# Experimental Demonstration of 73 Gb/s QPSK and 150 Gb/s QAM-32 Wireless Data Links in the Sub-THz Band Through Frequency Selective Surface Filters

Walter Fuscaldo, Daniele Pirrone, Dimitrios C Zografopoulos, Antonio Ferraro, Pascal Szriftgiser, Guillaume Ducournau, Romeo Beccherelli

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Walter Fuscaldo, Daniele Pirrone, Dimitrios C Zografopoulos, Antonio Ferraro, Pascal Szriftgiser, et al. Experimental Demonstration of 73 Gb/s QPSK and 150 Gb/s QAM-32 Wireless Data Links in the Sub-THz Band Through Frequency Selective Surface Filters. IEEE Access, 2025, 13, pp.63556 - 63565. 10.1109/access.2025.3558880. hal-05065660

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Received 11 March 2025, accepted 5 April 2025, date of publication 8 April 2025, date of current version 17 April 2025.

Digital Object Identifier 10.1109/ACCESS.2025.3558880

RESEARCH ARTICLE

# Experimental Demonstration of 73 Gb/s QPSK and 150 Gb/s QAM-32 Wireless Data Links in the Sub-THz Band Through Frequency Selective Surface Filters

WALTER FUSCALDO<sup>1</sup>, (Senior Member, IEEE), DANIELE PIRRONE<sup>1,2</sup>,

DIMITRIOS C. ZOGRAFOPOULOS<sup>1,3</sup>, ANTONIO FERRARO<sup>1,4</sup>, PASCAL SZRIFTGISER<sup>1,5</sup>,

GUILLAUME DUCOURNAU<sup>1,6</sup>, (Member, IEEE),

AND ROMEO BECCHERELLI<sup>1</sup>, (Member, IEEE)

Corresponding author: Walter Fuscaldo (walter.fuscaldo@cnr.it)

This work was supported in part by the "Ecosistemi dell'Innovazione"-Rome Technopole of Italian Ministry of University and Research, public call n. 3277, PNRR-Mission 4, Component 2, Investment 1.5, financed by European Union, Next GenerationEU under Project ECS00000024; in part by ANR Spatiotera (Grant ANR-19-CE24-0012); in part by IEMN Ultra-High Data-Rate (UHD) Flagship; in part by CPER (Contrat de Plan Etat Région) WAVETECH at HdF Project and Haut de-France Regional Council, PCMP-CHOP and RF Net Platform network; in part by CDP C2EMPI, funded by French State under the France-2030 Program; in part by the University of Lille; in part by the Initiative of Excellence of the University of Lille; in part by European Metropolis of Lille under Project R-CDP-24-004-C2EMPI; and in part by PEPR (Projets Exploratoires Prioritaires pour la Recherche) under Grant ANR-22-PEEL-0006 and Grant 22-PEFT-0006; in part by French RENATECH Network; and in part by the Equipex + Nanofutur under Grant IA-21-ESRE-0012.

**ABSTRACT** Investigations on the beneficial effects of microfabricated frequency selective surfaces (FSS) filters in terahertz (THz) wireless links have been recently proposed for amplitude-only on-off keying modulation schemes. Preliminary results on the error performance of amplitude-phase modulations were obtained and compared with a simple model to serve as a testbed for future, more accurate analyses. Here, we further increase the data rate of wireless data links based on FSS filters while maintaining an error below the forward error correction limit. This improvement is achieved by resorting to modulation schemes with higher spectral efficiency such as 4-level phase shift keying, and 32-level quadrature amplitude modulation, measuring 73 Gb/s and 150 Gb/s, with error vector magnitudes (EVM) lower than 16% and 10% respectively. Measurement results for the EVM are predicted through an innovative use of the *k*-means algorithm which is here suitably modified to deal with FSS-based communications. A remarkable agreement is observed, which makes the proposed tool a promising candidate for the calibration of future wireless links based on FSS filters for next-generation high data rate THz communications.

**INDEX TERMS** Terahertz, terahertz communications, frequency selective surfaces, filters, SNR estimation, EVM estimation, 6G.

## I. INTRODUCTION

The exponential growth in data production and in connected devices demand higher data rates which are associated with

The associate editor coordinating the review of this manuscript and approving it for publication was Walid Al-Hussaibi<sup>1</sup>.

wider communication bandwidths [1], with foreseen use of the terahertz (THz) band. In particular, it is crucial for the development of the 6G paradigm to achieve data rates as high as 100 Gbps and beyond [2], [3]. In order to avoid bottlenecks in the whole transmitter-to-receiver (Tx-Rx) chain, this requirement has to be met at any level: from fiber to

<footnote n="1">¹Consiglio Nazionale delle Ricerche, Istituto per la Microelettronica e Microsistemi, 00133 Rome, Italy</footnote>

<footnote n="2">²Department of Engineering, University of Uninettuno, 00186 Rome, Italy</footnote>

<footnote n="3">³School of Electrical Computer Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece</footnote>

<footnote n="4">⁴Consiglio Nazionale delle Ricerche, Istituto di Nanotecnologia, 87036 Rende, Italy</footnote>

<footnote n="5">⁵Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM), UMR 8523, CNRS, University of Lille, 59650 Lille, France</footnote>

<footnote n="6">⁶Institute of Electronics Microelectronics and Nanotechnology, CNRS, University of Lille, 59650 Lille, France</footnote>
chip to wireless THz communications. In the latter case, THz
devices have to be compliant with the band regulations of
the IEEE standard 802.15.3d-2017 [4], targeting the 100 Gb/s
wireless switched point-to-point physical layer.

In this regard, it is worthwhile to mention that a lot of
efforts (see, e.g., [5]) have recently been made to overcome
the typical hardware-related system impairments that notably
prevent from realizing wireless links over bandwidths as
large a several tens of GHz required to achieve such large
data rates [6], [7]. Nowadays, wireless front-end operating
at 300 GHz and capable of dealing with I/Q modulation
schemes found practical realizations [6], [7], [8], [9], [10].

