Ana Flávia

Reis

Yahia Medjahdi

Glauber Brante

Bruno Sens Chang

Faouzi Bader

Deep Learning Based Receivers for IEEE 802.11p Standard with High Power Amplifiers Distortions

Keywords: IEEE 802.11p standard, OFDM, HPA distortions, Channel estimation, Deep learning

In recent years, vehicular communication has attracted significant research attention for its potential as a fifth generation (5G) application. The IEEE 802.11p standard enables the wireless technology that defines vehicular communication and, due to the time-varying characteristic, one of its critical challenges is to ensure communication reliability. Moreover, this standard is based on orthogonal frequency division multiplexing (OFDM) transmission scheme, which may suffer from nonlinear distortions induced by high power amplifiers (HPA) at the transmitter, degrading the channel estimation and detection performance of the receivers. In this work, the application of deep learning (DL) based channel estimation schemes to the IEEE 802.11p standard in presence of HPA distortions is presented. Simulation results show that the deep neural network (DNN) based estimation schemes outperform conventional data-pilot aided (DPA) and spectral temporal averaging (STA) estimators in terms of bit error rate and normalized mean squared error, evidencing their superiority in providing reliable estimation in mobility scenarios in presence of HPA nonlinear distortions. Furthermore, the hybrid solution, employing a joint DNNbased post-processing and conventional estimation, achieves less computational complexity than the DL-based proposal on top of the initial DPA estimation.

I. INTRODUCTION

Vehicular communication systems are important to enable some of the key 5G applications, such as autonomous driving, route planning optimization and real-time traffic safety information. The IEEE 802.11p [START_REF]IEEE guide for wireless access in vehicular environments (WAVE)architecture[END_REF] standard defines the physical layer specifications of these communication scenarios. However, by considering OFDM transmission and using only four pilot subcarriers to estimate the channel, combined to a high mobile and complex communication environment, this standard introduces several challenges to achieve accurate estimation and, therefore, ensure communication reliability.

Several methods considered to perform channel estimation in IEEE 802.11p networks are based on the DPA estimation, that employs the demapped data symbols in order to improve the limited number of data pilots, providing a low computational complexity solution. By averaging the channels estimations in both time and frequency domains, the STA introduced by [START_REF] Fernandez | Performance of the 802.11p physical layer in vehicle-to-vehicle environments[END_REF] improves the DPA initial estimation in low SNR region, where the impact of noise and interference are high and the averaging steps are capable to alleviate the error. However, it suffers from relevant performance decrease compared to the DPA in high SNRs, where this noise impact becomes neglected, but there is a large impact from the demapping error.

Recently, DNN-based schemes have been successfully employed to several wireless communication problems. In the context of channel estimation to vehicular communication scenarios, DNN techniques improve the accuracy from conventional solutions by learning the channel frequency correlation and correcting the error from previous estimators. The AE-DNN proposed by [START_REF] Han | A deep learning based channel estimation scheme for IEEE 802.11p systems[END_REF] improves the DPA method by implementing an offline trained DNN to reduce the error propagation, while correcting the errors between the initial DPA estimation and the ideal channel. However, besides these improvements, this proposal presents considerable complexity. The authors in [START_REF] Gizzini | Deep learning based channel estimation schemes for IEEE 802.11p standard[END_REF] show that it is possible to reduce the complexity of the DNN-based channel estimation schemes by applying the offline trained DNN on top of the classical STA estimator, in order to achieve fine channel estimation. The goal of the DNN in [START_REF] Gizzini | Deep learning based channel estimation schemes for IEEE 802.11p standard[END_REF] is to reconstruct the estimation from the conventional method as close as possible to the ideal channel. This nonlinear processing allows the estimator to capture more features of the channel, providing less computational complexity and performance improvements.

Furthermore, even though OFDM improves capacity and spectral efficiency, it introduces significant power consumption due to the high peak-to-average power ratio (PAPR) [START_REF] Sandoval | Hybrid peak-to-average power ratio reduction techniques: Review and performance comparison[END_REF]. This high PAPR leads to nonlinear distortions in the outputs of the high power amplifiers (HPA) required at the transmitter, affecting the channel estimation at the receivers and considerably degrading the system performance. Several works in the literature show the impact of a high PAPR in multicarrier modulation techniques. For instance, the bit error rate (BER) performance effects due to the presence of memoryless HPA in OFDM are evaluated in [START_REF] Bouhadda | Theoretical analysis of BER performance of nonlinearly amplified FBMC/OQAM and OFDM signals[END_REF]. In addition, different multicarrier waveforms are further discussed in [START_REF] Shaiek | Analytical analysis of SER for beyond 5G post-OFDM waveforms in presence of high power amplifiers[END_REF], where the authors presented a theoretical characterization of nonlinear distortions caused by HPAs in terms of symbols error rate, as well as the analytical expressions to model communications systems subjected to these distortions.

At the transmitter side, digital linearization is one of the most employed techniques to mitigate the high PAPR in mul- Notations: We use capital letters and lowercase letters in boldface to denote matrices and vectors, respectively. Notation exp(•) denotes an exponential function.

The remainder of this paper is organized as follows. The IEEE 802.11p communication scenario is presented in Section II. The main features of the considered HPA model are provided in Section III. The conventional and DNN-based methods considered to provide channel estimation are detailed in Section IV, while results and discussions are presented in Section V. Finally, Section VI concludes the paper.

II. SYSTEM MODEL

Let us consider a vehicular communication scenario following the IEEE 802.11p standard [START_REF]IEEE guide for wireless access in vehicular environments (WAVE)architecture[END_REF], which is used to provide vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication. This standard considers an OFDM transmission scheme, with Figure 1 describing the IEEE 802.11p frame structure, where each transmitted packet consists in a preamble that includes known short and long training symbols to conduct the synchronization of the channel, a signal field, which carries the physical layer information, and a data field. In the data field, K = 64 subcarriers are employed within each OFDM symbol, in which only K on = 52 are active and 12 are virtual, i.e., inactive subcarriers. For simplicity, perfect synchronization at the receiver is assumed and the signal field is ignored. In addition, considering the K on subcarriers, only 4 of them are allocated as pilots, while the remaining 48 subcarriers carry the data. The channel estimation is constantly updated utilizing the pilots, as well as the estimation from the previous OFDM symbol. For each active subcarrier k ∈ K on , with K on being the set of K on active subcarriers, the OFDM frame at the receiver is written as

