Franc ¸ois Septier
email: francois.septier@telecom-lille1.eu

Yves Delignon
email: yves.delignon@telecom-lille1.eu

MCMC Sampling for Joint Estimation of Phase Distortions and Transmitted Symbols in OFDM Systems

Keywords: Phase Noise, Carrier frequency offset, OFDM Systems, Markov Chain Monte Carlo

In this paper, we address the challenging problem of the OFDM reception in the presence of phase distortions. Phase noise and carrier frequency offset seriously degrade the performances of OFDM systems by destroying orthogonality of the subcarriers. Based on a Markov Chain Monte Carlo sampling mechanization, our approach consists in jointly estimating the phase noise, the frequency offset and the transmitted symbols. The proposed algorithm is implemented in the time domain in order to benefit from the redundancy information induced by the cyclic prefix and from the time correlation of the OFDM signal owing to the presence of virtual and/or pilot subcarriers. The algorithm's efficiency is enhanced by incorporating the Rao-Blackwellization technique as well as various sampling improvement strategies.

Simulation results, provided in terms of bit error rate (BER) and mean square error (MSE), clearly illustrate the efficiency and the robustness of the proposed estimator.

I. INTRODUCTION

Multicarrier modulation has been selected as the transmission scheme for the majority of communication systems such as the "Digital Subscriber lines" (DSL), the "Digital Audio Broadcast" (DAB), the IEEE 802.11 "Wireless Local Area Network" (WLAN), or the IEEE 802.16 "Wireless Metropolitan Area Network" (WMAN). Unfortunatly, such techniques are very sensitive to phase noise (PHN) and carrier frequency offset (CFO) caused by oscillators' impairments. These phase distortions destroy the subcarriers' orthogonality and lead after the Fourier Transform to rotation of every subcarriers, known as common phase error (CPE), and to inter-carrier interferences (ICI).

Many approaches have been proposed to estimate and eliminate phase noise effects in OFDM systems over frequency selective channels. Theses techniques can be divided into frequency domain [START_REF] Robertson | Analysis of the effects of phase noise in orthogonal frequency division multiplexing (OFDM) systems[END_REF]- [START_REF] Nikitopoulos | Phase-impairment effects and compensation algorithms for OFDM systems[END_REF] and time domain approaches [START_REF] Casas | Time domain phase noise correction for OFDM signals[END_REF]- [START_REF] Septier | Non-pilot-aided sequential monte carlo method to joint October 22, 2010 DRAFT signal, phase noise, and frequency offset estimation in multicarrier systems monte Carlo Methods for Channel, Phase Noise, Frequency Offset Estimation with Unknwon Noise Variances in OFDM Systems[END_REF]. For both of them, two different strategies based either on pilot or non-pilot aided algorithms have been employed. The latters are a challenging task since they have the advantage of being bandwidth more efficient as it does not require the transmission of pilots symbols.

The frequency domain approaches in [START_REF] Petrovic | Intercarrier interference due to phase noise in OFDM -estimation and suppression[END_REF], [START_REF] Wu | A new phase noise mitigation method in OFDM systems with simultaneous CPE and ICI correction[END_REF] consist in correcting both CPE and ICI, induced by phase noise only, in the received signal obtained after the Fourier transform using pilot subcarriers. In a first step, CPE estimation is carried out with either a Kalman filter or a minimum mean square error pilot aided algorithm. Secondly, a decision feedback algorithm, using the demodulated symbols obtained after the CPE correction, is performed to obtain ICI estimate. However, noise-induced symbol decision errors may propagate through the feedback loop, leading to unreliable transmissions with error bursts. In [START_REF] Nikitopoulos | Phase-impairment effects and compensation algorithms for OFDM systems[END_REF], unlike the previous algorithms, the proposed scheme does not require the presence of pilot subcarriers.

A decision-directed scheme is used at the initialization step in order to make a tentative decision on a prespecified set of subcarriers without any phase distortion correction. To have reliable tentative decision for the CPE estimation, slow phase noise variations and a residual CFO are considered.

In the time-domain approaches [START_REF] Lin | OFDM phase noise cancellation via approximate probabilistic inference[END_REF], [START_REF] Lin | The variational inference approach to joint data detection and phase noise estimation in OFDM[END_REF], an approximate probabilistic inference technique associated with the minimization of variational free energy is proposed to jointly estimate phase noise and transmitted symbols without any pilot subcarriers. However, in order to derive the algorithm, the phase distortions term is linearized by the assumption of small phase noise rate (i.e. e jθ(t) ≈ 1 + jθ(t)). Moreover, like in [START_REF] Nikitopoulos | Phase-impairment effects and compensation algorithms for OFDM systems[END_REF], a tentative symbol decision without any phase correction is made at initialization step and thus leads to a severe performance degradation when phase distortions are significant, especially in the presence of CFO (which is not considered in [START_REF] Lin | OFDM phase noise cancellation via approximate probabilistic inference[END_REF], [START_REF] Lin | The variational inference approach to joint data detection and phase noise estimation in OFDM[END_REF]). Finally, a nonpilot-aided Sequential Monte Carlo method has been recently proposed in [START_REF] Septier | Non-pilot-aided sequential monte carlo method to joint October 22, 2010 DRAFT signal, phase noise, and frequency offset estimation in multicarrier systems monte Carlo Methods for Channel, Phase Noise, Frequency Offset Estimation with Unknwon Noise Variances in OFDM Systems[END_REF] to address this problem.

October 22, 2010 DRAFT

In this paper, we propose a novel time domain approach for the joint estimation of the phase noise, CFO and transmitted symbols. The time-domain processing allows us to benefit from the redundancy information induced by the cyclic prefix and from the time correlation of the OFDM signal owing to the presence of virtual and/or pilot subcarriers. To solve this problem, the proposed algorithm is based on the Markov Chain Monte Carlo (MCMC) methodology, which have played a significant role in statistics, econometrics, physics and computing science over the last two decades [START_REF] Chen | Monte Carlo Methods for Bayesian Computation[END_REF]. Given the high-dimensional system, the algorithm's efficiency is enhanced by using the Rao-Blackwellization technique as well as powerful proposal distributions that faster drives new candidate samples towards high probability regions.

The paper is organized as follows. Section II is devoted to the problem formulation by introducing the OFDM system and the phase distortions. The proposed inference algorithm is detailed in Section III.

Numerical results are shown in Section IV. Through different scenarios, our approach is compared to algorithms proposed in [START_REF] Petrovic | Intercarrier interference due to phase noise in OFDM -estimation and suppression[END_REF], [START_REF] Wu | A new phase noise mitigation method in OFDM systems with simultaneous CPE and ICI correction[END_REF], [START_REF] Septier | Non-pilot-aided sequential monte carlo method to joint October 22, 2010 DRAFT signal, phase noise, and frequency offset estimation in multicarrier systems monte Carlo Methods for Channel, Phase Noise, Frequency Offset Estimation with Unknwon Noise Variances in OFDM Systems[END_REF] and to a perfect CPE correction scheme.

In this paper, N , N cp and T denote respectively the number of subcarriers, the cyclic prefix length and the OFDM symbol duration excluding the cyclic prefix. Let N (x; µ, Σ) and N c (x; µ, Σ) represent respectively the real and circularly symmetric complex Gaussian random vectors with mean µ and covariance matrix Σ. I n , 0 n×m and diag(x) are respectively the n × n identity matrix and the n × m matrix of zeros and a diagonal matrix with the vector x on its diagonal. Finally, lower case bold letters are used for column vectors and capital bold letters for matrices; (.) * ,(.) T and (.) H denote respectively conjugate, transpose, and Hermitian transpose.

II. PROBLEM FORMULATION

A. OFDM System model

First, input independent and identically distributed (i.i.d.) bits are encoded into M-QAM symbols d n,i , where i denotes the i th subcarrier, n the n th OFDM symbol. Practical OFDM systems are generally not fully loaded in order to avoid aliasing. In this case, some of the subcarriers at the edges of the multicarrier block are not modulated. These N g subcarriers are referred to as virtual subcarriers (VSCs). This number is dictated by system design requirements and is, in general, about 10 % of subcarriers. We denote by Ω g the set of virtual subcarriers. Moreover, to stay in a general multicarrier transmission, let us introduce a set of N P pilot subcarriers located on Ω p , with {Ω p ∩ Ω g } = ∅ and Ω p ∪ Ω g = Ω. These considerations October 22, 2010 DRAFT can be summed up as :

d n,i =          Information Data i / ∈ Ω Pilot i ∈ Ω p 0 i ∈ Ω g (1)
After the Inverse Discrete Fourier Tranform (IDFT), the samples of the transmitted signal can be written, for l = 0..N -1, as :

s n,l = 1 √ N N -1 i=0 d n,i e j2πil/N (2)
By considering the presence of virtual or pilot subcarriers, the transmitted signal s n,l is decomposed into a known signal κ n,l and an unknown signal u n,l :

s n,l = κ n,l + u n,l (3)
with, using (1) and ( 2),

κ n,l = 1 √ N i∈Ω d n,i e j2πil/N (4)
and

u n,l = 1 √ N N -1 i=0 / ∈Ω d n,i e j2πil/N (5)
As a consequence, u n = [u n,N -1 , . . . , u n,0 ] T represents the signal of interest. Based on the central limit theorem, a rigorous proof given in [START_REF] Wei | The complex enveloppe of a bandlimited OFDM signal converges weakly to a Gaussian random process: proof and application[END_REF] establishes that the complex envelope of a bandlimited uncoded OFDM signal converges to a Gaussian random process:

p(u n ) = N (u n |0 N ×1 , C u ) (6)
where the covariance matrix is defined as :

