# Reconfigurable Intelligent Surfaces:
Interplay of Unit-Cell- and Surface-Level Design and Performance under
Quantifiable Benchmarks

Ammar Rafique, Naveed Ul Hassan, , Muhammad Zubair, , Ijaz Haider Naqvi,
Muhammad Qasim Mehmood, Chau Yuen, , Marco Di Renzo, , and Mérouane Debbah A.
Rafique, M. Q. Mehmood and M. Zubair are with the Electrical Engineering
Department of Information Technology University (ITU) of the Punjab, Lahore,
Pakistan 54600. (Emails<EMAIL_ADDRESS><EMAIL_ADDRESS>muhammad.zubair@itu.edu.pk).N. U. Hassan and I. H. Naqvi are with the
Department of Electrical Engineering at Lahore University of Management
Sciences (LUMS), Lahore, Pakistan 54792. (Emails<EMAIL_ADDRESS>ijaznaqvi@lums.edu.pk).C. Yuen is with the Engineering Product Development at
the Singapore University of Technology and Design (SUTD), 8 Somapah Road,
Singapore 487372. (Email: yuenchau@sutd.edu.sg).M. Di Renzo is with Université
Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systemes, 3
Rue Joliot-Curie, 91192 Gif-sur-Yvette, France. (marco.di-renzo@universite-
paris-saclay.fr)Mérouane Debbah is with the Technology Innovation Institute,
Masdar City 9639, Abu Dhabi, UAE, and also with the CentraleSupélec,
University ParisSaclay, 91192 Gif-sur-Yvette, France (e-mail:
merouane.debbah@tii.ae).Correspondence may be sent to N. U. Hassan, M. Zubair
and M. D. Renzo

###### Abstract

The ability of reconfigurable intelligent surfaces (RIS) to produce complex
radiation patterns in the far-field is determined by various factors, such as
the unit-cell’s size, shape, spatial arrangement, tuning mechanism, the
communication and control circuitry’s complexity, and the illuminating
source’s type (point/planewave). Research on RIS has been mainly focused on
two areas: first, the optimization and design of unit-cells to achieve desired
electromagnetic responses within a specific frequency band; and second,
exploring the applications of RIS in various settings, including system-level
performance analysis. The former does not assume any specific radiation
pattern on the surface level, while the latter does not consider any
particular unit-cell design. Both approaches largely ignore the complexity and
power requirements of the RIS control circuitry. As we progress towards the
fabrication and use of RIS in real-world settings, it is becoming increasingly
necessary to consider the interplay between the unit-cell design, the required
surface-level radiation patterns, the control circuit’s complexity, and the
power requirements concurrently. In this paper, a benchmarking framework for
RIS is employed to compare performance and analyze tradeoffs between the unit-
cell’s specified radiation patterns and the control circuit’s complexity for
far-field beamforming, considering different diode-based unit-cell designs for
a given surface size. This work lays the foundation for optimizing the design
of the unit-cells and surface-level radiation patterns, facilitating the
optimization of RIS-assisted wireless communication systems.

###### Index Terms:

6G, RIS, Unit-cell

##  I Introduction

Reconfigurable intelligent surface (RIS) allows the reconfiguration of
wireless channels [1, 2]. The design of an RIS includes a basic planar micro-
structure called unit-cell equipped with integrated electronic components such
as diodes to allow the tuning of the magnitude and phase of the incident
electromagnetic (EM) waves [3, 4]. A surface is then fabricated by repeating
the unit-cells at sub-wavelength periodic intervals. An appropriate control
circuit is also added to tune the RIS unit-cells to achieve the desired
radiation patterns. An RIS made up of a sufficiently large number of unit-
cells can generate complex radiation patterns [5].

