Vincent Choqueuse

Mohamed Benbouzid

Maximum Likelihood Frequency Estimation in Smart Grid Applications

Keywords: Frequency Estimation, Power System, Smart Grid, Maximum Likelihood Estimator, Cramér-Rao Bounds

This paper focuses on the estimation of the fundamental frequency in balanced three-phase power systems. Specifically, we propose a Maximum Likelihood Estimator (MLE) that exploits the multidimensional nature of electrical signals.

For perfectly sinusoidal signals, we show that the MLE can be expressed according to the periodogram of the instantaneous positive component. For harmonic signals, we demonstrate that the MLE can be approximated by a cumulated periodogram of the zero, positive and negative sequence components. As compared to single-phase estimators, statistical analysis and simulation results prove that the proposed estimator decreases the Mean Square Error by a factor of three, whatever the Signal to Noise Ratio (SNR) or data length. Furthermore, simulations with experimental data show that the proposed technique outperforms classical spectral estimators such as MUSIC.

I. INTRODUCTION

The electrical network has undergone profound changes during the last decades. These changes are mainly due to two factors: the integration of renewable energy sources and the emergence of new consumer usages. Despite its ecological benefit, this mutation greatly complicates the management of the electricity grid. On one hand, renewable energy sources are intermittent and diffuse that make the energy generation hardly controllable and predictable. On the other, new usages such as the charging of Electric Vehicles are large energy consumers and make difficult to maintain the balance between energy production and consumption. To solve this problem, a promising solution relies on the use of Information and Communications Technology. The future "Smart Grid" is expected to be able to monitor and optimize its structure to maintain the balance between energy production and consumption.

In Smart-Grid, the electrical signal is measured and analyzed at substations with Phasor Measurement Units (PMUs) to monitor the grid state. A PMU is a device that is able to estimate several signal parameters from the current or voltage signals, such as the phasor or fundamental frequency. Among these parameters, the fundamental frequency plays a key role. Indeed, deviation from the nominal value can indicate a mismatch between production and consumption [START_REF] Kwasinski | Signal processing in the electrification of vehicular transportation: Techniques for electric and plug-in hybrid electric vehicles on the smart grid[END_REF]. Furthermore, a large deviation can cause damage to equipment and should be detected at an early stage. For these reasons, frequency estimation is the backbone of smart grid monitoring.

Many frequency estimation techniques have been proposed [START_REF] Kay | Spectrum analysis -a modern perspective[END_REF], [START_REF] Stoica | Introduction to Spectral Analysis[END_REF] and applied to electrical signals. These include the Discrete Fourier Transform [START_REF] Begovic | Frequency tracking in power networks in the presence of harmonics[END_REF], PLL [START_REF] Karimi-Ghartemani | A nonlinear adaptive filter for online signal analysis in power systems: applications[END_REF], high resolution approaches [START_REF] Lobos | High-resolution spectrum-estimation methods for signal analysis in power systems[END_REF], [START_REF] Bracale | On some spectrum estimation methods for analysis of nonstationary signals in power systems. part i. theoretical aspects[END_REF], Least square [START_REF] Kusljevic | On LS-Based Power Frequency Estimation Algorithms[END_REF], and adaptive filtering [START_REF] Mojiri | Estimation of power system frequency using an adaptive notch filter[END_REF]. Nevertheless, these techniques are general and do not take into account the particularities of electrical signals. From a statistical point of view, these particularities offer opportunities to improve the frequency estimation. Following this idea, several authors have developed parametric estimators specifically designed for electrical signals. A Least square estimators exploiting the harmonic structure of electrical signal has been described in [START_REF] Chudamani | Real-time estimation of power system frequency using nonlinear least squares[END_REF], [START_REF] Li | Computationally efficient parameter estimation for harmonic sinusoidal signals[END_REF]. Another interesting feature of electrical signals is their multidimensional nature. Indeed, electrical signals are composed of three "phases" that can be used jointly for frequency estimation. Several techniques that exploit this property are available in the literature [START_REF] Pradhan | Power system frequency estimation using least mean square technique[END_REF]- [START_REF]Joint frequency and phasor estimation in unbalanced three-phase power systems[END_REF]. Most of them are based on Power electronic analysis tools such as the Clarke or Fortescue Transform. Despite their simplicity, these techniques have several limitations. First, these techniques assume perfect sinusoidal signals and their performance degrade drastically in the presence of harmonic components. Then, since these techniques focus on instantaneous frequency estimation, they may produce suboptimal estimators if the fundamental frequency is near constant over a period of time.

Despite this rich literature, there is no technique that jointly exploits the multidimensional and harmonic structure for frequency estimation. Furthermore, it is not clear how these particularities improve the performance of the frequency estimator. In this study, we address the fundamental frequency estimation problem for three-phase systems. Specifically, under the assumption of a balanced system, we propose a parametric frequency estimator that jointly exploits the multidimensional and harmonic structure of electrical signals. The contribution of this study is twofold: first, we derive the Maximum Likelihood Estimator (MLE) of the fundamental frequency, then we provide a statistical analysis aiming at measuring the benefit of using the multidimensional and harmonic structure. The remainder of the paper is organized as follows. Section II presents the signal model and the assumptions. Section III describes the MLE frequency estimator and Section IV provides an analysis of the Cramér-Rao Bounds. Finally, Section V reports on the performance of the proposed estimator with synthetic and experimental signals.

II. SIGNAL MODEL

In a three-phase system, voltage or current signals are composed of three components. Under balanced conditions, these components are phase-rotated from each other by 2π 3 . In the ideal case, each component is a sinusoidal signal with (normalised) angular frequency ω 0 ∈ [0, π[. In practice, electrical signals may be corrupted by harmonic content [START_REF]IEEE standard for synchrophasor measurements for power systems[END_REF]. These frequency components are introduced by large nonlinear loads [START_REF]IEEE standard for synchrophasor measurements for power systems[END_REF], [START_REF] Top | Observing the power grid: Working toward a more intelligent, efficient, and reliable smart grid with increasing user visibility[END_REF]. Using these properties, the n th sample on the m th phase (m = 0, 1, 2) can be expressed by [START_REF]IEEE Trial-Use Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Non-sinusoidal, Balanced, Or Unbalanced Conditions[END_REF] x

m [n] = L l=1 a l cos lω 0 n + ϕ l - 2mlπ 3 + b m [n]. ( 1
)
where a l and ϕ l correspond to the amplitude and initial phase of the l th harmonic component

