Dr Olivier Julien

Ikhlas Selmi

Jean-Baptiste Pagot

Extension of EWF Threat Model and Associated SQM

Est, Marne la Vallée

INTRODUCTION

In 1993, the first important GNSS signal distortion due to a payload failure was observed. This type of distorted signal could be broadcast for a long time without the system raising an alert while it could generate large measurement errors for both standalone and differential users, thus their nickname Evil WaveForm (EWF). This raised two important questions among the user communities, and more particularly the civil aviation community: What kind of signal distortions due to payload failure could affect a GNSS signal in a hazardous way? How is it possible to protect a user against this threat? Civil aviation then dedicated efforts to characterize this threat and put specific protection mechanisms in place for SBAS and GBAS users. Three signal distortion types (due to payload failure), also referred as Threat Models (TM), leading to dangerous correlation function distortions were adopted in 2001 by ICAO for GPS L1 C/A [ICAO, 2006]. These TM were defined based on the satellite payload knowledge and the observation of the 1993 event:

-TM-A which is associated with a failure in the navigation data unit (NDU), the digital part of a satellite. It consists of the normal C/A code signal except that all the positive chips have a falling edge that leads or lags relative to the correct end-time for that chip (Δ). -TM-B which introduces amplitude modulation and models degradations in the analog section of a satellite. More specifically, it consists of the output from a second order system when the nominal C/A code baseband signal is the input. Two parameters are defined for this threat model: the damping factor σ and the ringing frequency fd. -TM-C which is a combination of the two first failures. This definition of these TM was associated with the need to have a monitoring mechanism in order to ensure that the occurrence of a signal distortion according to the defined TM would not affect adversely an airborne user: either the distortion is detected and the user warned in due time, or the distortion is not detected, but in this case it should not create an integrity issue. This monitoring mechanism is referred to as Signal Quality Monitoring (SQM) and is currently implemented in SBAS and GBAS ground infrastructures (in different ways).

It is well known that the current ICAO TM for GPS L1 C/A is only a model of the EWF phenomenon based on the observation of a limited number of events and that with the evolution of payload technologies and the transmission of new GNSS signals using different modulations, new EWF TM might need to be defined for new GNSS signals. This issue was already studied in [Phelts, et al, 2006;[START_REF] Fontanella | [END_REF], Pagot et al, 2015] where the investigation was turned towards an adaptation of the same types of TM (A, B and C) as the accepted GPS L1 C/A ICAO TM on new signals, but revising the range of parameters the distortions could take.

However, this approach might restrict the TM family to a set of distortions that do not encompass all potential distortions created by current payloads and signals. As a consequence, the present article aims at investigating a wider TM definition that would allow protecting the airborne user against a wider range of potential signal distortions. Obviously, assuming a wider TM also means that the SQM has to be adapted to this TM, and more likely more protective. Consequently, the second goal of this article is to look at the performance of a baseline SQM that would be adapted to the new TM. The core of the article will be oriented towards the case of Galileo E1 OS signal. Note that this investigation is also done in the frame of a future Dual Frequency Multi-Constellation (DFMC) SBAS system. This article is thus organized as follows:

 The first part of the paper will provide the foundations that are used to define the new TM.

 The second part of the paper will discuss how this new TM could be reduced (in terms of parameter range) in order to facilitate the design of the SQM and allow for an easier testing.  The third part of the paper will describe the considerations used for the proposed baseline SQM.  The fourth part will describe the testing scenarios  The fifth part will discuss results obtained with Galileo E1 OS.  For comparison purpose, the sixth part will look at the impact of the generic TM on GPS L1 C/A  Finally a conclusion on the presented results and the way forward will be provided.

DEFINITION OF THE PROPOSED GENERIC THREAT MODEL

Presentation of the Generic Threat Model and its Key Parameters

The proposed generic TM consists in defining the unfiltered correlation function distortion 𝑅 𝑑 due to a payload malfunction as the finite sum of cosine components according to the following model:

𝑅 𝑑 (𝜏) = ∑ 𝑑 𝑘 cos(2𝜋𝑓 𝑘 𝜏 + 𝜑 𝑘 ) 𝑁 𝑘=0 𝑤𝑖𝑡ℎ ∑|𝑑 𝑘 | 𝑁 𝑘=0 < 𝐷
where the key parameters of the model are:

-𝑑 𝑘 is the amplitude of the 𝑘 𝑡ℎ cosine component.

-𝑓 𝑘 is the frequency of the 𝑘 𝑡ℎ cosine component.

-𝜑 𝑘 is the phase of the 𝑘 -𝑡ℎ cosine component.

-𝑁 is the number of components constitutive of the distortion.

-𝐷 is fixed to a finite value

The idea is to try to define a generic model based on the Fourier decomposition of any distortion. As a consequence, there are different ways to express this model (with complex exponential terms, with real or complex amplitude terms, etc…). All these notations being equivalent, the one above will be used in this document. Although the proposed generic TM is expressed in the correlation domain, it can also be translated in the time domain.

The limitation of 𝐷 to a finite value is meant at making this model realistic as the distortion coming from the payload will have a finite power. This generic TM differs from the current ICAO TM for GPS L1 C/A in different ways:

-The GPS L1 C/A TM makes a priori assumptions on the shape of the distortions, while the generic model assumes that the distortion can have any shape. -The threat space of the proposed generic TM is much larger than that of the ICAO TM. In fact, the threat space of the generic TM is for now infinite, which could significantly complicate the testing of a system considering the generic TM as its TM.

A Priori Range of Parameters of the Generic TM

Range of the Frequency Components

A component with 𝑓 𝑘 = 0 is equivalent to a constant amplitude change of the whole distorted correlation function. After the correlation function normalization, this amplitude change would be totally absorbed. This is why the zero frequency component is not taken into account in the model.

The distortion can be composed of high frequency components. Nevertheless, the important criteria to take into account in the evaluation of the worst different tracking bias is the impact of a filtered (by the payload and receiver RF front-end) distortion added to a filtered correlation function. Consequently, it can be assumed that distortions' high frequencies can be removed from the TM because they will have a negligible impact after applying the RF filter. It is well known that the SBAS reference and airborne civil aviation receivers have a double-sided RF front-end filter that will not exceed 24 MHz (3-dB). It is thus reasonable to only consider frequency components of the distortion that are slightly in excess of 12 MHz. In order to take into account a potential slower attenuation of the filter amplitude response with frequency, it was decided to take a margin and to set a maximum frequency to any distortion component equal to 30 𝑀𝐻𝑧.

Range of 𝐷

One way of limiting the value of 𝐷 in the generic TM is to assess the maximum possible distortion power that could be created by the payload. This data not being readily available, it is possible to assess a rough value of 𝐷 by looking at its value if we represent the current GPS L1 C/A ICAO model as a member of the generic TM. The analysis performance showed that the maximum value of 𝐷 for the current GPS L1 C/A ICAO model is 0.13. Such a value gives an interesting order of idea for reasonably bounding 𝐷, although this is not based on direct payload information.

Conclusions

Based on the above analysis and the will to include some key parameters of the current ICAO TM for GPS L1 C/A in the proposed generic TM (in particular the power of the distortion), the initial range of values of the key parameters of the generic TM, also known as Threat Space (TS) is summarized in Table 1. The generic TM proposed above is clearly very large and it is important to make an effort to reduce it so that it can be workable. By doing so, the model will lose some of its original characteristics, which is to represent almost any type of distortion, but this is essentially for practical reasons. One way to reduce the generic TM threat space is to remove the ranges of parameters that would make the corresponding distortions easily detected by a baseline SQM. In this case, it is important to define a baseline SQM that could be representative of an SQM adapted to a future DFMC SBAS reference receiver. This is done in the next section.

PROPOSED BASELINE SQM AND PERFORMANCE ASSESSMENT

Baseline SQM and Required Performance

The SQM required performance can be derived from ICAO requirements [SARPS, 2006] or from other performance data that are available, such as [START_REF] Phelts | Signal Deformation Monitoring for Dual-Frequency WAAS[END_REF]. It can then be derived to the reference receiver-level based on the choice of a SBAS SQM architecture. Finally, it can be derived to the EWF detector level using assumptions on the type of detectors used, and the correlation between the detectors used. In the present case, a decentralized SBAS SQM architecture is assumed, where the EWF detection is performed at each SBAS reference station level, with a decision on the presence of an EWF at system level taken by the Central Processing Facility (CPF) based on majority voting of at least 4 reference stations. Based on these assumptions, and on the fact that the SBAS reference receiver and airborne receivers is expected to fulfill other requirements expressed in [ESA, 2016], Table 2 provides the key baseline reference receiver configuration. Note that Table 2 also provides the considered airborne receiver range of configurations, also known as User Design Space (UDS) [ESA, 2016]. The proposed baseline SQM has to be adapted to the reference receiver configuration. In this article, a reference receiver configuration significantly more complex than the one currently used in WAAS or EGNOS is assumed for mainly two reasons: receiver technology has significantly evolved since the design of the current SQM, and the generic TM is anticipated to require a stronger SQM. This reference receiver complexity could anyway be reduced a posteriori if it is assessed that the SQM does not need such a complex receiver.

The baseline SQM is thus based on the use of 51 correlators mapping the correlation function from -0.25 to 0.25 chips with a step of 0.01 chip between correlators. as it is expected that the proposed generic TM, due to its significantly greater UDS, would require a quite complex SQM. Only 3 types of metrics are considered for the SQM: simple ratio, difference ratio and sum ratio metrics all normalized by the prompt correlator output, as presented in [Pagot et al, 2016]. The consideration of these 3 types of metrics coupled with the availability of 51 correlators provides a total of 100 usable metrics that can be used to detect the presence of an EWF. Each metric is associated to a distortion detector that corresponds to the difference between the measured metric value and the expected metric value based on the expected nominal correlation function. A distortion detector will then flag the presence of an EWF when its value is greater than a predefined threshold. This threshold is based on a required false alarm probability and the knowledge of the detector distribution, which will be assumed Gaussian in the rest of this document. It is to be noted that a detection is declared at the reference receiver level when at least one of the distortion detectors of the baseline SQM flags an EWF.

