Ihsen Hedhli
email: ihsen.hedhli@inria.fr

Gabriele Moser

Josiane Zerubia

Sebastiano B Serpico

FUSION OF MULTITEMPORAL AND MULTIRESOLUTION REMOTE SENSING DATA AND APPLICATION TO NATURAL DISASTERS

Keywords: Natural disasters, multiresolution data, supervised classification, hierarchical Markov random fields, maximizer of posterior marginals

In this paper, we propose a novel method to fuse multidate, multiresolution, and multiband remote sensing imagery for multitemporal classification purposes. The proposed method is based on an explicit hierarchical graph-based model that is sufficiently flexible to deal with multisource coregistered time series of images collected at different spatial resolutions. An especially novel element of the proposed approach is the use of multiple quad-trees in cascade, each associated with an image acquired at a different date, with the aim to characterize the temporal correlations associated with distinct images in an input time series. Experimental results are shown with multitemporal and multiresolution Pléiades data 1 .

INTRODUCTION

The capabilities to monitor the Earth surface, and especially urban and built-up areas, from environmental disasters such as floods or earthquakes, and to assess the ground impact and damage of such events play primary roles from multiple social, economic, and human viewpoints. Nowadays, a wide variety of remote sensing images are available, that convey a huge potential for such applications, as they allow a spatially distributed and temporally repetitive view of the monitored area at the desired spatial scales. In this framework, accurate and time-efficient classification methods are especially important tools to support rapid and reliable assessment of the ground changes and damages induced by a disaster, in particular when an extensive area has been affected. Given the huge amount and variety of data available currently from last-generation very-high resolution (VHR) satellite missions (e.g., Pléiades, COSMO-SkyMed, WorldView-2), the main difficulty is to develop a classifier that can take benefit of multiband, multiresolution, multidate, and possibly multisensor input imagery. Several approaches to land cover change detection using multitemporal data have been proposed in the literature. In this work, we will focus on multitemporal classification methods; these methods consist of independently or jointly classifying the images in a time series and fusing them in order to map the temporal transitions among land cover classes. Specifically, the proposed method addresses the problem of multitemporal image classification and allows both input data collected at multiple resolutions and additional multiscale features derived through wavelets to be fused. The approach consists of a supervised contextual Bayesian classifier that combines a joint class-conditional statistical model for pixelwise information and a hierarchical Markov random field (MRF) [START_REF] Kato | Markov random fields in image segmentation[END_REF] for spatiotemporal [START_REF] Serpico | Weight parameter optimization by the Ho-Kashyap algorithm in MRF models for supervised image classification[END_REF] and multiresolution contextual information [START_REF] Moser | Multiscale unsupervised change detection on optical images by Markov random fields and wavelets[END_REF]. A non-iterative multitemporal formulation of the maximizer of posterior marginal (MPM) rule [START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF] is applied and combined with probability density function (PDF) estimators based on copula functions [START_REF] Nelsen | An introduction to copulas[END_REF] and on the stochastic expectation-maximization (SEM) algorithm [START_REF] Celeux | Stochastic versions of the EM algorithm: an experimental study in the mixture case[END_REF]. Experimental results are shown with Pléiades data.

MULTI-DATE HIERARCHICAL MODEL

Given an input time series of remote sensing images acquired at multiple spatial resolutions, a multiscale and multitemporal model is proposed to fuse the related spatial, temporal, and multiresolution information. This model is a hierarchical spatio-temporal and multiresolution MRF integrated in a quad-tree structure presented in Figure 1. The choice of a quad-tree allows to take benefit from its good analytical properties (e.g., causality) and to apply noniterative classification algorithms such as MPM, which associates, with each spatio-temporal site in the considered time series, the most probable class label , given the entire multitemporal data set [START_REF] Laferte | Discrete Markov modeling and inference on the quad-tree[END_REF]. An especially novel element of the proposed approach is the use of multiple quad-trees in cascade, each associated with one of the images available at each observation date in the considered time series (see Figure 5). Specifically, for each date, the input images are inserted in the quad-tree structure on the basis of their resolutions, while missing levels of the tree are filled in with wavelet transforms of the images embedded in finer-resolution levels [START_REF] Moser | Multiscale unsupervised change detection on optical images by Markov random fields and wavelets[END_REF]. parent node in the quad-tree associated with the previous date, with the aim to characterize the temporal correlations associated, at different scales, with distinct images in the input time series. In particular, we proved that, under mild assumptions:

∑ [ ∑ ] (1)
where boldface type highlights the recursively computed posterior marginal. The proposed method extends the singledate technique in [START_REF] Voisin | Supervised Classification of Multisensor and Multiresolution Remote Sensing Images with a Hierarchical Copula-based Approach[END_REF] through the recursive integration of multitemporal information in the computation of such posteriors as well as the probabilities are made available, where indicates the set of the descendants of site . This could be computed using:

( ) ( ) ( ) ( ) (2)
The proposed hierarchical MRF is achieved by two recursive steps, referred to as "bottom-up" and "top-down" passes (see Figure 5):

 A top-down pass to compute the prior probability ( ) via:

( ) ∑ [ ( ) ] (3)
Where ( ) characterize the relationship across consecutive scales within the same quad-tree, we use the transition probability model proposed by Bouman and Shapiro [START_REF] Bouman | A multiscale random field model for Bayesian image segmentation[END_REF], which favors identity between the class labels of children and parent.

 A bottom-up recursion allows computing the posterior marginal ( ) using the formulation introduced by Laferte [START_REF] Krylov | Supervised high resolution dual polarization SAR image classification by finite mixtures and copulas[END_REF] for the single-date case:

( ) ( ) ( ) ∏ ∑ [ ( ) ( )] (4)
Where denotes the set of the children of site . This step involves the pixelwise class-conditional PDFs of the image data at each node of each quad-tree (described in Section 3). Then, the probabilities ( ) could be computed given the transition probabilities between consecutive scales and consecutive dates:

-The child-parent transition probability (

) is computed through a new formulation of the transition probability model proposed by Bouman and Shapiro, which favors identity between children and parents in current and previous dates to account for the temporal correlation between images taken over the same area at different times. -The transition probabilities between class labels at different dates [START_REF] Serpico | Weight parameter optimization by the Ho-Kashyap algorithm in MRF models for supervised image classification[END_REF] and at the same level of the quad-tree ( ) is computed through a specific formulation of the expectationmaximization (EM) algorithm [START_REF] Bruzzone | A Neural-Statistical Approach to Multitemporal and Multisource Remote-Sensing Image Classification[END_REF].

 A top-down pass allows computing recursively the posterior marginal ( ) in each level of the quad tree of each date. Classification maps are obtained using modified metropolis dynamics [START_REF] Kato | Unsupervised Parallel Image Classification Using Markovian Models[END_REF] applied to maximize the posterior marginal.

MULTIVARIATE PDF MODEL

In order to model, for each date, class, and scale level in the multitemporal hierarchical graph, the conditional joint statistics of the input features, first, the corresponding marginal statistics of each feature is estimated; then the joint statistics is modeled using copulas [START_REF] Nelsen | An introduction to copulas[END_REF]. In particular, given a training set for each date (completely supervised approach), we model the class-conditional marginal PDF corresponding to each class, scale, acquisition time, and (satellite or wavelet) feature using a finite Gaussian mixture. The use of finite mixtures instead of single PDFs offers the possibility to consider heterogeneous distributions, usually reflecting the contributions of the different ground materials in each land cover class. Such class heterogeneity is especially relevant because we deal with VHR images. The parameters of the mixture model are estimated through SEM [START_REF] Celeux | Stochastic versions of the EM algorithm: an experimental study in the mixture case[END_REF], which is an iterative stochastic parameter estimation technique developed for problems characterized by data incompleteness and approaching, under suitable assumptions, maximum likelihood estimates. Given the resulting marginal conditional PDF estimates, joint conditional PDF estimates are obtained through copula functions. According to Sklar's theorem [START_REF] Nelsen | An introduction to copulas[END_REF], an arbitrary joint PDF can be expressed in terms of the corresponding marginal PDFs and of a copula function. In the proposed method, we determine this specific joint PDF for each scale level of each quad-tree in the cascade model, given the aforementioned marginal distributions. To determine the joint PDF and maximize the flexibility of the resulting estimate, we do not predefine a single copula model but we consider a dictionary of three parametric copulas (Clayton, Ali-Mikhail-Haq and Gumbel). To estimate the corresponding parameters and identify the best fitting copula, we use the relationship between the unknown copula parameters and Kendall's (rank statistics) and we choose the best fitting copula according to the highest p-value reported by a Pearson Chi-square goodness-of-fit test [START_REF] Krylov | Supervised high resolution dual polarization SAR image classification by finite mixtures and copulas[END_REF]. The advantage of using copulas, over the choice of a specific parametric model (e.g., multivariate Gaussian), is that they enable modeling the dependence structure of any type of features. The use of copulas in the joint PDF modeling becomes especially relevant when the dependence between the source features is strong [START_REF] Voisin | Supervised Classification of Multisensor and Multiresolution Remote Sensing Images with a Hierarchical Copula-based Approach[END_REF].