Y[k, i] = H[k, i]U[k, i] + N[k, i], (1)
where for all k subcarriers within the i-th OFDM symbol, H[k, i] represents the time variant frequency response of the channel, U[k, i] is the transmitted OFDM symbol affected by the HPA distortion and N[k, i] is the Gaussian noise, with power

η 0 = ε p ξ • K , (2)
with ε p being the preamble power per sample and ξ the average signal-to-noise ratio (SNR) at the receiver. Due to the mobility, the Doppler shift affects the performance of the OFDM transmission. In this sense, H[k, i] coefficients are modeled over a Rayleigh fading with Jakes' Doppler spectrum with Doppler frequency given by

f D = v c f c , (3)
where v is the velocity of the vehicle in m/s, c is the speed of light in m/s and f c is the carrier frequency. To simplify this analysis, the received OFDM symbols can be expressed as

y i [k] = h i [k]u i [k] + n i [k], (4)
where u i [k] denotes the k-th subcarrier in the i-th transmitted OFDM data symbol affected by the HPA distortion.

Let us denote the signal at the input of the HPA as x i [k], so that following [START_REF] Shaiek | Analytical analysis of SER for beyond 5G post-OFDM waveforms in presence of high power amplifiers[END_REF] we have the output given by ũi

[k] = γ 0 x i [k] + δi [k],
where δi [k] is a nonlinear distortion with zero mean and variance σ δ 2 , that is uncorrelated with the input, while γ 0 describes a complex gain. Then, since γ 0 is usually compensated at the transmitter, we can write the output of the HPA as

u i [k] = x i [k] + δ i [k], (5)
where

δ i [k] = δi [k]
/γ 0 is the remaining nonlinear distortion of the HPA, so that we can re-write (4) as

y i [k] = h i [k]x i [k] + h i [k]δ i [k] + n i [k], (6)
in which the effect of the term

h i [k]δ i [k]
usually yields a BER floor at the receiver [START_REF] Bouhadda | Theoretical analysis of BER performance of nonlinearly amplified FBMC/OQAM and OFDM signals[END_REF].

III. HIGH POWER AMPLIFIER

To address the high PAPR issue and, therefore, the distortions caused by HPA in OFDM transmission, we use a memoryless HPA based in the polynomial model as in [START_REF] Shaiek | Analytical analysis of SER for beyond 5G post-OFDM waveforms in presence of high power amplifiers[END_REF]. This model is based on a commercial evaluation of a HPA following the 3GPP model and the description in [START_REF]Realistic power amplifier model for the new radio evaluation[END_REF], which exhibits both amplitude to amplitude (AM/AM) and amplitude to phase (AM/PM) distortions by approximating its characterizations with a polynomial. Thus, for a given input signal x i [k], the amplified output signal u i [k] can be expressed as

u i [k] = ϕ a (ρ[k]) exp [j(ϕ p (ρ[k]) + φ[k])] = ς (ρ[k]) exp (jφ[k]), (7)
in which ρ[k] = |x i [k]| is the input signal modulus, φ[k] = ∠x i [k] is the input signal phase, ϕ a (ρ[k]) and ϕ p (ρ[k])
represent the AM/AM and AM/PM characteristics of the HPA, respectively, while

ς (ρ[k]) = ϕ a (ρ[k]) exp [jϕ p (ρ[k])] is the complex soft envelope of the amplified output signal u i [k].
Moreover, the soft envelope of the amplified signal employed in our simulations is approximated by

ς (ρ[k]) ≈ P l=1 a l ρ[k] l , (8)
where, following the description to the polynomial model [START_REF] Shaiek | Analytical analysis of SER for beyond 5G post-OFDM waveforms in presence of high power amplifiers[END_REF], a l denotes the complex coefficients of the polynomial with order P = 9, obtained with a least square (LS) method. Finally, in order to reduce the effects of the nonlinearities, the HPA operates at a given Input Back-off (IBO) from the 1 dB compression point, which refers to the input power level where the characteristics of the amplifier have dropped by 1 dB from the ideal linear characteristics [START_REF] Colantonio | High efficiency RF and microwave solid state power amplifiers[END_REF]. In this matter, before amplifying the signal by the HPA, it is scaled by the gain ϱ to ensure the desired IBO, given by

ϱ = τ 1dB 10 IBO 10 τ xi[k] , (9)
where τ 1dB is the input power at 1 dB compression point and τ xi[k] is the mean power of the input signal.

IV. CHANNEL ESTIMATION SCHEMES

Several methods to provide channel estimation in time varying channels have been proposed in the literature. In this section, we present the DPA and STA conventional estimators, as well as DNN-based estimators such as the AE-DNN and the STA-DNN.

A. Conventional Channel Estimators 1) DPA initial estimation: The basic method considered to provide initial channel estimation in the IEEE 802.11p standard is the LS estimator [START_REF] Fernandez | Performance of the 802.11p physical layer in vehicle-to-vehicle environments[END_REF]- [START_REF] Gizzini | Deep learning based channel estimation schemes for IEEE 802.11p standard[END_REF]. In this case, the preamble is divided into two long training predefined symbols t p,1 and t p,2 , which are demodulated to obtain the received frequency domain symbols for each k-th subcarrier, denoted by y p,1 [k] and y p,2 [k]. Thus, the LS channel estimation is given by

ĥLS [k] = y p,1 [k] + y p,2 [k] 2p[k] , (10)
where p[k] is the predefined preamble sequence in frequency domain. Then, the estimate ĥLS [k] is applied to equalize all received data in the frame, which causes significant degradation due to variations over its duration.

The DPA method enhances the LS estimator performance by exploring the high correlation characteristics between adjacent symbols in OFDM, so that it employs the previous received symbol as a preamble to estimate the channel for the current symbol. Considering the initial estimate as ĥDPA0 [k] = ĥLS [k], the equalization of the current i-th symbol at the k-th subcarrier is given by

ŷeq i [k] = y i [k] ĥDPAi-1 [k] , (11)
so that ŷeq i [k] is then demapped to the nearest constellation point to result in the

d i [k]. The DPA initial channel estimate is obtained as ĥDPAi [k] = y i [k] d i [k] . (12)
2) STA estimation: Several channel estimation schemes based on DPA method have been proposed in the literature to rapidly track varying channels. For instance, the STA method has been introduced in [START_REF] Fernandez | Performance of the 802.11p physical layer in vehicle-to-vehicle environments[END_REF], where an average of the estimated channels in time and frequency domains is performed after the DPA estimation. First, averaging [START_REF]Realistic power amplifier model for the new radio evaluation[END_REF] in the frequency domain we have that

ĥupdate i [k] = λ=β λ=-β ω λ ĥDPAi [k + λ], (13)
where ω λ = 1 2β+1 , with β being the frequency averaging coefficient. Next, the STA channel estimation is computed as

ĥSTAi [k] = 1 - 1 α ĥSTAi-1 [k] + 1 α ĥupdate i [k], (14)
with α being the time averaging coefficient that, as well as β, is an integer parameter inherent to the STA method. It is worth to mention that to improve the STA performance, α and β must be chosen experimentally depending on the channel variation and fixing these parameters can increase the gradually accumulated demapping error from

d i [k] [2].