C u =         C u (0) C u (1) • • • C u (N -1) C u (-1) C u (0) • • • C u (N -2) . . . . . . . . . . . . C u (-N + 1) C u (-N + 2) • • • C u (0)         (7)
The correlation between discrete-time samples of the unknown signal is obtained using the definition of

u n,l in (5) and E[d n,i d * n,i ′ ] = δ(i -i ′ ) : C u (l) E[u n,t u * n,t-l ] = 1 N N -1 i=0 / ∈Ω N -1 i ′ =0 / ∈Ω E[d n,i d * n,i ′ ]e j2πit/N e -j2πi ′ (t-l)/N = 1 N N -1 i=0 / ∈Ω e j2πil/N (8)
October 22, 2010 DRAFT Before transmission, a cyclic prefix (CP) of length N cp is introduced to remove inter-symbol interference (ISI). The resulting signal (Fig. 1) is transmitted in a time varying frequency selective channel h(t, τ )

which is assumed to be static over one OFDM symbol and characterized by L p independent propagation paths. Assuming perfect frequency, phase and timing synchronization, the n th received OFDM symbol can be expressed, in a matrix form, as :

r n = H n As n + ν ν ν n + b n = H n A(κ κ κ n + u n ) + ν ν ν n + b n (9)
where

r n = [r n,N +Ncp-1 , . . . , r n,0 ] T , s n = [s n,N -1 , . . . , s n,0 ] T , κ κ κ n = [κ n,N -1 , . . . , κ n,0 ] T , u n = [u n,N -1 , . . . , u n,0 ] T and b n = [b n,N +Ncp-1 , . . . , b n,0 ]
T correspond to the received signal, the transmitted signal, the known and unknown component of the transmitted signal and the additive white Gaussian noise with covariance matrix σ 2 b I N +Ncp , respectively. The matrices H n of dimension (N + N cp ) × (N + N cp ) and A are defined as follows :

H n =         h n,0 h n,1 • • • h n,Lp-1 0 • • • 0 0 h n,0 h n,1 • • • h n,Lp-1 . . . . . . . . . . . . . . . . . . 0 0 • • • • • • • • • • • • 0 h n,0         (10)
and

A =   I N I Ncp 0 Ncp×(N -Ncp)   (11)
Finally, ν ν ν n represents the ISI between two consecutives OFDM symbols caused by the multipath channel :

ν ν ν n =         0 N +Ncp-Lp+1×1 Lp-1 p=Lp-2 h n,p s n-1,N +Lp-p-3 . . . Lp-1 p=1 h n,p s n-1,N +Lp-p-3         (12)
Then by assuming N cp L p and after discarding the cyclic prefix, a fast Fourier transform is applied on the remaining N samples (i.e. {r n,k } N +Ncp-1 k=Ncp

) in order to recover the desired data using an equalization technique. However, analog front-end impairments, such as noise, distortion and mismatch, may affect performance by degrading the integrity of the desired signal. In this paper, we focus on phase noise (PHN) and carrier frequency offset (CFO) caused by oscillator instabilities.

October 22, 2010 DRAFT

• • • s n-1,N -1 n th OFDM symbol s n,N -Ncp • • • s n,N -1 Cyclic Prefix s n,0 s n,1 • • • s n,N -Ncp • • • s n,N -1 s n+1,N -Ncp • • • Fig. 1.
Example of an OFDM flow.

B. Phase Distortion

Imperfect oscillators at the transmitter and at the receiver introduce a phase noise and a carrier frequency offset ∆f so that, at the sampling rate N/T of the receiver, the discrete form of the carrier delivered by the noisy oscillator on the k th sample of the n th OFDM symbol is :

p n,k = exp(jθ n,k + 2πkǫ N ) ∀k = 0, • • • , N + N cp -1 (13)
where θ n,k and ǫ correspond respectively to the phase noise (PHN) and the normalized CFO. In this work, we assume that ǫ is uniformly drawn on [-∆ CFO ; ∆ CFO ]:

p(ǫ) = U (ǫ| -∆ CFO , ∆ CFO ) (14)
The discrete-time samples of the PHN process form a random-walk process θ n,k = θ n,k-1 + w n,k , k = 0, . . . , N + N cp -1, where w n,t is a white Gaussian noise with variance σ 2 w = 2πβ T N . β is the bandwidth of the Brownian phase noise normalized with respect to the OFDM symbol rate 1 T , namely the parameter βT . If a perfect phase synchronization at the beginning of the OFDM symbol (i.e. θ n,-1 = 0) is assumed as in [START_REF] Lin | The variational inference approach to joint data detection and phase noise estimation in OFDM[END_REF], [START_REF] Tomba | On the effect of Wiener phase noise in OFDM systems[END_REF], the prior distribution of the PHN vector θ θ θ n = [θ n,N +Ncp-1 , . . . , θ n,0 ] T is given by:

p(θ θ θ n ) = N (θ θ θ n |0 N +Ncp×1 , Θ) (15)
with

Θ = 2πβT N         N + N cp 2 1 . . . . . . . . . 2 • • • 2 1 1 • • • 1 1         (16)
The received signal r n in (9) corrupted by both phase noise and frequency offset becomes :

r n = Φ n (H n A(κ κ κ n + u n ) + ν ν ν n ) + b n ( 17
)
where

Φ n = diag(e j(θ θ θn+gǫ) ) with g = [2π(N + N cp -1)/N, . . . , 2π/N, 0] T .
If no correction method is employed, these phase distortions lead, after the discrete Fourier transform, to two types of distortions on the useful signal, a multiplicative one which is common to all subcarriers and known as Common Phase Error (CPE) and an additive inter-carrier interference (ICI). Larger the phase noise rate βT and the CFO support ∆ CFO are, the worse the SINR (signal to noise plus interference ratio) is. Furthermore, on a same bandwidth a larger number of subcarriers leads to worse system performance due to the shorter subcarrier spacing distance for a same two-sided 3 dB bandwith of the phase noise [START_REF] Wu | OFDM systems in the presence of phase noise : consequences and solutions[END_REF].

In order to have a reliable multicarrier system, a phase distortion compensation scheme is consequently required.

III. BAYESIAN SOLUTION

In a Bayesian context, the aim is to compute the posterior distribution p(u n , θ θ θ n , ǫ|r n ). However, this complex and highly nonlinear distribution cannot be obtained analytically and approximations should be made instead. We propose to approximate it by using a Markov Chain Monte Carlo (MCMC) algorithm. Moreover, in order to improve the accuracy of the algorithm, we propose to apply the Rao-Blackwellization principle to the unknown OFDM signal u n .

A. Some Generalities about MCMC methods

The key idea of MCMC methods is to generate samples by running an ergodic chain whose equilibrium distribution is the desired distribution [START_REF] Chen | Monte Carlo Methods for Bayesian Computation[END_REF], [START_REF] Gilks | Markov Chain Monte Carlo in Practice[END_REF], [START_REF] Robert | Monte Carlo Statistical Methods[END_REF]. An aperiodic and irreducible Markov chain has the property of converging to a unique stationary distribution, π(x), which does not depend on the initial sample or the iteration number m. After convergence, a MCMC method produces samples from the target distribution, π(x), so that :

π(x) ≈ 1 M M m=1 δ(x -x m ) (18)
The Metropolis-Hastings (MH) algorithm, summarized in Algorithm 1, is the most popular MCMC method [START_REF] Hastings | Monte Carlo sampling methods using Markov chains and their application[END_REF]. We should remark that it is standard practice to discard a number of initial "burn-in" samples, denoted here by B, to allow the MCMC algorithm to converge to the stationary distribution. The MH algorithm is very simple, but it requires careful design of the proposal ditribution q(x|x m-1 ), especially when the dimension of the state x is large. Another well-known MCMC method is the Gibbs sampler [START_REF] Geman | Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images[END_REF]. This scheme is a special case of the MH algorithm that generates samples from conditional densities which make the probability of acceptance equal to one. The Gibbs sampling method is generally more October 22, 2010 DRAFT effective than the MH algorithm in high-dimensional systems. When the full conditionals are available and belong to the family of standard distributions (Gamma, Gaussian, etc.), samples can be sampled directly from them. Otherwise, we can draw samples with MH steps embedded within the Gibbs algorithm.

Algorithm 1 Metropolis-Hastings (MH) Algorithm Propose a point x * ∼ q(x|x m-1 )

4:
Compute the acceptance ratio :

ρ(x m-1 , x * ) = min 1, π(x * ) π(x m-1 ) q(x m-1 |x * ) q(x * |x m-1 )
5:

Sample a uniform random variable u from U (u|0, 1).

6:

if u ≤ ρ(x m-1 , x * ) then x m = x * else x m = x m-1 end if 7: end for

B. Rao-Blackwellization Technique

In this work the target distribution is the posterior distribution, p(u n , θ θ θ n , ǫ|r n ). Given the high dimensionality of the state space, it is not straightforward to design an efficient MCMC algorithm. However, by using the linear and Gaussian sub-structure of the system, the state space can be reduced significantly by marginalizing out the unknown OFDM signal u n . Indeed, using the Bayes' theorem, the posterior distribution of interest can be expanded as :

p(u n , θ θ θ n , ǫ|r n ) = p(u n |r n , θ θ θ n , ǫ)p(θ θ θ n , ǫ|r n ) (19)
Since both the prior distribution of u n , defined in [START_REF] Wu | A new phase noise mitigation method in OFDM systems with simultaneous CPE and ICI correction[END_REF], and the likelihood distribution, obtained using [START_REF] Hastings | Monte Carlo sampling methods using Markov chains and their application[END_REF], are Gaussian, it is straightforward to show that

p(u n |r n , θ θ θ n , ǫ) = N c (u n | u n , Σ n ) (20)
with,

u n = C u Λ H n Λ n C u Λ H n + σ 2 b I N +Ncp -1 (r n -Λ n κ κ κ n -Φ n ν ν ν n ) (21)
and

Σ n = I N -C u Λ H n Λ n C u Λ H n + σ 2 b I N +Ncp -1 Λ n C u ( 22
)
where

Λ n = Φ n H n A.
October 22, 2010 DRAFT

Using the Rao-Blackwellization principle on u n , only p(θ θ θ n , ǫ|r n ) needs to be approximated using a MCMC method. The posterior distribution [START_REF] Hrycak | Low-complexity time-domain ICI equalization for OFDM communications over rapidly varying channels[END_REF] will therefore be approximated by :

p(u n , θ θ θ n , ǫ|r n ) ≈ 1 M M m=1 p(u n |r n , θ θ θ m n , ǫ m )δ(θ θ θ n -θ θ θ m n ; ǫ -ǫ m ) (23)
where {θ θ θ m n , ǫ m } M m=1 represents the converged samples of the MCMC algorithm.

C. Proposed MCMC method

In this paper, we propose to design a MCMC for approximating p(θ θ θ n , ǫ|r n ) which can be written, using the Bayes' theorem, as:

p(θ θ θ n , ǫ|r n ) ∝ p(r n |θ θ θ n , ǫ)p(θ θ θ n )p(ǫ) (24)
The prior distribution of θ θ θ n and ǫ are defined in ( 15) and ( 14), respectively. The likelihood distribution is given, using ( 17) and ( 6), by :

p(r n |θ θ θ n , ǫ) = p(r n |u n , θ θ θ n , ǫ)p(u n )du n = N c r n |Λ n κ κ κ n + Φ n ν ν ν n , Λ n C u Λ H n + σ 2 b I N +Ncp (25)
Careful design of the sampling strategy plays an important role in the success of a MCMC algorithm.