As discussed in [11], different schemes are proposed
to allocate 69.12 GHz of the available bandwidth in the
frequency range 252.72–321.84 GHz. For instance, one can
have four channels, about 18 GHz each (viz., channels 62–
65 [4]), as well as eight channels, about 9 GHz each (viz.,
channels 49–56 [4]), depending on the targeted application.

In order to ensure frequency separation among each
channel, a passband filter is needed at some point of
the entire Tx–Rx THz chain for electromagnetic shielding
purposes [12], as well as for improving the signal-to-noise
ratio (SNR) of the channel [13]. Such a filter would also
be beneficial to protect the channel from the potential
interference, e.g., from existing ground-to-orbit links [11],
as well as from jamming [14]. In spite of the strong
interest in high data rate THz communications, the key
performance indicators (KPIs) for the transmission reliability
of modulated signals, e.g., the bit error rate (BER), the error
vector magnitude (EVM), the signal-to-noise ratio (SNR),
etc., are mostly reported for *free-space*, line-of-sight (LOS)
THz links, whereas the presence of the filter is rarely
accounted for. Even numerical models based on (non)data-
aided [15], [16], [17], [18], [19], [20], [21] and more recently
machine/deep-learning approaches [22], [23], [24] are often
tested in the simpler free-space, LOS, THz link scenario.

In this regard, we have recently proposed frequency selective surfaces (FSS) for passband filtering in the sub-THz range, with only minor measured insertion loss and phase distortion [25], [26]. In particular, we measured the BER and the EVM of on-off keying (OOK) and 16-levels quadrature amplitude modulation (QAM-16) modulated signals in free-space and with the FSS along the LOS. The experiment has shown that the presence of the FSS only marginally affect the BER and the EVM with the significant advantage of rejecting the out-of-band interference (simulating the carrier-to-interference ratio) in case of amplitude-only modulated signals.

Interestingly, we also proposed a hybrid, simple, and fast
method to estimate the KPIs in FSS-based THz links by
resorting to full-wave simulations, analytical formulas, and
numerical means (see [25] for further details), obtaining good
agreement with measurements of OOK (QAM-16) signals.
In addition, it is worthwhile to stress that FSS are versatile
elements that can not only be used to realize passband filters,
but also to realize radomes and/or metasurface antennas

<figure><img src="image_2.png" /><figcaption>FIGURE 1. a) Schematic view of the experimental testbed. MZM: Mach–Zehnder Modulator. EVOA: Electronic Variable Optical Attenuator. UTC-PD: THz photodiode, coupled to the horn antenna. SHM: Sub-Harmonic Mixer, RF amp: SHF 810. SMA: Synthetizer for the LO. b) Photo of the UTC-PD coupled to the horn antenna, and the 25 mm THz lens (L1). c) SHM-based receiver with the IF amplifier (SHF 810).</figcaption></figure>

when their spatial filtering features are used in place of their
frequency filtering ones (see, e.g., [26], [27], [28], [29], [30],
[31] or [32], [33] and refs. therein). Therefore, the analysis
of an FSS-based THz link has a rather general extent and can
be applied to different scenarios, once the transfer function of
the FSS is accurately modeled by means of either analytical
means or full-wave simulations.

Building upon the results achieved in [25] and [34],
we here significantly extend our work along three different
directions, by developing *i*) a new paradigm for the modeling
of the filter-based THz link, *ii*) proposing an improved
method for the estimation of the KPIs, and *iii*) reporting
new measurement results at higher data rates. In particular,
we first show that by means of simple design rules and
fast and accurate full-wave simulations it is possible to
construct a database of FSSs that can easily meet the
bandwidth requirements dictated by the IEEE standard for
sub-THz communications [4]. An FSS filter is then selected
as a proof-of-concept to demonstrate the accuracy of the
proposed design rules and then used in the remainder of
this paper for the experimental results. Second, a method
is proposed to refine the estimation of the centroids of
the constellation diagrams by using a *k*-means algorithm
[35], [36]. The method employed here provides a more
accurate EVM performance metric and allows to evaluate
the effects on the EVM in the aforementioned coherent
modulation schemes [37] for any known spectral response.
Third, we test our models at higher data rates and for different
modulation schemes. The experimental setup is similar to
that reported in [25] with due modification for the quadrature
phase-shift-keying (QPSK) schemes (see Fig. 1). In this
respect, we experimentally validate the method at 25–73 Gb/s
in QPSK and 60–150 Gb/s in QAM-32, as a predictive model
for the evaluation of the effects of the FSS. The method can be
applied to QAM-16 and QAM-64 that are explicitly foreseen
in IEEE 802.15.3d [11].

The paper is organized as follows. In Section II, we present
the model for a THz channel in presence of an FSS and obtain
the constellation diagrams. A convenient analytical frame-
work is proposed to tailor the bandwidth response of the FSS filter to meet the frequency allocations required by the IEEE standard. As a proof of concept an FSS filter is fabricated and inserted in the channel. A numerical approach is proposed for accurately estimating the SNR from the constellation for both modulation schemes. In Section III, we report information on microfabrication of FFS filter and on the hardware used for the THz link. In Section IV we predict the effects of the FSS on the EVM once the EVM in free space is known. We numerically study the effect of one of these filters (centered at 330 GHz and hereafter referred to as FSS-330) in the communication channel for the QPSK and QAM schemes at 60 Gb/s. Finally, conclusions are drawn in Section V.