(l = 1, 2, • • • L) and b m [n]
is the additive noise. Note that this signal model corresponds to the one described in the IEEE Standard 1459 for three-Phase nonsinusoidal balanced systems (see [START_REF]IEEE Trial-Use Standard Definitions for the Measurement of Electric Power Quantities Under Sinusoidal, Non-sinusoidal, Balanced, Or Unbalanced Conditions[END_REF]Section 3.2.3]). In this paper, the problem of interest is to estimate ω 0 from N observations of the three-phase signal. Using matrix notation, the three-phase signal can be expressed as

x = G(ω 0 )s + b (2)
where • x and b are 3N × 1 column vector which are defined respectively as

x [x 0 [0], • • • , x 0 [N -1], • • • , x 2 [0], • • • , x 2 [N -1]] T b [b 0 [0], • • • , b 0 [N -1], • • • , b 2 [0], • • • , b 2 [N -1]] T
where (.) T denotes the matrix transpose. • s is a 2L × 1 vector containing the amplitude and initial phase. This vector is defined as s

[a 1 cos(ϕ 1 ), a 1 sin(ϕ 1 ), • • • , a L cos(ϕ L ), a L sin(ϕ L )] T . • G(ω 0 ) is a 3N × 2L matrix that is defined as G(ω 0 )   G 0 (1, ω 0 ) G 0 (2, ω 0 ) • • • G 0 (L, ω 0 ) G 1 (1, ω 0 ) G 1 (2, ω 0 ) • • • G 1 (L, ω 0 ) G 2 (1, ω 0 ) G 2 (2, ω 0 ) • • • G 2 (L, ω 0 )   where G m (l, ω 0 ) [ e[a T m (l, ω 0 )], -m[a T m (l, ω 0 )]] is a N × 2 matrix and a m (l, ω 0 ) is defined as a m (l, ω 0 ) e -j 2πlm 3 × 1, e 2lω0 , • • • , e lω0(N -1)
From a statistical point of view, the goal of this study is to estimate ω 0 from x when s and b are unknown. To achieve this goal, we make the following assumptions:

• AS1) The number of components L is known.

• AS2) The signal on each phase is corrupted by an additive white gaussian noise with zero mean and covariance σ 2 , i.e. b = N (0, σ 2 I 3N ), where I 3N corresponds to the identity matrix of size 3N × 3N . • AS3) The number of samples, N , is greater than (2L + 1)/3. Note that if L is unknown, it can be estimated with information criteria techniques [START_REF] Stoica | Model-order selection: a review of information criterion rules[END_REF]. Concerning AS2), this assumption is motivated by the Central Limit Theorem.

III. MAXIMUM LIKELIHOOD ESTIMATION

In this section, we derive the Maximum Likelihood Estimator (MLE) of the fundamental frequency. Under assumption AS2), the MLE corresponds to the least squares estimator. The estimate of ω 0 and s are therefore obtained by minimizing

x -G(ω)s 2 (3)
with respect to ω and s, where . 2 corresponds to the vector norm. This nonlinear problem is a separable least squares problem. Consequently, it can be shown that the estimate of ω 0 is obtained by maximizing [25, Section 8.9]

C(ω) = x T G(ω) G T (ω)G(ω) -1 G T (ω)x (4)
In the general case, the maximization of ( 4) must be performed by a grid-search algorithm or iterative techniques. Another issue is the computation of the inverse of G T (ω)G(ω) in ( 4).

Using the expression of G(ω), this matrix can be decomposed as

G T (ω)G(ω) =      P 1,1 (ω) P 1,2 (ω) • • • P 1,L (ω) P 2,1 (ω) P 2,2 (ω) • • • P 2,L (ω) . . . . . . . . . P L,1 (ω) P L,2 (ω) • • • P L,L (ω)      (5)
where

P u,v (ω) 2 m=0 G T m (u, ω)G m (v, ω) (6)
Although P u,v (ω) has a simple form, the inverse of G T (ω)G(ω) is difficult, if not impossible, to obtain analytically. However, in some particular cases, the structure of P u,v (ω) can be simplified and the inverse of G T (ω)G(ω) derived analytically.

A. Single sinusoidal component (L = 1)

In the ideal case, the electrical signal contains only a sinusoidal component. Setting L = 1 in (5), we obtain

G T (ω)G(ω) = P 1,1 (ω) = 3N 2 I 2 . (7)
Using this result, the cost function in (4) can be expressed as

C(ω) = 2 3N G T (ω)x 2 (8)
This expression can be simplified using the definition of G(ω) and x. By introducing the complex number j 2 = -1, we obtain

C(ω) = 2 3N N -1 n=0 2 m=0 x m [n]e -j(ωn-2mπ 3 ) 2 (9)
where |.| corresponds to the complex modulus. Theorem 1: When L = 1, the MLE of the fundamental frequency is obtained by maximizing

P y1 (ω) = 1 N N -1 n=0 y 1 [n]e -jωn 2 (10)
where

y 1 [n] 2 m=0 x m [n]e 2jmπ 3
is called the (instantaneous) positive sequence component.

Theorem 1 shows that the MLE of ω is given by the highest peak of the periodogram of the positive sequence component. We can note that the three-phase MLE is closely related to the MLE proposed by Rife [START_REF] Rife | Single-tone parameter estimation from discrete observations[END_REF]. Indeed, the main difference between these two estimators is the analysed signal. Specifically, the estimator proposed by Rife is based on the analytic signal whereas our estimator uses the positive sequence component.

B. Estimation for N 1

For N 1, it can be shown that

P u,v (ω) ≈ 3N δ(u -v) 2 I 2 (11)
where δ(u) corresponds to the Kronecker delta. Using [START_REF] Li | Computationally efficient parameter estimation for harmonic sinusoidal signals[END_REF] in [START_REF] Karimi-Ghartemani | A nonlinear adaptive filter for online signal analysis in power systems: applications[END_REF], we obtain

G T (ω)G(ω) ≈ 3N 2 I 2L (12)
Using this approximation in (4) and the definition of G(ω), the cost function can be simplified as