The occurrence of an EWF entailing a differential measurement error greater than the Maximum ERRor (MERR) of 1.55m at on Galileo E1 is here considered as a threat. The choice of 1.55m is derived from the MERR value of 3.5m often found for an SBAS L1 mapped to the case of a DFMC SBAS that uses ionosphere-free measurements [START_REF] Phelts | Signal Deformation Monitoring for Dual-Frequency WAAS[END_REF]. Note that more advanced choices for the MERR have been discussed in [Shively, 1999, Schloss et al, 2002, Rife and Phelts, 2008;[START_REF] Phelts | Signal Deformation Monitoring for Dual-Frequency WAAS[END_REF] and will be taken into in later studies.

The required false alarm and missed detection probability per distortion detector to protect the user was derived from the global ICAO SQM requirement, the assumed SBAS architecture and considering the different metrics correlation.

It is finally assumed that the metrics are smoothed over 50-sec as suggested in [START_REF] Phelts | Signal Deformation Monitoring for Dual-Frequency WAAS[END_REF] to reduce the noise present at the metric (and thus detector) level. The effect of this smoothing, taking into account the presence of a worst case multipath scenario, can be represented as a reduction of the raw metric standard deviation by a factor of 1.5 [Pagot et al, 2016].

Table 3 summarizes all the key elements of the SQM configurations. Baseline SQM Performance Assessment For a given distortion detector, the requirements can be directly related to the notion of minimum detectable metric bias. This minimum detectable metric bias is also referred to as Minimum Detectable Error (MDE) or Minimum Detectable Ratio (MDR).

For the sake of notation, we will only use the notation MDE in the rest of this article.

It can be shown that for long integration duration, the noise at the output of the unsmoothed metrics can be considered Gaussian. This means that the distortion detector can be assumed to be a centered Gaussian random variable in the absence of EWF, and a non-centered Gaussian random variable in the presence of an EWF (steady-state case). As a consequence, the MDE/MDR can be expressed for a given detector as:

𝑀𝐷𝐸 = (𝐾 𝑚𝑑 + 𝐾 𝑓𝑓𝑑 )𝜎 𝑚𝑒𝑡𝑟𝑖𝑐 𝑖 ̃
where  𝐾 𝑓𝑓𝑑 is a typical fault-free detection multiplier representing a given false detection probability;  𝐾 𝑚𝑑 is a typical missed detection multiplier representing a given missed detection probability;  𝜎 𝑚𝑒𝑡𝑟𝑖𝑐 𝑖 ̃ is the standard deviation of the distortion detector, which is equal to the standard deviation of the unsmoothed metric With the false alarm and missed detection probabilities given in Table 3, the MDE for each metric can be computed as :

𝑀𝐷𝐸 𝑖 = 7.13 × 𝜎 𝑚𝑒𝑡𝑟𝑖𝑐 𝑖 ̃
From this expression, it is easy to understand that an important element to improve the EWF detection is to have a standard deviation of the metric as small as possible. It is thus important to also accurately model 𝜎 𝑚𝑒𝑡𝑟𝑖𝑐 𝑖 ̃. This can be quite tricky as the effect of the metric smoothing (if any) has to be taken into account. As provided in Table 3, the baseline SQM assumes a smoothing corresponding to a worst case reduction of the metric standard deviation by a factor of 1.5 (assuming the presence of correlated multipath). As a consequence, the computation of 𝑀𝐷𝐸 𝑖 can be revisited as:

𝑀𝐷𝐸 𝑖 = 4.75 × 𝜎 𝑚𝑒𝑡𝑟𝑖𝑐 𝑖 ̃,𝑢𝑛𝑠𝑚𝑜𝑜𝑡ℎ𝑒𝑑
where 𝜎 𝑚𝑒𝑡𝑟𝑖𝑐 𝑖 ̃,𝑢𝑛𝑠𝑚𝑜𝑜𝑡ℎ𝑒𝑑 corresponds to the raw metric standard deviation associated to a 1-sec correlation duration.

Note that the possibility to use a centralized SBAS architecture that would be based on the reference stations transmitting their correlator outputs or metrics to the CPF has also been analyzed. In this case, it can be shown that the MDE would be (taking into account 4 reference stations providing their inputs):

𝑀𝐷𝐸 𝑖 = 3.55 × 𝜎 𝑚𝑒𝑡𝑟𝑖𝑐 𝑖 ̃,𝑢𝑛𝑠𝑚𝑜𝑜𝑡ℎ𝑒𝑑
This corresponds to a reduction of the MDE by 25% compared to the considered decentralized architecture, and thus an improvement by as much of the detectability of the EWF. The considered decentralized can thus be considered as a conservative case in terms of performance (although the centralized architecture also has its drawbacks with some fine-tuning to be done).

[ Pagot et al, 2016] provides a model of 𝜎 𝑚𝑒𝑡𝑟𝑖𝑐 𝑖 ̃,𝑢𝑛𝑠𝑚𝑜𝑜𝑡ℎ𝑒𝑑 as a function of the metric assuming thermal noise only. Note that 𝜎 𝑚𝑒𝑡𝑟𝑖𝑐 𝑖 ̃,𝑢𝑛𝑠𝑚𝑜𝑜𝑡ℎ𝑒𝑑 depends upon the metric and the location of the correlators used by the metric. This model will be used in the rest of this document.

As a consequence, in a given configuration, the performance of the SQM can be assessed by looking if a given distortion makes at least one of the distortion detectors greater than its corresponding 𝑀𝐷𝐸 𝑖 . If this happens, it means that the corresponding distortion should be detected by the reference station according to the ICAO requirements. This can then be played against the whole generic TM to distinguish between distortions that can be detected according to the requirements, and the ones that cannot. Note that this approach is only considering a steady-state behavior and ignores the effect of the different filters (airborne measurement smoothing, metric smoothing) and the Time-to-Alert (TTA) requirements. It thus only provides a first idea.

SQM TEST METHODOLOGY

Description of the test methodology

Because the proposed generic TM is for now consisting of an infinite threat space, it has been decided to first assess the impact of the new generic TM on the baseline SQM through heavy simulations. This solution is only a first step meant at better understanding the capability of the baseline SQM against the generic TM since:

 the simulations would require an infinite number of iterations to cover all possible cases. This is even more pronounced with the present generic TM which requires a huge number of simulations (at least several millions) to start converging (any number of components with any frequency and any phase and any amplitude).  The simulation are associated with a specific SQM and the results obtained with a specific SQM might be different with another SQM.

In any case, the idea of these tests is to try to gather a general knowledge of the sensitivity of the different parameters that could lead to a drastic reduction of the generic TM parameter space. To do so, the simulation mechanism has to be specified. The simulation set up is represented in Figure 1. The algorithm is the following:  Generate an ideal correlation function.

 Add a distortion based on the generic TM. In the frame of the simulations, the number of components of the distortion has been limited to a maximum of 10 in order to limit the number of distortions to generate to reach stable results. This can appear small, but it was assessed to still allow for representative results.

Visualisation of Results

For each distortion tested, the maximum value of all the ratios between the distortion detectors 𝐷𝑒𝑡 𝑖 of a reference station and its associated 𝑀𝐷𝐸 𝑖 can be computed as:

𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 = max 𝑖 ( 𝐷𝑒𝑡 𝑖 𝑀𝐷𝐸 𝑖 )
𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 is thus representative of the metric that "sees" the most the tested distortion at a given reference station. As a consequence, values of 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 exceeding 1 will be representative of distortions that have been detected according to the station requirements (in terms of Pfa and Pmd). 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 can also be referred to as the detectability of a given distortion. It is then possible to associate the value of 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 to the corresponding worst case differential tracking bias. As described earlier, the value of the 𝑀𝐷𝐸 𝑖 for each metric is dependent upon the standard deviation of the metric itself (assumed Gaussian), which means:

The location of the correlator used  The C/N0 of the received signal at the reference station at the correlator output  The correlation duration  The metric smoothing process (and its associate reduction of the metric standard deviation)

The figures representing the SQM performance will thus represent for each tested distortion:

 on the x-axis the value of 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 (thus the detectability of a given distortion), and  on the y-axis the worst value of the differential tracking bias across the UDS. As a consequence, the figures will represent a cloud of points, each point corresponding to a distortion. The figure will be segmented in 4 sections according to:

 the value of 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 with respect to 1 (detection according to the ICAO requirement or not)  worst value of the differential tracking bias (above or below the MERR of 1.55m for Galileo E1 OS and GPS L1 C/A in the case of a DFMC receiver as defined in [Julien et al, 2016])

Finally, the results for the generic TM will be shown as a cloud of blue points, and it will be superimposed by a cloud of green points corresponding to the baseline SQM performance against an ICAO-like TM defined for the corresponding signal. In the case of Galileo E1C, this cloud of green points is associated to the proposed ICAO-like TM defined in [Pagot et al, 2016] for Galileo E1C.