Here, we propose to use a series of Metropolis-Hastings-within-Gibbs. More precisely, at the m th MCMC iteration, the following procedure is adopted to produce samples from p(θ θ θ n , ǫ|r n ) :

1) We first make a proposal for ǫ using a MH step.

2) Then, the sampling of θ θ θ n is performed by dividing the PHN vector in I blocks, i.e. θ θ θ n = {θ θ θ n,i } I i=1 , that are successively sampled using a series of MH steps.

Let us now describe in more details these two steps.

1) Proposal for the CFO:

To carry out the draw of ǫ, we propose to use a MH procedure in which the proposal distribution is given by :

q(ǫ|ǫ m-1 ) = P ǫ U (ǫ| -∆ CFO , ∆ CFO ) + (1 -P ǫ )N (ǫ|ǫ m-1 , σ 2 ǫ ) (26)
with 0 ≤ P ǫ ≤ 1. This proposal is based on a mixture of the prior distribution of ǫ and a Gaussian distribution centered on the current Markov chain state, ǫ m-1 , and with variance σ 2 ǫ . The acceptance ratio is given by :

ρ 1 = min 1, p(r n |θ θ θ m-1 n , ǫ * )p(ǫ * ) p(r n |θ θ θ m-1 n , ǫ m-1 )p(ǫ m-1 ) q(ǫ m-1 |ǫ * ) q(ǫ * |ǫ m-1 ) (27)
October 22, 2010 DRAFT

2) Proposal for the PHN: Given the high-dimension of the PHN vector θ θ θ n , we propose to divide this vector in I blocks and then to successively sample them. The i th block is defined as θ θ θ n,i = [θ n,i N +Ncp I -1 , . . . , θ n,(i-1) N +Ncp I ] T and θ θ θ n,\i denotes the collection of {θ n,k } N +Ncp k=0 excluding θ θ θ n,i . For sampling θ θ θ n,i , we propose the following proposal distribution:

q(θ θ θ n,i |θ θ θ m n , ǫ m , r n ) = P θ p(θ θ θ n,i |θ θ θ m n,\i ) + (1 -P θ )q 1 (θ θ θ n,i |θ θ θ m n , ǫ m , r n ) (28)
with 0 ≤ P θ ≤ 1. Like for the CFO, this proposal is a mixture of two distributions. With probability P θ , θ θ θ * n,i is drawn from its conditional prior distribution p(θ θ θ n,i |θ θ θ m n,\i ). Since p(θ θ θ n ) is a Gaussian distribution, this conditional distribution is also a Gaussian distribution :

p(θ θ θ n,i |θ θ θ m n,\i ) = N (θ θ θ n,i | θ θ θ m n,i , Θn,i ) (29)
where the mean vector and the covariance matrix are respectively given by θ θ θ [START_REF] Gilks | Markov Chain Monte Carlo in Practice[END_REF]. With probability (1 -P θ ), θ θ θ * n,i is drawn from q 1 (θ θ θ n,i |θ θ θ m n , ǫ m , r n ) in which the observations are taken into account in order to improve the sampling process. As detailed in Appendix A, this proposal is defined as :

m n,i = Θ 12 i (Θ 22 i ) -1 θ θ θ m n,\i and Θn,i = Θ 11 i -Θ 12 i (Θ 22 i ) -1 Θ 21 i with Θ 11 i = E[θ θ θ n,i θ θ θ T n,i ], Θ 12 i = E[θ θ θ n,i θ θ θ T n,\i ], Θ 21 i = E[θ θ θ n,\i θ θ θ T n,i ] and Θ 22 i = E[θ θ θ n,\i θ θ θ T n,\i ] obtained from
q 1 (θ θ θ n,i |θ θ θ m n , ǫ m , r n ) = N (θ θ θ n,i | θ θ θ m n,i , Σ m θ,i ) (30)
where the mean vector and the covariance matrix are obtained using the linearization of exp j θn,i -Eqs.

(37)-(41). This proposal allows to drive new candidates towards high probability regions. The acceptance ratio associated to the PHN sampling is given by :

ρ 2 = min 1, p(r n |θ θ θ * n,i , θ θ θ m n,\i , ǫ m )p(θ θ θ * n,i , θ θ θ m n,\i ) p(r n |θ θ θ m n , ǫ m )p(θ θ θ m n ) q(θ θ θ m n,i |θ θ θ m n,\i , θ θ θ * n,i , ǫ m , r n ) q(θ θ θ * n,i |θ θ θ m n , ǫ m , r n ) (31)
The proposed MCMC algorithm for the joint estimation of the OFDM signal, the phase noise and the carrier frequency offset, denoted by JSPCE-MCMC, is summarized in Algorithm 2.

IV. RESULTS

In order to show the validity of our approach, extensive simulations have been performed. In a first Propose ǫ * ∼ q(ǫ|ǫ m-1 )

6:

With {ǫ * , θ θ θ m-1 n }, calculate the acceptance ratio ρ 1 in Eq. ( 27)

7:

Sample a uniform random variable u from U (u|0, 1).

8:

if u ≤ ρ 1 then ǫ m = ǫ * else ǫ m = ǫ m-1 end if 9: Set θ θ θ m n = θ θ θ m-1 n 10:
for each block i ∈ {1, ..., I} do

11: Propose θ θ θ * n,i ∼ q(θ θ θ n,i |θ θ θ m n , ǫ m , r n ) 12:
With {θ θ θ * n,i , θ θ θ m n,\i , ǫ m }, calculate the acceptance ratio ρ 2 in Eq. ( 31)

13:

Sample a uniform random variable u from U (u|0, 1).

14:

if u ≤ ρ 2 then θ θ θ m n,i = θ θ θ * n,i else θ θ θ m n,i = θ θ θ m-1 n,i end if 15:
end for

16:

With {θ θ θ m n , ǫ m }, compute the mean vector u n and the covariance matrix Σ n of p(u n |r n , θ θ θ m n , ǫ m ) using ( 21) and ( 22) 17: end for of mean square error (MSE) and bit error rate (BER) and compared to existing methods. Moreover, the BER performance of an OFDM system in the absence of phase distortions and using the classical frequency domain MMSE equalizer is also depicted and denoted below by MMSE-FEQ.

With regard to the system parameters, 16-QAM modulation is assumed and we have chosen N = 64 subcarriers with a cyclic prefix of length N cp = 8. A Rayleigh frequency selective channel with L = 4 paths and an uniform power delay profile, perfectly known by the receiver, has been generated for each OFDM symbol. The proposed JSPCE-MCMC is implemented with 200 MCMC iterations and a burn-in of 100 iterations. The particle approximation of p(u n , θ θ θ n , ǫ|r n ) is therefore obtained by using the MCMC samples after the intial burn-in iterations.

October 22, 2010 DRAFT

A. Performances with PHN only (i.e. ǫ = 0)

We first perform simulations with no CFO in order to study the joint PHN and multicarrier signal estimation. Performances of proposed algorithm are analyzed and compared to the CPE and ICI correction method proposed in [START_REF] Petrovic | Intercarrier interference due to phase noise in OFDM -estimation and suppression[END_REF], [START_REF] Wu | A new phase noise mitigation method in OFDM systems with simultaneous CPE and ICI correction[END_REF] and also to a perfect CPE correction scheme. From figure 2, it can be clearly seen that the JSPCE-MCMC outperforms the CPE+ICI correction scheme. In a phase distortion-free context and by excluding the cyclic prefix in the received signal, the proposed algorithm leads to a timedomain MMSE equalizer since only Eq. ( 20) is used to obtain an estimate of the OFDM signal. Time domain and frequency domain MMSE equalization are mathematically equivalent and result in the same performance [START_REF] Hrycak | Low-complexity time-domain ICI equalization for OFDM communications over rapidly varying channels[END_REF]. Consequently, the performance gain between the MMSE-FEQ and the JSPCE-MCMC without distortions clearly highlights the benefit of considering the additional information induced by the cyclic prefix as well as the time-correlation of the OFDM signal owing to the presence of virtual and/or pilot subcarriers. the proposed model of the multicarrier signal gives more prior information due to the correlation of time domain samples in C u -Eq. ( 6). As a consequence, this leads to an improvement of the estimator robustness against high phase distortions level. In order to illustrate this gain, the MSE of both multicarrier signal and phase distortions obtained using the JSPCE-MCMC with and without the correlation of the OFDM time domain samples is shown in Figs. 4 and5. For the latter configuration, the JSPCE-MCMC is performed by using in (6) the following covariance :

C u =         C u (0) 0 • • • 0 0 C u (0) • • • 0 . . . . . . . . . . . . 0 • • • 0 C u (0)         (32)
From these two figures, it can be observed that the MSE of both multicarrier signal and phase distortions is significantly improved by taking into account the correlation between time domain samples of the OFDM signal, especially in severe PHN context. Indeed, for E b /N 0 = 30 dB and βT = 10 -2 , the MSE of the multicarrier signal obtained with the JSPCE-MCMC using the time correlation is 7 × 10 -3 and 4 × 10 -3 for respectively N g = 0 and N g = 8.

Most of the works, related in multicarrier receivers, assume that the duration of cyclic prefix is longer than the maximum delay spread of the multipath channel. Under this assumption, the system is free from ISI. Nevertheless, the addition of the cyclic prefix reduces the bandwidth utilization efficiency. It is intuitive that the duration of cyclic prefix should be kept as short as possible. As a result, the duration of cyclic prefix may be shorter than the maximum delay of the multipath channel in some occasional cases.

In these cases, ISI and ICI exist and, hence deteriorate the performance of the system. Here, performances of the proposed JSPCE-MCMC algorithm are assessed with insufficient cyclic prefix and with P = 4 pilots inserted in each OFDM symbol (N g = 0).

B. Performances with both PHN and CFO

In the following simulations, the CFO term ǫ is generated from a uniform distribution in [-0.4; 0.4],

for each OFDM symbol. Such CFO severely degrades the received signal and a perfect CPE correction obtain unsatisfactory BER performances due to a large ICI. In this context, the existing algorithms based on pilot subcarriers leads consequently to poor performances since a CPE correction scheme is required for the decision-directed method at the initialization step. Fig. 7 shows the BER performance of the proposed algorithm for different PHN rate and also different number of null-subcarriers. Firstly, only a slight performance degradation is observed when a severe CFO is considered in the OFDM system.

