Francesco Guidi
email: francesco.guidi@cea.fr

Anna Guerra
email: anna.guerra3@unibo.it.

Antonio Clemente
email: antonio.clemente@cea.fr

Davide Dardari
email: davide.dardari@unibo.it.

Raffaele D'errico
email: raffaele.derrico@cea.fr

Energy Detection Performance with Massive Arrays for Personal Radars Applications

Keywords: Massive arrays, personal radar, target detection, side-lobes

The idea to adopt massive arrays for personal radars applications is facing a rapid growth, thanks to the high scanning resolution achievable with the large number of antennas employed. In fact, such multi-antenna systems enable the possibility to detect and localize surrounding objects through an accurate beamforming procedure. In this paper we show a classical energy-detection approach for target ranging and localization, where the threshold is designed according to the receiver noise only, since an ideal laser-beam antenna is considered. Successively, we show the ambiguities that could arise when the presence of side-lobes cannot be neglected (e.g., when considering real massive arrays instead of ideal pencil-beam like radiation patterns) and we propose a set of guidelines that can be followed from a system design point-of-view to overcome this issue.

Introduction

The adoption of massive arrays is facing a rapid growth in several ranging and localization applications, such as personal radars [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF], thanks to the possibility to achieve a precise and high-scanning resolution given by the large number of adopted antennas [START_REF] Clemente | Wideband 400-element electronically reconfigurable transmitarray in X band[END_REF].

The concept of personal radar has been recently proposed in [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF][START_REF] Guerra | Application of transmitarray antennas for indoor mapping at millimeter-waves[END_REF] where it has been shown the possibility to jointly use millimeter-waves (mmW) and wideband massive arrays technologies for indoor environment mapping. Thanks to this technology, it is possible to avoid the adoption of a dedicated very highdirectional antenna with mechanical steering, as proposed in [START_REF] Dissanayake | A solution to the simultaneous localization and map building (SLAM) problem[END_REF][START_REF] Jose | An augmented state SLAM formulation for multiple lineof-sight features with millimetre wave RADAR[END_REF][START_REF] Jose | Predicting Millimeter Wave Radar Spectra for Autonomous Navigation[END_REF], which can not be easily integrated into portable radar devices. The consequent near-pencil beam of massive arrays returns a precise angle and range information thus making the modeling and characterization of the environment with personal radars very similar to that based on laser.

Different literature has been produced for the analysis of the localization performance of wideband large antenna arrays. In fact, wideband signals are the best candidate to achieve high ranging performance [START_REF] Shen | Fundamental limits of wideband localization; part I: A general framework[END_REF], but a strict phase control in beamforming, i.e. the adoption of precise and costly phase shifters and delay lines, becomes necessary to assure a perfect signal alignment. A cheaper and alternative solution is to adopt digitally controlled phase shifters implementing a discrete set of phase shifts at the price of a reduced signal alignment and an increased level of side-lobes [START_REF] Rondinelli | Effects of random errors on the performance of antenna arrays of many elements[END_REF][START_REF] Ruze | Antenna tolerance theory -A review[END_REF]. Despite the high-ranging accuracy which can be achieved by the adoption of such systems, all these effects have to be accounted for when target detection is performed for different steering directions.

In this paper we propose a low-complexity non-coherent detection scheme, where the detection of objects is performed by a massive array which steers its beam in different directions in order to detect and localize objects. Thanks to the near-pencil beam array considered, all the measured contributions are associated to the considered steering direction. According to the receiver performance, we describe a set of guidelines to be followed when energy detection with massive arrays is performed.

The rest of the paper is organized as follows. In Sec. 2 we first show the threshold design, and successively we evaluate the side-lobe effects when the previously defined threshold based on receiver noise is adopted. Finally, in Sec. 3 we report a case study where real massive arrays are considered, and we discuss a possible solution to overcome the issue when energy detection is performed.

Target Detection Scheme

The personal radar concept is based on the idea that the surrounding objects are detected and localized thanks to the beamforming procedure enabled by massive arrays.

The system herein considered exploits monostatic scattering, i.e. the transmitter and receiver are co-located. For each steering direction θ b , the massive array steers its main beam towards that direction, and collects the overall backscattered response in order to detect and localize objects. To our purpose, first we account for a laser-like antenna, with a radiation pattern that permits to neglect the side-lobes effect, and thus, we adopt a classical constant false alarm rate (CFAR) approach accounting for the receiver noise only. Second, we focus our analysis to real antennas in which side lobes might cause false target detection. In fact, the presence of a target could be detected and assigned in a certain direction even if it is not effectively located in that part, as shown in Fig. 1. In addition, they could even cause errors in the ranging procedure, i.e. the distance of target 1 and 2 of Fig. 1 can be confused. Thus, once the threshold has been set, we theoretically evaluate the impact of real massive arrays on the detection performance. For our specific case, we consider massive arrays at 60 GHz which can be considered a natural candidate for personal radars applications due to their radiation characteristics.

In the following we describe the receiver scheme considered, and the threshold design by accounting for an ideal laser-beam antenna.

Receiver Scheme

The detection scheme we propose is a non-coherent approach based on energy detection to account for the complete uncertainty we have on the received waveform shape.

For each steering direction θ b , define the received signal as

r(t, θ b ) = s(t, θ b ) + n(t) . (1)
with n(t) indicating the noise term and s(t, θ b ) the received waveform including all the signals coming from the steering direction θ b . The received signal is first passed through an ideal bandpass filter with center frequency f c to eliminate out-of-band noise. 1 The filtered signal is denoted by

y(t, θ b ) = x(t, θ b ) + z(t) (2)
where x(t, θ b ) = s(t, θ b ) ⊗ h F (t) and z(t) = n(t) ⊗ h F (t) with h F (t) being the impulse response of the filter. Energy evaluations are performed over time interval T ED , with N bin = ⌊T f /T ED ⌋ representing the number of integration bins each time frame

T f is divided in, that is e m (θ b ) = m TED (m-1) TED [y(t, θ b )] 2 dt . (3)
with m = 1, . . . , N bin . The detection strategy consists in comparing each element e m (θ b ) with a threshold ξ m . If the energy value of at least one bin is above the threshold, then the target is detected and it is assumed present in the steering direction θ = θ b . We define the following two figures of merit: (i) the probability of false alarm (PFA) P FA as the probability of deciding that a target is detected, when it is not effectively within the considered scenario, due to presence of receiver noise; (ii) the crossing probability P c as the probability that the threshold is overcome due to the signal backscattered from a target placed in the scenario.

If the threshold is exceeded for m = m, the coordinate m leads to an estimate of the target time-of-arrival (TOA) and, jointly with the steering direction θ b , it provides the spatial position of the target in surrounding environment. Consider now the elements e m (θ b ) of the decision energy bins. The presented decision rule consists in Decide :

H 0 , if e m (θ b ) < ξ m ∀{m} , H 1 , if ∃ {m} s.t. e m (θ b ) ≥ ξ m . (4)
Define now, for each energy bin, the normalized energy detector test

Λ m (θ b ) = 2 N 0 e m (θ b ) H1 ≷ H0 ξm (5)
where ξm = N0 2 ξ m . According to [START_REF] Urkowitz | Energy detection of unknown deterministic signals[END_REF] we have

Λ m (θ b ) = 2 N 0 m TED (m-1) TED [y(t, θ b )] 2 dt ≃ 1 σ 2 mN i=(m-1)N [y i (θ b )] 2 (6)
where N = 2W T ED , σ 2 = N 0 W is the noise variance, and y i are the sampling expansion coefficient of the equivalent low-pass (ELP) of y(t) [START_REF] Urkowitz | Energy detection of unknown deterministic signals[END_REF], taken at Nyquist rate W in each interval T ED .

Threshold evaluation criteria with ideal pencil-beam pattern

When an ideal pencil-beam antenna is considered, we aim to preserve that the PFA due to the receiver noise does not exceed a certain value. Thus, in the presence of only the noise, i.e. y(t, θ b ) = z(t), eq. ( 5) can be written as

Λ m (θ b ) = 2 N 0 m TED (m-1) TED [z(t)] 2 dt ≃ 1 σ 2 mN i=(m-1)N (z i ) 2 . (7)
In order to set the threshold, it is well known that the output of the energy detector is distributed according to a central Chi-square distribution, with probability density function (PDF)

f C (α, β) = α ( β 2 -1) 2 β 2 Γ β 2 e -α 2 , α ≥ 0 ( 8
)
where Γ(•) is the gamma function [11, p. 255] and β is the number of degrees of freedom. given by [START_REF] Mariani | Effects of noise power e imation on energy detection for cognitive radio applications[END_REF] p

(m,b) FA = Γ N 2 , ξm 2 (9)
with Γ denoting the regularized Gamma function [START_REF] Chiani | Integral representation and bounds for marcum Q-function[END_REF].

To properly set the threshold, the joint false alarms for all bins have to be taken into account. Thus, for a considered steering direction θ b , the overall desired false alarm probability is given by

P ⋆ FA = 1 - N bins m=1 1 -p (m,b) FA ≈ N bins • p FA (10)
where we have assumed that all bins are statistically independent and p (m,b) FA = p FA ∀ m, and consequently we can set a desired p ⋆ FA per bin as

p ⋆ FA ≈ P ⋆ FA N bins . ( 11
)
Finally we can write

ξ = 2 Inv Γ N 2 , P ⋆ FA N bins (12)
where Inv Γ (•, •) is the inverse gamma regularized function. Note that with such approach, the threshold does not depend on the bin index, and it is set to keep the PFA due to the receiver noise to a desired value P ⋆ FA .