RESULTS FOR GALILEO E1C SQM Performance for Galileo E1C

Figure 2 represents with blue circles the worst differential tracking error in the above conditions as a function of 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 for Galileo E1C over a set of 10,000,000 distortions taken from the generic TM using 1,000,000 simulated distortions per number of components present in the generated distortion. Note that this way of generating the distortions is not completely fair as:  For small numbers of components in the generated distortion, only a small number of random parameters are drawn and the generation of 1,000,000 distortions might allow to represent most of the possible combinations of the different parameters  For high numbers of distortions, the above might not be true. It is thus possible that what is visualized for high values of N is not representative of worst case scenarios, even with 1,000,000 simulated distortions There are many early observations that can be made from Figure 2:

 the generic TM clearly overbounds the ICAO-like TM  there is a large number of distortions that are undetected (according to ICAO requirements) and that are creating differential tracking error greater than a targeted MERR of 1.55m. A total of 769,470 distortions are in this case  the undetected distortions can cause large differential tracking errors. The maximum differential error for an undetected (according to ICAO requirements) distortion, also referred to as Maximum Undetected Differential Error (MUDE) is close to 8 meters, thus well above the targeted MERR of 1.55m.  for a given value of detectability 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 , the corresponding worst case differential tracking error can be very different  there seems to be a fairly simple linear relation between the worst-case differential tracking error and the corresponding value of 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 . This would indicate that a bounding is potentially possible.  There are several worst case points that appear as singular points (for instance for values of 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 around and above 1). This might be caused by the fact that the number of simulated distortions, although very high, is not sufficient to be fully representative of all the types of distortions allowed by the generic TM.

In terms of absolute performance, there are several elements that have to be mentioned to fairly analyze these first results:  The baseline SQM is in no point an optimal SQM adapted to the generic TM or the ICAO GPS L1 C/A TM. It is just a representation of a SQM based on an achievable (but complex) receiver settings for a reference station.  Some of the values taken in the simulation might seem pessimistic (effect of smoothing, worst case C/N0, SBAS SQM architecture), while some others might be optimistic (effect of multipath, knowledge of the reference nominal correlation function)

Figure 2 can globally be considered as representative of a minimum SQM performance with respect to a true implemented SQM in operational conditions. It is expected that more advanced metrics and SBAS architecture could allow for a safe detection of all the distortion. This is part of a separate study.

Figure 2 also shows that the ICAO-like TM can reach high worst case differential biases for undetected distortions with a MUDE above 3 meters. The analysis of the worst cases show that the 3 green circles located around values of 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 of 0.8 and differential tracking error of 3 meters correspond to distortions of type TM-C.

Analysis of a Reduced Generic Threat Model Parameter Space for Galileo E1C

This section focuses mostly on the understanding of the characteristics of the distortions of the generic TM that are not detected (according to the ICAO requirements) and that are creating a differential tracking bias greater than the MERR of 1.55m. As mentioned before, there is a total of 769,470 distortions that are in this case among the 10,000,000 distortions generated (7.6947%). This set of distortions will be referred to as the "problematic" set of distortions.

A dedicated analysis was made to try to understand which parameters of the generic TM are more critical, and how the TS could be simplified or reduced. Among the many analysis performed, the effect of the number of components, the occurrence rate of the frequency components, or the amplitude of the components were looked at one by one. In order to keep the size of this article reasonable, only the main conclusions of this analysis are provided here. The main conclusion is that as long as the TS allowed for a wide variety of distortions, the worst case represented in Figure 2 (the linear link between the worst-case differential error value and the 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 ) could be reached. This was observed when reducing (in a reasonable way) the number of components, the maximum value of D or the maximum value of the frequency of each component. Obviously, this worst case would occur more or less often depending upon the selected parameter range, but it would generally be reached. The understanding of this phenomena was that as long as enough distortions were simulated, there would be cases where distortions would create a significant error (for its observability). As a consequence, playing with the different parameters (by reducing them, sometimes significantly) would almost systematically end up in obtaining the same worst case shape as shown in Figure 2.

Based on the analysis, it seems that the parameter that is the easiest to reduce is the maximum frequency of the components (below 20 MHz) as it is related to the RF front-end filter. It was also seen that it is possible to strongly stimulate the SQM, at least with a much greater impact than the ICAO-like model, with:  A small number of components, typically lower than 5  A unique value of 𝐷 that would be taken as the worst case As a consequence, the range of values of the parameters of a new reduced generic TM could be as defined in Table 5.

RESULTS FOR GPS L1 C/A

For the sake of comparison, the same 10 million unfiltered correlation distortions used in the previous section were also tested assuming that they now affect the correlation function of a GPS L1 C/A receiver. It is however understood that because of the correlation process, a same distortion at the correlation level does not necessarily corresponds to the same distortion at the transmitted signal level. In this frame, the baseline SQM is assumed the same in terms of required performance, location of correlators and metrics used.

SQM Performance for GPS L1 C/A

Figure 3 (left, blue circles) represents the worst case differential tracking error for GPS L1 C/A for the proposed generic TM using the exact same 10,000,000 distortions used for the Galileo E1C SQM. Superimposed to this is the worst case differential tracking error for the current GPS L1 C/A ICAO TM (green circles). For comparison purpose, the corresponding Galileo E1C is presented in Figure 3 Figure 3 also shows that with the proposed baseline SQM, the current ICAO GPS L1 C/A TM meets the requirement of an MERR of 3.5m associated to a single frequency SBAS (all distortions generated a differential tracking bias greater than 3.5m is detected with the required performance). However, the new generic TM is far from providing this performance with a MUDE in excess of 15m. The worst case differential errors are in fact much higher than for the Galileo E1C case for the same set of distortions and the same baseline SQM. This was however expected, as the SQM performance is generally better with a sharper correlation function, as already discussed in [Pagot et al, 2016]. Generally speaking, it can be seen that the linear function bounding the worst differential tacking error as a function of FOM ̅̅̅̅̅̅ max has a slope that is about 3 times greater for GPS L1 C/A than for Galileo E1 OS. This factor 3 also corresponds to the ratio between the BOC(1,1) and BPSK(1) autocorrelation slopes.

Impact of the "Problematic" Set of Galileo E1C Distortions on GPS L1 C/A SQM

Figure 4 represents the same figure as Figure 3, except that the 769,470 distortions corresponding to the "problematic" set of distortions of Galileo E1C (see earlier section) are now highlighted in red. It can be seen that:  many Galileo E1C "problematic" distortions can be easily detected on GPS L1 C/A  the Galileo E1C "problematic" distortions create worst case differential errors above 1.55m for Galileo E1C. It seems that this property is almost always preserve for GPS L1 C/A.  the Galileo E1C "problematic" distortions do not represent well the case of low detection/low worst case differential error for GPS L1 C/A. The set of GPS L1 C/A problematic distortions would thus need to be defined separately from the one for Galileo E1 OS.

Figure 4 : Worst differential tracking error as a function of the the 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 at the Reference Station for GPS L1 C/A highlighting the Galileo E1C problematic distortions

Specific distortions were analyzed in the GPS L1 C/A and Galileo E1C case to understand this behavior. To do so, for a common correlation distortion, the impact of that distortion on the GPS L1 C/A and Galileo E1 OS correlation function and on the ratio metrics were looked at. An example is presented in Figure 5 and Figure 6 for a distortion with 4 components creating a worst case differential error of 2.99m on Galileo E1C (for a 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 of 0.51) and 8.93m on GPS L1 C/A (for a 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 of 0.91). It can be seen that: o the effect of the same distortion is much more obvious on the GPS L1 C/A correlation function, due to its lower slope. This is the reason for resulting, in general, in a higher differential range error. o the MDE for the same metrics are much lower for GPS L1 C/A than for Galileo E1C. This is due to the fact that the correlation between close correlators is greater in the case of GPS L1 C/A (the correlation between 2 correlators separated by x chips is more or less the value of the correlation function at x chips). This explains a better detection capability of GPS L1 C/A SQM over Galileo E1C for a given distortion. To summarize, a same distortion will be generally easier to detect on GPS L1 C/A, however, it will generally create a larger worst case differential error (not that these are general rule of thumbs that might not systematically apply, for instance in the case where the worst user filter is not the same on the GPS L1 C/A and Galileo E1 OS). This thus explains Figure 4.

POSSIBLE REDUCTION OF THE GENERIC TM

As discussed previously, the drawback of the generic TM is that its threat space is infinite and does not provide a simple mean for testing. As a consequence, it would be important to find a way to drastically reduce its threat space, while still protecting the user against errors not represented by the current ICAO-like TM. This is the objective of this section.

Initial Reduction of the Threat Space of Each Key Parameter

It has been seen that the generic TM entails fairly large differential tracking errors compared to the ICAO-like TM, whatever the detectability of the distortion (according to the baseline SQM). This was expected as the number and nature of the distortions that are part of the generic TM are much greater than those of the ICAO-like TM. Even with a strong reduction of the threat space proposed in Table 5, the threat space of the generic TM remains extremely large. This is due to the fact that each component relies on 3 random variables (amplitude, phase and frequency). As a consequence, two drastic means for reducing the generic TM threat space are investigated hereafter.

Drastic Reduction of the Threat Space of Each Key Parameter

To further reduce the number of possible distortions to test, two decisions were made: to only take into considerations distortions with 3 components, and to roughly sample the parameter space, as shown in Table 6. The sampling of the parameters has been chosen only on the basis that it leads to a reasonably small number of distortions. As a consequence, although the sampling is very rough, the total number of distortions that can be generated based on Table 6 is equal to 13,824,000. This is higher than the 10 million distortions used before, however, it now span the entire threat space. The generic TM with the drastically reduced threat space (all 13,824,000 distortions) has been tested for Galileo E1C with the baseline SQM. The result is presented in Figure 7 (Left). For comparison purpose, the figure obtained with the 10,000,000 distortions used until now is provided in Figure 7 (Right). It can be seen that even with the drastically reduced threat space, the actual worst case differential tracking error for the same 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 is fairly similar to the original 10 million distortions. It can thus be noted that the MUDE is on the same order. It can also be noted that the generic TM with the drastically reduced threat space creates smaller differential tracking errors for low values of 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 . As a conclusion, although this drastic reduction appears very rough, it still allow to have a series of distortions that create difficulties for the SQM. Its drawback however is that:  it only represents a type of distortion (only 3 components), and is thus fairly away from the original intent of the generic TM, which is to represent a large range of potential distortions,  the TS is still quite large (although a"problematic" subset could be extracted)

Selection of a Finite Set of Distortions

Another approach to reduce the number of distortions from the generic TM to test is to select a number of distortions within the Galileo E1C "problematic" set of distortions. It is possible to extract a finite set of distortions that have different properties such as: easy to difficult detectability, small to large worst case differential errors, variety of number of components and frequencies. Based on the set of 769,470 problematic distortion for Galileo E1C, it should thus be easy to define a way to do that so that the characteristics of the distortion set are diverse (to avoid a set that is too dependent upon the SQM used to select the set). One way of reducing the set of problematic distortions was to select specific distortions that had specific properties, in particular, the property of testing the limits of the SQM. The goal of this section is to investigate this possibility.