-MCMC -N g =0 -βT=10 -3 JSPCE-MCMC -N g =8 -βT=10 -3 JSPCE-MCMC -N g =0 -βT=10 -2 JSPCE-MCMC -N g =8 -βT=10 -2
Like in the CFO-free case, the BER performance and also the MSE of both the multicarrier signal and the phase distortions depicted in Figs. 8 and9 are improved when the number of null subcarriers increases, owing to higher time correlation of the OFDM signal. These different results clearly highlight the efficiency of the proposed MCMC algorithm in this severe case.

V. CONCLUSION

In this paper, we address the difficult problem of the OFDM reception that suffers from the presence of phase noise and carrier frequency offset. To solve this problem, we propose a novel time domain approach which has the great advantage of taking into account the redundancy information induced by October 22, 2010 DRAFT

[dB] BER MMSE-FEQ Without correction MMSE-FEQ Without phase distortions -L p =12 JSPCE-MCMC -L p =12 -βT=10 -3 JSPCE-MCMC -L p =12 -βT=10 -2 Without phase distortions -L p =16 JSPCE-MCMC -L p =16 -βT=10 -3 JSPCE-MCMC -L p =16 -βT=10 -2
Fig. 6. BER performance of the proposed JSPCE-MCMC when the number of channel paths is superior to the cyclic prefix length, i.e Lp > Ncp = 8, for different PHN rates βT in an OFDM system (Ng = 0, P = 4,ǫ = 0).

Blackwellization technique as well as optimized proposal distributions.

Numerical simulations show that even with significant PHN rates, the JSPCE-MCMC achieves good performances both in terms of the phase distortion estimation and BER. In particular, it was found that, for a small PHN rate, the JSPCE-MCMC is more efficient in term of BER than a frequency MMSE equalizer in multicarrier system without phase distortions. Moreover, the proposed JSPCE-MCMC enables to cope with a channel delay spread longer than one of the cyclic prefix. Thus, the JSPCE-MCMC algorithm offers a significant performance gain in comparison to existing methods and can be efficiently used with the channel estimator proposed in [START_REF] Septier | Monte Carlo Methods for Channel, Phase Noise, Frequency Offset Estimation with Unknwon Noise Variances in OFDM Systems[END_REF] for the design of a complete multicarrier receiver in wireline and wireless communication systems.

APPENDIX A DERIVATION OF THE PHN PROPOSAL DISTRIBUTION BASED ON OBSERVATIONS

Let us firstly remark that the observation equation in ( 17) can be equivalently written as :

r n = Υ n exp(jθ θ θ n ) + b n (33)
October 22, 2010 DRAFT

The vector u m n is obtained using Eq. ( 21) and the current Markov chain state {ǫ m , θ θ θ m }. By using the block notation with the subscript i as described in Section III-C and since Υ m n is diagonal, the following model can be considered to build the proposal distribution for θ θ θ n,i : The conditional prior distribution is defined in (29). From this prior and likelihood information, we propose to use, as our proposal distribution for θ θ θ n,i , the approximation of the posterior distribution obtained using the linearization of exp(jθ θ θ n,i ). As a consequence, we obtain :

q 1 (θ θ θ n,i |θ θ θ m n , ǫ m , r n ) = N (θ θ θ n,i | θ θ θ m n,i , Σ m θ ) (36)
October 22, 2010 DRAFT

1 :

 1 Initialise x 0 ; Set m = 0 2: for m = 1, . . . , B + M do 3:

Initialization 2 : 1 3:

 21 part, the case of PHN without CFO is considered in order to study the joint PHN and OFDM signal estimation. Then in the last part, the performances of the JSPCE-MCMC are assessed when both CFO and PHN are present in OFDM systems. In these two different cases, JSPCE-MCMC is studied in terms October 22, 2010 DRAFT Algorithm 2 JSPCE-MCMC Algorithm 1: Initialize the ISI term, ν ν ν n , in[START_REF] Chen | Monte Carlo Methods for Bayesian Computation[END_REF] with the estimate of the previous OFDM signal: s n-1 = κ κ κ n-1 + u n-Set ǫ 0 = 0 and θ θ θ 0 n = 0 (N +Ncp)×14: for m = 1, . . . , B + M do 5:

3 JSPCE

 3 without phase distortions JSPCE-MCMC without phase distortions Without correction -βT=10 -3 CPE+ICI correction -βT=10 -

Fig. 2 .

 2 Fig. 2. BER performance of the proposed JSPCE-MCMC vs E b /N0 for different PHN rates βT in an OFDM system (Ng = 0, P = 4, ǫ = 0).

Fig. 3

 3 Fig.3shows the impact of the number of null-subcarriers on JSPCE-MCMC performance in term of BER. From this figure, it can be denoted that its performance increases with the number of nullsubcarriers, especially for large PHN rate. Indeed, if the number of pilots or null-subcarriers increases,

Fig. 6 shows

 6 Fig.6shows BER performance of the proposed scheme versus E b /N 0 for two different number of channel paths and PHN rates. Whatever the PHN rate is, the JSPCE-MCMC significantly outperforms a classical OFDM receiver using MMSE equalizer without PHN. Since the proposed scheme is implemented in time-domain and has the advantage of taking into account the redundancy of the cyclic prefix, the JSPCE-MCMC is more robust against the ISI than the classical MMSE equalizer.

Fig. 3 .

 3 Fig. 3. BER performance of the proposed JSPCE-MCMC vs E b /N0 for different PHN rates βT and number of null subcarriers Ng in an OFDM system (P = 4,ǫ = 0).

- 2 Fig. 4 .

 24 Fig. 4. MSE of the multicarrier signal estimate using the time correlation of the OFDM signal (blue solid lines) or not (red dashed lines) vs E b /N0 for different PHN rates βT (P = 4, ǫ = 0) with Ng = 0 (left) and Ng = 8 (right).

- 2 Fig. 5 .

 25 Fig. 5. MSE of phase distortion estimate using the time correlation of the OFDM signal (blue solid lines) or not (red dashed lines) vs E b /N0 for different PHN rates βT (P = 4, ǫ = 0) with Ng = 0 (left) and Ng = 8 (right).

  without phase distortions PSEM-SMC without phase distortions Perfect CPE correction -βT=10 -3 JSPCE-MCMC-N g =0 -βT=10 -3 JSPCE-MCMC -N g =8 -βT=10 -3 JSPCE-MCMC -N g =0 -βT=10 -2 JSPCE-MCMC -N g =8 -βT=10 -2

Fig. 7 .

 7 Fig. 7. BER performance of the proposed JSPCE-MCMC vs E b /N0 for different PHN rates βT and number of null-subcarriers (P = 4, ǫ = 0.4) .

  p(θ θ θ n,i |θ θ θ m n,\i ) = N (θ θ θ n,i | θ θ θ m n,i , Θn,i ) p(r n,i |θ θ θ n,i , ǫ m , u n,i = u n,i , θ θ θ m n,\i ) = N c r n,i |Υ m n,i exp(jθ θ θ n,i ), σ 2 b I N +Ncp I (35)

2 Fig. 8 .- 2 Fig. 9 .

 2829 Fig. 8. MSE of the multicarrier signal estimate vs E b /N0 for different PHN rates βT (Ng = 0, P = 4, ǫ = 0.4) with Ng = 0 (red dashed lines) and Ng = 8 (blue solid lines).

October 22, 2010 DRAFT


Laetitia Hédouin

Olivier Pringault

Paco Bustamante

Renaud Fichez

Michel Warnau
email: m.warnau@iaea.org

Validation of two tropical marine bivalves as bioindicators of mining contamination in the New Caledonia lagoon: Field transplantation experiments

Keywords: Molluscs, Oyster, Clam, Bioaccumulation, Biomonitoring, Metals

The bioaccumulation and retention capacities of some key local contaminants of the New Caledonia lagoon (Ag, As, Cd, Co, Cr, Cu, Mn, Ni and Zn) have been determined in the oyster Isognomon isognomon and the edible clam Gafrarium tumidum during transplantation experiments. In a first set of experiments, oysters and clams from a clean site were transplanted into contaminated sites. Uptake kinetics determined in the field indicated that for Cr and Cu in oysters and Co, Ni, and Zn in clams, concentrations in transplanted bivalves reached those of resident organisms after 100d, whereas for the other elements, it would require a longer time for transplanted bivalves to reach the same levels as in the resident populations (e.g., up to 3 years for Cd). However, the slow uptake rate for metals observed in the latter transplantation is rather related to low bioavailability of metals at the contaminated sites than to low bioaccumulation efficiency of the organisms. Indeed, results of a second transplantation experiment into two highly contaminated stations indicated a faster bioaccumulation of metals in both bivalves. Results of both transplantations point out that the clam G. tumidum is a more effective bioindicator of mining contamination than I. isognomon, since it is able to bioaccumulate the contaminants to a greater extent. However the very efficient metal retention capacity noted for most elements indicates that organisms originating from contaminated sites would not be suitable for monitoring areas of lower contamination. Hence, geographical origin of animals to be transplanted in a monitoring perspective should be carefully selected.

I. Introduction

New Caledonia is a small South Pacific island whose main economic resources are derived from nickel exploitation. Among other, local mining activities result in large anthropogenic inputs of metals into the SW lagoon and thereby constitute a potential threat to the local coastal marine ecosystems (e.g., [START_REF] Bird | The impacts of opencast mining on the rivers and coasts of New Caledonia[END_REF] but it is only recently that relevant information was made available regarding levels of metal contamination and their possible impacts on the local marine ecosystems (e.g., [START_REF] Hédouin | Trends in concentrations of selected metalloid and metals in two bivalves from the coral reefs in the SW lagoon of New Caledonia[END_REF], Metian et al. 2008a). Therefore monitoring of environmental contamination originating from mining activities in the lagoon still needs some significant scientific inputs.

