Jonathan Lusseau

Frédéric Robert

Yannick Landais

O-Methyl-N-Nitroisourea as a NCO Surrogate in Cu-Catalyzed Alkane C-H isocyanation. A Masked Isocyanate Strategy

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Introduction

The direct functionalization of the C(sp3)-H bond represents one of the most efficient, atom and step economic strategy to introduce functional groups on a hydrocarbon chain. 1 Late stage C(sp3)-H functionalization on highly functionalized molecules, is also of definite interest, allowing the conversion of known bioactive targets into new molecules with potentially increased biological activity. [START_REF] Huang | [END_REF] The selective C-H activation, however still remains an important challenge to synthetic organic chemists, due to the high energy of the C-H bond (BDE ~ 98-100 kcal/mol). 1 Over the past two decades, organic synthesis has made remarkable advances in this field and achieved direct functionalization of C(sp3)-H bonds of alkanes to forge C-C and C-X bonds (X = N, O, S, etc.). 3 In this context, several intermolecular amination process of simple unfunctionalized and functionalized hydrocarbons 1 have been reported (Figure 1,A). 4 In contrast, the direct incorporation of an isocyanate (NCO) moiety is a challenging process, which has received so far little attention, despite its high potential. The preparation of alkyl isocyanates via Mn-porphyrin catalyzed C-H activation of alkanes was first reported in 2017 by Groves et al. (Scheme 1, B). 5 A remote Cu-catalyzed C-H abstraction then isocyanation using TMSNCO proceeding through a sulfonamidyl radical was described by Zhang. 6 A more recent work by Stahl and coworkers 7 described the direct isocyanation of benzylic substrates using a copper catalyst and NFSI as the hydrogen atom transfer agent. Beside hydrocarbon precursors, isocyanates may also be accessed through the alkylation of alkyl halides using nitrocyanamide silver salts as reported earlier by Boyer et al. (Scheme 4, C). 8 This overlooked approach relies on a silver nitrocyanamide salt available through a basic treatment of S-methyl-N-nitroisourea 2. Thermal rearrangement of the resulting N-alkylnitrocyanamide 3 was believed to occur through N-nitrocarbodiimide I, finally decomposing into the isocyanate 4 and N2O. Recent studies by Churakov and co-workers clearly established the thermal decomposition of I into isocyanates. 9 Based on these premises, it was anticipated that the basic treatment of an O-alkyl-N-nitroisourea such as 6 would generate N-nitrocarbodiimide intermediate I, through elimination of MeOH (Scheme 4, D). In turn, 6 might be available through a metal-catalyzed C-H amination of hydrocarbons using simple O-methyl-N-nitroisourea 5a, available in only two-steps a. Univ. Bordeaux, CNRS, Bordeaux INP, ISM, UMR 5255, F-33400 Talence, France. Email : yannick.landais@u-bordeaux.fr Electronic Supplementary Information (ESI) available: Experimental procedures, characterization data ( 1 H and 13 C NMR, HRMS, FTIR) for all new compounds (PDF).

on gram scale from cheap urea (ESI). This sequence would thus offer a rapid entry toward isocyanates from shelf-stables, easy to handle and safe O-methyl-N-alkylnitroisoureas 6, avoiding the manipulation of the known carcinogenic isocyanates and the recourse to toxic phosgene or TMSNCO. We thus describe below the synthesis of 6, through a Cu(I)-catalyzed C-H functionalization of alkanes using O-methyl-N-nitroisourea 5a as a masked NCO (Figure 1,D). During the studies on the basemediated access to intermediate I from 6 we also uncovered an efficient entry to isocyanates 4 from 6 through an unprecedented Krapcho-type process. 10 This methodology thus gives rise to a range of aminated products from simple hydrocarbons, including polyolefin waste on demand using Nalkylnitroisoureas 6 as non-toxic isocyanate surrogates.

Results and discussion

The first part of the study was devoted to the development of the so far unknown C-H amination of alkanes using O-methyl-Nnitroisourea 5a as the aminating agent under Cu(I) catalysis. 4 Optimization of the C-H amination reaction was performed using cyclohexane as the model alkane, varying the nature of the copper salt, ligands as well as oxidants and solvents, as summarized in Table 1. After extensive studies, the soluble [Cu(MeCN)4]BF4 salt was found to be the most active copper salt for the reaction, leading to the desired product 6a in 78% isolated yield (Table 1, entry 1). The structure of 6a was unambiguously attributed through X-ray diffraction studies (XDRS, ESI) indicating that the reaction occurred at the NH2 moiety of 5a and not at tautomeric NH-NO2 center. A unique isomer of the nitrosourea was obtained, the stereochemistry of which was assigned based on XRDS, showing hydrogen bonding between the NH and one of the NO2 oxygen. The counter-anion of the copper salt had no effect on the yield (Entry 2). In contrast, other Cu(I) salts led to very low conversion (entries 3-5). The choice of the solvent proved also to be crucial, with the "greener" acetone leading consistently to higher yields (entries 6-10). Polarity of the medium also seems to influence the efficiency of the process as indicated by higher yields observed in both acetone and nitromethane (entry 9). The nature of the ligands was also studied with the 2,9-dimethyl-1,10phenanthroline (neocuproine) L1, leading to higher conversion (entry 1 vs entries 11-12), while the absence of ligand led to low efficiency (entry 13). Di-tert-butyl peroxide was found to be the most efficient oxidant, which contrasts with the very low conversion using AcOOt-Bu for instance (entry 14). It is worthy of note that at this temperature, the t-BuO radical is known to fragment, into acetone and the highly reactive methyl radical which can also act as a hydrogen atom transfer (HAT) agent (vide infra). 11 Interestingly, polarity of the solvent is also reported to accelerate this process. In the last part of the study, quantities of starting material 1a and 5a, as well as reagents in entry 1 were varied. For instance, reducing the amount of oxidant led to a slight decrease in yield (entry 15), so that 2.5 equivalent was kept as optimal conditions. Decreasing the amount of cyclohexane did not affect the isolated yield (entry 16), while simultaneously increasing the amount of 5a slightly improved the yield (entry 17). An excess of alkane is however required as shown in entries 18-20, where satisfying yields are maintained only when increasing in the same time the amount of 5a (entry 20). The efficiency of the process using only 1 equivalent of alkane is however noteworthy considering reported literature where the hydrocarbons is usually used in excess. 4d A temperature of 90°C was found to be optimal, as lowering the temperature to 60°C led to lower yield (entry 21) or no conversion at 30°C (entry 22). Finally, decreasing the amount of copper catalyst led to reduced yield (entry 23). Upscaling of the process was also performed starting from 5 mmol of 5a and cyclohexane (10 equiv.) which led to the isolation of 3.31 grams of 6a (66% yield).