RIS-assisted wireless communication deployments for an urban environment with
indoor/outdoor applications are illustrated in Figure 1. The typical structure
of a unit-cell, a PIN diode with ON/OFF control, the lumped-element models of
the PIN diode, an RIS comprising of multiple unit-cells, and a microcontroller
to turn ON/OFF the PIN diodes for the generation of specified radiation
patterns are also shown in this figure. Non-line of sight (NLoS) scenarios
dominate urban environments where buildings often block the signals. In such
situations, single-beam steering, multi-beam forming with equal power levels,
and multi-beam forming with unequal power levels can be enabled with the help
of RIS to reduce outages and improve the spectral efficiency [6, 7].

The near-field of an antenna or a unit-cell is conventionally defined up to
$\frac{2D^{2}}{\lambda}$ meters far from the antenna or the unit-cell, where
$D$ is the minimal diameter of a sphere that encloses the antenna or the unit-
cell, and $\lambda$ is the wavelength [8, 9]. Assuming that the RIS has
$N^{2}$ unit-cells, the near-field region of an RIS is $N^{2}$ times larger
than the near-field boundary of a unit-cell. Depending on the number of unit-
cells in an RIS, its near-field region can extend up to tens or hundreds of
meters. The users or receivers can, therefore, be located in either the far-
field or the near-field region of an RIS. Similarly, an RIS may be located in
either the far- or the near-field of a transmitter/source. If the RIS is
located in the far-field of a source, the EM waves appear as planewave to RIS,
and the source is referred to as a planewave source. On the other hand, if the
RIS is located in the near-field of a source, the EM waves appear as spherical
waves to the RIS, and the source is referred to as a point source for
simplicity. Therefore, in RIS-assisted wireless communications, four cases
emerge based on the source type and receiver location from the RIS.

  1. 1.

Case 1: The transmitter appears as a point source to the RIS and the receiver
is located in the far-field of the RIS.

  2. 2.

Case 2: The transmitter appears as a planewave source to the RIS and the
receiver is located in the far-field of the RIS.

  3. 3.

Case 3: The transmitter appears as a point source to the RIS and the receiver
is located in the near-field of the RIS.

  4. 4.

Case 4: The transmitter appears as a planewave source to the RIS and the
receiver is located in the near-field of the RIS.

The analytical methods to compute the radiation pattern produced by an RIS
differ in each case. The far-field assumption greatly simplifies the
computation of the radiation pattern because the elevation and azimuth angles
from every unit-cell of the RIS are approximately the same in the far-field
[10]. In this paper, we consider the first two cases (case 1 and case 2) and
study the ability of an RIS to produce various radiation patterns. This is
motivated by the fact that an RIS usually performs better when it is closer to
the source [11], and it may be likely that the receivers are located in the
far-field of the RIS.

Figure 1: Example of RIS-assisted urban environment.

RIS can play a crucial role in indoor and outdoor scenarios for single-beam
steering, multi-beam forming with equal or unequal power levels, and improving
the performance of RIS-assisted communication systems, using both point and
planewave sources. Various studies have investigated the theoretical gains of
RIS in different application settings, as illustrated in Figure 1, across
different frequency ranges. These studies have been comprehensively reviewed
in [6]. However, these theoretical analyses tend to overlook the shape and
size of the unit-cells, the complexity and power requirements of the RIS
control circuit, and other factors beyond surface-level capabilities. With the
increasing use of RIS in practical settings, there is a pressing need to
develop tools for selecting appropriate unit-cell designs that align with
specific application scenarios using point or planewave sources. The process
of optimizing the unit-cells entails considering the trade-offs between unit-
cell optimization, surface-level radiation pattern generation capabilities,
and control circuit complexity alongside the associated channel sensing
overheads. Recently, it was demonstrated in [12] that the optimal positioning
of RIS in a 3D environment can also enhance the system-level performance of
RIS-assisted communication systems. This paper’s primary focus is on unit-cell
and surface-level RIS design considerations, and it does not delve into
system-level optimization.

Figure 2: (from left to right) Unit cell layouts of $\text{S}_{1}$ [13],
$\text{S}_{2}$ [14], $\text{S}_{3}$ [15], $\text{S}_{4}$ [16], $\text{S}_{5}$
[14].