B. DNN-Based Channel Estimation

It is worth mentioning that the estimators presented in Section IV-A suffer from considerable performance degradation when applied to high mobility scenarios, due to the increasing error propagation over the OFDM frame [START_REF] Gizzini | Deep learning based channel estimation schemes for IEEE 802.11p standard[END_REF]. Therefore, DNNbased solutions appear as reasonable tools, since these algorithms are capable of capturing varying characteristics and, given the proper training and architecture, they involve low computational complexity. Figure 2 illustrates the AE-DNN and the STA-DNN deployments considered in this work. As we can notice, both designs receive as input the ĥDPAi [k] estimate obtained in [START_REF]Realistic power amplifier model for the new radio evaluation[END_REF], while different structures for the DNN are used in these methods, which are detailed as follows.

1) AE-DNN estimation: The AE-DNN solution proposed in [START_REF] Han | A deep learning based channel estimation scheme for IEEE 802.11p systems[END_REF] improves the DPA method by combining it with an offline trained AE with three hidden layers, consisting respectively of 40, 20 and 40 neurons, which are used to update the channel estimations while correcting the errors between the DPA estimate and the ideal channel. The authors in [START_REF] Han | A deep learning based channel estimation scheme for IEEE 802.11p systems[END_REF] have shown that the AE-DNN is capable of learning the frequency However, the drawback of the AE-DNN solution is its high computational complexity, due to the high number of neurons of the hidden layers, necessary to deploy a network capable to relate the ideal estimation to the initial DPA estimation. Figure 2 illustrates such approach as a complete DNN that uses ĥDPAi [k] as input and delivers ĥAE-DNN i [k] at its output.

ĥDPAi-1 [k] ĥSTAi-1 [k] ĥDPAi [k] ĥSTAi [k] ĥSTA-DNN i [k] ĥAE-DNN i [k] ĥupdate i [k] y i [k] ŷeq i [k] d i [k]
2) STA-DNN estimation: In order to reduce complexity when compared to the scheme proposed in [START_REF] Han | A deep learning based channel estimation scheme for IEEE 802.11p systems[END_REF], the authors in [START_REF] Gizzini | Deep learning based channel estimation schemes for IEEE 802.11p standard[END_REF] considered a three layer DNN, with 15 neurons in each layer, which is used as a post-process to the conventional STA estimator. Figure 2 illustrates such approach, in which ĥDPAi [k] is used by the STA estimator in [START_REF] Acosta-Marum | Six time-and frequency-selective empirical channel models for vehicular wireless lans[END_REF], so that ĥSTAi [k] is used as the input of the DNN in order to produce ĥSTA-DNN i [k].

The goal of the employed DNN is to minimize the mean squared error (MSE) between the ideal channel and the STA estimate, so that

MSE STA-DNN = 1 N T • NT i=1 h ideali -ĥSTAi , (15)
where N T is the number of training samples. Unlike the proposal in [START_REF] Han | A deep learning based channel estimation scheme for IEEE 802.11p systems[END_REF], the nonlinear processing along with the classical STA allows the proposed estimator to capture more features of the time and frequency correlations of the channel. The results demonstrated that the proposed STA-DNN scheme provides a performance improvement while reducing the computational complexity of the solution.

In the present work, the same training objective and hyperparameters from the learning process presented in [START_REF] Han | A deep learning based channel estimation scheme for IEEE 802.11p systems[END_REF] and [START_REF] Gizzini | Deep learning based channel estimation schemes for IEEE 802.11p standard[END_REF] are considered. However, while employing the DNNs to reduce the MSE between the ideal performance and the channel estimation from the conventional method, HPA-induced distortions are considered into the communication environment and, in order to provide proper channel estimation, the DNNs are required to deal with both mobility and HPA-induced nonlinear effects. Since the STA scheme is suited to deal with the correlation between successive OFDM symbols, we expect to reduce the complexity of the DNN, in terms of number of neurons, when comparing STA-DNN and AE-DNN schemes. In addition, the HPA-induced nonlinear distortions are usually seen at the receiver as an additional source of noise, so that we also expect that the DNN training will be able to deal with this effect, reducing the BER floor typically observed in these scenarios.

V. SIMULATION RESULTS

This section presents the performance analysis for the conventional and DNN-based channel estimators when applied to the IEEE 802.11p standard in presence of distortions due to HPA nonlinearities. V2V Urban Canyon (V2V-UC) [START_REF] Acosta-Marum | Six time-and frequency-selective empirical channel models for vehicular wireless lans[END_REF] is considered as vehicular channel model, that deploys the communication channel between two vehicles moving at v = 48 km/h in a dense traffic environment. We assume a carrier frequency of f c = 5.9 GHz and 10 MHz of signal bandwidth. The estimations are performed by considering 16-QAM modulation and a transmitted OFDM frame size of 100 symbols. Finally, we compare the IEEE 802.11p wireless communication scenario without HPA nonlinearities and when including HPA nonlinearities, based on the polynomial model as described in Section III.