Table 1 Optimization of the C-H amination of 1a with O-methyl-N-nitroisourea 5a.

a Unless otherwise mentioned, all reactions were performed with 1a (10 eq.), 5a (0.5 mmol), oxidant (2.5 eq.) Cu(I)X (0.05 eq.), L1 (0.05 eq.) in acetone (1.0 mL) under argon at 90°C for 24 h. b Isolated yields. c t-BuOOt-Bu (1.5 eq.) instead of 2.5 eq. d -1a (5 eq.) and 5a (0.5 mmol). e 1a (5 eq.) and 5a (1 mmol). f 1a (2 eq.) and 5a (0.5 mmol.). g 1a (1.5 eq.) and 5a (0.5 mmol.). h 1a (1 eq.) and 5a (1 mmol.). i 60°C instead of 90°C. j 30°C instead of 90°C. k [Cu(MeCN)4]PF6 (0.02 eq.), L1 (0.02 eq.).

The scope and limitation of the C-H amidination was then established using amidine 5a and varying the nature of the alkanes 1a-r (Scheme 2). Overall, nitroisoureas 6b-r were obtained with yields ranging between modest and good using 5 and up to 20 equivalents of alkanes relative to 5a, depending on the nature of the alkane. Volatile alkanes for instance generally led to improved yields when used in larger excess. Regioselectivities indicate a pro-eminence for the CH2 abstraction as compared to the CH3, in good agreement with studies of Hartwig et al. 4d Interestingly amination at the usually more reactive tertiary C-Hs are not observed likely for steric reasons. 12 Unsubstituted cyclic alkanes reacted smoothly to provide the desired nitroisoureas 6a-6d in satisfying yields.

Monosubstituted methylcyclohexane led to 6e as a mixture of inseparable regioisomers, indicating again a higher reactivity of the methylene C-H bonds. Reaction at the C5 methyl substituent was however observed in small amount. The reaction was also moderately efficient on chlorocyclohexane as shown with the isolation of 6f as a 2.2:1 mixture of regioisomers in which the C-H bond away from the chlorine atom appears as the more reactive. Cis-and trans-1,4-dimethylcyclohexanes led to CH2/CH3 activation (i.e. 6g-h) and no reaction at the tertiary site, with site-selectivities in good agreement with reports on related amidation. 4d The methodology was successfully extended to aliphatic systems. Similarly to their cyclic analogues, methylene C-H were also more reactive than primary and tertiary C-H. This is illustrated with regioisomers ratio in 6j, 6k and hexadecane 6n. When steric effects become significant and CH2 less accessible, then functionalization at CH3 is favoured, as in 6l and 6m, albeit obtained in poor yields. Polycyclic substrates were also reacted under the same conditions producing the expected regioisomers 6p-r as mixtures of regio and diastereomers, which structure could not be determined. Adamantane led to nitroisourea 6o as a mixture of C1/C2 regioisomers where the tertiary C-H was the most reactive in good agreement with previous literature reports. 4d Finally, it is worth mentioning that with poorly reactive alkanes, variable amount of O-methyl-N-methylnitroisourea 6s was also isolated, as a result of the coupling between methyl radical, issued from the decomposition of the t-BuO radical, 11 and the Cu-amine complex. 4d As discussed below, 6s may find interesting applications as methylisocyanate (MIC) surrogate. The optimized conditions above (Table 1, entry 16) were extended to other nitroisoureas 5b-e, possessing a different leaving group (R) on the central carbon center (vide infra). 5b-e were readily available from the corresponding urea or thiourea (ESI). S-methyl-N-nitroisothiourea 5b and nitroguanidine 5c provided the desired C-H amination product 7a-b, albeit in low yields (Scheme 3). In contrast, azole 5d led only to recovered starting material, while 5e suffered from the nucleophilic displacement of the chlorine atom by the NH2 group, thus preventing the formation of the desired 7d.

Scheme 3. C-H amination using nitro-isoureas 5a-e.

The conversion of O-methyl-N-alkylnitroisoureas 6 into isocyanates 4 has not been reported to date (Scheme 4). 9 However, it was anticipated that treatment of 6 under appropriate basic conditions would generate the Nnitrocarbodiimide intermediate I, discussed above, through elimination of MeOH (Figure 1,D). The methanol elimination from O-methyl-N-cyclohexylnitroisourea 6a thus investigated varying the nature of the base. Carbonates, NaOH, KOH, K3PO4 or NaOEt in alcohols as solvents thus tested (ESI), K2CO3 invariably leading to the best yields in urethanes 8ad (Scheme 4). As expected, higher conversion in urethanes were obtained using primary alcohols at 80°C, although secondary alcohols were also shown to react, but a higher temperature (130°C). 13 Amines also added to 6a at 80°C under these conditions, but surprisingly, the elimination of MeOH did not take place, but instead N-cyclohexyl-N-alkylisourea 9 was isolated in good yield (Scheme 5). Treatment of the latter under acidic conditions finally afforded urea 11. The conversion of 6a into 9 suggests that more nucleophilic reagents such as amines preferentially adds onto the isourea carbon center, prior to elimination. Finally treatment of 6a under basic conditions in water led to the symmetrical urea 10. Although the treatment of O-methylnitroisoureas 6 under basic conditions provides urethanes and urea using simple and reproducible conditions, the access to unsymmetrical ureas such as 11 in 3 steps from cyclohexane is not satisfying. In the course of our studies, we eventually discovered an unusual and more general pathway to urethanes and urea starting from 6.

