Keisuke Hirata

Ken-Ichi Kasai

Shun-Ichi Gilles Grégoire
email: gilles.gregoire@universite-paris-saclay.fr

Masaaki Ishiuchi

Fujii
email: mfujii@res.titech.ac.jp

Shun-Ichi Ishiuchi
email: ishiuchi.s.aa@m.titech.ac.jp

Masaaki Fujii

Hydration-controlled excited-state relaxation in protonated dopamine studied by cryogenic ion spectroscopy

Keywords: catecholamine, excited state proton transfer, infrared spectroscopy, photodissociation, quantum chemistry calculations

come

insertion. Dopamine (DA), one of the catecholamines, plays an important role in homeostasis and addiction. 1 DA is a neurotransmitter involved in motor coordination, memory, reward processes and signal transmission from neurons. The lowering of the level of DA in the human brain is generally associated with the symptoms of Parkinson's disease. 2,3 The generally low expression level of DA in vivo renders its detection difficult by optical methods such as fluorescence. 4 Some indirect photodetection methods of DA have been reported but no photophysical properties including excited state dynamics have been reported. Interestingly, polydopamine (PDA) nanoparticles that are efficiently formed by oxidation under alkaline conditions show high fluorescence efficiency with possible application for cellular imaging. 5 By their importance, the intrinsic conformational varieties of DA, which are strongly related to molecular recognition by the DA receptor, have been studied by infrared (IR) spectroscopy in the gas phase and theoretical calculations. 6,7 On the other hand, its photophysical properties have not been understood sufficiently. Under physiological conditions, DA is protonated thus the excited state dynamics of protonated DA (DAH + ) should be studied. In addition, hydration and dehydration effects on its photophysical properties are also important because DAH + is hydrated in vivo but has to be dehydrated when it is recognized in the hydrophobic binding pocket of the DA receptor. 8 In the last decade, cryogenic ion spectroscopy has emerged as a powerful method to reveal the structures and intrinsic photophysical properties of bare biomolecules. Studying mass-selected hydrated clusters in a cold ion trap allows revealing the solvation effects gradually through direct a comparison with quantum chemistry calculations. While excited state dynamics in small peptides and related systems have been investigated in the last decade as recently reviewed, 9 the studies on hydrated species remain scarce and so to be explored.

Recently, excited state dynamics of protonated adrenaline, a closely related catecholamine, has been reported. 10 It was found that the excited state proton transfer from the amine chain to the aromatic ring and H atom loss from the ammonium group compete with a branching ratio that depends on the excess energy. The energy barrier for both processes is relatively large, about 0.3 eV and 0.8 eV respectively, so the excited state dynamics is not ultrafast with lifetime in the nanosecond range. Nevertheless, because the most favored hydration site is the protonated ammonium group, both processes should be perturbed by hydration, which has however never been reported so far. Drastic protonation and hydration effects on the excited state dynamics of biomolecules have only been reported in a very few cases, as for instance in the aromatic amino acid tryptophan. The ultraviolet (UV) spectrum of neutral tryptophan is well-structured, however, the spectrum becomes significantly broad by protonation due to a barrierless excited state proton transfer reaction. 11 Furthermore, the spectrum turns to a sharp, structured one when two water molecules are hydrogen-bonded to the protonated tryptophan. 12 From this motivation, we apply cryogenic ion spectroscopy to DAH + and its hydrated clusters.

The cold ion trap setup in Tokyo Tech 13,14 allows us to hydrate DA in a stepwise manner, so the spectral changes due to hydration can be accurately measured for each cluster size. Conformerselected IR spectroscopy is measured by IR-UV double resonance spectroscopy, which eases comparison with quantum chemical calculations to assign the structure. The excited state lifetime of DAH + has been recorded in Orsay by ps pump-probe photodissociation spectroscopy. 15 Quantum chemical calculations were also performed to track the excited state dynamics changes with hydration at the molecular level. From these approaches, we have found that the excited state dynamics of DAH + is governed by a proton transfer process that is insensitive to hydration up to two water molecules, but drastically changed in a dominant conformer of the DAH + -(H2O)3 cluster.

The experimental setups in Tokyo 16 and Orsay 17 have already been described in detail. They are based on an ESI source, cold ion trap and time-of-flight mass spectrometer. In Tokyo, a clustering trap maintained at a low temperature by a liquid nitrogen cryostat is added to produce hydrates as developed in the group of E. Garand. 18 UV photodissociation spectroscopy and double resonance IR/UV spectroscopy of bare and hydrated DAH + have been performed in Tokyo while ps excited state dynamics of bare DAH + have been recorded in Orsay. DFT and CC2 calculations have been performed by the two groups. Detailed experimental and computational procedures can be found in the supplementary material. Fig. 1 shows the UV photodissociation spectra of DAH + and its hydrated clusters DAH + (H2O)n (n = 0 -3). All the spectra are obtained by monitoring the intensity of the fragment ion m/z 137, which corresponds to NH3 + nH2O loss from DAH + (H2O)n. NH3 loss is the main fragment of the bare molecule through collision induced dissociation 19 and IRMPD, 6 thus this channel is assigned to the dissociation in the ground state after internal conversion (IC). Interestingly, the second most intense photofragment is detected at m/z 30 (CH2NH2 + ), emphasizing the C-C bond cleavage with one hydrogen transferred to the neutral catechol ring moiety (Fig. S1). Such photo-specific bond cleavage has also been observed in related systems, such as protonated aromatic amino acids 20 and catecholamines 10,21 and assigned to an excited state proton transfer reaction from the ammonium to the aromatic ring. 9 FIG. 1 UVPD spectra of DAH + (H2O)n (n = 0 -3).

The UVPD spectrum of the monomer (Fig. 1a) is broad and consists of two band systems: a low intensity progression starting from ~ 33700 cm -1 and an intense broad band at ~ 34800 cm -1 of 300 cm -1 width. DAH + has two low energy conformers G1 syn and G1 anti (Fig. S2), which differ by the orientation of the CH2NH3 + group above the catechol ring. Their adiabatic excitation energies are quite similar (Table 1) and predicted within 800 cm -1 to the red of the onset of the experimental excitation spectrum, in line with the expected error of the SCS-CC2 method (see ESI). In addition, the simulated vibronic spectra of both conformers are broad with a long progression of low frequency modes (Fig. S2), revealing a significant geometry change in S1. Both calculated band origins and simulated Franck-Condon spectra are thus consistent with the observed unstructured vibronic spectra. The excited state lifetime of DAH + excited at the maximum of the intense broad band has been measured by pump-probe photodissociation spectroscopy (Fig. S3).

The transient is characterized by a Gaussian function reflecting the cross correlation of the lasers, evidencing that the lifetime is much shorter than 20 ps. It is noteworthy that the lifetime of DAH + is significantly shorter than those of neutral catecholamines that display well-structured vibronic spectra consistent with nanosecond excited state lifetimes. [22][23][24] The short lifetime of the locally excited state of DAH + suggests that a fast relaxation channel accounts for the deactivation process. To assign the structure of DAH + (H2O)3, its infrared (IR) spectrum is measured by IR dip spectroscopy (Fig. 2a). The IR dip spectroscopy is a double resonance spectroscopy, which detects the IR transition by depletion of the UVPD signal. The IR spectrum shown in Fig. 2a is measured by labeling the S1 origin by the UV laser. Blue shaded bands are assigned to OH stretching of water molecules because these bands disappear in the IR dip spectrum of DAH + (D2O)3 (Fig. S4). To assign the structure of the cluster, quantum chemical calculations are performed and the 10 lowest energy conformers of DAH + (H2O)3 (Table S1) are shown in Fig. S5 along with the theoretical spectra in the 3 m range in Fig. S6. The structures and theoretical IR spectra of the two most stable conformer G1-1 and G1-2 are shown in Fig. 2b and2c, respectively. The OH stretching of water molecules in the clusters are shown with blue bars, while other vibrations of DAH + are indicated with red bars. As can be seen in Fig. 2, the theoretical IR spectrum of the most stable conformer G1-1 provides a fair agreement with the observed IR dip spectrum. It should be noted that the set of the three water stretches observed between 3400 and 3500 cm -1 is predicted only for the G1-1 conformer, none of the other nine conformers display such a pattern. The adiabatic excitation energy, corrected by the difference in zero-point-energy between the excited and ground state, is calculated at 34 747 cm -1 , only 750 cm -1 to the red of the experimental 00 0 transition. In addition, the simulated Franck-Condon spectrum shown in Fig. 2e (see the supplementary material for details) also reproduces the main spectral features of the UV spectrum (Fig. 2d). The S1 origin is the strongest and low frequency bands appear within 400 cm -1 from the origin. The active low frequency modes in S1 are identified as out-of-plane bending of OH catechol and vibrational motions of hydrated amine chain (Fig. S7). Thus G1-1 can be confidently assigned to the structure of the DAH + (H2O)3. It is clear that the binding of three water molecules to DAH + changes the excited state dynamics significantly. Based on the assigned structures of DAH + and its tri-hydrated cluster, the possible relaxation pathways are investigated by excited state calculations. In the bare molecule, the lowest excited state S1 corresponds to a * transition, the S2 * state lying more than 1 eV above at the optimized geometry of the * state. In the S1 * state, the N-H bond pointing toward the catechol ring elongates by 0.031 Å as compared to the ground state structure. The inter atomic distance between H and C is reduced to 1.96 Å. The Minimum Energy Path (MEP) along the N-H coordinate exhibits a small barrier of less than 0.15 eV, leading ultimately to a proton transfer reaction as shown in Fig. 3a. Full optimization of this structure leads to internal conversion (IC) with the ground state providing an efficient nonradiative deactivation mechanism (Fig. S8).