Figure 3 and Figure 4 present the normalized mean squared error (NMSE) and the BER performance, respectively, when considering a fixed IBO = 4 dB. Let us highlight that the objective of the DNN in both DL-based solutions is to minimize the MSE between the ideal channel and the channel estimation from the chosen conventional method. However, in our proposed scenario, this is done without any prior knowledge regarding the HPA nonlinearities. The superiority of the DNN-based methods in estimating the channel can be seen in Figure 3, presenting that using DNN as a nonlinear process considerably enhance the conventional estimators performance, adding the ability to learn features about the channel and reducing the error between its estimation and the ideal channel, even when impacted by non-expected distortions. Figure 3a shows that, starting from the SNR of ξ = 20 dB, the AE-DNN presents less channel estimation error than the STA-DNN estimator, once the impact due to demapping error is small for high SNR region and the initial DPA estimation emerges over STA. Moreover, the results presented by Figure 3b show that, when the impacts from HPA distortions are considered, the STA-DNN hybrid solution slightly outperforms the AE-DNN, proving to be more likely to capture the nonlinearities of the HPA while reducing also the computational complexity due to its DNN architecture. In addition, Figure 4 shows that the DNN-based estimators outperform the BER provided by the conventional estimators in all considered scenarios. Moreover, in Figure 4b we observe that the DNN-based estimators still present a BER floor at high SNR when the HPA-induced distortions are included. Nevertheless, they are still capable to provide a BER of around 10 -2 at ξ = 20 dB, while the conventional estimators suffer from severe performance degradation.

It is worth to highlight that, in performing an average of the estimated channels in time and frequency domains, the classical STA takes more about the correlation of the channel gain over successive received OFDM symbols into account than the initial DPA estimation, providing a better entry for the DNN. As a consequence, the complexity of the STA-DNN in terms of number of neurons of the DNN can be considerably reduced when compared to the AE-DNN, while still providing a slightly better BER performance in all considered scenarios.

In order to compare the estimators with different nonlinear distortion effects, Figure 5 presents the BER performance by employing different IBO values. Intuitively, since increasing the IBO represents an approximation to the characteristics of the ideal HPA and its linear properties, a lower IBO implies in a worse BER performance as an expected result. In accordance with that, it is possible to notice that both classical and DNN-based estimators show better performance with the increase of the IBO. Nevertheless, the DNN-based estimators are more robust to these nonlinear effects, since the variation in performance is smaller than the one from the conventional estimators. The results presented in Figures 5a and5b show that, even for the scenario with IBO = 2 dB, both AE-DNN and STA-DNN are capable to achieve BER lower than 10 -2 at ξ = 25 dB, whereas the conventional initial DPA estimator and the STA estimator exhibit respectively high error rates of 0.25 and 0.22. This performance difference validates the hybrid approach, using classical estimation techniques together with a DNN, considered in this work. It is also possible to notice a performance improvement when we compare the results obtained with the STA-DNN estimator with the ones from the AE-DNN scheme.

VI. CONCLUSION

This work analyzes the impact of HPA nonlinearities on the performance of channel estimation schemes employed in a vehicular scenario, typical of the IEEE 802.11p standard. The simulations show that the use of DNNs present better performance compared to conventional estimators, in terms of both NMSE and BER. In addition, the combination of the DNNs with conventional estimators is also shown as an important design characteristic. By comparing the AE-DNN scheme, which is composed by a neural network processing after the initial DPA estimation, with the STA-DNN scheme, which employs a DNN after the conventional STA estimator, we observe that STA-DNN presents the best performance, with less complexity, i.e., with a smaller number of neurons per layer. As future works, we aim to explore noise cancellation techniques in order to further reduce the effects of the HPA distortions, as well as to investigate how to improve the DNN training by inserting more information regarding the dynamic scenario, the HPA model and by considering more advanced DL algorithms such as long short-term memory (LSTM). Another work extension aims to consider more vehicules communicating in the traffic environment and, with this increase in the complexity of the channel, we expect that DL-based solutions will be even more suitable for channel estimation given their generalization properties.

Fig. 2 :

 2 Fig. 2: Block diagram of the DNN-based estimators: AE-DNN and STA-DNN.

  With HPA nonlinearities and IBO = 4 dB.

Fig. 3 :

 3 Fig. 3: NMSE performance in the IEEE 802.11p wireless communication scenario with v = 48 km/h.

Fig. 4 :

 4 Fig. 4: BER performance in the IEEE 802.11p wireless communication scenario with v = 48 km/h.

  STA and STA-DNN estimators.

Fig. 5 :

 5 Fig. 5: BER performance for IBO ∈ {2, 4, 6} dB.

VII. ACKNOWLEDGEMENTS

The authors would like to thank Mr. Abdul Karim Gizzini and Dr. Marwa Chafii from ETIS lab from ENSEA at University Cergy-Pontoise-France, for their valuable technical discussions on DL tools and their implementation in wireless systems. This work was supported in part by CNPq Brazil and INESC P&D Brasil.


H H Ratsimbazafy

A Laborel-Préneron

C Magniont

P Evon

Comprehensive Characterization of Agricultural By-Products for Bio-Aggregate Based Concrete

Keywords: Multi-physical characterization, building materials, agricultural by-products, plant aggregates, vegetal concretes

The valorization of available agricultural by-products is important for the development of bio-aggregate based concretes as eco-friendly solutions for building materials. However, their diversity requires to assess their potential of use in vegetal concretes. This study aims to propose simple and relevant multi-physical characterization methods for plant aggregates. Basic and complementary characterizations were carried out on hemp shiv as a reference plant aggregate, and nine by-products available in the South-West part of France, i.e., oleaginous flax shiv, sunflower pith and bark, coriander straw, wheat straw, wheat chaff, corn shuck, miscanthus stem and vine shoot. The basic characterizations performed were those recommended by the TC-RILEM 236 BBM, i.e., particle size distribution, bulk density, water absorption and thermal conductivity. Complementary characterizations have also been proposed, taking into account the possible environment of the binder and the vegetal concrete manufacturing method. The additional tests developed or adapted from previous research assess the following properties: the content of water-soluble compounds at pH 7 and 12, the dry density of plant aggregates compacted in wet state, the real water absorption after compaction and the compression behavior of these compacted aggregates. This complete characterization highlights the distinct behavior of the different agroresources and allows to correlate these characteristics to the use properties of hardened composites.

Introduction

The building sector is the world leader in energy consumption (36%) and carbon dioxide emissions (39%). Therefore, a change in current construction practices must be undertaken in order to reduce its environmental impact. The use of local agricultural resources as a source of new building materials could be an answer to this problem since they are renewable, biodegradable and constitute a carbon sink. Over the past couple of decades in France, most of the research incorporating agricultural by-products with mineral binder to form insulating vegetal concretes has been carried out with hemp shiv. However, this by-product represents only less than 0.02% of the total crop byproducts available in the metropolitan France, and it is almost absent in the South-West (Laborel-Préneron et al., 2018). Nine by-products available in this region were identified as alternative bioaggregates for construction. However, their diversity requires adequate multi-physical characterizations in order to assess their potential as plant aggregates for vegetal concretes.