During 1 H NMR studies on the base-catalysed elimination reaction of 6a in CDCl3 using DBU as a base, we observed the unexpected formation of the isocyanate 4a after heating the reaction mixture at 130°C for 12h (Scheme 6). The 1 H NMR of the crude reaction mixture showed the formation of 4a along with a compound presenting a singlet at 3.05 ppm attributed to MeCl, which was confirmed through GC-MS (ESI). N,N-Dimethylnitroamine 12 was also formed after 3 h as shown by 1 H NMR and GC-MS (ESI), but progressively disappeared due to its known instability at this temperature. 14 Scheme 6. Conversion of O-methyl-N-alkylnitroisourea 6a into isocyanate 4a. 4a could be isolated in high yield, but was more conveniently reacted in situ with a suitable nucleophile. As summarized in Scheme 7, the scope of these new conditions was established and showed that urethanes and ureas could be prepared in generally high yield, using a two-steps one pot procedure, including the generation of the isocyanate which was directly treated with a given alcohol or amine using Et3N as a catalyst. The reaction was shown to proceed in excellent yield, whatever the alkane precursor, alcohol or amine. For instance, less nucleophilic naphthol and aniline led to urethane 8e and urea 13c in excellent yields. Secondary amines also proved reactive under these conditions as shown with the synthesis of 13d.

A tentative mechanism to rationalize the quantitative formation of isocyanate 4 from 6 in the presence of a catalytic amount of DBU in CHCl3 is depicted in Figure 2. Formation of both MeCl and 12 as by-products strongly support the displacement of the methyl substituent in 6 by a chloride anion as for instance in Krapcho decarboxylation. 10 The formation of Cl -might result from the deprotonation of chloroform by DBU to produce a dichlorocarbene and DBU-H + Cl -, although our efforts to trap Cl2C:, through cyclopropanation of styrene or C-H insertion in adamantane, met with failure. Nucleophilic substitution of a chlorine atom from CHCl3 by DBU constitutes another option. This demethylation would thus form intermediate i, the protonation of which with DBU-H + (pka(DMSO) = 12) leading to the nitroisourea ii (estimated pK ~ 20), which could then react with the free DBU to form the isocyanate 4, along with a nitroamine anion iii. The latter would then be methylated by MeCl to form a N-methylnitroamine iv and regenerate DBU-H + Cl -, the true catalyst of the process. iv which was not detected in GC-MS may be further alkylated with MeCl to form 12. An alternative pathway proceeding through a demethylation reaction of 6 by iii could also generate iv and i. However, the monitoring of the reaction indicates a continuous formation of MeCl during the reaction, supporting the demethylation of 6 by the chloride anion as shown in Figure 2. efforts to substitute the DBU-CHCl3 medium by other of chloride anion (as LiCl in DMSO, DBU-H + Cl -or pyridinium hydrochloride) led to the formation of the desired isocyanate albeit in lower yields due to the unavoidable presence of traces of water in these salts. For instance, treatment of 6a with pyridinium hydrochloride in chlorobenzene led to urea 11 (Scheme 8) in 68% yield supporting the role of Cl -as a catalyst and the presence of water in this hydrochloride salt. Similarly, reaction of 6a with HCl in dioxane led to the amine as it hydrochloride salt 14 in excellent yield, demonstrating that the nitroisourea route may also constitute an attractive method to prepare free amines from alkanes. As mentioned before, when the C-H amination of alkanes with O-methyl-N-alkylnitroisourea 6a was less efficient, variable amount of O-methyl-N-methylnitroisourea 6s accompanied the desired product. 4d Application of the above protocol to 6s would produce the methylisocyanate (MIC) a key component in the elaboration of the important family of carbamate pesticides (carbaryl, aldicarb, metolcarb,….). 15 MIC is a volatile and flammable colorless liquid, potentially explosive when mixed with air. It is highly toxic and was responsible for thousands of deaths in Bhopal disaster in 1984. 16 It is prepared industrially by the reaction of methylamine with poisonous phosgene leading to the N-methylcarbamoyl chloride, the reaction of which with Et3N providing MIC. Among the measures taken by the chemical industry to avoid the dangerous handling of MIC, one was to develop a less hazardous alternative to MIC production that would consume the MIC immediately upon its generation. [START_REF]The Use and Storage of Methyl Isocyanate (MIC) at Bayer CropScience[END_REF] The above protocol was thus applied to the preparation of some methylcarbamates exploiting the high reactivity of both 6s and MIC under these conditions. Previous conditions in Scheme 7 were slightly modified to avoid the accumulation of MIC at the end of the process. The alcohol was directly mixed at the start of the process with an equimolar amount of base (Et3N) in CHCl3 as a solvent, leading to reaction completion in less than 3h (as compared to 24h for other isoureas). Fenobucarb® 15b used for the control of hemipteran pests on rice and cotton was thus prepared in this way in 75% yield, while Sevin® 15c, a broadspectrum systemic insecticide, was obtained in a 64% overall yield (Scheme 9). Carbamoylation of oestrone was also efficiently performed, leading to 15d in excellent yield. Finally, urea 16a could also be prepared following this method. It is worthy of note that 6s may also be prepared, by a simple heating of 5a, t-BuOOt-Bu, Cu(CH3CN)4]PF6 and L1 at 90°C for 12h (75% yield, ESI). Scheme 9. Nitroisourea 6s as a masked "MIC". Synthesis of carbamate insecticides.

Finally, the strategy was extended to the functionalization of a linear polyolefin such as polyethylene. 35% of the polymers produced in the world are polyolefins, of which an estimated 95% are single-use and account for plastic wastes. [START_REF] Geyer | [END_REF] Therefore, in the same way that it is particularly attractive to functionalise bioactive molecules at a late stage in order to access new druglike molecule platforms, the functionalization of branched polyolefins would allow the recycling of these plastic wastes in order to produce new high-performance thermoplastic materials. The functionalization of these aliphatic chains in a controlled manner under mild conditions is however challenging, considering the strength of the C-H bonds, but also the insoluble nature of these materials in organic solvents. Several studies have however recently emerged in this context 19 that prompt us to describe our own investigations. The C-H amination sequence devised above was thus applied to a linear low density polyethylene (LLDPE). Solubilization of the LLDPE was achieved in chlorobenzene at 105°C, using 0.1 eq. of 5a as aminating agent. After heating overnight at this temperature, the polymer P1 was precipitated in acetone. The LLDPE functionalization was determined to be 1.25 mol% by 1 H NMR (relative to repeat unit). 19f DBU-catalyzed decomposition of the isourea functional group led to the -NCO-modified LLDPE, which was directly treated with an excess of benzylamine to afford P2, showing urea fragment incorporated along the carbon chain. The above experiment thus demonstrates that upcycling of post-consumer waste offers an opportunity to create new materials, with novel mechanical properties, which would be difficult to elaborate for instance through co-polymerization.

