Weike Feng

Jean-Michel Friedt

Grigory Cherniak

Zhipeng Hu

Motoyuki Sato

Direct path interference suppression for short-range passive bistatic synthetic aperture radar imaging based on atomic norm minimisation and Vandermonde decomposition

A novel direct path interference (DPI) suppression method is proposed for passive bistatic synthetic aperture radar (SAR) imaging applications. Conventional time-domain processing methods cannot mitigate the DPI completely and will introduce errors into the target position estimation. By exploiting the sparsity of the DPI signal and the properties of its covariance matrix, the proposed method solves these problems by accurately estimating the time delay of DPI based on the atomic minimisation algorithm and Vandermonde decomposition in the frequency domain. The amplitude of DPI is then calculated by the least squares method. Simulations and experimental results of Wireless Fidelity-based passive bistatic SAR imaging of short-range targets show that the proposed method can suppress DPI more effectively and estimate the position of the target more accurately than the classical method.

Introduction

Passive bistatic radar (PBR), which exploits existing illuminators of opportunity (IOs) instead of a dedicated radar transmitter, has received renewed interest for its large coverage capacity, low vulnerability, low cost, and reduced electromagnetic pollution to the environment [START_REF] Palmer | An overview of an illuminator of opportunity passive radar research project and its signal processing research directions[END_REF][START_REF] Capria | Multifunction imaging passive radar for harbour protection and navigation safety[END_REF]. Various ground-based and space-based IOs, such as frequency-modulated broadcasting emitters, digital audio broadcasting emitters, digital terrestrial television broadcasting emitters, global navigation satellite system, and existing satellite synthetic aperture radar (SAR) systems, were employed for different applications [START_REF] Howland | FM radio based bistatic radar[END_REF][START_REF] Coleman | Passive bistatic radar based on target illuminations by digital audio broadcasting[END_REF][START_REF] Feng | Novel algorithm for high resolution passive radar imaging with ISDB-T digital TV signal[END_REF][START_REF] Zeng | A novel subsidence monitoring technique based on space-surface bistatic differential interferometry using GNSS as transmitters[END_REF][START_REF] Zhang | Spaceborne/stationary bistatic SAR imaging with TerraSAR-X as an illuminator in staring-spotlight mode[END_REF]. Techniques of moving target detection and localisation, high-resolution SAR and inverse SAR imaging, and direction of arrival (DOA) estimation based on the PBR system have been proposed during the past decades [START_REF] Falcone | Two-dimensional location of moving targets within local areas using WiFi-based multistatic passive radar[END_REF][START_REF] Wu | Space-time adaptive processing and motion parameter estimation in multistatic passive radar using sparse Bayesian learning[END_REF][START_REF] Gromek | Experimental results of passive SAR imaging using DVB-T illuminators of opportunity[END_REF][START_REF] Qiu | Compressive sensing-based algorithm for passive bistatic ISAR with DVB-T signals[END_REF][START_REF] Wang | Direction finding in frequency-modulatedbased passive bistatic radar with a four-element adcock antenna array[END_REF].

For short-range applications [START_REF] Chetty | Through-the-wall sensing of personnel using passive bistatic wifi radar at standoff distances[END_REF][START_REF] Huang | Feasibility and limits of WI-FI imaging[END_REF][START_REF] Feng | Passive radar delay and angle of arrival measurements of multiple acoustic delay lines used as passive sensors[END_REF][START_REF] Feng | WiFi-based imaging for ground penetrating radar applications: fundamental research and experimental results[END_REF], such as tracking indoor human beings or man-made objects, through the wall target movement detection, and subsurface target mapping by ground penetrating radar technique, a suitable IO should be exploited to satisfy the system requirement. Among different IOs, wireless local area network (LAN) may be a good choice for its wide bandwidth (40/80 MHz) and thus high range resolution (7.5/3.75 m in the air), its reasonable ambiguity function, its wide accessibility and coverage, and its wall/ground penetration capacity. As indicated in [START_REF] Colone | WiFi-based passive bistatic radar: data processing schemes and experimental results[END_REF], IEEE 802.11 standards-based Wireless Fidelity (WiFi) signal is one of the most popular systems in wireless LAN that can be used for PBR applications. For WiFi-based PBR, the ambiguity function analysis, range and Doppler frequency sidelobe reduction, high-resolution SAR imaging by fusion of different IEEE 802.11ac WiFi signal bands, and cross-range resolution improvement by ISAR technique have been conducted in the past decade [START_REF] Colone | Ambiguity function analysis of wireless LAN transmissions for passive radar[END_REF][START_REF] Shi | High-resolution synthetic aperture radar based on the IEEE 802.11 protocol[END_REF][START_REF] Colone | WiFi-based passive ISAR for highresolution cross-range profiling of moving targets[END_REF].

Since the transmitted signal from an existing IO is not within the control, a PBR system normally consists of two channels, the reference channel and the surveillance channel. The reference channel provides the time-delayed copies of the transmitted signal obtained by a directional reference antenna facing to the IO transmitter, while the surveillance channel records the echoes of the targets, which is obtained by a second antenna with broader radiation pattern, called as surveillance antenna, facing to the targets. Then, for moving target detection, a range-Doppler (RD) map is generated by calculating the 2D cross-ambiguity function between the reference channel and the surveillance channel based on the matched filtering approach. For stationary target imaging, the 1D cross-correlation is conducted at each antenna position for range compression, and then the back projection (BP) algorithm is used for the azimuth focusing [START_REF] Feng | Novel algorithm for high resolution passive radar imaging with ISDB-T digital TV signal[END_REF][START_REF] Gromek | Experimental results of passive SAR imaging using DVB-T illuminators of opportunity[END_REF]. However, it is well known that the surveillance channel also contains the direct path interference (DPI) from the IO transmitter, which may be significantly stronger than the reflections of targets. Without suppressing the DPI, the targets are normally not detectable. Therefore, various methods have been proposed to confront this problem [START_REF] Garry | Evaluation of direct signal suppression for passive radar[END_REF][START_REF] Ansari | A novel sequential algorithm for clutter and direct signal cancellation in passive bistatic radars[END_REF][START_REF] Colone | A multistage processing algorithm for disturbance removal and target detection in passive bistatic radar[END_REF][START_REF] Cardinali | Comparison of clutter and multipath cancellation techniques for passive radar[END_REF][START_REF] Palmer | Evaluation of adaptive filter algorithms for clutter cancellation in passive bistatic radar[END_REF], including the CLEAN algorithm, least mean square (LMS) algorithm, fast and block LMS algorithm, extensive cancellation algorithm (ECA) and its variants, such as the batchbased ECA (ECB) algorithm and the sequential cancellation batch (SCB) algorithm.

In the research of DPI suppression for PBR applications, it is found that the conventional time-domain-based algorithms mentioned above may cause some problems when used in the short-range applications. When the DPI is much stronger than the target reflections, the DPI cannot be completely mitigated since the time delay of DPI is not exactly integral times of the data sampling interval which forms the basis of these time-domain-based algorithms. Therefore, the targets may still not be distinguished from the remaining components of DPI. When the targets become stronger, although these algorithms can suppress the DPI and make the targets clearer, the inaccurately estimated DPI components will introduce estimation errors of the target time delay, resulting in inaccurate target position estimation. To overcome this problem, we turn our attention to frequency-domain processing and propose a novel DPI suppression method based on the atomic norm minimisation (ANM), Vandermonde decomposition, and LS method [START_REF] Tang | Compressed sensing off the grid[END_REF][START_REF] Yang | Exact joint sparse frequency recovery via optimization methods[END_REF][START_REF] Feng | Airborne radar space time adaptive processing based on atomic norm minimization[END_REF][START_REF] Yang | Vandermonde decomposition of multilevel Toeplitz matrices with application to multidimensional super-resolution[END_REF]. In the proposed method, we first estimate the time delay of the DPI and then estimate its amplitude in order to cancel it from the surveillance channel. The DPI time delay estimation problem is modelled as a simple 1D frequency estimation problem. By exploiting the sparsity of the DPI signal and the positive semidefinite (PSD), Toeplitz and low rank properties of its covariance matrix, the signal subspace of DPI is estimated by the ANM algorithm. Then, the Vandermonde decomposition is conducted and the DPI time delay is calculated by extracting the most significant frequency component from the surveillance signal. Finally, the amplitude of the DPI component is estimated by the LS method. We have carried out several semi-experimental simulations and experiments of WiFi-based passive bistatic SAR imaging to validate the proposed method. It is shown that the proposed method has better performance than the classical ECA method. The DPI can be effectively suppressed and the target position can be accurately estimated.

The rest of the paper is organised as follows. In Section 2, the signal model for PBR is established, and the classical DPI suppression methods are briefly introduced and their problems are discussed. In Section 3, the proposed DPI suppression method is presented and analysed, and the signal processing flowchart for WiFi-based passive bistatic SAR imaging is also described. Simulation and experiment results are given in Section 4 to validate the performance of the proposed method. Finally, Section 5 concludes this paper and presents some considerations of the future work.