Currently, no standard governs the characterization of plant aggregates as constituent of building material. However, some characterization methods like the particle size distribution, bulk density, water absorption and thermal conductivity have been recommended by TC RILEM 236-BBM [START_REF] Amziane | Recommendation of the RILEM TC 236-BBM: characterisation testing of hemp shiv to determine the initial water content, water absorption, dry density, particle size distribution and thermal conductivity[END_REF]. These methods have been implemented with hemp shiv. Nevertheless, these characterizations are not sufficient to qualify the aggregates for use with a mineral binder. Indeed, the literature has shown the existence of deleterious chemical interactions between the watersolubles inside plant aggregates and reactive mineral binders, thus causing a perturbation of the setting at early age, the hardening mechanism which impacts the mechanical performance of the composite and its durability [START_REF] Bourdot | Impact of Bio-Aggregates Properties on the Chemical Interactions with Mineral Binder, Application to Vegetal Concrete[END_REF][START_REF] Diquélou | Impact of hemp shiv on cement setting and hardening: Influence of the extracted components from the aggregates and study of the interfaces with the inorganic matrix[END_REF]. In their studies so far, the amounts of water-soluble compounds have been determined in a neutral medium. However, most of the binders used like cement, lime, and pozzolanic binders generate an alkaline medium. Hence, it is necessary to determine the content of water-solubles extracted under alkaline conditions. In addition, the bulk density does not represent the behavior of aggregates, which have been wetted and then compacted in the composite. So, it is necessary to set up a characterization method making to get closer to the behavior of the aggregates in the composite by wetting and compacting. It could also give the real water demand of each aggregate inside the formulation, due to the water need competition with the hydration of the binder affecting the mechanical performance of the composite [START_REF] Arnaud | Experimental study of parameters influencing mechanical properties of hemp concretes[END_REF]. Few authors have studied the mechanical behavior of plant aggregates without binders [START_REF] Arnaud | Experimental study of parameters influencing mechanical properties of hemp concretes[END_REF][START_REF] Cérézo | Propriétés mécaniques, thermiques et acoustiques d'un matériau à base de particules végétales : approche expérimentale et modélisation théorique[END_REF][START_REF] Tronet | Study of lime hemp composite precasting by compaction of fresh mix -An instrumented die to measure friction and stress state[END_REF]. [START_REF] Cérézo | Propriétés mécaniques, thermiques et acoustiques d'un matériau à base de particules végétales : approche expérimentale et modélisation théorique[END_REF] concluded that for a hemp concrete with a low binder dosage, the mechanical compression behavior of the composite is influenced by the highly compressible behavior of hemp particles alone. The behavior of the composite could then be predicted by a compression test on samples of aggregates alone.

In the present study, relevant multi-physical characterization methods are applied on ten plant aggregates in order to compare their various behaviors, which could influence the use properties of the composites and serve as parameters for the manufacture of the latter. This conference article only deals with the characterization of aggregates, but the correlation with the mechanical and thermal properties of composites has been realized and will be the subject of a journal article.

Materials and Methods

Materials

Ten agricultural by-products were chosen for this study. Apart from hemp shiv, which was chosen as the reference plant aggregate, the other by-products were chosen for their availability in the South-West part of France and low cost, and they were subjected to the same transformation process in order to obtain the studied plant aggregates. This process was a series of grinding, sieving and mechanical separation. After a drying step, by-products were ground using a hammer mill fitted with a 32 mm diameter grid. Then, the ground by-products were sieved through a 1 mm sieve to remove fine particles. In the case of sunflower stem, a tilted conveyor belt and a blowing system were used to separate the pith particles (soft internal part of the stem) from the bark one (rigid and ligneous external part). Finally, they were screened on a 12 mm square mesh screen to obtain the plant aggregates used in this study (Fig. 1). According to their origin, the ten plant aggregates can be classified into four categories:

• Fiber plant by-products: hemp shiv (HS) and flax shiv (FS); • Oilseed stems or straw: sunflower pith (SP), sunflower bark (SB) and coriander straw (CSt); • Cereal plant by-products: wheat straw (WS), wheat chaff (WC) and corn shuck (CSh); • Other by-products: miscanthus stem (MS) and vine shoot (VS);

Basic physical characterizations

The basic physical characterizations were carried out according to the recommendations of the RILEM TC 236-BBM (Amziane et al., 2017).

Content of water-soluble compounds at pH 7 and 12

The test was conducted with a Foss Fibertec FT 122 hot extractor on aggregate powders according to the method of Van Soest and Wine (1968), using a neutral solution of distilled water (pH 7), and a sodium hydroxide solution having a pH value equal to 12. The mass loss of the analyzed sample was measured after one hour in the boiling solution.

Dry density of aggregates compacted in wet state, and real water absorption after compaction

The main steps of the protocol to determine these properties are shown in Fig. 2. First, the aggregates were immersed in water for 30 sec, drained by shaking 50 times, and mixed manually to ensure good homogeneity (Fig. 2, steps 1 and 2). Then, as for the manufacture of a concrete specimen with immediate demolding, the wet aggregates were introduced and compacted in three layers of equal thickness in a cubic mold (15 × 15 × 15 cm 3 ) (Fig. 2, step 3). The load applied for compaction was adjusted until the sample became cohesive after immediate demolding. The sample was then demolded and dried in an oven at 60°C until the weight was constant (weight variation of less than 0.1% between two weighings, 24 h apart) (Fig. 2, step 4). For each plant aggregates, three samples were manufactured. The dry density of aggregates compacted in wet state, ρcomp (kg.m -3 ), and the real water absorption after compaction, wreal (%), are calculated from equations ( 1) and ( 2

Where md and Vd are, respectively, the mass (kg) and volume (m 3 ) of the dry sample, and mwet the mass of the wet compacted sample (kg).

Fig. 2: Experimental protocol to measure wet compacted dry density and real water absorption

Compressive strength and Young's modulus

The mechanical characterization was carried out by performing a monotonic compression test on the previously manufactured cubic samples of dry plant aggregates compacted in wet state without binder. The compression test was performed on a Zwick/Roell Z100 press equipped with two circular plates (13 cm in diameter) and a 5 kN force transducer. In order to properly distribute the forces on the surfaces of the analyzed sample, a rigid plywood was placed on the bottom plate and a thin rigid metal plate above the sample. The compression test was controlled in displacement with a speed of 3 mm/min up to 20% deformation. In order to compare the results on plant concretes with those in the literature, the compressive strength (σ) recorded was the stress at 1.5% deformation (ε=1.5%) [START_REF] Bourdot | Impact of Bio-Aggregates Properties on the Chemical Interactions with Mineral Binder, Application to Vegetal Concrete[END_REF][START_REF] Nguyen | Effect of compaction on mechanical and thermal properties of hemp concrete[END_REF]. The Young's modulus (or elastic modulus) was calculated by the Hook's law on the linear part of the curve at its very beginning (i.e., between 0% and 0.5% deformation).