Side-Lobes Effects in Energy Detection Schemes

The previous threshold has been set according to a central Chi-square distribution, having accounted for the presence of the noise receiver only. On the contrary, during the steering procedure, in real scenarios we associate all the contributions deriving from the antenna pattern to that of the steering direction θ b . This approximation is often incorrect, especially when real arrays are adopted, as shown in Fig. 2. Thus, in order to evaluate the impact of the side-lobes in the target detection performance, we evaluate the probability that the threshold is crossed due to the presence of a target in the side-lobe direction. In particular, define x(t, θ b ) = x sl (t, θ b ) the received backscattering response under the assumption that no target is in the steering direction θ b , i.e. the target 1 of Fig. 1 is not present. The new random variable (RV) is now distributed as a non-central Chi-square distribution

f NC (α, λ, β) = 1 2 e -α+λ 2 α λ β-2 4 I β 2 -1 ( √ αλ) , α ≥ 0 ( 13
)
where I κ (•) denotes the κth order modified Bessel function of the first kind [11, p. 374] and PDF f NC (α, λ, β) [START_REF] Urkowitz | Energy detection of unknown deterministic signals[END_REF], with β being the number of degrees of freedom and λ the non-centrality parameter (NCP). Due to the presence of signals coming from side-lobes direction, the normalized decision variable results into

Λ m (θ b ) = 2 N 0 m TED (m-1) TED [x sl (t, θ b ) + z(t)] 2 dt ≃ 1 σ 2 mN i=(m-1)N (x sli (θ b ) + z i ) 2 (14)
where x sli (θ b ) are the sampling expansion coefficients of the ELP of x sl (t, θ b ) [START_REF] Urkowitz | Energy detection of unknown deterministic signals[END_REF].

In particular, the presence of x sli (θ b ) leads to the NCP λ m (θ b ) = 2γ m (θ b ) [START_REF] Urkowitz | Energy detection of unknown deterministic signals[END_REF][START_REF] Guidi | Detection of multiple tags based on impulsive backscattered signals[END_REF] , where γ m (θ b ) is the side-lobe-level-to-noise ratio (SLLNR) per bin, given by

γ m (θ b ) = 1 N 0 m TED (m-1) TED x sl (t, θ b ) 2 dt ≃ 1 2σ 2 mN i=(m-1)N [x sli (θ b )] 2 . (15)
A threshold-crossing event at the mth bin, that is, Λ m (θ b ) > ξm , results in a single-bin p (m,b) c

given by [START_REF] Mariani | Effects of noise power e imation on energy detection for cognitive radio applications[END_REF]

p (m,b) c = Q h λ m (θ b ), ξm (16)
with

Q h (α, β)= ∞ β x ( x α ) k-1 exp -x 2 +α 2 2 I k-1 (αx) dx denoting the generalized Marcum's Q function of order h = β/2 [13].
Since the signals components deriving from side-lobes direction are undesired, we aim that the threshold is not exceeded due to such signals, i.e. p

(m,b) c ≤ p ⋆
FA . If it is not the case, target detection and ranging could be wrongly performed. In the following, the impact of real antenna patterns on the detection performance is investigated, and possible solutions to counteract such effect are reported.

Case Study

We now consider the previously described system in order to evaluate what happens when real antennas are employed instead of ideal laser-beam antennas, which are accounted for the threshold design. Despite the analysis conducted is general, i.e. it can be applied to any frequency bandwidth, here we focus on mmW massive arrays, which could be one of the next fifth generation (5G) key technologies. This choice leads to an effective radiated isotropic power (EIRP) constrained by Federal Communications Commission (FCC) regulations as described in [START_REF]0000d1, Amendment of Part 15 Rules for License-Exempt 57-64 GHz Band[END_REF]. Thus, we first report threshold values in order to achieve a desired P ⋆ FA based on the receiver noise only. Once the threshold has been defined, we evaluate the bin-crossing probability for different values of the NCP, and finally we evaluate possible values in practical scenarios.

Threshold Setting

According to the analysis of Sec. 2, we now evaluate the threshold considering the receiver noise level. In particular, if otherwise indicated, we consider a time frame T f = 100 ns, a bandwidth W = 1 GHz and a time integration interval T ED = 1 ns. 2 In this way, by setting an overall P ⋆ FA = 10 -3 , it is p ⋆ FA = 10 -5 which gives the threshold ξ⋆ reported in Fig. 3. What it is important to remark is that such desired normalized threshold has been set according to the noise receiver only. Consequently, the impact of signals deriving from side-lobe directions has to be evaluated.

0 0.5 1 1,5 2

Side-Lobes Effects

When realistic antennas are adopted, and targets outside the steering direction are present, the threshold might be overcome. Consequently, such targets are wrongly associated with θ b , which translates into a possible detection and localization error. Thus, by considering [START_REF] Slepian | Eigenvalues associated with prolate spheroidal wave functions of zero order[END_REF], it is possible to estimate such effects when λ m (θ b ) is greater than 0.

In particular, we considered in [START_REF] Slepian | Eigenvalues associated with prolate spheroidal wave functions of zero order[END_REF], the ξ ⋆ obtained in Fig. 3 in order to preserve an overall P ⋆ FA = 10 -3 . The obtained results are reported in Fig. 4, where it is evicenced that for λ m (θ b ) < 0.2, the single bin p (m,b) c is still close to the desired value of 10 -5 . On the contrary, if we account for λ m (θ b ) ≈ 2.25, it is even p c = 10 -3 = P ⋆ FA . Obviously, for such values of λ m (θ b ), the system is not robust for target detection in θ b , as it is extremely sensitive to the presence of a target outside the desired direction.

In the following, we try to map generic values of the NCPs λ m (θ b ) to those which can be obtained when massive arrays, as the ones described in [START_REF] Guerra | Application of transmitarray antennas for indoor mapping at millimeter-waves[END_REF], are adopted in practical applications.

Numerical Evaluation of the NCP

Considering the previous results, we now map the obtained NCP λ m (θ b ) into possible real values. In particular, we considered a receiver noise figure F = 4 dB and T 0 = 290 K. A simple and practical solution is to consider free-space propagation from the target to the radar section, and to assume the entire backscattered energy contained into one bin, which represents a worst case scenario. Successively, we dimension λ m (θ b ) according to the expected path-loss of the signal in each bin from a side-lobe direction. We obtained where M is the target radar cross-section in the side-lobe direction,3 G sl (f, θ b ) is the maximum side-lobe gain in the steering direction θ b , S(f ) is the transmitted power spectral density (PSD) and d m is the target-array distance. Note that the PSD has been set so that EIRP, evaluated according to G max , is compliant with the FCC regulations. In our scenario we fixed EIRP= 30 dBm.

λ m (θ b ) = 2γ m (θ b ) = 1 σ 2 W S(f ) • G 2 sl (f, θ b )M c 2 f 2 (4π) 3 d 4 m df (17
As existing antennas, we consider 15 × 15 massive arrays, which are a possible candidate for this kind of applications thanks to their narrow beam [START_REF] Guerra | Application of transmitarray antennas for indoor mapping at millimeter-waves[END_REF], by accounting for a different number of quantization bits which impact in the array pattern. As an example, Table 1 reports different values of G max and G sl at the central frequency f c = 60 GHz. 4 The SLL represents the difference (in [dB]) between the maximum gain and the peak of the main side lobe G sl .

In Fig. 5, λ m (θ b ) values are reported according to different quantization bits, the bin index (i.e. the target distance from the TX/RX) and different values of M . Consequently, according to Fig. 4, we found that λ m (θ b ) is often above 0.2, which was found as a limit value in order to preserve p (m,b) c = p ⋆ FA in the presence of side-lobes. Note that the values of λ m (θ b ) are also strictly related to the steering direction. In fact, when electronically beamsteering is performed, the SLL might increase, as also reported in Table 1. Indeed, also the λ m (θ b ) values change, as clearly evidenced in Fig. 6, especially when a low number of quantization bits is adopted. This effect suggests that the SLL should be treated differently for each steering direction, as it is a key design parameter to be taken into account both for the massive array choice and for the threshold evaluation criterion. From one side, in order to reduce the interfering signal coming from directions different from θ b , it is important to reduce at most the SLL: for example, in our case study, at least 3 quantization bits are required to preserve reliable performance. On the other side, the choice of the massive array could be jointly performed with other operations in order to improve the performance. In fact, different techniques can be adopted in order to counteract side lobes effects on target detection. A possibility could be the adoption of a sidelobe blanker. In particular, a guard channel, which can be omni-directional or adaptive according to the direction, can be implemented to eliminate impulsive interference (hostile or from other neighboring radars) [START_REF] Nickel | Detection with adaptive arrays with irregular digital subarrays[END_REF][START_REF] Richmond | Performance of the adaptive sidelobe blanker detection algorithm in homogeneous environments[END_REF]. Analogously, in [START_REF] Tsao | Reduction of sidelobe and speckle artifacts in microwave imaging: the CLEAN technique[END_REF], a technique to mitigate the image artifacts due to the sidelobes of the random array is reported. All these solutions are appealing, but they can not be adopted due to their computational complexity and the use of coherent receivers.

A simple and effective solution could be the conception of new threshold design strategies, which accounts for both the receiver noise and the impact of the non-central parameters λ m (θ b ). Future works will consider a CFAR approach where the P ⋆ FA and the different level of interferers per bin are used to properly set the threshold.

Conclusions

In this paper we analyzed the impact of massive arrays side-lobes into detection performance for personal radars applications. In particular, in order to keep both the antenna array complexity and the cost low, a discrete set of phase shifts are often adopted for beamforming at the expense of an increased side-lobe level. In these situations, the design of a threshold accounting only for the receiver noise is not sufficient to guarantee the correct functioning of the system in terms of detection performance. In fact, as demonstrated by simulation results, the presence of side-lobes could drastically increase the crossing probability even when there is no target in the steering direction. This effect poses several attentions in the massive array choice according to its maximum SLL. Future studies will investigate the design of a threshold which accounts for the side-lobes effect in each steering direction.

