Florian Jean

Frédéric Schoenstein

Mustapha Zaghrioui

Micka Bah

Pascal Marchet

Julien Bustillo

Fabien Giovannelli

Isabelle Monot-Laffez

F Ceramics

Jean

Composite microstructures and piezoelectric properties in tantalum

Keywords: A, Spark plasma sintering / B, Composite ceramics, Spectroscopy / C, Piezoelectric properties /D, Perovskites / Tantalum

Introduction

Lead zirconate titanate (PZT) based piezoceramics are widely used in industry as actuators, sensors, transducers and in other electromechanical devices thanks to their excellent piezoelectric properties. However, the lead contained in these materials is a real issue because of its high toxicity for human health and environment, which lead to its ban by the European Union in 2003 [START_REF] Jean | Directive 2002/95/EC of the European Parliament and of the Council of 27 January 2003 on the restriction of the use of certain hazardous substances[END_REF]. Since that time, many works focused on the development of new lead-free piezoelectric materials with properties equivalent to those of PZT for target applications. Among the different new lead-free materials, the sodium and potassium niobate K0.5Na0.5NbO3 (KNN) seems to be an interesting alternative, since Saito et al. published high piezoelectric performances obtained for textured KNN ceramics doped with lithium, tantalum and antimony of global composition (Li,Na,K)(Nb,Ta,Sb)O3 [START_REF] Saito | Lead-free piezoceramics[END_REF]. Among the abundant literature following these results, many dopings of this composition were published [START_REF] Rubio-Marcos | Control of the crystalline structure and piezoelectric properties of (K,Na,Li)(Nb,Ta,Sb)O3 ceramics through transition metal oxide doping[END_REF][START_REF] Lévêque | )(Nb,Ta,Sb)O3 piezoelectric ceramics: influence of sintering atmosphere and ZrO2 doping on densification, microstructure and piezoelectric properties[END_REF]. On the other hand, ultrasonic transducers made of pure KNN were recently elaborated in our group, showing the possibility to use this material for concrete applications [START_REF] Bah | Ultrasonic transducers based on undoped leadfree (K0.5Na0.5)NbO3 ceramics[END_REF].

In order to improve the piezoelectric properties in KNN system, Ba, Ca, Sr, Zr, Ti or Co doping [START_REF] Taub | Phase structure and piezoelectric properties of Ca-and Ba-doped K1/2Na1/2NbO3 lead-free ceramics[END_REF][START_REF] Malic | Alkaline-earth doping in (K,Na)NbO3 based piezoceramics[END_REF][START_REF] Vendrell | Improving the functional properties of (K0.5Na0.5)NbO3 piezoceramics by acceptor doping[END_REF][START_REF] Zang | 3 doped (Na0.65K0.35)NbO3 piezoceramics[END_REF] were reported as improving the piezoelectric charge coefficient d33 (pC/N or pm/V), which quantifies the volume change when a piezoelectric material is subjected to an electric field or the polarization on application of a stress, the relative permittivity εr and the associated electric losses represented by tanδ. But, in most cases, KNN is substituted by the combination of different chemical elements. The substitution of KNN with Bi0.5(Na0.7K0.2Li0.1)0.5TiO3 combined with manganese doping leads to the coexistence of orthorhombic and tetragonal phases near room temperature generating enhanced piezoelectric properties [START_REF] Lin | Structure, dielectric and piezoelectric properties of K0.5Na0.5NbO3-Bi0.5(Na0.7K0.2Li0.1)0.5TiO3 ceramics[END_REF]. In the same way, the substitution of KNN with (Bi0.5Na0.5)ZrO3 induce a mixture of both rhombohedralorthorhombic and orthorhombic-tetragonal phase boundaries increasing kp, d33 and curie temperature values. Furthermore, by adding zinc oxide to this compound, grains become smaller and more homogeneous, allowing a decrease of tanδ [START_REF] Li | Phase structure and electrical properties of (K0.5Na0.5)NbO3-(Bi0.5Na0.5)ZrO3 lead-free ceramics with a sintering aid of ZnO[END_REF]. Finally, the substitution of KNN with Bi, Sc, Ti and Mn leads to ceramics with a more homogeneous grain size and higher density presenting higher piezoelectric and pyroelectric properties [START_REF] Jiang | Effects of MnO doping on properties of 0.97K0.5Na0.5NbO3-0.03(Bi0.5K0.5)TiO3 piezoelectric ceramics[END_REF][START_REF] Li | Enhanced piezoelectric properties in Mn-doped 0.98K0.5Na0.5NbO3-0.02BiScO3 lead-free ceramics[END_REF].

The present work develops the study of the effect of niobium substitution by single element tantalum on the microstructure and piezoelectric properties of K0.5Na0.5Nb1-xTaxO3 ceramics sintered by (i) conventional sintering and (ii) spark plasma sintering technique; this latter associates low temperature and high pressure, in a confined environment, which are effective conditions to avoid alkali volatilization and grain coarsening, easily occurring in KNN system, and thus to carefully control the microstructure and composition. Moreover, most of the literature on KNN system does not consider single element doping or substitution and multiple substitutions can lead to versatile properties and difficulties to get a reproducible process, if one considers the future exploitation of this material. In this study, tantalum is chosen because of its ionic radius very close to that of niobium, in order to ensure the substitution and site in the perovskite lattice. In addition, tantalum presents interesting grain growth inhibitor properties [START_REF] Harkulich | Ferroelectrics of ultrafine particle size: II, grain growth inhibition studies[END_REF]. Indeed, Bah et al. have highlighted the impact of a fine and homogeneous grain size on pure KNN densification and properties [START_REF] Bah | High electromechanical performance with spark plasma sintering of undoped K0.5Na0.5NbO3 ceramics[END_REF].

For what concern tantalum doping, the inspection of the literature shows in several studies that this element is generally combined with lithium and antimony [START_REF] Lin | .925Ta0.075)O3-LiSbO3 lead-free piezoelectric ceramics[END_REF][START_REF] Wu | Phase structure and electrical properties of (K0.48Na0.52)(Nb0.95Ta0.05)O3-LiSbO3 lead-free piezoelectric ceramics[END_REF][START_REF] Qian | Phase transition, microstructure, and dielectric properties of Li/Ta/Sb co-doped (K, Na)NbO3 lead-free ceramics[END_REF][START_REF] Rubio-Marcos | Role of sintering time, crystalline phases and symmetry in the piezoelectric properties of lead-free KNNmodified ceramics[END_REF], showing morphotropic phase boundary and improved piezoelectric properties.

Other elements such as lithium [START_REF] Zhou | Phase structure and electrical properties of (Li,Ta)-doped (K,Na)NbO3 lead-free piezoceramics in the vicinity of Na/K = 50/50[END_REF][START_REF] Zhen | Normal sintering of (K,Na)NbO3-based ceramics: influence of sintering temperature on densification, microstructure, and electrical properties[END_REF][START_REF] Hollenstein | Piezoelectric properties of Li-and Tamodified (K0.5Na0.5)NbO3 ceramics[END_REF], iron [START_REF] Li | Room-temperature magnetocapacitance in Fedoped K0.5Na0.5Nb0.95Ta0.05O3 ceramics[END_REF] or zirconium and barium [START_REF] Zhang | Rhombohedral-orthorhombic phase coexistence and electrical properties of Ta and BaZrO3 co-modified (K, Na)NbO3 lead-free ceramics[END_REF] are also added to tantalum in order to improve the density and the microstructure leading to enhanced piezoelectric properties of KNN.

The effects of tantalum as single doping element on niobium site was studied on thin films [START_REF] Lee | Enhanced piezoelectric properties of Ta substituted-(K0.5Na0.5)NbO3 films: a candidate for lead-free piezoelectric thin films[END_REF][START_REF] Lee | Influence of piezoelectric property on annealing temperature of Ta-substituted (K0.5Na0.5)NbO3 thin films by chemical solution deposition[END_REF], single crystal [START_REF] Zheng | Large size lead-free (Na,K)(Nb,Ta)O3 piezoelectric single crystal: growth and full tensor properties[END_REF][START_REF] Hattori | Growth and ferroelectric/piezoelectric properties of (K,Na)(Nb,Ta)O3 ferroelectric single crystals[END_REF][START_REF] Bah | Crystal growth and piezoelectric properties of lead-free based K0.5Na0.5NbO3 by the floating zone method[END_REF] and bulk ceramics [START_REF] Chen | K0.5Na0.5)(Nb1-xTax)O3 ceramics with a higher d33: preparation from a two-stage microwave hydrothermal process[END_REF][START_REF] Hussain | Sodium excess Ta-modified (K0.5Na0.5)NbO3 ceramics prepared by reactive template grain growth method[END_REF][START_REF] Lv | Tantalum influence on physical properties of (K0.5Na0.5)(Nb1-xTax)O3 ceramics[END_REF]. Concerning bulk ceramics, Chen et al. prepared Ta doped KNN ceramics from a powder obtained with a two-stage microwave hydrothermal process. They managed to reach a d33 value of 233 pC/N attributed to tantalum and to the morphology of their powders obtained with this process [START_REF] Chen | K0.5Na0.5)(Nb1-xTax)O3 ceramics with a higher d33: preparation from a two-stage microwave hydrothermal process[END_REF]. For their part, Hussain et al. synthesized sodium excess and Tamodified (K0.470Na0.545)(Nb0.55Ta0.45)O3 textured ceramics by a reactive templated grain growth method. They observed an increase of 44 % for the d33 value compared to nontextured ceramics [START_REF] Hussain | Sodium excess Ta-modified (K0.5Na0.5)NbO3 ceramics prepared by reactive template grain growth method[END_REF]. Finally, Lv et al. prepared tantalum doped KNN by the solidstate reaction technique. Their best results in terms of d33, kp and ε ' at 1 kHz are 205 pC/N, 45 % and 967 respectively, obtained for a substitution of niobium by 30 mol% of tantalum with a densification of 94 %, while kt decreased with increasing the tantalum content [START_REF] Lv | Tantalum influence on physical properties of (K0.5Na0.5)(Nb1-xTax)O3 ceramics[END_REF]. In order to increase the relative density of KNN doped with tantalum, sintering aids such as CuO [START_REF] Matsubara | Piezoelectric properties of (K0.5Na0.5)(Nb1-xTax)O3-K5.4CuTa10O29 ceramics[END_REF][START_REF] Matsubara | Processing and piezoelectric properties of lead-free (K,Na) (Nb,Ta) O3 ceramics[END_REF], LiF [START_REF] Zhou | Low-temperature sintering of (K,Na)NbO3-based lead-free piezoceramics with addition of LiF[END_REF] or ZnO [START_REF] Watanabe | Effect of Mn-doping on the piezoelectric properties of (K0.5Na0.5)(Nb0.67Ta0.33)O3 lead-free ceramics[END_REF] were also used. Another way to reach high density for KNN based ceramics is the use of alternative sintering techniques such as hot pressing [START_REF] Jaeger | Hot pressing of potassium-sodium niobates[END_REF], flash sintering [START_REF] Corapcioglu | Microstructure and microchemistry of flash sintered K0.5Na0.5NbO3[END_REF] or spark plasma sintering [START_REF] Li | Ferroelectric and piezoelectric properties of fine-grained Na0.5K0.5NbO3 lead-free piezoelectric ceramics prepared by spark plasma sintering[END_REF][START_REF] Delorme | Thermoelectric properties of oxygen deficient (K0.5Na0.5)NbO3 ceramics[END_REF]. This latter may allow reaching high density without grain coarsening, thus keeping the benefit of Ta as grain growth inhibitor. Thus, the aim of the present work is to study the effects of niobium substitution by tantalum in K0,5Na0,5Nb1-xTaxO3 on the structure, the microstructure and the piezoelectric properties of ceramics sintered by spark plasma sintering techniques and then to compare the benefits of such microstructure with the same ceramics elaborated by conventional sintering process.