Passive radar signal model

As mentioned previously, a PBR system normally consists of a reference channel and a surveillance channel. The reference signal received by an antenna directly oriented to IOs (e.g. TV or WiFi transmitter) can be expressed as

s ref (t) = A ref s 0 (t -t ref ) + n ref (t), (1)
where s 0 (t) is the transmitted signal, t denotes time, A ref is the complex amplitude, t ref denotes the time delay from the IO emitter to the reference antenna, and n ref (t) denotes the thermal noise. Without considering the multipath echoes and moving targets, the received signal from a surveillance antenna, which includes the DPI, stationary target echoes, and thermal noise, can be expressed as [START_REF] Capria | Multifunction imaging passive radar for harbour protection and navigation safety[END_REF], where A surv is the amplitude of the DPI signal with time delay t surv ; P is the number of targets, a p and t p are the amplitude and time delay of the pth target; and n surv (t) denotes the thermal noise in the surveillance channel.

s surv (t) = A surv s 0 (t -t surv ) + ∑ p = 1 P a p s 0 (t -t p ) + n surv (t) = s dpi (t) + s tar (t) + s n (t) . (2)
In practice, the DPI is always much stronger than the target reflections, therefore needs to be suppressed to make the target detectable. Normally, time-domain processing methods, such as above mentioned ECA and LMS methods, are applied to this purpose. For these methods, the DPI signal is first estimated by the following equation with calculated coefficients h(m) in the discrete form:

s dpi (nT s ) = ∑ m = 0 M -1 h(m)s ref (n -m)T s , (3)
where T s is the data sampling interval, n = 0, 1, …, N -1 is the sample index, N is the number of samples, and M is the number of discrete time delays to properly model the maximum range of the DPI [START_REF] Garry | Evaluation of direct signal suppression for passive radar[END_REF]. The differences among different time-domain DPI suppression algorithms are the methods used to estimate the coefficient h. For example, in the ECA method, we have

h = (P H P) -1 P H s surv , (4)
where P ∈ C N × M is a matrix formed by the delayed copies of the reference signal vector s ref (without considering the Doppler shifts of moving targets), ( ⋅ ) H denotes the conjugate transpose operation, ( ⋅ ) -1 denotes the matrix inverse operation, and s surv denotes the surveillance signal vector. Then, the DPI suppressed surveillance signal can be obtained by

s ~surv = s surv -s ~dpi = s surv -Ph ~.
(5)

Finally, the time delay of the target can be estimated by calculating the cross-correlation function between the received reference signal and the DPI suppressed surveillance signal as

χ(τ) = ∑ n = 0 N -1 s ~surv (nT s )s ref * (nT s -τ), ( 6
)
where τ is the expected time delay of the reflected signal from the target and ( ⋅ )* denotes complex conjugate. However, since the time-domain DPI suppression algorithms are based on the data sampling interval T s , as shown in (3), the DPI cannot be accurately estimated and completely suppressed because the delay of DPI, i.e. τ dpi = t reft surv , is not exactly integral times of T s . Besides, by substituting ( 2) and ( 5) into ( 6), we can obtain

χ(τ) = ∑ n = 0 N -1 s surv (nT s ) -s ~dpi (nT s ) s ref * (nT s -τ) = ∑ n = 0 N -1 s tar (nT s ) + s dpi error (nT s ) s ref * (nT s -τ), (7)
where s dpi error (nT s ) = s dpi (nT s )s ~dpi (nT s ) is the error produced by the inaccurate estimation of the DPI component, which will cause the inaccurate estimation of the time delay (i.e. range) of targets. Therefore, advanced algorithms are desired to accurately estimate the DPI component in the surveillance channel.

ANM-based DPI suppression

In order to accurately estimate the DPI and then cancel it, we turn our attention to frequency-domain signal processing. By Fourier transform, the frequency-domain reference signal and surveillance signal are given by ( 8) and [START_REF] Wu | Space-time adaptive processing and motion parameter estimation in multistatic passive radar using sparse Bayesian learning[END_REF].

s ref ( f ) = A ref s 0 ( f )e -j2π f t ref + n ref ( f ), (8)
where f denotes the frequency.

s surv ( f ) = A surv s 0 ( f )e -j2π f t surv + ∑ p = 1 P a p s 0 ( f )e -j2π f t p +n surv ( f ) = s dpi ( f ) + s tar ( f ) + s n ( f ) . (9)
Since the DPI is normally much stronger than the reflections of the targets, we can rewrite (9) as

s surv ( f ) = A surv s 0 ( f ) e -j2π f t surv + s n ~( f ) = s dpi ( f ) + s n ~( f ), (10)
where

s n ~( f ) = s tar ( f ) + s n ( f
) is assumed to be the additive noise to the main signal component s dpi ( f ).

Based on ( 8) and [START_REF] Gromek | Experimental results of passive SAR imaging using DVB-T illuminators of opportunity[END_REF] and expressed in the discrete form, by using an inverse filter [START_REF] Wojaczek | Reciprocal filter-based STAP for passive radar on moving platforms[END_REF][START_REF] Glende | PCL-signal-processing for sidelobe reduction in case of periodical illuminator signals[END_REF], it can be derived that

s( f n ) = A 0 e j2π f n τ dpi + s noise ( f n ), s ref ( f n ) ≥ δ 0, s ref ( f n ) < δ , (11)
where

f n = f c + nΔ f is the (n + 1)th frequency, f c is the carrier frequency, Δ f is the frequency step, A 0 = A surv / A ref ,
and δ is a userdefined threshold to avoid the numerical instability. We note that, ( 11) is obtained by

s( f n ) = s surv ( f n )/s ref ( f n ). Compared to s( f n ) = s surv ( f n )s ref * ( f n
), the division process can help to reduce the negative influences of the IO signal structures (i.e. the influence of s 0 ( f )) for range compression [START_REF] Wojaczek | Reciprocal filter-based STAP for passive radar on moving platforms[END_REF][START_REF] Glende | PCL-signal-processing for sidelobe reduction in case of periodical illuminator signals[END_REF]. However, in some cases, direct division is numerically unstable. Therefore, according to the amplitude of s ref ( f n ), a user-defined threshold δ should be used to make [START_REF] Glende | PCL-signal-processing for sidelobe reduction in case of periodical illuminator signals[END_REF]. In this paper, we set

s( f n ) = 0 if s ref ( f n ) < δ
δ = ∑ n = 0 N -1 s ref ( f n ) /4N.
Besides, in order to fairly show the advantages of the proposed method over conventional method, ( 6) is changed to

χ(τ) = ∑ n = 0 N -1 s ~( f n ) e j2π f n τ , (12)
where

s ~( f n ) = s ~surv ( f n )/s ref ( f n ) if s ref ( f n ) ≥ δ and s ~( f n ) = 0 otherwise,
s( f n ) = A 0 e j2π f c τ dpi e j2π(n -1)Δ f τ dpi + s noise ( f n ) = A ~0 e j2π(n -1)Δ f τ dpi + s noise ( f n ) = s 0 ( f n ) + s noise ( f n ), (13)
and, in the vector form, we have the following N 1 × 1 signal vector:

s = Φs 0 + s noise , (14)
where Φ is the measurement matrix with size N 1 × N that used to sample s 0 according to the criterion s ref ( f n ) ≥ δ, N 1 ≤ N is the number of frequencies that satisfy this criterion, s 0 = A 0 s steer is an

N × 1 vector, s steer = [1, e j2π f dpi , …, e j2π(N -1) f dpi ] T , (15)
is the steering vector corresponding to f dpi , [ ⋅ ] T denotes the transpose operation, and

f dpi = Δ f τ dpi .
It can be learned from ( 14) that the DPI time delay estimation problem is a 1D frequency estimation problem of the sinusoidal signal s 0 with time samples (0, 1, …, N -1) and frequency f dpi . Recently, based on the intrinsic sparsity of s 0 , sparse representation (SR) and compressive sensing (CS)-based methods have been proposed to estimate the frequency of s 0 from its noise polluted under-sampled signal s by solving the following minimisation problem:

α ~= min α 0 s . t . ∥ s -ΦΘα ∥ 2 2 ≤ ε n , (16)
where

Θ = [e j2πΔ f τ 1 , e j2πΔ f τ 2 , …, e j2πΔ f τ L ] ∈ C N × L , (17)
Δ f = [0, 1, …, N -1] T Δ f , α is the coefficient vector corresponding to the time delay [τ 1 , τ 2 , …, τ L ],
and ε n denotes the noise level (containing weak targets and thermal noise). Although ( 16) is a non-deterministic polynomial-time hard (NPhard) problem, a number of computationally efficient algorithms can be used, such as the smooth L0 (SL0) algorithm and orthogonal matching pursuit algorithm [START_REF] Mohimani | A fast approach for overcomplete sparse decomposition based on smoothed ℓ 0 norm[END_REF][START_REF] Tropp | Signal recovery from random measurements via orthogonal matching pursuit[END_REF]. However, for these conventional SR/CS-based algorithms, as formulated by [START_REF] Feng | WiFi-based imaging for ground penetrating radar applications: fundamental research and experimental results[END_REF], the expected frequencies are assumed to be located at fix discretised grids

[Δ f τ 1 , Δ f τ 2 , …, Δ f τ L ].
The off-grid problem, i.e. the mismatch between the pre-defined frequency grid and the actual frequency of signal, may cause the performance degradation [START_REF] Chi | Sensitivity to basis mismatch in compressed sensing[END_REF][START_REF] Bai | Parameter-searched OMP method for eliminating basis mismatch in space-time spectrum estimation[END_REF].