Such a process has already been proposed in related systems, such as protonated aromatic amine, 25 amino acids 20 and catecholamine. 10 At the conical intersection with the ground state, there is a competition between IC and direct dissociation from the excited state proton transfer structure.

The molecule can return to the ground state with a back proton transfer reaction and dissociates by ammonia loss through a statistical type of fragmentation. The second path implies dissociation along the C-C bond, which is destabilized in the proton transferred structure. 9 The low energy barrier for the proton transfer reaction is thought to be responsible for the short excited state lifetime (less than 20 ps, the cross correlation of the ps lasers) measured at 286 nm, i. e. with about 0.15 eV of excess energy in S1.

For the 1-3 complex, the adiabatic excitation energy is calculated within less than 800 cm -1 compared to the experimental band origin. In addition, the simulated Franck-Condon spectrum compares quite well with the experimental vibronic spectrum, with a strong band origin and few vibronic transitions up to 400 cm -1 of excess energy. Interestingly, the ammonium group is now involved in two H-bond with two water molecules, preventing direct interaction of the NH3 + moiety with the catechol ring. The N-H bond interacting with the water molecule is slightly elongated by 0.015 Å as compared to the ground state structure. MEP for the proton transfer from the ammonium to the water sitting above the catechol ring has been evaluated. As reported in Fig. 3b, the excited state energy continuously increases up to 0.75 eV above the adiabatic * energy as the N-H bond stretches until 1.65 Å. Full optimization starting from this structure without geometrical constraints leads to the initial * optimized structure. The proton transfer reaction is impeded in the hydrated complex by the inclusion of three water molecules. Therefore, it can be concluded that the water molecules block the non-radiative mechanism invoked for the bare DAH + .

In conclusion, we have evidenced the drastic hydration effect on the photophysics of DAH + embedded in small water clusters. Hydration by three water molecules blocks the excited state proton transfer occurring in DAH + and the 1-1 and 1-2 complexes. The complete survey including the structural assignment of the 1-1 and 1-2 and the small background signal of the 1-3 complexes will be published in a forthcoming paper. The combination of cryogenic ion spectroscopy with mass-selected hydrated species allows us to precisely investigate the subtle hydration effects on the photophysical processes of such neurotransmitters. Studying mass-selected hydrated biomolecules paves the way to disentangle the complex photochemistry occurring in solution, while it provides stringent tests for developing theoretical methods applied to the molecular excited state.

  37 a) a) Tentative origin. Onsets are difficult to identify because of poor Franck-Condon factors around the origin. The hydrated clusters DAH + (H2O)1, 2 show similar spectral features, which consist of low intensity background and intense broadened bands. The onsets of the background and position of the broad bands are systematically blue-shifted by stepwise hydration. This suggests that the ring system of DAH + is perturbed by hydration with a destabilization of the * orbital. The spectral feature changes drastically when DAH + is hydrated by three water molecules. The background signal is weakened significantly and the broad bands become very sharp. Clearly it shows the drastic change in the dynamics in the excited state by addition of the third water molecule. For this cluster size, vibronic bands are now well resolved. The lowest frequency band, i. e. S1 origin, is the most intense, which indicates that the structure of DAH + (H2O)3 is similar in both S1 and S0. Thus, the structural assignment in S0 gives a good clue to understand such a change in dynamics by hydration.

FIG. 2

 2 FIG. 2 Observed (a) and calculated (b and c) IR spectra of DAH + (H2O)3. Observed (d) and calculated (e) UV spectra around the S1 origin.

FIG. 3

 3 FIG. 3 Minimum Energy Path (MEP) along the N-H coordinate for (a) DAH (b) DAH + (H2O)3. Energy above the adiabatic * excitation transition in eV.

TABLE 1

 1 Adiabatic excitation energies corrected by the difference of the zero-point-energy between the S0 and S1 state of DAH + and DAH + -(H2O)3

	System	Structure	E adia S1 (calc) cm -1	eV	00 0 (exp) cm -1	eV
	DAH +	G1-syn G1-anti	32 973 33 427	4.08 4.14	33 715 a) 4.18 a)
	DAH + -(H2O)3	G1-1 G1-2	34 747 34 446	4.31 4.27	35 485 4.40 35 240 a) 4.

ACKNOWLEDGMENTS

This work was supported in part by KAKENHI (JP18H01938, JP20K20446, JP19K23624, and JP20H00372) of JSPS, the World Research Hub Initiatives in Tokyo Institute of Technology, the Cooperative Research Program of the ''Network Joint Research Center for Materials and Devices'' from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan, and the RIKEN Pioneering Project, ''Fundamental Principles Underlying the Hierarchy of Matter: a Comprehensive Experimental Study''. The computations were performed at the Research Center for Computational Science, Okazaki, Japan, the HPC resources from the "Mésocentre" computing center of CentraleSupélec and École Normale Supérieure Paris-Saclay supported by CNRS and Région Île-de-France (http://mesocentre.centralesupelec.fr/) and the HPC resources MAGI from University Paris 13.

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

SUPPLEMENTARY MATERIAL

See the supplementary material for the experimental and computational methods, the UV-PID mass spectrum, ps pump-probe photodissociation spectrum, Franck-Condon simulated spectra of DAH + , the structures, Gibbs energies and calculated IR spectra of the ten lowest energy conformers of DAH + -(H2O)3 and the IR spectrum of DAH + -(D2O)3.


S Benaissa

L Verloock

Denys Nikolayev

M Deruyck

G Vermeeren

L Martens

F A M Tuyttens

B Sonck
email: bart.sonck@ilvo.vlaanderen.be

D Plets

W Joseph
email: wout.joseph@ugent.be

Joint Antenna-Channel Modelling for in-to-out-Body Propagation of Dairy Cows at 868 MHz

Keywords: path loss, cows, capsule antenna, internet-of-animals, link budget, propagation, radio channel

published or not. The documents may come   L'archive ouverte pluridisciplinaire

I. INTRODUCTION

The size of dairy farms and the number of animals per stockperson are increasing. Within larger herds, timely detecting health problems of individual cows becomes a challenging and costly task. Monitoring health indicators in real time using sensors enables large dairy farms to optimize their profits as well as increase their cow welfare. Ruminal temperature and pH are important parameters to assess the nutritional and health status of dairy cows and to predict anomalies (e.g., metabolic disorders after calving) [START_REF] Antanaitis | Usefulness of acidity and temperature of the rumen and abomasum in diagnosing SARA in dairy cows after calving[END_REF]. However, these parameters can be measured only using in-body sensors. In practice, for a real-time data collection, the in-body sensor would wirelessly transmit the measured data to a gateway. Therefore, the reliability of the in-to-out-body wireless communication is crucial for collecting such data. Wireless Body Area Networks (WBANs) and Internet-of-Things (IoT) can be effectively used for health tracking of dairy cows to facilitate herd management and enhance cow welfare (IoA, Internet-of-Animals) [START_REF] Benaissa | Characterization of the on-body path loss at 2.45 GHz and energy efficient WBAN design for dairy cows[END_REF]. Moreover, recent advances in low-power wireless communication technologies (e.g., Long Range (LoRa), Sigfox) working at 868 MHz allow long-range wireless communications and are scalable towards a large number of devices. Several studies have investigated the on-and off-body wireless communication for WBANs and IoT applications for animals [START_REF] Benaissa | Characterization of the on-body path loss at 2.45 GHz and energy efficient WBAN design for dairy cows[END_REF], [START_REF] Benaissa | Experimental characterisation of the off-body wireless channel at 2.4 GHz for dairy cows in barns and pastures[END_REF]. The in-to-out-body path loss has been characterised for cows at 433 MHz in previous work [START_REF] Benaissa | Experimental characterisation of in-to-out-body path loss at 433 MHz in dairy cows[END_REF]. However, to the best of authors' knowledge, the in-to-outbody wireless link has not been investigated yet for dairy cows at 868 MHz. The aim of this study was to characterize the path loss between a transmitter placed inside a cow's rumen and a distant gateway at 868 MHz for different dairy cows accounting for the in-body antenna gains. Accurate link budget calculations will safeguard the reliability of the in-body-based monitoring system for dairy cattle.