Let us assume, as an example, that the set of distortions of interest would be common to all signals in the L1 band, meaning GPS L1 C/A and Galileo E1C signal. This means that it would be a common set that would be used to test the GPS L1 C/A and Galileo E1 OS SQM. As it was seen earlier, the worst distortions for GPS L1 C/A are not necessarily the worst distortions for Galileo E1 OS, and vice-versa. As a consequence, a specific mean of selection of a set of 1000 distortions (which seems like a reasonable number for testing purposes) has been put in place:

 Isolate the common undetected (according to ICAO requirements) distortions for both GPS L1 and Galileo E1 signals.

 Extract 1001 distortions based on at least one of the following criterions: o The induced differential error on GPS L1 is close to the Galileo E1c one (maximum difference of 1m) o The highest metric to MDE ratios on GPS L1 and Galileo E1c are close (with 0.02 maximum difference) o The highest metric to MDE ratios is higher than 0.99 for GPS L1 and Galileo E1c o Few additional distortions with less restrictive criterion have been add to cover the whole undetected space. It can be seen that the selected distortions do not necessarily create high worst case differential errors on Galileo E1C, but can be hard to detect. These same distortions generally create higher worst case differential error, and are also closer to detection. This is in line with the description of the effect of a same distortion on GPS L1 C/A and Galileo E1C given earlier.

Figure 8. Selected set of distortions and Baseline SQM Performance

Figure 9 represents the distribution of the number of components and the distribution of the frequency of these components in the selected set of 1001 distortions. It can be seen that all numbers of components are well represented with an emphasis on the once with a large number of components, which seems normal as they have more degrees of freedom to create "complicated" distortions. It can also be seen that all frequency components are fairly uniformly distributed. As a consequence, this distortion set seems to represent a fairly diverse set of distortions. Finally, it is important to understand that the set of 1001 selected distortions, although fairly diverse, has its roots in the weakness of the SQM used to define the problematic distortions. As a consequence, it is important to test a wider set of distortions (potentially the whole 10,000,000 distortions) with more advanced SQM before really deciding if this selected set is of interest. Finally, this selected set of 1001 distortions could be used together with the ICAO-like model for testing purposes.

CONCLUSIONS AND WAY FORWARD

Conclusions

The objective of this paper was to analyze a possible new TM that could allow capturing some existing uncertainties regarding the current types of TM used by ICAO for GPS L1 C/A. Because the types of payload failure and their effects on the transmitted signal are very hard to predict, and difficult to observe as they are such rare events, the starting point was then to define a broad generic TM. This broad generic TM was then reduced essentially by taking into account some receiver considerations (maximum frequency), payload considerations (maximum power of the distortion) and its effect on a baseline SQM assumed to be achievable for future DFMC SBAS reference stations, and by trying to have a reasonable size of the TM. In particular, sections of the TM that could be detected by the baseline SQM were considered as not necessary. The TM reduction methodology thus has to be understood as a first step, since it is for now dependent upon the choice of the baseline SQM.

The investigated generic TM and its reduced versions were seen to create larger differential tracking errors than the current GPS L1 C/A ICAO TM, or than the proposed [Pagot et al, 2016] ICAO-like Galileo E1C TM, thus confirming that they represent distortions that can be more harmful than the current GPS L1 C/A ICAO TM. Such type of generic model could then be used:

 As a TM for Galileo E1 OS signal or any other new signal used in DFMC SBAS or GBAS  To test an SBAS SQM function without being part of the ICAO TM

The analysis showed that some SQM optimization is still necessary to make the SQM fully adapted to protect the airborne user. This is not the case with the baseline SQM. However, to do so a certain number of further studies have to be performed and are listed in the next sub-section.

Way Forward and On-Going Tasks

The way forward will consist in several aspects:  Consolidation of the value of the MERR for DFMC SBAS, most notably by using the concept of time-varying MERR [Rife and Phelts (2011), [START_REF] Phelts | Signal Deformation Monitoring for Dual-Frequency WAAS[END_REF]] that also includes the notion of convergence time of the smoothing process after the occurrence of an EWF and the notion of TTA. This will have an impact on the way to better select the set of distortions that could be part of the final TM.  Improve the metric standard deviation model by analysis a set of real data coming from a reference station. This is necessary to improve the assessment of the SQM performance. This will also allow to better assess the impact of the metric smoothing process in presence of multipath.  Think about an SBAS SQM architecture that would allow to better detect EWF, such as the centralized architecture discussed in the article  Improve the SQM performance by finding new metrics with better performance. It was for instance observed that o metrics looking at the slope of the distortion, or metrics made out of a linear combination of simple ratio metrics could be interesting. o metrics based on PRN chip observation seem to be quite promising at presented in [Thevenon et al, 2014;[START_REF] Phelts | Signal Deformation Monitoring for Dual-Frequency WAAS[END_REF].  Rationalize the SQM. This might sounds contradictory with the above bullet, but it was noted that over the 100 metrics used by the baseline SQM, some were only redundant, or at least not as critical as others. This would also be very important to make the SQM less complex.

NOTE

This paper reflects on-going R&D of a potential approach for EWF-monitoring in SBAS. This paper should not be understood as a consolidated approach for EWF-monitoring in EGNOS.

  Figure 1. Different Tracking Bias Estimation Simulation Set UpThe different airborne/reference user configurations used during the simulations are provided in Table4(they are in line with the UDS described earlier).

Figure 2 -

 2 Figure 2 -Worst differential tracking error as a function of the 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 at the Reference Station for Galileo E1C

  (right). It can be seen that the proposed generic TM significantly overbounds the current ICAO TM for GPS L1 C/A. The generic model thus integrates distortions that can create much worse situations than the current ICAO TM for GPS L1 C/A.

Figure 3 .

 3 Figure 3. Worst differential tracking error as a function of the 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 at the Reference Station for GPS L1 C/A (Left) and Galileo (Right)

Figure 5 .Figure 6 .

 56 Figure 5. Distorted correlation function at reference and user receiver for a distortion (Left: GPS L1 C/A, Right: Galileo E1C)

Figure 7 .

 7 Figure 7. Worst differential tracking error as a function of the 𝐹𝑂𝑀 ̅̅̅̅̅̅̅ 𝑚𝑎𝑥 at the Reference Station for Galileo E1C with the Drastically Reduced Threat Space (Left) and the Distortion Set Used Until Now (Right)

  The 1001 selected distortions and the associated SQM performance for GPS L1 C/A and Galileo E1 OS are represented in Figure 8. The figure reads as follows: o The red circles represent all the generic TM distortions that are in the area of interested on GPS L1 C/A o The black crosses represent the selection distortions on GPS L1 C/A o The red circles represent all the generic TM distortions that are in the area of interested on Galileo E1C o The black crosses represent the selection distortions on Galileo E1C

Figure 9 .

 9 Figure 9. Distribution of the Number of Components (Left) and Frequency (Right) for the Selected Set of Distortions

Table 1 .

 1 Threat Space associated to the proposed generic TM

	𝑵	𝑫	𝝋 𝒌 (rad)	𝒇 𝒌 (MHz)
	[0 ; +∞]	[0; at least 0.13]	[0 ; 2𝜋]	]0 ; 30]

Table 2 -Receiver Baseline Configuration Signal SBAS SQM architecture Worst Case C/N0 Reference station receiver constraints Airborne receiver constraints and User Design Space Galileo E1 OS

 2

	at least 4 Reference Stations (RS) observing a given satellite. Decision of EWF based on at least 3 RS with positive detection	30 dB-Hz	 BOC(1,1) receiver  BW2 of 24 MHz (6 th -order Butterworth)  EML discriminator  E-L spacing of 0.1 chip	 BOC(1,1) receiver  BW2 within [12-24] MHz (4 different filters)  EML discriminator  E-L spacing within [0.08-0.12] chip

Table 3 -

 3 SQM per Reference Station Baseline Configuration

		Location correlators	of	Metrics	Metric Smoothing	MERR	False missed probabilities alarm detection and
	Galileo E1 OS	51 correlator outputs at -0.25:0.01:0.25 chips	 Simple ratios  Difference ratios  Sum ratios	50-s corresponding to a reduction of the std by a factor of 1.5	1.55 m	 Pfa per metric per test of 10 -4  Pmd per metric per test of 1.2.10 -3

Table 4 .

 4 Tested user and reference configurations

		Galileo E1C signal (CBOC(6,1,1/11)) and GPS L1 C/A	GPS L1 C/A signal (BPSK(1))
		Reference	User	Reference	User
	Tracking	E-L (BOC(1.1)	E-L (BOC(1.1)	E-L (BPSK(1)	E-L (BPSK(1)
	technique	local replica)	local replica)	local replica)	local replica)
	Correlator spacing	0.1 chip	0.08, 0.09, 0.1, 0.11, 0.12 chip	0.1 chip	0.1 chip
	Pre-correlation bandwidth (double sided)	24 MHz	12, 14, 16, 18, 20, 22 24 MHz	24 MHz	12, 24 MHz
	Equivalent reception filter	6-th order Butterworth	4 filters are tested	6-th order Butterworth	4 filters are tested

Table 5 .

 5 Reduced Threat Space associated to the proposed generic TM

		𝑫 (correlation
	𝑵	function	𝝋 𝒌 (rad)	𝒇 𝒌 (MHz)
		amplitude)
	[3 ; 5]	0.13	[0 ; 2𝜋]	]0 ; 20]

Table 6 .