RESULTS

Preliminary experiments have been performed with a time series of panchromatic and multispectral Pléiades images acquired over Port-au-Prince (Haiti). Results associated with a set of images acquired on 2011, 2012 and 2013 are shown in this paper (see Figure 2). The finest resolution of the multiresolution pyramid (level 0) is set equal to the finest resolution of the input images (0.5-m panchromatic). Coregistered 2-m multispectral images are integrated in level 2 of the pyramid. Level 1 is filled in through Haar wavelet decomposition of the panchromatic image. Preliminary experiments suggested the Haar transform to be especially effective in the application within the proposed method.Morevoer, both a nonstationary (pixelwise) and a stationary (classwise) versions of EM have been formulated for the estimation of the temporal transition probabilities. Preliminary experiments omitted for brevity pointed out that there was no significant difference in terms of accuracy, whereas the stationary version has remarkably shorter computation time. Four land cover classes have been considered: urban (red), water (blue), vegetation (green) and bare soil (yellow). A preliminary analysis of the resulting classification maps has suggested that the proposed hierarchical method leads to accurate results (see Figure 3), especially as compared to separate hierarchical classification at each individual date (e.g., [START_REF] Voisin | Supervised Classification of Multisensor and Multiresolution Remote Sensing Images with a Hierarchical Copula-based Approach[END_REF]). These results suggest the effectiveness of the proposed multitemporal hierarchical model in fusing the temporal, spatial, and multiresolution information associated with the input data (see Figure 2). In particular, one of the main sources of misclassification in the single-date results is the confusion between the "urban" and "soil" classes (see highlighted regions in Figure 2

CONCLUSIONS

A novel method has been proposed to address the joint classification of multidate, multiband, and multiresolution imagery. It combines a joint statistical model of the considered input images and a hierarchical MRF model for spatio-temporal and multiresolution contextual information, leading to a statistical supervised classification approach. Moreover, a major advantage of the proposed classifier is that it can be extended to the use not only of optical data, but also of synthetic aperture radar (e.g., COSMO-SkyMed) or multisensor data. The extension to the multisensor case will be a major direction of further research.

Figure 1 :

 1 Figure 1: Quad-tree structure Then, a novel formulation of MPM is proposed for the resulting multitemporal quad-tree. The posterior marginal ( ) of the class label of each spatio-temporal site is expressed as a function not only of the posterior marginal ( ) of the parent node in the corresponding quadtree but also of the posterior marginal ( ) of the

  (e)); this misclassification is reduced in the multitemporal classification obtained by the proposed method thanks to the modeling of the temporal relationships among the input multiresolution data. A change map is also presented in Figure4(c) by comparing the classification maps produced by the developed joint multitemporal classifier (changes are highlighted in black).

Figure 2 :

 2 Figure 2: ((a) to (c)) Panchromatic image of Port au Prince (Pléiades, © CNES) for 2011 to 2013 respectively, ((d) to (f)) monotemporal classification maps for 2011 to 2013 respectively, (g) Classification map for 2012, obtained through the proposed cascade method using images acquired in 2011 and 2012, (h) Classification map for 2013, obtained through the proposed cascade method using all multispectral and panchromatic images.

Figure 3 :

 3 Figure 3: Superposition of the obtained classification result and the ground truth made by visual interpretation. (white = classification error and black = no GT available)

Figure 4 :

 4 Figure 4: (a) Classification map for 2012, obtained through the proposed cascade method using images acquired in 2011 and 2012, (b) Classification map for 2013, obtained through the proposed cascade method using all images. (c) Change map derived from the classification result of the proposed method.

Figure 5 :

 5 Figure 5: Multidate MPM estimation on the quad-tree: R=2 and three dates.

We would like to thank the French Space Agency (CNES) for providing the data and for partial financial support.


Axel Garcia Peña

Marie-Laure Boucheret

Christophe Macabiau

Jean-Louis Damidaux

Lionel Ries

Stéphane Corazza

Anne-Christine Escher

Implementation of Code Shift Keying signalling technique in GALILEO E1 signal

Keywords: CSK, demodulation performance, BER, WER, likelihood ratio, CSK mapping, CSK tracking, CSK acquisition I

One of limitations of the current GNSS signals is their low data information rate. This low data information rate does not allow, for example, the transmission of additional commercial services or the transmission of redundant ephemeris data. The Code Shift Keying (CSK) is a signaling technique specifically designed to increase the transmission bit rate of a spreading spectrum signal. Therefore, one solution to increase the data information rate of the GNSS signals is to introduce the CSK technique in them.

In this paper, the implementation of the CSK technique into GNSS signals is inspected through the development and analysis of the likelihood ratio expression of the bits transmitted inside a

CSK symbol, and through the identification of the best mapping between bits belonging to a word and bits transmitted inside a CSK symbol. Finally, the impact of the CSK technique on the GALILEO E1 signal is analyzed by calculating the CSK demodulation performance for a given scenario and the drawbacks of the technique on the signal acquisition and tracking processes.

INTRODUCTION

The current and future GNSS signals such as GPS L2C, GPS L5, GPS L1C and GALILEO E1 signals have improved the demodulation performance of the original GPS L1 C/A signal by means of new navigation message structures, the implementation of more advanced channel codes and the introduction of interleavers.

One last option still to be explored in order to improve the demodulation performance of these signals is the increase of the temporal diversity of the transmitted information by increasing the repetitions of the satellite ephemeris data in order to allow the receiver to obtain the information more quickly or to accumulate the information for a lower required demodulation C/N 0 threshold. Moreover, the mass market of the GNSS systems is still growing and new applications as well as services which were not thought as useful or profitable in the past can now present themselves as great commercial opportunities.

The problem with these future services, as well as with the repetition of the ephemeris data, is the lack of available signal transmission bit rate of the GNSS signals.

In order to increase the GNSS signals data information rate, we introduce a signalling technique specially designed to increase the transmission bit rate of a spreading spectrum signal. This technique is known as Code Shift Keying or CSK. The CSK signalling technique consists in circularly shifting each transmitted PRN code in order to represent with each circularly shifted version of the PRN code a different CSK symbol mapping a fixed quantity of bits. Therefore, if each period of the data channel PRN code is equal to the duration of the data symbol, the bit transmission rate is increased proportionally to the number of bits mapped by a CSK symbol.

In this paper, first we present the fundamentals of the CSK signalling technique. After, we analyze the CSK technique by first presenting its general demodulation performance when using hard decision output demodulators. Second, we develop the theoretical mathematical expressions of the likelihood ratios of the bits mapped by a received CSK symbol. Third, we analyze what is the optimal mapping between the bits of the code words to be transmitted and the bits mapped by a single CSK symbol.

Moreover, the demodulation performances of the GALILEO E1 signal when implementing the CSK technique for different number of bits mapped by a single CSK symbol is presented for hard decision output demodulators and for soft output demodulators when the information is protected by an LDPC channel code.

Finally, the drawbacks introduced by the CSK implementation to a modern GNSS signal on the acquisition and tracking processes are presented.

Note that the CSK technique is implemented in the LEX signal of the Japanese global positioning service, QZSS, as indicated in the public released interface specification [START_REF]Interface Specification for QZSS (IS-QZSS) Draft V1[END_REF].

978-1-4244-8739-4/10/$26.00 ©2010 IEEE

II. CSK FUNDAMENTALS

The CSK fundamentals consist of the CSK definition, of the mathematical characterization, of the CSK modulator and demodulator blocks schemes and of the biorthogonal CSK.

A. CSK Definition

The Code Shift Keying is a direct-sequence spreadspectrum (DS-SS) signaling method which overcomes the spreading gain versus data rate limitations [START_REF] Escher | Code-Phase-Shift Keying: A Power and Bandwidth Efficient Spread Spectrum Signaling Technique for Wireless Local Area Network Applications[END_REF].

The CSK is a form of M-ary orthogonal signaling over a communication channel [START_REF] Endsley | Multi-access properties of transform domain spread spectrum systems[END_REF] since M orthogonal signaling waveforms are used in order to transmit k = log 2 (M) bits. The special characteristic of the CSK modulation with respect to the typical M-ary orthogonal signaling is that each waveform is obtained from a different circular phase shift of a single maximal length PRN code; where each circular phase shift is made by an integer number of chips [START_REF] Escher | Code-Phase-Shift Keying: A Power and Bandwidth Efficient Spread Spectrum Signaling Technique for Wireless Local Area Network Applications[END_REF]. In other words, the CSK modulation generally adopts a maximal-length sequence (m-sequence) with its period equal to M as its fundamental sequence. And each set of input data bits is represented by a signaling code, where each signaling code is obtained by cyclically shifting the adopted fundamental sequence. Each cyclically shifted sequence is assumed to be a full period version of the fundamental sequence [START_REF] Tsai | M-ary Spreading Code Phase Shift Keying Modulation for DSSS Multiple Access Systems[END_REF].

