furthermore, according to the figure 12, unloading curves (in grey) are all the same and they are superposed on the 0°-reloading area.

Lastly, let's note that all curve-foots are superposed up to 5 MPa. That means the M2 viscoelastic behaviour is history-independent. One more time, damage has not been detected. We can also notice that the 0°-reloading (blue) and the initial loading (red) have superposed areas up to 15 MPa. Same phenomena were observed by Cambou and Lanier. a)

0 1 2 3 -1 -2 -3 b) 0 1 2 3 -1 -2 -3
The material behaviour observed with this experimental campaign can be interpreted using a plastic flow model with a kinematic hardening. During a 0°-0° test (top of figure 13), the initial loading displaces the plasticity surface to 30 MPa. Then, unloadings and 0°-reloading remain inside this surface and an elastic response is obtained. During a 0°-90° test (bottom of figure 13), the initial load displaces the plasticity surface in such a way that the yield stress decreases in the 90° direction. Since σ Y1 <σ Y0 , there is more plasticity during the 90°-reloading than during the first loading. Then, plasticity surface is bringing up to 30 MPa in the new direction, the last unloading being elastic. Thus, in this interpretation all unloadings and the 0°-reloading are elastic (and so similar). Moreover, the initial compression yields lower plastic strain than the 90°-reloading. It corresponds to what was experimentally observed on M2. However, to properly apply this theory to our case, the zero-stress point must stay into the plasticity surface, implying an initial yield stress higher than 0.5*σ max thus 15 MPa. If this condition is not satisfied, unloading at 90° would be different from the other unloading curves. However, the assumption of elastic unloading has been previously refuted. Nevertheless, if unloadings from cyclic compression of cylindrical samples (ø10h20 geometry) get some plastic flow, it may be possible that for cubes an artificial confinement induced an artificial increase of the yield stress even if the contact areas were lubricated. This paradox will be studied in a close future.

Conclusion 5.

Experimental campaigns realized on M2 have shown that the elastic moduli are constant during loading. Compressing samples twice in the same direction induces an increase of the stiffness. Moreover, curve-foots were always the same whatever the confinement and the loading history. All these observations lead us to conclude that damage can be neglected for M2. Thus, the straininduced anisotropy has been interpreted as a consequence of a kinematic hardening.

To go on with the thermomechanical characterization of M2, researches have to be oriented toward plasticity. Experimental researches on the initial plasticity surface and on the hardening rule will be done using compression/traction/torsion multiaxial tests.

Thanks 6.

This study has been carried out within the framework of the Corresponding Research Laboratory gathering the CEA and the mechanical laboratory Gabriel LaMé. Bibliographie 7.

Figure 1 :

 1 Figure 1: Micrograph of material M2 before loading.

Figure 2 :

 2 Figure 2: Alternated compressive/ tensile test on M2 (in black), compared to respective monotonic curves (in red). Longitudinal strain ε L negative in compression.

Figure 3 :

 3 Figure 3: Alternated tensile/compressive test on M2 (in black), compared to respective monotonic curves (in red). Longitudinal strain ε L negative in compression.

Figure 4 :

 4 Figure 4: Comparison between the cyclic compressive test and the corresponding monotonic test (no confinement).Longitudinal strains ε L negative.

Figure 5 :

 5 Figure 5: Comparison between the cyclic compressive test and the corresponding monotonic test under a 10 MPa pressure.Longitudinal strains ε L negative.

Figure 6 :

 6 Figure 6: Secant and tangent longitudinal moduli for a no confined compressive test.

Figure 7 :

 7 Figure 7: Secant and tangent longitudinal moduli for a confined (10 MPa) compressive test.

Figure 8 :

 8 Figure 8: Schema of the compressive test called "0°-0°".

Figure 9 :

 9 Figure 9: Schema of the compressive test called "0°-90°".

Figure 10 :

 10 Figure 10: Transversal displacement field of a sample compressed at 30 MPa, a) without lubrication at interfaces, b) with Teflon and lubrication at interfaces (unit: pixel).

Figure 11 :

 11 Figure 11: One of the "0°-0°" compressive test (in blue) compared with a "0°-90°" one (in green).

Figure 12 :

 12 Figure 12: Curves for initial loading (red), 0°-reloading (blue), 90°-reloading (green) and unloadings (grey). Coloured areas represent the dispersion of the results.

Figure 13 :

 13 Figure 13: Interpretation of the M2 behaviour in 0°-0° compressive test (top) and in 0°-90° compressive test (bottom) using a model with a kinematic hardening.