 6 Drastically Reduced Threat Space associated to the proposed generic TM

	𝑵	𝑫 (correlation function amplitude)	𝝋 𝒌 (rad)	𝒇 𝒌 (MHz)
		0.13 (individual
		amplitudes of each
	3	component can take	1:1:6	1:2:15
		values 0.2:0.2:1 before
		normalization)

Dr. Ikhlas Selmi is currently part of the SIGnal processing and NAVigation (SIGNAV) research group of Jean-Baptiste Pagot is a PhD candidate in the Department of Signal Processing and Navigation (He received his master degree as an Electronics and Telecommunication engineer in 2013 from the ENAC. He is currently working on GNSS Signal Distortions. Jaron Samson has been working as a System Engineer at ESA's EGNOS Project Office in Toulouse (France) since 2012. Prior to 2012, he worked as a Navigation Engineer at ESA's Technical Centre (ESTEC), supporting Galileo, EGNOS and the GNSS Evolutions Program. Jaron holds an M.Sc-degree in Physical and Mathematical Geodesy from Delft University of Technology (The Netherlands). Francisco Amarillo-Fernández received his Master's Degree in Telecommunication by the Polytechnic University of Madrid (UPM) Spain in 1997, and his Master's Degree in Surveying Engineering by the UPM in 1992. He has been working for the ESA Navigation Directorate since 2001 and has participated/led in numerous research activities in the GNSS field since 1997.


Michaël Dr

Hardy

PROF Jonathan Douxfils

PROF Pierre Fontana

Michael Hardy

Marion Bareille

Sarah Lessire

Isabelle Gouin-Thibault

Pierre Fontana

Thomas Lecompte

Prof François Mullier
email: francois.mullier@uclouvain.be

Studies on hemostasis in COVID-19 deserve careful reporting of the laboratory methods, their significance and their limitations

Keywords: COVID-19, Heparin, Blood coagulation tests, Factor Xa, Thrombelastography

Dear Editor,

We read with much interest the recent observational study of Nougier et al., which aimed at studying thrombin generation (TG) and fibrinolysis profiles of COVID-19 patients admitted to an intensive care unit (ICU) or to an internal medicine ward and receiving various schemes of prophylactic heparin. [START_REF] Nougier | Hypofibrinolytic state and high thrombin generation may play a major role in sars-cov2 associated thrombosis[END_REF] They reported that thrombin potential remained within normal range despite heparin and that fibrinolysis was decreased in relation with increased plasminogen activator inhibitor 1 (PAI-1) and thrombin-activatable fibrinolysis inhibitor (TAFI) antigen plasma levels. Using the rotational thromboelastometry (ROTEM) delta device with EXTEM reagents and the addition of 0.625µg/mL tPA (referred to as 'TEM-tPA'), they reported decreased clot lysis in COVID-19 patients, which was more pronounced in patients who presented a thrombotic event, compared to event-free patients.

This important report provides us the opportunity to raise some crucial methodological issues.

First, a high variability in heparin plasma levels measurements between the available anti-Xa kits has been reported, especially for unfractionated heparin (UFH) and for low anti-Xa levels. [START_REF] Hollestelle | Quality performance for indirect Xa inhibitor monitoring in patients using international external quality data[END_REF] The authors did not specify the kit they used. If they have used a reagent that contains dextran sulfate (as most currently available reagents do), this could have led to an overestimation of the heparin levels. Indeed, dextran is reported to displace heparin from its binding to plasma proteins other than antithrombin (AT), including acute phase reactants, which are increased in COVID-19 patients, and from platelet factor 4 (PF4), which can be released by activated platelets. [START_REF] Hardy | Management of the thrombotic risk associated with COVID-19: guidance for the hemostasis laboratory[END_REF] Furthermore, the authors did not differentiate in the analysis patients according to the heparin they received (UFH or low molecular weight heparins (LMWH)) while they have different effects on laboratory tests (anti-Xa activity, TG and ROTEM). Of note, some anti-Xa kits containing exogenous AT can also lead to an overestimation of heparin levels in case of AT deficiency, which was infrequent in this series though. [START_REF] Hardy | Management of the thrombotic risk associated with COVID-19: guidance for the hemostasis laboratory[END_REF] Second, the authors found in vitro TG (calibrated automated thrombogram (CAT), reagent with the high tissue factor (TF) concentration (PPP-High)) within normal range despite prophylactic heparin

Accepted Article

administration. Based on this finding, they conclude that the patients presented a major hypercoagulability that was not controlled by heparin administration. However, they could measure heparin levels in a limited number of samples only while two different dosages were used (standard and intensified prophylaxis). Mean anti-Xa levels measured were low (0.35 +/-0.20 IU/mL) and those levels could have been overestimated in the presence of dextran in the reagents as discussed above. It would thus not be unexpected to observe normal TG profiles. Of note, the reagent they used for TG (i.e. the PPP High Reagent®) has been designed to measure thrombin potentials in plasma samples containing anticoagulant drugs and therefore uses high TF concentrations to initiate TG (i.e. 20 pM TF). The ability of such analytical conditions to evidence a prothrombotic profile is therefore likely to be poor. The utilization of less intense activation seems more appropriate for this objective, but would require neutralization of heparin.

Third, the authors also suggested that what they refer to as 'heparin resistance' could be an explanation to the normal TG profiles observed, but they thought it not likely because AT plasma levels were normal, in most patients at least. However, laboratory 'resistance' to UFH (i.e. failure to achieve the therapeutic target (activated partial thromboplastin time (aPTT) or anti-Xa levels) despite the administration of recommended UFH doses (i.e. 400 to 600 IU/kg/day)) cannot be asserted based on TG, since the corresponding inhibition of TG under current, commercially available conditions (CAT or ST-Genesia), has not been determined, and definitely not without linking the assessment of heparin activity to the doses administered. [START_REF] Hardy | Management of the thrombotic risk associated with COVID-19: guidance for the hemostasis laboratory[END_REF] Furthermore, other factors besides low AT levels have been identified as potential causes of laboratory 'resistance' to heparin, such as elevated PF4 or heparanases. Elevated factor VIII or fibrinogen levels can also shorten the aPTT but without any effect on the anti-Xa assays. Altogether, to our opinion, the observation of normal TG profiles despite heparin administration rather reflects the low heparin levels measured with regards to the hyperinflammatory state observed in most COVID-19 patients.

To illustrate differences among anti-Xa reagents and among types of heparin (UFH vs. LMWH), we measured in parallel anti-Xa levels with kits containing or not dextran sulfate (Biophen Heparin LRT, calibrated with Biophen Heparin Calibrator, Hyphen biomed, Neuville-sur-Oise, France -and STA-

Accepted Article

Liquid anti-Xa, calibrated with STA-Multi Hep Calibrator, Stago Diagnostica, Asnières-sur-Seine, France, respectively) with a STA-R Max analyzer (Stago Diagnostica) in 28 COVID-19 plasma samples prospectively prepared from six COVID-19 patients admitted to the ICU (11 samples from patients treated with weight-adjusted UFH (Leo Pharma, Lier, Germany) and 27 samples from patients treated with weight-adjusted enoxaparin (Sanofi, Paris, France)). We included both peak and trough samples to cover a wide range of anti-Xa levels. Blood was drawn into 109mM sodium citrate tubes, underwent a double centrifugation (at 1500g for 15 minutes at room temperature) within one hour after blood collection and plasma samples were frozen at -80°C. We studied TG with the ST-Genesia analyzer using STG-DrugScreen reagent (i.e. the reagent with the highest TF concentration available for the ST Genesia) according to manufacturer's recommendations (Stago Diagnostica). [START_REF] Douxfils | Assessment of the analytical performances and sample stability on ST Genesia system using the STG-DrugScreen application[END_REF] Results were normalized using a reference plasma provided with STG-DrugScreen kit of reagents and expressed in percentage.

We observed an overall good correlation between anti-Xa levels measured with both reagents (Pearson's correlation coefficient = 0.98 for UFH samples and = 0.98 for LMWH samples). However, for UFH samples, the reagent containing dextran showed an overestimation of the anti-Xa levels compared to reagents that did not contain dextran (proportionally to anti-Xa levels; slope of the regression line: 1.47, 95% confidence interval: 1.24-1.71; Fig. 1A); by contrast, anti-Xa levels were not different between both methods for samples from patients treated with enoxaparin. These results further support the importance of a careful and thorough report on the methods used and of a clear differentiation of the anticoagulants, which frequently differently influence laboratory tests.

A decreased thrombin potential was evidenced in relation with enoxaparin levels as assessed with anti-Xa assays (Fig. 1B). With more effective LMWH levels, thrombin generation was proportionally reduced. This suggests that that the normal TG profiles identified by the authors could first be the consequence of the low heparin levels measured, either as a consequence of the uncontrolled timing of blood collection with regards to LMWH administration (trough samples) or because heparin doses were too low with regards to the hyperinflammatory state described in severe COVID-19 patients.

Accepted Article

Fourth, to what extent viscoelastometric tests (VETs) are truly "global" can be challenged.