C(ω) ≈ 2 3N L l=1 N -1 n=0 y l [n]e -jlωn 2 (13)
where

y l [n] 1 e 2jπl/3 e 4jπl/3 x[n]. The components y l [n] have a particular structure since y l+3 [n] = y l [n].
To simplify the cost function, we make use of the Fortescue transform, which is defined as

  y 0 [n] y 1 [n] y 2 [n]     1 1 1 1 e 2jπ/3
e 4jπ/3 1 e -2jπ/3 e -4jπ/3

    x 0 [n] x 1 [n] x 2 [n]   ( 14
)
where y 0 [n], y 1 [n] and y 2 [n] are called the zero, positive and negative sequence components, respectively. This transform has been introduced by Fortescue in 1918 to simplify the analysis of unbalanced polyphase systems [START_REF] Fortescue | Method of symmetrical co-ordinates applied to the solution of polyphase networks[END_REF], [START_REF] Furfari | Charles LeGeyt Fortescue and the method of symmetrical components[END_REF]. Using [START_REF] Choqueuse | Diagnosis of three-phase electrical machines using multidimensional demodulation techniques[END_REF] in [START_REF] Freijedo | A generic open-loop algorithm for three-phase grid voltage/current synchronization with particular reference to phase, frequency, and amplitude estimation[END_REF], we obtain the following theorem. Theorem 2: For N 1, the MLE of the fundamental frequency is obtained by maximizing

S(ω) = L l=1   1 N N -1 n=0 y lmod(3) [n]e -jlωn 2   (15)
where mod(.) is the modulo operator.

Theorem 2 shows that the cost function corresponds to a cumulated periodogram involving the periodogram of y 0 [n], y 1 [n] and y 2 [n]. It is interesting to note that the Fortescue transform separates the harmonic content of the three-phase signals. Indeed, for a particular harmonic order, only one sequence component contributes to the cost function. Specifically, information about the harmonics of order l = 3q, l = 3q + 1 and l = 3q + 2 (q ∈ N) are respectively carried by the zero, positive and negative sequence components.

IV. CRAMER RAO BOUND

A natural criterion to assess the performance of an estimator is the mean square error (MSE). The MSE of ω is defined as M SE[ ω] = bias 2 ( ω) + var( ω), where bias( ω) and var( ω) correspond to the bias and variance of the estimator. The variance of any unbiased estimator of the fundamental frequency, ω, is bounded by [START_REF] Kay | Fundamentals of Statistical Signal Processing: Estimation Theory[END_REF] var ( ω) ≥ CRB( ω) [START_REF] Chen | Accurate parameter estimation for unbalanced three-phase system[END_REF] where CRB( ω) corresponds to the Cramer Rao Bound of ω.

Let us define θ [a 1 , ϕ 1 , • • • , a L , ϕ L , ω] T the 2L + 1 vector containing the unknown parameters. The CRB of ω is given by

CRB( ω) = F(θ) -1 2L+1,2L+1 (17)
where F(θ) -1 is the inverse of the Fisher information matrix and [.] ij corresponds to the element located at the i th row and the j th column. As b[n] ∼ N (0, σ 2 I 3N ), the ij th element of the Fisher Information Matrix is given by [START_REF] Kay | Fundamentals of Statistical Signal Processing: Estimation Theory[END_REF] [

F(θ)] ij 1 σ 2 ∂G(ω)s ∂θ i T ∂G(ω)s ∂θ i (18)
Using the definitions of G(ω) and s, we obtain

∂G(ω)s ∂a l =   G 0 (l, ω) G 1 (l, ω) G 2 (l, ω)   cos(ϕ l ) sin(ϕ l ) (19)
∂G(ω)s ∂ϕ l =   G 0 (l, ω) G 1 (l, ω) G 2 (l, ω)   -a l sin(ϕ l ) a l cos(ϕ l ) (20)
∂G(ω)s ∂ω =   H 0 (1, ω) • • • H 0 (L, ω) H 1 (1, ω) • • • H 1 (L, ω) H 2 (1, ω) • • • H 2 (L, ω)   s (21)
where

H m (u, ω) -u m[Da T m (u, ω)] e[Da T m (u, ω)] and D = diag ([0, 1, 2, • • • , (N -1)
). In the general case, the inverse of the Fisher Information Matrix is difficult to obtain analytically. However, we show in the next subsections that analytical forms can be derived when L = 1 and N → ∞. For the sake of comparison, the Signal to Noise Ratio (SNR) is defined in the next subsections as

ρ 1 2σ 2 L l=1 a 2 l . (22)
A. Closed form expression for L = 1

For L = 1, the Fisher Information Matrix can be expressed as

F(θ) = 3 σ 2         N 2 0 0 0 a 2 1 N 2 a 2 1 2 N -1 n=0 n 0 a 2 1 2 N -1 n=0 n a 2 1 2 N -1 n=0 n 2         (23)
The CRB of ω is derived from the inverse of F(θ). After some manipulations, the CRB for sinusoidal signals, denoted CRB 1 ( ω), reduces to

CRB 1 ( ω) = 4 N (N 2 -1)ρ . ( 24
)
Equation [START_REF] Stoica | Model-order selection: a review of information criterion rules[END_REF] shows that the CRB depends on the sample length, N , and Signal to Noise Ratio, ρ. Specifically, the CRB decreases as ρ or N increases. Furthermore it shows that the CRB is highly sensitive to N since this bound decreases as 1/(N 3 ). It is interesting to compare this CRB with that obtained for single-phase systems [START_REF] Kay | Fundamentals of Statistical Signal Processing: Estimation Theory[END_REF]Example 3.14]. First, we note that the CRB expression in ( 24) is exact for all N while the expression provided in [START_REF] Kay | Fundamentals of Statistical Signal Processing: Estimation Theory[END_REF] holds asymptotically.

Next, we observe that the CRB of ω for three-phase systems is three times smaller than that obtained for single-phase systems. This result can be generalized to M -phase system and demonstrates the benefit of using the multidimensional nature of electrical signals for frequency estimation.

B. Asymptotic expression for N 1

For N 1, the Fisher Information matrix can be decomposed as follows

F(θ) = 1 σ 2         K 11 (ω) 0 • • • 0 f 1 (ω) 0 K 22 (ω) . . . . . . . . . . . . . . . . . . 0 . . . 0 • • • 0 K LL (ω) f L (ω) f T 1 (ω) f T 2 (ω) • • • f T L (ω) t(ω)         (25)
where

K uu (ω) = 3N 2 1 0 0 a 2 u (26a) f u (ω) = 3ua 2 u N 2 4 0 1 (26b) t(ω) = N 3 2 L l=1 l 2 a 2 l (26c)
Using the result on the inverse of a partitioned matrix, the asymptotic CRB, denoted CRB ∞ [ ω], can be expressed as

CRB ∞ ( ω) = 4β N 3 ρ (27)
where β ≤ 1 is defined as

β L l=1 a 2 l L l=1 l 2 a 2 l . (28)
From ( 27), we observe that the CRB depends on the signal length, SNR and parameter β. Comparing the asymptotic bound in [START_REF] Fortescue | Method of symmetrical co-ordinates applied to the solution of polyphase networks[END_REF] with that derived in [START_REF] Nehorai | Adaptive comb filtering for harmonic signal enhancement[END_REF], we observe that the CRB for three-phase systems is three times smaller than that obtained for single-phase systems. Comparing the asymptotic bound with that obtained for sinusoidal signals, we observe that CRB ∞ ( ω) ≈ βCRB 1 ( ω). As β ≤ 1, it follows that the CRB for harmonic signals is 1/β times smaller than that obtained for sinusoidal signals. This statement demonstrates the utility of using the harmonic content for frequency estimation.