## II. METHODS

### A. FSS FILTER DESIGN

An FSS filter consists of a dielectric layer of thickness $d$ and relative permittivity $ε_r$ with a patterned metallic sheet on top. The latter typically consists of a 2-D arrangement of unit cells with a period $p$ of about $λ/2$. Different geometries can be used, such as square patches, Jerusalem crosses, strip gratings, and so on [33]. Here, we consider a fishnet-like unit cell as the one shown in the inset of Fig. 2(b), whose design parameters are the short and long side of the cross, $w$ and $W$, respectively, and the period $p$, here fixed to $p = 650$ µm. As per the dielectric layer, we consider a 188 µm-thick layer of the cyclo-olefin polymer Zeonor, for its excellent properties in the low THz range ($ε_r = 2.32$ and $tan δ ≃ 0.0012$) [38], [39].

As discussed in [40], the resonant frequency $f_0$ of the FSS filter realized with this unit cell is determined at a first approximation by the equation

$$f_0 = c_0/(2.1W\sqrt{ε_{r,avg}}) \quad (1)$$

$c_0$ being the speed of light in free space and $ε_{r,avg} = (ε_r + 1)/2$ for substrate thickness as in the considered scenario. The $-3$ dB fractional bandwidth (FBW) can be empirically found from the general equation

$$FBW = a_0 + a_1f(w/g) \quad (2)$$

where $a_0$ and $a_1$ are fitting coefficients to be determined from measurements and/or full-wave simulations and $f(w/g)$, represents a smooth monotonically growing interpolating function of the ratio between the short side of the cross and the small gap $g = p - W$ between the crosses.

Interestingly, the aforementioned equations may serve as useful design rules for the preliminary design of FSS filters with given properties. As a proof of concept we show here that one can easily design these FSS filters to be compliant with the IEEE channels 62–65, whose features in terms of sub-carrier frequencies $f_{scn}$ with $n = 1, ..., 4$ and $-3$ dB bandwidths (BW) (calculated with respect to the 0 dB level of the free-space channel as shown by the dashed black line in Fig. 2(a)) are reported in Table 1. These values cover the 252.72–321.84 GHz band, as required by [4].

Indeed, the resonant frequency mostly depends on the long side of the slot $W$, thus the values of $W$ to resonate at $f_{scn}$ with $n = 1, ..., 4$ are immediately found from (1). A filter can then be designed by fixing the other two parameters, viz., $p$ and $w$, so as to determine the bandwidth performance and in turn retrieve the fitting coefficients by means of (2). (A simple but effective choice is $f(w/g) = w/g$, $a_0 = 0.1$ and $a_1 = -1.7$. This provides sufficiently accurate results.) In the example reported in this work, we set $p = 650$ µm and after a few rounds of optimizations in a full-wave solver (namely, CST [41]) we obtained the optimal parameters reported in Table 1 that realize the four filters reported in Fig. 2(a). The values of $f_{scn}$ and BW in square brackets are those obtained with full-wave simulations with the given FSS filter parameters for Channels 62–65.

The full-wave results and measurements of the FSS-330 filter with parameters $p = 490$ µm, $w = 10$ µm, and $W = 335$ µm used in [25] are here reported to assess the accuracy of the design approach. For the FSS filter we obtained $f_{sc} = 330$ GHz with a bandwidth of BW = 31.50 GHz from full-wave results and $f_{sc} = 326.31$ GHz and BW = 22.64 GHz from measurements. The slight disagreement between measurements and full-wave results for the FSS-330 are mostly due to photolithographic fluctuations occured during the fabrication process.

To complete the picture, in Fig. 2(c) we also show the group delay $τ_g$ for all the simulated filters and the measured FSS-330. The latter has a lower Q-factor (the $-3$ dB transmittance bandwidth is larger) and this implies a lower group delay. Remarkably the peak group delay for all layouts is as low as about 15 ps (lower than 10 ps from the measured values of the FSS-330) and shows a desirable flat response within the $-3$ dB bandwidth of their respective filters. This feature is of key importance for the targeted QPSK and QAM-32 modulations.

A comment is also needed about the polarization and angular sensitivity of this filter. As is known [42], FSS structures generally exhibit a polarization and angular dependence. FSS filters based on fishnet-like unit cells are no exception, and typically have a more pronounced angular dispersion under vertical polarization with respect to the horizontal polarization. More precisely, the FSS shows the same response under normal incidence to both polarization states. As the angle incidence increases up to $30°$ the transmittance remains almost the same for horizontal polarization, whereas it starts to change significantly for vertical polarization. This aspect is beneficial to realize an angular filtering of radiation that protects the channel from interference coming from undesired directions.

Overall, the proposed FSS design is capable to reproduce the desired spectral features with good accuracy. Although the minimum design feature ($3$ µm gap) appears below the current capabilities of current printed circuit board manufacturing, this feature is common for large-area lithography used for flat panel display manufacturing and is also easily
<table><caption>TABLE 1. IEEE 802.15.3d Communication channels frequency information and related FSS Filter parameters.</caption><thead><tr><th>Channel Nr.</th><th>f<sub>sc</sub> (GHz)</th><th>BW (GHz)</th><th>p (μm)</th><th>w (μm)</th><th>W (μm)</th></tr></thead><tbody><tr><td>62</td><td>261.36 [261.58]</td><td>17.28 [16.94]</td><td>650</td><td>3</td><td>423</td></tr><tr><td>63</td><td>278.64 [279.08]</td><td>17.28 [16.52]</td><td>650</td><td>8</td><td>390</td></tr><tr><td>64</td><td>295.92 [296.16]</td><td>17.28 [16.52]</td><td>650</td><td>14</td><td>355</td></tr><tr><td>65</td><td>313.20 [313.66]</td><td>17.28 [16.38]</td><td>650</td><td>50</td><td>310</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>FIGURE 2. (a) Modulus and (b) phase of the transmittance, and (c) group delay of the four FSS filters designed to match channels 62–65 of [4]. Full-wave and measurements results for the modulus of the transmittance and group delays of the FSS-330 are also reported in solid gray line and gray crosses, respectively. The inset in (a) shows a zoomed plot of the insertion loss of the measured and simulated FSS-330 filter. The inset in (b) shows the 3-D layout of the FSS filter and the relevant parameters of the unit cell.</figcaption></figure>

achieved in roll-to-roll processing. Hence, these passive filters can be manufactured at low cost.