This paper aims to introduce a benchmarking framework and metrics that can be
used to assess the radiation pattern generation capabilities, energy
requirements, and control circuit complexity of RIS fabricated from various
unit-cells, specifically those employing PIN diodes for tuning, under
point/planewave source assumptions for far-field beamforming. Additionally, we
examine the possibility of trading the radiation pattern generation capability
for control circuit complexity through unit-cell grouping. To achieve our
goal, we establish a set of radiation patterns, both simple and complex, as
benchmarks within our framework because some recent studies emphasize the
importance of considering the entire patterns to maximize the power towards
the desired directions while keeping it low in the unwanted directions [17].

Our study focuses on evaluating the effectiveness of the proposed benchmarking
framework and analyzing the tradeoffs for five RISs built using five different
unit-cell designs [13, 14, 15, 16]. Among these designs, two RISs utilize
1-bit control achieved through a single PIN diode, while the remaining two
RISs utilize 2-bit control via multiple PIN diodes. The unit-cells used in
these four RISs are optimized to generate the maximum phase differences
between different diode control states, i.e., 180∘ for 1-bit unit-cells and
90∘ for 2-bit unit-cells. The fifth RIS also utilizes a single PIN diode for
1-bit control, but its unit-cell design is unoptimized and results in only a
50∘ phase shift. At normal incidence, all unit-cells in our study exhibit
reflection coefficients between 0.85 and 1.

Numerical experiments are conducted to assess the ability of these RISs to
replicate the benchmarking patterns in the far-field, assuming a normal angle
of incidence for incoming EM waves using point or plane wave sources, which is
widely used in the literature [18]. We also analyze and discuss the resulting
complexity of the RIS control circuit and power requirements for each RIS. Our
key findings are summarized below.

  * •

When assuming a point source (case 1), we observe that RIS made from a 1-bit
unit-cell design outperforms RIS made from a 2-bit design in terms of control
circuit complexity and power requirements due to the spherical curvature of
the wavefronts.

  * •

In the case of a planewave source (case 2), RIS made from a 1-bit unit-cell
design exhibits significantly poorer beam steering performance compared to RIS
made from a 2-bit unit-cell design.

  * •

When the unit-cells on RIS are controlled in groups, the performance of poor
designs is less affected, which also reveals that making large surfaces out of
poor designs would hardly improve surface-level performance.

  * •

If a simple radiation pattern, such as a single beam steering at small
reflection angles (less than 40∘), is required, un-optimized unit-cell designs
can be used.

  * •

For generating complex radiation patterns, such as multiple beams at different
non-uniform angles, complex and highly-optimized unit-cell designs with multi-
bit control and large-sized surfaces are helpful.

  * •

The power requirements and size of the RIS control circuit increase with the
number of PIN diodes per unit-cell design and the operating frequency.

  * •

RISs are almost passive devices as they do not add new power to the incoming
radio signals, but the power requirements of the control circuit cannot be
ignored.

  * •

To effectively compare the generation capabilities of RIS radiation patterns,
multiple metrics are required. In this work, we introduce three useful metrics
- directivity error (DE), normalized mean squared error (NMSE), and side lobe
ratio (SLR) - to quantify the relative performance of various RIS.

The rest of the paper is organized as follows. In Section II, we discuss the
unit-cell designs and the electric field (E-field) produced by RIS in the far-
field; in Section III, we discuss the RIS control circuit and analyze its
complexity and power requirements; in Section IV, we present our benchmarking
framework and performance metrics; in Section V, we present our simulation
results and their discussion; and in Section VI, we conclude the paper.

##  II Unit-cell & RIS

###  II-A Unit-Cell —The basic element of RIS

A fundamental element of RIS is a planar micro-structure called unit-cell. A
flat surface is obtained by arranging unit-cells in rectangular arrays. The
unit-cell size depends on the frequency of operation, with higher frequencies
requiring smaller dimensions. The total number of unit-cells in a fixed-size
RIS depends on its shape and size. By joining multiple smaller surfaces with
the repeating pattern of unit-cells, large-sized RIS can be made. It is
important to note that we define RIS as a repeating pattern of unit-cells
jointly controlled either with a single controller or a set of controllers.