Results and Discussion

Physical properties

Circularity is a shape parameter determined from image analysis, and its value ranges from 0 (infinitely elongated) to 1 (perfect sphere). The results of this parameter on the studied plant aggregates allowed to classify them into three categories (Fig. 3). The first type, which includes CSt, WS, WC, CSh and VS, is characterized by low circularity, of which more than 60% of the projected areas of the aggregates have circularities between 0 and 0.25. The second type, containing HS, FS, SB and MS, has an average circularity with more than 60% of the projected areas having circularities between 0.20 to 0.50. The last type, formed by SP only, is the most circular with more than 60% of the projected areas having circularities between 0.40 and 0.65. Although shape and size are parameters that can be changed from the transformation process, these results show the tendency of straws, chaffs, husks and shoots to be more elongated than the shiv, bark and stem, which are moderately elongated. For their part, the pith particles are more circular.

In addition to the shape, the size of the aggregates is also important especially for the mechanical properties of the composite. Most of the authors have concluded that the mechanical performance of the composites is reduced when the size of the aggregates increases for the same type of aggregate, but no trend was clear between aggregates of different types [START_REF] Stevulova | Lightweight Composites Containing Hemp Hurds[END_REF]. The evolution of the results of the mechanical parameters of each aggregate as a function of the major axis in Fig. 4 could provide more clarification on the effect of size on the mechanical properties of the composites. In general, it is observed that for aggregates having a comparable nature, the more the major axis increases, the more the compressive strength or the elastic modulus of the aggregates decreases. In fact, CSh, WC and WS are formed by flexible particles that are easily compressible, and the decreasing tendency is observed between them. It is the same for the family composed of HS, FS, SB, VS, MS and CSt, which are formed by more consistent particles. Between these two families of aggregates, for the same size of aggregate, the mechanical performance of the aggregates of the first family is always lower than those of the second one. The size of the aggregates linked to their nature could then be correlated with the mechanical properties of the composite. The high mechanical performance of sunflower pith is due to the binding properties of the pectins released on the surface of the aggregates in their wet state, resulting in cohesion between the particles in their dry state. The comparison between the bulk density and the density of dried plant aggregates compacted in wet state allows to observe two distinct behaviors of aggregates subjected to compaction in the wet state and then dried (Fig. 5a). The first behavior, for VS, SB, FS, HS and CSt, is a swelling of the aggregates resulting in a diy density of plant aggregates compacted in wet state much lower compared to the bulk density. In fact, wet aggregates swell that the amount of paiiicles that can be intrnduced into the mold is less than a loose aggregate, despite the compaction. The second behavior is that of CSh, WS and SP, whose wet compacted diy density is higher than the bulk density. This can be explained by reanangement and flattening of porous aggregates, due to their compaction in the wet state. When the density remains the same in bulk and under compaction, as in the case of MS and WC, a neutrnlization between the swelling of the aggregates and their reaiTangement occurs. These results show the variability of the volume behavior of the aggregates between the bulk anangement and the di•ied paiiicles after having been compacted in wet state, which could be linked to the porosity, rigidity and water abso1ption of the aggregates. Given that the density of di• ied aggregates compacted in wet state clearly reflects their behavior as in the manufacture of the composite, it would be a good fonnulation parameter in order to detennine the adequate quantities of aggregates according to its behavior.

The result of the thennal conductivity of the aggregates as a fonction of the density (Fig. 5b) shows a linear c01Telation between these two parameters regardless of the nature of the aggregates. The low thennal conductivity of aggregates (all less than 0.080 W.m-1 .K-1 ) also shows their perfo1mance as bulk thennal insulators. The the1mal conductivity of the order of 0.033 W.m-1 .K-1 for SP is even lower than those ofbulk insulators akeady in the market, i.e., cellulose wadding or wood wool, which are in the 0.038-0.045 W.m-1 .K-1 range.

Fig. 5: (a) Comparison of bulk density and d1y density of plant aggregates compacted in wet state, and (b) plant aggregates thermal conductivity as afunction of their bulk density

Usually, to assess the abso1ption capacity of aggregates, the IRA (Initial Rate of Abso1ption), which conesponds to the abso1ption rate at 1 min, is used. With the dete1mination of the real water abso1ption after compaction, it can be seen in Fig. 6a that the real quantities of water absorbed significantly differ from the tendency of IRA, and they ai•e much greater for all aggregates. This parameter then allows to adjust the quantity of water necessaiy for the manufa cture of the composites. However, the representation in mass percentage is not relevant for the comparison of the aggregates in the composite given that they do not have the same mass dosages. A representation of the amount of water per volume of dried aggregates compacted in wet state, more closely reflects the amount of water of the aggregates inside the composite (Fig. 6b ). fudeed, if the difference in water absmptions is considerable between SP and the other aggregates for a mass representation, a volume one shows a clear reduction of this difference. The order of the aggregates has also changed, due to the volume variation.

Chemical properties

The results of the water-solubles inside the aggregates at pH 7 and 12 show a large difference with an increase ranging from 33% for VS up to 126% for HS (Fig. 7a). This difference depends on the content of components soluble at pH 12 but insoluble at pH 7, in paiiicular hemicelluloses. fu addition, the impact of pH on the water soluble extracts also varies from one aggregate to another. fudeed, if the water-solubles of CSh (12%) and WC (16%) are respectively lower than those of WS (14%) and VS (17%) at pH 7, they become higher at pH 12 (CSh (23%), WC (25%), WS (19%) and VS (22%)). These results show that it is judicious to detennine the water-solubles at pH 12 for a better understanding of their impact on the composites. As for water abso1ption, a volume representation of the water-solubles extracted per cubic meter of wet compacted dried aggregates shows more reality in the composite since the aggregates are not comparable in mass because of their different dosages (Fig. 7b ). If for a mass representation SP seems to have the highest amount of water-solubles at pH 12, and therefore possibly a detrimental effect for the composite, a volume representation shows its low amount in water-solubles, which is of the same order of magnitude as HS. On the other hand, water-solubles in SV become considerable because of its high density. These results could be conelated with the mechanical prope1iies of the composites.