It is known that the covariance matrix of s 0 , i.e.

R 0 = E[s 0 s 0 H ] = E A 0 2 s steer s steer H , (18)
is a rank-1 PSD block-Toeplitz matrix with size N × N, where E[ ⋅ ] denotes the expectation. Therefore, by exploiting these structures, the frequencies of s 0 can be exactly retrieved from its covariance matrix R 0 by the classical Vandermonde decomposition, with which as the basis some subspace-based methods, such as MUSIC and ESPRIT, have been proposed to estimate the frequency of s 0 . However, for these methods, a sufficient number of training samples is required to estimate the signal subspace. In this paper, the ANM algorithm, which directly deals with the continuous frequencies and completely resolves the off-grid problem of SR/CS-based methods without the requirement of training samples as other subspace-based methods, is applied to estimate s 0 and its subspace. We know that, rather than in the discretised frequency domain, s 0 is sparse in the continuous frequency domain. We can further learn from ( 14) that s 0 can be formed by an atom in the atomic set

A ≜ s steer ( f ) f ∈ [0, 1) , (19)
that collects all the potential steering vectors s steer . Thus, with the atomic L0 norm of s 0 defined as

∥ s 0 ∥ A, 0 ≜ inf α o ∈ C, f o ∈ [0, 1) O s 0 = ∑ o = 1 O α o s steer o ( f o ) , (20)
to exploit the sparsity of s 0 , where O is the number of atoms in A that represent s 0 , the DPI component can be extracted from s by the following ANM problem:

s ~0 = min ∥ s 0 ∥ A, 0 , s . t . ∥ s -Φs 0 ∥ 2 2 ≤ ε n . (21)
Furthermore, because ∥ s 0 ∥ A, 0 = rank(R 0 ) = 1, it can also be derived that (21) equals the following problem [START_REF] Yang | Exact joint sparse frequency recovery via optimization methods[END_REF]:

[s ~0, R 0 ] = min R 0 , s 0 rank(R 0 ) s . t . 1 s 0 H s 0 R 0 ≥ 0, ∥ s -Φs 0 ∥ 2 2 ≤ ε n , (22)
where rank( ⋅ ) denotes the rank of a matrix. The rank minimisation problem in ( 22) is also NP-hard as ( 16), therefore more computationally efficient methods should be adopted. Besides, although it is expected that R 0 in [START_REF] Ansari | A novel sequential algorithm for clutter and direct signal cancellation in passive bistatic radars[END_REF] is the estimation of the covariance matrix of s 0 , it is shown that R 0 is only the estimation of the subspace of s 0 . Therefore, the following nuclear norm relaxation of ( 22) [START_REF] Feng | Airborne radar space time adaptive processing based on atomic norm minimization[END_REF] is used to estimate s 0 and its subspace T(u), i.e. a Toeplitz matrix formed by a vector u.

[s ~0, u ~] = min s 0 , u trace[T(u)] s . t . 1 s 0 H s 0 T(u) ≥ 0, ∥ s -Φs 0 ∥ 2 2 ≤ ε n , (23)
where trace[ ⋅ ] denotes the trace of a matrix. In this paper, ( 23) is solved by the SDP solver in CVX. Then, since DPI is the strongest component in s, instead of s tar + s n = s -Φs ~0 after obtaining the estimation of s 0 , which may also suppress the target components, we propose to use the following method to achieve the DPI suppressed pure signal:

s pure = s tar + s n = s -βΦs ~steer 1 , (24)
where

s ~steer 1 = [1, e j2π f τ 1 , …, e j2π(N -1) f τ 1 ] T , (25)
is the estimation of the steering vector of DPI, ) H s, [START_REF] Tang | Compressed sensing off the grid[END_REF] is the amplitude of the DPI estimated by least square method, f τ 1 = Δ f τ 1 is the most significant frequency of s 0 estimated by the Vandermonde decomposition of T(u), i.e.

β = [(
T(u) = ∑ k = 1 K p k s ~steer k (s ~steer k ) H = APA H , (27)
and τ 1 is the time delay estimation of the DPI. Finally, the inverse Fourier transform can be carried out to estimate the time delays of targets, giving

χ anm (τ) = ∑ n 1 = 0 N 1 -1 s pure ( f n 1 )e j2π f n 1 τ , ( 28
)
where f n 1 is the (n 1 + 1)th frequency that satisfy the criterion

s ref ( f n 1 ) ≥ δ.
We should note that, for moving target detection by PBR, beyond the DPI suppression, the strong echoes of the ground stationary targets should also be mitigated from the surveillance channel. Since we are focusing on the passive bistatic SAR imaging applications, all the stationary targets should be imaged. Therefore, in the established signal model and the derivation of the proposed method, s dpi is assumed to only contain one strong signal, thus s 0 only has one significant frequency and the rank of the signal covariance matrix equals to 1, i.e. rank(R 0 ) = 1. However, the proposed method can be easily extended to the multiple components suppression problem, such as the moving target RD mapping, or the reduction of strong multiple echoes, or the specific SAR imaging case where the strong stationary targets make the weak stationary targets undetectable and thus a CLEAN-like approach is desired to apply. In such a case, the DPI component should be changed to

s dpi (t) = ∑ i = 1 I A surv i s 0 (t -t surv i ), (29)
and

s 0 = ∑ i = 1 I A 0 i s steer i , ( 30
)
where I is the number of unwanted components in the surveillance channel. As the consequence, ( 23) and ( 24) should be modified to

[s ~0, u ~] = min s 0 , u trace[T(u)] s . t . I s 0 H s 0 T(u) ≥ 0, ∥ s -Φs 0 ∥ 2 2 ≤ ε n , (31)
and

s pure = s tar + s n = s -ΦΨβ, (32)
where

Ψ = [s ~steer 1 , s ~steer 2 , …, s ~steer I ], (33)
and

β = [(ΦΨ) H (ΦΨ)] -1 (ΦΨ) H s . ( 34
)
Since we are focusing on the short-range passive bistatic SAR imaging with WiFi signals, the signal processing procedure based on the proposed DPI suppression method for target imaging is also presented. In a passive SAR system, in order to achieve a high azimuth resolution, the surveillance antenna is moved linearly to form a synthetic aperture. When the surveillance antenna is at the lth position (x l , 0), the proposed DPI suppression method can be used and the lth range-compressed profile can be obtained by ( 28) as

χ anm l (τ) = ∑ n 1 = 0 N 1 -1 s pure l ( f n 1 ) e j2π f n 1 τ , (35)
where l = 1, 2, …, L and s pure l is the lth DPI suppressed frequency signal. Then, by using the BP algorithm, the reflection coefficient of the target at (x, y) can be estimated by

σ ~(x, y) = ∑ l = 1 L χ anm l [t ref -τ l (x, y)], ( 36
)
where τ l (x, y) = [r l (x, y) + r 0 (x, y)]/c, c is the velocity of light, r 0 (x, y) = (x 0x) 2 + (y 0y) 2 is the distance between the target and the IO emitter, i.e. the WiFi access point (AP) in our case, at (x 0 , y 0 ), r l (x, y) = (x lx) 2 + y 2 , and σ ~(x, y) is the estimated amplitude of the target at (x, y). During the coherent summation of the range-compressed signal from all the antenna positions, many high-level artefacts will be produced by BP algorithm. It has been shown in [START_REF] Feng | Near range radar imaging based on block sparsity and cross-correlation fusion algorithm[END_REF] that the cross-correlation-based BP (called as CC-BP in this paper) algorithm can effectively suppress the artefacts. Therefore, in this paper, the CC-BP algorithm is applied to estimate the reflection coefficients of targets, which can be expressed as

σ ~(x, y) = ∑ l 1 = 1 L -1 ∑ l 2 = l 1 + 1 L { χ anm l 1 [t ref -τ l 1 (x, y)] × χ anm l 2 [t ref -τ l 2 (x, y)]} . ( 37
)
In summary, the signal processing chain for passive bistatic SAR imaging is presented in Fig. 1.