These results clearly demonstrate the flexibility of the proposed FSS to realize passband filters for THz communications. In particular, it is worth mentioning that the linearity of the phase within the passband ensure minimal distortion when amplitude-phase modulations schemes such as M-QAM and M-PSK are considered, as in the scenarios presented in the next Sections. In the following, we consider the FSS-330 filter, designed to resonate at $f_0 = 330$ GHz (microfabricated and experimentally validated in previous works [25]), to demonstrate its effectiveness in a realistic scenario where a THz source transmits amplitude-phase modulated signals through the filter towards a THz receiver in line of sight. Full-wave results and measurements of the transmittance of the FSS-330, are reported in Fig. 2(a) for the reader's convenience. (The interested reader can found more experimental results and details in e.g., [25], [43]). The excellent agreement between measurements and full-wave simulations demonstrates the capability to realize FSS filters with a given spectral response in the THz range.

We should note that although we presented full-wave results for shaping the FSS to match the spectral features of Channels 62–65 of [4], comparable results (not shown for brevity) are obtained for realizing FSS filters that cover Channels 66–67 (viz., 25.92 GHz bandwidth) as well as Channels 68 and 69 (viz., 51.84 GHz and 69.12 GHz bandwidth). Conversely, the typical spectral behavior of FSS prevents from designing filters with very small fractional bandwidth as required by Channels 2–61 (fractional bandwidths spanning from less than 1% to about 5%). As a matter of fact, the physics of FSS filters, based on the dipole-like resonance of the unit-cell element, gives a lower bound to the minimum FBW as also suggested by the presence of

the constant term $a_0$ appearing in (2). Such term cannot be predicted *a priori* as it depends on many factors, such as the chosen unit-cell geometry, the dielectric and metallic material properties and thicknesses. However, experimental results in various publications [13], [40], [44], [45], rarely show FBW lower than 10%. In addition, FSS filters are subject to the typical trade-off among insertion loss, Q-factor, fractional bandwidth, and group delay. An FSS with a low insertion loss will feature a high Q-factor, but also a narrow fractional bandwidth and a relatively large group delay.

Filters with more design flexibility will be investigated in future works to fully respond to the needs of the IEEE Standard 802.15.3d-2017 [4].

## B. WIRELESS THz CHANNEL MODEL

The wireless THz channel in free space is modeled as an additive white Gaussian noise (AWGN) channel where the modulated signals is detected with a simple homodyne scheme. The SNR is a KPI of a communication channel and it is defined as $SNR = P_s/\sigma_n^2$, where $P_s$ is the average signal power, and $\sigma_n^2$ is the noise variance of the AWGN channel. For data-aided receivers the EVM and SNR are related through the approximate expression [46]:

$$ \text{EVM}_{\text{rms}} \approx \sqrt{1/\text{SNR}} \qquad (3) $$

This formula holds for a sufficiently long pattern length, a case fulfilled in our scenario. We first obtain the EVM from measurements in free space, i.e., without any FSS in the path. Hence, the SNR of the free space channel is retrieved from (3). Then, from the knowledge of the SNR and the carrier power $P_s$, the noise power $2\sigma_n^2$ is readily obtained. The transfer function of the filter is defined in general as:

$$ H(\omega) = H_0(\omega)e^{i\phi(\omega)} \qquad (4) $$
where $H_0(\omega)$ is the amplitude and $\phi(\omega)$ is the phase of the FSS filter transmission coefficient. These values can be retrieved from either measurements or full-wave simulations. In this work, we use the measurements results for the filter FSS-330 as discussed in the previous Subsection.

### C. EVM EVALUATION IN FILTER-BASED THz COMMUNICATIONS

The method implemented here can simulate several modulation schemes in the presence of FSS filters without the need of processing huge amount of data. The method can be summarized in the following steps:

1) Generating a pseudo-random sequence of modulated signal $s(t)$ of a suitable pattern length.

2) Measuring the EVM in free space for different modulation schemes at various bit rates and carrier frequencies in the 320–345 GHz range.

3) Using the measured EVM of step 2) to retrieve the SNR of the free-space channel from (3), and thus the noise power of the free-space channel.

4) Estimating the minimum pattern length that would provide accurate estimation of the experimentally retrieved data.

5) Feeding the above free-space noise power in a numerical model that accounts for the transfer function (4) of the filter in the frequency domain to compute the EVM for the filtered communication data stream.

6) Generating the constellation diagram for the free space and filtered received symbols.

7) Comparing the minimum distance (this operation will be discussed in Section III) of symbols received past the filter to the symbols received in free space.

We stress that the measured free space EVM is specific to each combination of modulation scheme, bit rate, and carrier frequency as it is affected by several aspects of the transmit and receive Tx–Rx THz chain. For instance, the measured free space EVM for 60 Gb/s modulated at the 330 GHz central frequency of the filter is ~ 7.9% and ~ 4.8% for QPSK and QAM-32 respectively. This specificity is further enhanced for higher bit rate and narrow-band filtering effects such as the introduction of the FSS-330 in the channel. Hence, the above procedure is repeated for each combination of modulation scheme, bit rate, and carrier frequency, as well as spectral response.

With respect to point 2) and 4) it will be shown in Section IV that a pattern length of $10^4$ is sufficient to provide accurate results for measuring an EVM as low as 9.2%.