II. MATERIALS AND METHODS

A. Experimental environments and Animals

Measurements were conducted in a research barn at the Flanders Research Institute for Agricultural, Fisheries and Food (ILVO) in Melle, Belgium. In-to-out-body measurements were performed in a large area of about 6×18 m 2 . Five different fistulated Holstein dairy cows (parity 2.8±1.3) were used for the measurements. Fistulated cows are cows that have been surgically fitted with a cannula. A cannula acts as a porthole-like device that allows access to the rumen of a cow, to perform research and analysis of the digestive system. The cows were tied at a fixed position as shown in Fig. 1-a.

B. In-body capsule antenna

The design of the capsule antenna was presented in [START_REF] Nikolayev | Dielectric-loaded conformal microstrip antennas for versatile in-body applications[END_REF]. To characterize the radiation performance, the previously proposed approach [START_REF] Nikolayev | Robust ultra-miniature capsule antenna for ingestible and implantable applications[END_REF] was used. The antenna was centered inside of a ∅100-mm spherical glass jar containing a muscleequivalent phantom (the details of the experiment are provided in [START_REF] Nikolayev | Dielectric-loaded conformal microstrip antennas for versatile in-body applications[END_REF]). CST Microwave Studio 2018 [7] was used for the simulations. Detailed description of the numerical approach is given in [START_REF] Nikolayev | 434 MHz ISM band antenna for in-body biotelemetry capsules[END_REF]. and implantable applications (see [START_REF] Nikolayev | Dielectric-loaded conformal microstrip antennas for versatile in-body applications[END_REF] for more details), and (c) The antenna after the preparation for the measurements Fig. 2-a shows the impedance characteristics of the capsule antenna in the muscle-equivalent environment and in free space. The -10 dB bandwidth in the muscle-equivalent environment was 90 MHz (fractional BW=10%). The obtained bandwidth fully covers the relevant bands of wireless communication standards such as MedRadio, LoRa, Sigfox, etc. The |S 11 | in free space was -3.4 dB since the antenna was specifically designed for in-body applications. To derive the antenna gain, the gain substitution technique was used. A reference antenna of a known gain [START_REF]06 Quad-Ridged Horn[END_REF] substituted the capsule antenna, and the measured gain of the reference antenna was used to calibrate the results. Fig. 2-b shows the far-field characterization results. The maximum measured gains G were -18 and -34.5 dBi for the in-body and free space, respectively. The radiation patterns and maximum gain values were consistent with the simulated ones. The low gain in free space is due to the strong mismatch in air (|S 11 | ≈ -3.4 dB) since the antenna was specifically designed for inbody applications and relies on dielectric loading by tissues to achieve higher impedance matching [START_REF] Nikolayev | Impact of tissue electromagnetic properties on radiation performance of in-body antennas[END_REF]. The presented values in this section were used for the antenna de-embedded path loss calculation (Section II-D).

C. Path loss measurements and scenarios

The setup of the path loss measurements is shown in Fig. 1a. The transmitter part was composed of a transmitting antenna (T X) and a signal generator. As the T X, the capsule antenna described in [START_REF] Nikolayev | Dielectric-loaded conformal microstrip antennas for versatile in-body applications[END_REF] was used (Fig. 1-b, c). The T X antenna was placed in the rumen bottom of the fistulated cow and connected to an amplifier and a signal generator. The Rohde & Schwarz SMB100A (100 kHz-12.75 GHz) signal generator was used to inject a continuous wave signal at 868 MHz. The power at the output of the amplifier (injected to the antenna) was 32 dBm. The receiver part was composed of the EMF probe (Rohde & Schwarz TS-EMF, Italy) connected to a spectrum analyser and a laptop to store the data. The EMF probe was used to measure the three components of the received electric field. The measurements were carried out for different T X-RX separations (1 to 20 m). At each measurement location, 300 samples were recorded. The mean value of the samples was considered as a received power for the corresponding T X-RX separation. The measurements were performed also without cows. In this case, the T X antenna was mounted in free space at a height of 0.8 m (i.e., the distance from the bottom of the rumen to the ground). The measurements without cow were carried out to quantify the increase of path loss due to the cow body.

D. Joint antenna-channel:Path loss difference for body loss estimation

From the measured average received power P RX (dBm) for a given T X-RX distance, the path loss P L(dB) in free space (P L F S ) is calculated as follows:

P L F S = P T X + G T X F S -L T X + G RX -L RX -P RX (1)
where P T X is the transmitter power (dBm) (input power to the antenna), G T X F S the TX antenna gain (dBi) in free space, L RX the transmitter cable losses (dB), G RX the receiver antenna gain (dBi), and L RX the receiver cable losses (dB).

The definition of the path loss given by ( 1) cannot be applied directly to WBANs due to the inevitable interaction between the antennas and the cow's body. Because the antennas are positioned in the cow's body, their characteristics (e.g., gain) are influenced by the body. In this situation, the free space antenna gain cannot be used for calculating the in-to-out-body path loss. In literature [START_REF] Hall | Antennas and propagation for on-body communication systems[END_REF], [START_REF] Reusens | Characterization of on-Body communication channel and energy efficient topology design for wireless body area networks[END_REF] the antenna gains are included in the WBAN path loss calculation given by (1). Thus, the path loss including the antenna gains as a part of the channel model (P L incl ) is calculated as follows:

P L incl = P T X -L T X -L RX -P RX (2)
However, with this approach, the obtained path loss models determined by simulations or measurements are specific for the used antenna type. To separate the antenna from the underlying channel, several new studies have tried to establish the so called antenna de-embedding path loss [START_REF] Grimm | Electromagnetic wave propagation on human trunk models excited by half-wavelength dipoles[END_REF], [START_REF] Kurup | Extraction of antenna gain from path loss model for in-Body Communication[END_REF], [START_REF] Naganawa | FDTD-based antenna de-embedding in WBAN on-body channel modeling[END_REF]. In this paper, the antenna gains provided in [START_REF] Nikolayev | Dielectric-loaded conformal microstrip antennas for versatile in-body applications[END_REF] are used for the path loss calculation instead of the free space gains. Thus, the path loss P L excluding the antenna gains (i.e., antenna de-embedded path loss) is given by:

P L body = P T X + G T X b -L T X + G RX -L RX -P RX (3)
with G T X b is the in-body antenna gain of the TX antenna. Finally, the increase of the path loss [P L(cow) -P L(without cow)] due to the cow body (i.e., body loss) for each individual cow is calculated as follows:

δ P L = P L body -P L F S (4)

E. Link budget

In this Section, LoRa technology (Long Range) is proposed for in-body data collection for dairy cows accounting for the capsule antenna gains. A link budget is presented to calculate the network range. Table I lists the parameters used for the range calculation. Three bit rates are investigated (bandwidth 125 kHz, [START_REF]MHz to 1020 MHz low power long range transceiver[END_REF]): 0.25 kbps (min), 0.98 kbps (typical), and 5.47 kbps (max) (Table I). To determine the range, we firstly calculate the maximal path loss P L max , to which a transmitted signal can be subjected while still being detectable at the receiver. The P L max in dB is calculated as follows:

P L max = P T X + G T X + G RX -S RX (5)
In ( 5) , P T X is the transmitter power in dBm, G T X is the T X antenna gain in dBi, G RX is the RX antenna gain, and S RX is the receiver sensitivity in dBm. Next, the maximal path loss is compared to the distance-dependent path loss model including the body loss. [START_REF] Nikolayev | Robust ultra-miniature capsule antenna for ingestible and implantable applications[END_REF] with P L d (dB) is the path loss at a distance d in m, P L d0 in (dB) is the path loss at reference distance d 0 = 1 m, n the path loss exponent (-), d the separation distance between T X and RX in m, M s the shadowing margin in dB, and M f the fading margin in dB [START_REF] Benaissa | Internet of animals: characterisation of LoRa sub-GHz off-body wireless channel in dairy barns[END_REF]. Finally, the range R in meter of the wireless system under consideration accounting for the body loss is the distance to the maximal path loss and can be determined by solving the following equation: 7) can be solved for R using (6): R = d 0 .10 (P Lmax-Ms-M f -Body Loss-P L d 0 )/10n (8) II). This variation was expected since the cows have different sizes and the quantity and type of feed in their rumen differ. The standard deviation between T X-RX locations varied from 4.8 to 8.4 dB, with an average of 4.8 dB for all cows. We note that these values quantify the real loss in power due to cow body (in-to-out-body antenna de-embedded path loss). 2) Network range: The path loss models obtained in previous studies [START_REF] Benaissa | Internet of animals: characterisation of LoRa sub-GHz off-body wireless channel in dairy barns[END_REF] were considered (antenna de-embedded path loss models). The shadowing margin (M s ) was determined such that 95% of the locations at coverage cell edge are covered by the wireless system. This margin was derived from the standard deviation σ around the path loss model (σ P Lmodel ) [START_REF] Benaissa | Internet of animals: characterisation of LoRa sub-GHz off-body wireless channel in dairy barns[END_REF] and the standard deviation of the body loss (σ Body loss ) and equals 1.65σ, with σ = σ 2 P Lmodel + σ 2 Body loss . Fade margin (M f ) of 8 dB in indoor and 4 dB outdoor were considered for an outage probability of 0.01 (99% of the time, the variation around the median will not exceed the fade margin) [START_REF] Benaissa | Internet of animals: characterisation of LoRa sub-GHz off-body wireless channel in dairy barns[END_REF].

