domain: spi phys

text:
W Ghedhaïfi
email: weeded.ghedhaifi@onera.fr

L Desprez

E Montreuil

E Terrenoire

T Henry-Lheureux

F Garnier

3D Simulation of aircraft emissions dispersion in the CAEPport area by tracking aircraft as mobile sources

Keywords: CAEPport, CFD, emission dispersion

Meeting the air quality objectives is becoming a challenging task for the development of the air transport sector since it has to cope with the environmental constraints. In fact, in and around airports, aircraft main engines and APU contribute to pollutants emission such as NO x and Particle Matter (non-volatile and volatile, Ultra Fine Particles). To evaluate their impact, the proposed study aims at developing an innovative modelling methodology that better takes into account aircraft emissions evolution at micro-scales, both spatially and temporally in order to increase the accuracy of airport air pollution monitoring and prediction. In this study, the CAEPport airport model has been used as defined in the modelling capabilities and intercomparison ICAO study. This airport is typical of medium size airports infrastructure. In order to achieve CFD simulations, a 3D geometry of the airport is built using CATIA software and the mesh is carried out using ICEM software. In the present approach, individual aircraft movements and emissions are tracked with a time resolution down to a second. Meteorological conditions (wind velocity, temperature, relative humidity, etc.) and background species concentrations are also taken into account as they influence dispersion and species chemical evolution respectively. The modelled domain extends up to 8 km around the airport and as the buildings geometry and location influence strongly the dispersion of the pollutants, the spatial resolution can be as fine as 1 m.

INTRODUCTION

Airport air quality is becoming an important issue that has to be considered carefully as air traffic keeps growing. The expected growth of the air transport industry may create significant environmental and societal challenges over the coming decades. By 2050, the number of commercial flights landing and taking off in Europe is forecast to be 18.6-26.1 million per annum which is 2-2.7 times the number of 2012 [1] [2]. In and around airports, emissions from aircraft (engines and APU), from the airport infrastructures and also from roads leading to the airport have an impact on chemical species concentrations, contributing to public health concerns within neighboring communities. The impact both on human health and on the environment makes the surveillance and the search for mitigation solutions essential.

Modeling airport air quality is particularly complex since it involves multi-scale phenomena such as micro-scale dispersion, microphysics, chemistry, etc. Numerical simulations have often been used to investigate these physical processes and thus providing detailed information in terms of temporal and spatial distribution of species concentrations (e.g. [START_REF] Gousseau | Simulation of near-field pollutant dispersion on a high-resolution gris[END_REF], [START_REF] Tominaga | CFD simulation of near-field pollutant dispersion in the urban environment: a review of current modeling techniques[END_REF] and [START_REF] Tominage | Ten questions concerning modeling of nearfeild pollutant dispersion in the built environment[END_REF]). Nevertheless, these models were mainly focused to the pollutant dispersion in the urban environment and tri-dimensional CFD of aircraft emission dispersion have been little considered over the past few years. On account of these facts, a new approach to investigate 3D emissions dispersion in the CAPort area is implemented. Indeed, an artificial but realistic airport has been set up by ICAO in order to demonstrate the abilities of modeling to handle the various emission groups at an airport in emission and dispersion calculations [START_REF] Refloch | Cedre Software[END_REF]. In this study, simulations are based on using the ONERA CFD code CEDRE [START_REF] Refloch | Cedre Software[END_REF] which is a MPI parallel, three-dimensional, multi-species, multi-physics compressible Navier-Stokes solver.

In the original methodology developed here, each aircraft engine is considered as an individual source that moves along its own LTO trajectory. Missions' properties depend on the engine type, real-time power settings associated with specific exhaust temperature, jet flow velocity and chemical composition. Atmospheric conditions are taken into account through ambient wind speed, temperature, relative humidity and background chemical species concentrations. The air traffic is described using the CAEPport database that provides aircraft position and current status in the LTO cycle (landing, take off, taxiing, etc.). Numerical simulations give instantaneous and mean distribution of chemical species within the CAEPport platform. In particular, it allows investigations of chemical species concentrations where buildings can influence their spatial distribution.

This comprehensive knowledge and understanding will ultimately guide the most relevant solutions to control and reduce the environmental impact of airports emissions

The paper is organized as follows: Section 2.0 presents the CFD model including equations and gas phase chemistry capabilities. Section 3.0 describes the numerical simulation set-up including the airport configuration, the computational domain, the grid mesh, the boundary and initial conditions and the aircraft traffic used in the present study. Finally, results are presented in section 4.0

CFD MODEL

Fluid flow

The CEDRE numerical code used for the present study is a compressible Navier-Stokes solver with multi-species [START_REF] Refloch | Cedre Software[END_REF]. The differential equations related to the RANS 3D compressible Navier-Stokes equations in the code CEDRE read in:

