Nicolas Alibert
email: n.alibert@fr.merce.mee.com

Karine Amis Cavalec

Charlotte Langlais
email: charlotte.langlais@imt-atlantique.fr

Damien Castelain
email: d.castelain@fr.merce.mee.com

Comparison of signal predistortion schemes based on the contraction mapping for satellite communications with channel identification

Keywords: Satellite communication, predistortion, contraction mapping theorem, power amplifiers, spectral regrowth

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Comparison of signal predistortion schemes based on the contraction mapping for satellite communications with channel identification Nicolas Alibert * † , Karine Amis † , Charlotte Langlais † , Damien Castelain *

I. INTRODUCTION

The need for higher data rates over satellite communication links has pushed to develop an evolution of the DVB-S2 [START_REF]Digital Video Broadcasting (DVB); Second generation framing structure, channel codding and modulation systems for Broadcasting, Interactive Services[END_REF], the DVB-S2X [START_REF]Digital Video Broadcasting (DVB); Second generation framing structure, channel coding and modulation systems for Broadcasting, Interactive[END_REF], which introduces more spectrally-efficient constellations and sharper roll-off. However, the higher-order constellations are more sensitive to non-linear interference generated by the on-board amplifier. The compensation of the impairment resulting from the non-linearity is, then, a key point for higher satellite throughput [START_REF] Beidas | Adaptive Digital Signal Predistortion for Nonlinear Communication Systems Using Successive Methods[END_REF].

The mitigation of non-linear interference can either be done at the transmitter with predistortion [START_REF] Beidas | Adaptive Digital Signal Predistortion for Nonlinear Communication Systems Using Successive Methods[END_REF]- [START_REF] Karam | A data predistortion technique with memory for QAM radio systems[END_REF] or at the receiver with equalization [START_REF] Benedetto | Nonlinear Equalization of Digital Satellite Channels[END_REF]. In the literature, the predistortion techniques are separated into two categories, the data predistortion, which operates at symbol rate [START_REF] Deleu | Iterative Predistortion of the nonlinear satellite channel[END_REF], [START_REF] Karam | A data predistortion technique with memory for QAM radio systems[END_REF], and the signal predistortion which operates at a higher sample rate after the pulse shaping filter [START_REF] Beidas | Adaptive Digital Signal Predistortion for Nonlinear Communication Systems Using Successive Methods[END_REF]- [START_REF] Ding | A Robust Digital Baseband Predistorter Constructed Using Memory Polynomials[END_REF].

One class of signal predistortion techniques relies on the application of the contraction mapping theorem, which aims to linearize the non-linear channel with [START_REF] Nowak | Volterra filter equalization: a fixed point approach[END_REF]- [START_REF] Hotz | Linearization of time-varying nonlinear systems using a modified linear iterative method[END_REF] or without [START_REF] Kim | Compensation of nonlinear distortion using a predistorter based on the fixed point approach in OFDM systems[END_REF] memory. These techniques use an iterative optimization algorithm. The optimization error is defined from the desired signal at the non-linear system output. The objective is to converge towards the fixed-point of the associated contraction mapping.

In [START_REF] Alibert | 26ème Colloq. du Group. Rech. en Trait. du Signal des Images[END_REF], we considered satellite communications and we proposed to apply the contraction mapping theorem to develop a data-optimized signal predistortion, with an optimization error defined from the data sequence. Assuming perfect channel identification, the resulting scheme, referred to as dataoptimized signal predistortion in this paper, outperforms one of the best signal predistortion technique in satellite communications [START_REF] Beidas | Adaptive Digital Signal Predistortion for Nonlinear Communication Systems Using Successive Methods[END_REF] 1 .

However, most of these papers assume the perfect knowledge of the non-linear system model. In practice, this model has to be identified. [START_REF] Hotz | Linearization of time-varying nonlinear systems using a modified linear iterative method[END_REF] investigates the impact of modeling errors on the linearization method by considering an arbitrary erroneous Volterra model without implementing the identification process and concludes that such techniques are robust provided the condition for convergence keeps satisfied.