P L d = P L d0 + 10nlog(d/d 0 ) + M s + M f + Body Loss
P L max = P L d0 + 10nlog(R/d 0 ) + M s + M f + Body Loss (7) Equation (
The obtained ranges are listed in Table III. A maximum transmit power of 14 dBm was used. For the indoor scenario, the ranges were between 36 and 175 m. In outdoor (pasture), the ranges were higher and reach 364 m. In free space, LoRa provides higher ranges (10-19 km outdoor). This shows the high attenuation of the signal due to the cow body. The range could be extended by using lower bit rates, although this would limit the amount of collected data.

IV. CONCLUSION

The in-to-out-body path loss in dairy cows was characterised for the first time at 868 MHz. Based on the obtained results for five cows, the antenna de-embedded path loss increased on average by 50.6 dB, with a standard deviation of 4.8 dB. The obtained results were used to calculate the range of a LoRa based network accounting for the antenna channel. Ranges up to 175 m in indoor and 364 m in outdoor were obtained depending on the used bit rate.

Fig. 1 .

 1 Fig. 1. (a) Measurement setup, (b) the capsule antenna designed for ingestible and implantable applications (see [5] for more details), and (c) The antenna after the preparation for the measurements

Fig. 2 .

 2 Fig. 2. (a) The reflection coefficient |S 11 | in free space and in a phantom (in-body) with muscle-equivalent EM properties. (b) In-body measured and computed radiation patters.

Fig. 3 .

 3 Fig. 3. Boxplot of the path loss (PL) increase due to the cow body for each individual cow and the average along all cows

TABLE II The

 II mean, the median, and the standard deviation (SD) of the path loss difference for each individual cow and for all cows (Avg)

	Cows	1	2	3	4	5	Avg
	Mean (dB)	47.6 52.9 43.7 53.3 55.3 50.6
	Median (dB) 48.0 52.7 43.4 51.8 53.5 50.0
	SD (dB)	4.8	5.7	4.8	6.0	8.4	4.8

TABLE III

 III Parameters of the path loss models and the obtained ranges for the investigated scenarios

	Scenarios		Indoor	Outdoor	Unit
	Channel P L(d 0 ) 38.6	33.3	dB
	model	n	2.04	2.2	[-]
		Ms	5.2	5.6	dB
		M f	8	4	dB
	Body loss		50.6	50.6	dB
	Range		36; 100; 175	78; 210; 364	m

ACKNOWLEDGMENT

This work was supported by the EOS project MULti-Service WIreless NETwork (MUSE-WINET). Margot Deruyck is a Post-Doctoral Fellow of the FWO-V (Research foundation Flanders, Belgium). The authors would like to thank Leen Vandaele and Sara Van Lembergen for their help during the measurements.


Zvonimir Sipus
email: zvonimir.sipus@fer.hr

Marko Bosiljevac
email: marko.bosiljevac@fer.hr

Denys Nikolayev
email: denys.nikolayev@epfl.ch

Anja Skrivervik
email: anja.skrivervik@epfl.ch

Design Concerns for In-body Antennas Based on Frequency Analysis of Fundamental Radiation Limitations

Keywords: body antennas, radiation limitation, spherical-mode analysis

Fundamental radiation limitations of in-body or implantable antennas should give us an estimate on the feasibility of some desired system. It was shown that near-field effects and distance to the body -freespace boundary are critical aspects, while the shape doesn't play a major role in the achievable power. Through the frequency analysis of these limitations in this paper we provide another perspective and show how rigorous and approximate approach to near-field and reflection losses manifest in the results. This is demonstrated on a spherical body example which contains a small spherical implant which can be placed at different positions within the body in order to simulate different implant depths. The results reveal that reasonably accurate description of in-body loss mechanisms can be achieved using our previously defined fundamental radiation limitations for power density, however, depending on the frequency different loss aspects must be treated with special care.

INTRODUCTION

Recent advances in electronics and wireless possibilities have inspired a large growth of interconnected sensors and devices which are dedicated to improving health care for various types of patients. Design of such medical implants is quite a challenge for engineers due to numerous restrictions in terms of size, allowed materials, required longevity and similar. Also, from the perspective of communication link and antenna design the small size and losses of the body tissue result in a very complex design situation.

In order to estimate the possibilities of a certain design it is beneficial to understand the limits in the performance of small antennas placed in body environment. Many studies exist where limits of the performances of electrically small antennas have been studied (pioneering work started by Chu [START_REF] Chu | Physical limitations on omni-directional antennas[END_REF], Wheeler [START_REF] Wheeler | Fundamental Limitations of Small Antennas[END_REF], Harrington [START_REF] Harrington | On the Gain and Beamwidth of Directional Antennas[END_REF], and continued by Collin et al. [START_REF] Collin | Evaluation of Antenna Q[END_REF], Fante [START_REF] Fante | Quality factor of general ideal antennas[END_REF] and Fano [START_REF] Fano | Theoretical limitations on the broadband matching of arbitrary impedances[END_REF]). Also, further advances in this topic have been demonstrated in [START_REF] Yaghjian | Impedance, Bandwidth and Q of Antennas[END_REF][START_REF] Hansen | Electrically small, Superdirective and Superconductive Antennas[END_REF][START_REF] Best | The Lower Bound on Q for Lossy Electric and Magnetic Dipole Antennas[END_REF][START_REF] Gustafsson | Physical limitations on antennas of arbitrary shape[END_REF]. These principles, however, are valid for antennas in free space environment, while the implanted scenario places the antenna into a very lossy medium. Commonly used practices cannot be applied in these scenarios and alternative strategies need to be defined. In [START_REF] Moore | Effects of a surrounding conducting medium on antenna analysis[END_REF] it was shown that fundamental antenna characteristics like the far field, the antenna radiation pattern or the bandwidth do not apply when the antenna radiates into an infinite lossy medium.

This inspires us to investigate theoretical and practical limits of antennas when radiating into a lossy medium. Recent advances in characterization and in-body link modelling can be found in [START_REF] Ehrenborg | Calculating physical bounds for in-body antennas[END_REF][START_REF] Faerber | In vivo characterization of wireless telemetry module for a capsule endoscopy system utilizing a conformal antenna[END_REF] however, our aim is to use canonical models (spherical and cylindrical phantoms) to investigate fundamental physical limits on the total power and maximal power density that can reach free space for a specific implanted antenna scenario. This gives a rough estimate of the realistic scenario but provides useful insights into the fundamental radiation limitations. [START_REF] Bosiljevac | Propagation in Finite Lossy Media: an Application to WBAN[END_REF][START_REF] Bosiljevac | Study of wearable WBAN antenna properties based on spherical body model[END_REF].

II. MODEL AND ANALYSIS METHOD

The basis of our analysis is a spherical model of a human body which is a rough estimate, but it gives valuable insight [START_REF] Kim | Implanted antenna inside a human body: simulations, design, and characterization[END_REF] into the investigated topic. Fig. 1 presents the analyzed structure and its geometry. The outer sphere represents the body tissue (with radius rbody) and the smaller sphere is the encapsulation of the implanted antenna. The sphere modeling the body can be either homogeneous or formed by concentric layers in order to mimic a part of the human body (skin, fat, muscle, etc.) by using dielectric properties that are similar to those of real human tissues. The implanted antenna is modeled as either an electric or a magnetic dipole encapsulated in a small sphere with radius rimpl filled with air.