𝜕 𝜕𝑡 (𝜌𝑦 ̃𝑘) + 𝜕 𝜕𝑥 𝑗 (𝜌𝑢 ̃𝑗𝑦 ̃𝑘) = 𝜕 𝜕𝑥 𝑗 (𝜌𝐷 𝑘 𝜕𝑦 ̃𝑘 𝜕𝑥 𝑗 -𝜌𝑢 𝑗 " 𝑦 𝑘 " ̃) + 𝜔̇𝑘 ( 1 )
𝜕 𝜕𝑡 (𝜌𝑢 ̃𝑖) + 𝜕 𝜕𝑥 𝑗 (𝜌𝑢 ̃𝑗𝑢 ̃𝑖) = - 𝜕𝑝 𝜕𝑥 𝑖 -𝜌𝑔𝛿 𝑖3 + 𝜕 𝜕𝑥 𝑗 (𝜇𝑆 ̃𝑖𝑗 𝑑 -𝜌𝑢 𝑖 " 𝑢 𝑗 " ̃) ( 2 )
For compressible flows, a density-weighted, time-average decomposition (also called Favre average) is used: variables are then defined as Φ ̃= 𝜌Φ 𝜌 ⁄ and Φ = Φ ̃+ Φ " .

The Reynolds tensor is given by a Boussinesq hypothesis and the two-equation k-w with SST correction [START_REF] Menter | Two-equation eddy-viscosity turbulence models for engineering applications[END_REF]. Numerical methods are based on a cell-centered finite-volume approach for general unstructured grids.

Gas phase chemistry

The mass of non-ideal combustion products is very low, but the consequences for atmospheric chemistry are significant. When interacting together and with ambient species during the mixing process, emitted materials undergo chemical transformations that determine their atmospheric impact by direct or indirect effects involving secondary products. Their concentration depends on various parameters such as the engine type, the fuel composition, the plume dilution and the ambient conditions.

The main gaseous emissions from aircraft engines and APU are carbon dioxide CO 2 and water vapor H 2 O (v) . Minor species are nitrogen oxides NO x , carbon oxide CO and hydrocarbons, which are regulated. Furthermore, Sulfur is found in aircraft fuel at different concentrations. Sulphur products are quite important because they act as aerosol precursors, which can promote homogenous nucleation and form volatile sulfate aerosols. A finite number of kinetic reactions with a finite number of species can be handled by CEDRE in order to provide reactive chemistry which may be essential for a better comprehension of the processes in the exhaust plume. Examples of complex chemistry including SO x , NO x and HO x are available in [START_REF] Khou | CFD simulation of contrail formation in the near field of a commercial aircraft: Effect of fuel sulfur content[END_REF] [START_REF] Montreuil | Numerical simulation of contrail formation on the common research model wing/body/engine configuration[END_REF], for contrail formation.

NUMERICAL SIMULATION SETUP

3.1

Airport configuration As already mentioned, the airport configuration used in this study has been setup by the Modelling and Databases Group of The International Civil Aviation Organization (ICAO) Committee on Aviation Environmental Protection (CAEP). It is called CAEPport and it is representative of medium size airports [START_REF] Group | Assembly of the CAEPport database[END_REF]. The model is used to evaluate new LAQ models capabilities, intercomparisons and benchmarking studies.

In this work, the platform area has been modelled in 3D (see Figure 1) according to the two-dimensional plan provided in the CAEPport database [START_REF] Group | Assembly of the CAEPport database[END_REF].

Figure 1: CAEPport airport 3D geometry Table 1 gives buildings height defined in the study where the fuel farm, the power plant and the terminal parking heights are provided in the CAEPport database [START_REF] Group | Assembly of the CAEPport database[END_REF]. Other heights have been chosen from real airports typical values.

Computational domain

The computational domain is detailed in Figure 2. It is a box which has 8,000 m length in the X and Y directions and 1,500 m in the Z direction. The Airport Reference Point (ARP) of the CAEPport airport is placed, by convention, in the middle of the runway, at the ground location X=10,000 and Y=10,000. The inlet and outlet surfaces are aligned with western side and eastern side of the airport. The two other surfaces are then aligned with the Northern and Southern sides. According to this configuration, a wind coming from west is then normal to the inlet surface, for example.

Grid mesh

The mesh is non-structured and made of tetrahedral elements. Figure 3 illustrates surface mesh of the outer box, the ground in and around the CAEPport area and several close-ups of three dimensional parts such as the fuel farms (a), buildings (b) and (c). The main characteristics of the mesh elements size is summarized in Table 3. The total number of cells is about 12.4 million.

3.4

Boundary and initial conditions Boundary conditions are detailed on Table 4 while initial conditions are based on the meteorological data and background composition, also used in the inlet of the calculation domain (the western side) and the outlet (eastern side). Symmetry or slip conditions have been set for the southern, northern and top sides of the simulation domain. These profiles correspond to a neutral atmosphere stability case.

Table 4 Boundary conditions

3.5

Aircraft traffic Aircraft traffic is taken from the CAEPport data base. This data base has a full year journal of movements. A specific day has been chosen: the October 8 th 2004. This day has the maximum number of movements of the year with 311 movements planned. Figure 6 shows the aircraft LTO trajectories where blue lines correspond to landing and taxi-in and red lines correspond to taxi-out and take-off.

Figure 6: Aircraft landing and taxi-in (blue lines) and take-off and taxi-out (red lines) trajectories Aircraft movements along these trajectories (speed, position [START_REF] Ghedhaïfi | Chemical impact of aviation in airports[END_REF]), as well as their respective plume properties (temperature, exhaust speed and composition) are updated every second of the corresponding LTO cycle phase.