B. CSK Mathematical characterization

Each single CSK symbol modulates k bits using the CSK technique. The number of circularly shifted versions of the fundamental code is equal to M, where M = 2 k . The CSK fundamental code is called c d (t) and has a period length equal to T which spans over L chips. L is not necessarily equal to M and the chip interval is equal to T c . From this fundamental code c d (t), the modulator generates the M circularly shifted versions of the code which are called c d (t) to c d-M+1 (t). Each symbol is represented by different k bits, and the set of symbols generates a M-ary alphabet. Moreover, each circularly shifted version of the fundamental code is also called waveform. A mathematical expression of a generic circularly shifted version of the code is shown below:

[ ] ( ) ( ) 1 .. 0 ) ( mod - = ⋅ - = ⋅ - M x T m t c t c Tc L c x d x d (1) [ ] L x d x d m k c k c mod ] [ - = - (2)
• m x : Integer number representing the code shift of the x th waveform

Once the waveform has been selected, it is modulated at a carrier frequency 0 , and after its transmission through an AWGN channel the received signal at the receiver antenna output can be modeled as:

) ( ) ( ) ( t n t s t v + = (3) ) cos( ) ( ) ( 0 t t c A t s x d ω ⋅ ⋅ = - (4)
• v(t): Received signal at the receiver antenna output • s(t): Transmitted signal at the transmitter antenna input

• n(t): AWGN with power equal to 2 .

C. Modulator Block Scheme

The modulator scheme of a CSK transmitted signal can be modeled as shown below:

D. Demodulator Block Scheme

One possible demodulator block scheme is presented. This demodulator block uses Fourier and Inverse Fourier transforms [START_REF] Dillard | Cyclic Code Shift Keying: A Low Probability of Intercept Communication Technique[END_REF] whereas another possible demodulator scheme uses matched filters, one filter for each circularly shifted version of the PRN code. Nevertheless, the mathematical expression of the output of each demodulator is the same. Assuming that w(t) can be mathematically modeled as:

) ( ) ( ) ( t n t s t w + = (5)
• n(t): Additive narrow-band Gaussian noise with a power Pn = B•N 0

• B: RF/IF filter bandwidth
The mathematical expression of the output of the CSK demodulator block scheme is:

1 .. 0 1 - = ≠ = + ± = M i i x n i x n y i i i (6)
• n i : Independent narrow-band Gaussian noises with power equal to 2 = R s •N 0

• R s : CSK symbol transmission rate

E. Biorthogonal and Orthgonal CSK

In addition to use M circularly cyclic shifts of the fundamental PRN code to encode k = log 2 (M) bits, we can also use the polarity of the fundamental PRN code in order to map one extra bit with the same number of M circularly cyclic shifts as done in the M-ary biorthogonal signaling technique. Therefore, in this paper, we call orthogonal CSK the CSK method inspired from the M-ary orthogonal signaling technique and biorthogonal CSK to the CSK method inspired from the M-ary biorthogonal signaling.

Note that a M-ary biorthogonal signaling method is equivalent to a M/2-ary orthogonal signaling method where the two polarities -or signs-of the M/2 different symbols are used.

III. CSK IMPLEMENTATION INTO A GENERIC GNSS SIGNAL

In this section, the characteristics of a CSK technique implemented on a generic GNSS signal are analyzed. These characteristics are the CSK demodulation performance when using a hard output decisions, the likelihood ratio expressions of the CSK bits and the optimal CSK mapping between the bits belonging to a word and the bits transmitted inside a CSK symbol.

A. CSK theoretical hard decision demodulation perfromance

The CSK is a type of M-ary orthogonal signaling (MOS) as verified by [START_REF] Dillard | Cyclic Code Shift Keying: A Low Probability of Intercept Communication Technique[END_REF]. Therefore, the hard demodulation performance in terms of BER as a function of the E b /N 0 has already been calculated and largely commented in the literature [START_REF] Proakis | Digital Communications[END_REF]. The same can be said for a biorthogonal CSK with respect to a Mary biorthogonal signaling.

The BER of an orthogonal CSK as a function of the message E s /N 0 is equal to [START_REF] Proakis | Digital Communications[END_REF]:

∞ + ∞ - - ∞ - - - - - = dy N E y dx e P S M y x M 2 0 1 2 / 2 2 1 exp 2 1 1 2 1 2 π π (7) M k k P BER 1 2 2 1 - = - (8) () k N E N E S b 10 0 0 log 10 ⋅ - = (9)
• E s /N 0 : signal symbol energy per symbol to noise power density ratio

• P M : Probability of orthogonal CSK symbol error

The BER of a biorthogonal CSK as a function of the E s /N 0 is equal to [START_REF] Proakis | Digital Communications[END_REF]:

( ) ∞ + - - - + + - - - = 0 2 0 0 2 / 2 2 / 1 2 / / 2 / 2 2 / 2 1 2 1 1 N E v M N E v N E v x M S S S dv e dx e P π π (10) M k k P BER 1 2 2 1 - ≈ - (11)
• E s /N 0 : signal symbol energy per symbol to noise power density ratio

• P M : Probability of biorthogonal CSK symbol

B. CSK likelihood ratios mathematical expressions

The bits transmitted inside the CSK symbols will very probably be encoded with a channel code in order to decrease the E b /N 0 required to obtain a desired BER. The most powerful channel codes use soft inputs; therefore in order to implement these channel codes, the likelihood ratio (LR) expressions of the bits transmitted inside a CSK symbol have to be developed.

1) M-ary orthogonal signaling likelihood ratio expression

The likelihood ratio (LR) of the transmitted m th bit (b m ) of a orthogonal CSK is defined as shown below:

) 0 ( ) 1 ( ) ( Y b P Y b P b LR m m m = = = ( 12
)
This expression when the transmitted bits are equiprobable is equal to:

) 0 ( ) 1 ( ) ( = = = m m m b Y P b Y P b LR ( 13
)
The numerator and denominator probabilities cannot be directly obtained since the probabilities obtained from the observation of the Y vector (CSK demodulator) determine the probability of receiving a symbol rather than the probability of receiving only one individual bit.

The observed probability expression for a given group of transmitted bits or symbol is shown below. From equation ( 14), the probability of receiving Y when b m is equal to 0 or to 1 can be calculated as presented next:

( ) ( )

k k observed B Y P b b b Y P P = = - 0 1 1 , , , (14) , , , , 0 1
( ) ( ) ( ) 0 0 1 1 1 1 0 0 1 1 1 1 , , , 1 , , , , , , 1 , , 1
1 x b x b b x b P x b x b b x b Y P b Y P m k k xx m k k m K = = = = ⋅ = = = = = = - - - - (16)
Note that in equation ( 16), the only summation which is not applied is the summation having as subindex x m .

The summation having as subindex x p has to be interpreted as shown below.

) 0 ( ) 0 ( ) 1 ( ) 1 ( ) ( ) ( = ⋅ = + = ⋅ = = = ⋅ = p p p p x p p p p b P b P b P b P x b P x b P p (17)
Since the bits are equiprobable, equation ( 16) is simplified to:

( ) ( ) - - -= = = ⋅ = = 01 1 1 1 0 0 , , 1 , , 1 1 xx x k k m m k x b b x b Y P M b Y P (18)
The individual terms of equation ( 18) can be determined since they are the probability of the Y vector observation when a determined group of bits, B k , is transmitted. Using equation ( 14), the previous expression can be expressed as

( )( ) = ⋅ = = n bm n k m B Y P M b Y P 1 , 1 1 (19) • B k
n,bm=1 : Set of k bits mapped by symbol n. The bit b m of symbol n is equal to 1.

The conditioned probability of the Y vector observation can be modeled as a product of the conditioned probabilities of the observation of each individual Y vector component since the Y vector components are independent among them: the noise of each Y vector component is independent from the noise of any other component. The conditioned probability of the Y vector observation can be expressed as:

( ) ( ) ( ) ( ) k M k k k B y P B y P B y P B Y P 1 1 0 - ⋅ ⋅ ⋅ = (20)
From equation ( 6), the conditioned probability of each individual component observation can be modeled as a Gaussian variable with variance equal to 2 , and with a mean that depends on the transmitted groups of bits, B k n : the mean of the y i component observation is equal to 1 if the transmitted group of bits, B k n , is mapped by the M-ary orthogonal symbol i; in other words, if i is equal to n. Otherwise the mean is 0.

The probabilities of the observation of the Y vector components when the group of bits, B k n , is transmitted are: Finally, equation (19) can be written as shown below:

( ) ( ) = - ⋅ - ⋅ ≠ ⋅ - ⋅ = n i y n i y B y P i i n k i
( ) = ⋅ = = m m x b i i m m y Y K x b Y P 2 exp ) ( σ (23) - ⋅ = - = 1 0 2 2 1 2 1 exp 2 2 1 ) ( M i i y M Y K σ πσ (24)
The summation of the second term of equation ( 23) means the summation of all the y i components which represent a symbol, or group of bits, B k , having b m = x m .

Finally, since K(Y) has the same value for b m =1 and b m =0, the final expression of the likelihood ratio of the bits mapped by a M-ary orthogonal symbol is:

= = = 0 2 1 2 exp exp ) ( m m b i i b i i m y y b LR σ σ (25)
Finally, an algorithm to speed the bits likelihood ratio calculation is presented:

2) M-ary biorthogonal signaling likelihood ratio expression

In the case of a M-ary biorthogonal signaling, the search of the bits likelihood ration expression is different from the bit indicating the polarity of the transmitted waveform to the bits selecting the transmitted waveform.