1 TARGET 2 Fig. 1 .

 121 Fig.1. Considered scenario, where for a steering direction θ b , the signal reflected from a target in the side-lobe direction is collected.

ξFig. 2 .

 2 Fig. 2. Example of energy detector output, where energy-bins are compared with the threshold and might cause errors in the localization procedure.

Fig. 3 .

 3 Fig. 3. Threshold choice in order to guarantee the target p ⋆ FA .

Fig. 4 .

 4 Fig. 4. Bin-crossing probability when the threshold ξ⋆ of Fig. 3 is adopted.

3Fig. 5 .

 5 Fig. 5. NCP values for different values of M and for θ b = 0 • .

3Fig. 6 .

 6 Fig. 6. NCP values for different values of M and for θ b = 20 • .

Table 1 .

 1 SLL and maximum gain at fc = 60 GHz for different phase compensation conditions.

		θ b = 0 •			θ b = 20 •
	Quantization Gmax [dBi] SLL [dB]	Quantization Gmax [dBi] SLL [dB]
	Perfect	27.1	23.3	Perfect	26.8	22.8
	3 bits	26.9	24.6	3 bits	26.5	20.7
	2 bits	26.4	20.6	2 bits	25.9	19.4
	1 bit	23.5	16.8	1 bit	22.2	13.6

This operation is necessary since the receiver is energy-based.

From[START_REF] Slepian | Eigenvalues associated with prolate spheroidal wave functions of zero order[END_REF], the threshold is accurate for large values of N , whereas for low W TED values, approximations could improve the accuracy of the threshold. Here we kept N = 2 W TED since the effects do not affect the validity of the analysis.

Note that here we neglected the dependency of M with the frequency.

The values account also for the spillover loss when massive arrays, such as transmitarrays[START_REF] Clemente | Wideband 400-element electronically reconfigurable transmitarray in X band[END_REF], are excited with an external source.

Acknowledgments

This research was supported in part by the IF-EF Marie-Curie project MAPS (Grant 659067) and by the European H2020 project XCycle (Grant 635975).


Francesco Guidi
email: francesco.guidi@cea.fr

Anna Guerra
email: anna.guerra3@unibo.it

Davide Dardari
email: davide.dardari@unibo.it

Antonio Clemente
email: antonio.clemente@cea.fr

Raffaele D'errico
email: raffaele.derrico@cea.fr

Environment Mapping with Millimeter-wave Massive Arrays: System Design and Performance

Keywords: Millimeter-waves, massive antenna arrays, indoor mapping, personal radar

Recently, several studies have been moving towards the idea to adopt massive arrays for localization and mapping applications thanks to the high scanning resolution achievable. In this framework, this paper investigates the impact of different design parameters in order to maximize the mapping performance while keeping the receiver architecture as simple as possible when a Bayesian approach is used. To this end, thresholding strategies to filter out unwanted received signal components (cleaning operation before soft mapping), e.g. thermal noise, are analyzed together with other design parameters that can operate directly on raw data. Considerations about possible system design configurations are then drawn inspired by results obtained using measured data, which showed a more pronounced impact of the cleaning approach for 1 GHz bandwidth with respect to 3 GHz.

I. INTRODUCTION

Nowadays, several studies are focusing towards the miniaturization and the adoption of large scale arrays [START_REF] Hong | Study and prototyping of practically large-scale mmwave antenna systems for 5G cellular devices[END_REF] for several ranging and localization applications, such as mobile communication [START_REF] Roh | Millimeter-wave beamforming as an enabling technology for 5G cellular communications: theoretical feasibility and prototype results[END_REF], simultaneous localization and mapping (SLAM) [START_REF] Dissanayake | A solution to the simultaneous localization and map building (SLAM) problem[END_REF], [START_REF] Jose | Predicting Millimeter Wave Radar Spectra for Autonomous Navigation[END_REF] or personal radars [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF], thanks to the possibility to achieve a precise and high-scanning resolution given by the large number of adopted antennas [START_REF]High-accuracy localization for assisted living[END_REF]- [START_REF] Clemente | Wideband 400-element electronically reconfigurable transmitarray in X band[END_REF].

In traditional SLAM, a robot equipped with a laser-based radar or a camera (visual SLAM) moves in an unknown indoor environment and is able to reconstruct a map of it while inferring its own position and orientation inside the generated map [START_REF] Dissanayake | A solution to the simultaneous localization and map building (SLAM) problem[END_REF]. The main shortcomings of traditional approaches are mainly related to technological aspects. Indeed, laser-based radar as well as camera-based systems work well only in perfect visibility conditions and they require a mechanical steering in order to perform a scanning operation [START_REF] Jose | An augmented state SLAM formulation for multiple line-of-sight features with millimetre wave radar[END_REF]. Instead, when moving towards human-centric systems, as for example personal radars [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF], electronic steering capabilities are highly appreciated to reduce the user active participation to the mapping process and to overcome the shortcomings of laser.

When considering millimeter-wave (mmW) massive arrays, different technological issues could arise. In fact, a tradeoff has to be met to assure electronic steering capabilities, high directivity, low side-lobes as well as to maintain the array complexity and cost low. In [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF], [START_REF] Guerra | Millimeter-wave personal radars for 3D environment mapping[END_REF], [START_REF] Guerra | Millimeter-wave backscattering measurements with transmitarrays for personal radar applications[END_REF], mapping Motivated by this background, in this paper we exploit real measured data to investigate and propose different techniques to ameliorate the mapping capabilities of a low complexity and cost non-coherent receiver, based on mmW massive arrays, for personal radars applications. In our specific scenario, a unique receiver section is considered where the signals received at each antenna branch are properly combined by phase shifters blocks. We propose also a cleaning operation in which the threshold strategy is intended to improve the mapping performance. By investigating the impact of different design parameters, we show that environment reconstruction can become more reliable.

The rest of the paper is organized as follows. Sec. II describes the system model whereas Sec. III reports some details related to the mapping algorithms considered, and some of the key parameters involved for the design of the algorithm. Finally, in Sec. IV mapping results are reported and commented. Sec. V concludes the work.

II. SYSTEM MODEL

We consider a personal radar in monostatic configuration, i.e. with TX and RX sections co-located, which moves in the surrounding space and, for each position, it performs a scanning operation by steering its beam in different N steer directions. For each steering direction θ b , a train of N p pulses with bandwidth W is transmitted. To perform radar-like operations, we consider a noncoherent approach based on energy measurements, according to the receiver architecture reported in Fig. 2. As it can be noticed, the received signals at each antenna branch are properly combined by phase shifters blocks to maximize array gain in a particular direction in space. Then the collected responses are filtered to eliminate the out-of-band noise. From the filtered received signals, energy bins are evaluated during a time frame T f after the transmission of each pulse by considering N bins = ⌊T f /T ED ⌋ time slots (bins) of duration T ED ≈ 1/W . Energy measurements are accumulated for each time bin over the N p frames of the interrogation signal. The accumulated measured energy vector, containing the values for all the steering directions at the output of the receiver, is defined as e = [e 11 , . . . , e 1Nbin , . . . , e bs , . . . , e Nsteer1 , . . . e NsteerNbin ] T [START_REF] Hong | Study and prototyping of practically large-scale mmwave antenna systems for 5G cellular devices[END_REF] where [•] T indicates the transpose operation and e bs is given by

e bs = Np-1 l=0 s TED (s-1) TED y 2 (t + lT f , θ b ) dt (2)
with s = 1, 2, . . . , N bin , b = 1, 2, . . . N steer and where we have indicated with y(•) the received filtered signal.

Then, two different steps can be followed: (i) a soft decision mapping (Fig. 2-top), where data are directly included in the mapping algorithm; (ii) a cleaning procedure on the measured energy vector in order to limit the impact of unwanted components in the mapping approach. Thus, based on these two different approaches, it is possible to infer the map of the explored environment by exploiting the algorithm defined in Sec. III.

III. MAPPING ALGORITHM

In the considered approach, measured energy bins are included in the mapping algorithm. In particular, we consider the grid-based state-space model for probabilistic mapping in [START_REF] Guerra | Millimeter-wave personal radars for 3D environment mapping[END_REF], where performance is investigated by means of real measured data. To this purpose, we assume that the radar orientation and trajectory are known.

We represent the environment with a grid of N L = X grid Y grid cells, where each cell is associated with a root radar cross section (RRCS) value to be inferred by the estimation process. 1As it will be described later, the choice of cell size impact both the mapping accuracy and the computational complexity.

Algorithm 1: Mapping algorithm including measured data.

Input: N p , T , position p initialized to p = p 1 , with p 1 ∈ T being the initial radar position. 1 Initialize the state vector and the covariance matrix 2 while p ∈ T do

• Collect a new radar energy measurement ;

• Time Update (Prediction); 1) Estimate the mean of the state to the next trajectory point; 2) Estimate the covariance matrix to the next trajectory point.

• Measurement Update (Correction); 1) Compute the innovation by comparing the measurement with the prediction related to the previous trajectory point; 2) Compute the extended Kalman-Filter (EKF) update; 3) Update the estimate of the state; 4) Update the covariance matrix. Go to the next radar position

return RCS value for each grid point

The mapping algorithm is reported in Algorithm 1, where we considered T = [p 1 , ..., p NPOS ] the vector containing the N POS radar positions (i.e. the spatial coordinates) inside the room. Moreover, since we accounted for a stationary environment, the transition model is neglected. In particular, we assume the following state vector of the system

x(k) = m(k) = [m 1 (k), . . . , m i (k), . . . , m NL (k)] T ( 3
)
where k is the discrete time instant and m i (k) indicates the RRCS of the ith cell of the grid, where the frequency dependency has been neglected. In case a soft mapping approach is considered, the mapping process is not preceded by a detection phase related to the vector e(k) containing the accumulated measured energy at the output of the receiver at time k. The corresponding Gaussian observation model z(k) is fully described in [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF].