Among the common approaches used to study environmental contamination, the use of bivalve molluscs as bioindicator species has proved to be a valuable and informative technique (e.g., Mussel Watch, [START_REF] Goldberg | Mussel Watch: 1977-1978 results on trace metals and radionuclides[END_REF]. This approach has been particularly developed in temperate areas, whereas in sub-tropical and tropical areas the scarcity of available information makes the identification of species that could be used as suitable bioindicators difficult (e.g., [START_REF] Phillips | Selected trace elements and the use of biomonitors in subtropical and tropical marine ecosystems[END_REF]. However, the screening of metal concentrations in a variety of marine organisms from several parts of the SW lagoon of New Caledonia has identified the oyster Isognomon isognomon, the edible clam Gafrarium tumidum, and the alga Lobophora variegata as potential bioindicators [START_REF] Hédouin | Trends in concentrations of selected metalloid and metals in two bivalves from the coral reefs in the SW lagoon of New Caledonia[END_REF]. It has been shown recently that the alga L. variegata was an efficient bioindicator of metals in seawater in both controlled and in situ conditions [START_REF] Hédouin | The tropical brown alga Lobophora variegata as a bioindicator of mining contamination in the New Caledonia lagoon: a field transplantation study[END_REF], Metian et al. 2008b). In addition, recent experimental works on the oyster I. isognomon and the clam G. tumidum have indicated that these two species bioconcentrate and efficiently retain several elements when exposed via seawater, sediments or their food (Hédouin et al. 2010b). More importantly, both bivalve species were shown to concentrate As, Cd, Co, Cr, Mn, Ni, and Zn in direct proportion to their concentrations in seawater and food [START_REF] Hédouin | Nickel bioaccumulation in bivalves from the New Caledonia lagoon: seawater and food exposure[END_REF](Hédouin et al. , 2010b)).

Although the former experiments were carried out under controlled conditions simulating as closely as possible those in the natural environment, laboratory experiments cannot reproduce exactly the conditions in the field. In this respect in situ experiments offer a more ecologically-realistic approach, since they encompass all the factors that actually occur in the field and may possibly interfere with or influence bioaccumulation processes (e.g., [START_REF] Cain | Copper and silver accumulation in transplanted and resident clams (Macoma balthica) in South San Francisco Bay[END_REF]Luoma 1985, Hédouin et al. 2008).

Active biomonitoring using transplantation of organisms from one site to another is a very efficient way to follow the degree of contamination at various sites (e.g. [START_REF] Hédouin | The tropical brown alga Lobophora variegata as a bioindicator of mining contamination in the New Caledonia lagoon: a field transplantation study[END_REF]. The main advantages over the traditional passive biomonitoring (viz. monitoring of metal concentrations using resident natural populations) are that (1) the sites to monitor may be chosen independently of the presence of natural populations and (2) the influence of external and internal factors (e.g. seasonal variation, size or age) susceptible to induce bias in data comparison is reduced [START_REF] Phillips | Biomonitoring of trace aquatic contaminants[END_REF].

The aim of the present field study was to determine the relevance of using the oyster I. isognomon and the clam G. tumidum as bioindicator species of metal contamination in tropical waters. Through two different field transplantation experiments, the ability of both species to bioaccumulate and depurate 9 selected elements (Ag, As, Cd, Co, Cr Cu, Mn, Ni and Zn) under natural conditions has been assessed as well as their ability to inform about the contamination status of their surrounding environment. A power analysis was also carried out to determine the sample size required to allow differentiating among realistic field contamination levels.

II. Materials and methods

Between March and June 2005, two series of transplantation experiments were performed in New Caledonia using the oyster Isognomon isognomon and the clam Gafrarium tumidum. Based on previous field results [START_REF] Hédouin | Trends in concentrations of selected metalloid and metals in two bivalves from the coral reefs in the SW lagoon of New Caledonia[END_REF]) sampling stations were selected according to their apparent degree of metal contamination. Maa Bay (subtidal station for oysters) and Ouano Beach (intertidal station for clams) were identified as clean stations with low element concentrations in bivalve tissues and sediments for all elements except As. In contrast, Boulari Bay (for oysters) and Grande Rade -GR Int -(intertidal station for clams) were designated as highly contaminated stations (Fig. 1).

II.1. Experimental design

Since body size is well known to affect metal concentrations in marine invertebrates (e.g. [START_REF] Boyden | Effect of size upon metal content of shellfish[END_REF], only individuals with shell length longer than 70 mm for I.

isognomon [START_REF] Metian | Bioaccumulation des métaux lourds chez 4 espèces marines du lagon de Nouvelle Calédonie: Caractérisation de leur potentiel bioindicateur pour le monitoring des activités minières locales[END_REF] and shell width greater than 35 mm for G. tumidum [START_REF] Hédouin | Allometric relationships in the bioconcentration of heavy metals by the edible tropical clam Gafrarium tumidum[END_REF] were considered in order to minimize size-related variability.

Two types of transplantations were conducted. A first reciprocal transplantation aimed at assessing metal bioaccumulation and depuration processes in natural populations living in two contrasted environmental conditions (see Fig. 2). A second transplantation was conducted to test the ability of both selected species to inform about the contamination level of their surrounding environment in a heavily polluted area (unidirectional transplantation in Grande Rade; Fig. 2).

II.1.1. Experiment 1: Reciprocal transplantations

Eighty oysters and 80 clams were collected from the two selected clean stations, Maa

II.1.2. Experiment 2: Unidirectional transplantation in Grande

Rade

Grande Rade is locally influenced by anthropogenic inputs from the 'Société Le Nickel' (SLN), a nickel processing plant. Two stations (GR 1 and GR 2 ) were chosen in Grande Rade for this experiment because they had different levels of metal contamination [START_REF] Migon | Geochemical and hydrodynamic constraints on the distribution of trace metal concentrations in the lagoon of Nouméa, New Caledonia[END_REF]. GR 1 station is a highly polluted site due to its proximity to the off-loading wharf of the SLN, whereas the second station GR 2 , on the opposite side of the Rade just in front of the SLN factory, is less contaminated than GR 1 (Fig. 1).

II.1. Sampling preparation and analyses

Back to the laboratory, the bivalves were kept for 24 h in 30 l seawater from the same sampling station to allow depuration of gut contents and of particulate material present in the mantle cavity. Soft tissues were removed from the shells and were weighed (wet weight; wwt), dried at 60°C until constant weight, and weighed again (dry weight; dwt). They were then stored in acid-washed, hermetically sealed plastic containers until analysis.

Sediments were similarly stored in acid-washed, hermetically sealed plastic bags and frozen at -20°C. Sediments were then dried at 60°C for 5 d. In order to eliminate heterogeneous materials (e.g., stones, fragment of corals), sediments were sieved (1mm mesh size) prior to analysis.

Aliquots of the biological samples (300 to 500 mg dwt) and sediment samples (300 mg dwt) were digested using a 3:1 (v:v) nitric-hydrochloric acid mixture (65% suprapur HNO 3 and 30% suprapur HCl, Merck). Acid digestion of the samples was carried out overnight at room temperature. Samples were then mineralized using a CEM Corp. MARS 5 microwave oven (30 min with constantly increasing temperature up to 100°C for sediments and 115°C for biological material, then 15 min at these maximal temperatures). Each sample was subsequently diluted with milli-Q water according to the amount of sample digested (10 ml / 100 mg).

Elements were analyzed using a Varian Vista-Pro ICP-OES (As, Cr, Cu, Mn, Ni, and Zn) or a Varian ICP-MS Ultra Mass 700 (Ag, Cd and Co). Three control samples (two Certified Reference Materials -CRM -and one blank) treated and analyzed in the same way as the samples were included in each analytical batch. The CRM were dogfish liver DOLT-3 and lobster hepatopancreas TORT-2 (NRCC). The results for CRM indicated recoveries of the elements ranging from 81 % (Ni) to 113 % (Zn)

(Table 1). The detection limits were 31.0 (As), 1.3 (Cr), 3.8 (Cu), 0.15 (Mn), 1.1 (Ni) and 2.4 (Zn) µg g -1 dwt for ICP-OES and 0.1 (Ag), 0.15 (Cd) and 0.1 (Co) µg g -1 dwt for ICP-MS. All element concentrations are given on a dry weight basis (µg g -1 dwt).

II.2. Data treatment and statistical analyses

The uptake kinetics of the elements examined were described using either a simple linear regression model (eq. 1) or a saturation exponential model (eq. 2):

C t = C 0 + k u t (eq. 1)

C t = C 0 + C 1 (1 -e -k e t ) (eq. 2)
where C t and C 0 are the element concentrations in organisms at time t (d) and 0, respectively (µg g -1 ); C 1 + C 0 is the concentrations at steady state (C ss ; µg g -1 ); k u is the uptake rate constant (µg g -1 d -1 ) and k e is the depuration rate constant (d -1 ) [START_REF] Whicker | Radioecology: nuclear energy and the environment[END_REF].

Depuration kinetics of elements was described by either a simple linear regression model (eq. 3) or a single-component exponential equation (eq. 4):

C t = C 0 -k e t (eq. 3)

C t = C 0 e -k e t + A (eq. 4)

where A is a constant (µg g -1 ) .

Model constants and their statistics were estimated by iterative adjustment of the model and Hessian matrix computation using the nonlinear curve-fitting routines in the Statistica TM software 5.2.1.

Element concentrations of sediments and control organisms were plotted against time and fitted using simple linear regression. Statistical analyses of the data were performed using 1-way analysis of variance (ANOVA) followed by the multiple comparison test of Tukey [START_REF] Zar | Biostatistical analysis[END_REF]. The level of significance for statistical analyses was always set at α = 0.05.

A power analysis was performed using the whole set of data in order to assess the minimal sample size of organisms (oysters and clams) required to detect realistic (field-observed) differences in element concentration with statistical significance (p < 0.05) [START_REF] Zar | Biostatistical analysis[END_REF].

III. Results

III.1. Experiment 1: Reciprocal transplantations

III.1.1. Sediments

Comparison of element concentrations in sediments from the two stations naturally inhabited by the oysters I. isognomon (Maa Bay and Boulari Bay) indicated that levels of As, Co, Cr, Mn and Ni in sediments collected from Boulari Bay were significantly higher (p Tukey ≤ 0.0008) than those collected from Maa Bay, whereas concentrations of Cu and Zn were significantly higher (p Tukey ≤ 0.0002) in Maa Bay compared to Boulari Bay (Table 2). No significant difference was observed between Cd concentrations in sediments from the two bays.

Element concentrations measured in sediments from the two stations naturally inhabited by the clams G. tumidum showed that concentrations of all elements in sediments collected in Grande Rade (GR Int , contaminated station,) were significantly higher (p Tukey always ≤ 0.0002) than those from Ouano Beach (clean station) (Table 2).

Element concentrations in sediments collected from the four stations at the different times showed no significant variation with time.