Simulation and experiment results

In this section, we present some simulation and experiment results to demonstrate the effectiveness of the proposed DPI suppression method and the performance of the presented short-range passive bistatic SAR imaging scheme. The classical ECA algorithm with

Semi-experimental simulation results

In the first study step, we did some semi-experimental simulations, where the reference signal is obtained by directly sampling the IEEE 802.11n 2.422 GHz signal with 40 MHz bandwidth from a WiFi AP using a horn antenna, while the surveillance signal at each antenna position is simulated with time delays corresponding to the assumed target position. The synthetic aperture length is set to 3 m with a step of 5 cm from (-1.5, 0) to (1.5, 0), the reference antenna and the AP are assumed to be located at (0, 0), and the data sampling frequency is 10 GSamples/s (0.1 ns data sampling interval and thus 0.03 m long for each range cell) to avoid the signal aliasing. We simulate the DPI with random time delay for each antenna position, and the amplitude of DPI is 100 times (40 dB) stronger than the target. The minimal DPI delay corresponds to ∼50 range cells and the maximal one is ∼100 range cells.

For the first simulation, only one target at (0, 5) is simulated. Before DPI suppression, the range compressed profiles for different surveillance antenna positions and the imaging result by CC-BP algorithm are shown in Fig. 2. It can be observed that, since the DPI is much stronger than the target echo, the target cannot be distinguished.

As to the proposed DPI suppression-based method, the time delay of DPI for each antenna position is estimated accurately, as shown in Fig. 3. Therefore, with further processing by Vandermonde decomposition and LS method, the DPI can be effectively suppressed, the target can be clearly seen and its estimated position is also accurate, as shown in Fig. 4. For the ECA method, different range cells are considered (i.e. 51 and 101 range cells, which are decided by the minimal and maximal DPI delays). Since the delays of DPI are randomly simulated and are not integral times of the sampling interval (0.1 ns), the strong DPI cannot be effectively suppressed by the ECA technique, and the target is still undistinguished, as shown in Fig. 5.

Then, three targets at (0, 5), (-2.5, 5), and (2.5, 5) are simultaneously simulated. The imaging results obtained after DPI suppression by the ECA method with 101 range cells and the proposed method are shown in Fig. 6. The advantage of the proposed method over the ECA method is unchanged for the multiple targets case.

In the second study step, we change the strength of the DPI. Although we still consider random DPI time delay at each surveillance antenna position, the amplitude of the simulated DPI is changed to five times (14 dB) stronger than the target. In such a case, for the proposed ANM-based signal subspace estimation approach, the signal-to-noise ratio (SNR) is decreased, which is used to mimic a much more noisy condition than the previous simulations.

The imaging result obtained by CC-BP algorithm before DPI suppression, DPI time delay estimation result, range compressed profiles, and focused image obtained after the DPI suppression by the proposed method are shown in Fig. 7. It can be learned from Fig. 7a that, before DPI suppression, the target is already detectable but not clear enough, therefore DPI suppression is still necessary. Compared with Fig. 3, Fig. 7b demonstrates that, in the more noisy condition (26 dB), the performance of the proposed method will be degraded. However, the time delay of DPI can still be estimated for each surveillance antenna position. Therefore, as shown in Figs. 7c andd, the DPI can be mitigated effectively and the target is much clearer than Fig. 7a.

The range profiles and focused images obtained after DPI suppression via ECA method with 51 range cells (minimal DPI delay) and 101 range cells (maximal DPI delay) are shown in Figs. 8a andb, respectively. Different from the strong DPI case as shown in Fig. 5, for weaker DPI, the ECA method with 51 range cells and 101 range cells can work well. Since most energy of the DPI can be suppressed, a smaller DPI energy than the target can be obtained, making the target clearer. However, compared with the proposed method, there are some random artefacts in the focused SAR images. Furthermore, the inaccurate estimation of the DPI component will cause the inaccurate estimation of the target position, i.e. the target will be shifted in the focused SAR images, as shown in Fig. 9. It can be observed that, because of DPI estimation error, the ECA method will give incorrect target position estimation, especially in the y direction, which is actually 5 m. Compared with 51 range cells, the ECA method with 101 range cells shows an even worse result.

Experiment results

Experiments are also conducted to validate the proposed DPI suppression method. The experiment setup is shown in Fig. 10, where a metallic plate located at about (-0.5, 6) is set to be the imaging target. The WiFi AP is at (-1.5, 1), the reference antenna is at (-1.5, 2), and the surveillance antenna is sledded on a rail from (-1.5, 0) to (1.5, 0) with a step of 5 cm.

The imaging result without DPI suppression is shown in Fig. 11a. Since the DPI is stronger than the reflection of the metallic plate in this experiment, the target cannot be well observed from the focused image. Besides, because the position of WiFi AP is unchanged for each surveillance antenna position, the DPI time delay is not randomly distributed as in the simulation case, but follows a hyperbolic function of the antenna position. Therefore, the WiFi AP can be focused by the CC-BP algorithm with accurate position (-1.5, 1), as indicated by the white rectangle in Fig. 11a. First, with 21 range cell, the DPI can be suppressed by the ECA method to some extents, as shown in Fig. 11b. However, due to the residual of the DPI component, there are many artefacts in the focused image; because of some errors introduced by the inaccurately estimated DPI component, with 121 range cells, ECA method can further suppress the DPI but with the cost of the degraded accuracy of target position, as shown in Fig. 11c and indicated by the white circle. For the proposed method, even though the DPI is not significantly dominant in the received surveillance channel, its influence can still be effectively suppressed, as shown in Fig. 11d, where the target is clearly Then, we present the target position estimation accuracy comparison between the proposed method and the ECA method with different number of rang cells. Two cross-sections along the xdirection and y-direction of the focused images obtained by different methods are shown in Fig. 12. It can be learned that, with the increase of the processing range cells, the target will be further shifted by the ECA method. The proposed method can provide more accurate estimation of the target position. Moreover, although the ECA method with 21 range cells can obtain the similar target position estimation accuracy with the proposed method, its artefact level is higher than the proposed method.

Finally, the computational complexity of the proposed method is discussed. For the proposed method, solving [START_REF] Colone | A multistage processing algorithm for disturbance removal and target detection in passive bistatic radar[END_REF] is the most time consuming step, compared to which the computing time of other steps can be ignored. In our study, ( 23) is solved by the SDP solver SDPT3 implemented in CVX, where the semi-definite constraint is of size N × N. As indicated in [START_REF] Yang | Frequency-selective Vandermonde decomposition of Toeplitz matrices with applications[END_REF], the SDP step has the computational complexity of O(N 4.5 ). For the ECA method, the computational complexity is about O(NM 2 + M 3 ) [START_REF] Ansari | A novel sequential algorithm for clutter and direct signal cancellation in passive bistatic radars[END_REF]. In the simulation and experiment, the data sampling frequency is 10 GSamples/s and the number of samples is N = 4096, which implies the proposed method is much more time consuming. However, we note that, since not all the sampled signal that within 10 GHz bandwidth is useful for the passive bistatic SAR imaging, but only the WiFi signal is needed to extract for processing. Therefore, in the implementation of the proposed method, only the frequencies within the 40 MHz WiFi bandwidth around the 2.422 GHz central frequency were processed. In other words, in the proposed method, the value of N can be much reduced.

Therefore, measured by the TIC and TOC instruction in MATLAB, averaged by 100 Monte Carlo trials, and implemented in MATLAB 2015b on a Core i5, 2.5 GHz, 8 GB RAM PC, the computing time of the proposed method and the ECA method with 100 rang cell, 200 range cells and 400 range cells (corresponding to the maximal DPI distance of 3, 6 and 12 m) for passive SAR imaging are 40.17, 6.95, 15.73, 45.48 s, respectively. This indicates that the proposed method is more time consuming than the ECA method with a small number of processing range cells, but is comparable with the ECA method with a large number of processing range cells.

Conclusion

In this paper, we have proposed and validated an effective DPI suppression method for PBR applications. By employing the advanced ANM algorithm and the classical Vandermonde decomposition algorithm, we can estimate the time delay of DPI accurately, and thus the influence of DPI on the short-range target imaging can be reduced by the least squares method. Compared to the classical time-domain DPI suppression method, the proposed method demonstrates the advantages in terms of DPI suppression capacity and target position estimation accuracy. We have carried out several semi-experiment simulations and experiments of WiFibased passive SAR imaging to demonstrate the effectiveness of the proposed method. When the DPI component is not significantly stronger than the echoes of targets in the surveillance channel, i.e. with the noisy conditions, the proposed method can still work well. Furthermore, we also presented the potential implementations of the proposed method for moving target RD mapping and strong stationary target removal in some specific passive SAR applications. The computational complexity of the proposed method is comparable with the conventional ECA method with large number of range cells, but needs to be further reduced. In practice, the sparsity of the DPI and the low rank property of its covariance matrix may be destroyed by some practical factors. Therefore, our next study is to further improve the performance of the proposed method in practical environments and to reduce its computing time to realise real-time processing.