2. Material and methods K0.5Na0.5Nb1-xTax03 (KNNT) (with x = 0.00, 0.05, 0.10, 0.20, 0.30, 0.50 and 1) powders are prepared by the conventional solid-state reaction technique. Oxide and carbonate powders of K2CO3 (99+ %, ChemPUR), Na2CO3 (99.9+ %, ChemPUR), Nb2O5 (99.9 %, ChemPUR) and Ta2O5 (99.9 % ChemPUR) are used as starting materials. The raw powders are first dried at 200 °C during 4 h, weighted in stoichiometric ratios and then mixed during 15 min at 400 rpm in an agate grinding bowl with agate balls. The resulting mixtures are calcined at 830 °C for 5 h. After the first calcination, these powders are milled again and calcined a second time at 830 °C for 5 h. After both calcinations, ceramic pellets are sintered using two different techniques: conventional sintering and spark plasma sintering. For conventional sintering, the powders are uniaxially pressed into 12 mm in diameter and 2 mm thick disks, under 170 MPa, using polyvinyl alcohol (PVA) as a binder. The pellets are then sintered in a tubular furnace under air at 1120 °C for 10 h with a heating rate of 3 °C/min. For spark plasma sintering, SPS Syntex 515S (FUJI) equipment is used. 2.5 g of calcined powders are inserted in a 15 mm diameter graphite die, and placed between two graphite electrodes. The system is then submitted to a heating cycle combined with a pressure cycle. Uniaxial pressures from 20 to 200 MPa can be applied on the graphite die.

Several sintering parameters, under argon atmosphere, are studied: heating rates (50 ° and 100 °C/min), dwell temperatures (920, 940, 960 and 980 °C), dwell times (5 and 10 min), and pressure conditions (50 and 200 MPa). After spark plasma sintering, the samples are annealed under oxygen flow at 900 °C for 1 hour using heating rate 300 °C/h from room temperature to 600 °C and then 50 °C/h from 600 to 900 °C; the cooling rate was 300 °C/h. This thermal treatment allows to recover full oxygen content, and to burn out carbon contamination from the die. All the pellets are then polished to obtain a thickness of 1 mm with parallel surfaces for the piezoelectric characterizations. Phase identification of the ceramics is carried out by X-ray diffraction with a Cu-Kα radiation filtered by Ni (BRUKER D8 X-Ray diffractometer) equipped with a high performance linear detector, between 20 ° and 80 °, with a 0,02 ° step and 1 s exposition time, equivalent to 192 s for a point detector. Rietveld refinements are performed using FullProf program [START_REF] Rodriguez-Carvajal | Recent advances in magnetic structure determination by neutron powder diffraction[END_REF]. The fitting procedure consists in refining the cell parameters, then atomic positions. Then (Na, K) and (Nb,Ta) are assigned to the same site respectively, and defined as randomly distributed. The ratio between Na and K, and the ratio between Nb and Ta have been fixed to the nominal compositions respectively.

Raman spectroscopy is performed at room temperature on sintered samples surfaces using Renishaw Invia spectrometer. A 514 nm argon laser is used as an excitation with a power of 1 W focused by X 50 lens. The relative densities of the different samples are measured by geometrical and weight measurements, and referring to the theoretical density, calculated from Rietveld refinements.

Microstructure and compositions are checked on polished surfaces, with scanning electron microscopy (FEI -Quanta200 and TESCAN-MIRA 3 SEM) coupled with energy-dispersive X-ray spectroscopy analysis (EDS -Oxford Inca X-act). Due to low energy of oxygen, its quantification is very much challenging; thus for this ABO3 perovskite system, the number of oxygen atoms is assumed to be 3 for all the compositions and the quantification of elements is calculated on the cations.

To perform electrical measurements, high purity silver paint (SPI supplies) is pasted on both sides of the pellets and fired at 900 °C for 20 min for the adhesion of the electrodes. All samples are then poled at 130 °C in oil under 3 kV/mm for 10 min using a DC power supply and cooled to room temperature under electrical field. The complex electrical impedance is then measured according to frequency, using a Vector Network Analyzer (Omicron Lab Bode 100). The planar coupling factor kp is calculated by the resonance-antiresonance method on the basis of IEEE standards on Piezoelectricity [START_REF]IEEE Standard on Piezoelectricity[END_REF]. Relative permittivity (εr) and dielectric losses (tanδ) are measured at 1 kHz using a precision impedance analyzer (Agilent 4294A). Piezoelectric coefficients are measured with a Berlincourt -d33 -meter (Piezotest PM-200). In order to quantify these evolutions, Rietveld refinements are performed on the diffraction patterns. For x = 0, 0.05, 0.10, 0.20 and 0.30, the structure is correctly described by the orthorhombic Amm2 symmetry. For x = 1 (KNT), experimental XRD data are well described by the cubic Pm-3m phase. For x = 0.5, both orthorhombic and cubic structures are tested. As a result, orthorhombic phase describes better the experimental data, but "a" and "c" cell parameters are found to be very close, strongly suggesting P4bm tetragonal phase, rather than the orthorhombic one [START_REF] Mgbemere | Structural phase transitions and electrical properties of (KxNa1-x)NbO3-based ceramics modified with Mn[END_REF].

Results and discussion

Obtained cell parameters are plotted in Fig. 2 as a function of the increasing amount of Ta, and according to a pseudo cubic cell (i.e. ac = aO, bc = bO / √2, cc = cO / √2

for the orthorhombic Amm2 samples). One can observe that at least three domains can be identified and the structure evolution of K0.5Na0.5Nb1-xTaxO3 composition undergoes orthorhombic to tetragonal transition between x = 0.30 and x = 0.50 and then a cubic transition for x = 1.

These results confirm that tantalum is effectively incorporated in the KNNT ceramics, all along the substitution but not in a continuous process. It can be noticed also that when increasing the tantalum amount until x = 0.50, all diffraction peaks become broader and this can be attributed to chemical disorder and possibly to the presence of smaller crystallites, in accordance with the grain growth inhibitor role of tantalum.

In order to confirm and complete the X-Ray diffraction analyses, Raman spectroscopy is performed on all the samples and compositions and the spectra are presented in Fig. 3a.

For the end members x = 0 and x = 1, Raman spectra are consistent with the literature [START_REF] Mahesh | Raman and Dielectric Studies on Lead free (K0.5Na0.5)NbO3 Piezoelectric Ceramics[END_REF][START_REF] Zhu | Raman tensor analysis of (K0.5Na0.5)NbO3-LiSbO3 lead-free ceramics and its application to study grain/domain orientation[END_REF][START_REF] Ahn | Effect of Ta content on the phase transition and piezoelectric properties of lead-free (K0.48Na0.48Li0.04)(Nb0.995-xMn0.005Tax)O3 thin film[END_REF][START_REF] Polomska | Raman scattering dtudies of lead free (1x)K0.5Na0.5NbO3-xSrTiO3 relaxors[END_REF][START_REF] Mirza | High pressure Raman study of KNbO3-KTaO3 and KNbO3-NaNbO3 mixed crystals[END_REF][START_REF] Vendrell | Effect of lanthanide doping on structural, microstructural and functional properties of K0.5Na0.5NbO3 lead-free piezoceramics[END_REF][START_REF] Wang | The NbO6 octahedral distortion and phase structural transition of Eu3+doped K0.5Na0.5NbO3-xLiNbO3 ferroelectric ceramics[END_REF]. For x = 1, K0.5Na0.5TaO3 (KNT) crystallizes in a cubic structure with Pm-3m space group, which must not present any active Raman mode. However, the spectrum presents some peaks that might be attributed to second order Raman modes or even infrared modes, activated by some structural disorder [START_REF] Glinšek | Lattice dynamics and broad-band dielectric properties of the KTaO3 ceramics[END_REF][START_REF] Perry | Ferroelectric soft mode in KTaO3[END_REF]. For x = 0, the observed Raman spectrum is similar to that reported by several authors [START_REF] Mahesh | Raman and Dielectric Studies on Lead free (K0.5Na0.5)NbO3 Piezoelectric Ceramics[END_REF] for KNN and related compositions, and corresponds to the orthorhombic structure with Amm2