RESULTS

Hereunder, results from 3D numerical simulation using CEDRE are presented. The objective is to solve the flow dynamics taking into account buildings and atmospheric conditions. The wind coming from the west side crosses the area of interest creating recirculation zones behind buildings and a specific flow dynamics in their wake. Figure 7 gives the velocity fields on a cut plane at 2 m above the ground. It shows the typical flow (wakes) generated by the existing buildings. After a first step of simulations dedicated to the flow stabilization, aircraft traffic, using mobile sources, is implemented into calculations. It includes aircraft emissions and movements in the CAEPport between 12:00 pm and 13:00 pm.

Simulations provide instantaneous fields of concentrations as shown in Figure 8 and Figure 9 for NO and NO 2 concentrations, respectively. The highest concentrations of NO appear in the apron area (see Figure 1) and at the runway threshold, just before aircrafts take-off when engines have the maximum thrust. Figure 8 (b), corresponding to 12:30 pm, illustrates an aircraft emission at the end of the runway but after being transported by the wind coming from the west.

ISABE 2019

Figure 8: Instantaneous NO concentration at three moments between 12:00 pm and 13:00 pm Figure 9 shows that the highest concentrations of NO 2 are observed on apron areas where aircrafts park after the taxi-in step and before the taxi-out step. This is related especially to the use of APU. The instantaneous fields are very useful to visualize aircraft traffic and for a better understanding of emissions differences between different regimes and operation zones. However, LAQ models usually give averaged fields for specified durations to estimate chronical effects. Thus Figure 10 and Figure 11 present hourly mean concentrations of NO and NO 2 respectively. They correspond to means between 12:00 pm and 13:00 pm (a), 13:00 pm and 14:00 pm (b) and 14:00 pm and 15:00 pm (c). Since there is a higher number of movements between 14:00 pm and 15:00 pm comparing to the two previous hours, NO emissions are higher too as shown in Figure 10 (c) whereas NO2 emissions are lower (see Figure 11

CONCLUSION

Three dimensional CFD simulations of emissions dispersion in airport areas is a promising way for a better analysis of their impact on air quality in and around airports. The main objective of the performed studies is first to improve the understanding and the modelling of the important phenomena involved in airport air quality. Then, they can be used to improve airport strategies to reduce their environmental impact. Several parameters have been included into the simulations presented in this paper such as atmospheric conditions, aircraft emissions along their own trajectories taking into account their engine types and regimes within the LTO cycle. The airport infrastructure is also considered with 3D modelling of buildings which play a key role in the flow dynamics near the ground. Indeed, dispersion is strongly dependent on the flow which is itself dependent on topography and meteorology.

As a perspective, future simulations should also include species reactivity and ground radiative properties according to their type (tar, vegetation, etc.). Parametric studies varying atmospheric conditions and distinguishing different emission sources (aircraft, APU but also other vehicles used at the airport and those borrowing roads around the airport) may be carried out. Moreover, the problematic of volatile particulate matter and ultra-fine particles (diameter less than 100 nm) is of great importance for the next coming years because of their greater toxicity.

Figure 2 :

 2 Figure 2: Computational domain The box exact coordinates are given in meter in Table2.

Figure 3 :

 3 Figure 3: Surface mesh of the computational domain including the CAEPport platform

  Boundary conditions 𝑥 = 7,500 𝑚 Inlet 𝑥 = 15,500 𝑚 Outlet 𝑦 = 4,971 𝑚 Symmetry 𝑦 = 12,971 𝑚 Symmetry 𝑧 = 0 No-slip 𝑧 = 1,500 𝑚 Slip Buildings (Passenger terminal, Terminal parking, Fuel Farms, etc.) No-slip As mentioned above, the numerical simulations performed in this study use the description of the meteorological conditions such as temperature (Figure 4 left) and wind speed (Figure 4 right) as well as the atmospheric background composition like NO (Figure 5 left) and NO 2 (Figure 5 right).

Figure 4 :Figure 5 :

 45 Figure 4: Ambient temperature (left) and wind velocity (right) vs altitude

Figure 7 :

 7 Figure 7: Velocity field at 2 m above the ground.

Figure 9 :

 9 Figure 9: Instantaneous NO 2 concentration at three moments between 12:00 pm and 13:00 pm

Figure 10 :Figure 11 :

 1011 Figure 10: Hourly mean concentration of NO, between 12:00 pm and 13:00 pm (a), 13:00 pm and 14:00 pm (b), 14 pm and 15 pm (c)

Table 1 : Buildings Height

 1

	Building name	Building number	Height (m)
	Fuel Farm	5	22
	Power Plant	6	15
	Passenger Terminal	9	20
	Terminal Parking	16	20
	Other buildings	3, 4, 7, 8, 10, 11, 12

Table 2 Computational domain sizes Domain size L

 2

x

[7,500;

15,500] L y [4,971; 12,971] L z [0,000; 1,500] ISABE 2019

Table 3 : Mesh elements size

 3

			Element
	Part name		maximum size
			(m)
	Runway		3
	Taxiway		3
	Aircraft Maintenance		2
	Catering		2
	Fuel Farm		2
	Power Plant		2
	Airport Maintenance Cargo Building	(see Figure 1)	2 2
	Passenger Terminal		2
	GA Terminal		2
	Fire Station and Emergency Power		2
	Fire training site		2
	Airside Service Roads		3
	Landside Access Roads		3
	Parking Facilities		5

ACKNOWLEDGMENTS

The authors would like to acknowledge the French Civil Aviation (DGAC) for their funding in the frame of the MOSIQAA project. They also acknowledge Xavier Vancassel for helpful advice.