According to [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF], [START_REF] Guerra | Position and orientation error bound for wideband massive antenna arrays[END_REF], the map estimation process is performed by adopting the EKF method to efficiently evaluate the posterior distribution p(x(k)|e(1 : k)) of x(k) given the set of measurements e(1 : k) = {e(1), e(2), . . . , e(k)}, from which a maximum a posteriori estimate of the state x(k) is derived.

Differently from the literature, here a detection phase is not accounted for in the mapping process. In the following, we briefly describe a simple approach to reduce the impact of noisy bins into the algorithm herein reported.

A. Cleaning of Measured Data

Define now, for each energy bin, the energy detector test

Λ bs = e bs D1 ≷ D0 ξ bs (4)
where ξ bs being the threshold for the bth steering direction and sth bin, and D 1 and D 0 represent the two states in which the target in the θ b steering direction and for the sth time overcomes or not the threshold, respectively. The presented decision rule consists in Assign:

P w T f , if D 0 e bs , if D 1 (5)
where

P w = σ 2 TEDNp T f
is the power noise. Contrarily to classical detection schemes, where the bins below the threshold are discarded, here they are assigned to a fix value to let the mapping algorithm to converge quickly, as P w T f represents the initialization value of the cells. To mask noisy bins, the threshold can be designed accounting for a global requirement on the probability of false alarm (PFA) P ⋆ FA for the bth steering direction, which can be written as

P ⋆ FA = 1 - N bins s=1 1 -p (FA) bs ≈ N bins • p FA ( 6
)
where it is assumed that all bins N bins are statistically independent for a steering direction, and p (FA) bs ≪ 1. Consequently, the required p ⋆ FA per bin can be expressed as

p ⋆ FA ≈ P ⋆ FA N bins (7)
which gives a constant threshold per bin given by

ξ bs = ξ = 2 Inv Γ N 2 , P ⋆ FA N bins ( 8
)
where Inv Γ (•, •) is the inverse gamma regularized function, and N = N p 2W T ED is the number of degrees of freedom.

Note that with such approach, the threshold does not depend on the bin and steering index, i.e. ξ bs = ξ, and it is set to keep the PFA due to the receiver noise to a desired value P ⋆ FA .

B. Design Parameters Impact

According to the previously defined mapping algorithm, we have different competing effects entering the mapping algorithm.

A key design parameter is represented by the transmitted number of pulses N p . In fact, the higher it is, the higher will Reduced noisy bins vs level of complexity be the signal-to-noise ratio (SNR) of the accumulated received waveforms. On the other side, increasing too much N p implies a higher transmitted power. Last but not least, consider the scanning time per position defined as

T scan = N steer • T ob = N steer • N p • T f . ( 9
)
where T ob is the observation time. If the system is constrained by a certain scanning time, N p should be preserved as low as possible.

Another possibility is to reduce the maximum range, i.e. the number of bins, with the purpose to avoid the inclusion of noisy bins into the mapping process. Such procedure has to account for the environment characteristics (which are not a-priori known), and thus the parameters should be cautiously changed. In addition, if too many bins are discarded, there is the risk to waste useful source of information. The alternative is to reduce T f with the problem to have a system affected by inter-frame interference.

As also shown in [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF], the bandwidth W impact the mapping resolution, thus if possible it has to be increased with an augmented impact of array non-idealities into the performance.

Another important parameter is the grid size: the lower it is, the more accurate is the environment representation. On the other side, the computational complexity is increased as a more complex state vector has to be updated.

In the numerical results, we briefly investigate how the parameters and techniques impact the performance.

IV. RESULTS

A. Measurement Campaign

In order to validate the personal radar concept, a measurements campaign has been conducted at CEA-Grenoble in a corridor, where we adopted transmitarrays (TAs) which are a possible candidate for massive arrays applications [START_REF] Guerra | Millimeter-wave backscattering measurements with transmitarrays for personal radar applications[END_REF].

We connected a 4-ports Vector Network Analyzer (VNA) operating in the frequency range 10 MHz-24 GHz with 2 mmW converters (frequency range 50 GHz-75 GHz) and to 2 linearly polarized TAs (size 20 × 20, 1 bit, F/D = 0.5) with gain 23.1 dBi [START_REF] Kaouach | Wideband low-loss linear and circular polarization transmit-arrays in V-band[END_REF]. The two TAs were placed in a bistatic configuration on a X-Y-Azimuth positioner, spaced apart of 0.16 m to reduce the antenna coupling and to separate the transmitting and receiving channels. Measurements have been collected in 12 different positions spaced of 0.405 m in the frequency range between 55 -70 GHz with a step of 5 MHz. Thanks to mechanical rotations (the TAs exploited for measurements were not electronically reconfigurable), the X-Y-Azimuth positioner rotates the radar in the semi-plane from -90 • to 90 • with a step of 5 • according to the TA half power beamwidth (HPBW).

B. Mapping Results

We now report mapping results using the previously described algorithm, and by varying the parameters of interest in order to investigate the achievable performance. If otherwise indicated, we consider a noise figure of N F = 4 dB, T 0 = 290 K and a signal bandwidth of W = 1 -2 -3 GHz (with T ED = 1/W ). We account for root raised cosine (RRC) pulses centered at frequency f c = 60 GHz and roll-off factor α = 0.6, compliant with Federal Communications Commission (FCC) mask at 60 GHz [START_REF]Revision of Part 15 of the Commissions Rules Regarding Operation in the 57-64 GHz Band[END_REF] by considering an effective radiated isotropic power (EIRP) of 30 dBm. The time frame has been set to T f = 100 ns, and thus a maximum range MR = 15 m is considered.

a) Impact of System Design Parameters: We first report the impact of the bandwidth in the mapping performance, as it was also deeply analyzed in [START_REF] Guerra | Millimeter-wave backscattering measurements with transmitarrays for personal radar applications[END_REF]. In fact, Fig. 3 shows that by increasing the bandwidth it is possible to improve the mapping resolution and, for example, the contour of walls in the environment.

Then, Fig. 4 reports results for a grid cell size of 0.2 × 0.2 m 2 . The prize of a reduced complexity is paid in terms of highly degraded map resolution. Consequently, during the design of the system, it is preferable to reduce as much as possible the size of the grid cells. In our specific case, 0.1 × 0.1 m 2 has been found as a good compromise.

Successively, we investigate the impact of reducing N p for different bandwidths. As shown in Fig. 5, the measured SNR could be dramatically affected in certain areas of the perimeter. Consequently, N p = 100 represents a good choice to achieve reliable SNR for the considered environment, at the prize of around 3.3 times the scanning time needed for N p = 30. On the other side, it is expected that this parameter could limit the performance in other environments, so its variations should be carefully considered. If from one side part of measured data is wasted by reducing the maximum range, it is not possible to reduce T f to avoid inter-frame interference, as T f should be chosen to accomodate the entire backscattered response.

b) Approach with Filtered Energy Values: We successively apply the threshold to measured data, in order to avoid the contribution of undesired components into the mapping algorithm. To this purpose we adopted the following three approaches: (approach 1) exploitation of the threshold ξ derived in (8); (approach 2) the threshold is set by lowering the maximum measured power in p 1 of 24 dBm; (approach 3) the maximum measured power in p 1 is lowered of 18 dBm. Note that the second and third approaches were conceived in order to mask higher non-ideal radiation pattern effect (i.e. those coming from side-lobes).

Results are reported in Fig. 7 and 8 for the three approaches and different W . As it is possible to observe, when the threshold is set to mask the noise only, i.e. with approach 1, the performance variations with respect to Fig. 3 are not evident. On the other side, by increasing the threshold, i.e. by using approaches (2) and (3), the artifacts are reduced with a rough degradation of the contour of the corridor, especially for W = 3 GHz and approach 3. Consequently, we remark that the cleaning technique is more useful when W = 1 GHz, and thus it could be a good compromise for real applications where the bandwidth is limited by the available technology.

In summary, the best option seems to be the exploitation of a 3 GHz bandwidth by limiting the maximum range. On the other side, this solution can work well in the considered scenario, but it could dramatically reduce the map reconstruction in other larger environments. The joint choice of N p = 100 with a smaller grid size lets to achieve good mapping performance. The adoption of a threshold seems more indicated whenever a system with 1 GHz is considered. Furthermore, it could be interesting to relate the approaches 2 and 3 herein considered to the massive arrays characteristics, as in part proposed in [START_REF] Guidi | Joint energy detection and massive arrays design for localization and mapping[END_REF]. V. CONCLUSIONS

In this paper we investigated the impact of different design parameters into the mapping performance when mmW massive arrays are used for personal radars applications. In particular, by means of measured data and of a grid-based Bayesian statespace approach for map reconstruction, we showed the impact of different design parameters as well as of cleaning approach for measured data. In particular, from the obtained results we experienced that the joint adoption of W = 3 GHz, N p = 100 and 0.1 × 0.1 m 2 grid size cells let to achieve good mapping performance, which can be further improved with a reduction of the maximum range MR. On the other side, MR has to be cautiously diminished not to lose useful information from the measured energy vectors.

From the obtained results it has also been evidenced that if the bandwidth is limited to 1 GHz, a cleaning approach is helpful to improve the performance. To this purpose, enhanced algorithms could be conceived in order to account for the adopted massive arrays characteristics into the algorithm design (i.e. side-lobes).

Fig. 1 .

 1 Fig. 1. Personal radar scenario.

Fig. 3 .