The mathematical notation for a biorthogonal CSK mapping is: The likelihood ratio expression of the bit setting the waveform polarity is calculated using equation (13):

{ } 0 2 2 , , , , b b b R k k k - - = β (26) { } 1 , - = k k B R β (27) • R k : Set of k input
) 0 ( ) 1 ( ) ( = = = β β β Y P Y P LR ( 28
)
In this case, the observed probability at the demodulator output is:

( ) ( ) k k observed R Y P b b b Y P P = = - 0 1 1 , , , , β (29)
Therefore, denoting each different group of transmitted bits mapped by the M/2-ary orthogonal symbol as B k n and denoting each different group of transmitted bits by the M-ary biorthogonal symbol as R k n , the conditioned probability of the observation of the Y vector component y i can be modeled as:

( ) ( ) = - ⋅ + ⋅ - ⋅ ≠ ⋅ - ⋅ = n i y n i y R y P i i n k i 2 2 2 2 1 2 2 1 exp 2 1 2 1 exp 2 1 σ β πσ σ πσ (30)
Consequently, expression P(Y|R k n ) is equal to:

( ) - - ⋅ ⋅ - ⋅ - ⋅ = - = 1 2 1 2 2 1 exp 2 1 exp 2 1 2 1 2 / 0 2 2 n M i i n k y y R Y P β σ σ πσ (31)
The likelihood ratio expression of the bit setting the waveform polarity can be found from equations ( 19), ( 28) and (31):

- = - = - = 1 2 / 0 2 1 2 / 0 2 exp exp ) ( M i i M i i y y LR σ σ β (32)
The likelihood ratio expressions of the bits selecting the transmitted waveform are calculated taking into account the probability of having received the bit equal to 0 or equal to 1. The terms P(Y|b m , ) can be calculated as showed in equation (19) using equation ( 14) for the M-ary orthogonal signaling case. The only difference is found when =1 since the value of y m has its sign inversed in this case.

( ) ( ) ( ) = ⋅ - ⋅ ⋅ = = m m x b i i m m y Y K x b Y P 2 5 . 0 2 exp , , σ β β β (35) - ⋅ = - = 1 2 / 0 2 2 1 2 1 exp 2 1 ) , ( M i i y M Y K σ πσ β ( 36
)
As before, K(Y, ) has the same value for b m = 0 and for b m = 1. Therefore, the likelihood ratio expression is:

3) Likelihood ratios mathematical expression verification

We have simulated the transmission of a CSK signal through an AWGN channel and we have calculated the BER using hard decisions outputs and using the likelihood ratio expressions developed previously. The simulations show that all the inspected methods provide the same BER as a function of the signal E b /N 0 at the correlator output. This means that the previous CSK bits likelihood ratio expressions are verified as the equivalent soft output method of the hard decision method defined by the literature [START_REF] Proakis | Digital Communications[END_REF].

The demodulation performance of the transmission of a CSK signal through an AWGN channel when 8 bits are mapped by a CSK symbol is presented below. Figure 4 shows the BER as function of the signal E b /N 0 at the correlator output. The same results have been obtained for 6 and 10 bits mapped by a CSK symbol [START_REF] Garcia-Pena | Optimisation of Demodulation Performance of the GPS and GALILEO Navigation Messages[END_REF].

C. Source Words Mapping of a CSK modulation

The implementation of a channel code on the bits transmitted by a CSK modulation introduces a new interesting element of study: the CSK source word mapping.

The source word mapping is defined as the distribution between the bits mapped by each CSK symbol and the bits belonging to the same word: which bits mapped into a CSK symbol belong to a given word A, which bits belong to a given word B, etc. Therefore, one question to be asked is which source word mapping provides the lowest BER.

In fact, the variance of the number of errors of a word transmitted by a CSK signal depends significantly on the used CSK source word mapping. And, as justified next, it can be much more interesting to have either a low or a large variance depending on the transmission channel.

On one hand, if the variance is low and the error correction capacity of the implemented channel code is larger than the average number of errors, the channel code could correct almost all the words. On the other hand, if the variance is large and the error correction capacity of the implemented channel code is much smaller than the average number of errors, the channel code could correct some words whereas with a low variance no word should be corrected.

The calculation of the variance of the number of errors of a word transmitted inside CSK symbols is made in three steps. The first step is to calculate the probability of having n erroneous bits among x bits belonging to the same packet when the transmitted CSK symbol maps K bits and has a probability of error equal to P M . The mathematical expression of the probability is given next [START_REF] Garcia-Pena | Optimisation of Demodulation Performance of the GPS and GALILEO Navigation Messages[END_REF]:

( ) ( ) x n m x K n x n P K n p x K n m K M x ≤ - - + ⋅ - = - = ) ( 1 2 ) ( 1 δ δ (38) • (n): Dirac delta function
The second step consists in calculating the probability of a word of L bits having 0 erroneous bits, the probability of having 1 erroneous bit, etc, until the probability of having L erroneous bits. This second step is made using Matlab since it is the raw combination of the probabilities expressed in (38).

The third and final state is the calculation of the average and the variance of the number of errors of a word transmitted into CSK symbols using the probabilities determined in step 2.

Finally, the CSK source word mappings determining the lowest and largest variance of the number of errors of a word transmitted inside CSK symbols are determined by inspecting the results of step 3 for a CSK symbol mapping 8 bits. Figure 5 show the desired variance as a function of the signal E s /N 0 for a word of 1200 bits. From figure 5, it can be observed that the CSK source word mapping which obtains the lowest variance of the number of errors of a word transmitted inside a CSK symbol is the mapping where all the bits transmitted inside a CSK symbol belong to different words. Moreover, it can be observed that the largest variance belongs to the mapping where all the bits transmitted inside a CSK symbol belong to the same word.

The same results have been observed for 4, 6, 10 and 12 bits mapped by a CSK symbol [START_REF] Garcia-Pena | Optimisation of Demodulation Performance of the GPS and GALILEO Navigation Messages[END_REF].

IV. CSK IMPLEMENTATION IN THE GALILEO E1 SIGNAL

The CSK implementation on the GALILEO E1 signal consists in applying the CSK technique, the circular shift of the PRN code, on the data channel and in using the pilot PRN code as synchronizer in order to identify which circular shift has been transmitted.

In this section, the hard decision output demodulation performance of the GALILEO E1 signal is given, the demodulation performance of the GALILEO E1 signal with an implemented LDPC code is presented, and the CSK influence on the tracking and the acquisition process is analyzed.

A. CSK hard output demodulation of the GALILEO E1

The hard output performance of the GALILEO E1 signal without implemented channel code is calculated from the theoretical expressions ( 8) and (11). This calculation assumes that the signal C/N 0 or E s /N 0 is fixed for any number of bits transmitted inside a CSK symbol which means that the E b /N 0 varies for the different number of bits.

The number of chips of the GALILEO E1 PRN data code is 4092 which means that a maximum of 11 bits are transmitted with an orthogonal CSK and a maximum of 12 bits are transmitted with a biorthogonal CSK. The bit transmission rate (R D ) is equal to 250 bit/s. Figures 6 and7 show the BER of the GALILEO E1 signal for a hard decision demodulation as a function of the signal C/N 0 at the correlator output. From these figures, it is observed that due to the constant value of E s , a larger number of bits mapped by a single CSK symbol leads to a worse demodulation performance in terms of BER of the CSK modulation in the GALILEO E1 signal.

B. CSK soft demodulation performance for GALILEO E1

The demodulation performance of the GALILEO E1 signal which implements the CSK and which has a channel code applied on the CSK information bits is presented. This section uses the likelihood expressions developed in section III.B.

The bit transmission rate of the signal is 250 bits/s. The size of the information word is 600 bits which are encoded with the LDPC code of GPS L1C [START_REF]Navstar GPS space Segment/User segment L1C interfaces[END_REF] resulting into a coded word of 1200 bits. The orthogonal and biorthogonal CSK are implemented and the CSK source word mapping providing the lowest and the largest variance are analyzed. For the latter mapping, an interleaver applied over the word is introduced in order to break the burst of errors and, thus, to improve the demodulation performance.

The next figures show the BER of the GALILEO E1 signal implementing a CSK technique which maps 8 bits for each CSK symbol as a function of the signal C/N 0 at the correlator output. An ideal estimation of the signal carrier phase and the code delay is assumed. From figure 8, it can be seen that the CSK source word mapping providing the lowest variance outperforms the mapping providing the largest variance. This demodulation performance difference grows along the increase of the number of bits mapped by a CSK symbol as seen in [START_REF] Garcia-Pena | Optimisation of Demodulation Performance of the GPS and GALILEO Navigation Messages[END_REF]. Moreover, it can also been observed that the orthogonal CSK slightly outperforms the biorthogonal CSK, but this difference decreases along the increase of the number of bits as seen in [START_REF] Garcia-Pena | Optimisation of Demodulation Performance of the GPS and GALILEO Navigation Messages[END_REF].