Simon Bicaïs
email: simon.bicais@cea.fr

Jean-Baptiste Doré

Grégory Gougeon

Yoann Corre
email: ycorre@siradel.com

Optimized Single Carrier Transceiver for Future Sub-TeraHertz Applications

Keywords: Sub-TeraHertz communications, Ray-tracing, Phase noise, Digital modulation, Design optimization

The performance of sub-THz communications, contemplated for the next generation of wireless networks, are significantly degraded by oscillator phase noise. In this paper, we address the design of a single carrier transceiver resilient to phase noise. This problem is treated in two steps: First, we derive for phase noise channels the optimum symbol detection criterion. Second, we propose a phase noise robust modulation scheme with a comprehensive and efficient structure. System level simulations modeling the sub-THz propagation channel of a rich outdoor environment through ray tracing are also presented. Results show that optimizing the modulation and demodulation schemes is necessary to achieve high spectral efficiency in the presence of phase noise.

I. INTRODUCTION

With an important amount of unused spectrum, the sub-TeraHertz (sub-THz) frequencies between 90 and 300 GHz are contemplated to realize high-data rate wireless communications and hence to fulfill the requirements of the nextgeneration of wireless networks [START_REF] Rappaport | Wireless Communications and Applications Above 100 GHz: Opportunities and Challenges for 6G and Beyond[END_REF]. Several beyond 5G applications are considered for sub-THz systems [START_REF] Doré | Above-90GHz Spectrum and Single-Carrier Waveform as Enablers for Efficient Tbit/s Wireless Communications[END_REF]: high capacity backhaul, enhanced hot-spot kiosk and also short-range communications. Despite the evolution of semi-conductor technology, the design of new physical layer algorithms is required to achieve high data-rate sub-THz communications. Traditional coherent schemes do not consider the specific radio-frequency (RF) impairments related to the sub-THz bands, and therefore, cannot be directly used in these frequencies. In particular, sub-THz systems suffer from strong phase impairments due to the poor performance of high-frequency oscillators. We therefore investigate in this paper the optimization of the digital signal processing to mitigate the impact of phase noise (PN) on communication performance within the frame of the highcapacity backhaul.

Optimum receivers for common PN models are listed in [START_REF] Krishnan | Constellation optimization in the presence of strong phase noise[END_REF]. However, these detectors result in complex implementation. Furthermore, optimizing the constellation for PN channels is a widely investigated problem. Stat-of-the art researches have exploited numerical optimization algorithms to design the constellation [START_REF] Kayhan | Constellation design for channels affected by phase noise[END_REF] [START_REF] Krishnan | On the impact of phase noise in communication systems -performance analysis and algorithms[END_REF] or to define its parametric shape [START_REF] Ugolini | Spiral constellations for phase noise channels[END_REF] in order to minimize the symbol error probability or maximize the mutual information. Most of the proposed constellations are efficient but local and unstructured solutions leading to complex binary labelling and demodulation. Conversely, we pursue in this work a pragmatic approach supported by a theoretical framework.

The contributions of this paper are the following. First, we characterize the sub-THz propagation channels using ray-based deterministic numerical simulations. In addition, we outline the appropriate oscillator PN model for sub-THz systems. Second, the design of PN robust communications is addressed from both receiver and transmitter perspectives. The optimum symbol detection criterion and the corresponding probabilistic demapper is derived for PN channel upon the maximum likelihood (ML) decision rule. We also propose a PN robust modulation scheme defined upon an efficient and structured constellation, adaptable to any signal-to-noise ratio (SNR) and PN variance. Third, the results of systemlevel simulations are presented, considering a high-capacity backhaul scenario in a North-American city downtown. These simulations are based on ray-tracing channel predictions using accurate LiDAR point cloud and a realistic link budget. It is shown that conventional modulation schemes cannot achieve high data rate communications over sub-THz channels while the proposed dedicated signal processing enables to maintain high spectral efficiency.

The paper is organized as follows. Sec. II introduces the system model by detailing the sub-THz propagation channel and the oscillator PN. Sec. III is dedicated to the design of PN robust communications. In Sec. IV, system-level simulations are presented and discussed. Finally, Sec. V concludes the paper and outlines some potential perspectives to this work.

II. SYSTEM MODEL A. Propagation channel

Sparse propagation channel is a kind of norm in mmWave (millimeter-wave) bands, where the line-of-sight (LoS) directpath often is the most dominant component. Many propagation paths that would bring significant power at the sub-6GHz frequencies are either attenuated/blocked by obstacles or suffer from the weakness of diffractions. Besides, the specular reflections that occur on flat surfaces large compared to the wavelength and do not cross any obstacle, do still produce multiple propagation paths with significant delays and angles diversity, and possibly cause non-LoS reception. Those characteristics are true in the sub-THz spectrum as well, however slightly accentuated.

