# Model independent calibration for sound horizon combining observations of
supernovae and transversal BAO measurements

Tonghua Liu  School of Physics and Optoelectronic, Yangtze University,
Jingzhou 434023, China;  Xinyi Zhong  School of Physics and Optoelectronic,
Yangtze University, Jingzhou 434023, China;  Jieci Wang<EMAIL_ADDRESS>Department of Physics, and Collaborative Innovation Center for Quantum Effects
and Applications, Hunan Normal University, Changsha 410081, China;  Marek
Biesiada<EMAIL_ADDRESS>National Centre for Nuclear Research,
Pasteura 7, PL-02-093 Warsaw, Poland;

###### Abstract

The sound horizon is a key theoretical prediction of the cosmological model
that depends on the speed of sound and the rate of expansion in the early
universe, before matter and radiation decoupled. The standard ruler for low
redshift calibration of baryon acoustic oscillations (BAOs) is a direct
measurement that would exist even if the standard cosmological model and the
standard assumptions of early physics did not. We propose a new model-
independent method to calibrate sound horizon $r^{h}_{s}$ (relative standard
ruler) by using the latest observations of SNe Ia and transversal BAO
measurements. The final result reports $r_{s}^{h}=107.10^{+1.36}_{-1.32}$
$Mpc/h$ in the framework of the Pantheon dataset. This result changes to
$r_{s}^{h}=105.63^{+1.33}_{-1.31}$ $Mpc/h$ when uses Pantheon+ dataset. Note
that even without an estimate of dimensionless Hubble constant $h$, the
combination of BAO and SNe Ia datasets already constrain the low-redshift
standard ruler scale $r_{s}^{h}$ at the $\sim 1.26\%$ level. More importantly,
it is interesting to find that most of the $r_{s}^{h}$ obtained at high
redshifts have a larger value (9 out of 15 results are larger than the result
obtained by combining all BAOs). This finding may give us a better
understanding of the discordance between the data sets or Hubble tension or
reveal new physics beyond the standard model.

##  I Introduction

In the past few decades, observations of Type Ia supernovae (SNe Ia) have
revealed that the expansion of the Universe is accelerating Riess et al.
(1998); Perlmutter et al. (1999). Based on Einstein’s theory of General
Relativity (GR) Wald (1984), and assuming that the Universe is homogeneous and
isotropic on large scales (Weinberg, 1972), it is generally accepted that the
so called cosmological constant $\Lambda$ plus cold dark matter ($\Lambda$CDM)
model correctly describes our Universe, where the cosmological constant term
$\Lambda$ modeling dark energy drive the accelerated expansion of the
Universe. However, with the improved precision of the latest surveys, the
standard cosmological model is being severely tested, such as, the Hubble
tension (Freedman, 2017; Di Valentino et al., 2021). Assuming the $\Lambda$CDM
model, Planck Collaboration yields a low value on Hubble constant,
$H_{0}=67.36\pm 0.54\mathrm{~{}km~{}s^{-1}~{}Mpc^{-1}}$, from cosmic microwave
background (CMB) anisotropy (both temperature and polarization) data (Planck
Collaboration et al., 2020). This result suffer challenge by some
compatibility tests at low redshifts. In particular, the Supernova $H_{0}$ for
the Equation of State collaboration (SH0ES) (Riess et al., 2019) gives the low
redshift measurement result on the Hubble constant, $H_{0}=74.03\pm
1.42\mathrm{~{}km~{}s^{-1}~{}Mpc^{-1}}$, through a local distance ladder
approach from the Cepheid variable stars. The local measurement of $H_{0}$ is
model independent because it does not depend on cosmological assumptions. This
inconsistency on $H_{0}$ is called Hubble tension, which possible explanations
for this tension are unknown systematic errors in one or both observations, or
problems on the standard model with unrevealed new physics. (more works on
Hubble tension please see the references Poulin et al. (2019); Feeney et al.
(2019); Dainotti et al. (2021); Liu et al. (2022) and references therein). The
search for other high-precision and accuracy astronomical observations may be
an important way to relieve or even determine Hubble tension.

The baryon acoustic oscillation (BAO) leaves measurable signatures in the
distribution of galaxies and is probably the most easily understood standard
scale (ruler) in the Universe. For instance, the Sloan Digital Sky Survey
(SDSS) has increased the three-dimensional catalog of galaxies Abolfathi et
al. (2018) , making it possible to accurately measure BAO scales at various
redshifts. Thus, probing the BAO scale at different times is a powerful tool
in constraining cosmology. However, it should be noted that the BAO acting
standard ruler need to know the comoving length of the ruler, the sound
horizon at radiation drag $r_{s}$ Eisenstein & Hu (1998); Hu & White (1996).
Without knowing the length of the ruler, BAO probes can only give relative
measurements of the expansion history. The $r_{s}$ is usually calibrated at
$z\approx 1100$ relying on the CMB observations. If one use BAO data with
calibrated $r_{s}$ by CMB observations to measure $H_{0}$, in some sense, the
constraint on $H_{0}$ is not completely independent on the CMB data Zhang &
Huang (2020). An alternative approach is to combine BAO measurements with
other low-redshift observations. The BAO signature can independent estimates
of the the Hubble parameter $H(z)$ and the angular diameter distance
$D^{A}(z)$ through the line-of-sight and transverse BAO modes, when one knows
the length of the ruler, respectively Alam et al. (2017, 2021). This means
that if we calibrate the length of the ruler of BAO from low redshift
observations, we need to add both $H(z)$ and $D^{A}(z)$ data. Although
astronomical observations such as cosmic chronometers can directly provide
cosmological model-independent measurements of $H(z)$, and SNe Ia can restore
the distance redshift relationship and provide the expansion history of the
Universe, using these data together makes it impossible to determine the
contribution of the various data to calibrating the length of the ruler in
BAO.

Even relative measurements of the expansion history provided by observations
of SNe Ia, combined with a measurement of the BAO signature, can impose
constraints on the relative standard ruler $r_{s}^{h}$, which is the ruler
length in units of $h^{-1}$Mpc. An absolute ruler length can be measured by
multiplied dimensionless Hubble constant
$h=H_{0}/100\mathrm{~{}km~{}s^{-1}~{}Mpc^{-1}}$. The importance of this scale
is that it is a key theoretical prediction for cosmological models that depend
on the speed of sound and the rate of expansion in the early Universe, before
matter and radiation decoupled. However, this standard scale still exists even
without the hypothetical cosmological model and early cosmology, which means
that we can calibrate this standard ruler with astronomical observations at
low redshifts. We refer to Refs Heavens et al. (2014); Gómez-Valent (2022);
Bernal et al. (2016); L’Huillier & Shafieloo (2017); Aylor et al. (2019);
Macaulay et al. (2019); Wojtak & Agnello (2019) for more papers about the
sound horizon. Inspired by the above, this work will use the observational
datasets of SNe Ia, combined with the measurement of transverse BAO, to
calibrate the relative standard ruler $r_{s}^{h}$. This has several
advantages. First, the whole work has nothing to do with cosmological models
and the early universe; Second, we only calibrate the relative standard ruler,
which has nothing to do with the Hubble constant; Third, the work only
involves the SNe Ia and BAO datasets, and has nothing to do with other
astronomical observations, which highlights the contribution of each datasets
in the overall work.