A category of RIS research focuses entirely on unit-cell design and its EM
properties. By including active electronic components, such as PIN diodes,
into unit-cell, flexible and real-time functionality is expected from the
resulting RIS. Based on these ideas, the RIS made from the unit-cell designed
in [13] demonstrates agile scattering, planar focusing, beam steering, and
beam forming. The unit-cell proposed in [13] has a sandwich structure composed
of a simple rectangular patch, a metal ground plane, and a single PIN diode
(1-bit control) connects one edge of the patch to the ground through a
metallic via. In [14], the authors propose a three-layer unit-cell design,
which is again controlled through a single PIN diode (1-bit control). A
relatively more complex unit-cell is proposed in [15]. This design consists of
5 PIN diodes, but only two control signals are required; therefore, we can
classify this as a 2-bit design. Four configurations of 5 PIN diodes produce
four almost 90∘ apart phase shifts. The unit-cell is symmetric but has a
relatively complex structure and consists of an upper patch, a slot-loaded
plane, and a ground. Another 2-bit unit-cell design using only 2 PIN diodes is
proposed in [16]. The layouts of all the unit-cells are shown in Figure 2.
Table I summarizes the design frequency, reflection amplitudes, and phases of
all these unit-cells in different control states at a normal incidence angle.

In this paper, the RISs made from the unit-cell designs proposed in [13, 14,
15, 16] are denoted as $\text{S}_{1}$, $\text{S}_{2}$, $\text{S}_{3}$, and
$\text{S}_{4}$ respectively. An unoptimized unit-cell design obtained from
[14] is also considered and referred to as $\text{S}_{5}$. This design has a
maximum phase shift of only 50∘ between its two configurations, allowing for
testing the necessity and extent of unit-cell optimization for achieving good
performance.

###  II-B E-Field of RIS

In general, the E-field of an RIS comprising of $M\times N$ unit-cells of the
same type, arranged in a rectangular planar array, at elevation and azimuth
angles denoted by $\theta$ and $\phi$ respectively on the observer side, can
be calculated in the far-field as:

$E(\theta,\phi)=\sum_{m=1}^{M}\sum_{n=1}^{N}\big{[}E_{in_{mn}}e^{j\alpha_{mn}}f(\theta_{mn},\phi_{mn})\times\\\
\Gamma e^{j\Phi_{mn}}f(\theta,\phi)e^{jk.\hat{r}_{mn}}\big{]}.$ (1)

where, $e^{jk.\hat{r}_{mn}}$ represents the wave-vector, $E_{in_{mn}}$ and
$\alpha_{mn}$ are the illuminating amplitude and phase (source radiation
response), $f(\theta,\phi)$ is the unit-cell radiation response (scattering
pattern), the angles $\phi_{mn}$ and $\theta_{mn}$ are the azimuth and
elevation angles of the source relative to $(m,n)^{th}$ unit-cell, $\Gamma$ is
the reflection coefficient of the unit-cell, and $\Phi_{mn}$ is the phase
shift produced by $(m,n)^{th}$ unit-cell. This phase shift is controlled by
changing the state of the PIN diodes. For example, for an optimized 2-bit
unit-cell the value of $\Phi_{mn}\in\\{0,\pi/2,\pi,3\pi/2\\}$. Thus, by
varying the configuration of unit-cells, different responses can be achieved
by RIS, i.e., it can steer the incoming signal in the arbitrary desired
direction(s).