V. SIMULATION RESULTS

In this section, we evaluate the performance of the proposed frequency estimators. Specifically, we focus on three estimators, namely the exact MLE in (4), the sinusoidal MLE in [START_REF] Chudamani | Real-time estimation of power system frequency using nonlinear least squares[END_REF], and the approximated MLE in [START_REF] Choqueuse | Estimation of Amplitude, Phase and Unbalance Parameters in Threephase Systems: Analytical Solutions, Efficient Implementation and Performance Analysis[END_REF]. For sake of brevity, we refer to these technique as M LE, M LE 1 , and M LE ∞ , respectively. These estimators are compared with the singlephase MLE [START_REF] Chudamani | Real-time estimation of power system frequency using nonlinear least squares[END_REF] and with the Cramer Rao Bounds reported in Section IV. For each estimator, the maximisation step is performed using the Nelder-Mead simplex algorithm [START_REF] Lagarias | Convergence properties of the nelder-mead simplex method in low dimensions[END_REF]. This algorithm is initialized at the nominal fundamental frequency, i.e. w = 2π × 50/F s rad/s, and the termination tolerance is set to 10 -8 . The frequency estimators are tested using signals modeled by (1) under different signal length, N . The performance are evaluated in terms of Mean Square Error (MSE). The MSE is estimated using K = 1000 Monte Carlo Trials by

M SE ≈ 1 K K-1 k=0 (ω 0 -ω) 2 (29)
where ω 0 is the (true) fundamental frequency and ω corresponds to the frequency estimate. In each simulation, the sampling frequency and the fundamental frequency are set to F s = 1kHz and ω 0 = 2π × (51.5)/F s rad/s, respectively.

A. Estimation for L = 1

In this subsection, we evaluate the performance for sinusoidal signals. In each simulation, parameters are fixed to L = 1, a 1 = 1, ϕ = 0.3 and SN R = 10dB. Figure 1 presents the performance of the three-phase and single-phase MLE. We note that the three-phase MLE achieves the CRB. Furthermore, we observe that the three-phase estimator outperforms the single-phase estimator, whatever the number of samples. Specifically, the former decreases the MSE by a factor of three, which is consistent with the conclusions of subsection IV-A.

B. Estimation for L ≥ 1

In this subsection, we present the performance of M LE, M LE 1 and M LE ∞ for harmonic signals with L = 4. Simulation parameters are given in Table I. Figure 2 displays the MSE versus the data-length at SN R = 10 dB. We observe that the exact and asymptotic CRBs have similar values whatever the signal length. Furthermore, among the considered estimators, we note that the exact MLE is the only one that achieves the CRB at high SNRs. As compared to single-phase and M LE 1 estimators, the exact MLE significantly decreases the MSE. Concerning the approximated MLE, M LE ∞ , we see that the performances highly depend on the signal length N . Indeed, the performances tend to those of the exact MLE for N → ∞. In addition, we observe that the MSEs are broadly similar for N ≈ 2kπ/ω (k ∈ N). This behaviour comes from the fact that the equality in [START_REF] Li | Computationally efficient parameter estimation for harmonic sinusoidal signals[END_REF] is attained for these particular values of N .

C. Experimental signals

In this subsection, the frequency estimator M LE is applied to experimental data. Experimental signals come from the DOE/EPRI National Database of Power System Events. The sampling frequency is equal to F e = 15360 Hz. The analysed signals are presented in Figures 3 and4. These signals correspond to the events 3127 and 3163. The fundamental frequency is estimated using the exact three-phase MLE estimator with L = 3. Frequency estimates obtained with the single phase MLE (L = 3) and root MUSIC are also shown for comparison.

Figure 3 displays the estimated fundamental frequencies versus N for the event 3127. We observe that the three estima- tors converge to the same value, f 0 = 59.9Hz, when N > 500.

we see that the exact MLE converges more rapidly than the single-phase MLE and root MUSIC. In particular, the exact MLE is the only estimator that provides accurate results even for a small number of samples. Specifically, this estimator converges roughly after 275 samples (≈ 1 cycle).

As shown in Figure 4, the event 3163 introduces a moderate amount of three-phase unbalance in the voltage signal. Although the proposed estimator is designed for balanced systems, we note that the single-phase and proposed estimator lead to the same frequency estimate for N > 500 samples (≈ 2 cycles). Nevertheless, the three-phase MLE exhibits extra oscillations due to the unbalanced conditions. We can note that these oscillations significantly increase the estimator's settling time. Under unbalanced conditions, it is clear that better estimates could be obtained by treating the unbalance parameters as nuisance parameters.

VI. CONCLUSIONS

In this paper, we have focused on the Maximum Likelihood estimation of the fundamental frequency in threephase balanced systems. A new estimator that jointly uses the multidimensional and harmonic structure of electrical signals has been proposed. For sinusoidal signals, this estimator is obtained by maximizing the periodogram of the positive sequence component. For harmonic signals, the estimator is obtained by maximizing a cumulated periodogram of the zero, positive and negative components. The analysis of the Cramer Rao Bound has clearly demonstrated the benefit of using the multidimensional and harmonic structure for frequency estimation. Indeed, the use of the multidimensional nature of electrical signals allows to decreases the CRB by of a factor of 3, and the use of the harmonic structure by a factor of 1/β.

Fig. 1 :

 1 Fig. 1: MSE versus signal length for sinusoidal signals (L = 1, SN R = 10dB).

Fig. 2 :

 2 Fig. 2: MSE versus signal length, N , for harmonic signals (L = 4, β = 0.5, SN R = 10dB).

  phase MLE Estimator: single phase MUSIC Estimator: MLE (b) Frequency estimation versus the number of samples N .