space group [START_REF] Mahesh | Raman and Dielectric Studies on Lead free (K0.5Na0.5)NbO3 Piezoelectric Ceramics[END_REF][START_REF] Zhu | Raman tensor analysis of (K0.5Na0.5)NbO3-LiSbO3 lead-free ceramics and its application to study grain/domain orientation[END_REF][START_REF] Ahn | Effect of Ta content on the phase transition and piezoelectric properties of lead-free (K0.48Na0.48Li0.04)(Nb0.995-xMn0.005Tax)O3 thin film[END_REF][START_REF] Polomska | Raman scattering dtudies of lead free (1x)K0.5Na0.5NbO3-xSrTiO3 relaxors[END_REF][START_REF] Mirza | High pressure Raman study of KNbO3-KTaO3 and KNbO3-NaNbO3 mixed crystals[END_REF][START_REF] Vendrell | Effect of lanthanide doping on structural, microstructural and functional properties of K0.5Na0.5NbO3 lead-free piezoceramics[END_REF][START_REF] Wang | The NbO6 octahedral distortion and phase structural transition of Eu3+doped K0.5Na0.5NbO3-xLiNbO3 ferroelectric ceramics[END_REF][START_REF] Kreisel | High pressure Raman study of a relaxor ferroelectric: The Na0.5Bi0.5TiO3 perovskite[END_REF][START_REF] Xia | Soft-mode spectroscopy in Fe:KTa1-xNbxO3 crystals[END_REF][START_REF] Petzelt | Infrared, Raman and high frequency dielectric spectroscopy and the phase transition in Na1/2Bi1/2TiO3[END_REF][START_REF] Amira | Structural and Raman properties of the tetragonal tungsten bronze ferroelectric Pb2(1x)K1+xGdxNb5O15[END_REF].. This spectrum can be described by means of internal vibrations of the octahedral NbO6 (Oh symmetry). As well known, the A1g (ν1) and Eg (ν2) modes correspond to a symmetrical and asymmetrical stretching vibrations; and T2g (ν5) mode is related to a symmetrical bending vibration [START_REF] Zhu | Raman tensor analysis of (K0.5Na0.5)NbO3-LiSbO3 lead-free ceramics and its application to study grain/domain orientation[END_REF][START_REF] Ahn | Effect of Ta content on the phase transition and piezoelectric properties of lead-free (K0.48Na0.48Li0.04)(Nb0.995-xMn0.005Tax)O3 thin film[END_REF][START_REF] Polomska | Raman scattering dtudies of lead free (1x)K0.5Na0.5NbO3-xSrTiO3 relaxors[END_REF][START_REF] Vendrell | Effect of lanthanide doping on structural, microstructural and functional properties of K0.5Na0.5NbO3 lead-free piezoceramics[END_REF][START_REF] Wang | The NbO6 octahedral distortion and phase structural transition of Eu3+doped K0.5Na0.5NbO3-xLiNbO3 ferroelectric ceramics[END_REF].

The spectrum evolution between x = 0 and x = 0.5 shows that the high frequency modes at 600 cm -1 and 850 cm -1 wavenumbers are not significantly shifted or modified in their shape with the increasing substitution of niobium by tantalum. For what concerns the low wavenumbers modes around 200-300 cm -1 a significant evolution can be observed. For x = 0.05 and x = 0.10 the spectra are similar to that of x = 0, corresponding to an orthorhombic structure, in accordance with XRD results. For x = 0.20 and x = 0.30, these two spectra present a real difference with the previous ones.

Indeed, the mode numbers still correspond to an orthorhombic structure but their intensities are different. This result is also consistent with the evolution of XRD diagrams and the cell parameters (Figs. 1 and2). For x = 0.50, the number, the intensity and the positions of the peaks are clearly different from the previous ones and do not correspond to a cubic Pm-3m structure; the environment, thus modified, can correspond to a tetragonal structure, as was found in the Rietveld analysis.

Structural phase transition in perovskite is often identified by means of the band shift of some selected modes. For KNN and related compositions, wavenumber of A1g (ν1) and Eg (ν2) modes in the region 500 -700 cm -1 were largely used to identify phase transitions [START_REF] Zhu | Raman tensor analysis of (K0.5Na0.5)NbO3-LiSbO3 lead-free ceramics and its application to study grain/domain orientation[END_REF][START_REF] Ahn | Effect of Ta content on the phase transition and piezoelectric properties of lead-free (K0.48Na0.48Li0.04)(Nb0.995-xMn0.005Tax)O3 thin film[END_REF][START_REF] Polomska | Raman scattering dtudies of lead free (1x)K0.5Na0.5NbO3-xSrTiO3 relaxors[END_REF][START_REF] Vendrell | Effect of lanthanide doping on structural, microstructural and functional properties of K0.5Na0.5NbO3 lead-free piezoceramics[END_REF][START_REF] Wang | The NbO6 octahedral distortion and phase structural transition of Eu3+doped K0.5Na0.5NbO3-xLiNbO3 ferroelectric ceramics[END_REF][START_REF] Rout | High-temperature X-ray diffraction and Raman scattering studies of Ba-doped (Na0.5Bi0.5)TiO3 Pb-free piezoceramics[END_REF]]. Hence, both band modes were fitted to the sum of two Gaussian-Lorentzian curves and wavenumbers versus tantalum content is plotted in figs. 3b and 3c. One can observe a discontinuous change in wavenumbers versus tantalum content, notably the shift of both modes to higher wavenumbers. This feature can be attributed to the structural phase transition from orthorhombic structure (Amm2) to tetragonal structure (P4bm). Also note that Eg (ν2) mode evolution shows two behaviors between x = 0 and 0.3 (Fig. 3b), with a slight increase in the wavenumber for x = 0 to 0.1 and then a decrease above. These features are in total agreement with the cell parameters evolution obtained from Rietveld analyses.

From these structural and vibrational considerations, it can be concluded that tantalum is successfully introduced in the KNN structure, with the creation of some chemical disorder. Two structural transitions occur with increasing the amount of tantalum, from Amm2 orthorhombic structure to P4bm tetragonal structure above x = 0.30 and finally to Pm-3m cubic structure for x = 1 (KNT).

Microstructural features

Microstructure of KNNT ceramics sintered with the conventional route at 1120 °C for 10 h are shown in Fig. 4. All ceramics present cuboid grains with a bimodal distribution of micron size grains. For x = 0 (Fig. 4a), the first population of grain sizes is centered on 2 µm and the second one is centered on 5-6 µm. With increasing the amount of Tantalum, a drastic decrease of grain size can be observed (Fig. 4b -f). Thus for x = 0.50 (Fig. 4e), grain size ranges from submicrometric to 1 µm values and is similar to x = 1 (KNT, Fig. 4f). Another significant point is the apparent density, which decreases with increasing the amount of tantalum. The use of grain growth inhibitors (like tantalum) is known to inhibit the densification during the sintering step, and is confirmed here by the observations in Fig. 4. The use of tantalum thus allows obtaining ceramics with a micrometric and narrow grain size, which is also confirmed by the evolution of the diffraction peaks towards slightly broader peaks, which can correspond to smaller domains.

The increase of densification with the use of spark plasma sintering technique is clearly shown in Fig. 5c and5d, compared to conventional sintering. The results of the relative density measurements, shown in Fig. 6, clearly emphasize the benefit of Spark Plasma Sintering for the sintering of tantalum substituted KNNT, whatever the amount fo Ta.

A relative density over 95 % can be maintained for all the substitution levels in SPS sintered samples, at 920 °C, during 5 minutes and under 50 MPa, while the relative density continuously decreases with the increase of niobium substitution by tantalum in conventionally sintered samples, even by modifying the sintering conditions (times and temperatures). Otherwise, another important feature on these microstructures is the different chemical contrasts that can be detected in these large scale micrographs using backscattered electron detector, for all the substituted samples and whatever the sintering process. A focus on these microstructures is given in the zoom presented Fig. 7. Three kinds of contrast levels appear, homogeneously distributed, consisting in light and dark inclusions embedded into a grey matrix (Fig. 7a). The number of light inclusions increases with the tantalum content, the dark inclusions remaining in the same proportions. Similar observations made for pure KNN (not shown here) point out that this phenomenon does not occur in non-substituted samples, prepared in the same conditions. Thus, KNNT ceramics appear to have a composite microstructural aspect.

To go further, analyzes by energy dispersive X-ray spectroscopy (EDXS) coupled with Scanning electron microscopy (SEM) observations were carried out on spark plasma sintered KNNT ceramics (x = 0.20) corresponding to the microstructures of Fig. 7. On the one hand, it appears light inclusions composed of submicrometric cuboid grains, as shown in Fig. 7b. They are tantalum rich, with a very low amount of niobium and sodium deficient. On the other hand, dark inclusions are made of bigger grains with an average size of 3 to 5 µm, similar to x = 0 grain size, and with less defined shapes;

these inclusions are niobium rich and tantalum deficient compared to the nominal composition. The matrix around these two kinds of inclusions (Fig. 7c) suggests a homogeneous mixture of small and coarse grains. Energy dispersive X-Ray spectroscopy analysis shows a ratio of 1:5 between tantalum and niobium, which corresponds to the nominal substitution rate of tantalum for K0.5Na0.5Nb0.8Ta0.2O3 composition. It can also be underlined that the A-site and the B-site occupancy rates of the ABO3 perovskite are preserved for each analyzed areas, the ratio between (Na + K) and (Nb + Ta) remaining 1 in all cases. Actually, KNNT ceramics prepared in this study appear as a several phases composites. Considering again the XRD analyses presented in the first part of this study, one can consider that tantalum is effectively introduced in the KNN structure forming K0,5Na0,5Nb1-xTaxO3 (KNNT) and corresponding to the main phase observed in Raman study. But even for a low value of x, new phases appear rapidly, regularly dispersed at a large scale in the microstructure but also at a lower scale. Thus the dark areas are close to KyNa1-yNbO3 composition (KNN) and in the form of few micrometers grains, and the light areas correspond nearly to KyNa1-yTaO3 composition (KNT), constituted of submicrometric to one micrometer grains. These last two phases certainly present very similar diffraction patterns that could not be differentiated from the whole sample by basic XRD analyzes. To our knowledge, such composite structures have not been reported for tantalum doped KNN. In recent literature on KNN and other related lead-free piezoelectric systems [START_REF] Lalitha | Hardening of electromechanical properties in piezoceramics using a composite approach[END_REF] the composite approach is one way to provide chemical disorder, structural strains and distortions, or morphotropic phase boundaries. In polycrystalline ceramics, interfaces and grain-tograin interactions can also contribute to modify the movement of the domain walls, with a hardening or softening effect [START_REF] Hall | A high energy synchrotron x-ray study of crystallographic texture and lattice strain in soft lead zirconate titanate ceramics[END_REF]. These different microstructural factors can modify electromechanical response upon application of an electric field, and significant improvement in relaxor systems were shown with this approach.