Equation (1) is valid for both case 1 and case 2. However, under the planewave
source assumption (case 2), we can further simplify some terms in this
equation. The radiation response from the source simplifies to
$E_{in_{mn}}=E,\>\forall m,n$, and $e^{j\alpha_{mn}}=1,\>\forall m,n$ (or some
constant). Similarly, the unit-cell radiation response becomes
$f(\theta_{mn},\phi_{mn})=f(\theta,\phi)$ because all the azimuth and
elevation angles of the source are nearly equal, i.e.,
$\theta_{mn}\approx\theta,\>\forall m,n$ and $\phi_{mn}=\phi,\>\forall m,n$.
Suppose we further assume that RIS lies in the x-y plane and unit-cell
radiates equally on all sides in the plane. In that case, the unit-cell
radiation response further simplifies to $f(\theta),\>\forall m,n$ (there is
no dependence on angle $\phi$). With all these simplifications, the E-field
equation for case 2 becomes:

$E(\theta,\phi)=E\>\Gamma\>f^{2}(\theta)\sum_{m=1}^{M}\sum_{n=1}^{N}e^{j\Phi_{mn}}e^{jk.\hat{r}_{mn}}.$
(2)

When we compare (1) and (2), it becomes evident that the planewave source
assumptions limit the options for beam manipulation to a relatively lesser
degree, however, this simplifies the E-field computations because the unit-
cell radiation response $f(\theta)$ remains unchanged for all indices $(m,n)$,
and it can be factored out as a constant from the summations.

The design of the unit-cell generally influences the shape of $f(\theta)$.
Figure 3 displays the normalized radiation response of the four unit-cells
studied in this paper and also plots $f(\theta)=\cos^{\frac{1}{q}}(\theta)$
for certain values of $q$ for comparison. The radiation response of the unit-
cells used in $\text{S}_{1}$ and $\text{S}_{3}$ is similar to
$\cos^{\frac{1}{3}}(\theta)$, while that of $\text{S}_{2}$ and $\text{S}_{4}$
is similar to $\cos^{\frac{1}{5}}(\theta)$. However, assuming a planewave
source, a sufficiently large-sized RIS constructed using any $n$-bit optimized
unit-cell with $\Gamma=1$ and maximally separated phase shifts between diode
states should produce almost similar surface level performance, regardless of
the differences in $f(\theta)$. In other words, the number of unit-cell diode
states ($2^{n}$) plays a more critical role in determining the surface-level
performance of the RIS than the unit-cell radiation response $f(\theta)$ does.
As $n$ increases, the RIS’s ability to generate relatively complex radiation
patterns grows, as does the control circuit’s complexity and power
requirements (discussed in more detail in the following section). However,
under point source assumptions, the shape of $f(\theta)$ plays a more
significant role in determining the surface level response, as it appears
inside the summation in (1). Thus, in case 1, we should anticipate
considerable surface-level performance variations based on the unit-cell
design.

Figure 3: Normalized radiation response $f(\theta)$ of the four unit-cells
used in $\text{S}_{1}$-$\text{S}_{4}$. The powers of
$\cos^{\frac{1}{q}}(\theta)$ for $q=1,3,5$ are also plotted.

There is a lack of standardized benchmarks to evaluate and compare the
radiation pattern generation abilities of RIS made of different unit-cells,
their control circuit complexity, and power requirements. Moreover, various
authors assume different numbers of RIS elements and spacing between them,
with some using 40x40, 20x20, 16x16, or 30x30 unit-cells in their studies.
Such differences make it challenging to compare the relative performance of
different unit-cell designs in generating surface-level radiation patterns
under point/planewave source assumptions. In practical applications, the
conventional design approach involves selecting or designing a unit-cell
structure, including the control mechanism (PIN diodes), and then using
multiple unit-cells to create a surface capable of generating specific
radiation patterns. However, this method has limitations, as the resulting
finite-sized RIS may not possess the necessary pattern generation
capabilities, may not be suitable for the intended application, or may consume
excessive power.