Viscoelastometric tests are attractive because they are performed with whole blood and address not only the platelet-dependent coagulation process, but also clot mechanical properties and at fibrinolysis. In our opinion such tests have major intrinsic limitations though, among which the initiation of clotting with massive TF concentrations (EXTEM reagents), the weak association with platelet function assays and the fact that fibrinolysis is initiated by endogenous, blood-borne uninhibited plasminogen activators, which are most often so low that fibrinolysis is negligible. [START_REF] Ranucci | Sensitivity of Viscoelastic Tests to Platelet Function[END_REF][START_REF] Rijken | Development of a new test for the global fibrinolytic capacity in whole blood[END_REF] To account for the latter issue, the authors added exogenous tPA (of note very high concentrations, i.e. 625 ng/mL). [START_REF] Kuiper | Validation of a modified thromboelastometry approach to detect changes in fibrinolytic activity[END_REF] However, such modifications of commercial reagents still lack of clinical validation, and could lack sensitivity to the effect of the transient increase of tPA that could be present during initial stages of the disease. [START_REF] Keragala | Fibrinolysis and COVID-19: a tale of two sites?[END_REF] In addition, regarding D-dimers assays, the performance (i.e concordance with other reagents, analytical precision) in high values such as those observed in COVID-19 patients is highly variable, making comparisons of results from studies using different assays hazardous. [START_REF] Suzuki | A re-evaluation of the D-dimer cut-off value for making a diagnosis according to the ISTH overt-DIC diagnostic criteria: communication from the SSC of the ISTH[END_REF] Moreover, to the best of our knowledge, the performance in high values of the kit used by the authors (HemosIL D-Dimer HS 500) has not been evaluated yet.

Finally, little information was provided regarding the preanalytical step of laboratory tests. For example, the timing of blood collection and centrifugation conditions were not specified, while these variables may have important influence on the tests. [START_REF] Rodgers | Evaluation of preanalytical variables in a commercial thrombin generation assay[END_REF] In order to cope efficiently with hemostatic disturbances related to COVID-19, authors of such studies should be urged to fully report on the laboratory methods used and to acknowledge and to comprehensively discuss their potential drawbacks. This is essential to enhance the interpretability and the applicability of the results. Studies should also be appropriately designed with regards to their objectives, otherwise they are at the risk of not being able to make robust conclusions. Therefore it is of upmost importance to provide the reader all relevant information needed to integrate the ever-

Accepted Article

growing data accumulating on this topic with the ultimate aim of an elaboration of well-grounded clinical guidance.

Funding

This work was supported by the Fonds National de la Recherche Scientifique: 'Anticoagulation fibrinolysis COVID19' (reference: 40002796).

Declarations

Ethical Approval

The observational study was approved by the Ethics Committee of the CHU UCL Namur (NUB B0392020000031).

Competing interests

The authors declare no competing interest.

Accepted Article


Christophe Wu

Darcel

Dr Duo Wei

Chakkrit Netkaew

Prof. Dr Jiajun Wu

Christophe Darcel
email: christophe.darcel@univ-rennes1.fr

in the presence of amines: a new route to cyclic amines

Keywords: iron catalysis, hydrosilylation, dicarboxylic acid, cyclic amines, one-pot

Iron-catalyzed hydrosilylation of diacids in the presence of amines: a new route to cyclic amines

Duo Wei, Chakkrit Netkaew, J

Amines are crucial derivatives in the area of molecular chemistry as demonstrated by their preponderance in pharmaceuticals, agrochemicals, dyes, and material science. Furthermore, in 2015, 170 of the top 200 drugs, representing more than US$ 500 million retail sales contained a nitrogen atom or an amino moiety in their structure. [START_REF]Top 200 Brand Name Drugs by Retail Sales in[END_REF] (Figure 1) Thus, the synthesis of amine compounds is still a crucial task in modern chemistry. [START_REF] Larock | Comprehensive Organic Transformations: a Guide to Functional Group Preparation[END_REF] Figure 1. Examples of cyclic amines as drugs.

Over the numerous methodologies developed, well exemplified catalytic reduction of carboxylic derivatives such as acids or amides is still an important area of research mainly with non-noble transition metals such as iron, manganese or cobalt. More particularly, the reduction of carboxamides is far away the most challenging to perform due to the lower electrophilicity of the carbonyl group and the chemoselectivity issues. Indeed, the reduction of amides can lead to the formation of amines, imines, enamines or nitriles by C-O bond cleavage, whereas alcohols, aldehydes and degraded amines are obtained by cleavage of the C-N bond (Scheme 1). [3] Scheme 1. Two pathways for the reductive transformations of amides: (i) to amines via dissociation of the C-O bond and (ii) to alcohols and degraded amines via cleavage of the C-N bond.

Additionally, catalytic hydrogenation of amides still suffered from drastic and harsh reaction conditions (elevated temperatures, high hydrogen pressures), and moderate level of chemoselectivity (deoxygenation vs hydrogenolysis pathways). [START_REF] Smith | For selected reviews on amide hydrogenations[END_REF] Since the first report on the hydrogenolysis of amides into amines and alcohols with ruthenium pincer catalysts, [5] such Ru based catalysts have shown promising activities for the selective hydrogenation of amides to amines. [6] For the other reduction pathway involving a C-O bond cleavage, a significant breakthrough was made by Cole-Hamilton [7,8] using a catalyst based on Ru(acac)3 and triphos (1,1,1-tris(diphenylphosphinomethyl)ethane) in the presence of a stoichiometric amount of methanesulfonic acid able to perform the selective deoxygenation of aromatic amides leading to the corresponding amines (10-40 bar H2, 200-220 °C). The use of an additional Lewis acid such as Yb(OTf)3, [9] BF3•Et2O, [10] or B(C6F5)3 [11] as cocatalysts had also a beneficial effect on the activity and the chemoselectivity for the hydrogenation of secondary and tertiary amides then performed in less drastic conditions. Recently, a PNP-manganese catalyst associated to a Lewis acid was reported for the same reaction by Milstein (150 °C, 50 bar of H2). [12] Iron can also be employed for the hydrogenation of amides. [13] Indeed, in 2016, Milstein reported the first example of a homogeneous iron-catalyzed hydrogenation of N-substituted 2,2,2-trifluoroacetamides using an iron-pincer (PNP) catalyst leading to the corresponding amines and trifluoroethanol through 10.1002/cctc.202000881

Accepted Manuscript

ChemCatChem C-N bond cleavage (140 °C, 60 bar of H2). [14] By contrast, performing the reduction under hydrosilylation conditions [START_REF] Wen | For examples of recent reviews on iron-catalyzed hydrosilylation[END_REF] permitted to reverse the chemoselectivity since the C-O bond cleavage was favoured as demonstrated by the pioneering contributions of Nagashima [16] and Beller [17] using Fe3(CO)12 or Fe(CO)5 as pre-catalysts with either PMHS or TMDS as the hydride source. Similar results could be obtained using iron-NHC complex [CpFe(CO)2(IMes)][I], [18] [bis-(N-Dipp-imidazole-2ylidene)methylene-Fe(η 6 -benzene)], [19] and in situ prepared species from Fe(OAc)2, [Ph-HEMIM][OTf] and PMHS. [20] Notably, the association of two catalytic systems [NHEt3][Fe3H(CO)11] and Fe(OAc)2/terpyridine efficiently reduced primary amides to primary amines. [21] Scheme 2. Novel route to N-substituted cyclic amines via iron-catalysed hydrosilylation of diacids with amines.

Following our recent development on cyclic amine synthesis via iron-catalyzed one-pot sequential transformations under hydrosilylation conditions starting from keto-acids or ω-amino fatty acid derivatives, [22] we herein report the use of diacids as the starting substrates to prepare pyrrolidines, piperidines and azepanes. (Scheme 2) Indeed, over the other alternative methods involving such iron-catalyzed reductive amination sequences, diols can be also envisaged as starting materials. In this area, significant breakthrough has been made in the development of methods for the cyclization of primary amines starting from diols via hydrogen borrowing catalyzed with noble metals, [23] base metals, [24] γ-Al2O3 [25] as well as organic catalysts. [26] The advantages of such methodologies were clearly atom-economic and without generation of harmful waste (only water as by-product) even if most of these systems required high reaction temperature. Additionally, Barta reported elegant methodologies based on hydrogen borrowing pathways involving iron-catalyzed alkylation of amines with alcohols [START_REF] Yan | For selected examples for the synthesis of cyclic amines via hydrogen borrowing methodology[END_REF] or decarboxylative N-alkylation of cyclic α-amino acids. [28] On the other hand, carboxylic acids can be interesting alternative starting materials for N-alkylation of amines. Indeed, a straightforward catalytic N-alkylation of amines with carboxylic acids was reported by Beller et al. in 2014 using Karstedt's type catalyst and hydrosilanes as reducing reagents. [29] Even if diacids are more readily available, to the best of our knowledge, the direct hydrosilylation of diacids with amines yielding Nsubstituted cyclic amines remains unknown to date. Nevertheless, it must be noticed that the reduction of diesters with anilines under hydrogenation conditions led to N-aromatic heterocycles when catalyzed by Ru(acac)3 associated with triphos. [30] However harsh reaction conditions (220 o C) were generally required and its scope was limited to aniline derivatives.

Based on our previous contributions, we then began our initial optimization work using the iron(0) N-heterocyclic carbene complex Fe(CO)4(IMes) 4 as the catalyst (5 mol%) for the reaction of glutaric acid 1a with aniline 2a in the presence of PhSiH3 (6 equiv.). Under solvent free conditions, after 20 h at 100 °C upon visible light activation (24 W compact fluorescent lamp), both conversion (70%) and selectivity were moderate as a mixture of N-phenylpiperidine 3a, N-phenylglutarimide 5a and N-phenyl-2-piperidone 6a was obtained in a ratio of 54/11/5 (Table 1, entry 1). Performing the reaction in toluene under similar conditions didn't permit to increase the conversion, but the selectivity towards the formation of desired product 3a increased to 67% yield, along with 3% of 6a. Conducting the transformation at 110 °C for 20 h permitted to convert 75% of the starting materials and obtained 3a exclusively (75%, Table 1,entry 3). Conv.

[%] [a] Yield [%] [a] 5a 6a 3a

1 [b] 6 Neat -70 11 5 54 2 [b] 6 [d] 6 DMC -50 50 0 0 11 [d] -DMC -0 0 0 0 [a] General conditions: 4 (5 mol%), 1a (0.5 mmol), 2a (0.5 mmol), PhSiH3 (0-6 equiv.) and solvent (1 mL), visible light irradiation, 110 °C, 20 h; then hydrolysis (THF/NaOH 2 N). The conversions and yields were determined by 1 H NMR using dibromomethane as the internal standard. [b] 100 °C. [c] [CpFe(CO)2(IMes)][I] 7 (5 mol%) as the catalyst. [d] in the absence of Fe catalyst 4.