In this paper, we focus on the best signal predistorsion schemes in a realistic single carrier satellite communication environment with channel model identification. We first describe the linearization method of [START_REF] Nowak | Volterra filter equalization: a fixed point approach[END_REF]- [START_REF] Kim | Compensation of nonlinear distortion using a predistorter based on the fixed point approach in OFDM systems[END_REF] that leads to a signaloptimized signal predistortion suited for satellite communications. Then we present the data-optimized signal predistorsion scheme [START_REF] Alibert | 26ème Colloq. du Group. Rech. en Trait. du Signal des Images[END_REF]. In order to determine whether it is better to define the optimization error from the data sequence or from the modulated signal, we compare both schemes in terms of normalized minimum mean square error (NMSE), adjacent channel interference (ACI) and total degradation (TD). To be as close as possible to the practice, we implement an identification algorithm to obtain the non-linear model with memory and our study completes the conclusion drawn by [START_REF] Hotz | Linearization of time-varying nonlinear systems using a modified linear iterative method[END_REF]. Finally, we show the robustness of the data-based signal predistorsion scheme towards identification mismatch. The paper is organized as follows. Section II describes the system model. The signal-optimized and the data-optimized signal-predistortion techniques are described in Section III and Section IV respectively. The comparison of both schemes in terms of NMSE, ACI, TD and robustness towards non-linear model mismatch is carried out in Section V. Finally, Section VI concludes the paper.

II. SYSTEM MODEL

The article focuses on single-carrier-per-transponder scenario of a satellite communication link. This scenario allows to improve the amplifier efficiency by operating closer to the saturation [START_REF] Ugolini | Advanced techniques for spectrally efficient DVB-S2X systems[END_REF]. The main source of impairment is due to the satellite transponder which behaves as a non-linear channel with memory [START_REF] Benedetto | Modeling and Performance Evaluation of Nonlinear Satellite Links-A Volterra Series Approach[END_REF]. The non-linear channel with memory is the result of the cascade of the input multiplexer (IMUX), the non-linear high power amplifier (HPA) and the output multiplexer (OMUX). The IMUX selects the carrier of interest. The OMUX limits the spectral regrowth caused by the distortion and reduces the spillage over adjacent channels. We suppose that the signal-to-noise ratio (SNR) is sufficient on the uplink channel to be considered noise-free. On the other hand, on the downlink channel, we consider that the signal is corrupted by AWGN and ACI. We also assume that the overall impulse response h * g, where h and g are respectively the transmitter and the receiver filters, satisfies the Nyquist intersymbol interference (ISI) criterion. A block diagram of the satellite transmission model is depicted in Fig. 1.

III. SIGNAL-OPTIMIZED SIGNAL PREDISTORTION

Let us consider a non-linear system with memory modeled by the operator R{.}. The desired signal at the non-linear system output is denoted by x(t) and x(t) stands for the

Nonlinear model R + + + x(t) x(k) (t) - + + x(k+1) (t)
Fig. 3. k-th stage of the signal-optimized signal predistortion [START_REF] Nowak | Volterra filter equalization: a fixed point approach[END_REF]- [START_REF] Kim | Compensation of nonlinear distortion using a predistorter based on the fixed point approach in OFDM systems[END_REF].

predistorted signal. The purpose of linearization as described in [START_REF] Nowak | Volterra filter equalization: a fixed point approach[END_REF]- [START_REF] Kim | Compensation of nonlinear distortion using a predistorter based on the fixed point approach in OFDM systems[END_REF] is to solve the following equation:

R{x(t)} = x(t). (1)
To express the predistortion problem as a fixed-point problem, one can either inverse the linear part of the non-linear system, as it is done in [START_REF] Nowak | Volterra filter equalization: a fixed point approach[END_REF], [START_REF] Aschbacher | Iterative linearization methods suited for digital pre-distortion of power amplifiers[END_REF] or add (I -R){x(t)} on both sides of (1) as it is done in [START_REF] Hotz | Linearization of time-varying nonlinear systems using a modified linear iterative method[END_REF]. The latter solution is preferable since it avoids a computationally expensive operation of inversion and we get:

(I -R){x(t)} + x(t) = x(t), (2)
where I is the identity operator.

According to the contraction mapping theorem, if the operator T {.} = (I -R){.} + x(t) is a contraction mapping, the solution is unique and can be reached iteratively by applying the operator T , namely:

x(k+1) (t) = T {x (k) (t)}, (3)
= x(k) (t) + x(t) -R{x (k) (t)}. (4)
The condition for the operator T {.} to be a contraction mapping, when the non-linear system can be described as a Volterra model, is given in [START_REF] Nowak | Volterra filter equalization: a fixed point approach[END_REF], [START_REF] Hotz | Linearization of time-varying nonlinear systems using a modified linear iterative method[END_REF]. The iterative structure is illustrated in Fig. 3.