III.1.2. Oysters I. isognomon

At the beginning of the experiment, concentrations of all elements in oysters from Boulari Bay were significantly higher (p Tukey ≤ 0.0002, except for Zn: p = 0.006) than those collected from Maa Bay, except for As, Cd and Mn for which no significant difference was found.

Resident populations of I. isognomon from Maa Bay and Boulari Bay did not exhibit any significant variation in concentrations of any element during the experiment time course.

In oysters transplanted to the Boulari Bay station, the concentrations of Cr, Cu and Ni showed a significant linear increase (k u : 0.054, 0.065 and 0.031 µg g -1 d -1 ; p < 0.003; R² = 0.14-0.24) with time (Fig. 3). At the end of the experiment, Ni concentrations in oysters were significantly lower (p Tukey = 0.046) than those in resident oysters from the Bay. No significant difference was found for Cr and Cu.

In oysters transplanted to the clean station (Maa Bay), only Ag, Co and Ni showed significant depuration. Ag and Co concentrations showed a significant linear decrease over time (k e : 0.059 and 0.013 µg g -1 d -1 ; p < 0.03; R²: 0.08 and 0.10, respectively; In clams transplanted to the contaminated station (GR Int ), the concentrations of Ag, Cd, Co, Cr, Cu and Zn displayed a significant linear increase (Ag, Cu and Zn k u : 0.092, 0.105 and 0.21 µg g -1 d -1 , respectively; p < 0.0001; R²: 0.26 -0.83; Cd, Co and Cr k u : 0.0014, 0.02 and 0.019 µg g -1 d -1 , respectively; p < 0.02; R² ≤ 0.12) (Fig. 3).

The uptake kinetics of Ni in clam soft tissues was best fitted by an exponential model (R² = 0.65, p < 0.0001) for which the estimated uptake rate constant, k u , was 1.28 µg g -1 d -1 . The uptake rate of Ag, Cu, Ni and Zn was higher by one order of magnitude compared to that of the other elements (Fig. 3).

When clams from GR Int were transplanted to the clean station, Ouano Beach, Ag and

As concentrations displayed a significant linear increase (k u : 0.078 and 0.541 µg g -1 d -1 ; p < 0.001; R²: 0.17 and 0.56, respectively) (Fig. 4). For the other elements, no significant depuration was observed.

When a significant increase/decrease in element concentration was observed, concentrations in transplanted organisms were compared to those of resident organisms. Statistical analyses indicated that at the end of the experiment, Ag, Cd, Cr and Cu concentrations in clams transplanted to GR Int were significantly lower (p Tukey ≤ 0.005, except for Ag, p = 0.047) than in resident clams from GR Int (up to 3.9 fold lower for Cd and Cr). No significant difference was found for Co, Ni and Zn concentrations between transplanted and resident clams.

At the end of the experiment, Ag concentrations in clams transplanted to Ouano Beach were significantly higher (p Tukey = 0.0001) than those in resident clams at Ouano Beach, whereas for As, the opposite was observed (p Tukey = 0.0003).

III.2. Experiment 2: Transplantation in Grande Rade

III.2.1. Sediments

Sediments collected from Ouano Beach, Maa Bay, GR 1 and GR 2 revealed that concentrations of all elements were significantly higher (1 to 3 orders of magnitude higher) in sediments from GR 1 (p Tukey always ≤ 0.0002) compared to the other three stations, except for As that reached its highest concentration in GR 2 (p Tukey = 0.0002) (Table 2).

III.2.2. Oysters I. isognomon

Element concentrations in resident oysters from Maa Bay showed no significant variation over the duration of experiment.

At the most contaminated station (i.e., GR 1 ), Co, Cr, Cu and Ni concentrations at 35 and 69 d were significantly higher than those at 0 d (p Tukey ≤ 0.0006 for Co, Cr, and Cu and p = 0.005 for Ni; Fig. 5). Among these four metals, only Ni concentrations after 69 d were significantly higher than those after 35 d of transplantation. Ag concentration after 69 d was significantly higher than those at 0 d and after 35 d (p Tukey = 0.03), but no significant difference was found between concentrations at 0 d and after 35 d of transplantation. Concentrations of As, Cd, Mn and Zn exhibited no significant differences in the oysters at station GR 1 over the entire transplantation period.

At station GR 2 , which displays a lower degree of contamination than GR 1 according to the element concentrations in sediments (

III.3. Estimation of the minimum sample size required to detect a significant difference in concentrations

A power analysis was performed to determine the minimum sample size necessary to detect a significant difference (α = 0.05) between concentrations of a given element in two batches of clams or oysters. The variability of the data was shown to be dependent upon the element, the species, the stations and the concentration levels.

The highest variance was observed in the samples displaying the highest concentrations, consequently, minimum and maximum variance of the transplanted batches were used to determine the range of minimal sample size necessary to detect given differences of concentrations with statistical significance. Considered differences of concentrations were selected to be representative of those that are actually encountered in the field (Table 3). Generally, a sample of size ≥ 50 organisms would be required to detect realistic differences in element concentrations, ranging from 0.5 (Cd) to 150 (As) µg g -1 dwt.

IV. Discussion

This field study investigated the in situ accumulation and depuration of 9 selected elements in two tropical bivalves in order to validate their relevance as biomonitoring species. Element concentrations in resident control organisms from each site showed no significant variation with time during the transplantation time course, indicating that any increase (or decrease) of element concentrations in tissues of the transplanted individuals would actually reflect a higher (or a lower) metal contamination level at a given site, and should not be due to seasonal factors.

When the oysters and clams from the clean sites were transplanted into the contaminated sites (Experiment 1), the uptake of the selected elements displayed different trends (Figs 3 and4). At the end of the transplantation period, concentrations observed in the organisms were either lower than or similar to those measured in resident populations of the contaminated site, or did not change compared to their initial levels. [START_REF] Cain | Copper and silver accumulation in transplanted and resident clams (Macoma balthica) in South San Francisco Bay[END_REF] and the mussel M. edulis from Greenland [START_REF] Riget | Uptake and release of lead and zinc by blue mussels. Experience from transplantation experiments in Greenland[END_REF]). However, our results from the second transplantation (Experiment 2) indicated that when both species were transplanted to a more contaminated site (GR 1 ), accumulation of Ni in oysters and Cr in clams was faster than during the first transplantation experiment. Therefore, the slow uptake rate of Ni in oysters and Cr in clams observed in the latter transplantation is rather related to low bioavailability of these two metals at the contaminated site (Boulari Bay and GR Int for oysters and clams, respectively) than to low bioaccumulation efficiency of the organisms.

Concentrations of

In the case of Ag, As, Cd, Co, Mn and Zn in oysters and As and Mn in clams, concentrations did not show a significant increase during the transplantation from the clean site to the polluted one (Experiment 1). Even though similar observations were made for Cd and Zn concentrations in Crenomytilus grayanus after two months of transplantation [START_REF] Shulkin | Metal concentrations in mussel Crenomytilus grayanus and oyster Crassostrea gigas in relation to contamination of ambient sediments[END_REF], opposite trends have also been observed. For example, after 120 days of transplantation, a significant bioaccumulation of Cd and Zn was measured in tissues of oysters, clams and cockles [START_REF] Baudrimont | Geochemical survey and metal bioaccumulation of three bivalve species (Crassostrea gigas, Cerastoderma edule and Ruditapes philippinarum) in the Nord Medoc salt marshes (Gironde estuary, France)[END_REF].

Therefore, the lack of bioaccumulation of some elements in oysters and clams as observed in our study suggests that these elements were rather poorly bioavailable for the bivalves or that oysters and clams have efficient regulation mechanisms preventing these metals from being accumulated. In fact, when organisms were transplanted to GR 1 and GR 2 (Experiment 2), concentrations of Ag and Co in oysters and Mn in clams were actually efficiently bioaccumulated. In addition, in laboratory controlled conditions, metals including Co and Mn were efficient accumulated in isognomon and G. tumidum [START_REF] Hédouin | Nickel bioaccumulation in bivalves from the New Caledonia lagoon: seawater and food exposure[END_REF](Hédouin et al. , 2010b)). Although, elements like Ag, Cd, Ni and Zn were very efficiently retained with T b½ ≥ 5 months, the other elements displayed T b½ ranging from 1 to 3 months in both bivalve species, independently of the uptake pathway tested (seawater, food or sediments).

Comparison of the data indicates that, in the field, depuration processes would take longer for some metals than those previously estimated from laboratory experiments.

This confirms that laboratory results cannot always be extrapolated directly to environmental situations, probably due to physiological adaptations of organisms living in contaminated conditions (e.g. sequestration mechanisms). Since oysters and clams showed very low depuration for most of the studied contaminants, bivalve tissues would be able to retain information of contamination events over very long periods of time. However, the subsequent drawbacks in a biomonitoring perspective are that (1) the element concentrations in transplanted organisms are not actually able to reflect the lower contamination levels occurring at a given location over a mediumscale time period (i.e., 3 months), and (2) the element concentrations in organisms collected from natural areas can reflect past contamination which is no longer occurring rather than actual contamination. These drawbacks arise from the fact that depuration is influenced by the past contamination history of the organisms. It was for example shown that Cu was more easily eliminated (30% after 30 d) by oysters temporarily transplanted into a metal-rich area for 60 d, than by resident oysters from the same metal-rich area (decrease limited to 9% after 30 d) [START_REF] Wallner-Kersanach | Accumulation and elimination of trace metals in a transplantation experiment with Crassostrea rhizophorae[END_REF]. This suggests that our specimens from the more contaminated area, which were exposed to high metal concentrations possibly for their whole life, may have developed more efficient sequestrating processes of metals to store them in their tissues as non-toxic forms (e.g. in granules, [START_REF] Mason | Metal speciation and bioavailability in aquatic systems[END_REF]. Such adaptive mechanisms could occur in both studied species, and hence explain the efficient retention observed in the field. Therefore, further studies should be focused on the long-term depuration of elements in both bivalves from contaminated and clean sites, in which bivalves would be previously exposed to contaminants in the field for 2-3 months before being transplanted into clean sites. Such experiments would demonstrate whether the past contamination history of I. isognomon and G. tumidum plays a role in the strong retention of elements observed in the field.