Conclusions

In summary, we report here an unprecedented C-H amination of hydrocarbons using readily available O-methyl-Nnitroisourea 5a as a masked isocyanate functional group. This strategy allows the incorporation on a carbon backbone of the highly reactive isocyanate function using urea as phosgene surrogate. Various linear and cyclic alkanes were thus converted into O-methyl-N-alkylnitroisoureas 6 in moderate to good yields. The later were then converted through an unusual Krapcho-type demethylation, into the desired isocyanates, which were reacted in situ with alcohols and amines to give the corresponding urethanes and ureas in high yields. This simple procedure was extended to the in situ generation of poisonous, yet very useful, methylisocyanate (MIC). This safe method should find applications for late stage derivatization of biological active alcohols and amines. Finally, the method was applied to the functionalization of commodity polymers such as polyethylene. The recycling of these plastic wastes under mild conditions is particularly attractive giving access to new materials inaccessible by traditional polymerization methods. 19

Figure 1 .

 1 Figure 1. Literature precedent on C-H amination (A), isocyanation (B) and preparation of isocyanates from N-alkylnitrocyanamides (C). Present work on the C-H isocyanation using O-methyl-N-nitroisourea 5a (D).

Scheme 2 .

 2 Scheme 2. Scope of the Cu(I)-catalyzed C-H amination of alkanes 1a-r with O-methyl-N-nitroisourea 5a. a 5 eq. of alkane is used. b 20 eq. of alkane is used.

Scheme 4 . 8 .

 48 Scheme 4. Base-catalyzed decomposition of O-methyl-N-alkylnitroisoureas 6a into urethanes 8.

Figure 2 .

 2 Figure 2. Putative mechanism for the conversion of O-methyl-N-alkylnitroisoureas 6 into isocyanates 4.

Scheme 8 .

 8 Scheme 8. Treatment of O-methyl-N-alkylnitroisoureas 6a under acidic conditions.

10 .

 10 Cu(I)-catalyzed C-H nitroamination of low density polyethylene (LLDPE).

Scheme 7. Conversion of O-methyl-N-alkylnitroisoureas 6 into urethanes 8 and ureas 13.

Acknowledgements

We gratefully acknowledge the ANR (NCO-INNOV, N°20-CE07-0015-01), the University of Bordeaux and the CNRS for financial support. We thank the analytical facilities CESAMO for NMR, mass spectrometry and DRX studies.

Conflicts of interest

There are no conflicts to declare.


Zeaiter Hussein
email: hussein.zeaiter@femto-st.fr

Baala Oumaya
email: oumaya.baala@femto-st.fr

Francois Spies
email: francois.spies@femto-st.fr

Val Thierry
email: thierry.val@univ-tlse2.fr

Measuring accurate Angle of Arrival of weak LoRa signals for Indoor Positionning

Keywords: Autocorrelation function (ACF), peak detection, Fast Fourier Transform (FFT), Software Defined Radio (SDR), Angle of Arrival (AoA), Long-Range (LoRa), negative SNR.++++ UHD: USRP Source Sample rate: 2M Centre frequency: 868M Bandwidth: 1M Num items: 2.048k FFT FFT size: 2.048k Window: Blackmanharris Forward/Reverse: Forward Multiply Conjugate Vec Length: 2.048k FFT FFT size: 2.048k Window: Blackmanharris Forward/Reverse: Reverse Complex to Mag Vec Length: 2.048k 2.048k Max Threshold Low: α High: α Initial State: 0 FFT FFT size: 2.048k Window: Blackmanharris Forward/Reverse: Forward

In this paper, we propose an Autocorrelation method for measuring the angle of arrival (AoA) of a weak LoRa signal. A weak LoRa signal has a negative SNR down to -20 dB. The objective is to detect a LoRa signal that operates at low transmission power (TX). Operating at low transmission power (TX) reduces power consumption and extends the battery life of LoRa devices. Besides, the transmission of weak signals strengthens the radio communication protocol, preventing an enemy device from accessing the location coordinates. The detecting algorithm consists of finding Autocorrelation peaks of the LoRa signal. We show that Autocorrelation peaks decrease when the signal is buried in the noise. However, using a large number of Fast Fourier Transform (FFT) will increase the Autocorrelation peaks and the signal-to-noise ratio (SNR). Once the peak of the LoRa signal is detected under the noise, the algorithm will calculate the AoA. All of the proposed algorithms are implemented using a Universal Software Radio Peripheral (USRP), Software Defined Radio (SDR) receiver with the help of GNU Radio software. We, therefore, believe that our Autocorrelation method can detect the LoRa signal accurately and measure the AoA at very low SNR in real-time, being usable for indoor positionning.

I. INTRODUCTION

Nowadays, The Internet of Things (IoT) is experiencing rapid growth. The IoT is a network of connected devices that enables connectivity and data exchange for a wide range of applications, including smart cities, healthcare, industrial and infrastructural applications, transportation, and navigation [START_REF] Hassan | Internet of Things and Its Applications: A Comprehensive Survey[END_REF]. IoT applications face many challenges, including security, This work is supported by the Femto-st institute in collaboration with Jolliet-Innovation and SECA companies in the framework of the SYLOIN FEDER BPI Project. low-cost devices, long-range communication, low data rate, and low power consumption. Today, we can address these challenges with the new low power wide area network (LP-WAN) paradigm. LPWAN standards enable wide communication coverage, low data rates, and long battery life. These advantages led the researchers to investigate the performance of the LPWAN technology both outdoors and indoors [START_REF] Muzaffar | Longrange wireless sensor networks for geo-location tracking: Design and evaluation[END_REF][START_REF] Zafari | A survey of indoor localization systems and technologies[END_REF]. Many LPWAN technologies have been studied recently, such as LoRaWAN, Sigfox, and NB-IoT. LoRaWAN is one of the latest LPWAN technologies that has attracted many researchers interest in outdoor and indoor navigation [START_REF] Choi | Low-Power LoRa signal-based outdoor positioning using fingerprint Algorithm[END_REF][START_REF] Carvalho | Hybrid indoor and outdoor localization for elderly care applications with LoRaWAN[END_REF][START_REF] Kim | Feasibility of LoRa for smart home indoor localization[END_REF].