Substituting toluene by 2-Me-THF, 1,4-dioxane or dimethylcarbonate (DMC) did not increased the conversion, even if 3a was still exclusively obtained (70-72%; Table 1, entries 4-6). Nevertheless, since DMC gave comparable efficiency, its greener character prompted us to select it for the scope of this transformation. [31] Interestingly, using an iron(II) complex such as [CpFe(CO)2(IMes)][I] 7 (5 mol%) under similar conditions in toluene at 110 °C, 69% of glutaric acid 1a was converted, but the chemoselectivity was switched as only the N-phenylglutarimide 5a was obtained, showing that this iron(II) catalyst was able to promote only the transamidation reaction, but not the reduction of 5a leading to 6a then 3a (Table 1,entry 7). Additionally, reducing the amount of phenylsilane to 4 equiv. decreased the efficiency of the reaction as only 40% of conversion was observed and a mixture of 3a, 5a and 6a was obtained in a ratio of 24/12/4. With 2 equiv. of PhSiH3, similar conversion (38%) of 1a was observed, but with 5a (25%) as the major product (Table 1, entries 8-9).

Accepted Manuscript

ChemCatChem Noticeably, with 6 equiv. of phenylsilane, the reaction reached 50% conversion in the absence of catalyst 4 leading to exclusively N-phenylglutarimide 5a (Table 1, entry 10), whereas in the absence of both silane and Fe catalyst, or using 5 mol% of 4 without silane, no reaction occurred. (Table 1, entries 11-12). These results seem to indicate that the excess of PhSiH3 promotes the formation of imide 5a (see also SI Scheme S1), via the intermediate of silylated diester obtained from diacid derivatives. Taking into account that even if the conversion were not complete when using 4 as catalyst, N-phenylpiperidine 3a was obtained solely, indicating that the reduction of 5a and 6a was faster than the formation of 5a via transamidation between 1a and 2a, making the latter the rate-limiting step.

Lewis acids are known to promote the (trans)amidation of carboxylic acid derivatives with anilines. [32] Thus, several Lewis acids were evaluated in this reaction in association with the Fe(0) catalyst 4. Using iron(III) based Lewis acids such as FeCl3 or Fe(OTf)3 (10 mol%) led to disappointing results as only partial conversions into imide 5a were observed (32 and 26%, respectively, Table 1, entries 13-14). Among the trials with different Lewis acids (SI Table S1), Fe(OTf)2 exhibited the most promising results: using Fe(OTf)2 (10 mol%) with phenylsilane (6 equiv.) increased the conversion to 83% and Nphenylpiperidine 3a was exclusively obtained (Table 1, entry 16). Increasing the Fe(OTf)2 amount to 20 mol% enhanced the yield of 3a to 90%, while the use of 30 mol% of Fe(OTf)2 has a detrimental effect on both the reactivity and selectivity (84% conversion, 5a:3a = 17:67, Table 1, entries 17-18). Thus, the optimized conditions to obtain N-arylpiperidine were 5 mol% of 4 in combination with 20 mol% of Fe(OTf)2 and 6 equiv. of phenylsilane in DMC at 110 °C for 20 h. It is worth mentioning that attempts with different hydrosilanes such as Ph2SiH2, Et3SiH, Me2PhSiH, PMHS (polymethylhydrosiloxane), TMDS (1,1,3,3tetramethyldisiloxane) gave no conversion of aniline. [a] General conditions: 4 (0-5 mol%), 1a (0.5 mmol), 2a (0.5 mmol), PhSiH3 (2-6 equiv.) and DMC (1 mL), visible light irradiation, 110 °C, 20 h; then hydrolysis (THF/NaOH 2 N). The conversions and yields were determined by 1 H NMR using dibromomethane as the internal standard.

We then focussed on the reaction of alkylamine (cyclohexylamine 2b) with glutaric acid 1a in order to synthesize N-alkylpiperidines (Table 2). The optimization study was firstly performed using 4 as the catalyst (5 mol%) in the presence of PhSiH3 (6 equiv.) in DMC. After 20 h at 110 °C, Ncyclohexylpiperidine 3b was generated in quantitative NMR-yield (Table 2, entry 1), notably without the production of other intermediates: N-cyclohexylglutarimide 5b and N-cyclohexyl-2-piperidone 6b, and without the use of Lewis acid. The amount of PhSiH3 can be decreased to 4 equiv. without any loss of activity and selectivity, as 3b was still obtained quantitatively. (Table 2, entry 2) However, the selectivity dropped when decreasing the amount of PhSiH3 to 2 equiv. or the catalyst loading to 2.5 mol% (Table 2, entries 3-4). Finally, in the absence of the catalyst 4, 5b was found to be the sole product, demonstrating that Fe catalyst 4 was crucial to produce 3b.

With the optimized conditions for the catalyzed hydrosilylation of diacids in the presence of arylamines and alkylamines (Table 1, entry 17, andTable 2, entry 2, respectively) in hand, the substrate scope and its limitation were next studied (Table 3 for alkylamines, Table 4 for arylamines).

Starting from glutaric acid 1a, various alkylamines such as cyclohexylamine, 1-hexylamine and benzylamine can be applied leading to the corresponding piperidines in excellent isolated yields (3b-d, 93-95%, Table 3). The substitution of the benzyl moiety with electron donating or withdrawing groups such as methoxy or trifluoromethyl had nearly no influence on the efficiency of the transformation, leading to 3e and 3f in 91% and 85% yields, respectively. Additionally, heteroaromatic moiety, for instance, furyl and benzimidazolyl groups can be tolerated as 3g and 3h were generated in 91% and 80% yields, respectively. Noticeably, increasing the steric hindrance of the amine partner decreased the efficiency of the reaction: indeed, using 2,4,6trimethylbenzylamine or α-methylbenzylamine led to the corresponding piperidines 3i and 3j in moderate yields, 73% and 68%, respectively. Table 3. Hydrosilylation of diacids in the presence of aliphatic primary amines. [a] [a] General conditions: 4 (5 mol%), diacid 1 (0.5 mmol), amine 2 (0.5 mmol), PhSiH3 (4 equiv.) and DMC (1 mL), visible light irradiation, 110 o C, 20 h; then hydrolysis (THF/NaOH 2 N). Isolated yields of the products are shown. [b] NMR yield. [c] succinic acid 1b (1.0 mmol, 2 equiv. to amine 2), PhSiH3 (8 equiv.), 48 h.

Accepted Manuscript

ChemCatChem Starting from succinic acid 1b, pyrrolidines 8 can be also efficiently prepared in one step. Thus, 8a and 8b can be synthesized from the corresponding amines, 2,4dimethoxybenzylamine and furfurylamine, in 78% and 87% yields, respectively. Remarkably, using an amino-alcohol such as 6-aminohexanol, a chemoselective transformation occurred as the pyrrolidine 8c bearing a pending hydroxyl group was prepared in 89% yield. Furthermore, using more steric hindered 1-adamentylamine, 8d was obtained in 90% yield. As expected, cyclohexanemethylamine was a suitable substrate leading to 8e in 96% yield. Interestingly, ethylene-diamine also reacted selectively with succinic acid giving the corresponding bispiperidine 8f in 91% yield.

Larger cyclic amines, such as azepanes, can be also produced in moderate to good yields using this methodology: starting from adipic acid 1c, azepanes 9a and 9b were obtained in 77% and 68% yields when reacted with p-methoxybenzylamine and 2,4,6-trimethylbenzylamine (Table 3). With the more steric hindered 1-(1-naphyl)ethylamine, 9c was detected in a lower yield (34%), showing that the steric hindrance had a drastic effect on the activity for the azepane formation. The reaction also tolerated heteroaromatic groups such as thienyland pyridyl-methylamine which led to 9d and 9e with 75% and 70% yields, respectively. Nevertheless, it should be noticed that unsaturated amines such as allylamine and propargylamine led to unsatisfactory selectivity, as the C=C and C≡C were partially reduced.

Scheme 3. N-Alkylation of alkylamines bearing aniline moiety.

Since it was potentially competitive to alkylate anilines and aliphatic amines with diacids, we decided to perform the reaction with 4-(2-aminoethyl)aniline as the substrate associated with succinic, glutaric, and adipic acids. (Scheme 3) Noticeably, the N-alkylation of aliphatic amine moiety occurred exclusively as the corresponding cyclic 3k, 8g and 9f were isolated in 85%-91% yields, leaving aniline group untouched. Furthermore, we have demonstrated the synthetic utility of this methodology in the preparation of drug molecules Fenpiprane 3l and Prozapine 9g, which are used to treat functional gastrointestinal disorders, and as antispasmodic drug, respectively [33] (Scheme 4). Thus, reaction of the 3,3-diphenylpropylamine and glutaric acid 1a (adipic acid 1c) afforded 3l and 9g, in 89% and 83% isolated yields.

In order to prepare N-aryl cyclic amines (Table 4), the optimized reaction conditions depicted in Table 1, entry 17 was employed. By reaction of glutaric acid 1a with aniline, p-toluidine and 4-(benzyloxy)aniline, the corresponding N-arylpiperidines 3a, 3m and 3n were obtained in 80%-95% yields. Good functional group tolerance was achieved starting from p-aminophenol, as 3o was isolated in 95% yield. The transformation can be also conducted with p-phenylenediamine yielded the bis-pyrrolidine 3p in 65%. By contrast, the use of 2,4,6-trimethylaniline didn't permit to obtain efficiently the corresponding piperidine 3q (28%), indicating that steric hindrance decreased drastically the reactivity. Substituted glutaric acid, like 3-methylglutaric acid 1a' was also a suitable coupling partner with p-anisidine, leading to 3r in 61% yield.