Gas absorption and rain attenuation must be two critical factors for long-range sub-THz links, but their cumulative impact remains below 1 dB at range 200 m, except for the particular case of strong rainfall rate (greater than 50 mm/h) together with peak water-absorption at 180 GHz.

The free-space propagation losses increase with the square of the frequency, therefore in many foreseen applications, the propagation channel degradation will have to be compensated The propagation channel properties affect both the link-level performance at a given SNR and the service coverage. Thus a fine characterization is required for realistic evaluation of new sub-THz technologies. Today the channel measurements are complex and costly. However only few channel sounding campaigns have been published yet, we can mention those recently realized inside a commercial hall [START_REF] Nguyen | Comparing Radio Propagation Channels Between 28 and 140 GHz Bands in a Shopping Mall[END_REF], various indoor scenarios [START_REF] Pometcu | Characterization of Sub-THz and mmWave Propagation Channel for Indoor Scenarios[END_REF] [9], a data center [START_REF] Eckhardt | Measurements in a Real Data Center at 300 GHz and Recent Results[END_REF] or for outdoor-indoor penetration [START_REF] Xing | Propagation Measurement System and Approach at 140 GHzMoving to 6G and Above 100 GHz[END_REF]. Numerical simulation is a very convenient solution to complement this characterization, and produce on-demand channel samples. The Volcano ray-based model has been extended up to the sub-THz frequencies [START_REF] Gougeon | Ray-based Deterministic Channel Modelling for sub-THz Band[END_REF]. It is employed in the present study to predict the propagation of an in-street backhaul scenario; then the performance of the proposed modulation scheme has been assessed considering this data combined with highly-directive antennas and different PN conditions. Volcano is taking benefit of a light detection and ranging (LiDAR) point cloud collected in the streets of San José, California, USA. This provides a very accurate 3D representation of the environment, thus allows for a very realistic prediction of the blockages and losses due to trees and street furniture as depicted in Fig. 1.

B. Phase noise

In communication systems, oscillator PN results from the amplification and integration by the phase-locked loop (PLL) of noise sources within the circuitry [START_REF] Demir | Computing Timing Jitter From Phase Noise Spectra for Oscillators and Phase-Locked Loops With White and 1/f Noise[END_REF]. Subsequently, PN defines a correlated stochastic process. Under the assumption that the oscillator is only subject to thermal noise, the oscillator PN φ is described by the superposition of a correlated Wiener (Gaussian random-walk) process and an uncorrelated Gaussian one [START_REF] Demir | Computing Timing Jitter From Phase Noise Spectra for Oscillators and Phase-Locked Loops With White and 1/f Noise[END_REF] respectively expressing the integration and amplification of white noise by the PLL. The spectrum of oscillator PN is in this case described by a colored K 2 /f 2 characteristic (Wiener PN) and a white noise floor K 0 (Gaussian PN). Nevertheless, for high-rate communications, it has been shown in [START_REF] Khanzadi | Calculation of the performance of communication systems from measured oscillator phase noise[END_REF] that the influence on communication performance of Wiener PN is negligible compared to the Gaussian one. In other words, the oscillator noise floor amounts to the main contribution of the observed PN for wide-bandwidth systems. These results have been confirmed in [START_REF] Bicaïs | Phase Noise Model Selection for Sub-THz Communications[END_REF] and further characterized through the comparison of a correlated PN model to an uncorrelated one. The main result of this study is that the PN is appropriately modeled by an uncorrelated process if

N • f 2 0 • T 2 ≤ ln(2) 2π 2 , ( 1
)
where N is the frame length, f 0 the corner frequency of the oscillator and T is the symbol duration. Let us derive the numerical application for the considered scenario: 1/T = 1 GHz, N = 20 symbols and we may set f 0 = 1 MHz with regard to the state-of-the-art sub-THz oscillator in [START_REF] Li | A 200-GHz Sub-Harmonic Injection-Locked Oscillator with 0-dBm Output Power and 3.5DCto-RF-Efficiency[END_REF]. It follows that Eq. ( 1) is satisfied for these system parameters. For these reasons, it is relevant to describe the impact of PN on received symbols by a zero-mean Gaussian distribution with variance σ 2 p . Considering a complex additive white Gaussian noise (AWGN) channel impacted by PN, the received symbol r is hence expressed by

r = s • e jφ + n, (2) φ ∼ N (0, σ 2 p ). ( 3
)
where s is the modulated symbol from constellation C with modulation order M and average energy E s , φ denotes the PN and n is an additive white Gaussian noise (AWGN) modelling thermal noise. Regarding numerical simulations, we further consider three PN levels: no PN σ 2 p = 0 rad 2 , medium PN σ 2 p = 10 -2 rad 2 and strong σ 2 p = 10 -1 rad 2 . The medium and strong PN levels respectively correspond to a noise floor spectral density K 0 of -110 dB and -100 dB for a system bandwidth of 1 GHz. Numerical values are obtained using

σ 2 p = K 0 • B.