In order to optimize the speed and optimization, our numerical procedure is based on spherical-wave modal expansion. The electromagnetic field in a spherical structure (with zero free-charge density) can be represented using vector spherical harmonics [START_REF] Stratton | Electromagnetic theory[END_REF], [START_REF] Harrington | Time Harmonic Electromagnetic Fields[END_REF] as:

,

mn mn mn n m mn b a N M E + - =  (1)
where As it can be seen in Fig. 1 the structure of interest consists of two spherical structures -the spherical model of a body and the spherical model of an implanted antenna. Each spherical structure can be multilayered and can be separately analyzed using the spherical-wave modal expansion approach described with eqs. ( 1)-(3). Therefore, the main challenge in the analysis of the structure in Fig. 1 lies in connecting two spherical problems that have displaced centers of coordinate systems. Details of this procedure are given in [START_REF] Bosiljevac | Propagation in Finite Lossy Media: an Application to WBAN[END_REF][START_REF] Bosiljevac | Study of wearable WBAN antenna properties based on spherical body model[END_REF].

mn mn mn mn k M N r M × ∇ = × ∇ = 1 , ˆψ (2)

III. RESULTS

A. Initial observations

The scenario shown in Fig. 1. is simulated using our code and CST Microwave Studio for an antenna implanted in two different phantoms: a spherical phantom and a cubic body phantom where the cube side length is equal to the diameter of the considered sphere. The working frequency is 403.5 MHz, the body sphere has rbody = 9 cm radius and permittivity is εbody = 43.50 -j34.75 [START_REF]Evaluating Compliance With FCC Guidelines for Human Exposure to Radiofrequency Electromagnetic Fields[END_REF]IEEE Head model]. The implanted antenna in this case is a short electrical dipole located in a 2mm diameter air sphere (implanted antenna) placed in the center of the body phantom. The power density (real part) is observed on the line passing through the center of the cube side and perpendicular to the excitation electric dipole) and it is given in Fig. 2. This result indicates that the actual shape of the body is not crucial. Moreover, this result validates the applicability of the spherical model in our investigation since all the results agree very well. Note that the power density is normalized with the factor 2 0 (8 3) ( )

obs feed W r r π ⋅ -
, where W0 is the maximum value of the real part of the power density component normal to the surface of implanted antenna, i.e., just inside the lossy medium. The results in Fig. 2. show three regions crucial for understanding the propagation mechanism through the body when the source is implanted. This is further highlighted in Fig. 3. where the radial component of real part of the normalized power density is observed for two common frequencies, 403.5 MHz (as in the first case) and 2.45 GHz (εr,body = 39.2 -j13.2 at 2.45 GHz). Three regions are highlighted (near-field absorption, propagating field absorption, reflection from the boundary) and although there is a large difference in frequencies, in this particular case the final power density reaching free space is comparable. This led us to use the developed expressions for the available power reaching free space [START_REF] Skrivervik | Fundamental Limits for Implanted Antennas: Maximum Power Density Reaching Free Space[END_REF] and investigate what is the frequency behaviour of the available power.

A similar investigation was performed for a particular case in [START_REF] Nikolayev | Optimal Radiation of Body-Implanted Capsules[END_REF], however we wanted to expand on this by studying how the expressions for fundamental limits behave for different frequencies. These expressions were derived in [START_REF] Skrivervik | Fundamental Limits for Implanted Antennas: Maximum Power Density Reaching Free Space[END_REF], and here only the final results are repeated for convenience for the case of the dominant spherical mode due to an electric dipole excitation (the mode that is least attenuated in the lossy media; the Hankel functions and their derivatives are replaced with the analytic expressions);

The reactive near-field the losses and corresponding efficiency e can be expressed with { }

β η α β η β β β * - =         ⋅ + + - -               (4)
This expression can be approximated for the dominant term as

The spherical characteristic impedances and air body Z Z for the dominant spherical mode are equal to 2 ( ) ( )

j r j r j r J j r j r E E e je r e r Z r H H e je r β β β φ θ β β φ θ β β β η β - - - - - - - = =- = - (8)
The reflection losses can be well approximated using largeradius variation resulting in:

{ }

B. Frequency analysis

In order to compare the results with existing work the focus will be on the 10 cm radius sphere which was used in [START_REF] Nikolayev | Optimal Radiation of Body-Implanted Capsules[END_REF]. In order to discuss the formula for power density reaching free space a single-layer muscle structure was considered. The frequency variation of complex permittivity is given in [START_REF] Gabriel | The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues[END_REF], and the radius of the centrally positioned implanted antenna is 5 mm. Fig. 4. shows the frequency dependence of the power density reaching the free-space for several different ways of calculating the power density. Indicated as "Power density" in the figures is the power density calculated completely rigorously using the spherical harmonics code, while other curves are plotted using expressions ( 4) - [START_REF] Gustafsson | Physical limitations on antennas of arbitrary shape[END_REF] with different ways of calculating the reflection losses. From Fig. 4 it is clear that the fundamental limit gives the estimation of the maximum power density at the body surface. Note that in the expression for the fundamental limit there are no reflection losses since it is hard to predict the minimum reflection losses [START_REF] Skrivervik | Fundamental Limits for Implanted Antennas: Maximum Power Density Reaching Free Space[END_REF]. For lower frequencies the reflections are larger since the EM field just outside the body is in the reactive near-field which increases the magnitude of the reflection coefficient. Therefore, for a symmetric case, i.e. for the implantable antenna in the center of the body, one should use the rigorous expression for the efficiency due to reflections (eq. ( 7)).

In the presented results in Fig. 4.a there is a non-physical increase of the power density around 1 GHz, i.e. around frequencies for which the reactive near-field efficiency approaches one. For such frequencies we cannot just use the dominant-term expression (given with eq. ( 5)), i.e. we should use the more complicate rigorous expression given with eq. ( 4). The results obtained with the rigorous expression are given in Fig. 4.b, and an excellent prediction of the power density just outside the body is obtained. The same type of results is achieved for a dual case -magnetic (see Fig. 5). Note that there is a large difference in obtainable power density just outside the body for lower frequencies since the reactive near-field is present in a large part of the body and the losses in reactive near-field zone are much smaller for a magnetic dipole based implantable antenna. The magnetic dipole excites much stronger magnetic fields in the vicinity of the dipole, which do not dissipate in the body since there are no magnetic losses present in human tissues.

For non-symmetric case, i.e. for an implantable antenna with off-center position, for the estimation of the reflection losses one should use the approximate expression for the efficiency due to reflections given with eq. ( 9). The reason why one needs to use the expression that is based on largeradius approximation is based on the fact that the spherical symmetry is violated and consequently each spherical wave excited by the source is scattered from the outer boundary as a spectrum of spherical waves of different order. The results for both electric and magnetic dipole excitations are given in Fig. 6. Again, a good prediction of the power density just outside the body is obtained.

IV. CONCLUSION

Fundamental radiation limitations for small implanted antennas are largely undefined. Using a spherical body model as a starting point we previously demonstrated that limits on the available power density can be determined. In this paper we expanded the investigation and analyzed the frequency dependence of these limits and placed them in perspective with the loss mechanisms present in the body. The analysis of the results revealed different perspectives for handling near-field losses and reflection losses. In cases with spherical symmetry approximating the near-field losses with only the dominant term leads to errors in the prediction of the power density and needs to be corrected by using a more rigorous expression. This is also valid when considering reflection losses i.e. the rigorous formulation needs to be considered. However, when there is no spherical symmetry, i.e. the source is not in the center of the sphere, the large radius approximation for reflection losses provides much better results. These findings indicate that the developed limits have to be observed also in context of frequency and position in order to provide good initial approximations for the design of implanted systems.

Fig 1 .

 1 Fig 1. View of the analyzed structure with the excitation moved away from the center.

  solution of the Helmholtz differential equation, i.e. n Z ˆdenotes Schelkunoff type of spherical Bessel or Hankel functions [18], β denotes the wavenumber of the considered media and r ˆ is the unit vector in r-direction.

Fig. 2 .

 2 Fig. 2. Radial component of real part of the normalized power density at different distances from the implanted antenna placed in spherical and cubic body. The source is placed at the center of the body.

Fig. 3 .

 3 Fig. 3. Radial component of real part of the normalized power density at different distances from the implanted antenna. The source is in the center of 9 cm spherical phantom.

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

 456 Fig. 4. Radial component of real part of the normalized power density as a function of frequency for electric dipole excitation; (a) approximate nearfield expression, (b) rigorous near-field expression.

ACKNOWLEDGMENT This research has been supported in part by the European Regional Development Fund under the grant KK.01.1.1.01.0009 (DATACROSS).


Keywords: conformal array, beam scanning, directivity, scan loss, rapid code

Conformal antenna arrays are able to fit seamlessly on curved 3D-shaped surfaces, which are found ubiquitously on vehicles, aircraft, a human body, etc. In addition, conformal structures can overcome the scan loss limitations of conventional planar arrays. Yet, only a few computational analysis methods have been proposed with either performance or applicability limitations. In this study, a rapid analysis methodology is developed for the analysis of arbitrary-shaped conformal beamscanning arrays. The method requires only specifying the element position vectors and normals in space. Arbitrary individual antenna patterns could be specified. Finally, an example study is provided examining the beam-steering performance of halfcylinder conformal arrays vs a reference square planar array.