This paper is organized as follows: in Section 2, we present the methodology
of calibration of relative standard ruler, and the data used in this work. In
Section 3, we show our results and discussion. Finally, the main conclusions
are summarized in Section 4.

##  II  Methodology and Data

###  II.1 Transverse BAO measurements

BAOs are regular periodic density fluctuations of the visible baryonic matter
in the Universe. The matter clustering properties of BAOs can also be used as
a standard ruler for measuring cosmological distances, thus to constrain the
cosmological parameters (especially the density of baryonic matter), and
further understand the nature of the dark energy that causes the accelerated
expansion of the Universe. However, BAO data can not obtain a constraint on
$H_{0}$, it must be combined with other measurements in order to break the
degeneracy between $H_{0}$ and $r_{s}$. The sound horizon at the drag epoch is
given by

$r_{s}=\int^{\infty}_{z_{d}}dzc_{s}(z)/H(z),$ (1)

where $z_{d}$ being the redshift of the drag epoch, $c_{s}(z)$ is the sound
speed of the photon-baryon fluid, and $H(z)$ is the Hubble parameter. The BAO
angular scale $\theta_{BAO}(z)$ is related to the angular diameter distance
acting as standard ruler and given by following

$\theta_{BAO}=\frac{r_{s}}{(1+z)D^{A}(z)},$ (2)

where $D^{A}(z)$ is the angular diameter distance at the redshift $z$. The
calibration of $r_{s}$ enables the utilization of the BAO angular scale
$\theta_{BAO}$ to establish a precise correlation between angular diameter
distance and redshift. In this work, we consider the 15 transverse BAO angular
scale measurements. These values were obtained using public data releases (DR)
of the Sloan Digital Sky Survey (SDSS), namely: DR7, DR10, DR11, DR12, DR12Q
(quasars), without assuming a fiducial cosmological model, which are
summarized in Table 1 of Nunes et al. (2020). It is important to note that
because these lateral BAO measurements are performed using cosmology-
independent methods, their errors are larger than those obtained using the
fiducial cosmological method. Nevertheless, this dataset is larger than other
BAO datasets such as (3D-BAO only provides seven line-of-sight and transverse
measurements data points Alam et al. (2021), the Dark Energy Spectroscopic
Instrument only provides five data points DESI Collaboration et al. (2024)).

As we mentioned above, if the calibration of $r_{s}$ independent of
cosmological models is to be achieved, then other low redshift observations
need to be combined. Here we consider observations of SNe Ia. It is important
to note that the distance provided by SNe Ia is relative distance. Therefore,
we can only calibrate the length of the relative standard ruler
$r_{s}^{h}=r_{s}*h$. If the value of the Hubble constant was the one measured
locally, it would yield a smaller value on $r_{s}$.

Figure 1: Left panel: The 1000 reconstructed unanchored distance
$H_{0}D^{L}/c$ by using GPR with Pantheon dataset; Right panel: Similar to
left figure, but for Pantheon+ dataset. The dots with error bars represent
observations of SNe Ia.

###  II.2 Reconstructions of distance redshift relations from observations of
SNe Ia

As the most common transient source in the universe, the SNe Ia, by their very
nature, can act as standard candles in the Universe and are regarded as
powerful cosmological probes. It was observations of SNe Ia that revealed that
the universe is undergoing accelerated expansion Riess et al. (1998);
Perlmutter et al. (1999). Previously, Scolnic et al. (2018) combined the
subset of 279 Pan-STARRS1(PS1) ($0.03<z<0.68$) supernovae (Rest et al., 2014;
Scolnic et al., 2014) with the useful data of SNe Ia from SDSS, SNLS, and
various low redshift and HST samples to form the largest combined sample of
SNe Ia consisting of a total of 1048 SNe Ia ranging from $0.01<z<2.3$, which
is known as the “Pantheon” sample. We refer to work (Scolnic et al., 2018) for
more details about the SNe Ia standardization process including the
improvements of the PS1 SNe photometry, astrometry and calibration. Most
recently, an updated sample named “Pantheon+” was reported in work of Scolnic
et al. (2022), which consists of 1701 light curves of 1550 distinct SNe Ia
spanning the redshift range $0.001\leq z\leq 2.26$. This larger SNe Ia sample
has a significant increase compared to the original Pantheon sample,
especially at lower-redshifts.

However, while the SNe Ia datasets are rich enough, BAO data points are hard
to match at the same redshift. To combine the SNe Ia and BAO transverse
measurements datasets, we generate samples of the unanchored luminosity
distances $H_{0}D^{L}$ from the posteriors of the Pantheon and Pantheon+
datasets, respectively. We use the Gaussian process regression (GPR) (Holsclaw
et al., 2010b; Joudaki et al., 2018; Shafieloo et al., 2012; Aghamousa et al.,
2017) to realize posterior sampling by using the code
GPHist111https://github.com/dkirkby/gphist. without assuming cosmological
models (Kirkby & Keeley, 2017). GPR is a non-parametric regression method that
models relationships between data based on Gaussian process models. GPR is
performed in an infinite dimensional function space without overfitting
problems and is a powerful tool for function reconstruction (Joudaki et al.,
2018). Meanwhile, We use SNe datasets to generate a large number of function
samples $\gamma(z)=\ln([H^{\rm fid}(z)/H_{0}]/[H(z))/H_{0}])$, and obtain the
expansion histories $H(z)/H_{0}$. We refer to work (Liu & Liao, 2024; Li et
al., 2024) for more details about using GPR to reconstruct expansion history
from observations of SNe Ia. With the reconstructed expansion history
$H(z)/H_{0}$, the unanchored SN luminosity distances can be calculated by

$H_{0}D^{L}=(1+z)\int^{z}_{0}dz^{\prime}/[H(z^{\prime})/H_{0}]\ .$ (3)

The final reconstructed 1000 curves (or realizations) of unanchored luminosity
distance $H_{0}D^{L}$ from the two SNe datasets are shown in the Fig. 1,
respectively. These curves show the shape of distance-redshift relation very
well. It should be noted that the redshift of the SNe dataset well covers
redshift range of BAO data, so there is no need for extrapolation of the
redshift range. Further, based on the Etherington relation,
$D^{A}=D^{L}/(1+z)^{2}$, we convert the 1000 realizations $H_{0}D^{L}$ to
$H_{0}D^{A}$ served for BAO data.

##  III Results and Discussion

Figure 2:  Left panel: The probability distribution functions for the relative
standard ruler $r_{s}^{h}$ using transversal BAO plus Pantheon datasets. Right
panel: Similar to left figure, but for Pantheon+ dataset.

Let’s emphasize that calibration of BAO relative standard ruler $r_{s}^{h}$
using observations of SNe Ia is straightforward, we do not make assumptions
about cosmological models and other cosmological parameter. The BAO relative
standard ruler $r_{s}^{h}$ can be rewritten as

$r_{s}^{h}=\frac{(1+z_{BAO})\theta_{BAO}}{100}\cdot[H_{0}D^{A}]^{SNe}.$ (4)

By combining 15 transverse BAO measurements and reconstructed 1000
realizations $H_{0}D^{A}$ from SNe datasets, the individual Probability
Distribution Functions (PDFs) for $r_{s}^{h}$ are shown displayed in Fig. 2.
The uncertainty on $[H_{0}D^{A}]^{SNe}$ and $\theta_{BAO}$, as well as their
mutual correlation are intrinsically included in the respective PDFs. Then, we
use these samples to reconstruct the multi-variate distribution of the 15
$r_{s}^{h}$ measurements.