III. PHASE NOISE ROBUST COMMUNICATIONS A. Receiver algorithm design

We investigate in this paragraph the design of the optimum receiver for the considered PN channel. For independent and equiprobable symbols, the symbol error probability (SEP) is minimized by the ML detection criterion [START_REF] Proakis | Digital Communications 5th Edition, ser. McGraw-Hill series in electrical and computer engineering : communications and signal processing[END_REF]. The ML decision rule is expressed from the channel likelihood function p(r|s) by ŝ = arg max s∈C p(r|s).

It follows from the system model described in Eq. ( 2) and from a high-SNR assumption that the channel likelihood function may be efficiently approximated as a bivariate Gaussian -for a detailed derivation see [START_REF] Bicaïs | On the Optimum Demodulation in the Presence of Gaussian Phase Noise[END_REF]. Denoting the amplitude and phase of symbols respectively with subscripts ρ and θ, the received symbols are distributed as follows:

r ρ ∼ N (s ρ , σ 2 n ) r θ ∼ N (s θ , σ 2 p + σ 2 n /E s ) (5)
Substituting the latter equation into the ML rule, we obtain

ŝ = arg min s∈C d 2 γ (r, s), (6)
defined upon the polar metric

d 2 γ (r, s) = (r ρ -s ρ ) 2 + (r θ -s θ ) 2 γ 2 , ( 7
)
where γ 2 = σ 2 p /σ 2 n + 1/E s . This ML decision rule, hereafter referred to as the polar receiver, is expressed upon a welldefined metric d γ and demonstrates a simpler implementation than state-of-the art solutions [START_REF] Krishnan | On the impact of phase noise in communication systems -performance analysis and algorithms[END_REF]. It is worth mentioning that in contrast to the Euclidean detector -optimal for the AWGN channel, this receiver expresses a joint phase-amplitude detection criterion which adapts its decisions to the PN variance and to the SNR. Nevertheless, a probabilistic demapper is required when it comes to integrating a forward error correction (FEC) scheme with a soft-input decoding algorithm to improve communication performance. Accordingly, the evaluation of the bit log-likelihood ratio is straightforward from the definition of the polar metric d γ and is outlined in [START_REF] Bicaïs | On the Optimum Demodulation in the Presence of Gaussian Phase Noise[END_REF].

B. Modulation scheme optimization

In this paragraph, we propose an optimized modulation scheme achieving robustness over PN channels. Constellation design for PN channels is a well-studied problem. State-of-the art solutions use numerical optimization to minimize the SEP [START_REF] Krishnan | Constellation optimization in the presence of strong phase noise[END_REF] or to maximize the mutual information on PN channels. The obtained constellations exhibit significant performance gains in comparison to conventional ones. Nevertheless, the optimized modulations are unstructured and defined for a unique SNR and PN variance, and hence are local solutions leading to complex implementation. Conversely, we introduce in this paper a structured and robust constellation minimizing the SEP with a comprehensive approach for any SNR and PN variance. To do so, it is first required to state that the SEP is expressed upon the minimum polar distance between constellation points i.e. min d γ (s, s ). Subsequently, and similarly to the AWGN channel, designing the constellation that minimizes the SEP is equivalent to characterizing the constellation that maximizes the minimum distance. Under the constraints of fixed modulation order M and E s average energy, this problem may be interpreted as a sphere packing problem in the polar domain, i.e. the phase-amplitude coordinates space. It follows easily that the near-optimal constellation relies on an hexagonal lattice in the polar domain -similarly to the solution for the AWGN channel in the complex plane. However, exploiting a rectangular lattice in the polar domain rather than an hexagonal one leads to a greatly simplified implementation for a negligible performance loss. As a result, we propose the polar quadrature amplitude modulation (P-QAM). Its constellation, depicted in Fig. 2, is defined by two parameters M and Γ respectively the modulation order and the modulation shape characterized by the number of circles on which modulation points are distributed. The modulation scheme can be adapted to any SNR and PN variance by setting appropriately parameters M and Γ to achieve performance gain. By way of illustration, the constellation in Fig. 2a is suited for medium SNR -medium PN channels whereas the one in Fig. 2b is more efficient for a high SNR -strong PN scenario.

IV. SYSTEM-LEVEL SIMULATIONS A. Assessment of physical layer performance

The performance of the physical layer were first assessed to determine the best set of parameters: coding rate, modulation order M and modulation shape Γ given the SNR, the PN level and the targeted packet error rate of 10 -2 . Concerning the physical layer, we assume a single carrier modulation perfectly synchronized. The channel propagation gain and phase shift are considered perfectly estimated and compensated. A FEC scheme based on the 5GNR LDPC with an input packet size of no PN strong PN QAM -Euclidean rx QAM -polar rx P-QAM -polar rx Fig. 3: Highest achievable spectral efficiency given the SNR, the PN level and the modulation/demodulation strategy 1500 bytes is implemented with a coding rate ranging from 0.3 to 0.9. Fig. 3 present the highest achievable spectral efficiency for two PN levels: no PN and strong PN, and three modulation/demodulation schemes: quadrature amplitude modulation (QAM) with Euclidean receiver, QAM with polar receiver and P-QAM with polar receiver. These results clearly highlight the benefits of using optimized modulation and demodulation schemes especially to target high spectral efficiencies in the presence of PN. It should be mentioned that in low SNR regime and without PN, the polar receiver exhibits a spectral efficiency loss which can be explained by the derivation of the polar receiver from a high-SNR and strong PN assumption.