Fig. 1

 1 Fig. 1 Signal processing chain for passive bistatic SAR imaging

Fig. 2 Fig. 3 Fig. 4

 234 Fig. 2 Results for one target before strong DPI suppression (a) Range profiles, (b) Focused SAR image

Fig. 5 Fig. 6

 56 Fig. 5 Focused images of one target after strong DPI suppression via the ECA method with different range cells (a) 51 range cells, (b) 101 range cells

Fig. 7

 7 Fig. 7 Proposed method applied to one target case with weaker DPI (a) Focused image before DPI suppression, (b) DPI time delay estimation, (c) Range profiles after DPI suppression, (d) Focused image after DPI suppression

Fig. 8

 8 Fig. 8 ECA method applied to one target case with weaker DPI (a) Focused image after DPI suppression with 51 range cells, (b) Focused image after DPI suppression with 101 range cells

Fig. 9

 9 Fig. 9 Simulated target position estimation accuracy comparison (a) x-direction, (b) y-direction

Fig. 11

 11 Fig. 11 Focused images of the metallic plate at about (-0.5, 6) (a) Before DPI suppression, (b) After DPI suppression via ECA method with 21 range cells, (c) After DPI suppression via ECA method with 121 range cells, (d) After DPI suppression via the proposed method

Fig. 12

 12 Fig. 12 Real target position estimation accuracy comparison (a) x-direction, (b) y-direction

  and s ~surv ( f n ) is the (n + 1)th frequency component of the DPI suppressed surveillance signal.By simple reformulations of[START_REF] Qiu | Compressive sensing-based algorithm for passive bistatic ISAR with DVB-T signals[END_REF], in the case of s ref ( f n ) ≥ δ, we can obtain

  Φs ~steer

1 ) H Φs ~steer 1 ] -1 (Φs ~steer 1

Acknowledgments

This work was supported by JSPS Grant-in-Aid for Scientific Research (A) 26249058, OscillatorIMP and FIRST-TP grants from the French Projet d'Investissement d'Avenir (PIA), as well as Tohoku University through the funding of an invited scientist position for J.-M Friedt and a ROIS scholarship for Zhipeng Hu.


C Gilliers
email: camille.gilliers@univ-lille1.fr

O Le Pape

Y Désaunay

J Morin

D Guérault

R Amara

Are growth and density quantitative indicators of essential fish habitat quality? An application to the common sole Solea solea nursery grounds

Keywords: quantitative bio-indicators, essential fish habitat quality, flatfish juvenile

Bio-indicators were measured on juvenile fish to assess the quality of eight coastal and estuarine nursery grounds in the Eastern English Channel and in the Bay of Biscay during 3 years. Growth (size and otolith daily increment width), body condition (morphometric index) and abundance of juvenile common soles were analysed together with xenobiotic concentrations (heavy metals and organic contaminants).

Condition indices displayed important variations and did not allow relevant estimation of environmental quality. On the contrary, growth and density indicators showed good steadiness above years but varied among sites. In spite of difficulties of interpreting these indicators on such a meso-scale approach, analyses highlighted the estuaries of Seine and Gironde. In these nursery areas, the levels of contamination were especially high, and the combination of fish growth performances and density was significantly lower than in other sites. The combination of these variables appears to provide reliable indicators of habitat quality and anthropogenic pressure on nursery grounds, especially highlighting contaminated areas. Such indicators may thus contribute to improve assessment of environmental quality of essential fish habitats with the aim of a sustainable management of fisheries resources. A study at a different scale, from this meso-scale nursery approach with more precise analyses, on local habitats, will nevertheless be necessary to optimize the relevance of these indicators for the assessment of essential fish habitat quality.

Introduction

As habitat destruction and/or damage to habitat quality can prevent fish stock from recovery [START_REF] Hall | The response of estuarine fish and benthos to an increasing dicharge of sewage effluent[END_REF], one of the main areas of emphasis in current ecological research is the conservation and enhancement of essential fish habitats. Nevertheless, worldwide increasing industrial development and human population growth have led to a rise in environmental damage and human pressure on marine habitats keeps strong. This is especially true in coastal and estuarine marine areas [START_REF] Costanza | The value of the world's ecosystem services and natural capital[END_REF] having an important function in fish stock renewal, as nursery grounds for commercially important marine fish species [START_REF] Miller | Patterns, mechanisms and approaches to the study of migrations of estuarine-dependent fish larvae and juveniles[END_REF]. In these coastal habitats, fish can experience numerous stressors including unfavourable natural conditions (fluctuating temperature and salinity, changing substrate in response to river inputs...) in addition to anthropogenic stressors (chemical contamination, digging of channels, clapping of sediments …). These factors can impose considerable stress to organisms [START_REF] Wedemeyer | Stress and acclimatation[END_REF]. Assessment and monitoring of the quality of nursery areas should aim to prevent alteration and, thus, decline of fish populations [START_REF] Meng | Using winter flounder growth rates to assess habitat quality in Rhode Island's coastal lagoons[END_REF]. In this context, the European Union searches for biological indicators to assess environmental quality, and to implement the Habitat Directive (92/43/EC), the Water Framework Directive (2000/60/EC) and the Integrated Coastal Zone Management Program (European Commission, 2000). On the northern and western coasts of France, and especially in the bay of Biscay and in the Eastern English Channel (Fig. 1), inshore shallow waters and estuaries provide nursery areas for a wide variety of fish species and especially for commercially important flatfish [START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF]Le Pape et al., 2003a). The present study about young fish habitat quality focused on the common sole S. solea, which is one of the most important commercial species in these areas [START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF]Le Pape et al., 2003ab). Juvenile common sole are concentrated in coastal shallow nursery grounds [START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF]Le Pape et al., 2003a) and are sensitive to environmental changes. Young of the year sole have limited movements between nursery grounds [START_REF] Koutsikopoulos | Movement of sole (Solea solea) in the Bay of Biscay: coastal environment and spawning migration[END_REF][START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF], thus bio-indicator responses should properly reflect the quality of the different sampled nursery sites. The goal of the present study was to find suitable bio-indicators measured on fish to assess the quality of nursery habitat along the coasts of the Eastern English Channel and the bay of Biscay, with a focus on sites heavily impacted by human activities such as the important estuaries of Seine, Loire and Gironde. High quality nursery habitats are those where growth and survival of juvenile fish are enhanced, and where ultimately reproductive potential is optimized [START_REF] Gibson | Impact of habitat quality and quantity on the recruitment of juvenile flatfishes[END_REF]. Subsequently, growth, condition, and abundance of juvenile fishes have been used as relevant indicators of nursery habitat quality [START_REF] Guindon | Growth potential of juvenile southern flounder, Paralichthys lethostigma, in low salinity nursery areas of Pamlico Sound, North Carolina, USA[END_REF][START_REF] Able | Habitat quality for shallow water fishes in urban estuary: the effect of man-made structures on growth[END_REF][START_REF] Duffy-Anderson | Effects of municipal piers on the growth of juvenile fishes in the Hudson River estuary: a study across a pier edge[END_REF][START_REF] Phelan | Estuarine and habitat-related differences in growth rates of young of the year winter flounder (Pseudopleuronectes americanus) and tautog (Tautoga onitis) in three north-eastern US estuaries[END_REF]. Growth, body condition and abundances of juvenile fishes were compared to assess the habitat quality of different nursery areas. In the same time, indices of water contamination were used as indicators of human disturbances.

Materials and Methods

Studied sites and fish sampling

Coastal and estuarine nursery areas of the French coasts, in the bay of Biscay and in the Eastern English Channel (Fig. 1., Table 1) were investigated. The shore of the bay of Biscay is partitioned into open shallow muddy esturarine areas under the direct influence of freshwater inflows: the Vilaine (average river flow: 91 m 3 .s -1 ), the Loire (average river flow: 935 m 3 .s -1 ) and the Dordogne and Garonne (forming the Gironde estuary) (average river flow: 780 m 3 .s -1 ), and semi-enclosed sheltered muddy marsh areas with shellfish-farming, little affected by rivers: the bay of Bourgneuf and the Pertuis Breton and Antioche. In the French part of the Eastern English Channel, sheltered coastal areas identified as nursery grounds are dominated by sandbanks and mudflats in bays and estuaries [START_REF] Larsonneur | The superficial sediments of the Eastern Channel and its western approaches[END_REF]. The Seine estuary represents the main freshwater inflow (400 m 3 .s -1 ), and contributes with other smaller rivers (i.e. Somme) to a general decrease in the salinity of coastal waters. During surveys in September 2000September , 2001September and 2002, sole juveniles were collected in 6 nursery sites in the bay of Biscay and in 2 nursery sites in the Eastern English Channel (Fig. 1, Table 1). Autumn was chosen because it corresponds to the end of the growing season of juvenile sole on nursery grounds, which allow better assessments of growth rates at a period when YoY (Young of the Year) fish have not moved since their settlement [START_REF] Dorel | Seasonal distribution of young sole (Solea solea L.) in the nursery ground of the bay of Vilaine (Northern Bay of Biscay)[END_REF]. Moreover, problems of selectivity and size-dependent catchability for trawling, hence bias in estimate of YoY density and size, very important in early summer, are limited at the end of the growing period [START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF]. Stratified surveys were carried out with a 3 m beam trawl in depths from 5 to 25 m at each site. This net (20.10 -3 m stretched mesh in the codend) has been found to introduce no bias in length selectivity during surveys in September [START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF]. Depth and sediment were homogeneous for each nursery sector, in each strata [START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF]Le Pape et al, 2003b). An average of 20 hauls were made at each site with duration of 20 min and mean area swept of 4500 to 5000 m 2 per haul. All 0-group and 1group sole juveniles caught were counted and measured for total and standard length (TL and SL in cm). At each site, a subsample of 30 0-group individuals, was immediately frozen at -20 ° C, for laboratory analyses of recent growth and condition. The identification of 0 and 1group was performed using length-frequency analysis and confirmed from examination of otoliths.