### D. SNR ESTIMATION FROM THE CONSTELLATION DIAGRAM

For all considered modulation schemes, carrier frequencies, and bit rates, the estimation of the deterioration of the SNR for filtered transmission starts from the constellation diagram measured for free-space communication. In [25], the evaluation procedure of the EVM for QAM-16 simply assumed that all centroids (CC) where located on a regular

<figure><img src="image_4.png" /><figcaption>FIGURE 3. The constellation diagram of (a) QPSK and (b) QAM-32 modulated at the 330 GHz central frequency of filter. Black symbols are free space case, while the red symbols are for filter-based communication. In both cases, white crosses represent the centroids computed via k-means algorithm. Free space bit rate and EVM are assumed the same for both schemes (75 Gb/s and 4.8%). The effect of the filter appears mainly as an amplitude effect.</figcaption></figure>

grid. Conversely, we here remove this constraint and estimate the CC by using an unsupervised machine learning approach based on the partitional clustering of k-means algorithm. Briefly, the k-means algorithm iteratively partitions the clusters of the constellation diagram and computes the related centroids (CC) by exploiting to the principle of minimum Euclidean distance. The white crosses shown in Fig. 3 represent every single CC, where we measured the distances for each neighbor CCs pair and define the minimum distance $d_{min}$. In order to estimate the SNR value after the filtering, we computed the $d_{rms}^{(FS)}$, $d_{rms}^{(FSS)}$ for the transmitted and received symbols, where $d_{rms}^{(FS)}$ is the CCs pair distance in free space and $d_{rms}^{(FSS)}$ is the distance with FSS filter. With these values at hand, the deterioration of SNR caused by the FSS and represented through the noise figure $F = SNR_{in}/SNR_{out}$ can be evaluated through the following expression:

$$F = \text{SNR}_{\text{in}} \left( \frac{d_{\text{rms}}^{(\text{FSS})}}{d_{\text{rms}}^{(\text{FS})}} \right)^2 \quad (5)$$

Finally, the EVM for filtered communications is estimated through (2).

### III. HARDWARE AND EXPERIMENT DESCRIPTION

#### A. FILTERS MICROFABRICATION

The FSS-330 filter described in Section II-A has been micro-fabricated with UV photolithographic process, following the procedure outlined in [26] that is here briefly reported. The metallic part is realized by thermally evaporating a 200 nm layer of Al on the 188 µm-thick Zeonor substrate. Then, a film of positive photoresist was spin-coated, exposed through a mask aligner with a wavelength of 365 nm and intensity of 60 mW/cm², and developed to obtain the desired pattern. Next, the metallic layer was selectively removed using Aluminum etching solution. Finally the sample was rinsed with acetone and isopropanol to remove the residual photoresist.
## B. EXPERIMENTAL SETUP

In the experimental setup (see Fig. 1), two extended cavity tunable lasers are used to select the carrier frequency, which corresponds to the frequency difference between the two lasers. One of these lasers is modulated, while the other is continuous wave. The modulated data signal itself is composed of two baseband waveforms, I and Q, both generated by an arbitrary waveform generator (AWG). These baseband signals used a root raised cosine filter with a roll-off factor of 0.5, and the pseudo-random binary sequence (PRBS) length was typically $2^{13}-1$. These I and Q signals are injected into a Mach-Zehnder modulator (MZM), enabling in a QAM optical generation. Subsequently, the fiber output of the modulator is combined (using a fiber coupler) with the second laser. These two combined lasers are then amplified using an erbium doped fiber amplifier (EDFA).

The THz signal is then generated by an uni-travelling carrier photodiode (UTC-PD, model IOD-PMJ-13001) and radiated to the free space antenna using a standard horn antenna attached to the UTC-PD (typical gain 23 dBi at 280 GHz and 25 dBi at 330 GHz). The optical power sent into the UTC-PD was kept below 80 mW in all experiments, which lead to a photocurrent inside the PD < 7 mA, and the PD bias was -0.8 V. A set of two polymer lenses are used to collimate the signal from transmitter to receiver. During measurements, the reference signal is acquired without filter, for equalization of the system (details are given hereafter). Then, the filter is inserted in the THz link, keeping the same configuration.

The receiving horn antenna is the same type as in the transmitter. This horn directly feeds the THz receiver, which is based on an electrically pumped subharmonic mixer (SHM) (WR2.8 model from VDI [47]) allowing the modulated THz signal to be down-converted from the THz carrier frequency into an intermediate frequency (IF) < 40 GHz. This SHM is fed at half of the carrier frequency, by a signal generator (SMA100B, Rohde&Schwarz). The generated baseband signal is then amplified and acquired by a wideband 70 GHz real-time oscilloscope (UXR, Keysight). This enables a real-time analysis of usual performance metrics such as the EVM at different symbol rates and modulation orders.

The signal processing steps used in the experiments are described hereafter: first, short time sequences (lengths < 1 µs) are captured by the real-time oscilloscope to limit the effect of the lasers' phase noise. The center IF signal in the microwave range is directly analyzed by the commercial "digital demodulation" tool from the Keysight VSA 89600 software. Frequency equalization is used to compensate mostly for the frequency response induced by the UTC-PD, horn antenna and frequency-dependant IF losses inside the SHM used to down-convert the 300 GHz signal. During experiments, the reference signals (without filter) are captured. Keeping the same reference equalization parameters, the filter is placed in the THz path to evaluate the EVM penalty. The EVM values are calculated as described

<figure><img src="image_5.png" /><figcaption>FIGURE 4. Comparison between the EVM experimentally measured at the central frequency of the FSS-330 filter for QPSK/QAM-32 (black/blue) in absence/presence (triangle-up/triangle-down) of the filter and the evaluated EVM with the proposed k-means method (+) and the method (x) described in [25].</figcaption></figure>