From figures 6, 7 and 8, it can be observed that for a BER equal to 10 -6 , the provided gain between a CSK configuration mapping 8 bits without a channel code and the same configuration but with the GPS L1C LDPC code is about 6.45 dB for the orthogonal CSK and is about 6.5 dB for the biorthogonal CSK. This gain decreases along the increase of the number of bits mapped by a CSK symbol as seen in [START_REF] Garcia-Pena | Optimisation of Demodulation Performance of the GPS and GALILEO Navigation Messages[END_REF] These gains can be compared to the gain introduced by the application of the same LDPC code on a BPSK signal without the CSK technique; this gain is about 8.1 dB [START_REF] Garcia-Pena | Optimisation of Demodulation Performance of the GPS and GALILEO Navigation Messages[END_REF].

Finally, the BER and WER of the GALILEO E1 signal implementing an orthogonal or a biorthogonal CSK configuration with the source word mapping providing the lowest variance and for different number of bits mapped by a CSK symbol as a function of the signal C/N 0 at the correlator output are presented. From figures 9 and 10, it can be seen that for any number of bits mapped by a CSK symbol, in order to obtain a BER equal to 10 -6 or a WER equal to 10 -3 we need a C/N 0 larger than 34 dB-Hz.

C. Drawbacks of the CSK on the GALILEO E1 signal

The main disadvantage of the CSK technique implementation on the GALILEO E1 signal is the constant shift of the data PRN code which does not allow the use of the data channel in the acquisition and in the tracking process.

1) Tracking process:

The new GNSS signals are formed by two channels, the data channel and the pilot channel, in order to avoid the limitation of the maximal coherent integration time imposed by the data symbol duration. This means that the tracking of new GNSS signals was thought to be made only on the pilot channel.

Moreover, wipe-off techniques are also allowed by the data PRN code implementing the CSK technique, since the knowledge of the transmitted bits determines the next circular shift of the PRN code. The only difference is that a larger quantity of bits must be known to be able to apply the wipe-off techniques.

To sum up, the tracking process is not affected by the implementation of the CSK signaling technique.

2) Acquisition process:

The acquisition process of the GALILEO E1 signal is affected by the implementation of the CSK technique since both channels, pilot and data, are used to acquire the signal.

In order to quantify the impact of the CSK technique on the acquisition process, we have run some simulations which calculate the average acquisition time of the GALILEO E1 signal when we use both channels to acquire the signal without implementing the CSK, when we use both channels to acquire the signal implementing the CSK and when we only use the pilot channel.

The simulations use a coherent integration time of 4ms, a non-coherent integration time of 100ms, 2000 correlators and only 190 symbols out of the 250 symbols transmitted each second by the GALILEO E1 signal implement the CSK.

From figure 11, it can be observed that when the CSK is implemented, the signal has to be acquired only using the pilot channel. Moreover it can be seen that for C/N 0 larger than 29 dB-Hz, the GALILEO E1 signal is acquired faster using only the pilot channel than using both channels even when the CSK technique is not implemented. Finally, it can be seen that for an average acquisition time of 1000s, we require an extra 1 dB of C/N 0 when we only use the pilot channel than when we use both channels and the CSK is not implemented.

V. CONCLUSIONS

In this paper, the Code Shift Keying signaling technique has been presented as a possible option for the future GNSS signals in order to increase their data transmission rate. This increase of the data information rate could be use in order to transmit additional commercial services or in order to transmit redundant ephemeris data which will reduce the C/N 0 needed to obtain a desired BER or WER.

Different demodulation performance of the GALILEO E1 signal has been calculated for different CSK configurations, and the CSK impact on the tracking and acquisition process has been analyzed.

The likelihood ratio expressions of the bits transmitted inside a CSK symbol has been developed. A fast algorithm has been provided for their calculation.

Figure 1 .

 1 Figure 1. CSK Modulator Block Scheme

Figure 2 .

 2 Figure 2. CSK Demodulator Block Scheme Where w(t) is the received signal at the RF/IF block output. Each component of the vector represents the correlation between the received signal and a circularly shifted version of the fundamental PRN code.

•

  B k : Set of k bits determining the transmitted symbol • b x : Value of the x th bit of the set B k

1 .

 1 Calculating and storing all the exponential values: T m = exp(y m / 2 ) 2. Setting the value M = 2 k 3. For i = 0 to k-1 a. Calculating the b i likelihood ratio i. P 1 = T 1 + T 3 + … + T M-1 ii. P 0 = T 0 + T 2 + … + T M-2 iii. LR(b i ) = P 1 /P 0 b. Calculating the new T m values i. For m = 0 to (M/2 -1) T m = T 2m + T 2m+1 c. Setting the new M value: M = M/2This algorithm is illustrated and justified in the figure displayed below. In this example, 4 bits are modulated in a 16ary orthogonal symbol.

Figure 3 .

 3 Figure 3. 16-ary orthogonal signalling example -Bits likelihood ratio calculation for 4 bits mapping an orthogonal signal

  bits for a biorthogonal CSK symbol • : Value of the bit setting the waveform polarity • B k-1 : Set of k-1 input bits for a orthogonal CSK symbol • b x : Value of the x th bit of the set B k-1

  Thus, P(Y|b m , ) can be expressed from (31) and (34) as:

Figure 4 .

 4 Figure 4. BER vs Eb/N0 for a transmission employing CSK symbols which map 8 bits

Figure 5 .

 5 Figure 5. Variance of the number of bit errors of a word of 1200 bits transmitted by 256-CSK symbols with different CSK source packet mappings

Figure 6 .Figure 7 .

 67 Figure 6. BER vs C/N0 of the part of the GALILEO E1 signal implementing the CSK signalling technique for different number of bits mapped by an biorthogonal CSK symbol

Figure 8 .

 8 Figure 8. BER vs C/N0 of different CSK configurations where each CSK symbol maps 8 bits when the signal is transmitted through an AWGN channel

Figure 9 .

 9 Figure 9. BER vs C/N0 of the best GALILEO E1 signal CSK configurations

Figure 11 .

 11 Figure 11. Average acquisition time for GALILEO E1 OS signal as a function of the data + pilot C/N0

ACKNOWLEDGMENT

A.G.P. thanks to CNES, TAS-F and TéSA for the joint financing of the research fellowship.


Rawa Abdallah

Florence Geneste

Thierry Labasque

Hayet Djelal

Florence Fourcade

Abdeltif Amrane

Samir Taha

Didier Floner
email: didier.floner@univ-rennes1.fr

Selective and quantitative nitrate electroreduction to ammonium using a porous copper electrode in an electrochemical flow cell

Keywords: porous copper cathode, nitrates electroreduction, ammonium, electrochemical flow cell

The aim of this work was to set up a novel electrochemical system allowing an efficient transformation of concentrated nitrate solutions to ammonium and which can be subsequently implemented on a large scale application. First, this paper describes the preparation of a porous copper modified electrode by successive electrodeposition of nickel then copper on a graphite felt of large specific surface area. Homogeneous Cu coating of all fibres in the 3D porous structure was successfully obtained using low concentrations of copper salts and high applied current intensities. The porous copper electrode was then used in a flow electrochemical process to achieve a selective and quantitative transformation of concentrated nitrate into ammonium.

Different electrolytic solutions, slightly acid (acetate buffer) or neutral (phosphate buffer), and flow rates were investigated. The nitrate solution was quantitatively reduced into NH 4 + with high selectivity in only one pass through the electrode. When the applied current was similar to the theoretical one, the maximum selectivity (96 %) and the best current efficiency (72%) for NH 4 + formation were reached at pH 7.2 with a flow rate of 2 mL min -1 . The obtained ammonium solution can be subsequently used either as a potential nitrogen source during microbial culture or simply as a fertilizer.

Introduction

Nitrate ions (NO 3 -) contamination of ground and surface water resources has become a serious problem around the world. Removing nitrate is very important for various reasons. (i) Nitrate water pollution disturbs public health and ecological equilibrium [START_REF] Bhatnagar | A review of emerging adsorbents for nitrate removal from water[END_REF]. Consuming high NO 3 concentrations in drinking water can cause serious health problems in humans such as the -blue baby syndrome‖ in infants, liver damage and cancer [START_REF] Chan | Vegetable-borne nitrate and nitrite and the risk of methaemoglobinaemia[END_REF]. (ii) By considering the ecological balance, excess of nitrate favor eutrophication of lakes, rivers and seas, manifested through uncontrolled algal growth [START_REF] Primo | Nitrate removal from electro-oxidized landfill leachate by ion exchange[END_REF][START_REF] Talhi | Effective and selective nitrate electroreduction into nitrogen through synergistic parameter interactions[END_REF]. WHO and European community set stringent limits for the NO 3 concentrations in surface and groundwater to 50 mg L -1 and 25 mg L -1 respectively [START_REF] Organization | Rolling Revision of the WHO Guidelines for Drinking-Waters Quality, Nitrates and Nitrites in Drinking-Waters[END_REF].