We note that our results for $r_{s}^{h}$ are individual results, which means
that we achieve calibrations of $r_{s}^{h}$ at different redshifts. Work on
the Pantheon dataset, the final result obtained combining these individual
PDFs reports $r_{s}^{h}=107.10^{+1.36}_{-1.32}$ $Mpc/h$ (median value plus the
$16^{th}$ and $84^{th}$ percentiles around this). In order to highlight the
potential of our method, it is necessary to compare our results with previous
works. Assuming the standard cosmology with matter density parameter
$\Omega_{m}=0.27$, the Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP 9)
collaboration reported the value of sound horizon $r_{s}^{h}=106.61\pm 3.47$
$Mpc/h$ Hinshaw et al. (2013), and Planck Collaboration 2015 (Planck 15)
observation derived $r_{s}^{h}=100.29\pm 2.26$ $Mpc/h$ Planck Collaboration et
al. (2016). Other work such as Refs Carvalho et al. (2016, 2020) used the SDSS
data release 10 (SDSS DR10) and 11 (SDSS DR11) galaxies with a prior of matter
density parameter to obtain $r_{s}^{h}=107.6\pm 2.3$ $Mpc/h$ and
$r_{s}^{h}=107.4\pm 1.7$ $Mpc/h$, respectively. The work Verde et al. (2017)
also obtained constraints on the length of the low-redshift standard ruler
$r_{s}^{h}=107.4\pm 3.4$ $Mpc/h$ when using standard clocks+BAO measurements
with the local $H_{0}$ prior. It is important to note that these work either
assumes cosmological models or uses prior values, whereas our calibration of
$r_{s}^{h}$ comes only from observations. Nevertheless, compared with previous
work, our calibrated $r_{s}^{h}$ results are in agreement with the above
results, except for Planck 2015 results, as shown in Fig. 3, and the precision
of our results on $r_{s}^{h}$ is particularly high. In addition, it is
interesting to see from the Fig. 4 that most of the $r_{s}^{h}$ obtained at
high redshifts have a larger value (9 out of 15 results are larger than the
result obtained by combining all BAOs). Assuming absolute standard ruler
$r_{s}$ is a fixed value, the $H_{0}$ will decrease when $r_{s}^{h}$ increases
(or redshift increases) based on relation $r_{s}=100r_{s}^{h}/H_{0}$. This
finding may give us a better understanding of the discordance between the data
sets or Hubble tension or reveal new physics beyond the standard model.

Work on the Pantheon+ dataset, our model independent calibrated result is
$r_{s}^{h}=105.63^{+1.33}_{-1.31}$ $Mpc/h$ with median values plus 16th and
84th percentiles and shown in the right panel of Fig. 2. Comparing the results
obtained from the two SNe datasets, we find that the Pantheon+ results are
only slightly different from the result using Pantheon dataset. This is
because the lowest BAO redshift is 0.11. Compared with Pantheon sample, the
main change is the sample size of Pantheon+ (especially in $z<0.01$) and a
larger redshift span. The Pantheon+ sample comprises 77 data points from
Cepheid host galaxies at very low redshifts Riess et al. (2022); Brout et al.
(2022), but remaining or not remaining these data points has little impact on
our work. Since GPR is a completely data-driven method, the results of the
reconstruction depend on the input data, and the low redshift data is not
used, the reconstruction results based on the two datasets are almost
identical, we get almost the same results with the two SNe datasets. In
addition, the dataset using Pantheon+ does not improve the precision of
$r_{s}$ calibration (at the second significant digit). Note that even without
an estimate of dimensionless Hubble constant $h$, the combination of BAO and
SNe Ia datasets already constrain the low-redshift standard ruler scale
$r_{s}^{h}$ at the $\sim 1.26\%$ level.

Figure 3: The probability density function of $r_{s}^{h}$ using all
transversal BAO measurements and two SNe Ia datasets and comparing our results
with previous works. Figure 4: The 15 independent $r_{s}^{h}$ calibration
results combined transversal BAO measurements with two SNe Ia datasets.

##  IV Conclusion

In this work, we have proposed a new model-independent method to calibrate
sound horizon $r^{h}_{s}$ (relative standard ruler) by using the latest
observations of SNe Ia acting as standard candles and transversal BAO
measurements. We adopt the non-parameterized method GPR to reconstruct two SNe
Ia datasets, which provide history of the expansion of the universe. Our work
has some significant advantages: it has nothing to do with cosmological
models, and all the quantities used come from observations; no prior values
are taken for any and cosmological parameters, including $H_{0}$; only two
data samples are involved, highlighting the contribution of each dataset to
the overall work.

The final result obtained combining all transversal BAO measurements reports
$r_{s}^{h}=107.10^{+1.36}_{-1.32}$ $Mpc/h$ (median value plus the $16^{th}$
and $84^{th}$ percentiles around this) in the framework of the Pantheon
dataset. This result changes to $r_{s}^{h}=105.63^{+1.33}_{-1.31}$ $Mpc/h$
when uses Pantheon+ dataset. Note that even without an estimate of
dimensionless Hubble constant $h$, the combination of BAO and SNe Ia datasets
already constrain the low-redshift standard ruler scale $r_{s}^{h}$ at the
$\sim 1.26\%$ level. More importantly, it is interesting to find that most of
the $r_{s}^{h}$ obtained at high redshifts have a larger value (9 out of 15
results are larger than the result obtained by combining all BAOs). This
finding may give us a better understanding of the discordance between the data
sets or Hubble tension or reveal new physics beyond the standard model.

The GPR method we used here is not unique. It is still worth exploring whether
these conclusions will change with different reconstruction methods such as
machine learning method. However, these methods have their own advantages and
disadvantages, and show great potential in the studies of precision cosmology.
For instance, the GPR greatly reduces the uncertainty of data. Some work has
generally used non-parametric GP method to reconstruct the expansion history
of the universe. However, as mentioned in many works Mertens et al. (2018);
Mukherjee et al. (2022), one of the most recently debated topics for non-
parametric reconstruction in cosmology with GP is that this technique is
exposed to several foundational issues such as overfitting and kernel
consistency problems Colgáin & Sheikh-Jabbari (2021). GPR is different from
GP, since the GPR occurs in an infinite-dimensional function space without
overfitting problem. Meanwhile, a recent work Zhang et al. (2023) indicated
that using different kernels would not affect the GP reconstruction
significantly. Before the era of abundant available data, it is also very
necessary to carefully choose the method of data reconstruction.

As a final remark, the precision of calibration $r_{s}$ is currently
constrained mainly by samples of BAO data. The first is the BAO sample size,
followed by the observed error of the angle scale. The arrival of the next
generation of BAO surveys has great potential to improve low redshift standard
scale measurements. For example, the Dark Energy Spectroscopic Instrument
(DESI) collaboration recently release the first year data (DR1) of baryon
acoustic oscillations (BAO) to substitute the current BAO measurements DESI
Collaboration et al. (2024, 2024), thereby may directly or indirectly
affecting $H_{0}$ measurements. This shows that our method has great potential
to provide more precise and accurate measurements of $r_{s}$ in the future,
further precision cosmology research.