Data on the chemical contamination of coastal waters

The French national network for the observation of the quality of the marine environment (RNO, French ministry of the Environment, see details and process on http://www.ifremer.fr/envlit/surveillance/rno.htm) has been collecting and analysing the whole soft tissue of 2 mollusks: mussels Mytilus edulis and oysters Crassostrea gigas since 1979, to estimate the levels of chemical concentration in coastal waters [START_REF] Claisse | Chemical contamination of the French coasts. The results of a ten-year mussel watch[END_REF]. Chemicals measured are heavy metals (Cd, Hg, Pb, Cu, and Zn), pesticides gammahexachlorocyclohexane (γ-HCH or lindane) and 4,4 DDT and its metabolites 4,4 DDD and 4,4 DDE (measurements for the three latter are on their sum: ΣDDT), the concentration of a polychlorobiphenyle PCB (CB153) and the concentration of 15 1 polycyclic aromatic hydrocarbons (PAHs). All the studied nursery sectors correspond to a sampled site investigated by this network. In addition, in the RNO monitoring program, stations are selected to be representative of their surroundings, and point sources of chemical contamination are deliberatly avoided [START_REF] Beliaeff | Comparisons of chemical concentrations in mussels and oysters form the United State and France[END_REF][START_REF] Beliaeff | Comparison of polycyclic aromatic hydrocarbons levels in mussels and oysters in France and in the United States[END_REF]. Hence, we considered that each sampled station used in this network is representative of the water contamination of the considered nursery ground. Among the 8 study sites used in the comparisons, 4 (Somme, Seine, Vilaine, Loire) are nursery areas where the mussel M. Edulis was collected and 4 (Bourgneuf, Pertuis Breton, Pertuis Antioche, Gironde) are nursery grounds from which the oyster C. gigas was taken. The measures between the 2 species are standardized and expressed in mussels species equivalent (0'Connor, 1992).

In the present study, as the RNO program do not yet provide data for the years after 2000 for all chemical compounds, we standardized the chemical data set on the years 1995 to 2000. The sampling strategy of the RNO program vary between the different chemical compounds and makes it impossible to estimate concentrations of all chemical compounds in a same period or season in the year. In addition, juvenile soles were shown to stay all year long in the nursery areas in the Eastern English Channel [START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF] and at least 6 months in the bay of Biscay [START_REF] Koutsikopoulos | Role of coastal areas in the life history of sole (Solea solea L.) in the bay of Biscay[END_REF][START_REF] Dorel | Seasonal distribution of young sole (Solea solea L.) in the nursery ground of the bay of Vilaine (Northern Bay of Biscay)[END_REF]. Hence, comparisons of chemical contamination were made using data over the whole year, which means that we did not focus on a particular season of the year.

Biological indicators

Indicators of growth Recent growth of 0-group juveniles (RG)

The recent growth index was determined by measuring the width of the peripheral daily increments of the otoliths (distance between the margin of the otolith back to the 10th ring), to estimate fish growth during the previous 10 days. Sagittal otoliths were used for the microstructure analysis. Daily increment deposition of common sole sagittal otolith was validated on larval stages by [START_REF] Lagardère | Influence of feeding conditions and temperature on the growth rate and otolith increment deposition of larval Dover sole (Solea solea (L.)). Rapport P.-v[END_REF] and on juvenile stages by Lagardère et al., (unpublished data). The use of the width of otolith daily increments is justified when a linear relationship between the size of the fish and the size of the otolith exists [START_REF] Campana | Microstructure of fish otolith[END_REF], which has been verified for 0-group sole [START_REF] Gilliers | Growth and condition of juvenile sole (Solea solea L.) as indicators of habitat quality in coastal and estuarine nurseries in the Bay of Bicay[END_REF]. The preparation and the measurements of the otoliths are detailed in [START_REF] Gilliers | Comparison of growth and condition indices of juvenile flatfish in different coastal nursery grounds[END_REF].

Length of 0-group (L0) and 1-group (L1) juveniles

Mean total length (cm) was computed at each site for each year, from the catches of 0-group and 1-group sole captured during the surveys.

Condition of 0-group juveniles (K0)

Two condition indices: Fulton's K condition index and R relative condition index, were computed on 0-group juveniles: K = 100 (W.L -3 ), where W is the body weight (mg) and L is the standard length (mm) which was used to take damages to the caudal fin rays into account. R (mg) = log Wlog Wc where W(mg) is the observed body weight and Wc (mg) is the computed body weight derived from the logged length-weight relationships of the sample [START_REF] Blackwell | Relative Weight (Wr) Status and Management Current Use in Fisheries Assessment and Management[END_REF] (i.e. the deviation of predicted weight estimated from the common logged length-weight relationship in terms of fish general condition).

Densities of 0-group (D0) and 1-group (D1) juveniles

For a given nursery ground and a given year, on each stratum, estimated density was multiplied by area size, and the total density was estimated on the weighted sum of these four strata (Pennington and Grosslein, 1977). Log-transformed densities (ind.ha -1 ), computed from stratified sampling, of 0-and 1-group individuals have been used as biological indicators.

Data analyses

Development of indicators of the chemical contamination

Comparisons between sites are based on median values because unlike means, medians are robust with regard to both outliers and concentrations below detection. These medians, based on the whole series of measures from 1995 to 2000, were first computed for each chemical (Cd, Hg, Pb, Cu, Zn, ΣDDT, lindane, PCB, PAH) to obtain a single indicator of pollution by nursery and by contaminant. These medians are considered as indicators of contamination for the study period, as data were not available to provide yearly index of contamination by sector in 2001 and 2002. As spatial variability is very significantly higher than interannual variability, this method appeared reliable to discriminate nursery sectors with regards to differences in contamination [START_REF] Beliaeff | Comparisons of chemical concentrations in mussels and oysters form the United State and France[END_REF]. Claisse and Beliaeff (2000) underlined that statistical results are pertubated by irregular sampling from one year to another and from one chemical compound to another. From a general point of view, few significant increasing or decreasing trends are pointed out in the analyses of the time series. This method appears reliable to provide integrated descriptors based on several years of measurment to compare different coastal sectors . Then, to synthesize the information, we computed indices of overall contamination of coastal waters. Principal Components Analyses (PCA) were undertaken with the contaminants. The 5 heavy metals (Cd, Hg, Pb, Cu, Zn) and the 4 organic chemicals (ΣDDT, lindane, PCB, PAH) were used as variables and the 8 nursery sectors as individuals (rows).

Analyses of growth and density indices

To analyse a standardized dataset, a single value was used per year and per nursery ground for each indicator: the mean value of L0, L1, D0 and D1, computed from the total catches of the individuals, and the mean value of K, R and RG computed from the analysed samples of 0groups (30 fish). Inter and co-relationships between the 6 bio-indicators and the 8 studied nursery grounds were investigated with Multiple Factor Analysis MFA [START_REF] Escofier | Multiple Factor Analysis (AFMULT package)[END_REF][START_REF] Suthers | Bigger? fatter? or is faster growth better? Considerations on condition in larval and juvenile coral-reef fish[END_REF]. The 6 bio-indicators were used as variables (columns), the sites were undertaken as observations (rows); and the year as group of variables (one case of this multi-table is filled with a mean value of 1 indicator for 1 nursery site on 1 year). Instead of using three PCA for each group of variables (one per year), the use of a MFA allows an exploration of the entire data set and highlights relationships between groups of variables. Overall indices of contamination of coastal waters, obtained separately on PCAs, cf 3.1.), were not taking into account in the MFA analysis but were analysed as supplementary variables.