I. INTRODUCTION

Conformal antenna arrays provide powerful performance capabilities whenever an antenna has to fit in geometrically on 3D-shaped surfaces like that found on space-and aircraft. Traditional planar and reflector antenna arrays affect the aerodynamic performance of the aircraft as well as have limited scanning capabilities (usually up to ±60 • ) [START_REF] Josefsson | Conformal Array Antenna Theory and Design[END_REF]. Therefore, conformal antenna arrays are considered as an attractive alternative. Conformal array technology is still rarely used in commercial applications. It is limited mostly to military communications and aviation, missile electronic warfare, and radar systems. This is also important for future aircraft designs that use thrust vectoring and, thus, can decouple the flight and aircraft axes. In addition to military applications, the conformal antenna arrays are gaining importance in mobile communications. Future mobile base stations can be concealed for aesthetical reasons. One of the most important applications of the conformal arrays in the future is expected to be the smart skin approach [START_REF] Son | Development of a smart-skin phased array system with a honeycomb sandwich microstrip antenna[END_REF]. It envisages the integration of nonplanar active antenna apertures in curved surfaces adapted to the skin of the platform: aircraft, satellite, car, etc. Biomedical applications have been also considered recently for both inbody [START_REF] Nikolayev | Conformal antennas for miniature in-body devices: The quest to improve radiation performance[END_REF] and on-body [START_REF]Conformal phased surfaces for wireless powering of bioelectronic microdevices[END_REF] devices.

A fundamental problem in the analysis of conformal arrays is that there is an infinite number of the possible surfaces to conform to. Furthermore, if there is no symmetry, each Fig. 1. formulation: an arbitrary shaped surface containing a conformal antenna array defined in a global Cartesian coordinate system as {(r 1 , ..., r i ) | r i in R 3 and i = N × M }. Individual element orientations are defined using normals ni . Vector rp leads to the observation point in the far field and rs to the scan direction. element will see a different environment and this complicates the mathematics. As a consequence, the element factor cannot be factored out from the array factor. This is directly translated to the simulation time needed for the analysis.

Implementation of analysis algorithms is nontrivial as well. It requires interdisciplinary background in antennas and electromagnetics, analytic geometry, advanced linear algebra, and rapid code development. Therefore, only a few codes have been proposed so far. Brégains et al. proposed a methodology for the analysis of arbitrary conformal arrays [START_REF] Brégains | A MATLAB tool for visualizing the 3D polar power patterns and excitations of conformal arrays[END_REF]. The local coordinate systems have to be pre-specified explicitly for each array element. This code was later extended to deal with heterogeneous elements with potentially different polarizations [START_REF] Brégains | A MATLAB interface for analyzing conformal arrays composed of polarized heterogeneous elements[END_REF]. Kobayashi et al. have recently proposed a simple calculation method of equi-phase fronts of conformal arrays based on the direction-cosine relation [START_REF] Kobayashi | Simple calculation method for conformal beam-scanning array pattern[END_REF]. As for the commercial codes, to the best of authors' knowledge, only Phased Array System Toolbox TM implemented in MATLAB [START_REF] Mathworks | Phased Array System Toolbox[END_REF] provides a complete script-based framework for the analysis of conformal arrays.

In this study, we propose a new tool for rapid analysis of arbitrary-shaped conformal beam-scanning arrays. Compared to [START_REF] Brégains | A MATLAB interface for analyzing conformal arrays composed of polarized heterogeneous elements[END_REF], only the element position vectors r i and normals ni are required to set up the array. More than a twofold reduction of execution time and memory complexity was achieved compared to [START_REF] Mathworks | Phased Array System Toolbox[END_REF]. This enables the analysis of larger and more complex structures. Finally, an example study is provided that examines beam-steering performance of a halfcylinder conformal array vs a reference square planar array.

II. PROBLEM FORMULATION

A. Coordinate Systems

We define the array geometry in global coordinates (GCS) via the element position vectors r i = (x i , y i , z i ) and the normals ni = (θ i , ϕ i ) (Fig. 1). Transitions between spherical and Cartesian forms are as defined in [START_REF] Bronshtein | Handbook of Mathematics[END_REF]Sec. 3.5.3.1]. For the isotropic elements [i.e. f i is a scalar constant independent of (θ, ϕ)], defining only GCS is enough. However, for an arbitrary conformal array consisting of directive elements, it is useful to define the local coordinates systems (LCS). We accomplish this by, first, placing (r i ) and orienting (n i ) the array elements in GCS. Then, we use the rotation matrices X, Y, and Z (as defined in [9, Sec. 3.5.3.2]) around each axis (x, y, z) in Cartesian coordinates. The full 3×3 transformation matrix T is then generated for each element by multiplying successively the rotation matrices:

T = ZYX. (1)
Assuming no polarization, the rotation is required only around yand z-axes. X is therefore an identity matrix, or T = ZY.

The transformation matrices allow now to determine the set of observation point vectors {(r p1 , ..., r pi ) | r pi in R 3 } in LCS for each element by, first, multiplying T by a columnvector r p and, second, summing the columns of a resulting matrix R. Finally, r pi could be converted back to spherical coordinates. Now we can determine the contribution of each element at the direction r p .

B. Far-Field Superposition

For an arbitrary conformal array depicted in Fig. 1, the radiation pattern is obtained by superposition of contributions of each element [START_REF] Mailloux | Phased Array Antenna Handbook[END_REF]:

E (θ, ϕ) = N ×M i=1 f i w i e -jkri•rp , (2)
where θ = azimuth angle, ϕ = elevation angle, f i = individual element radiation patterns, w i = |w i |e -jβi are the complex weights, β i = phase of the i th element, k = 2π/λ is the wavenumber at the frequency f , r i = (x i , y i , z i ) is the position vector of the i th element relative to the center of GCS, and r p = vector to an arbitrary observation point P (θ, ϕ).

Individual array elements consist mainly of simple antennas: patches, dipoles, monopoles, etc. Their smooth radiation patterns can be accurately reproduced using simple analytical expressions. For the sake of simplicity, we represent here a generic directive antenna using a second-order cosine:

E i = cos 2 ϕ i cos 2 θ i . (3)

C. Array Scanning

Array scanning to an angular direction (θ scan , ϕ scan ) can be accomplished by applying the complex weights w i . These are chosen so that the path length differences for the generalized conformal array in Fig. 1 are compensated in order to make the radiated phase fronts from all elements arrive in phase at a given point S in far field. Therefore, the complex weights could be easily found as [10, p. 15]:

w i = a i e -jkri•rs , (4)
where a i is the real-valued amplitude of the i th element. Therefore, the phase β i = tan -1 [ (w i ) / (w i )] and r s is the steering vector obtained from (θ scan , ϕ scan ) as

r s =   -cos (ϕ scan ) cos (θ scan ) -cos (ϕ scan ) sin (θ scan ) -sin (ϕ scan )   . (5)
Note that ( 4) is exact for an array of isotropic elements. For anisotropic elements-as (3)-the solution is approximate with its error proportional to the steering angle.

D. Directive Properties

Directive gain is a ratio of the array radiation intensity in a given direction over the radiation intensity of an isotropic source. We calculate it as [START_REF] Balanis | Antenna Theory: Analysis and Design[END_REF]

D = 4πU (θ, ϕ) P rad , (6)
where U (θ, ϕ) = |E (θ, ϕ) | 2 is the radiation intensity and P rad is the total radiated power. The latter could be obtained by integrating U over the entire solid angle of 4π [11, Ch. 2.4]:

P rad = Ω U dΩ = ¢ 2π 0 ¢ π 0 U sin θ dθdϕ. (7)
We solve [START_REF] Kobayashi | Simple calculation method for conformal beam-scanning array pattern[END_REF] numerically as given in [START_REF] Balanis | Antenna Theory: Analysis and Design[END_REF]Ch. 2.7].

Finally, the directivity D 0 of the array is defined as the maximum value of the directive gain D 0 = max [D ((θ, ϕ)].

III. EXAMPLE RESULTS

Using the outlined methodology, we developed a MATLAB code for the analysis of arbitrary-shaped conformal beamscanning arrays. For demonstration and benchmark purposes, we perform a simple analysis of a half-cylindrical-segment conformal array and compare its beam-steering performance with a reference planar array. For instance, such problem can arise in an aircraft-wing antenna design when facing a decision of mounting a planar array behind an aerodynamic radome or conforming the array to a wing. A. Half-Cylindrical-Segment vs Planar Arrays Fig. 2 shows the geometries of the arrays under comparison. The element separation distance is λ/10 that allows obtaining the fundamentally achievable D 0 in a given steering direction (ϕ scan , θ scan ). The square planar array (Fig. 2a) contains 400 elements, and the conformal one (Fig. 2b) has 620 elements. Both arrays span the same (2λ) 2 area on the y-z plane. The individual element patters f i are given by (3), and the element normals ni are orthogonal to the array surfaces.