Let us now consider its application to satellite communications. The non-linear operator R{.} refers to the satellite transponder, which consists of the cascade of the IMUX filter, the HPA and the OMUX filter as illustrated in Fig. 2. The desired signal is the modulated signal defined by:

x(t) = n d n h(t -nT ), (5)
with h the impulse response of the transmitter filter, T the symbol duration and d n the n-th transmitted complex symbol of the symbol sequence d. This scheme aims at minimizing the error between the non-linear transponder output and the modulated signal. It thus reduces both the non-linear interference and the spectral regrowth, and so the ACI.

If the condition of contraction given in [START_REF] Nowak | Volterra filter equalization: a fixed point approach[END_REF], [START_REF] Hotz | Linearization of time-varying nonlinear systems using a modified linear iterative method[END_REF] is unsatisfied, few iterations might still improve the performance [START_REF] Hotz | Linearization of time-varying nonlinear systems using a modified linear iterative method[END_REF]. Otherwise, as in [START_REF] Kim | Compensation of nonlinear distortion using a predistorter based on the fixed point approach in OFDM systems[END_REF], a constant step-size can be introduced to ensure that T {.} is a contraction mapping. The convergence is validated numerically in Section V.

IV. DATA-OPTIMIZED SIGNAL PREDISTORTION

This section focuses on the data-optimized signal predistortion technique proposed in [START_REF] Alibert | 26ème Colloq. du Group. Rech. en Trait. du Signal des Images[END_REF]. In that case, the nonlinear channel consists of the transmitter filter, the satellite transponder and the receiver. The non-linear operator F{.} represents the discrete-time equivalent non-linear channel (cf. Fig. 2). The data-optimized signal predistortion scheme is obtained from a data predistortion scheme, which applied on the data sequence d. Let us first describe the data predistortion technique. The purpose of the data predistortion is to solve:

F{ d} = d, ( 6
)
where d is the predistorted sequence of symbols. From ( 6), we reformulate the problem as a fixed-point problem:

(I -F){ d} + d = d. (7)
This scheme minimizes the error between the discrete-time non-linear channel output and the desired data sequence. Then, here again, according to the contraction mapping theorem, if P{.} = (I -F){.} + d is a contraction, the solution is unique and can be reached iteratively using:

d(k+1) = P{ d(k) }. (8)
The condition for the operator to be a contraction mapping is the same as the one defined in Section III. Now, let us use the data predistortion scheme to define a data-optimized signal predistortion scheme as in [START_REF] Alibert | 26ème Colloq. du Group. Rech. en Trait. du Signal des Images[END_REF]. The data-based model, denoted by F, and the signal-based model, denoted by R can be linked as illustrated in Fig. 2. Denoting by g the impulse response of the low-pass receiver filter, the operator F depends on R as follows:

F{d} = [g(τ ) * R{x(τ )}] τ =t0+nT , (9)
where t 0 is the optimal sampling time instant that minimizes the distortion and * denotes the convolution. Assuming that h * g satisfies the Nyquist ISI criterion and combining (5), ( 9) and (8), we obtain:

x(k+1) (t) = x(k) (t) + n (d n -g(τ ) * R{x (k) (τ )} τ =t0+nT
)h(t -nT ). [START_REF] Deleu | Iterative Predistortion of the nonlinear satellite channel[END_REF] The resulting data-optimized signal predistortion scheme is illustrated in Fig. 4, where the error is computed from the data sequence and the discrete-time equivalent channel output.

Let us mention that R doesn't include the transmit and the receive filters contrary to F. As a consequence, compared to the original data predistortion, and in the context of realistic channel identification, the data-optimized signal predistortion scheme exhibits two advantages: first, it reduces the number of kernels to estimate and secondly, it limits the risk of identification errors. Both signal-optimized and dataoptimized signal predistortion schemes require the same nonlinear system identification (R) but differ from the update equation used in the iterative algorithm (see ( 4) and ( 10)).