Fig. 3 :

 3 Fig. 3: Event 3127: Estimation of the fundamental frequency.

  phase MLE Estimator: single phase MUSIC Estimator: MLE (b) Frequency estimation versus the number of samples N .

Fig. 4 :

 4 Fig. 4: Event 3163: Estimation of the fundamental frequency.

TABLE I :

 I Simulation parameters (L = 4).

	Parameter a 1	a 2	a 3	a 4	ϕ 1	ϕ 2	ϕ 3	ϕ 4
	Value	1	0.1 0.105 0.366 0.052 0.1 0.4 0.5
	10 -2 0 10				CRB CRB ∞ Estimator: MLE Estimator: MLE 1 Estimator: MLE ∞ Estimator: single phase
	MSE
	10 -4
	10 -6 10		20	30	40	50	60	70
					N (samples)


Sylvie Mazzella

North African migration under surveillance between home country and host country

In North Africa, the "Arab Spring" made 2011 a historic year, thanks to media coverage throughout the world. 1 The major political upheavals that occurred during this period had an immediate impact on the massive movement of refugees, whether within the region or to Europe.

According to statistics provided by the International Organization for Migration (IOM) for May 2011, nearly 780,000 people fled Libya to find refuge in neighbouring countries. In Tunisia, the official figures for the same period indicate the presence of more than 380,000 refugees 2 from Libya, as a result of the armed conflict between Gaddafi"s supporters and the opponents to his regime: among them, there were not only Libyans, but also foreign refugees, mainly from Somalia, Sudan, Eritrea, Ethiopia, Iraq and the Côte d"Ivoire.

Elsewhere in the Euro-Mediterranean area, there was a considerable increase in the number of illegal migrants with nearly 25,000 arriving on the Italian coastline during the months of January and February 2011, mostly Tunisians, Libyans and Sub-Saharan Africans. This sparked a debate on a proposal for reforming the Schengen Accords, which was adopted on 7

June 2012 and which included the possibility of re-establishing temporary controls on the European Union (EU)"s internal borders in "exceptional circumstances".

The spectacular nature of the migration crisis in 2011 can undoubtedly be seen as a singular and exceptional episode. It was in fact an important, though somewhat spasmodic, element in the migration policy followed over the last twenty years between Europe and North Africa.

1 Major political events in 2011 led to the downfall of existing regimes in Tunisia, Egypt and Libya, and serious political uprisings in other Arab countries (Yemen and Syria in particular): President Z. Ben Ali went into exile on 14 January 2011, after a month of violent popular unrest that the Tunisians call the "Jasmin Revolution", led to the dismantlement of the governing RCD party and election of a constitutional convention in October 2011; President M.

To support this hypothesis, this article will review the issues involved in readmission agreements between EU Member States and North African countries as a way of controlling migration, after a discussion of dual migratory flows that are on the increase: illegal departures towards Europe and the arrival of a Sub-Saharan population in North Africa since the 1990s. In addition, it will attempt to analyse the reinforcement of migratory controls in North Africa which were set up in 2003 when the EU decided to fix its external borders through the integration of new members.

In addition to participating in the policy for cooperation over border controls and humanitarian aid, North African countries were now part of a wider -Mediterranean-wideprocess as they found themselves becoming countries of destination and transit for populations from the South. Today, as work begins on drafting new constitutions, some of these countries, such as Tunisia, are reflecting on the terms of new national legislation on the rights of refugees.

North Africa: a region of emigration and transit

Traditionally, North Africa is a region of departures for Europe. More than 4 million North Africans now live abroad (nearly 2.5 million Moroccans, 1.2 million Algerians and 800,000 Tunisians) of which 85% are in Europe.

But there have been significant changes since the 1990s. The situation in terms of migration in North Africa is marked by two major factors: higher levels of illegal migration by North Africans to Europe; and a growing number of Sub-Saharan Africans in transit for Italy, Egypt, Turkey, the Balkans, or Israel, or staying for a few years in North Africa (Bredeloup and Pliez These sub-Saharan migrants can become long-term residents [START_REF] Peraldi | D'une Afrique à l'autre[END_REF]. For many years, they have provided cheap labour for North African countries. Libya, in particular, has taken advantage of this opportunity, having seen the benefitswell before Morocco, Algeria and Tunisia which have stricter labour lawsof having a labour force that could contribute to the country"s new economic boom. Over the last four decades, Libya has regularly encouraged the migration of workers from black Africa (Sudan, Chad, Eritrea) [START_REF] Pliez | Villes du Sahara[END_REF].

There are several factors behind the arrival of Southern migrants in North Africa: the lure of a "new Europe" in 1990 which created the illusion of freedom of movement, in other words that North Africa was already part of Europe; ethnic, economic and political conflicts and natural disasters which displaced populations across the African continent; cooperation policies between North Africa and the rest of Africa, encouraged over the last 15 years by countries, including Libya, as part of an African rapprochement policy (CEN-SAD) and by new agencies such as NEPAD (New Partnership for African Development). 5 South-South migration has also developed as a result of greater access of air transport and the development Regulation of inter-regional freedom of movement in Africa was a major priority for the Economic Community of West African States (ECOWAS/CEDEAO) which, on 18 January 2008, adopted a Common ECOWAS Approach to Migration with the objective of guaranteeing freedom of movement within the region, a condition sine qua non for encouraging economic development. At the same time, in partnership with the West African Economic and Monetary Union, ECOWAS proposed the reinforcement of controls on inter-regional and inter-continental migration by creating a unique biometric , similar to the Schengen visa, for certain non-West African countries. of major roads in Africa over the last 10 years (Choplin and Lombard, 2010).

One of the results of this dual cooperation policy has been the emergence of a multifaceted sub-Saharan migration: refugees, adventure-driven migrants, sportsmen and women, traders, students in public and private higher education, diplomats and international executives, such as the African Development Bank"s 800 employees and their families now living in Tunis [START_REF] Boubakri | La Tunisie entre transit et immigration. Politiques migratoires et conditions d"accueil des migrants africains à Tunis[END_REF].

Externalization of border controls

The North African region, because it has become an area of emigration and transit, participates in many trans-border cooperation programmes since the 1990s as part of European migration policy. This policy for Euro-Mediterranean collaboration has generated a large number of agreements which are expected to stop the passage of illegal migrants: There is a massive increase in the use of new technologies for external border surveillance: detection probes for CO 2 and heart beats, thermic and infra-rouge cameras, and new generation radar for the detection of landings. This neighbourhood policy provides additional funding for public and private actors with support from the African Development Bank and the World Bank. It is based on a financial and operational convention: the European Neighbourhood and Partnership Instrument (ENPI) and one of its priorities is the Cross-border Cooperation (CBC). Between 2007 and 2013, 13 cooperation projects were signed as part of these programmes by Tunisia and Italy, with €8 million in grants. and later as part of the Union for the Mediterranean. 9 The objectives that drove the multiplication of these political cooperation institutions were ambitious: to place the question of border security at the centre of a programme for economic development and to encourage Euro-Mediterranean cooperation.