A significant difficulty also lies in finding the states of the PIN diodes of
each unit-cell to achieve some desired radiation response. The search space
has exponential complexity, and the problem is NP hard[13] even for a
moderately sized RIS comprising 20 to 30 1-bit unit-cells. While efficient
algorithms exist to determine the states of the PIN diodes, they primarily
target wireless communications and rely on simplistic models. Data rates at
specific locations are their primary design objective rather than the entire
radiation pattern. Thus, these algorithms do not account for how an RIS
reflects signals in other directions during the design stage. It is crucial to
acknowledge that even the most efficient algorithms may not succeed if a
finite-sized RIS created from a given unit-cell design cannot generate a
specific radiation pattern that was not previously tested. These difficulties
motivate the need for helpful radiation patterns that can act as benchmarks to
test and compare the performance of various designs.

##  III Control and Power Requirements of RIS

This section discusses the control circuit complexity and power requirements
of RIS built from different unit-cell designs. Table I summarizes the control
circuit complexity, power requirements, and unit area power requirements of
RIS $\text{S}_{1}$-$\text{S}_{5}$.

Figure 4: RIS control circuit, unit-cell grouping and I/O expansion for
addressing.

###  III-A Physical and Logical Control Paths on RIS

Each unit-cell incorporates PIN diodes and therefore requires independent
control signals. For an $n$-bit unit-cell, $n$ separate control lines are
required, and $2^{n}$ distinct phases can be generated. It should be noted
that the total number of PIN diodes in an $n$-bit unit-cell may exceed $n$, as
in the case of [15], where five PIN diodes are used to produce four distinct
phase shifts with only two control signals. The control signals are generated
by a microcontroller or FPGA, which requires an additional interface circuit.
However, these controllers have a limited number of pins, which may not be
sufficient to control all the unit-cells on a large RIS simultaneously. To
address this issue, time division multiplexing is typically used, and this
control architecture type is referred to as active matrix architecture or I/O
expansion [19].

Compared to varactor diodes, control circuits made of PIN diodes are more
straightforward, and digital high and low states are sufficient for their
ON/OFF control [20]. Additionally, PIN diodes have a much lower forward
biasing voltage (0.7V–0.8V), but the forward-biased current is of the order of
mA. Conversely, varactors operate at a significantly higher voltage than a
digital high state of a PIN diode but require $\mu$A or less current when
fabricated with the same technology [21]. As a result, varactors generally
consume less power than PIN diodes. Nonetheless, PIN diodes are preferred
because of their control simplicity.

The rate at which an RIS can switch between different functionalities (we
refer to it as the RIS function switching) is directly dependent on the speed
of the control circuit. In fast-changing wireless channels, the RIS function
switching must also be fast. However, the number of unit-cells on the RIS
affects the channel sensing overhead and the complexity of the control
circuit. Fewer unit-cells mean a lower channel sensing overhead and less
complex control circuit, but it could affect the RIS’s ability to generate
complex radiation atterns [5]. To reduce channel sensing overhead and control
circuit complexity, unit-cells can be grouped and controlled simultaneously.
This also negatively impacts the RIS’s radiation pattern generation
capabilities and overall functionality. To investigate the extent to which
unit-cell grouping affects the performance of RIS S1-S5, it is necessary to
quantify these tradeoffs using the benchmarking framework and performance
metrics discussed in the next section.

Using Figure 4, we illustrate the concept of unit-cell grouping and
distinguish between physical and logical control paths. The figure depicts
groups of two unit-cells, where each unit-cell contains three PIN diodes
labeled as D1, D2, and D3, enclosed within a rectangular box. The RIS
comprises $MN$ unit-cells, with $K$ microcontroller pins available for control
purposes, where $K<MN$. The $K$ pins drive control signals to the first $K$
unit-cells or groups of unit-cells at the same time, while the remaining cells
or groups are disabled. Then, the next $K$ unit-cells or groups of unit-cells
are enabled, and the same $K$ pins provide new control signals. This sequence
continues until all the unit-cells or groups of unit-cells have been
addressed, leading to logically separated control paths. It is worth noting
that increasing the number of controllers that operate in parallel can
increase the overall design cost but also allow for an increase in the total
number of control pins.