<table><caption>TABLE 2. EVM estimation (target=9.2%).</caption><thead><tr><td>Pattern Length</td><td>EVM</td><td>Time (s)</td></tr></thead><tbody><tr><td>10<sup>2</sup></td><td>7.2</td><td>~ 10<sup>-3</sup></td></tr><tr><td>10<sup>3</sup></td><td>8.6</td><td>~ 10<sup>-2</sup></td></tr><tr><td>10<sup>4</sup></td><td>9.1</td><td>~ 10<sup>0</sup></td></tr><tr><td>10<sup>5</sup></td><td>9.3</td><td>~ 10<sup>1</sup></td></tr><tr><td>10<sup>6</sup></td><td>9.2</td><td>~ 10<sup>2</sup></td></tr><tr><td>10<sup>7</sup></td><td>9.2</td><td>~ 10<sup>3</sup></td></tr><tr><td>10<sup>8</sup></td><td>9.1</td><td>> 10<sup>4</sup></td></tr></tbody></table>

in [48], whereas all the BER evaluations are done by direct comparison of the PRBS sequences used for I and Q baseband signals and the detected I and Q data after demodulation. This comparison is performed as a post-process step based on the VSA demodulated data sequence.

## IV. RESULTS

In Fig. 4 we compare the measured EVM in free space and with FSS-330, with the estimated EVM as a function of the data rate by applying the k-means algorithm to the numerical results obtained from the numerical modeling of filter-based Tx-Rx chain. Figure 4 also shows the numerical results obtained with the simpler method that rigidly assumes the CC on a periodic grid. For both QPSK and QAM-32 simulation, we have set the carrier frequency ($f_c$) at the same resonant frequency ($f_0$) of the FSS-330 as in the experiment.

The consistency of the method is assessed with the same technique proposed in [25] and briefly outlined in the following. First, we had to calibrate the model in order to find a reasonably short pattern length that is sufficiently long to convey the full information on the effects of the filter. Clearly, this is related to the minimum hardware BER foreseen, which in turn, is related to the actual EVM. It is worthwhile to recall that the hardware BER is the BER without any error correction being applied, whereas the IEEE Std 802.15.3d-2017 [4] specifies only the much easier criteria to achieve the software BER. For the same Tx and Rx hardware, lower bit rates usually result in lower BER and lower EVM. Hence, we need to use sufficiently long pattern lengths to estimate a lower BER. In simulations, this may become computationally
<figure><img src="image_6.png" /><figcaption>FIGURE 5. EVM numerically estimated within the -3 dB bandwidth of the FSS-330 for QPSK (black dashed line with '+' marker) and QAM-32 (blue dashed line with '-' marker) respectively. The numerical analysis was performed at 60 Gb/s. The minimum EVM after the filter is found for the carrier tuned to the center frequency of filter and increases as detuning increases. The EVM of the free space channel is around 7.9 ± 0.2% for QPSK and 4.8 ± 0.2% in QAM-32. The satellites on the right side show the respective constellation diagram computed at $f_c = 330$ GHz.</figcaption></figure>

intensive. Hence, we varied the length in bits of the initial random sequence from $10^2$ to $10^8$ bits and numerically estimated EVM until we matched the experimental data.

Table 2 shows results obtained with a Matlab script on a simple 4-core desktop PC for the more computationally demanding case of QPSK modulation shown in Fig. 4, i.e. for 25 Gb/s. The measured EVM is 6% in free space, whereas in presence of the FSS-330, whose -3 dB bandwidth is approximately 40 GHz, the EVM increases to 9.2%. Clearly, the target EVM corresponding to an experimental length as short as $10^4$ bits represents a suitable choice. This length is comparable to the length of the data pattern used in the experiments (usually between $2^{11} - 1$ to $2^{15} - 1$).

The corresponding computing time is compatible with massive optimization of the filter spectral response tailored to a specific modulation scheme and bit rate. Alternatively, it becomes straightforward to estimate the effects of various undesired filtering effects, e.g., by means of Monte Carlo simulation. Similar results are obtained for other bit rates and for QAM-32 (not shown for the sake of brevity). Figure 4 shows the comparison of the EVM evaluation for QPSK digital modulation in black color. The EVM evaluated in presence of the bell-shaped FSS-330 for a signal modulated at 330 GHz exhibits a very similar trend to the EVM measured in free space. Moreover, the substantial overlap of the estimated EVM and the EVM measured in presence of FSS-330 corroborates the consistency of the proposed method in the 25–73 Gb/s data rate range. Conversely, with the simpler method proposed previously [25], the estimation of the EVM is worse.

The same comparison is shown in blue color for the QAM-32 modulation scheme but at a higher data rate range 60–150 Gb/s. Again, good agreement between the evaluated and measured EVM is found except for a slight disagreement at 60 and 140 Gb/s. This disagreement might be due to a minor derating from the expected monotonically growing trend of the measured free space EVM vs. data rate, since such data are used to estimate the EVM with the filter. We remark that

the experimentally acquired EVM in free space is affected by the physical Tx-Rx chain which has a frequency dependent response, coming mostly from the Tx (fast photodiode) and Rx frequency-dependance performance (conversion losses vs. frequency, IF response, etc.) in the proposed carrier frequencies (270 and 330 GHz). When the bitrate, and thus the bandwidth, of the modulated signal nears or exceeds the filter bandwidth, the received signal is distorted and the EVM gets larger (we recall that SNR/EVM/BER are interrelated). Clearly, Fig. 4 shows that the degradation of the EVM after the FSS-330 is worse for QPSK than for QAM-32 due to the larger bandwidth of the former (we recall that the spectral efficiency is 2 bit/s/Hz and 5 bit/s/Hz respectively). In particular, we note that the EVM vs. data rate in free space for QPSK has a different slope with respect to the one obtained with the filter. This condition does not occur for the QAM modulation scheme for which the slopes of the EVM in free-space and with the filter are almost the same. The reason for this difference is most likely due to the phase response of the FSS filter which is not ideally linear. Phase-only modulations as QPSK are more sensitive to the linearity of the phase, and thus the filter may introduce more errors and in turn contribute to larger EVM as the data rate increases.