Well-known scanning performance of a planar array is demonstrated in Fig. 3a: the scanning range is limited by a maximum of about 60 • in both azimuth and elevation planes. End-fire radiation in a given direction can only be achieved using the individual elements with appropriate patterns to satisfy the superposition in this direction [START_REF] Liu | Microstrip magnetic dipole Yagi array antenna with endfire radiation and vertical polarization[END_REF].

Conformal arrays allow to mitigate such limitations. Clearly, the elevation-scan range is improved as Fig. 3b shows: even at 90 • only a few dBi of scan loss is observed. A less obvious result is that the azimuth scanning range is also significantly improved for non-zero elevation angles. In other words, for the arrays in Fig. 2, the planar one has inaccessible scan range of about 30 • from y-z plane in any direction. However, the half-cylindrical conformal array has a blind zone only ≈ 20 • around the y-axis. Note that we analyzed the scanning range only for a +x half-space since we consider here the cosinesquared array elements with no back lobes. The conformal array has also a limited scanning capability in the -x halfspace, i.e. beyond ϕ scan > 90 • . As the scan loss will be high in this angular space, we omitted these results for clarity.

The obtained results were verified using the Phased Array System Toolbox TM implemented in MATLAB [START_REF] Mathworks | Phased Array System Toolbox[END_REF] and are in perfect agreement. As for the performance of our code, the analysis of D 0 for one scanning angle took 9.1 s, whereas [START_REF] Mathworks | Phased Array System Toolbox[END_REF] requires 21.9 s to execute (average times over 10 runs; Intel Core i7-6700 CPU, 32 GB DDR4 RAM). Note that (θ scan , ϕ scan ) ∈ [0, 90]

• has been analyzed to obtain the results in Fig. 3, which represent significant performance improvement.

The memory complexity is also significantly reduced compared to [START_REF] Mathworks | Phased Array System Toolbox[END_REF]. Low memory usage makes it possible to analyze much larger structures. For instance, the analysis of the 10λ half-cylindrical array (15.7k elements) was impossible using [START_REF] Mathworks | Phased Array System Toolbox[END_REF]: memory overflow occurred even on a computation server with 256 GB RAM. Using our code, the run time for one scanning angle took 48.2 min in average (over three runs) on the aforementioned 32-GB-RAM desktop computer.

IV. CONCLUSION

In this study, we proposed a new tool for fast analysis of arbitrary-shaped conformal beam-scanning arrays. Implementation of the proposed methodology allow for rapid and accurate analysis of the radiative properties of conformal beam-scanning arrays with arbitrary spatial configurations in R 3 . Considering nearly identical mathematical approach, the method can also be applied to the analysis of complex 3Dshaped apertures [START_REF] Balanis | Antenna Theory: Analysis and Design[END_REF]Ch. 12]. Future work includes the implementation of arbitrary element polarizations and existing inhouse optimization approaches (e.g. [START_REF] Fuchs | Shaped beam synthesis of arbitrary arrays via linear programming[END_REF]) to enable radiation pattern synthesis of arbitrary conformal arrays.

Fig. 2 .

 2 Fig. 2. Geometry of the example problem: comparison of beam-scanning performance of (a) square planar and (b) half-cylindrical-segment conformal arrays. Both arrays span the same area on y-z plane. The element separation distance is λ/10 so that the fundamental bounds on D 0 are obtained. The individual elements patterns are according to (3). The element normals ni (denoted by red arrows) are orthogonal to the array surfaces.

Fig. 3 .

 3 Fig. 3. Comparison of beam-scanning performance of (a) planar and (b) halfcylindrical-segment conformal arrays. The broadside scanning direction is (ϕ, θ) = 0 • . Only a quarter of the scanning range is shown due to the symmetry properties of the arrays in Fig. 2. Maximum directivity in the scanning direction is shown, and the corresponding elements weights w i are estimated using (4).


E Le Merle

D Hauser

C Peureux

L Aouf

P Schippers

C Dufour

DIRECTIONAL AND FREQUENCY SPREAD OF SURFACE OCEAN WAVES FROM CFOSAT/SWIM MEASUREMENTS

Keywords: CFOSAT, SWIM, radar, ocean, ocean waves, ocean wave spectra

The CFOSAT (China France Oceanography Satellite) mission launched in 2018 now routinely provides at the global scale, directional spectra of ocean waves. The principle is based on the analysis of the normalized radar cross-section measured by the instrument SWIM (Surface Waves Investigation and Monitoring), a near-nadir pointing Ku-Band real-aperture scanning radar. From the ocean wave spectra derived from SWIM, the principal parameters of ocean wave spectra as significant wave height, peak wavelength, and peak direction are now available to better characterize the sea-state. However, it is known that these principal parameters are not sufficient not fully characterize the distribution of wave energy and understand or validate the physical processes impacting its evolution during growth order decay. Here we show that the parameters characterizing the shape of the wave spectra (e.g directional and frequency spread) can be estimated at the global scale from the SWIM measurements. We also show that they can provide consistent values of the Benjamin-Feir index, an index proposed to estimate the probability of extreme waves. Similarities of differences with the shape parameters of the MFWAM numerical wave model are also discussed.

INTRODUCTION

Ocean surface waves are commonly described by their directional density spectrum of height, which characterizes the distribution of wave energy as a function of wave frequency (or wave number) and wave propagation direction. Apart from significant wave height, which is widely used to characterize or forecast the total energy of waves, the mean or peak period and the mean or peak directions are the most common parameters extracted and analyzed from these spectra. This reduces the information on directional spectra to only few parameters, whereas the directional or frequency spread are seldom analyzed. This limits the progress in the improvement of numerical wave models [START_REF] Resio | Characteristics of directional wave spectra and implications for detailed-balance wave modeling[END_REF]. Indeed, several approximations are done in these models, such as the discretized form of the non-linear wave-wave interactions, the angular distribution of wind input and wave dissipation. These assumptions may induce biases in the modeled wave spectra even if the total energy, characterized by the significant wave height is well reproduced. Another motivation for studying with more details the frequency and directional spread of the wave spectra is their link with the probability of occurrence of extreme waves. For example, [START_REF] Mori | On the estimation of the kurtosis in directional sea states for freak wave forecasting[END_REF] have shown the so-called Benjamin-Feir index (BFI) depends not only on the wave total energy but also on its distribution with frequency and direction.

SWIM is based on an original concept of near-nadir realaperture radar, proposed in the 90's by Jackson et al [START_REF] Jackson | Aircraft and satellite measurement of ocean wave directional spectra using scannig-beam microwave radars[END_REF] but implemented in space for the first tile with CFOSAT [START_REF] Hauser | SWIM: The first spaceborne wave scatterometer[END_REF]. It provides directional spectra of ocean waves with wavelengths between 70 and 500m [START_REF] Hauser | SWIM: The first spaceborne wave scatterometer[END_REF][START_REF] Hauser | New observations from the SWIM radar on-board CFOSAT: Instrument validation and ocean wave measurement assessmen[END_REF]. In [START_REF] Hauser | New observations from the SWIM radar on-board CFOSAT: Instrument validation and ocean wave measurement assessmen[END_REF], the performance on the wave height, dominant wave direction wavelength were analyzed. It was shown that except for waves which propagate in a ±15° sector along-track, the main parameters are in good agreement with the MFWAM model (French version of the WAM model of ECMWF) and in situ data.

In this paper, we go a step further by analyzing several parameters related to the frequency and angular distribution of the wave spectra obtained from the SWIM instrument. In section 2, we describe the SWIM and model data sets used in the analysis and recall the definition of the spectral parameters analyzed further below. We also present the wind and wave height conditions sampled in this study. In section 3, we present the spectral shape parameters (directional and frequency spread, BFI indexes) and discuss their geographic distributions and compare the results from SWIM and from MFWAM. We summarize and conclude in section 4.

DATA SETS AND METHODS

Ocean wave spectra from SWIM are those provided from the prototype processing chain in its V5.0.1. The products consist in 2D wave slope spectra sampled with 32 wavenumbers over the wavelength domain [70, 500] m and 12 directions every 15° in the range [0-180°], i.e. with a 180° ambiguity in the propagation direction. For the present analysis, we used the spectra obtained from the 10° incidence beam observations, and converted the 2D slope spectra into wave height spectra expressed as a function of frequency (32 frequencies on the range [0.056, 0.26] Hz. For this conversion, we took the linear dispersion relationship in deep water. The processing version used here is based on the option#3 for the Modulation Transfer Function (see [START_REF] Hauser | SWIM: The first spaceborne wave scatterometer[END_REF]) which means that the wave spectra are normalized so that the significant wave height is forced to be the same as the one estimate from the nadir-beam of SWIM.