Results

Indicators of overall contamination of coastal waters

Comparisons between annual medians for all the chemical compounds were carried out on the chemical data set using non-parametric Kruskall-Wallis tests to take into account the variability of the sample sizes (due to the irregularity of sampling). Few significant differences between years we found (p< 0.05 in the Loire estuary for Pb and Zn) and no trends were pointed out (Table 1). Hence, to sum up the chemical set including 9 types of contaminants for 8 sites, general indices of water contamination by organic and metal contaminants were computed. A first PCA (Fig. 2) has showed that, when the 9 contaminants were included all together as variables in a single analysis, the correlations between the organic and the metal compounds were too low to synthesize general indicators of contamination from the principal components, especially because of high discrepancies in spatial trends between organic and metallic contaminants between the different nursery sectors (Fig. 2, Table 2). Nevertheless, it appeared that the 4 organic contaminants were highly correlated with each other, while the 5 heavy metals were highly to moderatly correlated to each other (Table 2). Hence, two separate PCAs were led (Fig. 3, Table 3): one for heavy metals (PCA1) and a second for organic chemicals (PCA2). Two different indicators of contamination were developped: one for heavy metals and the second for organic chemicals. For heavy metals, the first principal component (PC1) explained 67.34% of the total variation. Except for Zn, heavy metals were well and significantly correlated each others (Table 2) and with the first factor of the analysis, (Table 3, Fig. 3). Thus, it was possible to use the 5 variables to synthesize contamination by heavy metals in the 8 nursery areas. Subsequently, coordinates of each site on (PC1) were used as overall index of heavy metals contamination (HM) in the the coastal study sites. Concerning organics chemicals, PC2 explained 96.62% of the total variation of the PCA (Fig. 3) and the first factor was highly correlated with the 4 contaminants (Table 3, Fig. 3). Organic contaminants were strongly and positively correlated each others (Table 2). These results clearly indicated that the organic contamination of water could be synthesized using these 4 variables Subsequently, we used the coordinates of each site on PC2 as overall index of organic chemicals contamination (OC) in the coastal study sites. Two sites were pointed out showing high levels, but different typology, of contamination in coastal waters. The Gironde estuary wass characterized by high levels of heavy metals whereas the Seine estuary was characterized by high levels of organic chemicals (Fig. 2).

Multiple Factor Analysis Results

The two first axis of the MFA allowed to explain 54.32 % of the global inertia in the data (respectively 30.18% and 24.14% of the total variation). According to this plan (Fig. 4), there was an important structure in the data with high correlation between variables inside several pools. The first result of this MFA was that temporal variability appeared to be less important than spatial variability with regards to growth and density variables (Fig. 4). Except for K and R, the position of the variables kept very steady from a year to another on this plan, indicating the good steadiness above years of the structure in variables and the difference between nursery sectors. The first axis of the MFA (F1) appeared to reflect mainly the variation of growth variables, notably the recent growth of 0-group juveniles (RG) (Fig. 4). Length of 1group (L1) and length of 0-group (L0) also mainly contributed to this axis, except for the year 2000. Densities of 1-group juveniles (D1) mainly accounted for the second axis (F2), whereas densities of 0-group juveniles (D0) contributed moderately to the 2 first two factors.

Hence, F2 could be identified as a density pattern mainly reflecting 1-group juveniles' abundances. The variables of condition (K) and (R) displayed a contribution varying between F1 and F2 among years and did not mainly contribute to one particular axis. Partial and mean observations (as mean value of indicator per site) appeared geographically structured from north to south along F1 that could be identified as a pattern of juvenile soles growth (Fig. 4). This was particularly obvious for the study sites in the bay of Biscay. Indicators of contamination, illustrative in the analysis, appeared opposed to the variables of growth and densities (Fig. 4). HM was mainly and inversely related to F1 whereas OC, was mainly related to F2 and inversely related to densities. Two sites were pointed out by the analyses: the bay of Seine and the estuary of Gironde, which are the two most contaminated areas. Common sole juveniles sampled in these two sites seemed to display lower biological performances in term of juvenile sole growth and abundance compared to the other nursery areas (Fig. 4).

Relationships between bio-indicators and environmental indicators

Biological indicators were moderately related to each other (Table 4). On the contrary, some biological indicators were well related to environmental indicators: RG and L1 were inversely related to HM, while L0 was inversely related to OC. D0 and D1 also displayed moderate negative but significant relationships with this latter indicator of water contamination.

Discussion

Reliability of indicators, differences between populations and geographical gradients

The interpretation of different indicators is complex and requires cautiousness. In the case of condition indices, as Fulton's K condition index has been criticized for assuming isometric growth and being size-dependent [START_REF] Suthers | Bigger? fatter? or is faster growth better? Considerations on condition in larval and juvenile coral-reef fish[END_REF], a second index R, potentially robust and unbiased by size effect, was computed from lenght-weight residuals. Even if they are correlated, these two morphometric indicators showed relatively different patterns. In addition, they displayed important interannual variations. Variations in condition have been related to the quality and the quantity of food [START_REF] Lambert | Can simple condition indices be used to monitor and quantify seasonal changes in the energy reserves of Atlantic cod (Gadus morhua)[END_REF] and may vary whitin weeks. Reflecting feeding conditions on the mid-term and varying upon seasons, morphometric type indices appeared not to be integrative enough to establish a relevant diagnostic of fish condition for the period of the study. In addition, 0-group juvenile soles from Eastern Channel (bay of Seine and Somme but also from other northern sites) displayed systematically higher values than individuals from the bay of Biscay (Gilliers, pers. comm.). [START_REF] Lloret | Effects of large-scale habitat variability on condition of demersal exploited fish in the north-western Mediterranean[END_REF] also demonstrated spatial -effect of latitude-and temporal variability of this type of condition indices measured on demersal fish in the north-western mediterranean. Hence, condition indices did not appear appropriate to develop standardized integrative indicators of habitat quality, in the case of this study at least. These bio-indicators may reflect differences due to stock variability or latitudinal gradients, which may mask the estimate of habitat quality. On the contrary, spatial comparisons of bio-indicators based on the growth of juvenile soles revealed a spatial heterogeneity. Unlike condition factors, the interpretation of their responses and the diagnostic of quality based on them is facilitated by their good steadiness above years. Juveniles from the Seine estuary and from the 3 southern nurseries presented the lowest growth performances; this was especially obvious in the Gironde estuary and in the Pertuis Antioche. Actually, in such a study, when differences in habitat quality are highlighted, it is necessary to determine the respective influences of variations in natural factors and humaninduced changes. In a previous study in the bay of Biscay [START_REF] Gilliers | Growth and condition of juvenile sole (Solea solea L.) as indicators of habitat quality in coastal and estuarine nurseries in the Bay of Bicay[END_REF] concluded that these differences in 0-group soles growth were not probably related to genetic heterogeneity [START_REF] Exadactylos | Population structure of the Dover sole, Solea solea L., in the Atlantic using randomly amplified polymorphic DNA (PCR-RADP) marking[END_REF], to variations in ages [START_REF] Arbault | Estimation du stock de sole (Solea vulgaris, Quensel 1806) dans le Golfe de Gascogne à partir de la production d'oeufs[END_REF], nor to temperatures between sites (Le Pape et al., 2003b). Hence, this spatial heterogeneity seems not explained by these natural factors and should be examined with regards to the same northsouth differences in chemical contamination. Nevertheless, discriminating natural or anthropogenic factors in the assessment of quality of habitats requires cautiousness and still remains difficult, as these different factors probably act conjointly.

Declining biological performances: influence of anthropogenic disturbances?

The examination of the results allowed to find a relation between the level of contamination and some indicators of growth and density. When these results were investigated thoroughly, it appeared that these relations came especially from two nursery areas: the Seine and the Gironde, where the coastal water pollution appeared to be related to low biological performances. Though, it is a large estuary characterized by an important water inflows and industrial and harbour activities, we did not find any signs of reduced biological performances in juvenile soles sampled in the nursery areas of the Loire estuary. In addition, the levels of contamination as indicated by the 2 indicators of water contamination did not reached the levels of the Gironde and the Seine estuaries. These results on Seine and Gironde estuary were not unexpected, as pollutants can impose considerable stress and impairments on the health of fishes. A growing number of studies have attempted to establish linkages between pollutants and fish health. [START_REF] Eastwood | Seasonal variation in condition and liver metal concentrations of yellow perch (Perca fluvescens) from a metal-contaminated environment[END_REF] have showed that individuals of yellow perch (Perca flavescens) from metalcontaminated environment displayed higher metallic concentrations in their tissues but also lower physiological condition and slower growth rates than those from less-contaminated environment. [START_REF] Forrester | Growth of estuarine fish is associated with the combined concentration of sediment contaminants and shows no adaptation of acclimatation to past conditions[END_REF] revealed possible association between the declining growth rates of a benthic fish (Gillichthys mirabilis) and combined concentration of multiple sediment contaminants from different estuaries. In the bay of Biscay, [START_REF] Marchand | Responses of European flounder Platichthys flesus populations to contamination in different estuaries along the Atlantic coast of France[END_REF] found declining genetic variability, probably resulting from chemical stress, of european flounder Platichthys flesus populations in contaminated estuaries of Vilaine, Loire, and Gironde compared with a northern estuary assumed to be a reference site in term of anthropogenic pollution. They also suggested that genotypic and phenotypic responses were specific of the contamination typology (metals or organic chemicals). A focus on the Seine and the Gironde sectors allowed investigating the consequences of human disturbances on the nursery function. According to RNO data between 1995-2000, these estuarine sites, that provide important nurseries for juvenile flatfishes, appeared heavily impacted with regards to water contamination. The Gironde is characterized by significant levels of trace metals (for example, cadmium concentrations in molluscs are of 27.35 mg.kg -1 versus 0.729 to 3.07 mg.kg -1 for all the other sites); whereas the Seine is characterized by significant levels of organic chemicals (PCB concentrations in molluscs are 10 times higher: 321 µg.kg -1 in Seine than in the other sites 26.20 to 55.65 µg.kg -1 ). Nevertheless, these 2 sites belong to two distinct ecosystems: the Eastern English Channel and the bay of Biscay, and contribute to two distinct stocks of sole. As differences in the biological indicators may be related to different factors from a system to another, it is necessary to consider separately these two highlighted sites to analyze the reasons of their low biological performances.