For all these reasons, in the following, the piezoelectric properties are considered in these new composite materials.

Piezoelectric properties

For what concern the physical properties, for both sintering techniques the piezoelectric coefficients d33 are measured and the coupling factors for planar mode kp, the relative permittivity εr and dielectric losses tanδ (at 1 kHz) are deduced from impedance measurements.

As shown in Fig. 8, the substitution of niobium by tantalum clearly impacts the piezoelectric coefficient d33. An increase of this property is observed with the increase of tantalum amount up to x = 0.20-0.30 for both sintering techniques. Note that the increase of d33 is more significant for the SPS samples, with the highest value of 160 pC/N for x = 0.30, comparable to the value (159 pC/N) obtained by Lv et al. [START_REF] Lv | Tantalum influence on physical properties of (K0.5Na0.5)(Nb1-xTax)O3 ceramics[END_REF] in a 20 mol% substituted KNN.

For what concern the planar electromechanical coupling factor kp, the conventional sintering appears to improve kp with the incorporation of tantalum from x = 0.05 until x = 0.10, with a slight decrease above this value. kp ranges between 23-26 % for x = 0.05 to x = 0.20, and it remains more than two times higher than for the nonsubstituted samples. With the spark plasma sintering technique, high kp values are obtained in all cases, compared to conventional sintering, ranging from 42 to 46 % with the optimum value for x = 0.10 but with a low variation until x = 0.20. In the case of SPS sintered sample, the benefit of niobium substitution by tantalum is less sensitive than for conventional sintering. For comparison, the best kp values obtained by Lv et al. are 44.6 % for x = 0.10 and 45 % for x = 0.30, with a low variation with tantalum content as well, similarly to the present study.

The relative permittivity is presented in Fig. 9; with conventional sintering technique, increasing the tantalum content has no impact on the relative permittivity with measured values around 250-300 on the whole range of substitution. Considering the low and decreasing relative density of these samples, often linked to the permittivity values, it seems that a positive effect of tantalum may balance the density losses. However, there is a significant increase of the relative permittivity with both SPS sintering and increase of tantalum amount, reaching a maximum value of εr = 805 for x = 0.30. These results highlight the joint benefit of the SPS technique and tantalum incorporation on the ceramics relative densities. Note that the best properties are obtained between x = 0.10 and x = 0.30, which are the compositions corresponding to distorted orthorhombic structure or between orthorhombic and tetragonal structures. This is a complementary proof of the necessity of phase boundaries or morphotropic phases coexistence for the improvement of some piezoelectric properties.

Finally, it can be observed in Fig. 9 that the dielectric losses remain under a value of 3 % for most of the samples, slightly increasing above 4 % for x = 0.30 and x = 0.50 in the case of SPS sintered samples.

SPS parameters considerations

To go further, the impact of spark plasma sintering conditions on electrical properties is studied for the KNNT ceramics with x = 0.20, corresponding to the optimum of all the properties. The studied sintering parameters are the temperature, the heating rate, the dwell time and the pressure. The results are summarized Table 1.

Using the sintering parameters corresponding to the above results (100 °C/min, 5 min dwell time and 50 MPa uniaxial pressure), the temperature is varied from 920 to and the values of Kp and εr are potentially interesting for the use of this material in transducer's element or energy harvesting devices for applications [START_REF] Bantignies | Lead-free high-frequency linear-array transducer (30 MHz) for in vivo skin imaging[END_REF], preparing thus the "after PZT" devices.

Fig. 1

 1 Fig. 1 presents the X-ray diffraction patterns of all the K0.5Na0.5Nb1-xTaxO3

Figure 1 :

 1 Figure 1: XRD patterns of the K0.5Na0.5Nb1-xTaxO3 ceramics from x = 0 to x = 1. Insert: enlargement of the 45-46.5 °, corresponding to (202) and (020) diffraction peaks. Intensities have been intentionally shifted.

Figure 2 :

 2 Figure 2: Evolution of the cell parameters as a function of x in K0.5Na0.5Nb1-xTaxO3, obtained from Rietveld refinements. All parameters are referred to the pseudo-cubic unit cell. Dashed lines are only guide to the eye.

Figure 3 :

 3 Figure 3: (a) Room temperature Raman spectra of K0.5Na0.5Nb1-xTaxO3 ceramics for x = 0 to x = 1. (b) and (c) wavenumber as function of x for Eg (ν2) and A1g (ν1) vibrations of the NbO6 octahedra, respectively.

Figure 4 :

 4 Figure 4: SEM images of K0.5Na0.5Nb1-xTaxO3 ceramics sintered by conventional sintering at 1120 °C -10 h. (a) x = 0, (b) x = 0.05, (c) x = 0.10, (d) x = 0.20, (e) x = 0.50 and (f) x = 1.

Figure 5 :

 5 Figure 5: SEM micrographs with backscattered electron detector of K0.5Na0.5Nb1-xTaxO3, sintered by conventional sintering (a) x = 0.05 and (b) x = 0.10, and sintered by spark plasma sintering (c) x = 0.05 and (d) (x = 0.10).

Figure 6 :

 6 Figure 6: Relative densities for the whole range of x in K0.5Na0.5Nb1-xTaxO3 and for the two sintering techniques: conventional sintering and spark plasma sintering.

Figure 7 :

 7 Figure 7: SEM images with a backscattered electron detector of K0.5Na0.5Nb1-xTaxO3 (a) sintered by spark plasma sintering (x = 0.20), (b) zoom on junction between dark and clear inclusions and (c) zoom on the matrix area.

Figure 8 :

 8 Figure 8: Evolution of Kp and d33 in K0.5Na0.5Nb1-xTaxO3 from x = 0 to x = 0.5, and for the two sintering techniques.

Figure 9 :

 9 Figure 9: Electrical properties of K0.5Na0.5Nb1-xTaxO3 ceramics at room temperature for conventionally and SPS sintered compositions, from x = 0 to x = 0.5. εr and tanδ were measured at 1 kHz.

Fig. 1

 1 Fig.1

Fig. 2

 2 Fig.2

Fig. 3 Fig. 4

 34 Fig.3

Fig. 5

 5 Fig.5

Fig. 6 Fig. 7

 67 Fig.6

Fig. 8

 8 Fig.8

Fig. 9 x

 9 Fig.9

  According to these results, it is confirmed that the evolution of d33 values is closely linked to the evolution of the samples density. Finally, the pressure parameter was increased from 50 to 200 MPa for one sample. Under 200 MPa at 920 °C for 5 minutes, a relative density of 92.3 % is obtained, which represents an increase of 30 % of the relative density compared to the same composition sintered under 50 MPa. This result shows the strong influence of the pressure on the densification during SPS process. Moreover, this sample presents the highest relative permittivity with a value of 1027, highlighting the benefit of the SPS technique on this property and confirming the results of Fig.9. Indeed, compared to the value obtained for the sample with the same composition, sintered by conventional sintering, the relative permittivity is multiplied by a factor of five and is higher than that obtained by many research groups in KNN-system ceramics. To conclude on the results summarized in Table1, SPS sintering techniques appears to be a powerful way to produce highly densified

	microscopy observations and energy dispersive X-ray spectroscopy analyses evidenced
	a composite microstructure of the ceramics with tantalum rich and niobium rich
	inclusions into a K0.5Na0.5Nb1-xTaxO3 matrix of the expected composition. However, this
	composite microstructure is not detrimental and tantalum incorporation in
	K0.5Na0.5Nb1-xTaxO3 has a beneficial effect on piezoelectric properties. In order to
	balance the difficulty to densify the KNNT ceramics, the use of the spark plasma
	sintering techniques enables to obtain highly densified substituted ceramics, 94 to 96
	% of relative density, with a significant impact of the sintering temperature and
	pressure on the density. With different optimized sintering parameters, interesting
	piezoelectric properties are obtained: kp = 46 %, d33 = 155 pC/N, εr = 1027. The cross
	influence of the different SPS parameters on piezoelectric properties is revealed here
	980 °C. As expected, it appears that the density of the ceramics is strongly influenced by the sintering temperature. It significantly increases with the increase of the temperature up to a maximum of 94 % densification, reached at 960 °C. The samples relative densities remain an important characteristic, because all the samples with the lowest densities undergo electrical breakdown during the poling step. Considering 960 °C as the optimal sintering temperature value, ramp speed and dwell time are varied. Decreasing the ramp speed to 50 °C/min depresses the density, while increasing the dwell time, from 5 to 10 min, allows reaching the highest relative density of 96.3 %. High coupling factor kp and piezoelectric coefficient d33 are obtained for this sample with values of 42.3 % and 155 pC/N, respectively, associated to low dielectric losses SPS technique, in x = 0.20 KNNT, relative permittivity higher than 900, Kp value over 40 % and piezoelectric coefficient d33 over 135 and up to 155 pC/N can be achieved and maintained. 4. Conclusion K0.5Na0.5Nb1-xTaxO3 (KNNT) (with x = 0.00, 0.05, 0.10, 0.20, 0.30, 0.50 and 1) ceramics were sintered by conventional and spark plasma sintering techniques. X-Ray diffraction and Raman analyses confirmed tantalum incorporation in KNN perovskite with the appearance of some chemical disorder with increasing substitution. structural (2.86 %). K0,5Na0,5Nb1-xTaxO3 ceramics with improved piezoelectric properties. Indeed, thanks to transitions are evidenced, from orthorhombic to tetragonal between x = 0.30 and x =
	0.50 and from tetragonal to cubic for x = 1 (K0.5Na0.5TaO3). Scanning electron

Table 1 :

 1 Summary of the main electrical results of the SPS parameters study for x = 0.2 composition in K0.5Na0.5Nb1-xTaxO3.

Table 1

 1

			Temperature (°C)	Dwell time (min)	Pressure (Mpa)	Relative density (%)	εr	tanδ (%)	d33 (pC/N)	kp (%)
	0.20	100	920	5	50	73.78	-	-	-	-
	0.20	100	940	5	50	85.29	-	-	-	-
	0.20	100	960	5	50	94.13	905	4.90	147.7	38.4
	0.20	100	980	5	50	93.00	-	-	-	-
	0.20	50	960	5	50	93.16	938	4.60	144.7	37.6
	0.20	100	960	10	50	96.25	763	2.86	154.5	42.3
	0.20	100	920	5	200	92.24	1027	5.41	135	35.0

Acknowledgments:

This work was supported by "Région Centre Val de Loire, France" in K-NNOPEE project (Contract N°20140091661).