V. PERFORMANCE EVALUATION

In this section, we compare the performance of the signaloptimized and the data-optimized signal predistortion, with perfect or imperfect knowledge of the non-linear channel through Monte Carlo simulations. In case of imperfect knowledge, a realistic channel identification is carried out as described in section V-A. In both cases, the algorithms are initialized with x(0) (t) = x(t).

For the simulations, the transmitter and receiver filter are square-root raised cosine (SRRC) filters with a 5% roll-off. The characteristics of the IMUX, OMUX filters, travelingwave tube amplifier (TWTA) and the 32-APSK constellation are those defined in the DVB-S2 [START_REF]Digital Video Broadcasting (DVB); Second generation framing structure, channel codding and modulation systems for Broadcasting, Interactive Services[END_REF]. The symbol rate is set to 38 MBd. The interferers are delayed and time-shifted version of the output of the OMUX filter located at 40 MHz on either sides of the carrier of interest. The interference can, then, be expressed as:

y AC (t) = Mi/2 m=-Mi/2 m =0 y(t + ∆ t,m ) • e j2πm∆ f t , (11)
where y(t) is the output of the OMUX filter, ∆ t,m is a timedelay chosen such that the interferer is not synchronized with the carrier of interest, ∆ f is the carrier spacing and M i is the (even) number of adjacent carriers. In our case, we consider only two adjacent carriers (M i = 2). An oversampling factor of 8 is used. In order to ensure the contraction condition, a real constant step-size is introduced, when needed. The stepsize reduces the amplitude of the updating term in eq.( 4) and eq.( 10), as it is done in [START_REF] Kim | Compensation of nonlinear distortion using a predistorter based on the fixed point approach in OFDM systems[END_REF]. In the simulations, the step-size is adjusted for an input back-off (IBO) of 13dB.

A. Identification

To identify the non-linear system R (composed of IMUX, HPA and OMUX), we use a memory polynomial model (MP) [START_REF] Morgan | A generalized memory polynomial model for digital predistortion of RF power amplifiers[END_REF], which is a reduced-complexity Volterra model [START_REF] Ding | A Robust Digital Baseband Predistorter Constructed Using Memory Polynomials[END_REF]. It allows practical on-the-fly implementation [START_REF] Beidas | Adaptive Digital Signal Predistortion for Nonlinear Communication Systems Using Successive Methods[END_REF]. We apply a least mean square (LMS) algorithm, as in [START_REF] Ogunfunmi | Adaptive Nonlinear System Identification[END_REF], with the step parameter set to 10 -5 and a training sequence that spans 500000 symbols. The memory polynomial is expressed as follows:

z(t) = K k=1 L l=-L a kl s(t -l)|s(t -l)| k-1 , (12)
where z(t) is the output of the model, s(t) is the input, the a kl are the polynomial coefficients of the non-linearity, K is the maximum order and L is the memory depth. As in [START_REF] Ding | A Robust Digital Baseband Predistorter Constructed Using Memory Polynomials[END_REF], only odd power terms up to the fifth order (K = 5) are considered. The memory depth is set to 2 (L = 2).

B. Figures of merit

The total degradation TD is a common measure of the quality of distortion compensation and of the efficient use of the amplifier. It depends on the difference in signal-tointerference-plus-noise ratio (SINR) for a given bit error rate (BER) between the non-linear case and the AWGN channel (without ACI), plus the output back-off (OBO). The SINR in the nonlinear case and for the AWGN channel are respectively denoted by

E b N0 N L and E b N0 AW GN
. The OBO is the difference between the maximum amplifier power output and the mean power output. The OBO is computed after the receiver filter. The TD reads:

T D = OBO + E b N 0 N L - E b N 0 AW GN [dB]. ( 13
)
The NMSE measures the in-band distortion. It is defined by:

N M SE = 10 log E n | dn -d n | 2 n |d n | 2 [dB], ( 14
)
where E is the mathematical expectation and dn is the n-th gain and phase corrected sampler output without ACI.

The spectral regrowth generated by the non-linear amplification can lead to spillage over adjacent carriers. We measure the interference at the output of the receiver filter g by the parameter denoted by ACI and equal to:

ACI = 10 log E |(y AC * g)(t)| 2 dt |(y * g)(t)| 2 dt [dB]. (15)

C. Results

The following results are obtained from to the identified non-linear channel after the training phase as described in section V-A.