Interestingly, when clams from Grande Rade (GR Int ) were transplanted to Ouano beach (Experiment 1), a significant bioaccumulation of As was observed in clam tissues, although lower As concentration was reported in sediments from Ouano beach (3.1 µg g -1 dwt). High level of As in clam tissues from Ouano beach has been recently reported [START_REF] Hédouin | Trends in concentrations of selected metalloid and metals in two bivalves from the coral reefs in the SW lagoon of New Caledonia[END_REF], and the authors suggested that food was the main pathway of As uptake in clams. Our transplantation experiment from Grande Rade (GR Int ) to Ouano beach showed that As was highly bioavailable for clams in Ouano beach. In addition, due to the low levels of As in sediments from Ouano beach, this result supports the assumption that the high levels of As are most probably bioaccumulated from the diet of the organisms [START_REF] Sanders | Pathways of arsenic uptake and incorporation in estuarine phytoplankton and the filter-feeding invertebrates Eurytemora affinis, Balanus improvisus and Crassostrea virginica[END_REF], Warnau et al. 2007[START_REF] Hédouin | Trends in concentrations of selected metalloid and metals in two bivalves from the coral reefs in the SW lagoon of New Caledonia[END_REF]. Since the clam G. tumidum is a seafood product in New Caledonia and that its tissues showed high levels of As, the sources of As in Ouano

Beach and the potential toxicity of As for consumers should be further investigated.

In the second transplantation (Experiment 2), element concentrations in sediments clearly indicated that GR 1 is the most contaminated site, reaching very high level of Co, Cr, Mn, and Ni (up to 10,500 µg Ni g -1 dwt). These high concentrations in metals, and more specifically in Ni, concur with the very high concentration of Ni observed in the particulate phase within the water column [START_REF] Migon | Geochemical and hydrodynamic constraints on the distribution of trace metal concentrations in the lagoon of Nouméa, New Caledonia[END_REF]). Ag, Co, Cr, Cu and Ni were efficiently accumulated in transplanted oysters and clams. In addition, results

indicate that bioaccumulation was dependent on sampling location and species, and difference in the contamination level of the two stations was easier to observe when organisms were transplanted for a longer time (69 vs 35 d). For example, our results

showed that the concentrations of 5 elements in bivalve tissues (Co, Cr, Cu, Mn and Ni in oysters and Cd, Co, Cr, Cu and Ni in clams) were significantly higher at GR 1 than at GR 2 after 69 d, whereas differences were significant only for 3 elements (Co, Cu and Ni) after 35 d.

In this second transplantation experiment, oysters and clams were transplanted to the same stations, hence exposed to the same environmental conditions. Their bioaccumulation capacities can thus be directly compared. Clams were more efficient than oysters in bioaccumulating the selected elements (e.g., concentrations measured after 69 d of transplantation increased by a factor 7 in oysters and by a factor 40 in clams). These findings were surprising considering previous results from laboratory radiotracer studies (e.g., Hédouin et al. 2010a) which indicated a more efficient bioconcentration capacity in oysters than in clams when exposed to dissolved elements (concentration factors were higher by several orders of magnitude). Such a difference between laboratory and in situ experiments strongly suggests that the seawater pathway is not the major route of accumulation driving global metal uptake in these organisms. Rather, ingestion of particulate materials would be the main pathway for metal uptake, an hypothesis that is supported by a previous study of Cd, Co and Zn bioaccumulation modeling in I. isognomon and G. tumidum [START_REF] Hédouin | Caractérisation d'espèces bioindicatrices pour la surveillance des activités minières et la gestion de l'environnement en milieu récifal et lagonaire: application au lagon de Nouvelle-Calédonie[END_REF](Hédouin , 2010b)). This may indeed explain the higher metal levels in G. tumidum which lives buried in the sediment, and feeds mainly on organic (and metal)-rich particles at the seawater-sediment interface.

Combining the results from transplantations 1 and 2 demonstrated the usefulness of bioindicator species to assess the degree of contamination present in the marine environment. Indeed, for some elements, the high levels of metals reported in sediments were reflected in organism tissues (e.g. Cr, Ni) and a significant bioaccumulation of these metals was observed in the tissues of the clams and the oysters during the transplantation experiments. However, for some elements, the metal bioaccumulation trends observed in clams and oysters were different from those expected based on metal concentrations found in sediments at the different sites of transplantation. For example, in sites characterized with low As concentrations in sediments (Ouano beach), efficient bioaccumulation of As was observed in clam tissues (Experiment 1), suggesting that other sources of As uptake are available for organisms (e.g. food, see discussion above). In contrast, for Mn, although high levels were measured in sediments, almost no bioaccumulation was observed in organism tissues (Experiment 2). This clearly points out that only a fraction of the metals present in the sediments is bioavailable for organisms. Mn bound in the lattice of naturally occurring Mn-rich ores (e.g., laterite and garnierite) may be less available for uptake by marine organisms compared to water-soluble forms. The different patterns of metal bioaccumulation observed in clams and oysters during the two transplantation experiments carried out in this work pointed out that the metal contamination status cannot be based solely on metal analysis from the sediments and this is the reason why the use of bioindicator species is an important asset to better characterize the contamination status of a particular site. In addition, although it was not performed in the present study, metal analysis in seawater is also a useful complementary information to those obtained from sediments and organisms.

However accurate analysis of metals in seawater is uneasy and expensive, and is therefore generally not integrated in biomonitoring programmes. Nevertheless, nowadays the development of techniques such as the diffusive gradients in thin films (DGT) (e.g., [START_REF] Davison | In situ speciation measurements of trace components in natural waters using thin film gels[END_REF]Zhang 1994, Webb and[START_REF] Webb | Measurement of environmental trace-metal levels with transplanted mussels and diffusive gradients in thin films (DGT): a comparison of techniques[END_REF] brings new insights to obtain time-integrated information on metal concentration in seawater. Ideally analysis of metals in sediments, seawater and organisms will be recommended for biomonitoring purposes since such combination enhances our understanding of the contamination status present in the marine environment, but also brings additional information for identifying the source of contamination.

In order to obtain accurate and reliable data in biomonitoring programmes, the determination of optimal sample size to be collected is of fundamental importance. In this context, the present study has investigated the minimum sample size required to detect a given difference in concentration. Results shown in Table 3 indicate that the detection of a 0.5 µg g -1 dwt difference in tissue concentrations in the highly contaminated organisms required the largest sample size. Relatively large variability in metal concentrations in organisms within a site has frequently been reported (e.g., [START_REF] Daskalakis | Variability of metal concentrations in oyster tissue and implications to biomonitoring[END_REF][START_REF] Gordon | Mytilus californianus as a bioindicator of trace metal pollution: variability and statistical considerations[END_REF]). In the present study, the concentration variability was higher with increasing average concentration. Consequently, detecting small differences in concentration among organisms with higher metal concentrations will require an increase in sample size. Nevertheless, it is important to keep in mind that to be feasible, the sample size required in a biomonitoring programme should always remain realistic.

Compared to the actual metal concentration range measured in the New Caledonia lagoon waters and sediments, the minimum difference in concentrations detectable with sample sizes of 50-60 organisms would allow for an efficient differentiation among sites naturally inhabited by the two targeted bivalves. For example, a difference of 2 µg Ni g -1 dwt can be detected with a sample size of 7 oysters and 36 clams in a population showing low Ni levels (Table 3). However, 62 oysters and 30 clams would be necessary to detect differences of 30 and 8 µg g -1 dwt, respectively, in a population characterized by high Ni concentrations (Table 3). A sample size of 50-60 organisms was similarly recommended by other authors in order to facilitate the detection of significant changes in concentrations (e.g. [START_REF] Gordon | Mytilus californianus as a bioindicator of trace metal pollution: variability and statistical considerations[END_REF][START_REF] Topping | Guidelines for the use of biological material in first order pollution assessment and trend monitoring Scottish Fisheries Research Report[END_REF]. In current biomonitoring programmes, organisms collected (20 oysters and 30 mussels for the NOAA Mussel Watch, [START_REF] Beliaeff | Comparison of chemical concentrations in mussels and oysters from the United States and France[END_REF]; 10 oysters and 50 mussels for the French RNO, Claisse 1989) are pooled before analysis in order to reduce costs of sample preparation and analysis. However, pooling leads to the loss of statistical information on inter-individual variability, which is obviously an important issue to assess significance of concentration differences among samples. These economic constraints are obvious in the case of large national and international biomonitoring programmes that assess the levels of numerous trace elements and organic contaminants in many stations. However, in New Caledonia, which is mainly impacted by mining activities, metal and metalloids are the contaminants of major concern. Therefore, analytical costs would be reduced compared to biomonitoring programmes that include the very expensive analysis of organic compounds. Hence, in the specific context of the New Caledonia lagoon, it is highly recommended to analyze individual samples in order to obtain information on inter-individual variability that would provide scientifically-supported best practices in environmental management.

V. Conclusion

This

  Bay and Ouano Beach, respectively. A sub-sample of 10 organisms from each station was used for determination of baseline concentrations of the 9 selected elements(Ag, As, Cd, Co, Cr Cu, Mn, Ni and Zn) at the beginning of the experiment. The remaining oysters and clams (n = 70 per species) were transplanted for 100 d to the heavily contaminated stations, Boulari Bay and Grande Rade, (GR Int , intertidal station), respectively. The reciprocal transplantation was undertaken with another batch of 80 oysters and 80 clams collected in Boulari Bay and Grande Rade (GR Int ), respectively, and transplanted to the clean stations, Maa Bay (for oysters) or Ouano Beach (for clams).Organisms (transplanted and control resident individuals) at each station were placed in plastic mesh cages (60 × 60 cm; 2-cm mesh size), which allowed free exchange of seawater. The plastic cages containing the oysters were placed at 5 m depth, which corresponds to their natural habitat; those with clams were fixed in an intertidal position and inserted within the sediments in order to reproduce to the best the living condition of the clams. In order to monitor possible natural variation in element concentrations at the different stations, resident organisms (n = 5 per species) and superficial sediments (top 3-cm layer) were sampled simultaneously with the transplanted organisms (n = 7) from clean and contaminated stations at different times. Oysters were collected by SCUBA diving and the clams by hand picking at low tide.