M = 16 Γ = 4

B. City center scenario

The performance of the proposed PN robust schemes, the polar receiver and the P-QAM, have been further assessed through system-level simulations. These numerical evaluations assume a city center environment (from the San José, USA, I. The propagation paths and losses are predicted from the ray-tracing tool. The throughput of each calculated link is obtained from the estimated SNR which is mapped to the spectral efficiency of the considered modulation scheme using the previous performance assessment in Sec. IV-A. It should be noticed that the throughput is estimated per channel of 1 GHz bandwidth. Thereupon, a channel bonding scheme could increase the aggregated throughput and allow to benefit from the available free spectrum offered in the sub-THz bands. The choice of a channelization of 1 GHz is motivated by the current technology of analog-to-digital converters [START_REF] Murmann | ADC Performance Survey 1997-2019[END_REF]. The heat maps in Fig. 4a illustrates how the lamppost-tolamppost link performs depending on the distance, the propagation condition, the PN level and the selected modulation scheme. The illustrated environment may be characterized as a square in the middle of a dense urban center with medium tree density. The peak throughput per channel is computed between two aligned sub-THz devices; the first one at the center of the figure; the second one at any pixel of the map. Note that the real lamppost locations, where this second device could precisely be positioned, are shown by black dots. The connectivity is strongly affected by building and foliage obstructions, while line-of-sight propagation and strong clear reflections leads to the best performance. These throughput heat maps demonstrate that optimizing the modulation and demodulation schemes for PN channels results in significant performance gains for future sub-THz systems.

Finally, Fig. 4b illustrates how the ray-based channel simulation and the link-level performance model could be together exploited to optimize the deployment of a sub-THz mesh network, as different device locations and heights can be tested very easily. In the shown example, the trees have a significant impact; therefore a change in the antenna height can strongly modify the propagation conditions and thus, the connectivity range.

V. CONCLUSION This paper proposes optimized modulation and demodulation schemes that significantly improve the performance, achievable spectral efficiency, of communication systems impaired by oscillator PN. This offers for future sub-THz systems a valuable low-complexity solution to reduce the severe performance degradation caused by PN. The performance of the proposed schemes have been characterized through systemlevel simulations. The numerical simulations modelling a realistic sub-THz mesh deployment scenario in the streets of a North-American city are based on a deterministic prediction of the propagation channel with ray-tracing tools. Coupling raybased channel simulations with link-level performance models will be further exploited to optimize deployments and propose relevant sub-THz network topologies.

ACKNOWLEDGMENT

The research leading to these results received funding from the French National Research Agency (ANR-17-CE25-0013) within the frame of the project BRAVE.

Fig. 1 :

 1 Fig. 1: Propagation paths with ray-tracing and LiDAR data by high-gain antennas, which comes with high-directivity and antenna alignment constraints.The propagation channel properties affect both the link-level performance at a given SNR and the service coverage. Thus a fine characterization is required for realistic evaluation of new sub-THz technologies. Today the channel measurements are complex and costly. However only few channel sounding campaigns have been published yet, we can mention those recently realized inside a commercial hall[START_REF] Nguyen | Comparing Radio Propagation Channels Between 28 and 140 GHz Bands in a Shopping Mall[END_REF], various indoor scenarios[START_REF] Pometcu | Characterization of Sub-THz and mmWave Propagation Channel for Indoor Scenarios[END_REF] [9], a data center[START_REF] Eckhardt | Measurements in a Real Data Center at 300 GHz and Recent Results[END_REF] or for outdoor-indoor penetration[START_REF] Xing | Propagation Measurement System and Approach at 140 GHzMoving to 6G and Above 100 GHz[END_REF]. Numerical simulation is a very convenient solution to complement this characterization, and produce on-demand channel samples. The Volcano ray-based model has been extended up to the sub-THz frequencies[START_REF] Gougeon | Ray-based Deterministic Channel Modelling for sub-THz Band[END_REF]. It is employed in the present study to predict the propagation of an in-street backhaul scenario; then the performance of the proposed modulation scheme has been assessed considering this data combined with highly-directive antennas and different PN conditions. Volcano is taking benefit of a light detection and ranging (LiDAR) point cloud collected in the streets of San José, California, USA. This provides a very accurate 3D representation of the environment, thus allows for a very realistic prediction of the blockages and losses due to trees and street furniture as depicted in Fig.1.