The Seine estuary

It seems unlikely that the low biological performances of juveniles caught in the Seine estuary (very low abundances, low growth performances) should result from differences in water temperature or food availability, which are the two main natural factors governing the habitat quality [START_REF] Gibson | Impact of habitat quality and quantity on the recruitment of juvenile flatfishes[END_REF]. In the Eastern English Channel, hydrological conditions, such as temperature and salinity, are assumed to be homogeneous along the coastline [START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF]. In addition, the seabed environment supports an abundant distribution of benthic fauna (i.e. potential preys; [START_REF] Desroy | Macrobenthic resources of the shallow soft-bottom sediments in the eastern Channel and southern North Sea[END_REF] and food is constantly available, unlimiting for growth of 0-group soles [START_REF] Amara | Feeding ecology and growth of 0-group flatfishes (sole, dab and plaice) on a nursery ground (Southern Bight of North Sea)[END_REF]. This suggests that lower growth performances and abundance of juvenile soles in the Seine estuary may probably due to other factors directly related to human activities such as contamination. Our results confirmed those from previous works conducted in the Seine estuary and may help to establish linkages between pollution, biological performances of fishes and habitat quality. A recent work, carried out on the same nursery grounds, has allowed to demonstrate that concentrations of organic contaminants in the liver of the young soles were ten times higher in the bay of Seine (500 ng.g -1 of 153CB) compared to the other sites (from 135 to 25 ng.g -1 of 153CB) (Loizeau, unpublished data). [START_REF] Riou | Relative contributions of different sole and plaice nurseries to the adult population in the eastern Channel: application of a combined method using generalized linear models and a geographic information system[END_REF] underlined that the bay of Seine, surprisingly displayed low amounts of juveniles sole and plaice despite a potential important carrying capacity as nursery area. Finally, Gilliers (pers.comm.) has showed that indices of condition, growth rates and lipid contents were lower for 0-group juvenile soles from the Seine estuary compared with individuals from other sites in the Eastern Channel (bay of Somme, Canche and Authie estuaries). Hence, we suggest that the Seine estuary provides nursery habitat of lower quality probably due to anthropogenic disturbances and especially pollution impact

The Gironde estuary

In term of food limitation, unlike growth variables, the condition parameter K, which has been identified as a good indicator of nutritional condition and lipid reserves [START_REF] Lambert | Can simple condition indices be used to monitor and quantify seasonal changes in the energy reserves of Atlantic cod (Gadus morhua)[END_REF], did not display differences from Loire to Gironde estuary [START_REF] Gilliers | Growth and condition of juvenile sole (Solea solea L.) as indicators of habitat quality in coastal and estuarine nurseries in the Bay of Bicay[END_REF]this study). This may suggest that nutritional conditions are equal on these nursery areas and confirmed previous results showing that juvenile soles were above the food deprivation threshold in the nursery grounds of the bay of Biscay (Gilliers et al., in press). Hence, despite low negative correlations between parameter of condition and abundances, our results did not provide evidence for density-dependant effects on juvenile sole growth in the southern bay of Biscay at the scale of this study. Nevertheless, as interannual variations of abundances and of condition indices are known to be important, cautiousness is required in the interpretation of such variables. On the other hand, as described above, the Dordogne-Garonne fluvial system discharges considerable inputs of heavy metals and notably cadmium into the Gironde estuary. The "French mussels watch program" [START_REF] Claisse | Chemical contamination of the French coasts. The results of a ten-year mussel watch[END_REF] reported cadmium concentrations in oysters that were about ten-times higher than those found in oysters from French non-industrial areas [START_REF] Boutier | Synthèse des résultats de la surveillance des micropolluants dans la matière vivante[END_REF]; Table 1). As a result, the Gironde estuary has been classified as "zone D" by the European Community, prohibiting the sale of mussels and oyster of this estuary. Despite important remediation efforts, heavy metals inputs remain high (e.g. [START_REF] Blanc | A cadmium budget for the Lot-Garonne fluvial system (France)[END_REF]cited by Audry et al., 2004). Studies have demonstrated that this contamination is not restricted to the Gironde estuary and spread towards the north, resulting in high levels of metals in the oyster of sites located in the north, as the Pertuis d'Antioche [START_REF] Boutier | Influence of the Gironde estuary outputs in cadmium concentrations in coastal waters: consequences in Marennes-Oléron bay (France)[END_REF]. Multiple studies have shown that fish living in metal-polluted environment experienced adverse effects ranging from severe tissue (liver, gill etc...) lesions [START_REF] Schwaiger | The use of histopathological indicators to evaluate contaminant related stress in fish[END_REF] to greater bioenergetics coasts [START_REF] Sherwood | Bioenergetic costs of heavy metal exposure in yellow perch (Perca flavescens): in situ estimates with a radiotracer (137Cs) technique[END_REF] that may affect the multiple levels of the biological organisation such as the whole fish community. Cadmium is one of the more toxic heavy metals [START_REF] Bryan | Pollution due to heavy metals and their compounds[END_REF] and it has been demonstrated that long-term exposure to this heavy metal reduces the growth and affects the survival of various freshwater and marine fish species [START_REF] Eaton | Metal toxicity to embryos and larvae of seven freshwater fish species-I[END_REF][START_REF] Miliou | Biochemical composition, growth, and survival of the Guppy, Poecilia reticulata, during chronic sublethal exposure to cadmium[END_REF][START_REF] Hansen | The effects of long-term exposure on the growth and survival of juvenile bull trout (Salvelinus confluentus)[END_REF]. Despite of these numerous studies that allow understanding the role played by pollution on growth and survival of fish, our ability to demonstrate such linkages between growth variables and heavy metals pollution in the bay of Biscay is still limited. At the stage of our investigations, we cannot conclude about the causes of the north-south pattern of growth of common sole juveniles soles, therefore our results could provide a possible explanation for the lower growth performances found in the Gironde estuary.

The interest of the approach

Few studies have attempted to use simultaneously a pool of bio-indicators measured on fish both at the individual (growth, size, condition) and at the population (aundances) levels to assess the quality of essential fish habitats on a mesoscale approach. Actually, several authors recommend the use of multiple indicators approach [START_REF] Suthers | Comparison of lipid, otolith and morphometric condition indices of pelagic juvenile cod (Gadus morhua) from the Canadian Atlantic[END_REF]Mc Cormick and Molony, 1993), as no single measure may provide an overall description of habitat quality. Finally, integrating the responses of young fish to a multitude of natural and man-made stressors requires building up a new category of composite indicators. As proposed by [START_REF] Neill | Ecophysiology of marine fish recruitment: a conceptual framework for understanding interannual variability[END_REF], a conceptual framework is necessary to identify the ecophysiological impacts of environmental factors. More than lethal effects, the loss of adaptative capacity may reduce the metabolic scope of fishes and thus the population size in altered habitats. Finally, if this study demonstrate that growth and density indicators can provide useful tools for the assessment of heavy anthropogenic impact and habitat quality at mesoscale, it also suggests that it would probably be pertinent to work on a more precise scale with the same methods to increase their sensivity and their usefulness, especially to avoid problems related

Naphtalene, Acenaphtene, Fluorene, Phenantrene, Anthracene, Fluoranthene, Pyrene, Benzo(a)anthracene, Chrysene, Benzo(b)fluoranthene, Benzo(k)fluoranthene, Benzo(a)pyrene, Dibenzo(a,h)anthracene, Benzo(g,h,i)perylene, Indeno(1,2,3-cd)pyrene.

to geographical gradients and to estimate eventual differences due to anthropogenic perturbations on habitat at a local scale.

Ackowledgment

This study was supported by the French Ministry for Ecology and Sustainable Development as part of the national program « ECTOPHY » and by the French national program Seine-Aval II. The authors are grateful to their colleagues and the crew of the R.V. Gwen Drez who participated to the cruise NURSE 2000NURSE , 2001NURSE , 2002 and to the surveys in the Seine estuary. The authors also want to thank the reviewers for their fruitful comments. 2000,2001,2002).

factor 1 -30.18 %