Mechanical properties

Compression of aggregates shows two types of behavior (Fig. 8a). The first one is characterized by the existence of a peak which can be explained by the achievement of a breaking stress maintaining the cohesion between the aggregates by entanglement (HS, VS and MS) or with the pectins (SP). The second behavior shows a stiffening of the samples (FS, SB, CSt, CSh, WC and WS). In fact, as the compressive sti• ess increases, the aggregates reanange and defonn without breaking, reducing their inter-and inu-a-paiticle porosities. The low rigidity of the CSh, WC and WS families is also evidenced compared to the other aggregates. These behaviors of aggregates alone could greatly affect the mechanical behavior of their composites manufactured with a commercial fonnulated lime binder at constant dosage of 258 kg.m-3 , as it is shown in Fig. 8b. The cubic specimens (15 x 15 x 15 cm 3 ) of the composites ai•e tested in cyclic compression, and their floating Young's modulus was detennined according to the method of [START_REF] Niyigena | RRT3: statistical analysis of hemp concrete mechanical properties variability[END_REF]. For most pa1ticles, a cleai• conelation can be evidenced between the Young's modulus of the composite and that of the paiticles anangement. Mixtures including vine shoots deviate from this ti• end, due to their high water-soluble content. Considering sunflower pith aggregates, as previously explained, the high degree of rigidity of the paiticles arrangement could be atti-ibuted to their binding by their own pectins. In this study, multi-physical chai•acterizations ai• e proposed and applied on ten agricultural by products in order to verify their relevance for an application with minerai binder. It was concluded that the size and fonn parameters, the d1y density compacted in wet state, the real water absmption after compaction, the content in water-solubles at pH 12 and the mechanical pai• ameters allow to compare the aggregates according to their nature, and to qualify them for their application in vegetal concretes. Neve1theless, the high porosities of the aggregates also require the development of another method to detennine them. With all these pai• ameters linked to the aggregates, future work would be to find a fo1mulation method applicable to any type of aggregate, taking into account these prope1ties.

Fig. 1 :

 1 Fig. 1: Plant aggregates: (a) HS, (b) FS, (c) SP, (d) SB, (e) CSt, (f) WS, (g) WC, (h) CSh, (i) MS, (j) VS

Fig. 3 :Fig. 4 :

 34 Fig. 3: Circularity of types 1 to 3 plant aggregates

  ................................................................. 0. 00+---.---.----.----,-.---.---,�C:J '?� <,_'? �C:J <,C:J\_,'?V::-�'? '?q �'? �<, 0 50 100 150 20 0 250 300 350 Bulk denslty(kg . m 3 )

4 -

 4 Fig. 6: (a) Comparison of IRA and real water absorption, and (b) volume and mass representations of real water abs01ption (i.e., mass of water absorbed in proportion of the aggregate volume and mass, respective/y)

Fig. 7 :

 7 Fig. 7: (a) Mass and (b) volume representation of water-solubles in plant aggregates at pH 7 and 12

Fig. 8 :

 8 Fig. 8: (a) Compression behavior of dried plant aggregates compacted in wet state, and (b) Young's modulus of composites at 120 days versus Young's modulus of aggregates

doi:10.4028/www.scientific.net/CTA.1.77

Acknowledgments

The authors would like to acknowledge the Occitanie Region, Ovalie Innovation, the Tarbes Lourdes-Pyrénées conurbation community and the IDT Tai• bes for the funding of this project.


E Bergeret

T Deleruyelle
email: thibaut.deleruyelle@l2mp.fr

P Pannier

J Gaubert

UHF RFID Tag Robustness

RFID systems (radio frequency identification) purpose is to transmit information between a reader and a passive receiver distant of few meters. The receiver or tag is powered by the conversion of the incident wave in a dc voltage. The amplitude of the wave decreases rapidly with distance and makes it necessary to use a RF / DC converter. The converter generates a continuous voltage higher than the incoming voltage amplitude. This study presents the impacts of some of the most fluent parameters on the effectiveness of multipliers RF / DC and on the antenna mismatch.

Introduction

The circuit is composed of three distinct parts, each representing about one-third of the total surface of the chip (for the chips that meet the EPC Gen2 standard with a memory of 400 to 500 bits)

The analog part, it includes the converter RF / DC, the voltage regulator with a reference oscillator and the receiver, and a block to the start and stop of the circuit depending on the strength of field (POR: Power On Reset). Digital, it handles the protocol and commands all the functions of the tag. It represents 15000 logic gates. The plan memory, its size is not limited by the EPC standard; however UHF products currently contained with a small map memory. It incorporates a portion analog high voltage needed to writing in the EEPROM cells The architecture of the tag is shown in figure I.

The configuration is close to the HF circuit. However, some important differences are worth noting. First, there's no matching circuit in IC. The antenna is designed to ensure impedance close to the conjugate impedance of the chip, so, matching networks are unnecessary. Second, in UHF RFID, the IC recovers power thanks to a voltage multiplier circuit. Indeed, received waves are too low to permit the rectifier to power the circuit. That's why a multiplier is used to increase the voltage. So it's crucial to warranty the system functionality. Its effectiveness directly affects the scope of the system: lower is the power for which it is able to deliver the voltage needed, longer is the range of the system. In this kind of circuit, an architecture based diodes or MOS transistor predominates, it is represented on figure 2.

The design of these circuits is subject to significant constraints. Paradoxically, the design parameters which affect the performance are often poorly defined. In this context the use of an analytical model allows to quickly determine the best design solution [START_REF] Curty | A model for mu -power rectifier analysis and design[END_REF][START_REF] Bergeret | Modeling and Design of CMOS UHF Voltage Multiplier for RFID in an EEPROM Compatible Process[END_REF]. However, as the conception of voltage multipliers is very sensitive, corners simulations have to be done in order to evaluate the robustness of the best solution. These corners simulations can consume huge time and prove that the chosen solution is not stable enough. In this study, the impact of variation in the fabrication process is discussed, the aims is to find the best and most robust solution in face of process variation for the chip or the antenna.

Multiplier's key parameters

The IC input impedance depends mainly of multiplier's design parameters such as Schottky size or number of stages. In fact, three elements are connected to the antenna pad and influence chip input impedance: the input pad, the ESD circuits and the multiplier.