 3 Fig. 3. W impact. RCS results for Np = 100, cell size 0.1 × 0.1 m 2 , MR = 15 m and no cleaning. Top-left: W = 1 GHz. Top-right: W = 2 GHz. Bottom: W = 3 GHz.

Fig. 4 .

 4 Fig. 4. Cell size impact. RCS results for Np = 100, cell size 0.2 × 0.2 m 2 , MR = 15 m and no cleaning. Top-left: W = 1 GHz. Top-right: W = 2 GHz. Bottom: W = 3 GHz.

Fig. 6

 6 Fig.6reports instead the impact of the maximum range by discarding the bins after MR = 10 m, MR = 5 m or MR = 2 m. Due to the environment chosen for measurements, we experienced a drastic performance improvement only for MR = 2 m. On the other side, it is expected that this parameter could limit the performance in other environments, so its variations should be carefully considered. If from one side part of measured data is wasted by reducing the maximum range, it is not possible to reduce T f to avoid inter-frame interference, as T f should be chosen to accomodate the entire backscattered response.b) Approach with Filtered Energy Values: We successively apply the threshold to measured data, in order to avoid the contribution of undesired components into the mapping algorithm. To this purpose we adopted the following three approaches: (approach 1) exploitation of the threshold ξ derived in (8); (approach 2) the threshold is set by lowering the maximum measured power in p 1 of 24 dBm; (approach 3) the maximum measured power in p 1 is lowered of 18 dBm. Note that the second and third approaches were conceived in order to mask higher non-ideal radiation pattern effect (i.e. those coming from side-lobes).Results are reported in Fig.7 and 8for the three approaches and different W . As it is possible to observe, when the threshold is set to mask the noise only, i.e. with approach 1, the performance variations with respect to Fig.3are not evident. On the other side, by increasing the threshold, i.e. by using approaches (2) and (3), the artifacts are reduced with a rough degradation of the contour of the corridor, especially for W = 3 GHz and approach 3. Consequently, we remark that the cleaning technique is more useful when W = 1 GHz, and thus it could be a good compromise for real applications where the bandwidth is limited by the available technology.In summary, the best option seems to be the exploitation

Fig. 5 .Fig. 6 .

 56 Fig. 5. Np impact. RCS results for Np = 30, cell size 0.1 × 0.1 m 2 , MR = 15 m and no cleaning. Top-left: W = 1 GHz. Top-right: W = 2 GHz. Bottom: W = 3 GHz.

Fig. 7 .

 7 Fig. 7. Cleaning approach for W = 1 GHz. RCS results for Np = 100, cell size 0.1 × 0.1 m 2 , MR = 15 m. Top-left: approach 1. Top-right: approach 2. Bottom: approach 3.

Fig. 8 .

 8 Fig. 8. Cleaning approach for W = 3 GHz. RCS results for Np = 100, cell size 0.1 × 0.1 m 2 , MR = 15 m. Top-left: Approach 1. Top-right: approach 2. Bottom: approach 3.

We choose to estimate the RRCS (with sign) instead of the radar cross section (RCS) because we model it as a Gaussian random variable.

ACKNOWLEDGMENT

This work has been supported in part by the H2020-EU.1.3.2 IF-EF Marie-Curie project MAPS (Grant 659067) and by the European H2020 project XCycle (Grant 635975).


Anna Guerra

Francesco Guidi
email: francesco.guidi@cea.fr

Lilia Ahtaryieva

Nicolo Decarli

Davide Dardari
email: davide.dardari@unibo.itlilia.ahtaryieva@studio.unibo.it

Crowd-based personal radars for indoor mapping using UWB measurements

Keywords: UWB, SLAM, indoor mapping, personal radar

teaching and research institutions in France or abroad, or from public or private research centers.

I. INTRODUCTION

Next Internet of Things (IoT) scenarios are expected to enable people and objects sharing their information in real time. Interconnected electronic devices acquire and exchange information on the surrounding world, thus creating a digital representation (mapping) of the real world into the so called smart space [START_REF] Palattella | Internetofthingsinthe5Gera:Enablers,architecture and business models[END_REF].

In this perspective, personal devices (e.g., smartphones, tablets and wearables) could represent a great sources of information allowing users to achieve an augmented ambient awareness thanks to the development of crowd-based applications. These latter, based on the "power of crowd", are expected to dramatically increase in their adoption thanks to the extreme connectivity and data sharing guaranteed by next 5th generation (5G) mobile devices [START_REF] Wu | Smartphones based crowdsourcing for indoor localization[END_REF]. The mobile crowd sensing paradigm has been intensely investigated [START_REF]Mobile crowd sensing[END_REF], but, as the amount of data transferred can be huge, efficient compression schemes must be devised in view of what can be defined as an "acceptable information loss" in the mapping process. Moreover, tracking and localization in indoor scenarios still remains very challenging and a matter of research studies. SLAM-oriented solutions based on lidars or on vision technologies have been proposed in literature but, despite their capabilities of reconstructing environments, they need perfect visibility conditions to operate and require human active participation in the exploration process. To overcome these shortcomings, the concept of a smart personal radar has been recently proposed in [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF] as well as the adoption of dedicated high gain massive arrays for this kind of application [START_REF] Guerra | A p p l i c a t i o no ft r a n s m i t a r r a ya n t e n n a sf o ri n d o o rm a pping at millimeter-waves[END_REF]. In these works, the personal radar is based on a massive array operating at millimeter-wave (mmW) frequencies able to electronically scan the surrounding environment and to reconstruct a map of it. The choice of these technologies has been driven from one side to allowing the integration of massive arrays in small size, to the other by the necessity of achieving a high-definition distance estimate and very narrow steering beams which allow a high level of mapping reconstruction.

Contrarily, in this paper, the possibility of realizing a crowd-based personal radar working at ultrawide-band (UWB) frequencies for indoor environments mapping is investigated. If from one side, the possibility to adopt a near-pencil beam antenna could be lost, on the other side, the complexity reduces because a technological shift for the system realization is not yet necessary. The main novelty in the mapping approach is that the crowd will be involved in this process by freely moving within the space to be mapped, providing partial views of the users' surroundings and sending them to cloud servers, where they will combined to form a more complete and less uncertain map. Such information will be then available to all users again for possible mapping refinements and for providing an infrastructure-less, low-cost, and highly accurate indoor localization system. The rest of the paper is organized as follows. Sec. II describes the measurement set-up and the considered UWB radar. Sec. III presents the mapping algorithm and finally, Sec. IV describes the case study and discuss the obtained measurement results. Sec. V concludes the work.

II. UWB INDOOR MEASUREMENTS

In order to validate the crowd-based personal radar concept, ameasurementcampaignhasbeenconductedattheUniversity of Bologna -Cesena Campus indoor premises. The considered scenario is shown in Fig. 2, and it consists of an area of 20 × 20 m 2 with two possible trajectories. Fig. 3 shows two photos taken during the measurement campaign. The measurement set-up consists of a Novelda R NVA-R661 impulse radar 1 connected to two UWB sinouos antennas with dielectric lenses and to a personal computer, placed on a mechanical positioner.

The considered antennas, operating in the bandwidth 6-8.5 GHz, present a gain of 6.7 dBi with an half power beam width (HPBW) of 40 • .T h eU W n t e n n a sa r ep l a c e di na quasi-monostatic configuration and spaced apart of 0.14 m. Consequently, the effect of antenna coupling is significant and has to be suppressed through a time-gating operation.

The UWB NVA-R661 chip comprises the impulse generator, capable of transmitting short pulses over a large range of frequencies (6-10.2 GHz), a receiver to collect the backscattered environmental response and to provide the band-pass samples of the received waveform.

Measurements have been collected in different positions spaced of 0.6 mi na c c o r d a n c ew i t ht h et w oc o n s i d e r e dp a t h s . At each measurement step, measurements have been collected from 8 different angles (i.e., the set of observation angles have been set to

O = {0 • , 45 • , 90 • , 135 • , 180 • , 225 • , 270 • , 315 • })
according to the sinuous antennas HPBW. To make the measurement set-up easily manageable, a rotating radar support position was placed on a trolley with wheels, as shown in Fig. 3. For each position and each steering direction, N p =1 0 0 pulses have been transmitted with a central frequency of 6.8 GHz and a bandwidth W =3 GHz. Starting from the collected received signals, two receiver schemes, whose block diagram is shown in Fig. 4, have been analysed. According to the receiver A (Fig. 4-top), first the received signals are accumulated to enhance the signal-to-noise ratio (SNR) and successively, the energy profile is computed; considering the receiver B (Fig. 4-bottom), energy profiles have been accumulated over the total number of emitted signals. The first approach could result in higher performance but at the expense of a higher receiver complexity while the second one is more appealing to be implemented in practical systems thanks to its simplicity, at the expense of a lower SNR. In both cases, before creating the energy profiles database, post-processing operations on the raw collected data have been performed to filter out the out-of-band interference and noise, and to suppress the coupling between the two UWB antennas.

In Figs.

III. MAPPING ALGORITHM

The described measurement campaign was conducted to enable the offline creation of the environment mapping by inferring the RCS of the surrounding objects. To this purpose, the extended Kalman filter (EKF) based probabilistic statespace approach described in [START_REF] Guerra | A p p l i c a t i o no ft r a n s m i t a r r a ya n t e n n a sf o ri n d o o rm a pping at millimeter-waves[END_REF] and reported in Algorithm 1 has been adopted. Differently from previous works, here, a crowd-based mapping approach is adopted in which the state estimation process could benefit from different users measurements. Specifically, referring to Fig. 2, 2 users following path Aareconsideredintheenvironmentandother2 moving along path B with the same moving direction. At each time instant, Bin index

e(θb =0 • ) [J]
Fig. 5. Accumulated received signal using the receiver A and energy profile using the receiver B over Np =1 0 0pulses.

the measurements of each users are exploited to estimate the updated version of the map by using the Algorithm 1.