## Acknowledgments

Liu. T.-H was supported by National Natural Science Foundation of China under
Grant No. 12203009; Chutian Scholars Program in Hubei Province (X2023007);
Marek. B. was supported by the Hubei Province Foreign Expert Project
(2023DJC040). Wang. J. C was supported by the National Natural Science
Foundation of China under Grants No. 12122504 and No. 12035005; the innovative
research group of Hunan Province under Grant No. 2024JJ1006; the Natural
Science Foundation of Hunan Province under grant No. 2023JJ30384; and the
Hunan Provincial Major Sci-Tech Program under grant No.2023ZJ1010.

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# Transmissive RIS for 6G Communications: Design, Prototyping, and
Experimental Demonstrations

Junwen Tang, Mingyao Cui, Shenheng Xu, _Member, IEEE_ , Linglong Dai, _Fellow,
IEEE_ , Fan Yang, _Fellow, IEEE_ , and Maokun Li, _Senior Member, IEEE_ Part
of this work has been accepted by 2020 IEEE International Symposium on
Antennas and Propagation and North American Radio Science Meeting [1]. All the
authors are with the Department of Electronic Engineering, Tsinghua
University, Beijing 100084, China (e-mails<EMAIL_ADDRESS><EMAIL_ADDRESS>{shxu, daill, fan_yang,
maokunli}@tsinghua.edu.cn).

###### Abstract

Reconfigurable intelligent surface (RIS) has been widely considered as a key
technique to improve spectral efficiency for 6G communications. Compared with
most existing research that only focuses on the reflective RIS, the design and
prototyping of a novel transmissive RIS are presented in this paper, and its
enhancement to the RIS-aided communication system is experimentally
demonstrated. The 2-bit transmissive RIS element utilizes the penetration
structure, which combines a 1-bit current reversible dipole and a 90° digital
phase shifter based on a quadrature hybrid coupler. A transmissive RIS
prototype with 16×16 elements is designed, fabricated, and measured to verify
the proposed design. The measured phase shift and insertion loss of the RIS
element validate the 2-bit phase modulation capability. Being illuminated by a
horn feed, the prototype achieves a maximum broadside gain of 22.0 dBi at 27
GHz, and the two-dimensional beamforming capability with scan angles up to
±60° is validated. The experimental results of the RIS-aided communication
system verify that by introducing the extra gain and beam steering capability,
the transmissive RIS is able to achieve a higher data rate, reduce the
transmit power, improve the transmission capability through obstacles, and
dynamically adapt to the signal propagation direction.

###### Index Terms:

Transmissive RIS, 2 bit phase shifter, prototyping

##  I Introduction

With the explosive growth of the emerging new applications, such as
holographic video and meta-verse, 6G is expected to achieve a 10$\times$
increase in spectral efficiency compared to 5G [2], [3]. To realize this goal,
the reconfigurable intelligent surface (RIS) has become an essential candidate
[4]. By adjusting the phase and amplitude responses to an incident
electromagnetic wave, RIS can achieve dynamic beamforming to enhance the
spectral efficiency and overcome blockage [5].

Nevertheless, existing research contributions mainly consider the employment
of reflective RIS [6, 7, 8], which may result in coverage holes in a cell.
Specifically, for reflective RIS, the base station and user need to be located
on the same side of the RIS, which brings extra geographical constraints on
the physical topology [9]. For instance, reflective RIS is difficult to assist
communication between a transmitter outside a vehicle and a receiver inside
it. To cope with this problem, transmissive RIS has been recently proposed
[10]. Rather than being reflected, signals can transmit through a transmissive
RIS to form directional beams. In this way, transmissive RIS can potentially
fill in the coverage holes of reflective RIS.

The phase reconfigurability is the most essential capability for a
transmissive RIS. Solid-state electronic devices are commonly integrated in
each constituent RIS element to dynamically control its phase response.
Continuous phase shifts can be realized using analog-type devices like
varactor diodes [10, 11, 12, 13, 14, 15, 16, 17]. The phase shift range
usually exceeds 360° so that the phase errors are negligible. However, the
transmissive RIS has a very high transmission insertion loss, which can be up
to 5.7 dB [13]. As a consequence, the aperture efficiency of the RIS is
considerably reduced. At high frequencies, switch-type devices are widely used
to produce discrete phase shifts, including PIN diodes, RF MEMS switches, and
etc [13, 15, 14, 16, 17]. Most existing designs focus on 1-bit phase
reconfigurability, wherethe design and fabrication difficulties are manageable
[18, 19, 20, 21, 22, 23, 24, 25, 26]. For example, a classic design of an
O-slot patch loaded with two PIN diodes was developed in [18] to achieve a
stable 180° phase shift in a large bandwidth using the current reversal
mechanism. The minimum measured insertion loss is 1.7/1.9 dB at 9.8 GHz.
Several other attempts were made to obtain a 2-bit phase resolution [27, 28].
Specifically, a monolithically fabricated 2-bit prototype using MEMS switches
[27] was able to produce 4 phase states, but the measured insertion loss is
4.2–9.2 dB at Ka band. A compact 2-bit element using a modified O-slot patch
[28] was designed, fabricated and measured. The measured insertion loss is
1.5–2.3 dB at 29.0 GHz, and the measured 3-dB transmission bandwidth is
10.1–12.1% for four phase states.

The phase quantization errors associated with discrete phase shifts inevitably
introduce performance degradation [29, 30, 31]. It is observed that the 1-bit
element designs suffer from 3–4 dB insertion loss attributed to the coarse
phase resolution, which results in a low aperture efficiency. The sidelobe
levels are significantly higher, sometimes even causing unwanted grating
lobes. By contrast, 2-bit designs are considered a well-balanced choice
between the element performance and the design complexity. The phase
quantization loss can be greatly reduced to less than 1 dB, and the sidelobe
envelop can be significantly improved as well.

Nonetheless, there are only a few 2-bit designs in the literature. One of the
important reasons is that, compared to 1-bit designs, more transition
structures, electronic devices and DC/RF biasing circuits are needed to
achieve four stable phase states. The conventional design approach solely
relies on the two-dimensional unit-cell footprint because of the printed-
circuit board (PCB) fabrication process. It becomes extremely challenging to
lay out a variety of constituent element parts in a greatly limited sub-
wavelength array grid. Consequently, more numbers of stacked layers are used,
which results in the higher fabrication complexity and cost. To the best of
our knowledge, the design, fabrication, and measurement of the 2-bit
transmissive RIS have not been well studied.

In this paper, the 2.5-D penetration structure [32] is exploited to make the
best of the longitudinal space in the propagation direction to develop the
2-bit transmissive RIS. Specifically, our contributions are summarized below.

  * •

Firstly, a 90° digital phase shifter with twoPIN diodes based on a quadrature
hybrid coupler [33] is proposed and realized. Combined with a 1-bit current
reversible dipole, 2-bit phase resolution is achieved at the millimeter wave
(mmWave) band. In addition to some preliminary results reported in the
authors’ conference paper [1], the 2-bit RIS element is further optimized and
more detailed analysis is presented in this journal paper.