LoRaWAN is a communication protocol and network architecture built on top of the LoRa physical layer. LoRa [START_REF] Vangelista | Frequency shift chirp modulation: The LoRa modulation[END_REF] is a radio technology based on Chirp Spread Spectrum modulation (CSS) operating at industrial, scientific, and medical (ISM) bands (169 MHz, 433 MHz, 868 MHz, 915 MHz, and 2.4 GHz). The most important benefit of the LoRa technology is the CSS modulation which enables a receiver device to demodulate a transmission up to -20 dB below the noise level. Demodulating a LoRa signal below the noise level reduces the battery lifetime of the LoRa device, makes the transmission distance longer, and secures our LoRa communication. All these benefits make LoRa an ideal candidate for indoor tracking. However, detecting a low signal transmission and maintaining a good location accuracy is always a challenge for most indoor tracking applications.

Software Defined Radio (SDR) is a well-known concept in radio tracking, bringing new possibilities, and allowing us to study existing technologies and detect a weak signal transmission and track it. First, it is possible to detect the presence of a weak signal using several methods. Detection can be done using some mathematical tools such as Autocorrelation. Autocorrelation [START_REF]Autocorrelation[END_REF] consists of determining the degree of similarity of the same variables between two successive time intervals. Second, tracking the signal can be done using the Angle of Arrival (AoA) direction-finding approach. AoA based Direction finding approach has been used in numerous fields, including tracking people and objects.

In this paper, we present an Autocorrelation approach for detecting and measuring the AoA of a weak LoRa signal using an SDR. The main idea consists of detecting the LoRa frequency peaks. The Autocorrelation technique offers an effective way to improve the SNR by reducing the unwanted noise components by a factor of n. Once the signal is detected, The AoA can be calculated using the method described in our previous work [START_REF] Hussein | SYLOIN: Measuring Angle of Arrival of LoRa signals using Software Defined Radio[END_REF]. To the best of our knowledge, no such system can measure the AoA of a LoRa signal up to -20 dB below the noise level.

The rest of the paper is organized as follows. Section II provides an overview of the existing LoRa AoA estimation solutions. Section III describes the theory behind the Autocorrelation method. Section IV presents our system design and implementation of the Fast Autocorrelation method for measuring the AoA of LoRa signal using SDR. Section V evaluates our system based on real experiments results. Section VI concludes the paper and provides guidelines for future research directions.

II. RELATED WORKS

The problem of detecting and measuring the AoA of radio signals in localization and tracking services is a rapidly developing area of science and technology. Developing new AoA methods is always a challenge for the research community. LPWAN technologies such as the Long-Range (LoRa) can provide a localization solution based on the time difference of arrival (TDoA) and the received signal strength (RSS) [START_REF] Anjum | RSSI Fingerprinting-Based Localization Using Machine Learning in LoRa Networks[END_REF][START_REF] Lam | RSSI-Based LoRa Localization Systems for Large-Scale Indoor and Outdoor Environments[END_REF][START_REF] Daramouskas | Localization in LoRa Networks Based on Time Difference of Arrival[END_REF][START_REF] Podevijn | TDoA-based outdoor positioning in a public LoRa network[END_REF]. Recently, some research works are trying to mix the RSS, and TDoA techniques with the angle of arrival (AoA) estimation method using the LoRa technology to provide a good localization solution [START_REF] Baik | Hybrid RSSI-AoA Positioning System with Single Time-Modulated Array Receiver for LoRa IoT[END_REF][START_REF] Aernouts | Combining TDoA and AoA with a particle filter in an outdoor LoRaWAN network[END_REF]. LPWAN technologies, including LoRa, utilize a minimum amount of power and a narrow bandwidth to transmit a signal. An RSS-based LoRa localization solution can't offer a good localization accuracy since lowering the power consumption of the LoRa device might result in a lower quality of the RSS and more multipath effect and channel fading. Time-based LoRa localization solutions such as ToA and TDoA also suffer from poor localization accuracy because they require a larger bandwidth or a high timestamp precision of the received signal at the gateway receiver. Addressing these limitations can be done using the AoA estimation technique [START_REF] Bnilam | Adaptive probabilistic model using angle of arrival estimation for IoT indoor localization[END_REF]. Using an AoAbased localization solution has several advantages. First, unlike the TDoA technique, the AoA technique does not require a large signal bandwidth and a high timestamp precision at the receiver. Secondly, the AoA-based localization solutions measure the angle between the transmitter and the receiver by measuring the phase of the received signal at the receiver gateway. Consequently, the narrow bandwidth of the LoRa signal will not affect the phase of the signal and, therefore, the accuracy of the AoA of the received signal. Third, the AoA technique does not depend on the received signal strength and, therefore, the phase and the angle of the received signal will not be affected by the multipath and channel fading. These benefits make the AoA a promising localization solution for the indoor environment.

Recently, AoA-based LoRa localization solutions have been introduced in the literature. In [START_REF] Bnilam | LoRay: AoA estimation system for long range communication networks[END_REF], an AoA localization technique of LoRa signals based on an SDR receiver has been proposed. The proposed method found an estimation error of 2 • in LOS (Line-of-Sight), and 10 • in NLOS. However, this method consists of 8-element uniform linear array (ULA). The 8 ULA consists of 8 independent SDR receivers for which a hand-crafted crystal oscillator is needed to achieve synchronization between the channels. Another AoA-based LoRa localization approach based on phase detectors has been presented in [START_REF] Bnilam | Angle of Arrival Estimation System for LoRa Technology based on Phase Detectors[END_REF]. The phase detectors make a cost-effective solution to measure the AoA with median and maximum estimation errors of 4 • and 14 • , respectively.