Table 4. Hydrosilylation of diacids in the presence of primary arylamines. [a] [a] General conditions: 4 (5 mol%), 1 (0.5 mmol), Fe(OTf)2 (20 mol%), amine 2 (0.5 mmol), PhSiH3 (6 equiv.) and DMC (1 mL), visible light irradiation, 110 °C, 20 h; then hydrolysis (THF/NaOH 2 N). Isolated yields of the products are shown. [b] glutaric acid 1a (1.0 mmol, 2 equiv.), PhSiH3 (12 equiv.), 48 h.

[c] Fe(OTf)2 (50 mol%).

The reaction of succinic acid 1b with aniline, p-methoxy, pdimethylamino, p-fluoro, o-fluoro, p-chloro and p-bromoanilines led to pyrrolidines 8h-n in 69-88% yields, highlighting the functional group tolerance towards electron donating and halogeno groups. However, deiodinated pyrrolidine product was 10.1002/cctc.202000881

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ChemCatChem mainly obtained starting from 4-iodoaniline. Notably, an important building block for pharmaceuticals such as 3,4-(methylenedioxy)aniline was effectively transformed to piperidine 8o in 84% yield. Electron deficient anilines like otrifluoromethyl and 2,4,6-trifluoroaniline were transformed into pyrrolidines 8p and 8q in moderate yields (50% and 57%, respectively). Additionally, o-phenylaniline led to 8r in 59% yield highlighted the drastic effect of the steric hindrance. Heteroaromatic amine like 2-aminopyridine was also successfully applied leading to 8s in 62% yield. Diacid bearing alkenyl moiety such as cis-4-cyclohexene-1,2-dicarboxylic acid 1b' gave 8t in 91% yield, with the remote C=C untouched. However, diacid with conjugated C=C, such as maleic acid and itaconic acid, led to a mixture of products due to the easy reduction of the C=C bond. Noticeably, anilines bearing more electron-withdrawing nitro, cyano substituents was not converted into the corresponding product.

Additionally, when adipic acid 1c was used in association with aniline under standard conditions, the desired product Nphenylazepane 9h was detected in ca. 10% NMR-yield. Noticeably, diol resulting of the reduction of diacid was observed in GC-MS as a by-product. To overcome the low reactivity of adipic acid with arylamine, 50 mol% of Fe(OTf)2 was employed to obtain 9h and 9i in 48% and 60% yields, respectively, starting from aniline and p-anisidine. 3-Methyladipic acid can also provide 9j in 52% yield. Albeit this protocol was quite general for aliphatic diacids, the attempts to perform the reaction of phthalic acid with either alkylamines or arylamines gave a mixture of products including the expected isoindoline products.

Even though the organometallic catalytic process involving the Fe complex 4 in catalyzed hydrosilylation reactions has been studied, [34] highlighting the crucial role of the light activation to generate a 16 electron active species able to promote the oxidative addition of the hydrosilane thus generating the related H-Fe-SiR3 intermediate which was isolated and characterized, we were interested to gain some insights of the reaction pathways. Then various dicarboxylic acid derivatives were employed as substrates to produce cyclic amines starting from cyclohexylamine 2b (Table 5).

Table 5. Hydrosilylation of various diacid derivatives with cyclohexylamine. [a] Entry R1 R2 n Conv. [a] Yield [a] 5 [b] R1, R2 = -O-(anhydride) 1 >99 >99 (93)

[a] General conditions: 4 (5 mol%), diacid derivative (0.5 mmol), cyclohexylamine (0.5 mmol), PhSiH3 (4 equiv.) and toluene (1 mL). visible light irradiation, 110 o C, 20 h; then hydrolysis (THF/NaOH 2 N). Conversions and yields were detected by 1 H NMR using dibromomethane as the internal standard. Isolated yields are shown in parenthesis. [b] using cis-1,2-cyclohexanedicarboxylic anhydride as substrate.

Under the optimized reaction conditions (Table 2, entry 2), dimethyl glutarate and adipate gave the corresponding cyclic amines in 14% and 4% NMR yields, respectively (Table 5, entries 1-2), while methyl adipamate and succinimide were totally inactive (entries 3-4). These results seem to imply that such derivatives were probably not involved as intermediates. Unexpectedly, cis-1,2-cyclohexanedicarboxylic anhydride led to the corresponding cyclic amine 8v in 93% isolated yield (entry 5), showing that cyclic anhydride may be a plausible intermediate of the reaction.

Further control experiments were then performed and summarized in Scheme 5. In the absence of amine, succinic acid 1b was converted into succinic anhydride 10 in 49% NMR yield, in the presence of both Fe catalyst 4 (5 mol%) and PhSiH3 (2 equiv.) (Scheme 5a and SI Table S2). Importantly, molecular hydrogen was detected by in situ 1 H-NMR at 4.47 ppm (Figure S1), and siloxane PhH2Si-O-SiPhH2 was also identified by GC-MS. It is described that silyl esters can be generated from dehydrogenative coupling of carboxylic acids and silanes under the catalysis of either transition metals or organo-catalysts. [35] Scheme 5. Control experiments. Conversion and yield were detected by 1 H NMR using dibromomethane as the internal standard, isolated yield in parentheses.

Thus, we heated bis(trimethylsilyl)succinate 11 at 110 °C for 20 h, and as expected, succinic anhydride 10 was produced in 42% yield (Scheme 5b), which indicated that cyclic anhydride can be produced via the intermediacy of silylated diester obtained from diacid and silane. Even if it was reported that imides can be prepared by condensation of dicarboxylic anhydrides and primary amines, we set up such reaction starting from cis-1,2-cyclohexane-dicarboxylic anhydride 12 and cyclohexylamine 2b. Indeed, the corresponding imide 13 was prepared quantitatively (Scheme 5c).

Afterwards, the direct hydrosilylation of imide was performed with hexahydro-N-phenylphthalimide 14 as the substrate, under reaction conditions described in Table 1, entry 3. Hexahydro-2phenyl-isoindoline 8w was thus isolated in 81% yield. Noticeably, 15% of amide 15 was also produced as a by-product. S3) Such results demonstrated that the production of cyclic amines from imide went through the reduction of amide via a Fe-catalyzed sequence. Additionally, since diol was formed during the formation of N-arylazapane (Table 4), it was shown that diol 16 was obtained in 47% yield by direct hydrosilylation of cyclic anhydride 12 under the same reaction conditions (Scheme 5e). In order to rule out a radical process, the addition of TEMPO (1 equiv.) to the reaction was performed. A full conversion of amine starting material was achieved giving 56% desired products and 41% amide byproduct along with 3% of imide (SI Scheme S2), indicating that a radical process may not happen during the catalytic process.

Finally, according to the above control experiments, a proposed reaction pathway is depicted in Scheme 6. The sequence started with the reaction of the diacid 1 such as succinic acid 1b with hydrosilanes leading to the silylated diester 17 via a dehydrogenative silylation and liberation of H2. After releasing of R3Si-O-SiR3, the cyclic anhydride intermediate 10 was formed, and reacted with amines to generate the imide 18, step where the presence of the Fe catalyst 4 was not necessary. Alternatively, cyclic anhydride 10 could also be reduced into diol 19 with silanes under the catalysis of Fe complex 4, however it was slower compared with the formation of imide 18. Afterwards, the first reduction of imide 18 into amide 20 took place via iron catalysed hydrosilylation. Then amide 20 was further reduced to the final cyclic amine product 8 under the same conditions. [22] On the other hand, compared with alkylamines, arylamines were less reactive to produce N-arylated cyclic amines, as Lewis acid was required to promote the transamidation step. (Scheme 5c and SI Table S4). Scheme 6. Proposed possible reaction pathway.

In summary, we have developed for the first time the Fecatalyzed hydrosilylation of diacids in the presence of amines to access N-substituted cyclic amines. This method has several advantages: i) it utilizes environmentally benign non-noble transition metal iron based complex as catalyst, ii) it enables onepot synthesis of cyclic amines, iii) it starts from inexpensive dicarboxylic acids and amines, iv) it exhibits good functional group tolerance, v) it allows the production of drug molecules Fenpiprane and Prozapine in good yields, and vi) it proceeds in dimethyl carbonate as a green solvent. Further detailed control experiments have shown that the cyclic anhydrides formed in situ from diacids played a key intermediate ahead of imides.

Entry for the Table of Contents

A ride in an "iron" balloon: a novel strategy for building N-substituted cyclic amines is reported via iron catalyzed one-pot hydrosilylation of dicarboxylic acids with amines, using silanes as hydride source. 50 examples of amine derivatives, including drug molecules Fenpiprane and Prozapine, were prepared in good yields with dimethyl carbonate as a green solvent. 10.1002/cctc.202000881

Accepted Manuscript

ChemCatChem

  10.1002/cctc.202000881

Scheme 4 .

 4 Scheme 4. One-pot catalytic synthesis of Fenpiprane 3l and Prozapine 9g.

Table 1 .

 1 Catalyzed hydrosilylation of glutaric acid with aniline.[a]

	Entry	PhSiH3 [equiv.]	Solvent	Additive [mol%]

Table 2 .

 2 Hydrosilylation of glutaric acid cyclohexylamine.[a]

	Entry	4 [mol%]	PhSiH3 [equiv.]	T [°C]	Conv. [%]	5b	Yield [%] 6b	3b
	1	5	6	110	99	0	a	0	99
	2	5	4	110	99	0		0	99
	3	5	2	110	99	0		40	60
	4	2.5	4	110	95	0		0	95
	5	-	6	110	99	99		0	0

Acknowledgements

We thank the Université de Rennes 1 and the Centre National de la Recherche Scientifique (CNRS). C. N. thanks the French Embassy in Thailand for a grant, J. W. acknowledges the China Scholarship Council (CSC) for a PhD grant.