  * •

Furthermore, a prototype with 16×16 RIS elements and a logic circuit control
board is fabricated and measured. The measured results show that the prototype
can achieve a maximum broadside gain of 22.0 dBi at 27 GHz, with the
corresponding aperture efficiency of 25.3%. Moreover, the measured radiation
performances for scan angles are presented as well, demonstrating the
beamsteering capability in a large angle up to 60°.

  * •

Finally, a transmissive RIS-aided mmWave wireless communication prototype is
developed to demonstrate the performance of the fabricated 2-bit transmissive
RIS. The experimental results verify that the 2-bit transmissive RIS can
achieve a higher data rate, reduce the transmit power, improve the
transmission capability through obstacles, and dynamically adapt to the signal
propagation direction.

_Organization_ : The reminder of this paper is organized as follows. The
communication model of transmissive RIS is introduced in Section II. Then, in
Section III, we describe the structure, biasing circuits, and simulated
performance of the element of the designed transmissive RIS. Section IV
provides the experimental results for the 16×16 elements RIS prototype in the
microwave anechoic chamber. A transmissive RIS-aided wireless communication
prototype is set up to further measure the performance of the proposed RIS in
Section V. Finally in Section VI, conclusions are drawn.

##  II System Model

In this section, we describe the system model of the transmissive RIS-aided
communication system.

###  II-A System Model

Figure 1:  System model of transmissive RIS-aided communication systems.

We consider that the transmitter (Tx) employs a horn antenna to communicate
with a single-antenna receiver (Rx), where an N-element transmissive RIS is
used for enhancing the signal power. As shown in Fig. 1, the RIS is a
uniformly planar array (UPA) placed in the x-y plane, and its geometric center
is located at the origin of the coordinate system. Let $N_{x}$ denote the
number of antennas on the row and $N_{y}$ denote the number of antennas on the
column, with $N=N_{x}N_{y}$. The antenna spacing along the $x$ axis and $y$
axis are $d_{x}$ and $d_{y}$ respectively, which are usually half of the
wavelength. The coordinates of the Tx and Rx are $(x_{t},y_{t},z_{t})$ and
$(x_{r},y_{r},z_{r})$. The coordinate of the $(m,n)$-th antenna in the $m$-th
row and $n$-th column of the RIS is $(\delta_{m}d_{x},\delta_{n}d_{y},0)$,
where $\delta_{m}=m-(N_{x}-1)/2$ and $\delta_{n}=n-(N_{y}-1)/2$ with
$m\in\\{0,1,\cdots,N_{x}-1\\}$ and $n\in\\{0,1,\cdots,N_{y}-1\\}$. We use the
symbols $d_{t}$, $\theta_{t}$, and $\phi_{t}$ to denote the distance, the
azimuth angle, and the elevation angle between the center of the RIS and the
Tx. The relationship between $(x_{t},y_{t},z_{t})$ and
$(d_{t},\theta_{t},\phi_{t})$ is shown in Fig. 1. Similarly, we use the
symbols $d_{r}$, $\theta_{r}$, and $\phi_{r}$ to denote the distance, the
azimuth angle, and the elevation angle between the center of the RIS and the
Rx, where the relationship between $(x_{r},y_{r},z_{r})$ and
$(d_{r},\theta_{r},\phi_{r})$ is shown in Fig. 1 as well.

We denote ${\mathbf{f}}\in\mathbb{C}^{N\times 1}$ as the Tx-RIS channel, and
denote ${\mathbf{g}}\in\mathbb{C}^{N\times 1}$ as the RIS-Rx channel. Since
this paper aims to evaluate the function of the transmissive RIS, the direct
link between the Tx and Rx is ignored in this paper. Denote
$[{\mathbf{g}}]_{m,n}$ and $[{\mathbf{f}}]_{m,n}$ as the channel from the
$(m,n)$-th antenna of the RIS to the Rx and Tx, respectively. Then, the free
space channel model is adopted to represent $[{\mathbf{g}}]_{m,n}$ and
$[{\mathbf{f}}]_{m,n}$ as [4]

$\displaystyle[{\mathbf{g}}]_{m,n}=\sqrt{\frac{\lambda
G_{g}F_{g}(\theta_{r},\phi_{r})}{4\pi}}\frac{e^{-j\frac{2\pi}{\lambda}d_{m,n}^{r}}}{d_{m,n}^{r}},$
(1) $\displaystyle[{\mathbf{f}}]_{m,n}=\sqrt{\frac{\lambda
G_{f}F_{f}(\theta_{t},\phi_{t})}{4\pi}}\frac{e^{-j\frac{2\pi}{\lambda}d_{m,n}^{t}}}{d_{m,n}^{t}},$
(2)

where $\lambda$ represents the wavelength, $d_{m,n}^{r}$ and $d_{m,n}^{t}$
denote the distance from the $(m,n)$-th antenna of the RIS to the Rx and Tx,
respectively. Moreover, $G_{g}$ and $F_{g}(\theta_{r},\phi_{r})$ denote the
antenna gain and the normalized power radiation pattern of the side of RIS
facing the receiver, while $G_{f}$ and $F_{f}(\theta_{t},\phi_{t})$ correspond
to those of the side of RIS facing the transmitter [4].

Let $s$ denote the transmitted symbol with $\|s\|_{2}=1$. We use symbols
$G_{t}$, $F_{t}$, $P_{t}$, $G_{r}$, $F_{r}$ to represent the transmitter
antenna gain, the transmit power, the normalized radiation power of the
transmitter, the receiver antenna gain, and the normalized radiation power of
the receiver. Then the noiseless received signal by the RX can be modeled as
[4]

$\displaystyle y$
$\displaystyle=\sqrt{P_{t}GF}\sum_{m=0}^{N_{x}-1}\sum_{n=0}^{N_{y}-1}[{\mathbf{g}}]_{m,n}[{\mathbf{f}}]_{m,n}\Gamma_{m,n}e^{j\phi_{m,n}}s,$
$\displaystyle=\frac{\sqrt{P_{t}GF\lambda}}{4\pi}\sum_{m=0}^{N_{x}-1}\sum_{n=0}^{N_{y}-1}\frac{\Gamma_{m,n}}{d_{m,n}^{t}d_{m,n}^{r}}e^{j\left(\phi_{m,n}-\frac{d_{m,n}^{t}+d_{m,n}^{r}}{\lambda}\right)}s,$
(3)

where $\Gamma_{m,n}\in[0,1]$ is transmission loss of the $(m,n)$-th antenna of
the RIS, $\phi_{m,n}\in[0,2\pi]$ denotes the phase shift of the $(m,n)$-th
antenna of the RIS, $G=G_{t}G_{f}G_{g}G_{r}$, and
$F=F_{t}F_{f}(\theta_{r},\phi_{r})F_{g}(\theta_{r},\phi_{r})F_{r}$.