Recently, we introduced the SDR-based localization system that can estimate the AoA of a LoRa signal by measuring the phase difference of the received signal at two antennas [START_REF] Hussein | SYLOIN: Measuring Angle of Arrival of LoRa signals using Software Defined Radio[END_REF]. We built our system based on an individual universal software radio peripheral (USRP) B210 SDR receiver. The choice of this front-end receiver was motivated by its two coherent RX channels. The prototype has been tested in an indoor laboratory office environment a with lot of furniture. The experimental results show that the AoA of the LoRa signal can be measured accurately with a maximum estimation error of 5 • in the range of [0 • ,180 • ]. However, our system can only achieve an accurate AoA measurement with high signalto-noise ratio (SNR) communication. In this paper, we aim to validate our AoA-localization system with a very low SNR up to -20 dB. A new approach is proposed to detect and measure the AoA of a very weak LoRa transmission signal. The presented approach is based on two-antenna reception to exploit the Fast autocorrelation signal detection and the phase difference AoA measurement. We, therefore, believe that an accurate AoA of a weak LoRa signal reduces the battery lifetime, extends the communication lifetime, and secures the communication of the LoRa devices. To the best of our knowledge, we are the first to implement a real AoA for a very weak LoRa signal.

In the following section, we will provide an overview of the two-antenna autocorrelation technique for weak signal detection.

III. DUAL-ANTENNA FAST-AUTOCORRELATION

A. Autocorrelation Function

An Autocorrelation is a mathematical tool used to amplify the signal from noise. The Autocorrelation analysis consists of finding the presence of useful segments in a signal. The autocorrelation of a signal is just the correlation coefficient. However, instead of applying the correlation between two different signals, the correlation is between the two segments of the same signal at times T i and T i+k .

Suppose we have two continuous signals x(n), y(n), n = 1,2,3,..,N, where N is the number of samples. The discrete correlation function of the two signals can be calculated by the following equation:

Corr(x, y) k = 1 N N -1 n=0 x k+n y n (1)
Equation ( 1) measures the correlation function of the two signals. When the two signals are similar, then their correlation coefficient will be 1. However, if the two signals are different, then their correlation coefficient will be 0. If we suppose that = y(n) = x(n), then Equation (1) will be:

Corr(x, x) k = 1 N N -1 n=0 x k+n x n (2)
Equation ( 2) measures the correlation function between two same signals x(n) and x(n+k) separated by a time lag k, which is the autocorrelation function of the signal x(n). The autocorrelation function presented by (2) reaches its maximum value at the lag=0, and is always symmetric around zero, which means that the autocorrelation values are equals at lags +k and -k. Using these properties, it is possible to solve the problem associated with the detection of weak signals. In the next section, we describe the application of FFT with the autocorrelation function.

B. Fast Fourier Transform Autocorrelation

Fast Fourier Transform (FFT) is one of the most commonly used tools in digital signal processing (DSP) applications. As the name implies, the FFT is a fast version of the Discrete Fourier Transform (DFT). FFT is an algorithm used to perform a series of computations that computes DFT much more rapidly than the other available algorithms. Therefore, using FFT will reduce the number of calculations necessary. Let x(n) be a discrete signal, the Discrete Fourier Transform of x(n) is given by:

X k = N -1 n=0 x n e -i2πkn N k = 0, 1, 2, .., N -1 (3)
Where X k is also known as the power spectrum of x(n). Equation (3) represents the DFT computation of N-point data sequence with O(N 2 ) multiplies and adds. Thus, when using FFT, the computation would take O(N logN ) multiplies and adds.

Signal detection is a key function of the FFT. Using FFT and the autocorrelation function can accelerate the autocorrelation computation. The Wiener-Khinchin theorem [START_REF] Bnilam | Angle of Arrival Estimation System for LoRa Technology based on Phase Detectors[END_REF] states that the autocorrelation function and the Power Spectral Density (PSD) of the signal are Fourier pairs. The autocorrelation function is the Fourier transform of the PSD.

Let x(n), y(n) be two discrete signals, the correlation function of the two signals is defined by:

Corr(x, y) k ⇔ X(f )Y * (f ) (4)
By multiplying the FFT of one signal by the complex conjugate of the FFT of the other gives the FFT of their correlation function. Since the autocorrelation function of the signal x(n) is the correlation with its delay copy, the autocorrelation will be:

Corr(x, x) k ⇔ X(f )X * (f ) ≡ |X(f )| 2 (5)
Where |X(f )| 2 is the Power Spectral Density of the signal. Using these properties of autocorrelation fucntion and FFT, it is possible to detect weak signal buried in noise.

The next section describes how to detect weak signals using Autocorrelation, FFT, and Dual-Antenna detection.

C. Dual-Antenna weak signal detection

This section discusses the Dual-Antenna Autocorrelation detection. The proposed detection method measures the Autocorrelation function between outputs of two sensors of the receiving antenna array.

The dual-Antenna approach is a very promising topic in radio communication systems. For the receiver side, Dual-Antenna offers a high potential solution to receive two replicas of the primary signal. The Correlation method can be used to determine whether the primary signal exists or not.

Figure 1 shows two signals X1(t) and X2(t) received by the antennas A1 and A2 respectively. When the transmitter and the receiver are in Line-Of-Sight (LOS) conditions, there will be a time delay ∆(t) between the two signals received at the two antennas. Since the two signals X1(t) and X2(t) are the same time series data received at a different time by the two antennas, X1(t) = X2(t + ∆(t)).

Using the properties of the correlation function between two same signals separated by a time lag t given by the Equation (2), and the Fast Autocorrelation function using FFT given by Equation ( 5), the detection of the signal using a Dual-Antenna receiver is possible.

By collecting enough samples of the received signals, the Fast Autocorrelation, of the signals received from the two Antennas can be built. Based on the Autocorrelation peaks finding and the threshold value, signal detection can be carried out.

In the next section, we present our solution of detecting a LoRa signal using a Dual-Antenna USRP B210 SDR Receiver with the help of GNU Radio.

IV. PROPOSED METHOD

The following method consists of detecting weak LoRa signals on a Dual-Antenna Receiver by measuring the Fast Autocorrelation function. We first determine whether the LoRa signal exists by using the Fast Autocorrelation signal detection. Then, we measure the AoA of the detected signal based on our published work [START_REF] Hussein | SYLOIN: Measuring Angle of Arrival of LoRa signals using Software Defined Radio[END_REF]. Finally, we compare the two methods in terms of accuracy level. The USRP B210 SDR receiver and the GNU Radio development environment form the basis for this research work.