Re-admission agreements: an instrument for trans-frontier cooperation

A re-admission agreement is a legal convention by which the signatory states agree to accept the return of their nationals after their arrest as illegal migrants in another country and, in addition, the return of foreigners who are not their nationals but who transited their territory prior to entering and being arrested in the other country. These are just one of the key instruments in the EU"s policy for reducing illegal migration over the last twenty years [START_REF] Charles | Accords de réadmission et respect des Droits de l'Homme dans les pays tiers[END_REF]. In return for signing bilateral re-admission agreements, the Euro-Mediterranean countries enter into negotiations for financial and technical aid, cooperation plans and quotas for legal immigrants from countries that express a real determination to combat illegal immigration. Since the mid-1990s, we have seen an increasing number and variety of cooperation programmes as part of readmission agreements between EU Member States and North African countries.

One of the first agreements between European and North African countries was signed by Spain and Morocco in 1992 which related to the situation in which Moroccan and Sub-Saharan migrants were camped outside the towns of Ceuta and Melilla. This agreement led to the annual expulsion of a thousand migrants receiving social assistance in 1993 and 1994. 10 However, it was nearly another four years before Rabat agreed to readmit 65 illegal migrants from Sub-Saharan Africa who had transited Morocco. This long delay was used to negotiate improvements in the situation of Moroccans in Spain, together with a reduction of Morocco"s external debt. In 1998, Tunisia was the first North African country to sign a readmission and 9

The Union for the Mediterranean, created in July 2008, brings together the 27 EU Member States, the 10 countries involved in the Barcelona Process since its foundation, and Eastern European countries who are candidates for entry into the EU. Its main priorities include: civil protection, depollution of the Mediterranean, development of solar energy in the Mediterranean and the Euro-Mediterranean University. 10 L'immigration irrégulière subsaharienne à travers et vers le Maroc, ILO, 2002. The solution applied later, and still in application, is to issue expulsion orders for these migrants and allow them to cross the Moroccan border in the hope that they will then voluntarily return to their country of origin. cooperation agreement with Italy 11 which contained conditions on migration controls and patrols in territorial and international waters with the EU. This agreement focused on ensuring fair treatment for nationals legally resident in the other"s territory. It also laid down conditions for cooperation on the prevention and reduction of illegal immigration: each country was obliged to readmit its nationals when they had entered or were resident illegally on its territory, and to readmit foreigners, except nationals of the Arab Maghreb Union Members States, who were arrested as illegal migrants in the territory of either party where there was proof of their having entered directly from the territory of the other party (Ben Jemia 2005).

The Euro-Mediterranean Association Agreements 12 with EU countries also include a readmission clause. Algeria signed four of these agreements between 1994 and 1997 (with France, Germany, Spain and Italy) for the return of its illegal migrants and of foreigners who had illegally transited its territory. In 2003, Mauritania signed a re-admission agreement with Spain for the return of its nationals and of migrants from third-party countries arrested in Spain having transited through its territory. Mauritania then sends third-party nationals to its borders with Mali and Senegal (Ahmed Salem 2010;[START_REF] Bâ | Tenter l"aventure par la Mauritanie : migration transsahariennes et recompositions urbaines[END_REF].

Since 1998, Italy and France, as Europe"s southern border, were particularly active in developing cross-border cooperation with North Africa. These two countries have signed no less than 30 re-admission agreements (with arrangements for police training in emigration countries, development and cooperation plans, and annual quotas of visas with priority given to certain categories of workers) with Morocco, Tunisia, Algeria, Mauritania, Egypt and Turkey. In 2004, Italy played a key role in persuading the EU to lift the embargo on sales of arms by Libya in exchange for a convention banning chemical weapons in Libya and an agreement on its active participation in the fight against clandestine migration [START_REF] Perrin | Fin de régime et migrations en Libye. Les enseignements juridiques d"un pays en feu[END_REF].

EU readmission agreements have evolved into a system of predominantly bilateral readmission, involving various migration countries, whether rich or poor, democratic or totalitarian, stable or fragile. In recent years, cooperation over readmission has become one 11 This agreement, which has not been published, came into force on 23 September 1999, is available on http://www.stranieri.it/legislazione/italia/accordi/accordi_TUV/Ab98_tn.htm. 12 Between 1998 and 2005, the European Union negotiated Euro-Mediterranean Association Agreements with seven Southern Mediterranean countries (Algeria, Morocco, Tunisia, Israel, Lebanon, Egypt, Jordan) for the creation of structures for North-South discussions on policy and free trade. method, among others, for consolidating the framework for wider bilateral cooperation, which covers other areas of strategic (and sometimes more important) policy such as security, energy, trade and the fight against terrorism.

Making third-party countries more responsible: the limitations Cross-border controls can contribute to a situation where migrants become illegal because of loopholes in political and legal measures: for example, by restricting the number of asylum applications over the last ten years, since rejected asylum seekers now find themselves in an inextricable situation; by refusing to allow students on study visas to renew their visas because they have failed their exams; and by not clarifying or not making the political and legal arrangements required for the implementation of re-admission agreements. Various studies [START_REF] Charles | Accords de réadmission et respect des Droits de l'Homme dans les pays tiers[END_REF][START_REF] Cassarino | La politique de réadmission dans l'Union Européenne[END_REF]) emphasize that a re-admission agreement does not guarantee respect for international standards or protection of fundamental rights. The Council of Europe is now calling for negotiation of re-admission agreements only with countries that fully comply with the Declaration of Human Rights and the 1951 Geneva Convention, that establish effective procedures for asylum-seekers, and that protect the right to freedom of movement for their nationals by not introducing penalties for illegal entry and exit from their territory (Cassarino 2010, 54).

What can be done, however, about procedures for the readmission of illegal migrants between third-party countries when there are no formal conventions between them? As readmission agreements do not exist between North African countries or between North African and Sub-Saharan countries, expulsions to neighbouring countries are governed by "informal" national practices.