SWIM wave spectral parameters are compared to parameters obtained from the MFWAM numerical model. This model is the French version of the third generation WAM model. It is based on the ECMWF version (ECW AM-IFS-38R2) with a parameterization taken from the WW3model [START_REF] Ardhuin | Semi empirical dissipation source functions for ocean waves. Part I: Definition, calibration, and validation[END_REF]. The MFWAM products used here have a grid resolution of 10 km and are provided every 3-hours. The model is forced by winds from the IFS-ECMWF atmospheric system. Waves/currents interactions are taken into account with daily surface currents provided by the global PSY4-CMEMS ocean forecasting system. The MFWAM wave spectra are discretized in 24 directions every 15° between 0° and 360°, and 30 frequencies evenly spaced frequencies in the range [0.035-0.58] Hz. In this study, we focus on a period of 13 days (a full orbital cycle of CFOSAT) between 9 and 21 September 2019. Figure 1 shows maps of the significant wave height from SWIM and of wind speed from MFWAM. During this period, high sea state conditions were encountered in the Southern Ocean with wind speed of more than 20 m/s and significant wave heights higher than 5m. These situations correspond to storms typical of the high latitudes in the Southern hemisphere where waves developing under high wind forcing are trapped within fast moving storms. The same kind of situation is also observed along the North American coasts where hurricane Humberto passed, and along the Greenland coasts where very an intense offshore wind event occurred.

In the following, three parameters are discussed to analyze the shape of the wave height spectra, namely the frequency width s f of the omnidirectional wave height spectrum E(f), the peakedness coefficient Q p as defined by Goda [START_REF] Saulnier | Wave groupiness and spectral band width as relevant parameters for the performance assessment of wave energy converters[END_REF], and the directional spread of s q .

𝜎 " = 𝐸 𝑓 𝑑𝑓

" ()* " (+, - / 𝐸 -𝑓 𝑑𝑓 " ()* " (+, (1)
𝑄 0 = 2 𝑓𝐸 -𝑓 𝑑𝑓 " ()* " (+, / 𝐸 𝑓 𝑑𝑓 " ()* " (+, - (2)
where E(f) is the omni-directional spectrum expressed as a function of frequency f.

𝜎 2 = 2 1 -𝑎 6 𝑓 - + 𝑏 6 𝑓 - ( 3
)
where a 1 (f) and b 1 (f) are the first pair of the Fourier coefficients used to represent the directional distribution [START_REF] Longuet-Higgins | The directional spectrum of ocean waves, and processes of wave generation[END_REF]. These parameters are estimated for both SWIM and MFWAM wave spectra by taking in both cases f min and f max as the limit of the SWIM frequency range ([0.056, 0.26 Hz]).

Two indexes for extreme waves characterization are also estimated, namely the BFI and BFI_2D as given by [START_REF] Mori | On the estimation of the kurtosis in directional sea states for freak wave forecasting[END_REF]:

𝐵𝐹𝐼 = 𝑘 = 𝑚 = 𝑄 0 2𝜋 (4)
where k 0 is the mean wave number of the omnidirectional spectrum and m 0 its 0 th order moment.

𝐵𝐹𝐼 -@ = 𝐵𝐹𝐼 1 + 7.10 𝜎 𝜙 -/2 𝜔 𝑓 -F=.G

(5) with 𝜔 " = 1/ 𝑄 0 𝜋

RESULTS

Figure (2a)

shows the map of the frequency width s f estimated on the SWIM spectra. Compared to Fig. 1a, it shows that regions corresponding to the smallest frequency width are generally those of the highest significant wave heights Hs. When plotting s f versus Hs (not shown) we find a clear decreasing trend. This behavior is also found on the WAM spectra (not shown). In opposite, when analyzed at the global scale, the relationship between s f and wave age (defined as Cp/U where Cp is the phase speed at the peak of the wave spectrum) is less clear.

Fig. 2b illustrates the histogram of SWIM-MFWAM differences for the s f parameter as a function of significant wave height. The overall agreement is very good with however a small negative bias at all Hs (-0.01 Hz) and rms error of 0.02 Hz. However, the scatter is significant for Hs less than about 1.5m (which correspond in the mean to s f > 0.15 Hz). In these situations of low sea states, SWIM height spectra are perturbed by parasitic peaks at low wave numbers (see [START_REF] Hauser | New observations from the SWIM radar on-board CFOSAT: Instrument validation and ocean wave measurement assessmen[END_REF][START_REF] Tourain | Evolutions and improvements in CFOSAT SWIM Products[END_REF]). Overall, MFWAM show largest values compared with SWIM. As suggested by [START_REF] Rogers | Frequency width in predictions of windsea spectra and the role of the nonlinear solver[END_REF], this overestimation by the model may be due to the approximations used in the representation of the non-linear save-wave interactions.

Figure 3 (a) shows the map of Qp parameter. The highest values of Qp are found in regions of extreme sea-state conditions mentioned in section 2. Compared to the case of s f , we find that Qp values are more clearly related to wave age with a clear negative trend for wave ages between 1 and 2 (not shown). Fig. (3b) shows the comparison between SWIM and MFWAM Qp values. It indicates that Qp is significantly larger for SWIM than for MFWAM, for all Hs > 1m. This indicates sharpest shapes of the omni-directional wave spectra. For Hs < 1m, the results from SWIM are much more scattered because of the difficulty to eliminate spurious peaks in the wave height omni-directional spectra (see [START_REF] Tourain | Evolutions and improvements in CFOSAT SWIM Products[END_REF]).

Figure (4a) shows the map of s f , where s f is estimated here at the frequency of the dominant waves (estimated for SWIM from the peak of the 2D wave slope spectra) . This map shows that the relationship between this parameter and sea-state conditions is not as clear as for s f or Qp. The most evident relationship is with the peak frequency or peak wavelength l p as shown in Fig. 4b for SWIM and 4c for MFWAM. Note that conclude from these figures that in both SWIM and MFWAM cases, the shortest wavelengths are associated to broader angular distributions. However, for the shortests wavelengths (70-150m) the most probable values of s f are between 30° and 50° from SWIM , significantly larger than the MFWAM values (around 20°). For longest waves (around 200m), SWIM and MFWAM seem in better agreemnt with s f values around 20°. Note that a 45° (resp. 20°) value for s f corresponds to s ~ 2 (resp. s ~16) in a cos 2s angular distribution. Figure (5a) shows the map of the index BFI. It clearly shows that the highest values of BFI (i.e. > 0.4) are associated to the extreme sea-states in the Southern Ocean storms, and also close to the US coasts (related to the Humberto hurricanes) and to the Greenland coasts (related during this period to the high winds along-shore event). Fig. 5b shows the scatter plot of BFI for SWIM versus MFWAM. It shows that in the mean, BFI from SWIM is larger than from MFWAM. We could check that this difference is amplified in regions of high sea-state like in the Southern Ocean. When analyzing BFI_2D (not shown) we find the same kind of geographical distribution and a better agreement between SWIM and MFWAM. But this agreement is due a compensating effect of biases in Q p or s q and BFI (see [START_REF] Hauser | New observations from the SWIM radar on-board CFOSAT: Instrument validation and ocean wave measurement assessmen[END_REF] and results here-above.

SUMMARY AND CONCLUSION

Here is presented an analysis of spectral shape parameters obtained from the observations of the SWIM instrument on-board CFOSAT. To our knowledge it is the first time that global statistics and maps of spectral shape parameters and BFI indexes are provided from observations. The order of magnitude of these parameters are consistent with what we know from previous studies and from models. Apart from cases with Hs < 1m, where SWIM data may be hampered by abnormal spectra at low significant wave height (Hs > 1), we can conclude that systematic biases between the MFWAM model and observations are found for the frequency width s f (smaller from SWIM), the peakedness parameter Qp (sharpest spectra for SWIM), and the angular spread of the dominant waves s f (broader angular distribution for SWIM for the shortest dominant waves (70-150m). These biases induce biases in the BFI index. Because of compensating effects, BFI_2D from SWIM and MFWAM are however in a good agreement.

Work is presently under progress to quality in more details these differences and try understand what are their origin.

Fig. 1 :

 1 Fig.1 : Maps of (a) SWIM significant wave height (b) ECMWF wind speed plotted for the period 9-21 September 2019 at the locations of the SWIM measurements

Fig. 2 :

 2 Fig.2 : (a) Map the parameter of spectral width sf deduced from the SWIM spectra.(b) histogram of the differences of sf valuesbetween SWIm and MFWAM as a function of the SWIM significant wave height.The data set is from 9 to 21 Sepetmber 2019.

Fig. 3 Fig. 4 :

 34 Fig.3 Same as in Fig.2 but for the parameter Qp. in Fig.4c (MFWAM), there are two populations of points, not clearly apparent in Fig.4b (SWIM). This is due to a non continuous distribution of l p for MFWWAM with two maximum (around 120 m and 280 m). Nevertheless we can (a)

Fig. 5 :

 5 Fig.5 : (a) Map of BFI from SWIM (b) Histogram of BFI (SWIM versus MFWAM)