###  II-B Beamforming for the Transmissive RIS

For the desired receiver, the transmissive RIS is designed for maximizing the
received signal energy through beamforming. The noiseless received signal
energy can be presented as

$\displaystyle
P_{r}=\frac{P_{t}GF\lambda^{2}}{16\pi^{2}}\left|\sum_{m=0}^{N_{x}-1}\sum_{n=0}^{N_{y}-1}\frac{\Gamma_{m,n}}{d_{m,n}^{t}d_{m,n}^{r}}e^{j\left(\phi_{m,n}-\frac{d_{m,n}^{t}+d_{m,n}^{r}}{\lambda}\right)}\right|^{2}.$
(4)

To maximize $P_{r}$, it is obvious that the optimal $\phi_{m,n}$ is

$\displaystyle\bar{\phi}_{m,n}=\mod\left(C+\frac{d_{m,n}^{t}+d_{m,n}^{r}}{\lambda},2\pi\right).$
(5)

Here, $C$ is an arbitrary constant. From (5), the phase shift $\phi_{m,n}$ can
be obtained according to $d_{m,n}^{t}$ and $d_{m,n}^{r}$. In our practical
employment, the RIS is deployed nearby the Rx and far away from the Tx. That
is to say, the Rx is within the near-field range of the RIS, while the Tx is
within the far-field range of the RIS. Based on this assumption, the distance
$d_{m,n}^{r}$ can be derived according to the spherical wave model as

$\displaystyle
d_{m,n}^{r}=\sqrt{(x_{r}-\delta_{m}d_{x})^{2}+(y_{r}-\delta_{n}d_{y})^{2}+z_{r}^{2}},$
(6)

while the distance $d_{m,n}^{t}$ can be simplified by the planar wave model as

$\displaystyle d_{m,n}^{t}$
$\displaystyle=\sqrt{(x_{t}-\delta_{m}d_{x})^{2}+(y_{t}-\delta_{n}d_{y})^{2}+z_{t}^{2}}$
$\displaystyle\approx
r_{t}-\delta_{m}d_{x}\sin\theta_{t}\cos\phi_{t}-\delta_{n}d_{y}\sin\theta_{t}\sin\phi_{t}.$
(7)

Therefore, the optimal solution to $\phi_{m,n}$ can be obtained accordingly.
Then, for practical implementation of RIS, the limited resolution of the phase
shift has to be considered. If there are $b$ bits for quantized phase shifter,
then the feasible set of phase shift is

$\displaystyle{\mathbf{\Phi}}_{b}=\left\\{0,\frac{1}{2^{b-1}}\pi,\cdots,\frac{2^{b}-1}{2^{b-1}}\pi\right\\}.$
(8)

Finally, the practical phased shift on a RIS element is given by

$\displaystyle\tilde{\phi}_{m,n}=\arg\min_{\phi\in{\mathbf{\Phi}_{b}}}|\phi-\bar{\phi}_{m,n}|.$
(9)

In our system, we design a transmissive RIS with $b=2$ bits. Notice that the
transmission model and the phase shift design mathematically have no
difference with the reflective RIS-aided communication system. Nevertheless,
the application scenarios and implementation and of them are quite different.
For instance, a transmissive RIS can be deployed on a vehicle window to
enhance communication between inside and outside the vehicle. In the following
sections, we will elaborate on the proposed transmissive RIS design in our
communication system.

##  III Proposed RIS Element Design

We describe the proposed transmissive RIS element in this section, including
element design, 90° phase shifter exploited in the element, biasing circuits,
and element performance in simulation.

###  III-A Element Design

Figure 2:  Proposed 2.5-D structure of the transmissive RIS for mmWave communications. TABLE I: Simulated Performance of the 2-bit RIS Element State |  | Element loss
---
@26.5 GHz
| Phase shift
---
@26.5 GHz
| 3-dB trans.
---
bandwidth
1 (state-0∘) | 1.1 dB | -141.2∘ | 23.6-28.9 GHz (20.1%)
2 (state-90∘) | 1.3 dB | -56.8∘ | 24.8-28.6 GHz (14.2%)
3 (state-180∘) | 1.1 dB | 34.9∘ | 23.5-28.6 GHz (19.6%)
4 (state-270∘) | 1.5 dB | 129.0∘ | 24.6-29.0 GHz (16.4%)

Fig. 2 illustrates the proposed 2.5-D structure of the 2-bit transmissive RIS.
Each RIS element consists of a number of one-dimensional subarrays aligned in
parallel. The constituent element utilizes the penetration structure, which is
composed of a RIS-side Rx and a RIS-side Tx to receive and transmit the RF
signals impinging on the RIS, respectively, and a microstrip transmission line
to convey the signal through the RIS aperture. Instead of laying them out in
the aperture plane, two vertical dipoles [34] are employed and arranged along
the propagation direction to circumvent the space constraint imposed by the
unit cell footprint. The slightly extended longitudinal space easily
accommodates a 90° digital phase shifter between the RIS-side Rx and the RIS-
side Tx. Combined with the 1-bit current reversible dipole, the 2-bit
transmissive RIS element can be readily realized.

The 2.5-D structure slightly increases the aperture profile by 1 2
wavelengths, but it is still much smaller compared with the aperture size.
Especially at mmWave frequencies, the aperture profile is merely a couple of
centimeters and will not considerably undermine the low profile and conformal
features of the RIS. Each subarray can be easily fabricated on a single layer
of substrate, thus avoiding the complicated multilayer PCB process and
lowering the overall cost. It is also a remarkable fact that the $//$-type
2.5-D structure can be further developed into a $\\#$-type or a $\Delta$-type
formation where two or three sets of subarrays can be arranged in the same
aperture, so that the 2.5-D unit cell space can be more fully exploited for
more constituent element parts. Hence, more advanced features such as dual-
polar or dual-band designs can be accomplished.

The linearly incident wave propagating along the z axis is received by the
passive RIS-side Rx composed of a vertical dipole. Then, the received signal
is converted into a guided wave and conveyed along the microstrip transmission
line. The phase shifter structure based on the quadrature hybrid coupler is
employed. Instead of the varactor diodes used in the analog phase shifter
design [33], it is terminated with reflection-type loads composed of two p-i-n
diodes (model MADP-000907-14020) to provide a 0°/90° digital phase shift. The
two loaded p-i-n diodes are always tuned at the same ON- or OFF-states,
resulting in a 90° phase shift. The RIS-side Tx is similar to the RIS-side Rx,
but the vertical dipole structure [34] is modified to integrate two p-i-n
diodes (MADP-000907-14020) that are symmetrically placed in the feeding
microstrip line. They are alternatively turned ON or OFF so that the
excitation current flows in opposite directions. Consequently, the reversible
current flow produces a stable 180° phase shift without significantly
affecting magnitude response. Finally, the RIS-side Tx re-radiates the guided
wave into the free space with four stable phase states of 0°/90°/180°/270°,
and hence, the 2-bit phase resolution is obtained.

The frequency of the designed transmissive RIS element is 26.5 GHz, and the
unit cell size is $4.9\times 4.9$ $\text{mm}^{2}$. The proposed 2-bit element
is printed on a single layer of Taconic TLX-8 substrate ($\epsilon_{r}$ =
2.55, $\tan\delta$= 0.0019, $h$ = 0.254 mm). The microstrip line and the 90°
digital phase shifter are on the top of the substrate, while the vertical
dipoles and the ground plane are arranged on the bottom of the substrate. The
total profile of the element is 21.8 mm, corresponding to 1.9$\lambda$ at the
design frequency. The following geometrical parameters are optimized after a
comprehensive parametric study: $l_{d}$ = 2.1 mm, $wd$ = 0.6 mm, $l_{s}$ = 1.6
mm, $w_{s}$ = 0.3 mm.