In order to further elucidate this degradation and the effect of detuning, we systematically investigated the EVM at 60 Gb/s for both modulation schemes as a function of the carrier frequency varying in the 320–345 GHz (Fig. 5). The EVM of the free space channel is around 7.9 ± 0.2% for QPSK and 4.8 ± 0.2% in QAM-32. The minimum EVM after the filter is found for the carrier tuned to the center frequency of filter as expected, while EVM increases as detuning increases. For instance, ΔEVM, the increase of EVM with respect to free space, grows from 2.4%(5.0%) to 3.9%(7.3%) for QAM-32(QPSK) respectively, when the carrier is detuned by 15 GHz. For the relatively narrowband 60 Gb/s data streams the EVMs evaluated at $f_0 = 330$ GHz in QPSK and QAM-32 formats are the lowest (see Fig. 5). This is also illustrated by the constellation plots of QPSK and QAM-32 taken at $f_0$ shown on the right end side of Fig. 5, which confirms significant overlap of the symbols received in the presence of the filter (red dots) with the symbols received without the filter (black dot). The increasing thickness of the red corona for increased detuning clearly indicates the degradation introduced by the filter. Similar conclusions can be reached when investigating the BER performance (not shown for brevity) by exploiting the well-known relations among EVM, SNR and BER [46] (we checked that this approximated BER matches well with the BER obtained from direct counting).

V. CONCLUSION

In this work, we have proposed a new SNR/EVM estimation method and validated throughout a systematic measurement campaign for a THz wireless communication channel with and without FSS filter. The experiment was conducted over a range of data rates between 25–73 Gb/s for QPSK
and 60–150 Gb/s for QAM-32. We modeled the THz transmission channel including a physical filter through its complex transfer function. We showed that the EVM/SNR can be estimated efficiently and accurately with patterns only $10^4$ bits long without the need to use terabit long sequences. The good agreement between the experimental and the computed results confirms that our proposed method is a robust approach for the analysis of filtering in digital THz wireless communication. For a well-characterized FSS with a bell-shaped response and 23 GHz-bandwidth, the received signal was not significantly deteriorated compared to the transmitted signal when the carrier frequency corresponded to the fundamental frequency of the filter ($f_0 = f_c$), whereas moderated detuning resulted in further increase of the EVM. Interestingly, the relatively narrowband FSS moderately increased the EVM from 6% to 10% in QAM-32 at 150 Gb/s and from 10% to 16% in QPSK at 73 Gb/s despite the relatively large frequency footprint.

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of Rome, and in July 2020, he joined the Institute for Microelectronics and Microsystems (IMM), National Research Council of Italy, Rome, as a Researcher, where he has been a Senior Researcher, since 2023. His current research interests include propagation of leaky, surface, and plasmonic waves, analysis and design of leaky-wave antennas, generation of electromagnetic localized waves, THz technology and spectroscopy, graphene electromagnetics, and metasurfaces.

Dr. Fuscaldo was awarded several prizes, among which the prestigious EurAAP Leopold B. Felsen Award for Excellence in Electrodynamics in 2025. Since 2021, he has been included in the Worlds Top 2% Scientists list by Stanford University. He is currently an Associate Editor of the *IET Microwaves, Antennas and Propagation and Electronic Letters* (IET).

<figure><img src="image_7.png" /></figure>

**DANIELE PIRRONE** received the B.Sc. degree in electronic engineering and the M.Sc. degree in bioengineering from Roma Tre University, Rome, Italy, in 2014 and 2018, respectively, and the Ph.D. degree in technology innovation engineering from the Faculty of Engineering, UniNettuno University, Rome, in collaboration with the Institute for Microelectronics and Microsystems (IMM), National Research Council, Rome, in 2023. During the master's thesis, he was involved in

the Cost Action TU1028, where he implemented the software GPRMAX for electromagnetic simulation based on the FTDT method previously developed by Dr. Antonis Giannopoulos, including the parallel and the distributed computing on multiple nodes. His research interests include terahertz devices, plasmonic structures, and nanostructured materials with particular focus on analysis and characterization of physical meta-surface filters in THz wireless communications.

<figure><img src="image_8.png" /></figure>

**WALTER FUSCALDO** (Senior Member, IEEE) received the B.Sc. and M.Sc. (cum laude) degrees in telecommunications engineering from the Sapienza University of Rome, Rome, Italy, in 2010 and 2013, respectively, and the Ph.D. degree (cum laude and with the Doctor Europaeus Label) in information and communication technology (applied electromagnetics curriculum) from the Department of Information Engineering, Electronics and Telecommunications (DIET) and the

Institut d'Électronique et de Technologies du numérique de Rennes (IETR), Université de Rennes 1, Rennes, France, in 2017, under a cotutelle agreement between the institutions.