Xuan-Chien Le
email: xuan-chien.le@irisa.fr

Baptiste Vrigneau
email: baptiste.vrigneau@irisa.fr

Matthieu Gautier
email: matthieu.gautier@irisa.fr

Malo Mabon
email: malo.mabon@irisa.fr

Olivier Berder
email: olivier.berder@irisa.fr

Energy/Reliability Trade-off of LoRa Communications over Fading Channels

LoRa is a technology for long range wireless communications that allows the development of new applications in domains such as smart agriculture, smart city or smart industry. Many in-field deployments and measurement campaigns have been performed in recent years, showing the sensibility of such communication to fading channels. In this paper, the LoRa transmission reliability is evaluated in simulations for different fading channels. Moreover, as the energy consumption also depends on the configurations, a trade-off between energy consumption and reliability needs to be considered when selecting a LoRa configuration. To this aim, experimental energy measurements are performed on a Semtech device, showing that energy difference between various configurations can reach up to two orders of magnitude. Results highlight that LoRa configuration impacts the energy/reliability trade-off and the best one strongly depends of the type of channel.

I. INTRODUCTION

In recent years, Low-Power Wide-Area Networks (LP-WANs) have been widely studied and deployed in many areas, particularly in smart agriculture applications, enabling large range of Internet of Things. The main advantage of LPWANs is that energy consumption is kept low for long communication ranges. This characteristic allows an end-device, powered by a battery or energy harvesting sources, to enhance its lifetime. Among various LPWAN technologies (SigFox, Adaptrum or Weightles . . . ), LoRa [START_REF] Alliance | White paper: A technical overview of LoRa and LoRaWAN[END_REF] physical layer has the particularity to be highly configurable regarding the spreading factor (SF ), bandwidth (BW ), coding rate (CR) and transmission power (P T x ), which are critical parameters permitting a trade-off between energy consumption, data rate and transmission range.

Many studies address this flexibility in the LoRa configuration choice and the resulting performance trade-offs. An experimental analysis is performed in [START_REF] Nolan | An evaluation of low power wide area network technologies for the Internet of Things[END_REF] to evaluate the coverage capacity of a base station in LoRa-based LPWAN using the LoRa default configuration. An area of 1380 km 2 can potentially be covered by one base station located 470 m above the sea level. Another study [START_REF] Augustin | A study of LoRa: long range and low power networks for the Internet of Things[END_REF] experimentally evaluates the LoRa network coverage in a suburban area. It is shown that the range can be increased from 650 m to 3.4 km by changing the configuration. In [START_REF] Aoudia | Long-short range communication network leveraging LoRa and wake-up receiver[END_REF], the trade-off between the energy consumption and the sensibility in LoRa communications is studied. Experimental results show that if the consumed energy is reduced when using configurations with high data rate, the communication range also decreases. The sensibility to device mobility is studied in [START_REF] Petjjrvi | Performance of a low-power wide-area network based on LoRa technology: Doppler robustness, scalability, and coverage[END_REF]. Measurement campaigns highlight that the LoRa modulation is reliable when the device velocity is maintained lower than a threshold depending on the configuration, e.g. 38 km/h with SF =12 and BW =125 kHz. Moreover, lower SF s allow higher velocities. Meanwhile, in [START_REF] Adelantado | Understanding the Limits of LoRaWAN[END_REF], the limitations of LoRaWAN are studied in different use cases, which require different types of data transmission patterns, latency and geographical features. Apparently, the constraints on delay and data rate prevent this technology from applying in some applications such as smart transportation and logistics or video surveillance, while small SFs are selected to reduce the time on air when deploying LoRaWAN for agriculture real time monitoring.

Therefore, configuration selection plays an important role in any LoRa communication. This feature is already used in the LoRaWAN standard that implements an Adaptive Data Rate (ADR) scheme which adapts both end-device configuration and transmission power according to the received Signal-to-Noise Ratio (SNR). However, ADR scheme does not take into account the LoRa sensitivity to fading channels and this sensitivity has just been experimentally observed in state-ofthe-art studies. In this paper, the fading channel influence is quantitatively evaluated using a Rice fading channel with a Doppler frequency. To this aim, six configurations with different data rates are considered and the reliability is imposed by a target Packet Error Rate (PER). Moreover, as the configuration also impacts the consumed energy [START_REF] Aoudia | A Low Latency and Energy Efficient Communication Architecture for Heterogeneous Long-Short Range Communication[END_REF], the aim of the paper is to link the reliability with the energy consumption. Thus, the energy consumption of each configuration is achieved using experimental measures on a Semtech LoRa device. Finally, the trade-off between energy consumption and reliability for LoRa communications according to Rice fading is analyzed.

In the remaining, the LoRa technology is introduced in Section II. Section III presents the channel models. Simulation results are shown in Section IV as well as the energy/reliability trade-off is discussed. Conclusions are given in Section V.

II. LORA TECHNOLOGY

LoRa is a long range communication technology promoted by the LoRa Alliance. The LoRa physical layer, which allows long-range, low-power and low data rate communications, is developed by Semtech [8][9]. LoRa communications can use frequency bands of 433 MHz and 868 MHz in Europe (respectively 915 MHz in US and 783 MHz in China) and its data rate can reach up to to 50 kbps. It uses the Chirp Spread Spectrum (CSS) modulation with a linear variation of frequency on time [START_REF] Springer | Spread spectrum communications using chirp signals[END_REF] [START_REF] Reynders | Chirp spread spectrum as a modulation technique for long range communication[END_REF], which allows the reduction of both interference and Doppler effects. LoRa modulation can be configured with three parameters: BW , SF and CR.

In LoRa, SF is defined as the logarithm in base 2 of the number of chirp per symbol. LoRa operates with SF from 6 to 12. LoRa uses three bandwidths: 125 kHz, 250 kHz and 500 kHz. A LoRa symbol is therefore composed of 2 SF chirps covering the entire bandwidth, starting with a series of upward (or downward) chirps from an initial frequency, which represents for a code word. The frequency will wraps around to the minimum frequency (or maximum frequency with downchirp) when the maximum (minimum with down-chirp) of the bandwidth is reached. A linear chirp signal is usually defined by:

s(t) = A ⇥ e j ⇣ 2⇡ ⇣ f0t+ µt 2 2 ⌘ + 0 ⌘ , ( 1
)
where 0 is the initial phase, A the amplitude, µ the chirp rate, f 0 the starting frequency of chirp and (t) = 2⇡

⇣ f 0 t + µt 2 2 ⌘
+ 0 is the instantaneous phase at time t. The corresponding instantaneous frequency is derived by:

f (t) = d (t) 2⇡dt = f 0 + µt. (2)
Applying CSS to LoRa modulation, each frequency f 0 in the band represents a code word. The frequency is swapped at the maximum value of bandwidth, the instantaneous frequency is therefore represented as a modulo operator of BW , given by:

f (t) = f min + [( f 0 + µt) mod BW ] , (3)
where f 0 = f 0 f min and f min is the minimum frequency of the bandwidth.

With 2 SF chirps per symbol, a code word can contain SF information bits. The duration T s of a symbol is given by: T s = 2 SF /BW . For a given bandwidth, increasing the spreading factor by one unit doubles the Time-on-Air (ToA) to transmit the same amount of data, resulting in the decrease of bit rate. The bit rate is calculated by:

R b = SF ⇥ BW 2 SF . (4)
Fig. 1 shows an example of LoRa transmitted symbols with different values of SF from seven to twelve. The third parameter in the configuration of LoRa modulation is the code rate. LoRa can use Forward Error Correction (FEC) code for each block of four information bits. The number of redundant bits for each block varies from one to four, corresponding to CRs of 4/5, 4/6, 4/7 and 4/8. Then, the bit stream is processed by an interleaver to make FEC code more robust to burst errors. Additionally, a whitening structure can also be used to make the signal like white noise, thus avoiding frequency selective channel penalties.

III. CHANNEL MODELS WITH MOBILITY

The performance of LoRa transmission is evaluated using both Rayleigh and Rice models. Moreover, Additive White Gaussian Noise (AWGN) is considered to model path-loss effects.

A. Rayleigh fading channel

In real-field deployment, the environment between the enddevice and base station has many obstacles such as buildings, trees, etc. These obstacles reflect the transmitted signal and generate other paths of transmission. The received signal at the base station is the combination of these replicas and corresponds to multi-path fading channel. In the case of Non Light-of-Sight (NLoS) paths between the end-device and base station, the channel gain h(t) can be considered as a sum of in-phase and quadrature-phase components, i.e. h(t) = h I (t) + jh Q (t). In some scattering environment, h I (t) and h Q (t) are independent Gaussian variables with zero mean and variance 2 h at any time t. Therefore, the amplitude |h(t)| follows a Rayleigh distribution. In this study, the Rayleigh fading channel is generated using the Jakes model [START_REF] Jakes | Microwave mobile communications[END_REF] defined by:

h(t) = 1 p L L X l=1 e j(2⇡fD cos ( l )t+✓ l ) , (5)
where L is the number of NLoS paths, ✓ l and l are the initial phase and incident angle of l-th path, respectively. The Doppler shift f D is due to the movement of the end-device and can be estimated by f D ⇡ v r c/f c , where v r is the relative velocity between the end-device and base station on the radius direction, c is the light celerity and f c is the carrier frequency. The Doppler shift affects the coherence time of the channel, given by T c = 1 fD . As a consequence, when T s > T c , or v r > cBW f02 SF , fast fading occurs that leads to signal distortion [START_REF] Petjjrvi | Performance of a low-power wide-area network based on LoRa technology: Doppler robustness, scalability, and coverage[END_REF].