###  III-B 90° Digital Phase Shifter

Figure 3:  Proposed 90° digital phase shifter based on a quadrature hybrid
coupler: (a) the illustrative structure; (b) simulated reflection magnitude,
(c) transmission magnitude, and (d) transmission phase.

The proposed 90° digital phase shifter integrated in the 2-bit transmissive
RIS element is designed to provide 0°/90° phase switching, as shown in Fig. 3
(a). It is a reflection-type phase shifter based on the quadrature coupler
terminated with two reflective loads, which are composed of p-i-n diodes and
short-circuited stubs. The realization of 90° phase shift is by tuning the two
p-i-n diodes to work at ON-ON or OFF-OFF state, respectively. Two tuning stubs
are introduced to maintain a stable desired phase shift by tuning their
lengths. The digital phase shifter is modeled and simulated with a periodic
boundary condition and a wave-port excitation. As can be observed from the
simulation results plotted in Fig. 3 (b) , a 10-dB return loss bandwidth of
22% (22.6-28.2 GHz) is achieved. Good impedance matching performance minimizes
the insertion loss to less than 1 dB within the frequency band from 24.2 to
28.0 GHz. Meanwhile, from the curves plotted in Fig. 3 (d) , we can find that
the phase difference is close to 90° in a wide frequency band. We can conclude
that the phase shifter is capable of generating desired 90° phase shift by
electrically adjusting the two p-i-n diodes, thus achieving the 0°/90° digital
phase switching capability with the low insertion loss.

###  III-C Performance of the designed Transmissive RIS Element

Figure 4:  Simulated transmission (a) magnitude and (b) phase of the proposed
2-bit RIS element.

We simulate the proposed 2-bit RIS element with a periodic boundary condition
to mimic an infinite array environment and the mutual coupling effect is also
considered. The element is simulated. The simulated element performances under
normal incidence for the four working states are plotted in Fig. 4. The
transmission magnitude responses at 26.5 GHz are summarized in Table I. It can
be seen that the average transmission insertion loss of the four states is
around 1.3 dB. Moreover, the insertion losses are maintained below 3 dB
ranging from 24.8 to 28.6 GHz, corresponding to the 3-dB transmission
bandwidth of 14.2%. The phase curves of the four states are roughly parallel
with around 90° phase difference in the operating frequency band. Hence, by
switching the p-i-n diodes alternatively, the RIS element successfully
achieves 2-bit phase tuning capability.

##  IV Ris Design, Fabrication, and Measurement

In this section, a transmissive RIS prototype composed of $16\times 16$
proposed elements is designed, fabricated, and measured to experimentally
validate the performance of the proposed RIS element.

Figure 5:  Photography of (a) the fabricated transmissive RIS prototype, (b)
the measurement setup in the microwave anechoic chamber.

The photographs of the fabricated RIS prototype and the measurement setup in
the microwave anechoic chamber are presented in Fig. 5. Taking advantage of
the PCB technology, the RIS is easy to fabricate. The RIS is space-fed by a
linearly polarized horn. The effective aperture size of the RIS prototype is
$78.4\times 78.4$ $\text{mm}^{2}$. The feeding horn illuminates the array at
an optimized distance of 50 mm. To achieve the goal of phase
reconfigurability, each element of the array needs to be controlled
independently. There are 512 biasing lines since each element has two biasing
lines to apply DC voltages to four p-i-n diodes. Two logic circuit controlling
boards are attached to supply independent DC voltages of 512 channels, and
they are connected to the biasing lines through several connectors.

Figure 6: Performance of the broadside beam: (a) measured gain bandwidth, (b)
calculated and measured normalized radiation patterns at 27.0 GHz.

We measure the fabricated prototype in a planar near-field anechoic chamber.
From the measured performance of the broadside beam depicted in Fig. 6, a peak
gain of 22.0 dBi is obtained at 27.0 GHz, which is 9.3 dB higher than that of
the feeding horn. The corresponding aperture efficiency is 25.3%. The slight
frequency shift to higher frequencies is mainly attributed to the tolerance in
fabrication and the supporting structure. The measured radiation pattern is in
good agreement with the theoretical prediction based on the array theory. The
measured sidelobe level is below -22 dB, remarkably lower than that of the
1-bit designs, which is mainly attributed to the finer phase resolution of the
2-bit RIS. The measured cross-polarization level is -21.3 dB.

Figure 7: Measured radiation patterns of scanned beams at 27.0 GHz in (a)
E-plane, (b) H-plane.

The radiation behaviors of the scanned beams are measured as well to
experimentally verify the dynamic beam scanning capability of the transmissive
RIS in two-dimensional space. By controlling the phase of each RIS element,
the transmitted focused beam can be formed by the RIS in the given direction.
As shown in Fig. 7, the measured scanned beams in the angular region from 0°
to -60° show accurate beam pointing and well-defined patterns in both E-plane
and H-plane. Note that the beams in the opposite angular region are omitted
due to the symmetry. The measured 60° scan gain losses are 4.0 dB and 5.0 dB
in two principal planes, respectively. Table II compares the performance of
the proposed 2-bit RIS with other RIS designs published in literature. It is
evident that this work achieves the highest aperture efficiency.

TABLE II: Performance Comparison with Other transmissive RIS Designs Ref. |  | Freq.
---
[GHz]
| Tunable
---
device
| Phase
---
resolution
| Gain
---
[dBi]
| Aper. eff.
---
[%]
[18] | 9.8 | p-i-n | 1-bit | 22.7 | 15.4
[26] | 34.8 | MEMS | 2-bit | 9.2 | 6.2
[27] | 29 | p-i-n | 2-bit | 19.8 | 15.9
Our work | 27 | p-i-n | 2-bit | 22.0 | 25.3

##  V Transmissive RIS-Aided Wireless Communication Prototype

In this section, a transmissive RIS-aided wireless communication prototype is
set up to further measure the performance of the designed transmissive RIS in
practical communication scenarios.

###  V-A Measurement Setup

Figure 8: Transmissive RIS-aided wireless communication prototype.

As illustrated in Fig. 8, we carry out the experiment in an office
environment. The prototype is composed of the transmitter side, the RIS, and
the receiver side. Both the receiver and the transmitter utilize the software-
defined radio (SDR) platform, composed of the PXI hardware architecture and
the LabVIEW system design software, to realize transmission at the mmWave
band.

TABLE III: System Parameters Parameters | Value | Parameters | Value
---|---|---|---
| Carrier
---
frequency
27.0 GHz |  Antenna gain | Tx | 22.7
System bandwidth | 800 MHz | Rx | 9.2
Waveform | CP-OFDM |  Trans. RIS | Array gain | 19.8
FFT size | 2048 | Frequency | 22.0
| Carrier
---
spacing
75 KHz |  | Phase
---
resolution
2 bit
ADC/DAC resolution | 14 bit | Array size | 16 $\times$ 16
Tx/Rx height | 1.5 m
Modulation | 16-QAM | $d_{1}$ | 2.4 m
Coding | Turbo | $d_{2}$ | 0.2 m
Code rate | 1/2 | $d_{3}$ | 0.05 m

The transmitter consists of the transmitter host, the FPGA, the ADC module,
the mmWave upconverter, and a horn antenna. The transmitter host controls the
system parameters, including modulations, the transmit power, the central
frequency, and so on. A high-speed bitstream is first delivered by the host to
the FPGA module. The FPGA module realizes complex signal processing, including
channel coding, constellation mapping, OFDM modulation, and etc. After that,
the signals are sequentially processed by the ADC and the mmWave upconverter
to form mmWave analog signals suitable for transmission in wireless channels.