The ACI performance is given in Fig. 5 for both perfect and identified non-linear system model. The signal-optimized signal predistortion scheme outperforms the data-optimized scheme up to 5.4 dB for both cases. However, whereas the data-optimized scheme exhibits similar performance in both cases, the signal-optimized scheme is more sensitive to identification mismatch (degradation of up to 3.3 dB).

Improvements might be obtained by, first, the use of a full-Volterra model instead of a memory polynomial model and, then, by increasing the order used to describe the channel. However, a higher order and/or a full-Volterra model would significantly increase the complexity. As for the NMSE, given in Fig. 6 the data-optimized scheme outperforms the signal-optimized one significantly in both cases (38 dB for the ideal case and 2.5 dB in the identified case). Both methods have converged after 10 iterations.

The total degradation TD with ACI is plotted in Fig. 7 as a function of OBO.We observe that, at their optimum point, the signal-optimized scheme performs slightly better (0.3 dB) than the data-optimized one when the non-linear channel is perfectly known. The trend is reversed in case of imperfect identification with MP model. The data-optimized scheme outperforms the signal-optimized scheme largely by 1.8 dB .

We conclude that the data-optimized signal predistortion scheme is more effective in practice. The complexities of both methods are nearly equivalent since they are mainly driven by the non-linear channel model and the number of stages of the iterative structure. The data-optimized scheme outperforms the signal-optimized one in terms of TD, NMSE and robustness towards identification mismatch. The remaining ACI can be dealt with at the receiver with an equalizer combined with a channel decoder.

VI. CONCLUSION

In this paper, we investigated a data-optimized and a signaloptimized signal predistortion schemes based on the contraction mapping theorem in the context of realistic satellite communications with channel model identification. We compared the performance in terms of NMSE, ACI, TD and robustness towards identification mismatch. The identification of the nonlinear channel with memory was done with a LMS algorithm applied on a reduced-complexity Volterra model which allows practical implementation. The complexities of both methods are nearly equivalent since they are mainly driven by the non-linear model and the number of stages. With realistic channel identification, the data-optimized scheme outperforms the signal-optimized one in terms of NMSE and TD (up to 1.8 dB). The residual ACI could be dealt with at the receiver. Thus, Data-optimized scheme -Ideal -30 ite Data-optimized scheme -MP -30 ite Signal-optimized scheme -Ideal -30 ite Signal-optimized scheme -MP -30 ite AWGN Fig. 7. Total degradation with ACI for a target BER of 10 -4 for the dataoptimized and the signal-optimized signal predistortion scheme with perfect knowledge of the channel (Ideal) or with identification (MP). the data-optimized scheme achieves a better trade-off between performance and robustness towards identification mismatch.

Fig. 4 .

 4 Fig. 4. k-th stage of the data-optimized signal predistortion.

Fig. 5 .

 5 Fig. 5. ACI at the output of the matched filter versus the OBO.

Fig. 6 .

 6 Fig.6. NMSE at the output of the matched filter for an IBO of 14 dB versus the number of stages.

In[START_REF] Beidas | Adaptive Digital Signal Predistortion for Nonlinear Communication Systems Using Successive Methods[END_REF] the author claims that his proposed scheme outperforms the wellknown indirect learning architecture described in[START_REF] Ding | A Robust Digital Baseband Predistorter Constructed Using Memory Polynomials[END_REF],[START_REF] Kang | On compensating nonlinear distortions of an OFDM system using an efficient adaptive predistorter[END_REF] and simulations support this comment.


Christine Amory-Mazaudier

Rolland Fleury

Sharafat Gadimova

Abderrahmane Touzani

Space weather, from the sun to the earth, the key role of GNSS

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

T his paper presents a study made for the Seminar on Space Weather and its effects on GNSS held in conjunction with United Nations/Nepal workshop on the applications of GNSS held in Kathmandu, 6 to 12 December 2016. . The Seminar focused on cross-cutting area, in particular resiliency, the ability to depend on space systems and the ability to respond to the impact of events such as adverse space weather.

The aim is to give an outline of the Space Weather and its effects on GNSS receivers, and this in relation to the international organizations in charge of the harmonization of the various GNSS systems.

the two main channels are: 1) The radiation channel 2) The particle channel.

Figure I.1 shows the different radiations and particles. From the top to the bottom, we have the light, the X-rays and the radio noise emissions. All these phenomena move at the speed of light (300000km / s) and reach the earth in 8 minutes.