High tension in Tunisia

During the period 2003-2010, Tunisia followed Morocco"s example in tightening up its legislation [START_REF] Jemia | Rapport national sur les droits des travailleurs migrants (Tunisie)[END_REF]): more police controls, legislation amendments (in February 2004) requiring new passports and travel documents and heavier penalties for crimes linked to trafficking of migrants which will apply to all persons having a direct or indirect link to the crime in question. Foreign migrants who entered Tunisia illegally during this period (or who have since become illegal, in the case of students with valid visas) have told harrowing tales of their delivery to the Libyan border manu militari.

Tunisian legislation allows African foreigners to stay in the country for three months after their visa has expired. However, Ivoirians and Malians arriving without a visa, as authorized by the legislation (unlike Cameroonians, for example), later find themselves in difficulty. If they do not have a university registration or work permit, i.e. without valid papers, they are arrested as illegal migrants. In numerous interviews carried out during this period, diplomatic staff in African Embassies (Senegal, Mali, Côte d'Ivoire, Nigeria) in Tunisia expressed concern about the confused and difficult situations in which their nationals found themselves: from repeated expulsions for overstays of valid visas (three months for tourists), arrests for forged travel documents or student cards, and attempts to emigrate illegally from Tunisia.

Few migrants are able to pay for a ticket home, especially as they probably used all their savings to pay for their journey. Although the African embassies can, in some cases, repatriate them and pay the re-admission costs, most of the time they do not have the funds to offer them any assistance.

The situation is even more complicated when Africans die or are lost at sea as they must contact families and arrange for the identification and burial of bodies. Managing migration and re-admission is all the more difficult for countries with no consulate and only an honorary consul with Tunisian nationality, as is the case for Cameroon.

Creation of retention centres in 2003

In 2003, Tunisia created retention centres known as "temporary welcome centres". Today, they no longer exist but, until 2010, they served as police out-stations along the Tunisian coast for housing illegal migrants before being expulsed across the Libyan border. This was confirmed by IOM"s representative in Tunis in 2005 who was investigating the existence of these "informal" centres in order to convince, in vain, the Tunisian government to organize official expulsions in collaboration with IOM and the Tunisian Red Crescent. "There"s a centre in Tunis. They don"t hit you, you can use the telephone. You spend about 15 days minimum to a month there. You are better treated than in Europe, at least that"s what the Nigerians I met there told me. You have a good lunch, hot water, mattresses, it"s clean but once you leave … From Tunis, you go to Sousse, from Sousse to Gabès and from Gabès to Medenine. They give you food, sometimes they put you in chains. The border is at Ben Guerdane. But there are bandits there, soldiers who know that the authorities are far away. There are no officers any more, they take your money.

They leave you at the border during the night, if you run quickly, you might dodge the Libyan customs officers. In the group, there were also women, we had to leave them. I walked through the night with another group, we walked as far as Zuara, and then to Surman. Our clothes were filthy. Between Zuara and Surman, there were marshes, wire fences 5 metres high. There was a tarmacked road about 1 kilometre away but we didn"t go near it, we stayed in the fields, it wasn"t the desert, just sandy clay. In Surman, no one tells you anything. The police don"t check on you." During the interview, he also mentioned that he was thinking about returning to Tunisia before his expulsion, because he did not want to stay in Libya. Extract from an interview with Jacob, a 40 year old Mauritanian shopkeeper from Nouakchott, former Fishing Officer (Tunis, 13 June 2005). He was arrested without legal papers and imprisoned in one of these retention centres in 2003. He talked about his prison experience and expulsion to Libya.

The future of Libyan refugees in Tunisia after the Jasmin Revolution

In 2011, the situation changed: illegal migrants could no longer be sent back to the Libyan border. On the contrary, Southern Tunisia had to cope with an influx of refugees from Libya.

Because of the political crisis in 2011, Sub-Saharan migrants were even more vulnerable.

They flee Libyan work camps only to find themselves in refugee camps in Tunisia, Egypt and Algeria. Some risked their lives by boat crossings while others who remained in Libya were heavily suspected of being in the pay of Muammar Gaddafi"s militia during this period. The emergency situation in South Tunisia is managed by the Tunisian Army, the UN High Commission for Refugees (UNHCR) and various other international agencies and charities such as IOM, the International Medical Corps, Caritas Middle East and North Africa (which provides material support for Libyan refugees and foreign asylum seekers living outside the camps in Tunisia (Iraqis and Ivoirians)), and NGOs such as the International Committee of the Red Cross, the International Federation of the Red Crescent, and the Danish Refugee Council.

The Choucha camp near the Tunisian-Libyan border at Ras Jdir was set up in order to take in people fleeing Libya during the 2011 war. Between January and March 2011, the most difficult period of the Libyan conflict, the camp held as many as 20,000 people and up to 4,000 more arrived every day. Libyans were rapidly moved into local towns and were accepted by the Tunisian population, but Sub-Saharan refugees were kept in Choucha.

By April 2012, a year after the war in Libya had ended, the camp held a total of 2,905 refugees who were living in Libya before December 2011, representing twenty different nationalities: Somalis (924 persons), Sudanese (910), Eritreans (456), Iraqis (292), and refugees in Africa, there is no national legal framework on this question in Tunisia. Closing the camp is thus dependent on the provisional Tunisian government"s agreement to change existing laws on asylum and according official refugee status to people whose applications for asylum have been rejected by UNHCR in the Choucha camp.

Conclusion

Controls of migrants between the European Union and North Africa are fairly similar mutatis mutandis to those established in countries along the EU"s external borders: Southern European countries now becoming countries of destination for new waves of migrants (Italy, Spain, Portugal, Greece) and border islands (Malta and Cyprus) which are being asked to act as border guards for the EU"s borders; 13 and countries situated on the Schengen borders whose participation on migratory controls is now a major issue for the EU. We have seen that the EU has introduced a double process: externalisation of border controls, and obligations on countries of origin to take responsibility as countries of origin and as new countries of destination and/or transit.

It is possible to see the strategies of bilateral and multilateral cooperation proposed by the European Union as a way of reinforcing the imbalance between wealth and poverty by transferring the cost of migration by increasing pressure on poorer nations without any guarantees of a return on their involvement. In short, this cooperation policy could, at best, be seen as an avatar for a withdrawal on economic policy or, at worst, as a new episode of neocolonialism.