The transmissive RIS has 256 2-bit elements. It receives the signals from the
transmitter, tunes the phase of received signals, and then directionally
transmits them towards the receiver. Moreover, for validating that a
transmissive RIS is able to overcome obstacles, we can also place an obstacle,
such as a piece of marble, between the RIS and the base station.

Similar to the transmitter, the receiver is composed of the receiver host, the
FPGA, a DAC module, a mmWave down converter, and a horn antenna. At the
receiver side, the Rx horn antenna first receives the signal and transforms
them the digital domain by the mmWave down converter and the DAC module. Then,
the FPGA module is responsible for recovering the bitstream by channel
estimation, OFDM demodulation, decoding, CRC check and etc. Moreover,
according to the results of the CRC check, the host obtains the block error
rate and calculates the data rate. Finally, the received constellation and the
data rate are illustrated on the screen of the host.

In Table III, the detailed settings of our mmWave platform are provided. We
consider a downlink communication scenario. The bandwidth is 800 MHz and the
carrier frequency is 27.0 GHz. The horn antenna of the transmitter, the
transmissive RIS, and the horn antenna of the receiver are on the same height
of 1.5 m and are all horizontally polarized. A piece of marble with thickness
of 0.03 m is employed to mimic the obstacle. Let $d_{1}$, $d_{2}$, and $d_{3}$
denote the the distance between the Tx antenna and the obstacle, the distance
between the obstacle and the RIS, the distance between the RIS and the Rx
antenna. They are set as $d_{1}$ = 2.4 m, $d_{2}$ = 0.2 m, and $d_{3}$ = 0.05
m, respectively. The fabricated transmissive RIS works at 27.0 GHz with an
additional 9.3 dB array gain when being illuminated by the Rx horn antenna.
The azimuth angle and the elevation angle from the RIS center to the Tx/Rx are
all zero, i.e., $\theta_{t}=\theta_{r}=\phi_{t}=\phi_{r}$ = 0° as shown in
Fig. 1. We verify the performance of this RIS in terms of array gain and data
rate.

###  V-B Array Gain Performance Assessment

TABLE IV: Array Gain Performance With or without RIS | Transmit power | Data rate
---|---|---
$\times$ | 13.6 dBm | 1024 Mbps
$\checkmark$ | 5.4 dBm | 1121 Mbps

To evaluate the array gain, we remove the obstacle and assess the system
performance with or without the transmissive RIS. The experiment results are
presented in Table IV. Specifically, without the transmissive RIS, when the
transmit power reaches 13.6 dBm, the data rate can reach 1024 Mbps. By
contrast, to achieve a similar transmission rate of 1121 Mbps, only 5.4 dBm
transmit power is required with the help of transmissive RIS. It is obvious
that the transmit power is reduced by 8.2 dB. As we measured in the anechoic
chamber, the RIS can provide a 9.3 dB array gain, which is consistent with the
transmit power reduction measured by our prototype. Therefore, it is obtained
that the transmissive RIS-aided communication prototype can reduce the
transmit power by the magnitude close to the array gain provided by the RIS,
while maintaining the similar communication performance.

###  V-C Data Rate Assessment

TABLE V: Data Rate Performance | With or
---
without RIS
| With or
---
without obstacle
| Azimuth
---
angle
| Data
---
rate
$\times$ | $\times$ | $0^{\circ}$ | 1024 Mbps
$\checkmark$ | $\times$ | $0^{\circ}$ | 1683 Mbps
$\times$ | $\checkmark$ | $0^{\circ}$ | 0 Mbps
$\checkmark$ | $\checkmark$ | $0^{\circ}$ | 1683 Mbps

To further validate that the fabricated transmissive RIS is able to overcome
obstacles, we also introduce a piece of marble into the system to evaluate the
data rate performance. Specifically, depending on whether the obstacle and/or
the RIS exist, there are in total four communication scenarios. The transmit
power is fixed to 13.6 dBm. The experiment results are tabulated in Table V.
Two conclusions can be derived accordingly. One is that the fabricated RIS is
able to improve the transmission data rate. When the obstacle is removed, the
introduction of the transmissive RIS increases the data rate from 1024 Mbps to
1683 Mbps. It is worth mentioning that 1683 Mbps is the highest data rate that
the communication prototype can support with 16-QAM modulation. The other is
that the transmissive RIS is able to overcome obstacles because of the
additional array gain it provides. Specifically, when the direct Tx-Rx link is
blocked by the marble, data transmission is completely interrupted without the
help of transmissive RIS. By contrast, the introduction of the transmissive
RIS re-establishes the communication link and achieves the highest 1683 Mbps.
This is because that the array gain provided by the RIS is higher than the
attenuation of the obstacle.

###  V-D Beam Steering Assessment

TABLE VI: Beam Steering Evaluation | With or
---
without RIS
| With or
---
without obstacle
| Azimuth
---
angle
| Data
---
rate
$\times$ | $\times$ | $30^{\circ}$ | 450 Mbps
$\checkmark$ | $\times$ | $30^{\circ}$ | 1683 Mbps
$\times$ | $\checkmark$ | $30^{\circ}$ | 0 Mbps
$\checkmark$ | $\checkmark$ | $30^{\circ}$ | 1683 Mbps

Finally, the beam steering ability of the fabricated transmissive array is
validated in this subsection. Compared to the communication settings in
previous experiments, the transmit power is fixed to 13.6 dBm and the azimuth
angle from the transmissive RIS to the transmitter is $\theta_{t}=$ 30°. The
other settings are the same. The experiment results are shown in Table VI.
Without the assistance of transmissive RIS, the data rate is reduced from 1024
Mbps to 450 Mbps due to the misalignment between the Tx and Rx horns. By
introducing the transmissive RIS and scanning the beam it forms to the 30°
direction, the maximum 1683 Mbps data rate is achieved. As a result, we can
conclude that the transmissive RIS is able to dynamically steer its beam to
adapt to the variation of the incident angle of the signal. Similar to the
experiment in the previous subsection, the obstacle is again introduced into
the communication prototype. The experiment results validate that the
transmissive RIS is able to improve the data rate and overcome obstacles at an
oblique incident angle $\theta_{t}=$ 30°.

##  VI Conclusion

The transmissive RIS has a promising prospect in 6G communications to provide
enhanced signal coverage in various communication scenarios. Compared to the
reflective RIS, the research and experimental demonstration of the
transmissive RIS and the transmissive RIS-aided communication system are
considerably fewer. This work proposes a novel 2-bit transmissive RIS design
with a 90° digital phase shifter and a 1-bit vertical current reversible
dipole. The 2-bit phase controlling capability is achieved and measured.
Experimental results show the transmissive RIS prototype with $16\times 16$
elements can provide a broadside gain of 22.0 dBi at 27.0 GHz. Moreover, a
transmissive RIS-aided communication prototype is set up, and the system
performances for three representative scenarios are measured. It is
experimentally demonstrated that the transmissive RIS is able to achieve
higher data rate, reduce the transmit power, improve the transmission
capability through obstacles, and dynamically adapt to the signal propagation
direction.

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