After, there are the energetic particles, Magnetic storms and the regular solar wind. For these physical processes, the time to arrive to the Earth depends on their speed, from few 15 minutes for the energetic particles to several days for the regular solar wind.

What is Space Weather and why it is important? The role of ionosphere Solar emissions affect the terrestrial electromagnetic environment. Figure I.2 presents some types of perturbations: energetic particles cause damage to satellites and solar radiation affects aviation.

As far as this presentation is concerned, we are more interested in the GNSS signal and thus in the effects of the ionosphere on the GNSS system. The ionosphere is an ionized layer located between 50 and more than 1000 km around the earth. It is the layer of the atmosphere that most disrupts the GNSS signal.

In this layer electric currents circulate [START_REF] Richmond | Ionospheric Electrodynamics, Hanbook of Atmospheric Electrodynamics[END_REF]. These ionospheric electric currents induce telluric currents in pipeline or submarine cables and can also cause power failure of transformers.

Space weather consists to anticipate the action of solar phenomena and try to predict how these phenomena can disrupt all our new technologies [START_REF] Lilensten | Du Soleil à la Terre, Aéronomie et météorologie de l'espace[END_REF][START_REF] Knipp | Understanding Space Weather and the Physics behind it[END_REF] The Sun and regular connections between the Sun and the Earth The amplitude of the poloidal field is 10 G and the amplitude of the toroidal field (sunspots) is 3-5 kG. The poloidal magnetic field reverses every 11 years [START_REF] Li | Cyclic Reversal of Magnetic Cloud Poloidal Field[END_REF]. The toroidal magnetic The regular solar wind is a constant stream of coronal material that flows off the sun at a speed of ~300-400km/s. It consists of mostly electrons, protons and alpha particles with energies usually between 1.5 and 10 KeV. The Earth's magnetic field acts as a shield for solar wind. However, there are regions of the ionosphere that are directly connected with the interplanetary medium and this the solar wind flow.

The Earth

Earth as the sun is a moving magnetic body. In the section The Sun and regular connections between the Sun and the Earth, we have presented the regular phenomena that connect the sun and the earth, in following sections we will present the perturbations of the sun that can dramatically affect our environment.

Solar flare and solar burst

The Solar flare is a significant emission of X-radiation and the solar burst a significant emission of radio noise, see figure I.3e on the spectrum of solar radiation.

The disturbed solar wind

The solar wind is a flux of particles that regularly escape from the sun. Some events such as coronal mass ejections or fast winds associated with coronal solar holes can disrupt this solar wind The solar wind carries with it a part of the solar magnetic field which is called interplanetary magnetic field IMF. This magnetic field acts as a trigger for magnetic storms. If it is directed southward, in the opposite direction to the terrestrial magnetic field, there is reconnection of the interplanetary magnetic field and the terrestrial magnetic field [START_REF] Dungey | Interplanetary Magnetic field and the auroral zone[END_REF]. The magnetosphere is open and is completely under the influence of the solar wind.

There is a magnetic storm.

The auroral zone

As mentioned earlier, the earth's magnetic field (magnetosphere) acts as a shield and protects the earth from particles from the solar wind. However, there exists near the poles a region where the solar particles can penetrate directly, it is the polar cusp. There is also a region around the pole where the particles precipitate and create an extra ionization which is not due to solar radiation but to particles of the solar wind.

The Coronal Mass Ejection: CME

Billions of tons of coronal matter are ejected from the sun and head towards the earth. If the magnetic field transported by the CME is directed towards the south, there is a magnetic storm. In general, coronal mass ejections are preceded by solar flares and associated with interplanetary shock. The Solar Flare arrives in 8 minutes on Earth while Coronal Mass Ejection takes 1 or more days depending on its speed.

High Speed Solar Wind Stream

As we have seen previously, there is a component of the poloidal solar magnetic field which has open field lines on the interplanetary space allowing rapid solar wind to escape from these structures called coronal holes There is a maximum occurrence of fast winds during the decay and minimum phase of the sunspot cycle, so that the poloidal magnetic field grows to its maximum.