The channel generated by ( 5) is normalized by 1/ p L to normalize the average gain. The initial phase ✓ l is assumed statistically independent and uniformly distributed in [0, 2⇡).

In Jakes model, the incident signal is assumed to come from all directions. Therefore, if assigning 0 as a random value uniformly chosen in [0, 2⇡), then l is given by

l = 0 + 2⇡ l 1 L with l = 1, 2, . . . , L. (6)

B. Rice fading channel

In

h I (t) = cos (2⇡f D cos ( 0 )t + ✓ 0 ) (7)
h Q (t) = sin (2⇡f D cos ( 0 )t + ✓ 0 ), (8)
where 2 = h

I (t) 2 + h Q (t) 2 is the non-centrality parameter of Rice distribution, f D cos ( 0 )
and ✓ 0 are the Doppler frequency and the phase of the LoS path, respectively.

The Rice fading channel can be set with the Rice factor K, defined as the ratio between the power of the direct path . When K = 0, the channel becomes a Rayleigh channel, while when K = 1, the channel does not have fading phenomenon anymore. Without loss of generality, the average power of the channel is normalized to 1 and the power of LoS and NLoS paths can be defined with the Rice factor as:

2 = K K + 1 (9) 2 2 h = 1 K + 1 . ( 10
)
Therefore, a Rice fading channel is composed of two components: the first one is generated by the NLoS paths and follows Rayleigh distribution with power 2 2 h = 1/(K + 1); the second one is the LoS path with deterministic time-varying parameters h I (t) and h Q (t) calculated by ( 7) and ( 8), with power 2 = K/(K + 1). The first scattered component h NLoS (t) is generated by [START_REF] Petjjrvi | Performance of a low-power wide-area network based on LoRa technology: Doppler robustness, scalability, and coverage[END_REF] and normalized in order to get the power of 1/(K+1), and the second part h LoS (t) corresponds to the LoS component determined by h LoS (t) = h I (t) + jh Q (t). As a conclusion, the Rice channel gain can be obtained by:

h(t) = 1 p K + 1 h h NLoS (t) + p Ke j[2⇡fD cos ( 0 )+✓0 i , (11)
with 0 and ✓ 0 uniformly distributed in [0, 2⇡).

IV. LORA TRANSMISSION SIMULATION A. LoRa Setup

To evaluate the transmission performance, six configurations of LoRa are used for both experiments and simulations. The configurations are detailed in Table I, the first one has the lowest data rate, while the last one has the highest. Configuration 3 is the LoRa default setup. For the simulations,

B. Energy measurements

First, energy measurements have been performed to estimate the energy per transmitted packet, a payload of 25 bytes per packet is considered. This energy is measured for each configuration and for three levels of P T x : 2 dBm, 10 dBm and 14 dBm. The experimental setup consists in a LoRa enddevice prototype and a high sensitive current analyzer. The prototype is composed of a Texas Instrument MSP430FR6989 micro-controller and a Semtech SX1276 transceiver. The measurements were obtained using an Keysight CX3324A current waveform analyzer (1 GSample/s, 100 pA accuracy). Fig. 2 shows an example of the current waveform when using the configuration 5. The different steps can be observed from the sleep mode to the transmission mode. Latency due to turning on the micro-controller and configuring the transceiver can be observed as well as high current peaks that must be taken into account when powering the platform.

Energy measurement results are shown in Table I. The energy required to send a packet using the highest data rate is 200 times lower than the one required to send a packet using the lowest data rate. The energy per packet is obviously increasing with the transmission power, about twice more between 2 dBm and 14 dBm.

C. Reliability evaluation

To evaluate the LoRa reliability over different channels, performance in terms of PER is obtained using simulations for all the configurations. The results are shown is Fig. 3 for both AWGN channel and Rayleigh channel with enddevice velocity of 30 km/h, PER are given according to the Signal-to-Noise Ratio (SNR) at the receiver. In a non-fading AWGN channel, LoRa transmission using the first configuration (SF 12, 125 kHz of BW ) shows the best performance, and can reach a PER of 10 1 at SNR = -22.5 dB and 10 2 at SNR = -21.5 dB. Meanwhile, configuration 6 (SF 6, 500 kHz of BW ) shows the worst performance with a PER of 10 1 at SNR = -5.47 dB and 10 2 at SNR = -4.36 dB. In AWGN channel, performance is globally better when increasing the spreading factor. On the other hand, the bandwidth does not affect the performance as configuration 3 (SF 7, 125 kHz of BW , CR 4/5) and configuration 4 (SF 7, 125 kHz of BW , CR 4/5) achieve the same performance. Finally, using a FEC code improves the performance and a 1.4 dB gain at PER = 10 1 can be achieved between configuration 4 (SF 7, 125kHz of BW , CR 4/5) and configuration 5 (SF 7, 125kHz of BW , CR 4/8).

In contrast, when Rayleigh fading channel is considered, the first configuration shows the worst performance with a PER always higher than 80%. This result can be explained by the symbol time of this configuration close to the coherence time of the channel at 30 km/h, i.e. T s = 32.8 ms and T c ⇡ 41.5 ms, respectively. The long symbol duration of configuration 1 makes it highly sensitive to fading channel. Fig. 4: Loss of received signal power to maintain PER=10 1 as in AWGN channel when the end-device velocity is 30km/h).

Similarly, configuration 2 with a SF of 8 also shows a bad performance, with a 20.55 dB loss compared to AWGN channel to reach a PER of 10 1 and the inability to obtain PER of 10 2 . While configurations 3 and 4 reach the same performance in an AWGN channel, configuration 4 outperforms configuration 3 in a Rayleigh fading channel. Using a larger bandwidth (500 kHz compared to 125 kHz for configuration 3) reduces the symbol duration and makes the transmission less disturbed by the fading.

To evaluate the performance changes of each configuration due to the channel variation, we defined the dBloss as the loss of received signal power to obtain the same PER as for AWGN channel. The dBloss are given in Fig. 4 for PER = 10 1 for different values of the K-factor in Rice channel model. When K ! +1, the channel can be considered as AWGN and the dBloss decreases to 0 dB for all configurations. Because PER = 10 1 can not be obtained with configuration 1, Fig. 4 only shows the results of five remaining configurations. The simulation results show that configuration 2 always obtains the highest dBloss, while configuration 6 gives the lowest. Meanwhile, configurations 4 and 5 get the same loss, meaning that they have the same sensitivity to fading channel. In a general way, configurations with higher spreading factor, i.e longer symbol duration, are more sensitive to the channel variation.

D. Energy-reliability trade-off

As illustrated in Table I and Fig. 3, a configuration with higher data rate consumes less energy but gives a worse performance in AWGN channel. Therefore, the selection of a configuration has to make balance between the energy consumption and the reliability depending on the fading channel. Fig. 5 illustrates the energy consumption for 14 dBm transmission power to send 25 bytes of payload and the minimum SNR at the receiver to obtain a target PER of 10 1 over different channels. Configurations 1 and 2 seem to be less efficient. While the PER of 10 1 can not be obtained with configuration 1, configuration 2 requires too much energy and high SNR at the receiver to obtain the target PER in Rayleigh fading channel. In contrast, configuration 6 is interesting in Rayleigh channel because it does not only require the smallest energy but also lower SNR to obtain PER of 10 1 than configurations 2 and 3, and same SNR as configurations 4. Although it still requires a higher SNR than configuration 5, it is worth noting that the coding rate of this configuration is highest than the one of configuration 5. In a general way, selecting a configuration with low data rate is better for AWGN channel in terms of minimum SNR required to obtain a target PER at the receiver. Meanwhile, configurations with higher data rate are good choices for deep fading channels, particularly in NLoS environment.

V. CONCLUSIONS

The LoRa standard considers different degrees of freedom to configure the transmission and includes the ADR mechanism to dynamically adapt the data-rates to the channel conditions. This algorithm is based on the received SNR to change the configuration. In this paper, we analyzed the trade-off between reliability and transmitter energy consumption according to channel parameters. In this context, we used simulation to

In addition, the transmitter energy consumption was studied for a Semtech device with three different values of transmit power. According to a target PER, we are able to connect the required SNR with the energy consumption for all configurations. One can then choose the best configurations according evaluate the reliability of LoRa modulation in a Rice fading channel (two parameters K factor and node speed were tuned). The PER was considered as a QoS criterion and six different configurations were selected (spreading factor, bandwidth, code rate). Simulation results showed that a high SF enhances the performance in AWGN channel. However, it is also more sensitive to channel variations, which is illustrated by the higher loss of received signal power to maintain the same PER as in AWGN channel. to a deployment. Ideally, the configuration may be chosen including not only SNR but also fading and velocity.

Fig. 1 :

 1 Fig. 1: LoRa transmitted symbols with different values of SF .

2 2 2 2 h

 22 and the power of NLoS paths 2 2 h , i.e. K =

Fig. 2 :Fig. 3 :

 23 Fig. 2: Microbenchmark showing the current waveform of transmitting a packet with configuration 5.

Fig. 5 :

 5 Fig. 5: Energy consumption (P T x =14 dBm) versus minimum SNR at the receiver to obtain PER of 10 1 .

  the case of LoS environment, h

						I (t) and h	Q (t) are inde-
	pendent Gaussian variables but with non-zero means, denoted
	h	I (t) and h	Q (t), respectively. Besides, h	I (t) and h	Q (t) are
	supposed to have the same variance 2 h at any time t. Then,
	the amplitude of h(t) follows a Rice distribution. A method to
	determine the value of h	I (t) and h	Q (t) is introduced in [13],
	in which h	I (t) and h	Q (t) are modeled as deterministic time-
	varying parameters:

TABLE I :

 I LoRa configuration parameters and energy measurements for different transmission power levels.