Multiplier model

The input impedance of an integrated multiplier circuit is capacitive. An antenna with inductive impedance is generally used to achieve a power matching [START_REF] Nikitin | Power reflection coefficient analysis for complex impedances in RFID tag design[END_REF]. The equivalent circuit including the antenna and the tag input at the fundamental frequency of the incident RF wave is given in figure 3. The input impedance (Zchip) of the chip is composed of R IC and C IC , which are non-linear functions of the magnitude of the input voltage Vrf.

For the multiplier shown in fig. 2, it has been established in previous study [START_REF] Vita | Design criteria for the RF section of UHF and microwave passive RFID transponders[END_REF] , that the current can be expressed in term of modified Bessel functions series:

0 exp 2 .cos( ) .
. .

cos( )

rf rf D s n i i i DC n V V Vd I I B B n t n vt n vt n vt I Id n t ω ω ⎡ ⎤ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎢ ⎥ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ≈ + ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎢ ⎥ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎣ = + ∑ ∑ (1)
B n are Bessel functions. The voltage applied on each diode called Vd can be expressed in function of multiplier output voltage and number of multiplier stages (N):

2. DC d V V N - = (2)
So for a fixed IDC and VDC, this equation can be solved numerically to get the value of incident voltage |Vrf| with. The expression of the first harmonic can then be calculated. And then the non-linear resistive part of each diodes impedance at first harmonic can be computed for a given V rf input voltage magnitude:

1 rf Rd V Id = (3)
Considering the multiplier topology for each stages, and if the impedance of the capacitors Cm is large enough to be negligible around 900 MHz, each impedance stage can be calculated with the equivalent circuit given on Fig. 4. On this circuit, substrate losses are taken into account by the network Rs, Cs.

Substrate losses are in parallel with the diode equivalent circuit Rd Cd. The complete chip input impedance including the input pads and the ESD protection circuit is given in Eq 4. ESD and pads effects are negligible on the resistive part of the IC impedance. However, they must be taken into account on the imaginary part of the input impedance.

1 2 ( ) 2 IC ESD C I Rd Rs R C N Cd Cs Cpad C N Rd Rs ⋅ = = ⋅ + + + + (4)
The maximum power transfer between antenna and chip is obtained under matching condition. It is possible to determine antenna impedance corresponding to the computed chip impedance thanks to Eq 5:

* ANT IC Z Z = (5)
Thanks to this model, we can determine the first harmonic impedance, the input power to reach a fixed operating point (V DC , I DC ) and the efficiency of the multiplier. The model allows determining main multiplier characteristic: input impedance and efficiency versus design and process parameters. Then, with this tool once the best design solutions was selected, its robustness can be evaluated thanks to a variation of process input parameters.

Results and robustness on the chip

Thanks to the model, main design parameters can be computed for a selected technology: Fig. 5 shows the diodes surfaces have to be chosen as small as possible and the number of stages reduce to the minimum. However, if this choice of diodes sizes and number of stages seems to be optimal, this result mainly depends on process parameters such as Is, Rs, and Cs. In order to estimate the impact of process deviation, a variation of 10% is applied on technologies parameters. First studied parameter is the loss capacitance, called Cs in the model; result on 10% variation for a one stage multiplier is presented in figure 6. This variations leads to an important imprecision on the efficiency (±8%), moreover a part of received power will be wasted due to the mismatch. Indeed antennas have fixed impedance and if it is matched to standard chip impedance process variation will be ignored and antenna and chip would be mismatched.

On Table 1, results on process variation for different parameters are presented. From these results many guidelines for robust design appear: increasing the number of multiplier stages decreases the efficiency variations The imaginary part of the matched antenna is robust versus process variation The saturation courant of diodes has less impact on performance than subtract losses ( Rs and Is) These results lead to a modification in the design methodology of a RFID chip, the key design parameter can be selected not only for their performances but also for their sensitivity on process variation.

Complete System robustness

Once a chip solution has been selected with minimum shift on the input impedance, a matched antenna has to be designed. Due to the chip impedance , the antenna need to be very inductive with a very low resistance as presented in [START_REF] Rao | Antenna design for UHF RFID tags: a review and a practical application[END_REF]. An antenna topology has been chosen to be adapted on the circuit impedance (Fig 7). Once the design finished a sensibility study is done on some of the antenna's parameters (table2) in order to estimate the robustness of the matching between chip and antenna. As for the chip, the imaginary part seems to be the most robust parameters on the antenna. Owing to the very low resistance of the RFID chip, variations about few ohms on the antenna's impedance involve great mismatch on complete system. So, the real part of the antenna's impedance is very sensitive to variation especially on line width.

Conclusion

This study showed the sensitivity of a tag to the fabrication process and guidelines are presented to increase the total system robustness. The most critic parameter to control is the real part of the chip and antenna. This parameter is very sensitive on chip and antenna variations, with a difference respectively about 4 to 15% on antenna and up to 6.3% on chip. A simple way to increase chip stability is to increase the number of stages, with considering that the efficiency do not become to small. Increasing the tag robustness is very important in RFID applications in which chip must be very low cost and operating of an important number of tag , should be preferred to the performance of a few.

Fig. 1

 1 Fig. 1 UHF RFID system Fig.2 RFID multiplier

Fig. 4

 4 Fig. 4 One multiplier stage equivalent circuit Fig.3 Tag equivalent circuit

Fig. 5

 5 Fig. 5 Efficiency vs aera and number of stages Fig. 6 Impact of capacitor losses variation

Table 1 :

 1 Impact on multiplier of ±10% variation on process parameters for different number of stages

	Number of stages	Variation	R ant	L ant	Efficiency
	N=1	Rsub ±10%	±4%	<1%	±10%
	N=1	Csub ±10%	±6.33%	<1%	±8%
	N=1	Is ±10%	<1%	<1%	<1%
	N=3	Rsub ±10%	±2.5%	<1%	±6%
	N=3	Csub ±10%	±1.4%	±2%	±5%
	N=3	Is ±10%	<1%	<1%	±0.6%
	N=5	Rsub ±10%	±2%	<1%
	N=5	Csub ±10%	±1.2%	±2.5%	±3.8%
	N=5	Is ±10%	<1%	<1%	±0.7%

Table 2 :

 2 Impact on antenna impedance of ±5% variation on antenna's parameter R ant maximum variation L ant maximum variation

	ε r ±5%	6.33%	1.8%
	T(metal tickness) ±5%	3.8%	1.3%
	W (line width) ±5%	15%	3%