A. USRP-Based SDR Receiver

Most Traditional radios use integrated circuits and specialized equipment for transmission and reception. Traditional radios are made up of mixers, amplifiers, analog/digital converters, modulators, and demodulates. An innovative concept named software defined radio (SDR) replaced the analogical traditional radios. In an SDR, signal processing functions are performed by a single device, which performs the functions of multiple hardware radios. Most of the functionality of the SDR are implemented in software rather than in hardware. GNU Radio founder Eric Blossom cites that the SDR is the technique of getting code as close as possible to the antenna. It turns radio hardware problems into software problems [START_REF] Eric | Exploring Gnu Radio[END_REF].

Ettus Research is one of the companies that have developed an open source hardware platform dedicated to the SDR. The development was focused on the Universal Software Radio Peripheral (USRP). The USRP is characterized by its accuracy, large bandwidth and low price compared to other hardware systems. This open source device defines the interface between the RF analog domain and the General Purpose Processor (GPP) and can generate and receive any kind of signals. The USRP can receive radio waves captured by the antenna and convert these waves into a digital signal that can be processed by the computer using an analog to digital converter (ADC). On the other hand, to generate a radio wave, the USRP converts a digital wave processed by the computer into a RF signal using a digital to analog converter (DAC).

The model of USRP used in this research was the USRP B210. The USRP B210 is a Dual channel SDR receiver which contains 2TX and 2RX ports with fully coherent 2 x 2 MIMO (Multiple Input Multiple Output) capabilities. The coherency between the 2RX ports is an important feature for computing the phase difference and the AoA between the received signals [START_REF] Hussein | SYLOIN: Measuring Angle of Arrival of LoRa signals using Software Defined Radio[END_REF]. The B210 covers frequencies from 70 MHz to 6 GHz with a maximum bandwidth of 56 MHz in real-time. Moreover, this SDR board combines the Spartan6 FPGA, and the AD9361 transceiver that performs the conversion of ADC and DSP. The B210 can be connected directly to a computer via a high-speed Ethernet local area network cable or a USB 2.0/3.0 cable and is compatible with the software development platform GNU Radio.

B. GNU Radio

GNU Radio is one of the most popular software platforms used to interface with a USRP SDR. The USRP implements the hardware part of the system, whereas GNU Radio handles the software part.

GNU Radio is an open source software platform which provides signal processing blocks for the development of SDR applications. GNU Radio signal processing blocks of GNU Radio are written using the C++ programming language and the connection between them is provided by the Python programming language. GNU Radio is widely used by academic research as well as in the industrial and commercial domain.

In the rest of this paper, the USRP B210 is used combined with GNU Radio development software platform.

C. USRP B210 Fast Autocorrelation signal detection

The block diagram in Figure 1 shows the basic principle of our proposed solution. The process starts by extracting the two signals received at the two channels using a UHD: USRP Source block which is responsible for receiving the data from the USRP B210 through the USB3.0 cable. Thereafter, the two signals diverge into two paths. For each path, the output of the UHD: USRP Source block is passed through a Stream to Vector block. The Stream to Vector block converts the stream of data to data in I and Q (vector) format. Once the data are in I and Q (vector) format, the FFT block performs the FFT to convert the data from time domain to frequency domain. Now that the data are in the frequency domain for each path, the Multiply Conjugate block performs the multiplication of the output of the first path by the conjugate of the output of the second path. To get back the data in the time domain, the result of the Multiply Conjugate block is passed through the FFT block which performs a reverse FFT to convert the data from the frequency domain to the time domain. Until now, the data are in complex vector format. The Complex to Mag block provides the output in a float format. It takes a complex number as its input and provides its magnitude in a float format as its output. The Vector to Stream block performs the opposite function of the conversion done by the Stream to Vector block. It converts the data back to the stream format and sends it to the Max block. Up to this point, the data are in stream float format in the time domain. Since the Autocorrelation function has a maximum peak at lag=0, the algorithm should find this peak. This is done by the Max block which takes a stream of data as its input and gives their maximum value as its output.

Once the maximum of the peak value is found, the output of Max block is passed to the Threshold block. The Threshold block is used to compare the output of the Fast Autocorrelation detection algorithm with a predefined threshold. This block has two parameters: High value and Low value. If the output of the Max block is higher than the value set for the High parameter, the output of the The Threshold block is 1. On the other hand, if the output of the Max block goes below the value set for the Low parameter, the output of the Threshold block is 0. The decision output of the Fast Autocorrelation detection algorithm is given by the following equation:

Decision = 1 if M ax > α 0 if M ax ≤ α (6)
where M ax is the peak of the Fast Autocorrelation detection and α is the predefined threshold. The predefined threshold α is determined using a post processing analysis. The F ileSink block is used to write the data in an empty file. The written data are processed in Matlab to determine the optimum predefined threshold value.

The case when the value of the Decision is equal to 1 meaning that the signal is detected, and the case when the value of the Decision is equal to 0 meaning that there is no signal. Once the signal is detected, the algorithm will determine the AoA of the signal using the phase difference method implemented in [START_REF] Hussein | SYLOIN: Measuring Angle of Arrival of LoRa signals using Software Defined Radio[END_REF]. The implementation of each block shown in Figure 1 is shown in Figure 2. A full description of the phase difference and AoA measurement blocks can be found in [START_REF] Hussein | SYLOIN: Measuring Angle of Arrival of LoRa signals using Software Defined Radio[END_REF].

V. EXPERIMENTATION AND RESULTS

The proposed method was evaluated by performing an experimental measurement in our ground floor office environment as shown in Figure 3. We first describe the equipment setup used in this experiment and later we introduce the measurements and the results.

A. Equipment Setup

The FFT Autocorrelation signal detection and AoA measurement is implemented with GNU Radio and USRP B210 SDR receiver for capturing a LoRa signal.

The real time LoRa signal captured by the USRP B210 is transmitted by the Adafruit Feather M0 board containing a RFM95 LoRa module. The Adafruit Feather M0 transceiver combines an Arduino-based microcontroller with a LoRa radio module. The radio transceiver can transmit or receive radio signals at both frequencies 868 MHz and 915 MHz, which can be programmed in software. The Feather M0 transceiver was programmed using the Arduino IDE development toolkit via a USB-to-Serial program. The transmitted signal was configured with the frequency 868 MHz.