Nowadays, many processes such as biological and physiochemical methods are used for nitrate removal from contaminated water but show drastic limits. Biodenitrification is considered as the method of choice [START_REF] Reyter | Nitrate removal by a paired electrolysis on copper and Ti/IrO2 coupled electrodes -Influence of the anode/cathode surface area ratio[END_REF][START_REF] Polatides | Electrochemical reduction of nitrate ion on various cathodesreaction kinetics on bronze cathode[END_REF]. However, this method is slow, requires continuous monitoring of microorganism's growth (carbon source, pH and temperature control) [START_REF] Mateju | Biological water denitrification-A review[END_REF]. Furthermore, it can be used only at concentrations lower than 1000 mg NO 3 -L -1 , since higher ones can be poisonous to the bacteria [START_REF] Badea | Electrocatalytic reduction of nitrate on copper electrode in alkaline solution[END_REF]. Physicochemical processes such as ion exchange, reverse osmosis and electrodialysis are costly [START_REF] Zhou | Nitrate removal from groundwater by a novel threedimensional electrode biofilm reactor[END_REF] and produce secondary brine wastes, because the nitrate are only separated but not destroyed [START_REF] Wang | The electrocatalytic reduction of nitrate in water on Pd/Snmodified activated carbon fiber electrode[END_REF]. Thus, these methods lead to concentrated effluents of nitrates (≥ 3g L-1) [START_REF] Kim | Modeling a novel ion exchange process for arsenic and nitrate removal[END_REF] that are very difficult to treat.

Electrochemical nitrate treatment can offer a promising and attractive solution due to its advantages regarding low cost effectiveness, convenience, ability to treat highly concentrated nitrate effluents and environmental friendliness [START_REF] Li | Simultaneous reduction of nitrate and oxidation of by-products using electrochemical method[END_REF][START_REF] Reyter | Electrocatalytic reduction of nitrate on copper electrodes prepared by high-energy ball milling[END_REF][START_REF] Pérez | Electro-oxidation of reverse osmosis concentrates generated in tertiary water treatment[END_REF] particularly if the resulting product is N 2 gas [START_REF] Rajeshwar | Environmental electrochemistry: Fundamentals and applications in pollution sensors and abatement[END_REF]. An ideal electrochemical method must combine a high rate of reduction, a selective conversion of nitrate to the desired product, a high current efficiency (% CE) and low energy consumption [START_REF] Katsounaros | Electrochemical reduction of nitrate and nitrite in simulated liquid nuclear wastes[END_REF].

Almost all recent electrochemical studies aim to convert nitrate to the non toxic nitrogen gas [START_REF] Dortsiou | Electrochemical reduction of nitrate on bismuth cathodes[END_REF].

In this context paired electrolysis seems to be the most efficient and hence the most widely used electrochemical method [START_REF] Reyter | Nitrate removal by a paired electrolysis on copper and Ti/IrO2 coupled electrodes -Influence of the anode/cathode surface area ratio[END_REF][START_REF] Cheng | Paired electrolysis in a solid polymer electrolyte reactor-Simultaneously reduction of nitrate and oxidation of ammonia[END_REF][START_REF] Katsounaros | Efficient electrochemical reduction of nitrate to nitrogen on tin cathode at very high cathodic potentials[END_REF][START_REF] Reyter | Optimization of the cathode material for nitrate removal by a paired electrolysis process[END_REF]. It consists to reduce NO 3 -to ammonium at the cathode, and then the produced ammonium is oxidized at the anode into N 2 with or without the contribution of hypochlorite ions (ClO -), which results from the oxidation of chloride ions on the anode [START_REF] Vanlangendonck | Influence of operating conditions on the ammonia electro-oxidation rate in wastewaters from power plants (ELONITA TM technique)[END_REF].

However, the main problem in this approach is that the transformation of NO [START_REF] Dortsiou | Electrochemical reduction of nitrate on bismuth cathodes[END_REF].

As the products of the nitrate electroreduction are critically dependent on the nature of the cathode material [START_REF] Shimazu | Electrochemical reduction of nitrate ions on tin-modified platinum and palladium electrodes[END_REF][START_REF] Peel | Electrocatalytic reduction of nitrate in water[END_REF][START_REF] Li | Electroreduction of nitrate ions in concentrated sodium hydroxide solutions at lead, zinc, nickel and phthalocyanine-modified electrodes[END_REF], this fact led to the search for selective and active cathode materials.

Many solid electrodes have been studied including Pb, Ni [START_REF] Li | Electrochemical reduction of nitrate and nitrite in concentrated sodium hydroxide at platinum and nickel electrodes[END_REF], Cu [START_REF] Pletcher | The reduction of nitrate at a copper cathode in aqueous acid[END_REF], Pt [START_REF] Petrii | Electroreduction of nitrate and nitrite anions on platinum metals: A model process for elucidating the nature of the passivation by hydrogen adsorption[END_REF], Ru [START_REF] Dima | Electrocatalytic reduction of nitrate at low concentration on coinage and transition-metal electrodes in acid solutions[END_REF], Ir [START_REF] De | Cyclic Voltammetric Studies of Nitrate and Nitrite Ion Reduction at the Surface of Iridium-Modified Carbon Fiber Electrode[END_REF],

Rh [START_REF] Cunha | Reaction pathways for reduction of nitrate ions on platinum, rhodium, and platinum-rhodium alloy electrodes[END_REF] and Fe [START_REF] Bockris | Electrochemical treatment of low-level nuclear wastes[END_REF]. Among these materials, copper is known to be the most efficient electrocatalyst for nitrate electroreduction producing ammonium as a final product [START_REF] Reyter | Study of the electroreduction of nitrate on copper in alkaline solution[END_REF][START_REF] Bouzek | Electrochemical reduction of nitrate in weakly alkaline solutions[END_REF][START_REF] Macova | Electrocatalytic activity of copper alloys for NO 3reduction in a weakly alkaline solution[END_REF]. Thus, electrochemical treatment of nitrates on pure Cu cathodes [START_REF] Reyter | Study of the electroreduction of nitrate on copper in alkaline solution[END_REF][START_REF] Lima | Scanning electrochemical microscopy investigation of nitrate reduction at activated copper cathodes in acidic medium[END_REF][START_REF] Li | Efficient electrochemical reduction of nitrate to nitrogen using Ti/IrO2-Pt anode and different cathodes[END_REF] or Cu alloys [START_REF] Reyter | Optimization of the cathode material for nitrate removal by a paired electrolysis process[END_REF][START_REF] Simpson | Electrocatalysis of Nitrate Reduction at Copper-Nickel Alloy Electrodes in Acidic Media[END_REF][START_REF] Li | Electrochemical reduction of nitrate using various anodes and a Cu/Zn cathode[END_REF][START_REF] Fan | Electrochemical denitrification and kinetics study using Ti/IrO2-TiO2-RuO2 as the anode and Cu/Zn as the cathode[END_REF] has been widely studied. But all these investigations are analytical studies and/or deal with relatively low nitrate concentrations [START_REF] Li | Electrochemical reduction of nitrate using various anodes and a Cu/Zn cathode[END_REF]. Moreover, the main problem in the electroreduction of nitrates on solid electrodes is the low reduction rate [START_REF] Polatides | Electrochemical reduction of nitrate ion on various cathodesreaction kinetics on bronze cathode[END_REF] owing to the low mass transport. This considerable drawback limits their use for large scale applications.

The use of a flow electrochemical cell with a graphite felt as porous electrode can resolve the problem related to the mass transport. This system has the advantage of oxidizing/reducing a large amount of substrate in short times, allowing quantitative electrochemical treatments [START_REF] Chamoulaud | Biomass conversion II: simultaneous electrosyntheses of furoic acid and furfuryl alcohol on modified graphite felt electrodes[END_REF].

The major advantages of graphite felt as porous electrode material are its high specific surface area, ranging from 0.7 m 2 g -1 to 2000 m 2 g -1 , the low cost and the availability of these materials.

But unfortunately, graphite felt is a poor electrode for the selective reduction of nitrates to ammonium. Hence, it's necessary to enhance its selectivity toward ammonium formation.

It is interesting to note that among the various nitrate electroreduction by-products (ie. N 2 , N 2 O, N 2 O -, NH 4 + ), ammonium has the highest economic value. It has an important potential as fertilizers [START_REF] Tabatabaei | Effects of shading and NO3:NH4 ratio on the yield, quality and N metabolism in strawberry[END_REF][START_REF] Nell | Nitrate-ammonium nitrogen ratio and fertilizer application method influence bract necrosis and growth of poinsettia[END_REF][START_REF] Sadat Taghavi | The effect of nitrate and plant size on nitrate uptake and in vitro nitrate reductase activity in strawberry (Fragaria × ananassa cv. Selva)[END_REF] and as nitrogen source for microorganism cultures producing biohydrogen [START_REF] Iyer | H2-producing bacterial communities from a heat-treated soil inoculum[END_REF][START_REF] Masset | Effect of pH on glucose and starch fermentation in batch and sequenced-batch mode with a recently isolated strain of hydrogen-producing Clostridium butyricum CWBI1009[END_REF][START_REF] Salerno | Inhibition of biohydrogen production by ammonia[END_REF]. The use of cheap inorganic nitrogen source appears relevant from an economical point of view, contrarily to organic nitrogen sources which are often more expensive [START_REF] Wang | Impact of carbon and nitrogen sources on hydrogen production by a newly isolated Clostridium butyricum W5[END_REF]. For this reason, an electroreduction of nitrate to NH 4 + over copper cathode can be considered as an attractive way, since it allows not only pollutant treatment, nitrate, but also possible valorization of the treated effluent.

Therefore, the first objective of the present study was the preparation of a new cathode material, a porous copper electrode by successive electrodeposition of nickel then copper on a graphite felt.