To this end, the environment has been discretized in N L = X grid Y grid cells, and a RCS value, which has to be estimated at the end of the mapping process, has been associated to each cell. According to the considered approach, the state vector of the system, that contains the parameters to be estimated in order to reconstruct the map, is given by

x(k)=m(k)=[m 1 (k),...,m i (k),...,m NL (k)] T ( 1
)
where k is the discrete time instant and m i (k) indicates the root radar cross section (RRCS) of the ith cell of the grid, where the frequency dependency has been neglected. To simplify our analysis, the environment is considered stationary with good approximation, with the possibility to neglect the transition model. The main difference of the algorithm herein exploited with respect to the other approaches, is that in our case the mapping procedure is not preceded by a detection phase as in [START_REF] Jose | An augmented state SLAM formulationf o r multiple line-of-sight features with millimetre wave radar[END_REF], [START_REF] Jose | PredictingMillimeterW aveRadarSpectraforAutonomous Navigation[END_REF]. In fact, in our case the vector e(k) containing the accumulated measured energy at the output of the receiver at time k is directly handled in the Gaussian observation model z(k) fully described in [START_REF] Guidi | Personal mobile radars with millimeter-wave massive arrays for indoor mapping[END_REF]. Thus, once

IV. MAPPING RESULTS

We now describe the mapping results obtained with the proposed model by including real measured data. As a metric for the environment reconstruction, the reconstructed RCS values is juxtaposed to the environment map in which the measurements took place. In the adopted grid-based approach, different grid cells size have been considered in order to study the trade-off between computational complexity and mapping accuracy. To emulate the crowd sourcing mechanism, four different users are accounted for: two moving along path A in the same direction, and the same for path B.

Fig. 6 shows examples of maps reconstructed by the 2 couple of users. In particular, Fig. 6-( not otherwise indicated. As it is possible to observe, despite it is possible to recognize walls and environment shapes, maps look incomplete. Then, by following the crowd-based principle, maps were fused together decreasing the single user uncertainty of the surrounding. First complete mapping results are reported in Fig. 7-top where the maximum range is imposed to 2 mt o reduce the inclusion of noisy energy bins. As it is possible to observe, the obtained results shown in Fig. 7-(a) are better performing and could be considered satisfactory due to the adoption of low directional antennas and the power emission constraints required by UWB technology. Note that the grid cells area and the radar maximum range are two important parameters in defining the mapping accuracy and the algorithm computational complexity. In Fig. 7-(b), a map obtained by discretizing the environment into a grid cells of 0.5 × 0.5 m 2 and a radar maximum range set to 5.3 mi sr e p o r t e d .I nt h i s case, the environment is completely reconstructed as before but the map contour does not exactly follow the walls due to the fact that the resolution is worsen with respect to the previous case.

Finally, the mapping result employing receiver B is reported in Fig. 8. As expected in this case, the mapping accuracy slightly degrades compared to Fig. 7-(a) but still remains acceptable.

V. C ONCLUSIONS

In this paper we presented an indoor backscattering measurement campaign at UWB frequencies for personal radar mapping applications. By combining different users' information, we showed that a good mapping accuracy could be reached. Moreover, we investigated the trade-off between algorithm complexity and mapping accuracy by comparing two receiver schemes and grid discretization. Future steps are intended to analyse better ways for data fusion, and how the prior knowledge on the correlation state between cells impact the mapping performance.

Fig. 1 .

 1 Fig. 1. Crowd-based mapping using personal radars.

Fig. 2 .

 2 Fig. 2. Map of the considered scenario consisting of two main paths where p A (1) is the starting position for users 1-2 and p B (1) for users 3-4.

  Fig. 3. Indoor measurements.

Fig. 4 .

 4 Fig. 4. Receiver schemes.

  5, an example of accumulated received signal according to the receiver A and an example of accumulated energy profile according to the receiver B are shown. In particular, they are collected in position p A (1),f o ras t e e r i n g direction equal to θ b =0 • .T h ee n e r g yp r o fi l eh a sb e e no btained by considering N bin time bins of duration T ED =1/W .

Algorithm 1 : 4 Correction and update step; 5 6 Compute the EKF update 7

 14567 Mapping Algorithm Data: Np, T set of positions in the considered trajectory, p(k)=p(1) the initial radar position Result:r a d a rc r o s ss e c t i o n( R C S )m a po ft h ee n v i r o n m e n t 1 Initialization 2 while p(k) ∈T do 3 Measurement step ◃ e(k) Compute the innovation ◃ e(k) -ẑ(k|k -1) Update the state ◃ x(k|k) 8 Update the observation ◃ ẑ(k|k) 9 Time Update (Prediction) 10 Predict the state ◃ x(k +1|k) 11 Predict the observation ◃ ẑ(k +1|k) 12 Go to the next radar position. ◃ p(k) → p(k +1)

Fig. 6 .

 6 Fig. 6. Reconstructing map using by different users using ther e c e i v e rA , A cell =0 .2 × 0.2 m 2 , R =2m.

Fig. 7 .

 7 Fig. 7. Reconstructing map using the receiver A, different sized grid cells and radar maximum range conditions.

Fig. 8 .

 8 Fig. 8. Reconstructed map using the receiver B, 4 users, a grid cell area of A cell =0 .2 × 0.2 m 2 ar a d a rm a x i m u mr a n g eo fR =2m.

ACKNOWLEDGMENT

This work has been supported by the H2020 project XCycle and in part by the H2020-EU.1.3.2 IF-EF Marie-Curie project MAPS (Grant 659067).


Francesco Guidi
email: francesco.guidi@cea.fr

Nicoló Decarli
email: nicolo.decarli@unibo.it

Davide Dardari
email: davide.dardari@unibo.it

Francesco Mani
email: francesco.mani@cea.fr

Raffaele D'errico
email: raffaele.derrico@cea.fr

Passive Millimeter-Wave RFID using Backscattered Signals

Keywords: RFID, Millimeter-Waves, Backscatter Modulation

In this paper we investigate the possibility to jointly adopt millimeter-wave technology with passive RFID based on backscattered signals, which paves the way to new identification and localization applications for next 5G scenarios. In particular, we assess the feasibility of this solution by comparing it with the passive RFID in the microwave UWB band. Results show that, despite the high path-loss at 60 GHz, it is possible to achieve interesting performance thanks to the less stringent requirements in terms of emitted power with respect to the UWB technology. Moreover, the possibility of localizing tags with a single reader is foreseen thanks to the adoption of narrow-beam antennas and beamsteering operations.

I. INTRODUCTION

Next Internet of Things (IoT) and fifth generation (5G) communication scenarios are expected to bring an increased connectivity between people and the surrounding environment, foreseeing a pervasive presence of tagged objects [START_REF] Boccardi | Five disruptive technology directions for 5G[END_REF]. Among the expected key technologies, radiofrequency identification (RFID) has attracted a great interest in the recent years. It has been adopted to overcome current bar-codes limitations in the short reading distance, with the opportunity to detect and identify batteryless tags attached to objects placed even at several meters from the reader. Current Gen. 2 ultra-high frequency (UHF)-RFID is widely exploited and studied [START_REF] Zhang | Item-level indoor localization with passive UHF RFID based on tag interaction analysis[END_REF], and new solutions have been proposed in order to enable tags localization [START_REF] Arnitz | Characterization and modeling of UHF RFID channels for ranging and localization[END_REF]. Recent studies have moved from UHF band to the ultrawide bandwidth (UWB) technology in the 3.1 -10.6 GHz microwave bandwidth in order to integrate the possibility to localize tags as well as to reduce the power consumption [START_REF] Dardari | Ultrawide bandwidth RFID: The next generation?[END_REF], [START_REF] Errico | An UWB-UHF semi-passive RFID system for localization and tracking applications[END_REF]. In particular, the use of passive UWB-RFID solutions has a great appeal in all those applications requiring low-cost as well as good ranging performance. Since passive tags are not equipped with a transmitter, the communication relies on the modulation of the backscattered signal and several techniques were conceived in order to maximize the performance [START_REF] Decarli | Passive UWB RFID for tag localization: Architectures and design[END_REF], [START_REF] Guidi | Analysis of UWB tag backscattering and its impact on the detection coverage[END_REF]. Unfortunately, due to power regulations constraints, it has been shown that passive UWB is strongly limited in terms of reader-tag communication range. Moreover, high accuracy localization requires multiple interrogations from at least three readers. To overcome such limitation, the joint adoption of RFID and millimeter-wave (mmW) technologies is a possible solution. In fact, despite the higher path-loss brought by the technological shift towards higher frequencies (e.g. at 60 GHz), the requirements in terms of power emission are less stringent [START_REF]Revision of Part 15 of the Commissions Rules Regarding Operation in the 57-64 GHz Band[END_REF] than those in the UWB band [START_REF]Revision of Part 15 of the Commission Rules Regarding Ultra-Wideband Transmission Systems, First Report and Order[END_REF] with an available bandwidth up to 7 GHz [START_REF] Boccardi | Five disruptive technology directions for 5G[END_REF], [START_REF] Rappaport | Millimeter wave wireless communications[END_REF]. Currently, only few preliminary studies concern the joint adoption of such technologies, which are at their infancy [START_REF] Pursula | Millimeter-wave identification -a new short-range radio system for low-power high data-rate applications[END_REF]- [START_REF] Pursula | Passive RFID at millimeter waves[END_REF]. In particular, [START_REF] Pellerano | A mm-wave powerharvesting RFID tag in 90 nm CMOS[END_REF] showed a tag which harvests energy from the mmW signal transmitted by the reader, and successively exploits a 60 GHz free-running oscillator to transmit back pulse-width modulated bursts. In [START_REF] Pursula | Passive RFID at millimeter waves[END_REF] instead, the use of a standard UHF-RFID architecture, compatible with that of mmW-RFID, has been proposed. Unfortunately, due to the proposed schemes, the achievable reader-tag ranges are strongly limited by the path-loss.