On the other side, the transmitted signal was received by the USRP B210 SDR receiver. The B210 was connected to a host PC with Linux-based operating system using high speed USB3.0. The SDR card was configured with the GNU Radio Companion (GRC) 3.7 and the USRP hardware Driver (UHD) 3.14.0. The GNU Radio Companion (GRC) is a graphical user interface used to compile GNU Radio flow graphs. The B210 was configured with the following parameters: center frequency: 868 MHz, sampling rate = 2 MHz, and the bandwidth is 1 MHz.

The Feather M0 LoRa transceiver and the USRP B210 are both equipped with a quarter-wavelength commercial off-theshelf omnidirectional antenna. Both transmitter and receiver were fixed on a tripod with a Line-Of-Sight (LOS) condition. The complete equipment setup is shown in Figure 3.

B. Measurement data

For the measurement data, a LoRa signal was transmitted using a Feather M0 with the following parameters: frequency = 868 MHz, bandwidth = 125 kHz, spreading factor = 7, and coding rate = 4/5. On the USRP B210 side, we assume that the sampling frequency is equal to 2 MHz, and the number of sampled points (FFT length) is equal to 1024 by default.

Our experiments were conducted into two parts: the first one to identify the suitable FFT length in order to improve the detection accuracy at very low power transmission (TX) or signal to noise ratio (SNR). The second to measure the angle of arrival of the LoRa signal at each SNR level.

In experiment 1, the transmitter is programmed to transmit a signal with a transmission power going from +20 dBm to -1 dBm. The detection accuracy of the proposed method is measured for different FFT length. The performance of the algorithm is shown in Figure 4. When the FFT length is equal to 1024, the LoRa signal can be detected effectively when the SNR is greater than -12 dB. When the FFT length is equal to 65536, the detection of the LoRa signal increases to -20 dB. The detection performance of the LoRa signal can be improved effectively when increasing the FFT length because the autocorrelation of noise become smaller when increasing the FFT length. Figure 5 and6 show respectively the values of the autocorrelation peaks for the LoRa signal with two different FFT length. It clearly appears that when using an FFT length equal to 65536 (sample size 30 Hz), the autocorrelation peaks are easier to detect than using an FFT length equal to 1024 (sample size 2 kHz). Therefore, the detection performance of the algorithm is better at high FFT length. In our next experiment, the FFT length is chosen to be equal to 65536.

In experiment 2, we measured the AoA of the LoRa signal at three different SNR levels: 20 dB, 0 dB, and -20 dB. For each SNR level, the AoA was measured in the range of [0, 180] degrees with 15 degrees increments. The results of this measurement is illustrated in Figure 7. We can clearly notice that for an SNR equal to 20dB, the measured AoA are very close to the real AoA values. The angular deviation increases significantly when the measurements were taken with SNR equal to 0dB. For an SNR equal to -20dB, the algorithm still gives a good measurements' accuracy for AoA between 45 degrees and 135 degrees. The angular deviation increases exponentially for AoA less than 45 degrees and greater than 135 degrees. Therefore, the AoA accuracy is better for large angles when the SNR is equal to -20 dB. The AoA deviation error of this experiment is shown in Figure 8. When the SNR is equal to 20 dB, the algorithm can successfully measure the AoA with a deviation error less than 4 degrees in the range of [45,135] degrees, and less than 6 degrees for small angles. Otherwise, when the SNR decreases to 0 dB and -20 dB, the deviation error increases to 9 and 12 degrees respectively for small angles.

According to these experimental results, we can indicate an efficient method to deploy an indoor location infrastructure exploiting low AoA. Indeed, the alignment of the dual antennas of a LoRa gateway must favor the angles located between 45 and 135 degrees in the building so that the other angle values are as much as possible outside the building as can be seen on the Figure 9. Thus, the accuracy of the AoA will be in the range 7 to 8 degrees. With this topology, the best accuracy will be obtained at the center of the building where the AoA are in the green area, while the worst accuracy will be obtained at the building edges where the AoA are in the red area. For an angle with 8 degrees of accuracy, the accuracy will be about 1 meter at a distance of 8 meters. To maintain an accuracy of less than one meter, the distance between two LoRa gateways in the building will be approximately 16 meters. During a critic situation, it will be possible for a gateway to send a specific message to an object in order to ask for a full transmit power reply to improve the accuracy with a factor of nearly 4. An accurate AoA on weak signals allow us to strengthen our existing localization algorithms which will merge signal attenuation, time of flight and AoA to make our coordinate calculations more robust. Moreover, our location functions are able to work in a larger space. Additionally, the asymmetry of the transmission power between the gateway and the object makes it possible to extend the communication lifetime of the objects both by reducing the transmission power and by facilitating the reception of strong signals coming from the gateway. Allowing objects to transmit weakly improves the stealth and the confidentiality of exchanges and makes it more difficult for an enemy device to receive and locate our broadcasting. Using low power transmissions allow us a significant budget link inside a building because the reception threshold is very low, between -125 and -140 dBm, conducting to a communication distance longer than Wi-Fi with a power transmission at 100 mW. Finally, we believe that it will be possible to decode the simultaneous transmission of 2 or 3 objects to avoid collisions and limit re-transmissions which would become unnecessary.

Fig. 1 .

 1 Fig. 1. A GNU Radio flow graph of the proposed system

Fig. 2 .

 2 Fig. 2. A GRC flow graph for the USRP B210 to compute the FFT Autocorrelation and AoA Measurements

Fig. 3 .

 3 Fig. 3. The complete installation setup. Both Feather M0 and USRP B210 are fixed on the tripod.

Fig. 4 .Fig. 5 .Fig. 6 .

 456 Fig. 4. Autocorrelation detection accuracy for different FFT length

Fig. 7 .Fig. 8 .Fig. 9 .

 789 Fig. 7. AoA measurements with different SNR level

ACKNOWLEDGMENT

This work is a partnership with Jolliet and SECA companies and is funded by the Franche-Comté region, the European FEDER fund and the French Public Investment Bank (Banque Publique d'Investissement). Authors want to warmly thank Stephane Givron for his highly valuable contribution.