Fig. 4 )

 4 Fig. 4). The depuration kinetics of Ni in oyster soft tissues was best fitted by an exponential model (k e : 0.19 d -1 , R² = 0.54, p < 0.0001). The concentrations of Ag, Co

  oyster and clam tissues(Hédouin et al. 2010a). Therefore, these results support the low bioavailability hypothesis, at least for Ag and Co in Boulari Bay and Mn at Grande Rade GR Int .When organisms were transplanted to a clean station (Experiment 1), the concentrations of all elements in both bivalves were almost the same after 100 d of transplantation, except for Ag, Co and Ni in oysters, which showed a low but significant decrease with time. However, Ag, Co and Ni concentrations in oysters were far from reaching the concentrations measured in natural resident populations by the end of the experiment. Such incomplete metal elimination has been reported by several authors when organisms from polluted areas were transplanted to clean areas (e.g., Zn in the mussel Mytilus edulis,[START_REF] Roesijadi | Behaviour of trace metals in Mytilus edulis during a reciprocal transplant field experiment[END_REF][START_REF] Simpson | Uptake and loss of zinc and lead by mussels (Mytilus edulis) and relationships with body weight and reproductive cycle[END_REF]; Cd and Cu in the oyster Crassostrea gigas,[START_REF] Geffard | Kinetics of metal elimination in oysters from a contaminated estuary[END_REF] Cr, Cu and Zn in the clam Mercenaria mercenaria,[START_REF] Behrens | The behaviour of heavy metals in transplanted hard clams, Mercenaria mercenaria[END_REF]. The biological half life (T b½ ) of these elements has been previously determined from radiotracer experiments in I.

  study clearly indicates that the clam G. tumidum can be recommended for an active monitoring of contaminants in subtidal and intertidal stations of the New Caledonia lagoon on a spatiotemporal scale. Biomonitoring studies using transplanted organisms would be an efficient solution to survey environmental levels of key local metal contaminants in areas lacking resident bivalves. The advantage of using transplanted organisms (active biomonitoring) over sampling resident populations (passive biomonitoring) is that it allows selecting organisms of uniform initial element concentrations, of common origins and past history, and thus ensures comparable biological samples. However, if further studies confirm the observed very long element retention times in these organisms, organisms from sites displaying a low contamination will have to be used in order to prevent bias in element concentrations due to physiological adaptation of organisms (e.g. sequestration mechanisms).

Figure 1 .

 1 Figure 1. Map showing the stations selected for transplantation experiments.

Figure 2 .Figure 3 .Figure 4 .Figure 5 .

 2345 Figure 2. Element concentrations (mean ± SD; µg g -1 dwt; n = 7 for transplanted

Table 2

 2 differences were found between 35 and 69 d. Ag concentrations after 69 d were significantly higher than those at 0 d (p Tukey = 0.0002) and after 35 d (p Tukey = 0.02), but no significant difference was found between concentrations at 0 d and after 35 d. No significant difference was found for the concentrations of As, Cd, Co, Mn and Zn in oysters over the entire transplantation period in GR 2 .After 35 d, oysters transplanted into GR 1 displayed concentrations of Co, Cu and Ni significantly higher than those at GR 2 (p Tukey ≤ 0.0001) whereas concentrations of Ag and Zn in GR 1 oysters were significantly lower than those at GR 2 (p Tukey = 0.02 and 0.048, respectively). After 69 d of transplantation, concentrations of Co, Cr, Cu, Mn and Ni were significantly higher in oysters transplanted at station GR 1 than those at GR 2 (p Tukey ≤ 0.002 for Co and Cu, and < 0.04 for Cr, Mn and Ni), whereas Ag concentrations at GR 1 were significantly lower than those at GR 2 (p Tukey = 0.009).At the most contaminated station (i.e., GR 1 ), Ag, Co and Ni concentrations after 35 and 69 d were significantly higher than those in clams measured at 0 d (p Tukey ≤ 0.0001 for Ni and ≤ 0.02 for Ag and Co) (Fig.6) and concentrations after 69 d were significantly higher than those after 35 d of transplantation. Concentrations of Cr and Cu after 69 d were significantly higher than those at 0 and after 35 d (p Tukey ≤ 0.0003), whereas no significant difference was found between the concentrations at 0 d and after 35 d of transplantation. No significant difference was found between the concentration of As, Mn and Zn after 35 and 69 d.At the second station, GR 2 , Ag and Ni concentrations after 35 and 69 d were significantly higher (p Tukey ≤ 0.0005) than those at 0 d, and concentrations after 69 d were significantly higher than those after 35 d (p Tukey = 0.0005 and 0.03 respectively).Cr concentrations after 35 and 69 d were significantly higher (p Tukey ≤ 0.0001) than those at the beginning of the transplantation, but no significant differences were observed between 35 and 69 d. Cu and Mn concentrations after 69 d of transplantation were significantly higher (p Tukey = 0.039 and 0.041) than those at the start of the experiment. No significant difference was found for Co and Zn concentrations at 0, and after 35 and 69 d. In contrast, As concentrations after 69 d were significantly lower than those at day 0 (p Tukey = 0.014).

	), Ni concentrations after 35 and

significantly higher than those after 35 d (p Tukey ≤ 0.0001). Concentrations of Cr and Cu after 35 and 69 d were significantly higher than those at 0 d (p Tukey ≤ 0.0001), but no significant Element concentrations after 35 and 69 d of transplantation were compared between stations GR 1 and GR 2 . Results indicated that after 35 d, Co, Cu and Ni concentrations in clams at GR 1 were significantly higher than those at GR 2 (p Tukey ≤ 0.0002, except for Cu: p = 0.01). For the other elements, no significant difference between GR 1 and GR 2 was found after 35 d. After 69 d of transplantation, the concentrations of Cd, Co, Cr, Cu and Ni in clams at GR 1 were significantly higher (p Tukey always ≤ 0.0002) than those at GR 2 .

  Cr and Cu in oysters and Co, Ni and Zn in clams reached values similar to those measured in resident organisms. Similar findings have been previously reported for Cu and Zn in the soft tissues of the mussel M. edulis transplanted to a temperate polluted bay[START_REF] Roesijadi | Behaviour of trace metals in Mytilus edulis during a reciprocal transplant field experiment[END_REF]. However, since metal uptake displayed linear kinetics over the transplantation period, the concentrations of these elements would most probably have continued to increase if the duration of the

	experiment was longer. This hypothesis is supported by the observations made in the
	second transplantation experiment, in which clams transplanted to GR 1 and GR 2
	displayed Co and Ni concentrations (up to 15.7 ± 4.8 and 140 ± 46 µg g -1 dwt,
	respectively) exceeding those of the resident clams from Grande Rade (7.2 ± 2.3 and
	63.2 ± 13.5 µg g -1 dwt for Co and Ni, respectively).

In contrast, concentrations of Ni in transplanted oysters and, Ag, Cd, Cr, Cu in transplanted clams significantly increased during the transplantation period but did not reach the values measured in resident organisms. Taking into account the measured uptake rate constants of these elements in oysters and clams, it can be estimated that reaching the resident concentrations would require, for example, about 6 months for Ni in oysters and approximately 3 years for Cd in clams. Comparable results have been previously reported for the oysters Crassostrea rhizophorae

[START_REF] Wallner-Kersanach | Accumulation and elimination of trace metals in a transplantation experiment with Crassostrea rhizophorae[END_REF]

, the clam Macoma balthica

Table 1 .

 1 ICP-OES and ICP-MS analysis of certified reference materials: certified values and measured values (mean ± SD µg g -1 dwt)

	TORT-2	DOLT-3

Table 2 .

 2 Element concentrations (mean ± SD; µg g -1 dwt, n = 3) in sediments collected in six sampling sites. GR Int : Grande Rade Interdital station; GR 1 : Grande Rade subtidal site 1; GR 2 : Grande Rade subtidal site 2

		Ouano beach	Maa bay	Boulari bay	GR Int	GR 1	GR 2
	Ag 0.019* ± 0.028	0.013* ± 0.014	0.06* ± 0.04 0.35* ± 0.13	0.17* ± 0.09	0.018* ± 0.015
	As	3.1* ± 1.2	6.4* ± 0.3	16.7* ± 1.3	8.0* ± 1.2	7.0* ± 5.9	15.4 ± 0.5*
	Cd	0.4 ± 0.2	1.0 ± 0.2	1.1 ± 0.3	2.5 ± 0.2	3.7 ± 1.2	0.8 ± 0.1
	Co	0.8 ± 0.4	4.4 ± 2.3	15.4 ± 11.1	49.2 ± 5.2	366 ± 145	6.1 ± 0.9
	Cr	7.8 ± 2.4	46.9 ± 4.0	71.5 ± 10.2	309 ± 39	1,290 ± 410	24.6 ± 2.9
	Cu	1.4* ± 0.7	7.0 ± 0.5	0.9* ± 0.1	27.0 ± 3.6	9.6 ± 3.3	2.8* ± 0.4
	Mn	44.7 ± 14.9	134 ± 6.7	545 ± 53.0	304 ± 15	1,600 ± 600	76.7 ± 8.1
	Ni	5.6 ± 3.0	69.2 ± 5.6	101 ± 12.9	848 ± 78	10,500 ± 3,300	66.4 ± 15.8
	Zn	3.5 ± 2.0	16.3 ± 1.3	7.1 ± 1.6	148 ± 11.0	73.3 ± 22.7	12.8 ± 1.8
	*: inferior to detection limit.

Table 3 .

 3 Minimal sample size of the oyster Isognomon isognomon and the clam Gafrarium 777 tumidum necessary to detect with 90 % significance a difference (p < 0.05) of concentrations 778 between two groups of organisms. 779 Observed range of element concentrations represents concentrations that have been 780 measured in the two species resident from different stations along the New Caledonia coast; 781 number between brackets represents concentrations that have been reached during 782 transplantation experiments. 783

	Sample size
	(number of individuals required)
	I. isognomon	G. tumidum

* from

[START_REF] Breau | Etude de la bioaccumulation des métaux dans quelques espèces marines tropicales: recherche de bioindicateurs de contamination et application à la surveillance de l'environnement côtier dans le lagon sud-ouest de la Nouvelle-Calédonie[END_REF], Hédouin et al. 2008a, Present study

Acknowledgements

The authors thank E. Folcher, C. Geoffrey and J.L. Menou (IRD-Nouméa Center) for their assistance at sea and C. Churlaud (LIENSs) for her assistance in ICP analyses. LH was beneficiary of a PhD grant (CIFRE, France) supported by the Goro-Nickel Company. MW is an Honorary Senior Research Associate of the National Fund for Scientific Research (NFSR, Belgium) and has benefited from a 2008-2009 Invited Expert position at LIENSs (CNRS-Université de La Rochelle), supported by the

Conseil Régional de Poitou-Charente. This work was supported by the IAEA, the IRD, LIENSs and the French PNEC programme. The IAEA is grateful for the support provided to its Marine Environment Laboratories by the Government of Monaco.