A homogeneous coating of all fibres of thick graphite felts was obtained. The method leads to the formation of a copper modified graphite felt (CuGF) of high specific surface area and low weight.

The second objective was the use of the CuGF electrode for the electrochemical reduction of a concentrated nitrate solution (3 g NO 3 -L -1 ) into ammonium in a divided flow cell. Results show that the system combining the performances of the flow cell and the CuGF electrode lead to high chemical yields and current efficiencies. MERSEN (Paris La Defense, France). Its specific surface area measured by the BET method was 0.7 m 2 g -1 , its density was 0.088 g cm -3 and its carbon yield was 99.9%.

Experimental procedure

Graphite felt modification consisted in two steps. First, nickel was electrochemically deposited on the graphite fibres of the graphite felt (diameter: 5.6 cm and thickness 0.3 cm) according to a previously described method [START_REF] Floner | Homogeneous coating of graphite felt by nickel electrodeposition to achieve light nickel felts with high surface area[END_REF]. Secondly, the electrodeposition of copper was performed on the nickel modified graphite felt according to the conditions described in Table 1.

Table 1 1 L of electrolytic solution (copper sulfate (3×10 -2 M); sodium sulfate (0.5 M); boric acid (0.25 M)) was flowed through the porous electrode in a home-made flow cell (Fig. 1). To obtain a good homogeneity of the potential distribution in the three dimensional working electrode, the Ni modified graphite felt was located between two counter-electrodes (platinum grids) [START_REF] Moinet | Electrosynthèse organique en continu. Méthodes directes et indirectes[END_REF] and the electrical contact with the working electrode was performed with a copper wire. The electroplating experiments have been realized without adding cationic exchange membranes. A periodically changing current (on-pulse: 0.1 A for 1 cm3 of felt, off-pulse: 0 A, see table 2 for the duration of the pulses) was applied between the electrodes, using a power Lab/4SP (Scope version 3.6.10, AD Instruments) coupled to an EG&G Princeton Applied Research model 362 operating under galvanic conditions. The flow rate of the electrolytic solution was maintained at 5 mL min -1 and the pH of the electrolyte solutions was adjusted with solutions of H 2 SO 4 (0.5 M)

or NaOH (5 M). The full electrodeposition time was 240 min without taking into account the relaxation time (Table 2).

Table 2 The SEM (scanning electron microscope) micrographs were obtained with a Jeol 630v1F (9 kv) microscope. The flow rate was monitored by a Gilson minipuls 2 peristaltic pump and the current by a homemade power supply (30 V/ 3A). The cell was thoroughly rinsed with distilled water before each experiment. The applied current was calculated from the Faraday law (Eq. 1) ) [START_REF] Chamoulaud | Biomass conversion II: simultaneous electrosyntheses of furoic acid and furfuryl alcohol on modified graphite felt electrodes[END_REF].

Flow electrolyses

i (A) = [NO 3 - ] t=0 × d × (10 -3 /60) × n × F (1)
where [NO 3 -] t=0 is the initial concentration of nitrates (mol L -1 ), d is the flow rate (mL mn -1 ), F is the Faraday's constant (96,487 C mol -1 ) and n is the number of exchanged electrons (8e -) for the conversion of nitrate to ammonium.

Analytical methods

Every 30 min, 5 mL of samples were collected from the electrolytic medium and filtered through a 0.45 µm membrane before analysis. NO

Definition of the parameters

The performance of the flow cell was evaluated from the electrochemical conversion of nitrates into ammonium in one pass through the flow cell at room temperature, using the following parameters: the normalized percentage of nitrate removal or the conversion yield (% τ) (Eq. 2), the chemical yield of reduction products (ammonium and nitrite yields) (% X i ) (Eq. 3) and the selectivity based on the ammonium yield (% S NH4+ ) (Eq. 4), [START_REF] Cheng | Paired electrolysis in a solid polymer electrolyte reactor-Simultaneously reduction of nitrate and oxidation of ammonia[END_REF].

% τ = ([NO 3 - ] t=0 -[NO 3 - ] t ) × 100 / [NO 3 - ] t=0 (2)
% X NH4+ = ([NH 4 + ] t × 100) / [NO 3 - ] t=0 and % X NO2-= ([NO 2 - ] t ×100) / [NO 3 - ] t=0 (3)
% S NH4+ = ([NH 4 + ] t × 100 ) / ([NO 3 - ] t=0 -[NO 3 - ] t ) = (% X NH4+ × 100) / (% τ) (4)
The current-denitrification efficiency (current efficiency (% CE)), calculated based on the cathodic current efficiency is defined by equation 5:

% CE = (([NH 4 + ] t × n × F × V t ) / (i × t)) × 100 (5)
where [X] t=0 and [X] t are the concentrations of X in solution at initial and time t (s), V t (L) is the electrolyzed volume at time t.

All the concentrations are in mol L -1 and 1 F = 96,487 C mol -1 .

Results and discussion

Galvanostatic method

Metal electrodeposition on porous material of high surface area such as graphite felt is not easy due to the strong heterogeneity of potential distribution inside the material [START_REF] Storck | The behaviour of porous electrodes in a flow-by regime-I. theoretical study[END_REF][START_REF] Doherty | An improved model of potential and current distribution within a flow-through porous electrode[END_REF]. At constant current, electrical potential rapidly decreases along the depth of the material. Metallization only appears at the external face of the material with formation of a metallic crust more or less rapidly according to the metal salts concentration. To avoid this phenomenon we developed a galvanostatic method well-adapted to the 3-D electrode.

Two fundamental points are necessary to achieve homogeneous coating of the fibres (i) an electrodeposition solution containing the metal salts in low concentration (around 10 -2 M) and (ii) a strong current (around 100 mA per cm 3 of felt). Thereby diffusion-limited currents are quickly reached on the external fibres limiting the rate of electrodeposition on the external face of the graphite felt. Consequently, the excess of current allows the electrodeposition on other fibres located inside the felt. As soon as the diffusion-limited current is reached on a fibre, the electrodeposition process is accelerated on another fibre located farther from the electrode surface. Due to the decrease of the metallic cations concentration in the vicinity of the fibres, hydrogen evolution occurs and becomes more and more important. An alternating current was therefore employed with long relaxation time to stop hydrogen evolution and reduce the local decrease of metallic cations concentration inside the felt.

Copper electrodeposition

Copper electrodeposition was achieved in the flow cell (Fig. 1) at a constant flow rate (d) of 5 mL min -1 and with a working electrode of volume V = 7.5 cm 3 . Unfortunately, first attempts to perform electrodeposition of copper on graphite felt led to non-homogeneous coating of the fibres. SEM images showed only small and friable particles of metallic copper, scattered along the fibres whereas copper powder predominated inside the felt. This result underlines the weak adherence between metallic copper and graphite. Since copper is known to efficiently adhere to metallic surfaces, the graphite felt was first covered by a homogeneous film of nickel (Fig. 2 a)

according to a previously reported method [START_REF] Floner | Homogeneous coating of graphite felt by nickel electrodeposition to achieve light nickel felts with high surface area[END_REF].

Fig. 2.

The flow rate (d) was kept to 5 mL min -1 and the volume of the working electrode to 7.5 cm 3 .

When a constant current is applied, the maximum time allowing the complete regeneration of the solution inside the felt is t max = V / d. Due to the convection inside the felt resulting from percolation, the regeneration time is lower than t max and depends on the initial concentration of copper. With this tendency in mind, different electrodeposition experiments were performed, varying the concentration of copper and the on-pulse and off-pulse times. The most relevant one are presented in Table 2. The best conditions are given in experiment 4 corresponding to a copper concentration of 3 × 10 -2 M with an off-pulse time (t off ) of 35 s and a on-pulse time (t on ) of 15 s.

We found that when t off was around t max /3 the renewal of the copper solution inside the felt was good. Moreover, a ratio t on /t off less than 2.3 led to a rapid decrease of the copper concentration inside the felt. Thus, hydrogen evolution became preponderant leading to an increase of the solution pH inside the felt and precipitation of copper hydroxide. In these conditions, a poor quality of copper deposition was obtained with a low current efficiency. Homogeneous copper electroplating was achieved with a current efficiency higher than 50% for a ratio t off /t on upper to 2.3. A decrease of t on led to higher values of current efficiencies but increased the full electrolysis time.

The homogeneity of the copper coating was checked by SEM. Fig. 2 b, c and d show copper coating fibres located inside the felt and cut transversally. The electrodeposition method led to a copper film with an average thickness around 2 µm that follows the shape of the graphite fibres.

This layer of copper was even visible to the naked eye. As seen in Fig. 2b andc the high porosity of the material was conserved. The copper deposit has a granular aspect and consists in crystallites of different sizes assembled on the surface of the fibres (Fig. 2c). Fig. 2d shows the two successive layers of nickel and copper obtained after the two successive electrodepositions.

Graphite felt is visible on the lower left quarter of the microphotograph. On the right from the bottom to the top of the microphotograph appear the nickel film on the graphite fibre and then the copper film deposited on the nickel layer. Since the brightness of nickel is very different from that of copper, SEM images clearly highlight the homogeneous structure of the copper deposit.

The specific surface area of the copper modified graphite felt was estimated by BET to 2 g m -2 .