Telluric induced currents

The currents induced in the Earth by the electric currents circulating in the ionosphere strongly disturbed the Earth's environment. During strong magnetic storms, the auroral oval descends towards (March, 17, 2015). From the top to the bottom, there are the solar wind in km/s, the Bz component of the IMF (in nT) , the magnetic index Ae (in nT) which is related to the ionospheric currents in the auroral zone, the magnetic index SYM-H (in nT) related to the electric currents, in the magnetosphere [START_REF] Mayaud | The K-derived planetary indices: description and availability[END_REF]Menvielle and Berthelier, 1991;[START_REF] Amory-Mazaudier | Electric Current Systems in the Earth's Environment[END_REF], the Global TEC and the solar index F10.7cm related to the solar radiation.

At the arrival of the CME on March 17, there is a large increase of the solar wind speed associated to a southward component Bz of the IMF; these two conditions are favorable for the development of a magnetic storm. (see section: the disturbed solar wind). the VTEC maps the signature of the equatorial fountain consisting of 2 VTEC maximum at 15° North and 15° South of the magnetic equator. The impact of CME is very different depending on the sector of longitude considered. In the Asian longitude sector, there is a total disappearance of the ionosphere on 18 March. In the American longitude sector, there was a marked increase in ionization on 17 March. In the African sector, the impact is lower. At the bottom of the figure there is the H-SYM magnetic index which illustrates the variation of magnetospheric currents during the magnetic storm.

Scintillations

Ionospheric scintillation is the rapid modification of radio waves caused by small scale structures in the ionosphere.

Ionospheric scintillation is primarily an equatorial and high-latitude ionospheric phenomenon, although it can (and does) occur at lower intensity at all latitudes.

Ionospheric scintillation generally peaks in the sub-equatorial anomaly regions, located on average ~15° either side of the geomagnetic equator.

Ionospheric scintillations are one of the major problems of GNSS propagation in the equatorial zone. They are not due to solar events such as coronal mass ejections or fast winds associated with coronal solar holes, there are related to Instabilities in the ionospheric Plasma, see the book [START_REF] Kelley | the Earth Ionosphere[END_REF] on equatorial ionosphere.

Concluding remarks

In this part we have presented the dominant physical processes of the space weather, without which there is no space weather. These dominant physical processes are:

-the magnetic fields and the motions of the Sun and the Earth, -the magnetosphere, the Ionosphere, the auroral zone, -the more common solar disturbances due to extra radiations: solar flare, solar burst, -the coronal Mass Ejection and High speed solar wind related to coronal hole, at the origin of magnetic storms, -The ionospheric scintillations, related to ionospheric plasma instabilities.

But, there are many other secondary physical processes that also influence the space weather. In short the space weather is the science of the dynamic and electromagnetic interactions of two magnetic bodies in motion: the sun and the Earth.

This new science includes two aspects: 1) the physics of Sun Earth relations and 2) the effects of solar disturbances on new technologies. In this paper we will focus in the second part on the GNSS technology.

In order to make progress in space meteorology there is the need for international interdisciplinary cooperation. This is the mission of the International Space Weather Initiative (ISWI: http://www.iswi-secretariat.org).

This network promotes a synthetic training on Sun-Earth Relationships.

This training is given in schools in the different countries over the world.

This network is based on different rules:

-Distribution of scientific instruments in countries where instruments are lacking, -The training of students over the world and particularly in developing countries, -The supervision of PhD, and capacity building in Space Weather, particularly in developing countries, -Public conferences on Space Weather for public science.

Some students trained in this network defended PhD connecting the recent discoveries of the physics of the sun to the ionosphere (Ouattara, 1999;[START_REF] Zerbo | Activité solaire, vent solaire, géomagnétisme et ionosphère équatoriale[END_REF] The

  The sun has been observed for several millennia. During the Middle Age, due to the use of the first telescopes by Galileo, the scientists began a study of the sunspots. They have recorded them since about 1611. Figure I.3a shows the motion of a sunspot drawn by Scheiner, Jesuit Father Mathematician working at the University of Ingolstadt (Near Augsburg in Germany). During the Middle Age, scientists did not know what these sunspots were. It was only at the beginning of the 20th century that Hale discovered the existence of the poloidal solar magnetic field. At the top left of figure I.3b is presented the poloïdal solar magnetic field. In fact, the sun turns on itself at a different speed between the pole and the equator. About ~27 days at the equator and ~ 31 days at the poles. The differential velocity between the poles and the equator twists the lines of the poloïdal field and creates magnetic loops which are the sunspots. Figure I.3b shows the formation of a sunspot.