Fig. 2 :

 2 Fig. 2: Illustration of the proposed modulation: P-QAM

Fig. 4 :

 4 Fig.4: Throughput heat maps for a city center 3D model) while targeting a high capacity mesh backhaul application. The system performance is characterized for an outdoor mesh backhaul situation, which could be exploited to feed an ultra-broadband mobile access network or fixed wireless access (FWA) network. The sub-THz devices are supposed to be installed on lampposts, located along the streets at 8 meters above the ground, in order to transport the data streams from a fiber PoP (Point of Presence) to dense local high-speed access points that either provide mobile or fixed wireless access typically at a lower frequency. The antennas of the sub-THz devices are considered with 6 • beamwidth, 25 dBi maximum gain. The antenna beam is supposed to be perfectly aligned on the dominant propagation path, which is either the direct LoS path, a reflected path, or an attenuated path. Other transmission parameters are given in TableI. The propagation paths and losses are predicted from the ray-tracing tool. The throughput of each calculated link is obtained from the estimated SNR which is mapped to the spectral efficiency of the considered modulation scheme using the previous performance assessment in Sec. IV-A. It should be noticed that the throughput is estimated per channel of 1 GHz bandwidth. Thereupon, a channel bonding scheme could increase the aggregated throughput and allow to benefit from the available free spectrum offered in the sub-THz bands. The choice of a channelization of 1 GHz is motivated by the current technology of analog-to-digital converters[START_REF] Murmann | ADC Performance Survey 1997-2019[END_REF].The heat maps in Fig.4aillustrates how the lamppost-tolamppost link performs depending on the distance, the propagation condition, the PN level and the selected modulation scheme. The illustrated environment may be characterized as a square in the middle of a dense urban center with medium tree density. The peak throughput per channel is computed between two aligned sub-THz devices; the first one at the center of the figure; the second one at any pixel of the map. Note that the real lamppost locations, where this second

TABLE I :

 I Simulation parameters

	Parameters	Notation	Values
	Carrier frequency	fc	150 GHz
	Channel bandwidth	B	1 GHz
	Allocated bandwidth	Ba	0.8 GHz
	Thermal noise	N 0	-174 dBm/Hz
	Noise figure	N f	10 dB
	Transmit power	P Tx	30 dBm
	Tx/Rx antenna gain	(g Tx , g Rx )	(25, 25) dBi
	Implementation loss	L	2 dB
	Control plane overhead	µ	20 p.c


text:
Wilfrid Quenum
email: wilfrid.quenum@onera.fr

Charles Antoine L'hour

Wireless systems assessment in confined metallic environment

The knowledge of the propagation channel is a key feature for communication systems but it can be tricky in multipath cases and requires a perfect characterisation to adapt the transmission through the channel. Imperfection sometimes leads to oversizing the physical layer against interference which makes the system energy and time consuming. We propose an experimental laboratory demonstrator providing various random channels useful to estimate signal integrity and potential performance of wireless link independently of SNR consideration.

INTRODUCTION

The attractiveness of the flexibility and modularity of standard wireless systems is well established. Extending this concept to the real-time questions of aeronautics needs a higher degree of requirement. In this context the accurate characterization of the channel and the environment is a significant point that we try to simplify by lab demonstrator approach on the well-known model of reverberating chambers (RCs) [1]. This under control test equipment allows us to design in advance wireless systems in difficult multipath transmission cases such as in an aircraft.

II. METHODOLOGY

The frequency band framework is 4.2-4.4 GHz specially defined by the WAIC consortium for wireless avionic application. The experimental setup (Figure 1) consists in characterizing the propagation channel of the three-cavitiesenvironment, with respect to the stirrer angular position, absorbers and walls interfaces between the cavities. The extensive exploitation of 4-port network analyser transfer functions measurements in several cavities configurations provides, after Inverse Fourier transformation, the spatial mapping of the RMS delay spread (T RMS ) and consequently coherence bandwidth (B C ) [2].

RESULTS AND DISCUSSION

This experimental approach shows that based, on the established T RMS mapping (or B C ) in the three-cavities and from the transmitted signal symbol time knowledge, it is possible to efficiently estimate the potential errors of transmission from a random channel emulated by the stirrer position (Figure 2). All configurations with a B C under the signal band limit (red curve) have a potential chance of transmission errors (Inter Symbol Interference). Figure 3 shows both the Q factor and B C behaviour with respect to a gradual decrease of cavities loading (bottom axis). According to the loading setup, the B C of the propagation channel (green curve) can be lower or higher than the IEEE 802.11 standard requirement (red dotted line). Therefore, only loading configurations giving B C above limit should be considered acceptable for the implementation of an IEEE 802.11 standard communication link.

Figure 1 :

 1 Figure 1: Multi-cavity Lab demonstrator synoptic III.RESULTS AND DISCUSSION

Figure 2 :

 2 Figure 2 : B C and selective area in cavity

Figure 3 :

 3 Figure 3 : B C & Q factor versus cavity load setup This result demonstrates the flexibility of RCs lab demonstrator to evaluate wireless communication and also propose rational perspective to optimize the physical layer. The GNU Radio soft tool and associated Universal Software Radio Peripheral appears as interesting tools to control and validate the integrity and robustness of the transmitted signal with the required BER. REFERENCE [1] W.Quenum, N. Jeannin I. Junqua "Channel propagation emulation in MSRCs" 2017 IEEE EMCSI [2] C. L. Holloway, D. A. Hill, JM. Ladbury, P. F. Wilson, G. Koepke, , and J. Coder, "On the use of reverberation chambers to simulate a rician radio environment for the testing of wireless devices," IEEE transactions antennas and propagation, 2006