The average density of deposited copper was about 0.265 g cm -3 of felt. Consequently, the electrodeposition method led to the preparation of a CuGF electrode having a high specific surface and a low density; this latter electrode was used afterward as a cathode for electrochemical denitrification studies.

Nitrate reduction

Electrolysis of nitrate was performed in a single passage in a homemade flow cell (Fig. 1) containing a porous copper electrode of 5.6 cm diameter and 0.3 cm thickness corresponding to a volume of 7.8 cm 3 . The experiments were performed with a high concentration of synthetic nitrate solutions (3 g NO 3 -L -1 ) to be in conditions similar to those of real effluents obtained after a classical physicochemical denitrification of polluted water [START_REF] Kim | Modeling a novel ion exchange process for arsenic and nitrate removal[END_REF]. The following parameters for nitrate electroreduction were studied: (1) pH (acid and neutral); (2) flow rate (1mL min -1 , 2 mL min -1 and 3 mL min -1 ); (3) applied current.

Reactions (1), ( 2) and ( 3) take place at the cathode and produce more hydroxyl anions than the protons formed at the anode (reaction 4). Consequently, the pH value increases during the electrolysis more or less strongly depending on the chemical yield of ammonium (% X NH4+ ).

NO

This behavior amplified by the high nitrate concentration led us to choose buffered solutions as electrolytic media. The pH of the solution was fixed to 4.8 or 7.2, since at pH higher than 8, a slight corrosion of copper occurred. Indeed, after electrolysis at pH 8, a light blue coloration of the solution appeared when the current was no more applied, due to the formation of copper salts in the solution. As soon as produced ammonia was evacuated out of the copper electrode, the coloration disappeared, showing that the corrosion process probably involved the formation of Cu(NH 3 ) 4 2+ .

Effect of flow rate and pH on electroreduction efficiency

Flow rate does not seem to have a great influence on the results of electrolysis. It is obvious from table 3 that for flow rates ranging from 1 to 3 mL min -1 , the conversion yield of nitrate (% τ) was more than 70 % and not quantitative mainly due to hydrogen evolution (reaction 3).

Table 3 Indeed, during the electrolysis, by-products such as hydrazine (H 2 N-NH 2 ), nitrous oxide (N 2 O) and hydroxylamine (H 2 N-OH) were not detected. Only the presence of a very small amount of nitrite can be noticed (Table 3). Beyond a flow rate of 3 mL min -1 , the formation of gaseous hydrogen became important and prevented the electrolysis due to an accumulation of gas in the working compartment.

The selectivity of the reaction 1 was strongly influenced by the pH of the solution, as seen with % S NH4+ in table 3. The nitrate reduction to ammonium is quasi quantitative in neutral solution but significantly decreases in acidic solution, probably due to the formation of a small quantity of gaseous nitrogen (reaction 2) [START_REF] Polatides | Electrochemical reduction of nitrate ion on various cathodesreaction kinetics on bronze cathode[END_REF]. The maximum ammonium selectivity of 96 % was obtained with a flow rate of 2 mL min -1 . For this reason, this flow rate was selected and considered thereafter.

It is interesting to note that all experiments were performed with the same copper porous electrode and that no degradation of this material was observed, showing a high stability and durability of the electrode

Effect of current and pH on electroreduction efficiency

Several experiments were performed using different ratios, Ri, of applied current (i app ) different to the theoretical calculated intensity (i th ) and linked by the ratio (R i = i app / i th ). As mentioned above (section 3.3.1), all electrolyses were carried out with a flow rate of 2 mL min -1 and the results are given in Table 4.

Table 4 The conversion yields of nitrate at pH 7.2 and 4.8 were similar and increased gradually with the applied current. However, it is interesting to take into account the apparent conversion yield (%τ app ) expressed according to the following relation:

%τ app = %τ / ([NO 3 - ] app / [NO 3 - ] t=0 ) (6)
where [NO The experimental results show that the lower is the applied current, the higher is the apparent conversion yield. A% τ app close to 100% was obtained when the ratio R i was equal to 0.5, corresponding to the reduction of 50% of the initial amount of nitrate. Higher R i values led to an increase of the amount of the nitrate reduced but decrease the % τ app (Table 4).This is due to the apparition of the electrochemical reduction of water, leading to hydrogen evolution. The behavior of the selectivity was first similar for the two solutions (pH 4.8 and 7.2) for Ri = 0.5 and increased from for Ri = 0.5 to 1. For higher values of Ri, the selectivity was remained the same for pH 7.2 but, decreased slightly for pH 4.8. Indeed, in neutral solution, the selectivity was close to 100 % for R i ≥ 1, showing that the secondary reaction 2 no more occurred. In acidic solution, a maximum selectivity of 75% was obtained for R i = 1, due to the formation of a constant amount of gaseous nitrogen.

The current efficiency calculated from the reduction of nitrate into ammonium was maximum for R i close to 0.9 (Fig. 3) and equal to 72 % and 50 % for pH 7.2 and pH 4.8, respectively. As seen above, the formation of nitrogen (reaction 2) and hydrogen (reaction 3) are the main secondary reactions. In acidic solution, whatever the value of R i , nitrogen formation always happened, decreasing the current efficiency. But in neutral solution, nitrogen formation stopped when R i reached the value of 1 and then only hydrogen formation limited the current efficiency.

Thus, the maximum value of current efficiency for R i = 0.9 corresponds to the end of nitrogen formation. Beyond this value, the formation of hydrogen is more and more important and affects the current efficiency (Fig. 3).

It is important to note that the conversion yield and current efficiency are mainly limited by contact probability between nitrates ions and metallic fibres. Consequently, they depend on the porosity and the surface area of the electrode. Thus, in neutral solution, the current efficiency should be improved by using a porous copper electrode of larger surface area.

Conclusion

Porous copper electrode has been prepared by copper electrodeposition onto nickel modified graphite felt according to an original process combining an optimized galvanostatic method and flowing conditions. Low concentrations of metal salts and high applied current were necessary to achieve a homogeneous metallic coating of the fibres. These results demonstrate the possibility to deposit a new metal layer on already metalized graphite felt and open the door for the preparation of metallic felt of different nature such as cobalt, tin and bismuth. One of the interests of these porous materials is their catalytic properties. Thus, the use of copper modified graphite felt as a cathode in an electrochemical flow cell allowed a selective and quantitative reduction of nitrate solutions of high concentration (3g NO In summary in this report we set up a novel electrochemical process allowing an efficient conversion of very concentrated nitrate solution to ammonium in neutral medium.

The feasibility of the use of the ammonium solution, obtained by the present process, to produce biohydrogen in dark fermentation via heat treated anaerobic activated sludge will be carried out in continuity of the present work.

Research Highlights

 A novel porous copper electrode of high surface areas and low densities was prepared  The copper cathode was examinated for electroreduction of nitrate to ammonium  selective and quantitative reduction of nitrate was obtained in neutral solution  High chemical yields and current efficiencies toward ammonium formation was recorded  Recycling of nitrates as an abundant and inexpensive source of ammonium

1 L 4 -Fig. 1 .

 141 Fig.1.

Fig. 3 .

 3 Fig. 3.

Fig. 1 .

 1 Fig. 1. Schematic diagram of the flow cell, a, porous electrode; b, counter electrodes (platinum

Fig. 2 .Fig. 3 .

 23 Fig. 2. SEM images of metal coated graphite felts

  Fig.1

  3 -to nitrogen is a difficult reaction since both the rate and the selectivity of the reduction of nitrate to ammonium are usually low, due to the large number of by-products such as NO 2 , NO 2

-, NO, N 2 O, NH 2 OH, NH 3 , NH 2 NH 2 involved in the reduction mechanism

Table 2

 2 Experimental conditions to achieve the electrodeposition of copper on nickel modified graphite felt

	Experiment	[Cu 2+ ] mol L -1	On pulse t on	Off pulse t off	t off /t on	On pulse total time	Full electrolysis Time	Electrode aspect	%CE
	1	10 -2	7 s	10 s	1.4	2 h 20 min	5 h 40 min	Poor deposit	24
	2	3 × 10 -2	7 s	10 s	1.4	2 h 20 min	5 h 40 min	Metallic crust	65
	3	10 -2	10 s	10 s	1	6 h 11 min	13 h	Metallic crust	13
	4	3 × 10 -2	15 s	35 s	2.3	4 h	13 h	Homogeneous film of cooper	58

Table 3

 3 Effect of flow rate and pH on the electrochemical reduction of nitrate to ammonium. (Initial nitrates concentration =3 g NO 3 -L -1 ; electrolyzed volume = 1liter).

				pH 4.8			pH 7.2
	Flow rate	Full electrolysis	%τ %S NH4	%X NO2 -	%τ	%S NH4 +	%X NO2 -
	(mL min -1 )	Time		+
	1	16 h 40 min	80	71	1	75	86	0.5
	2	8h 20 min	70	75	3.5	73	96	1
	3	5h 30 min	76	82	2	63	92	3

Acknowledgements

The authors are thankful to the Lebanese Social Association Azm and Saadeh, Doctoral school (SDLM)) and the CNRS for the financial support during this work. We are also grateful to Mr J.

Le Lannic for microphotographs and we thank O. Merdrignac and N. Pontais for BET measurements.