	Configuration	1	2	3	4	5	6
				CR	4/8	4/5	4/5	4/5	4/8	4/5
				SF	12	8	7	7	7	6
			BW (kHz)	125	125	125	500	500	500
			R	b (kbps)	0.37	3.91	6.84 27.34 27.34 46.88
			ToA (ms)	1712.13 102.91 56.58 14.14 19.52 7.71
			E (mJ)
	(P	T x = 2 dBm)	240	14.43	7.9	2.01 2.77	1.1
			E (mJ)
	(P	T x = 10 dBm) 379.12 22.74 12.41 3.15 4.32 1.72
			E (mJ)
	(P	T x = 14 dBm) 507.37 31.96 17.45 4.55 6.13 2.48
	the performance of LoRa is measured in term of PER, 2000
	packets with 25 bytes of payload per packet are transmitted
	for each configuration.


Philip-Dylan Gleonec
email: philip-dylan.gleonec@wi6labs.com

Jeremy Ardouin
email: jeremy.ardouin@wi6labs.com

Matthieu Gautier
email: matthieu.gautier@irisa.fr

Olivier Berder
email: olivier.berder@irisa.fr

A Real-World Evaluation of Energy Budget Estimation Algorithms for Autonomous Long Range IoT Nodes

In order to enable IoT nodes to efficiently use their energy harvesting capabilities, algorithms are used to determine a reasonable energy budget and allocate it to the node tasks, enabling energy neutral operation. However, most of these algorithms have been implemented and evaluated in simulation frameworks. In this paper, we evaluate the implementation of these algorithms to manage the energy of real-world LoRaWAN IoT nodes. We measure and compare the performance of the different energy budget estimation methods on a commercial LoRaWAN IoT platform. Results show that in this use-case, the choice of algorithm impacts the system Quality of Service by less than 15 %. This enables much simpler energy budget estimation methods to be used.

I. INTRODUCTION

Wireless sensor networking has recently been an active research area for both industries and academic institutions. In particular, a lot of work is focused on increasing the battery life of wireless sensor nodes. This can be achieved by reducing the power consumption of individual components power consumption, using duty-cycling strategies [START_REF] Sentieys | Wake-Up Interval Optimization for Sensor Networks with Rendez-vous Schemes[END_REF], or using low power transmission technologies such as LoRa. Yet the use of non-rechargeable batteries limits the lifetime of the system and creates waste when this battery is depleted. Thus, the use of energy harvesting and rechargeable batteries has been considered [START_REF] Chen | DuraCap : A supercapacitor-based, power-bootstrapping, maximum power point tracking energy-harvesting system[END_REF]. In such a system, more energy is made available to the node, enabling a longer lifetime of the system.

By adapting the Quality of Service (QoS) of the node to its energy harvesting capabilities, it is possible to reach an energy neutral operation point, and have a theoretically infinite battery life [START_REF] Kansal | Power management in energy harvesting sensor networks[END_REF]. To do so, energy harvesting nodes use a power manager subsystem. This subsystem can be divided in two elements : an Energy Budget Estimator (EBE) which calculates an energy budget based on the harvested energy and the state of charge of the battery, and an Energy Allocator that decides how to spend this energy budget on different tasks, such as sensing, transmitting a message or processing data. Instinctively, we can see that the node QoS is linked to its EBE : a larger energy budget will enable a higher QoS, but will deplet the battery more quickly.

EBE algorithms can be model-based [START_REF] Piorno | HOL-LOWS : A Power-aware Task Scheduler for Energy Harvesting Sensor Nodes[END_REF] [START_REF] Le | Energy-Efficient Power Manager and MAC Protocol for Multi-Hop Wireless Sensor Networks Powered by Periodic Energy Harvesting Sources[END_REF], in which case they use the behavior of the energy source to adapt the energy budget according to an estimation of the future harvested energy. On the contrary, model-free EBE can be used independently of the used energy harvesting source. LQtracker [START_REF] Vigorito | Adaptive Control of Duty Cycling in Energy-Harvesting Wireless Sensor Networks[END_REF], Fuzzyman [START_REF] Aoudia | Fuzzy Power Management for Energy Harvesting Wireless Sensor Nodes[END_REF] and RLMan [START_REF] Aoudia | Learning to survive : Achieving energy neutrality in wireless sensor networks using reinforcement learning[END_REF] are examples of such algorithms, which respectively rely on linear quadratic regression, fuzzy logic and reinforcement learning to calculate an optimal energy budget. The performance of these algorithms has been verified and studied with extensive simulations.

However, to our knowledge, none of these algorithms have been implemented on commercial wireless sensor platforms. Moreover, these designs target short range communications, and the use of energy harvesting for Long Range IoT nodes has not been studied. In this paper, we compare the performance of four different model-free EBE algorithms in the context of a commercial implementation of solar powered LoRaWAN sensor nodes.

The rest of the paper is organized as follows. Section II describes the energy harvesting node platform and our design choices for the power manager. Section III details the implementation and choice of EBE algorithms. Section IV explores the tuning requirements of each algorithm. Section V shows and analyses our experimental results. Finally, Section VI concludes this article.

II. EVALUATION PLATFORM AND REQUIREMENTS

Our evaluation platform targets long range applications with multi-source energy harvesting capabilities [START_REF] Gleonec | Architecture exploration of multi-source energy harvester for IoT nodes[END_REF]. Fig. 1 shows both hardware and software descriptions of the platform. An IoT node is usually composed of a micro-controller, a radio transceiver and some sensors, respectively a STM32L0, a SX1272 LoRa transceiver, and a connector to plug different sensors in our platform. Moreover, three SPV1050 energy harvesters enable simultaneous energy harvesting from a solar panel, a wind turbine and a thermo-electric generator. The harvesters use a common energy storage device which powers the platform through a DC to DC converter. The storage device can be a super-capacitor or a lithium-polymer (LiPo) battery. In this work, a 7.5 F super-capacitor is used. Due to the board configuration, it is used between 3.7 V and 4.1 V.

The LoRaWAN technology uses the LoRa chirp spread spectrum (CSS) modulation to send short messages over long distances with a limited power consumption. LoRaWAN uses a star topology, where all the nodes send their messages to a gateway over unlicensed frequency bands. These bands are regulated to avoid interferences between radio devices. In Europe, LoRaWAN transmitters must respect a maximum duty cycle (i.e. 1% in the 868-868.6MHz sub-band and 0.1% in the 868.7-869.2 sub-band), which limits the maximal QoS of a LoRa node. The duration of a LoRa transmission depends on the payload size and the CSS spreading factor, which isin short -the duration of a chirp and is dynamically modified according to the transmission conditions. A higher spreading factor enables a better sensitivity, increasing the transmission range, but reduces the throughput, increasing the energy cost of a transmission.

As we use a different radio technology, the operating conditions of the EBE algorithms differ from the state-ofthe-art. The delay between two messages in our application ranges from minutes to hours, while the delay targeted by state-of-the-art EBEs ranges from seconds to minutes. This means that EBE algorithms will need more time to converge to the best result. Moreover, the energy consumption of a LoRa transmission is higher than lower range technologies due to long packet transmissions, which creates higher variations in the battery state-of-charge.

Usually, EBE algorithms are periodically executed, at the end of a timeslot (e.g. 1 hour), and aim to reach the energy neutral operation point for the next timeslot. In our application, to avoid a long convergence time, the EBE algorithm is executed after each transmission. The delay D [k] to the next message is calculated based on the current energy harvesting conditions. This enables greater agility, as the EBE can recover from a previous bad estimation more quickly. However, this also increases the variance of the QoS, as the algorithm has more difficulty converging to an optimized result.

III. EBE IMPLEMENTATIONS

The EBE algorithms have been implemented in a C library. Since the micro-controller has no Floating-Point Unit, the library was implemented using a portable fixed-point arithmetics library. This enables the validation of the EBE library on a computer before being implemented on a target node and speeds up development time.

Most EBE algorithms calculate an energy budget E B for the starting timeslot based on the residual energy E R of the energy storage device when E B is calculated [START_REF] Vigorito | Adaptive Control of Duty Cycling in Energy-Harvesting Wireless Sensor Networks[END_REF]. Some EBE algorithms [START_REF] Aoudia | Fuzzy Power Management for Energy Harvesting Wireless Sensor Nodes[END_REF] also need the measurement of the harvested energy E H . However, the latter is difficult to perform with a good precision and low energy consumption overhead, and can sometimes be estimated by the residual energy variation ΔE R . Some algorithms [START_REF] Aoudia | Learning to survive : Achieving energy neutrality in wireless sensor networks using reinforcement learning[END_REF] are tightly coupled with the energy allocator and require typical energy consumption E Ctyp .

Additionally, we define two applications parameters D max and D min , respectively as the maximum and minimum delay in seconds between two transmissions, used to set a minimal QoS. The library uses these parameters to calculate a minimal and maximal energy budget E Bmin and E Bmax . We also define D REF as the delay between two transmissions when E B is equal to E Ctyp , set between D min and D max . These parameters are dependent on the end-application and are customizable. D (in seconds) is calculated from E B and E Ctyp as :

D = D REF × E Ctyp E B (1)
The library also needs information about the underlying hardware energy capabilities. We denote V BAT T , V min and V max the current, minimal and maximal battery voltage. V min if the voltage for which the platform stops functioning, or can be set with a margin before the battery is fully depleted. When the energy storage is a super-capacitor, its capacitance C is defined. Based on these parameters, the current, minimal and maximal residual energy in storage E R , E Rmin and E Rmax are calculated.