We can, on the other hand, consider that the policy on Euro-Mediterranean cooperation is the indicator of change, a new orientation for North-South relations, where Southern countries are seen as having a dissymmetric economic relationship with the EU while, as political partners in their own right and partly responsible, on condition that they negotiate compensation, for their emigrant nationals and their immigrants. In other words, we can see that some assumption of responsibility on the part of Southern countries on the way in which they 13 During an economic crisis, former countries of origin in Southern Europe (Italy, Portugal, Spain, and Greece) continue to send their unskilled labour to other European countries and further afield, with which they have links in their economic and political history, while becoming countries of destination and transit for people from Africa. Since 2004, new EU members have, to a lesser extent, followed the same pattern. The number of immigrants varies between 7% and 11% of the total population for former EU countries of destination (Germany, Belgium, the Netherlands, Austria, Great Britain, and France) and between 2% and 5% for the more recent entrants [START_REF] Ritaine | L'Europe du Sud face à l'immigration[END_REF]Sintès 2010).

introduce migration policies which, for too long, were neglected despite the economic opportunities it might offer.

Undoubtedly, these two interpretations are not mutually exclusive. It is not just a question of transferring the problem further south. Today, setting aside border controls on migrants and the emergency situation, North African countries, such as Tunisia, must ask themselves: to whom do we grant the right to asylum?

  2005; Boubakri and Mazzella 2005; Anteby 2009). There are few official statistics for these migrants in North African countries: either for reasons of deliberate policy, as officially revealed by the Tunisian National Institute of Statistics in March 2011, or because existing statistics collection methods make it impossible to obtain exact figures on migratory flows (entries and exits from the country) in this region and to distinguish between migrants who are long-term residents and those who are in transit for other countries. It should be noted that nationals from members in the Union du Monde Arabe and some Sub-Saharan countries who entered Tunisia without needing a tourist visa, as authorized by the CEN-SAD 3 Agreement, are not counted as foreign residents. Nevertheless, collective and comparative field surveys emphasize that, in recent years, sub-Saharan migration to North Africa and other countries along the south-eastern Mediterranean coast has increased for more than 10 years: Malians, Senegalese, Ivoirians, Gabonese in Tunisia and Morocco; Malians and Nigerians in Algeria; Senegalese, Malians, Gambians and Guineans in Mauritania; Sudanese and Chadians in Libya; and Sudanese, Ethiopians, Eritreans and Somalis in Egypt. 4

  5

  legislation covering sanctions against organizers and participants in illegal emigration networks, training of coastal patrol personnel, installation of new detection equipment, 6 transborder projects for increasing frontier security in return for more substantial economic and cultural cooperation projects. The Euro-Mediterranean Conference in Barcelona in November 1995 launched what is now known as the Barcelona Process and established a multilateral framework for cooperation between the EU and 12 Mediterranean countries and territories. This conference was the continuation of a first meeting held in 1990 as part of the fairly informal arrangements known as "the 5+5 Dialogue" 7 which is still active: its last summit was held in Tunisia in 2003. The Barcelona Conference led to other initiatives for cooperation under the European Neighbourhood Policy (ENP) that were later extended to cover the Southern Mediterranean, 8 6

7

  Group composed of Tunisia, Algeria, Libya, Morocco, Mauritania (North Africa) and Italy, France, Portugal, Spain and Malta (Europe).

  8

3 International organization with 28 African Member States, created on 4 February 1998 in Tripoli at a Heads of State Summit Meeting (Libya, Mali, Niger, Sudan, and Chad), with the aim of

  "guaranteeing freedom of movement by persons and capital between Member States and the freedom to live, work, acquire property and set up a business in any of the Member States".

	4	The Saharan Territories Programme, as part of a Concerted Incitation Action Espace et
	Territoires. Société, économie, cultures, langages, representations at the Ministry for Research
	(Project Leader: Olivier Pliez (CNRS, CEDEJ)), 2003-2006; the IRMC Progarmme Le Maghreb et les
	nouvelles configurations migratoires internationales: mobilité et réseaux, (Project Leader: H.
	Boubakri), 2000-2003; the FSP-IRMC Programme Etudiants étrangers au Maghreb et dans l'espace
	euro-méditerranéen (Project Leader: S. Mazzella), 2005-2009.

Ethiopians (213) (HCR 2012). Statistics show that most of the refugees are male, aged between 18 and 60 (16% are minors), heads of family and Muslim. For most of them, their applications have been accepted, or are being processed, for transfer to a foreign country, of which the five most important being: USA (800 cases accepted in 2011 and 700 being processed in 2012), Norway (500), Sweden (200), Australia (110), and the Netherlands (42).

This was the case of one Sudanese family among the 800 refugees who had been accepted for resettlement in the USA. Arriving in the Choucha camp in March 2011, the family group was composed of the couple with three young children, one having been born in the camp and the husband"s brother with his family, and had been living in Libya for more than 10 years. The two brothers were political refugees from Sudan who had worked in Libya as teachers of agronomics and economics in a high school. While waiting for their departure for the USA, they were teaching in the school set up 6 months ago in the Choucha camp. The ex-teacher of agronomics had used the waiting period in the camp to set up small vegetable patches in front of the tents marked out with plastic bottles and exposed to the wind and sand. "In Libya, I felt as if I was standing on a high wire between two buildings. I was living in an open air prison with my family. It was impossible to leave because I was afraid of being suspected of treason by the Gaddafi government and thus putting my family in danger. I was living in fear. One of my colleagues was imprisoned for treason, just because he had used a green cloth to wipe the blackboard, green being the colour of the Libyan flag. I was summoned to the police station every month to inform the officer of any changes in our situation: a move, birth of a child, a new car or television …" Today, he wants to live in a country which will guarantee him freedom of expression and movement (Interview in Choucha camp, 26 April 2012).

Today, the situation in the camp is even more difficult for the 240 persons, mainly young unmarried men from West Africa who, because they are not recognized as refugees, do not come under the UNHCR mandate. The Tunisian government and UNHCR are looking for a solution that will facilitate their departure and thus speed up its closure. The Tunisian government is keen to close the camp quickly in order to avoid its being turned into the second settlement area, after Lampedusa, for migrants shipwrecked in the Mediterranean: on 18 March 2012, 74 Somalis were saved at sea by the Tunisian army and transferred to the Choucha camp so that they could have access to humanitarian aid.

Current negotiations between UNHCR and the President of Tunisia and his Ministers for the Interior, Foreign Affairs, Justice and Human Rights focus on the adoption by the Tunisian government of legislation on the question of refugees and asylum. Although at the international level Tunisia is a signatory of the 1951 Geneva Convention on the status of refugees and the 1969 Organization of African Union (OAU) Convention on the problems of