Figure

  Figure I.3a: Sunspot drawn by Father Scheiner

Figure

  Figure I.3c shows a solar spot observed by the SOHO satellite. Figure I.3d shows the variation of the sunspot cycle over the last 6 decades.

Figure

  Figure I.3e shows the complete spectrum of solar radiation from gamma rays to radio waves. In this figure the visible and infrared radiation reaching the ground are presented in color.

Figure

  Figure I.3f shows the solar wind, which compresses the magnetosphere (cavity of the earth's magnetic field), at the front and

  Figure I.4a shows the Earth's magnetic field, which is approximately that of a dipole. Figure I.4b presents the two main movements of our planet which are the rotation on itself and the revolution around the sun. These two movements introduce diurnal and seasonal variability to all the terrestrial phenomena. Around the earth, solar radiation, mainly Ultra, Extreme Ultra Violet and X-rays, ionize the atmosphere at altitudes ranging from about 50 km to more than 1000 km. Figure I.4c shows the process of photo ionization. The

FigureFigure

  Figure I.3d: The sunspot cycle

Figure

  Figure I.4e shows on the left the layers of the atmosphere presented on a scale of

  photo ionization in the ionosphere which affects the GNSS signal and added a transmission delay see figure I.5b.

Figure

  Figure I.4d: Lonizing radiations from Friedman, 1987

Figure

  Figure I.6a shows a satellite which is located in front of the magnetosphere and which makes it possible to know the arrival of a solar wind that can generate strong magnetic storm. Figure I.6b shows the favorable conditions for the triggering of a magnetic storm, that is to say an interplanetary magnetic field directed towards the South.

FigureFigure

  Figure I.7a shows a light circle around the pole that corresponds to the auroral zone, where the particles precipitate. It is

Figure

  Figure I.8a shows a CME seen by the SOHO satellite. One distinguishes the coronal matter ejected from the sun. Figure I.8b shows the arrival of the CME near the earth, this figure is an artistic view. If the magnetic field carried by the CME is directed southward and therefore opposite to the earth's magnetic field, there is a magnetic storm. The occurrence of CME is related to the sunspot cycle. There is much more CME at the maximum of the sunspot cycle (toroïdal component of the solar magnetic field).

Figure

  Figure I.9a shows a coronal hole observed by the SOHO satellite, this hole presents itself as a large black spot on the sun.Figure I.9b shows the lines of the

  the mid-latitudes (see figure I.10a) and as a consequence the strong auroral electric currents will induce telluric currents at the middle latitudes or even the low latitudes (figure I.10b) and produce electrical failures in the transformers and cut down the electricity (figure I.10c). This was the case during the storm of 13 March 1989

Figure

  Figure I.9a: Coronal hole

Figure

  Figure I.11a shows two large increases of the Global Electron Content (GEC) occurring after increases of the Ae magnetic index (auroral currents) and large decreases of SYM-H (magnetospheric equatorial current). These large increases o the GEC are followed by large decreases of GEC.

Figure

  Figure I.11b shows the TEC maps obtained from 200 GPS stations. We have presented these maps for the 3 sectors of longitude: Asian, African and American, for the period March 14 to April 1 st 2015. The x-axis represents the magnetic latitudes with the magnetic

Figure

  Figure I.12: Scintillation index at GPS L1 (1575.42 MHz) assuming constant local time 23.00 at all longitudes (from http://www.sws.bom.gov.au)

  websites with the data concerning this part are: ISGI http://isgi.unistra.fr/ geomagnetic_indices.php Institut Royal Météorologique de Belgique http://aeronmie.be International Association of Geomagnetism and Aeronomy IAGA https://www.ngdc.noaa.gov/IAGA/vdat/ NASA SOLAR SCIENCE http:// solarscience.msfc.nasa.gov/ NASA SOLAR DATA https://igscb.jpl. nasa.gov/igscb/data/format/rinex211.txt NOAA ftp://ftp.swpc.noaa.gov/ pub/weekly/Predict.txt OMNIWEB : http://omniweb. gsfc.nasa.gov/ Satellite ACE http://www. swpc.noaa.gov/ace Satellite SOHO http://sohowww. nascom.nasa.gov/ Site web Space Weather http:// spaceweather.com/