The evaluation platform is able to use multiple energy sources simultaneously. Model-based EBE are developed for a single source type, and are unsuitable for this use-case. Thus, model-free EBE algorithms are used. The resulting platform is more generic, and can be used in more end-user applications. In particular, we studied LQ-tracker [START_REF] Vigorito | Adaptive Control of Duty Cycling in Energy-Harvesting Wireless Sensor Networks[END_REF] and Fuzzyman [START_REF] Aoudia | Fuzzy Power Management for Energy Harvesting Wireless Sensor Nodes[END_REF], which both showed good results in previous evaluation. LQtracker can be implemented using only the energy state-ofcharge as input. While Fuzzyman in its original design also requires E H , which is not measured in our platform. In this work, we consequently use a custom rule-set that uses ΔE R as input instead of E H , and uses the last energy budget E B [k -1] to determine the new E B . The rules are detailed in Table 1 and only depends on the application and platform parameters and can be reused for a variety of applications and energy sources.

E R Empty Full ΔE R < 0 E Bmin f (E B [k -1]) = 0 f (E B [k -1]) E B [k -1] > 0 E B [k -1] E Bmax TABLE I: Fuzzyman custom rule-set.
In Table 1 f

(E B[k-1]
) is a function defined by :

f (E B [k -1]) = max � E Bmin , E R -E Rmin E Rmax -E Rmin .E B [k -1]

�

(2) Besides, we implemented two naive EBE algorithms : Linear T and Linear E. Linear E calculates an energy budget between E Bmin and E Bmax as a prorata of V BAT T between V min and V max :

E B = E Bmin +(E Bmax -E Bmin )× � V BAT T -V min V max -V min � (3)
Linear T calculates a fixed delay between D min and D max as a proportion of V BAT T [k] between V min and V max . This delay is then converted to an energy budget based on E Ctyp . The full equation is given by :

E B = D REF × E Ctyp D max -(D max -D min ) × � V BAT T -Vmin Vmax-Vmin � (4)
These two algorithms are used as a performance baseline to evaluate the advantages of more advanced control algorithms. Their advantage is their simplicity, as no settings are required beyond the common platform settings. Finally, to avoid sharp E B variations due to temporary change in energy harvesting conditions, all algorithms outputs are smoothed by an adaptive filter with a parameter β = 0.9 :

E Bf iltered [k] = β × E B + (1 -β) × E Bf iltered [k -1] (5)
IV. EBE ALGORITHMS TUNING All the selected algorithms can be tuned in order to improve their performance. The library has been designed to be portable, which enables the algorithms to be tuned in a simulation framework using the same code and same results. Indeed, it is much longer to run a full measurement campaign to validate an algorithm tuning settings than to run a simulation. This is particularly true for algorithms which provide many settings, such as Fuzzyman.

Each EBE algorithm has its tuning capabilities. Linear T and Linear E only need the common platform parameters, V min and V max , which can be adjusted to increase the efficiency of the EBE. LQ-tracker requires more parameters : it takes as input an energy target level E T ARGET , a step-size µ and two parameter vectors Φ and Θ. E T ARGET value is dependent on the application. µ is set by default to 0.001 and impacts how quick LQ-tracker converges. Fuzzyman is the hardest one to tune, as it can be entirely redesigned to fit the application. Indeed, it requires four thresholds T HR Empty , T HR F ull , T HR P ositive and T HR N egative to set the limits of the fuzzy inputs. Moreover, the entire rule-set may be redesigned to provide better performances.

For our simulation, the delay between two messages is set between of 15 minutes to 3 hours. The energy consumed by a LoRaWAN transmission is estimated to 140mJ with a SF7 spreading factor. We set V min and V max respectively to 3.7 V and 4.1 V, as for our real energy storage. The system was tested with a solar energy source, using EnHANTS [START_REF] Margolies | Energy-Harvesting Active Networked Tags (EnHANTs) : Prototyping and Experimentation[END_REF] measurement data. The simulated solar panel measures 3.2 cm per 4.2 cm with an efficiency of φ = 10%, like the one used in experimentation. The simulation results, without tuning, are shown in Table II. The mean value x and standard deviation σ of V BAT T , E B and D are presented.

We can first notice that all algorithms have some failed transmission, meaning some transmissions were aborted due to V BAT T being lower than V min . Most of them occur around a lack of data in the solar traces, which we kept to simulate a long period without energy. Two algorithms, Fuzzyman and Linear T, are more conservative, which can be seen as they keep a higher and more stable V BAT T , and thus emit less messages than the other two. E B of Fuzzyman is high and unstable, which shows that it sometimes tries to deliver an E B too high and can not stabilize. Linear E and LQ-tracker, on the other hand, take more risks, showing a lower mean V BAT T , and are rewarded with a higher number of transmissions. We tried to improve the performance of each algorithm by tuning their parameters in order to maximize the number of transmissions. For Linear E and Linear T, we set V min to 3.75 instead of 3.7 V, and V max to 3.85 V instead of 4.1 V. This enables both algorithms to be more conservative when the energy storage is nearly depleted and take more risks when it is sufficiently replenished. We increase the step-size µ of LQ-tracker to 0.005, and leave Φ and Θ to their default values, fixed in [START_REF] Vigorito | Adaptive Control of Duty Cycling in Energy-Harvesting Wireless Sensor Networks[END_REF]. Fuzzyman was given a new ruleset, shown in Table III, while the fuzzification thresholds T HR Empty , T HR F ull , T HR P ositive and T HR N egative were respectively set to 1.03 × E Rf ail , 0.85 × E Rmax , 0.35 and -0.5. The simulation was run again with the new settings, and Table IV shows the results. After optimization, there is little difference between the performance of the different EBE algorithms. In our use-case, the energy budget E B is limited between a minimal value E Bmin and a maximal value E Bmax . Thus all EBE algorithms have a similar behavior in limit cases where energy storage is sufficiently charged or empty. As all algorithms are tuned to maximize throughput, they deliver E B = E Bmax for an extended range of input values, as shown in Fig. 2, which shows the evolution of E B as a function of the state-of-charge.

E R Empty Full ΔE R < 0 E Bmin 0.95 × E B[k-1] = 0 0.95 × E B[k-1] 1.5 × E B[k-1] > 0 1.5 × E B[k-1] E Bmax
This graph gives a quick insight of how the different algorithms behave at low and high states of charge. This is useful to choose the EBE algorithm, as it hints to which algorithm is more or less conservative. However, this visualization has its limits when applied to algorithms which use more data inputs than only V BAT T , such as Fuzzyman, since it doesn't show the other inputs. Since all algorithms try to maximize E B , they take less precautions and are more likely to fail if the environment conditions are bad for an extended time period. In the evaluated algorithms, LQ-tracker seems to be the most conservative, starting to reduce the delivered E B when the state of charge goes under 70 %. The Linear algorithms and Fuzzyman are more aggressive, delivering maximum E B when the state of charge is respectively over 35 % and 17 %.

V. REAL-WORLD EBE MEASUREMENTS

During our experiments, each hardware platform is powered by a solar panel which can provide up to 5 V and 40 mA from direct sunlight. The experiment was run for seven days in an office settings. Each algorithm ran on a different hardware platform. All sensors were located next to a north oriented window, and ran in parallel to reduce differences in ambient energy. After each transmission, the energy budget and delay to the next transmission are calculated and sent through an UART, along with V BAT T and a count of successful transmissions. This UART transmission is logged by a computer, parsed and analyzed to produce the graphs shown in Fig. 3.

The number of successful transmissions is approximately the same for all algorithms, within a 15 % margin. Only one transmission failed during the fifth night for Fuzzyman. This shows the algorithms are quantitatively equivalent provided they are properly tuned, which confirm the results obtained through simulation. Qualitative differences can however be observed between the different EBE implementations.

As expected, LQ-tracker, by being more conservative, keeps its V BAT T higher than the other algorithm, which makes it more able to survive long periods without energy. On the contrary, Fuzzyman delivers a competitive number of transmissions but keeps its V BAT T much closer to the failure threshold, making it more sensible to lack of energy input, as seen with the failed transmission. As Fuzzyman is highly tunable, this could be optimized by a carefully designed ruleset, to provide characteristics closer to LQ-tracker.

Moreover, Fuzzyman and Linear T show a high variance in the delivered E B and delay D, which can be explained by the quick decrease of E B when V BAT T goes under a certain threshold, defined by the tuning of the algorithm. This quick E B decrease translates into a much longer delay D, and decreases the performances of the algorithm, despite the aggressive tuning. On the other hand, Linear E and LQtracker reduce E B more progressively, which translates to a lower mean D and improved performances. This behavior also depends on how D is calculated from E B , and could be varied using a different energy allocation method. Finally, it can be observed that all algorithms show a sharp rise of E B when the energy storage gets replenished. As all the evaluated algorithms are model-free, they have no means to predict an approximate future energy state of charge. In our use-case, this is typically the case in the morning : the calculated D is long at the end of the night, when the energy storage starts getting replenished. When this long delay D is elapsed, the storage has been charging for a long time, and the EBE can deliver a higher E B . This effect would be less important with a model-based EBE algorithm, as it would predict that energy was going to be harvested.

VI. CONCLUSION

This paper presents a practical implementation of Energy Budget Estimator algorithms for LoRaWAN IoT nodes and their optimization. We show that the choice of network technology has an impact on EBE algorithms implementation and performance. The use of a simulator shows that in our usecase, there are few differences between the different algorithms, provided they are all properly tuned. This enables the use of simpler EBE algorithms, which can then be more easily integrated in mathematical framework to size energy storage and energy sources based on Quality-of-Service requirements. Future work will focus on the development of such a framework, and on the allocation of the energy budget, especially for multi-task contexts.

Fig. 1 :

 1 Fig. 1: Evaluation platform overview.

Fig. 2 :Fig. 3 :

 23 Fig. 2: E B as a function of the State-of-Charge.

TABLE II :

 II Simulation before algorithm tuning.

TABLE III :

 III Fuzzyman new ruleset.

		Fuzzyman	Linear E	Linear T	LQ-tracker
		x	σ	x	σ	x	σ	x	σ
	V BAT T (V) E B (J) D (min) Tx Failed Tx	3.978 0.530 20 26217 0.116 0.100 27 36	3.985 0.528 21 25947 0.109 0.107 27 33	3.996 0.526 21 25284 0.100 0.117 27 28	3.988 0.528 21 25800 0.107 0.107 28 31

TABLE IV :

 IV Simulation after algorithm tuning.