We aim here to study the feasibility and the opportunities that can be offered by the joint adoption of mmW and RFID technologies when ad-hoc reader-tag architectures are exploited [START_REF] Guidi | Detection of multiple tags based on impulsive backscattered signals[END_REF], and tags are assumed to be woken-up from stand-by mode by exploiting a dedicated signal as detailed in [START_REF] Errico | An UWB-UHF semi-passive RFID system for localization and tracking applications[END_REF]. In particular, we first describe the considered scheme, and successively we present a measurement campaign conducted at 60 GHz in order to enable a preliminary validation of the proposed system through both simulated and measured data.

Note that if near-pencil beam mmW antennas are exploited, the considered scheme could enable tags localization with only one reader which performs beamsteering, with the multi-tags interference phenomenon [START_REF] Guidi | Detection of multiple tags based on impulsive backscattered signals[END_REF] drastically reduced [START_REF] Dardari | The future of Ultra-Wideband localization in RFID[END_REF].

The rest of the paper is organized as follows. In Sec. II, the considered reader-tag signalling scheme and the readertag architectures here exploited are described; successively the measurement campaign is described in III. Finally, numerical results are reported in Sec. IV and conclusions and future perspectives end the paper.

II. SYSTEM ARCHITECTURE

A. Backscattering Principle

The reader-tag communication herein considered is based on the modulation of the backscattered signal. Usually, tags are in sleeping mode and they are woken-up thanks to the transmission of a wake-up signal (e.g., an unmodulated UHF carrier [START_REF] Errico | An UWB-UHF semi-passive RFID system for localization and tracking applications[END_REF]). Once the wake-up procedure is completed, the reader transmits an interrogation pulse train, which is reflected back by tags and objects (see Fig. 1 and Fig. 2). In particular, the signals backscattered by tags are composed of two parts: the structural and the antenna mode component, as depicted in Fig. 1 [START_REF] Decarli | Passive UWB RFID for tag localization: Architectures and design[END_REF]. While the former depends only on the antenna and support shape and materials, the latter is strictly related to how the antenna is loaded and thus it is the part of interest. In the ideal case, the antenna mode scattered waveforms present a phase difference of 180 • between the case of open and short circuit loads, which are usually adopted to discriminate different data symbols. Unfortunately, such signals are usually superimposed with those signals scattered by the surrounding environment (clutter), which could be even a few order of magnitude higher. To counteract such effects, ad-hoc signal processing algorithms have to be conceived in order to achieve long reader-tag reading distances.

B. Transmitted Signal Model

The reader is composed of a transmitter and a receiver section both connected to the same antenna through a TX/RX switch. According to the number of symbols N b in the data packet, during the interrogation phase the reader transmits a sequence of N b •N s pulses, each having energy E p , modulated by the specific reader code, in the form

s(t) = Nb-1 m=0 Ns-1 n=0 d n p(t -n T p -m T s ) (1)
where {d n } is the spreading code of the reader with length N s , and T s , T p are the symbol and frame time, respectively. 1The signal received by the kth tag is then modulated according to a bipolar code c (k) n , for n = 0, 1, . . . , N s -1 and to the data {b m } stored inside it. To extremely simplify the architecture, the backscatter modulator reduces to a simple switch (see Fig. 2). Operating in such a manner it is possible to discriminate a specific reader-tag couple among all the possible combinations. Moreover, the choice of a zero mean code (that is, with the same number of +1 and -1) allows the clutter suppression if the received signals composing one symbol are coherently accumulated [START_REF] Guidi | Detection of multiple tags based on impulsive backscattered signals[END_REF].

In addition, note that the longer the code sequence N s , the higher the reading range because of the higher accumulated signal-to-noise ratio (SNR). On the other side, N s should be limited mainly for two reasons: to reduce the power consumption (i.e., the tag active time), and to reduce the effect of clock drift during the SNR accumulation.

In the following, we describe two possible architectures to post-process the received signal.

C. Receiver Architecture

We foresee the adoption of two possible classical receivers for mmW-RFID: a matched filter (MF), exploitable for kth tag data demodulation, and an energy detector (ED), applicable in all those scenarios requiring low complexity.

1) Matched-Filter Receiver: Define w(t) as the antenna mode backscattered response to the transmitted pulse p(t), which is modulated by the load, and w (c) (t) as the clutter response. When the previously defined scheme is adopted, the kth tag signal of interest results modulated by both the tag code and the information symbol. The received signal can thus be written as

r(t) = k∈T Nb-1 m=0 Ns-1 n=0 d n c (k) n b m w (k) (t -nT p -mT s ) + Nb-1 m=0 Ns-1 n=0 d n w (c) (t -nT p -mT s ) + n(t) (2)
with T being the set of the tags in the environment. The received signal is first passed through a filter having impulse response h (MF) (t) to obtain v(t) = r(t) ⊗ h (MF) (t), where ⊗ is the convolution operator and h (MF) (t) is a local replica template of the received antenna mode component. 2Then, by assuming the intended tag is present, and by supposing perfect code and pulse synchronization, the output of the MF is sampled at time intervals t l,m = lT p + mT s + τ 0 ,3 with l=0, . . . , N s -1, thus obtaining the samples v l,m [START_REF] Dardari | Ultrawide bandwidth RFID: The next generation?[END_REF]. In order to remove the clutter contribution and the interference from other tags, the sampled values are multiplied by the reader and kth useful tag composite sequence and successively accumulated. Thus we can write for the mth symbol

y m = Ns-1 l=0 c (k) l d l v l,m = b m N s E r + z m (3)
where E r is the collected energy per pulse from the kth tag according to the considered template, the clutter has been suppressed thanks to the considered zero-mean codes which give

Ns-1 l=0 c (k) l
= 0 and z m is the thermal noise at the output of the processing scheme. 4 Among the possible choices for h (MF) (t), the simplest solution is the single-path matched filter where the template is chosen to be proportional to the received antenna mode backscattered component at a reference distance and in free-space propagation. In that case, E r reduces with good approximation to the energy of the first received path in line-of-sight conditions [START_REF] Dardari | Ultrawide bandwidth RFID: The next generation?[END_REF]. 5According to [START_REF] Dardari | Ultrawide bandwidth RFID: The next generation?[END_REF], for the considered scheme the bit error probability (BEP) can be written as

P b = 1 2 erfc E r N s N 0 (4)
where erfc(•) is the complementary error function and N 0 is the noise power spectral density. Consequently, the received energy per symbol in ideal conditions is E s = N s E r and, analogously, (4) can be written as

P b = 1 2 erfc P r N 0 R b (5)
where R b = 1/(N s T p ) is the data rate, and P r accounts for the transmitted power and the round-trip channel power gain. Finally, in order to find the required number of pulses to achieve a certain reader-tag distance for a target P ⋆ b , it is possible to write (4) as

N s ≥ Ns = N 0 • erfc -1 (2 P ⋆ b ) 2 E r (6)
which puts in relation the minimum required number of pulses per symbol Ns with the received energy E r .

2) Energy Detector: A simple and practical solution for wideband RFID, especially when the overall system complexity has to be kept low, is represented by the ED architecture which exploits the presence of a square-law device. Since the task here is only to accomplish tag detection, the receiver performs the coherent accumulation of the received signals corresponding to the N s transmitted pulses p(t) within a symbol [START_REF] Guidi | Detection of multiple tags based on impulsive backscattered signals[END_REF]. As for the previous scenario, we assume to have the clock of readers and tags synchronous, and the kth tag as the intended useful one. Then, the signal received back by the reader is expressed as in [START_REF] Zhang | Item-level indoor localization with passive UHF RFID based on tag interaction analysis[END_REF], with b m = 1 ∀ m, which can thus be neglected. According to [START_REF] Guidi | Detection of multiple tags based on impulsive backscattered signals[END_REF], first the received signal is passed through a band-pass filter to eliminate the out-ofband noise, obtaining r(t). Once the signal is filtered, it is de-spread and accumulated, giving

y(t) = Ns-1 l=0 c (k) l r(t+lT p ) (7)
with t ∈ [0, T p ]. From [START_REF] Guidi | Analysis of UWB tag backscattering and its impact on the detection coverage[END_REF], by passing y(t) through an ED, we obtain a vector of energy bins, where each element can be expressed by

e b = b TED (b-1) TED [y(t)] 2 dt (8)
with b = 1, 2, . . . , N bins , T ED being the integration time, and N bins = ⌊T p /T ED ⌋ is the number of bins at the output of the ED. Successively, each element e b is compared with a threshold. If there is at least one element overcoming the threshold, then the tag is assumed detected. Consequently, we have two pieces of information: the kth tag received energy, which can be obtained by the bin value, and the TOA of the received signal, given by the bin index.