In 2014, 2017, and 2018, he was a Visiting Researcher, and in 2023 a Visiting Scientist with the NATO-STO Center for Maritime Research and Experimentation (CMRE), La Spezia, Italy. In 2016, he was a Visiting Researcher with the University of Houston, Houston, TX, USA. From July 2017 to June 2020, he was a Research Fellow with the Sapienza University

<figure><img src="image_9.png" /></figure>

**DIMITRIOS C. ZOGRAFOPOULOS** received the Ph.D. degree from the Aristotle University of Thessaloniki (AUTH), in 2009. Subsequently, he was an AUTH Post-Doctoral Research Fellow, in 2010, a Post-Doctoral Fellow with Greek States Scholarship Foundation, and a Visiting Research Fellow with the Department of Electronics Technology, Carlos III University of Madrid, in 2011. He then moved under a Marie-Curie Fellowship to the Institute for Microelectronics

and Microsystems, Italian National Research Council, Rome, where he has been an appointed Researcher and a Senior Researcher, in 2011 and 2023, respectively. He is the author or co-author of more than 100 scientific articles in international journals, more than 90 presentations in international conferences, and three book chapters. His current research interests include the investigation of strongly resonant metasurfaces, tunable metamaterials, components for THz wave manipulation, and the interaction between electromagnetic waves and liquid crystals.
<figure><img src="image_10.png" /></figure>

ANTONIO FERRARO received the bachelor's degree in material science and the master's degree (cum laude) in science and engineering of innovative and functional materials from the Physics Department, University of Calabria, Rende, Italy, in 2009 and 2012, respectively, and the Ph.D. degree in physical, chemical, and materials sciences from the Physics Department, University of Calabria, in 2017, in co-supervision with the Institute for Microelectronics and Microsystems

(IMM), National Research Council, Rome, Italy. Until 2019, he was a Research Fellow with IMM, Italian National Research Council. Then, he has been a Research Fellow with the Physics Department, University of Calabria. He is currently a Researcher with the Institute of Nanotechnology (NANOTEC), Italian National Research Council, Rende. His research interests include terahertz devices, plasmonic structures, nanostructured materials, and liquid crystalline composite devices with particular focus on fabrication and characterization. He was awarded with the "Erasmus Placement Scholarship" enabling to perform an internship for his master's thesis at the Philips Research Campus, Eindhoven, The Netherlands, for six months under the supervision of Dr. Dick de Boer, where was involved in nanostructured luminescence materials project. His Ph.D. thesis with title "From Basic to Advanced: Design, Fabrication and Characterization of Functional Terahertz Devices" was awarded as the "Best Doctoral Thesis Award in Optoelectronics 2018" from the IEEE Photonics Society Italian Chapter.

<figure><img src="image_11.png" /></figure>

GUILLAUME DUCOURNAU (Member, IEEE) received the B.Sc. and M.Sc. degrees in electrical engineering from ESIGELEC, Rouen, France in 2000 and 2002, respectively, and the Ph.D. degree in optical communication systems from the University of Rouen Normandy, France, in 2005. He has been with the Institute of Electronics, Microelectronics and Nanotechnology (IEMN), UMR 8520, University of Lille, Villeneuve d'Ascq, France, since 2007. He has

authored or co-authored more than 180 publications in peer-reviewed international journals or peer-reviewed conferences proceedings and holds one patent. He is currently the Leader of the THz wireless communications activity with IEMN using optoelectronic THz photomixers, electronic receivers, THz instrumentation, and millimeter-wave (mm-wave) characterization. He worked on several European projects: STREP ROOTHz 2010-2013, ThoR H2020, GRAPH-X, TIMES (6G SNS), and the Marie-Sklodowska Curie TERAOPTICS Network. At national level, he was the Coordinator of the COMTONIQ Project, from 2014 to 2017, funded by ANR (INFRA 2013) dedicated to THz communications in the 300 GHz band, the ANR/DFG TERASONIC Project for the use of THz photonics technologies and electrical solid-state technologies for THz communications and SPATIOTERA for spatially-distributed photomixers. He received the 2020 ISAP Best Paper Award. He is involved in national France 2030 programs gathering several French laboratories under the PEPR programs funded by the Agence Nationale de la Recherche (ANR). In this framework, the FUNTERA Project (six partners) is investigating THz converters, while the SYSTERA project (12 partners) is dedicated to beyond 90 GHz systems for future networks. He also participates to the ST-IEMN Common Laboratory, and more specifically involved in the mm-wave technologies characterization part.

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PASCAL SZRIFTGISER received the Ph.D. degree in quantum physics from the Laboratoire Kastler Brossel, University Paris VI (now Sorbonne University), Paris, France, in 1996. In 1996, as a Researcher, he joined the Centre National de la Recherche Scientifique (CNRS), Laboratoire Physique des Lasers Atomes et Molécules (PhLAM). Since 2012, he has been the CNRS Research Director. From 2014 to 2021, he was the Leader of the Cold Atoms Group and the Deputy

Director of PhLAM, from 2019 to 2021. Since 2021, he has been a PI of the Contrat de Projet Etat Région (CPER) WaveTech@HdF, a consortium that brings together six research laboratories in Hauts-de-France country. He has authored or co-authored 145 publications in peer-reviewed international journals or conference proceedings. His expertise spans from cold atoms physics, quantum chaos, topology, and non-linear optics in optical fibers to high-speed coherent optical communications for THz applications.

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ROMEO BECCHERELLI (Member, IEEE) was born in Plovdiv, Bulgaria, in 1969. He received the Laurea (cum laude) and Ph.D. degrees in electronic engineering from the Sapienza University of Rome, Italy, in 1994 and 1998, respectively. In 1997, he joined as a Post-Doctoral Research Assistant with the Department of Engineering Science, University of Oxford, Oxford, U.K. In 2001, he was appointed as a Researcher, in 2006, a Senior Researcher, and the Director of

Research in 2021 at the National Research Council of Italy, Institute for Microelectronics and Microsystems, Rome. He has invented two patents and authored of more than 100 scientific articles in international journals, more than 110 conference proceedings papers, and eight book chapters. He has been a Principal Investigator in research projects funded by European Community, European Space Agency, the Italian Government, and the industry, and the co-coordinator of four bilateral projects. His research interests include liquid crystal display technology have evolved into sensor arrays, photonics and plasmonics based on liquid crystals, and into metamaterial and metasurface devices, and systems for wireless communications in the microwaves and terahertz frequency ranges. His Ph.D. thesis was awarded the International Otto Lehman Prize 1999 in liquid crystal technology by the University of Karlsruhe, Germany, and the Otto Lehmann Foundation.

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