There are two figures of merit which can be adopted to evaluate the performance of the considered detection approach: the probability of false alarm (PFA) and the probability of detection (PD). The former stems from the probability to wrongly detect a tag even if it is not present in the scenario, whereas the latter to correctly detect its presence when effectively the intended useful tag is in the considered scenario. To this purpose, performance of passive UWB-RFID has been extensively characterized in terms of PFA and PD [START_REF] Guidi | Detection of multiple tags based on impulsive backscattered signals[END_REF]. In particular, it has been shown that it is possible to achieve the desired performance in terms of PFA and PD by setting the minimum required number of pulses per symbol as

N s ≥ Ns = N 0 2E r Q -1 h P ⋆ D , ξ 2 (9)
where Q h is Marcum-Q function of order h [14], P ⋆ D is the apriori desired PD and ξ is the threshold set for a-priori desired PFA (P ⋆ FA ). 6

III. 60 GHZ MEASUREMENT CAMPAIGN

In order to validate the considered RFID architecture at mmW, a measurements campaign has been conducted at CEA-Grenoble indoor premises (see Fig. 3 and4.). In particular, we measured the S 21 (f ) parameter by placing the reader antenna at different distances from the tag antenna, with the reader antenna pointing towards the tag, as reported in Fig. 4. From this measure, the two-way channel comprising the reader and tag antennas gain can be easily found as H(f ) = S 2 21 (f ) [START_REF] Errico | An indoor backscattering channel characterization for UWB passive RFID applications[END_REF]. Note that the one-way channel is obviously easier to measure than a two-way backscattering channel in terms of SNR. This channel transfer function accounts for the antenna mode The exploited measurement set-up consists of a 4-ports Vector Network Analyzer (VNA) operating in the frequency range 10 MHz-24 GHz connected both to the reader antenna (a horn with 20 dBi gain and half power beamwidth (HPBW) of 20 • ) and to the tag antenna (a 0 dBi gain omni-antenna, reported in Fig. 4), respectively, thanks to two mmW converters operating in the frequency range 50 GHz-75 GHz. Consequently, a central frequency f c = 62 GHz and bandwidth of 6 GHz have been considered.

Table I presents the reader-tag distances considered in the conference room scenario with respect to the tag position, as reported in Fig. 3, which vary from 2.7 m to 6.7 m with a step of 0.8 m. For the planned set of measurements, the reader orientation has been kept constant towards the tag. Moreover, for each measurement point, co-polar and crosspolar measurements have been carried out. The cross-polar data have been obtained by rotating the reader horn antenna by 90 • with the help of a waveguide twist. In this way, we emulated the presence of a tag attached to an object which has been rotated from its expected working condition. In such a way, performance can result to be drastically degraded as shown in the next section.

IV. RESULTS

In this section we characterize the performance of the passive mmW-RFID through both simulation and measurement data. In particular, the comparison with the UWB backscattering based technology is performed in order to assess preliminary system performance. Results are obtained by means of ( 5), ( 6) and ( 9), for a target P ⋆ b = 10 -3 , a P ⋆ FA = 10 -3 and a P ⋆ D = 0.9.

A. Simulation Results

We first compare through simulations the performance of UWB and mmW-RFID in the additive white Gaussian noise (AWGN) scenario. In both cases, we considered the parameters reported in Table II, and a transmitted pulse centered at 4 GHz and 60 GHz, respectively, compliant with the Federal Communications Commission (FCC) mask in the two different bands [START_REF]Revision of Part 15 of the Commissions Rules Regarding Operation in the 57-64 GHz Band[END_REF], [START_REF]Revision of Part 15 of the Commission Rules Regarding Ultra-Wideband Transmission Systems, First Report and Order[END_REF]. The system parameters were selected according to [START_REF] Decarli | Passive UWB RFID for tag localization: Architectures and design[END_REF] for UWB. Consequently, by moving towards 60 GHz, we experience the variation of two parameters: the effective radiated isotropic power (EIRP), which is less stringent at 60 GHz with respect to lower frequencies [START_REF]Revision of Part 15 of the Commissions Rules Regarding Operation in the 57-64 GHz Band[END_REF], and the reader antenna gain which is higher due to the adopted antennas. For what the ED is concerned, we considered an ideal case where all the received energy is contained in one bin.

Figure 5 shows the values of Ns for the two receiver architectures. Note that under the EU mask constraint for UWB, a reading range of about 6.5 m can be achieved adopting Ns ≃ 1.5 • 10 4 for an ED, whereas only around 2 • 10 3 pulses are required for the same distance and conditions at mmW. We have different competing effects: if from one side, mmW-RFID suffers from the high path-loss experienced at 60 GHz, from the other side it benefits from the less stringent power regulations than at 4 GHz [START_REF]Revision of Part 15 of the Commission Rules Regarding Ultra-Wideband Transmission Systems, First Report and Order[END_REF]. In this way, if one of the main requirements is the system refresh rate, which is given by R f = 1/(T s N b ), mmW-RFID is more promising than a UWB solution as T s can be reduced for a given reader-tag distance. Such advantage is mainly given by the significantly power emission allowed in the mmW band to which more energy consumption corresponds. Fig. 6 shows the obtained BEP as a function of the different data rates for passive mmW-RFID by using [START_REF] Errico | An UWB-UHF semi-passive RFID system for localization and tracking applications[END_REF]. If we fix the target BEP to 10 -3 , results show that data rates in the order of 2 Mbit/s for distances around 2 m are achievable.

B. Measurement Results

We here exploit measured data to assess the feasibility of the proposed reader-tag communication scheme. In particular, the backscattering channel impulse response has been convoluted with a root raised cosine pulse centered at 60 GHz and with bandwidth BW= 2 GHz, compliant with the FCC mask. For the ED, we considered an ideal case scenario where the bin with T ED = 1 ns is centered to the received signal with the highest peak. 7 Moreover, for the MF we consider a single path MF whose template is perfectly matched to the received maximum peak pulse, without accounting for pulse distortion 7 With good approximation, it can be associated to the first path for the considered scenario. [4]. In addition, we compare the performance for co-polar and cross-polar measurements, thus simulating the two opposite scenarios for a tag randomly attached to an object. Fig. 7 reports Ns for the two receiver architectures. Now, with Ns ≃ 10 3 , it is possible to achieve p 6 = 6.7 m for a MF, whereas around 10 4 pulses are required for tag detection with an ED architecture. Thus, the performance is a bit degraded with respect to the AWGN scenario because of the simplifying assumptions done in simulations, that is the entire received energy is contained in one bin. On the contrary, it is expected that performance can be improved if architectures closer to ideal matched filters are exploited, thus giving the opportunity to collect the received energy from different multipath components. Note that cross-polar configurations need a really high number of accumulated pulses. This effect is detrimental when the tag orientation is not known or could change. In controlled environments (that is, where the tag orientation is always kept the same) this result could be exploited to limit the interference of close different reader-tag devices to cope with the high polarization loss.

As far as the localization capability is concerned, the adoption of near-pencil beam antennas at reader side could enable the opportunity to perform tags localization through beamsteering operations as well as to further increase the link budget and reduce the clutter. In this way, reliable localization performance is expected to be guaranteed by exploiting a single reader beamsteering [START_REF] Guerra | Position and orientation error bound for wideband massive antenna arrays[END_REF], and future scenarios can foresee the integration of such mmW-RFID readers into portable devices to search and localize the surrounding tags [START_REF] Dardari | The future of Ultra-Wideband localization in RFID[END_REF].

V. CONCLUSION

In this paper we investigated the possibility to adopt mmW technology for passive RFID systems. After briefing introducing the proposed architectures and a mmW measurement campaign, we evaluated the attainable performance by comparing results with those of UWB in the microwave band. Thanks to measured data, a preliminary system characterization has been also performed in a real environment. In ideal conditions we showed that the proposed scheme can outperform the UWB one, because of requiring a lower number of pulses to achieve the same reader-tag distance and consequently a reduced complexity. Future works are expected to investigate ad-hoc tags wakeup procedures, mmW energy-harvesting possibilities, and adhoc low-complexity single reader localization schemes, as well as to extensively characterize the performance for different tags orientations, positions and measurement scenarios.

Fig. 1 .

 1 Fig. 1. Considered RFID scenario.

Fig. 2 .

 2 Fig. 2. Reader-Tag considered architectures for detection and communication.

Fig. 3 .

 3 Fig. 3. Picture with the reader and tag antennas positions.

Fig. 4 .

 4 Fig. 4. Measurement scenario.

FA

Fig. 5 .

 5 Fig. 5. Required number of pulses for different receiver architectures.

Fig. 6 .

 6 Fig. 6. Obtained data rates for different reader-tag distances.

6 Fig. 7 .

 67 Fig. 7. Required number of pulses for different receiver architectures using measured data at 60 GHz.

TABLE II SIMULATION

 II PARAMETERS.

	Parameter	UWB Value	mmW Value
	EIRP	-11 dBm	30 dBm
	Bandwidth W	2 GHz	2 GHz
	Center frequency fc	4 GHz	60 GHz
	Time frame Tp	128 ns	128 ns
	Reader antenna gain Gr	5 dBi	20 dBi
	Tag antenna gain Gt	0 dBi	0 dBi
	Tag losses Lt	2 dB	2 dB
	Receiver noise figure F	4 dB	4 dB
	Desired PFA P ⋆

According to[START_REF] Guidi | Detection of multiple tags based on impulsive backscattered signals[END_REF], the analysis can be extended to multiple readers.

In practical applications, it could be more favorable to down-convert the received signal with a mixer and perform base-band post-processing to reduce the receiver complexity.

We assume that a perfect time-of-arrival (TOA) estimate is available, and consequently the time instant τ 0 is perfectly chosen.

Several codes have been proposed for multi-tag interference suppression[START_REF] Guidi | Detection of multiple tags based on impulsive backscattered signals[END_REF]. Here, since the system is assumed to be perfectly synchronous, classical orthogonal codes for readers and tags can be considered.

It is important to notice that the performance of this solution, and of the others accounting for Rake fingers synchronized to different paths of the received signal, is bounded by ideal matched filters able to collect the entire received energy, that is Er = Tp w 2 (t)dt.

For the herein considered case, ξ does not account for interference signal and for any system non-ideality, but only for the receiver noise.

ACKNOWLEDGMENTS

This research was supported in part by the H2020 IF-EF Marie-Curie project MAPS (Grant 659067) and by the European H2020 project XCycle (Grant 635975). Authors would like to thank Anna Guerra and Antonio Clemente for the fruitful discussions.