The number of physical control circuit paths can be expressed as
$\frac{MNn}{G}$, where $MN$ is the total number of unit-cells, and $G$ is the
number of unit-cells in each group. By increasing the size of the unit-cell
groups, we can significantly reduce the complexity of the control circuits.
The order of the RIS function switching rate can be quantified as
$O\left(\frac{GK}{MNn\tau}\right)$, where $\tau$ represents the response time
of the slowest element in the control path. For example, if we consider an RIS
composed of 2-bit unit-cells with $G=2$, $M=N=40$, $K=40$, and $\tau=20$ns,
the function switching rate would be 1.25 MHz, enabling the RIS to switch from
one radiation pattern to another in approximately 0.8$\mu$s. In the frequency
range of 1 GHz to 30 GHz, the typical wireless channel coherence time varies
from a few hundred $\mu$s to a few $\mu$s, which implies that the RIS can
quickly adapt to changing wireless channel conditions. Additionally, several
PIN diodes, including SMP1340, can operate at a GHz switching rate, which can
make the RIS function switching even faster. However, the actual switching
rate would depend on several factors, such as the channel sensing overhead and
the power requirements of the switching circuitry. We can also observe a
tradeoff between the number of physically independent control circuit paths
and the function switching rate.

Table I: Control circuit complexity and maximum power requirements of RIS $\text{S}_{1}$-$\text{S}_{5}$ each made from $MN$ unit-cells. $P_{D}=8mW$. RIS | $n$ | $d$ |  | RIS Control Circuit
---
Complexity
Maximum RIS Power Requirements
| RIS Physical
---
Control
Circuit
Paths
| RIS Function
---
Switching
Rate
| RIS Total
---
Power
$(dMNP_{D})$
| Unit-Cell
---
Dimensions
(mm)
| Unit
---
Cell
Area
$\times 10^{-4}$
(m2)
| Reflection
---
Coefficient
at normal incidence angle
(magnitude$\angle$phase∘)
|  $f$ (GHz)
---
| RIS
---
Power
Per
Unit
Area
(W/m2)
$\text{S}_{1}$[13] | 1 | 1 | $MN/G$ | $GK/(MN\tau)$ | $MNP_{D}$ | $5.8\times 4.9$ | $1.82$ |  | 0.95$\angle_{1}0^{\circ}$, 0.92$\angle_{2}180^{\circ}$
---
11.1 | 44
$\text{S}_{2}$[14] | 1 | 1 | $MN/G$ | $GK/(MN\tau)$ | $MNP_{D}$ | $6\times 6$ | $2.89$ |  | 0.90$\angle_{1}0^{\circ}$, 0.88$\angle_{2}180^{\circ}$
---
8.82 | 27.7
$\text{S}_{3}$[15] | 2 | 5 | $2MN/G$ | $GK/(2MN\tau)$ | $5MNP_{D}$ | $50\times 50$ | $42.3$ |  | 0.95$\angle_{1}0^{\circ}$, 0.95$\angle_{2}90^{\circ}$,
---
0.98$\angle_{3}180^{\circ}$, 0.92$\angle_{4}270^{\circ}$
2.3 | 9.46
$\text{S}_{4}$[16] | 2 | 2 | $2MN/G$ | $GK/(2MN\tau)$ | $2MNP_{D}$ | $8.8\times 8.8$ | $2.72$ |  | 0.88$\angle_{1}0^{\circ}$, 0.85$\angle_{2}90^{\circ}$,
---
0.92$\angle_{3}180^{\circ}$, 0.90$\angle_{4}270^{\circ}$
9.08 | 58.8
$\text{S}_{5}$[14] | 1 | 1 | $MN/G$ | $GK/(MN\tau)$ | $MNP_{D}$ | $6\times 6$ | $6.25$ |  | 0.92$\angle_{1}0^{\circ}$, 0.94$\angle_{2}50^{\circ}$
---
6.00 | 12.8

###  III-B Power Requirements of RIS Control Circuit

The power consumption of a PIN diode when in the ON state depends on its
forward voltage drop and forward operating current. While the power
consumption of a single PIN diode is relatively low, typically around 7-8mW
[20], it becomes significant when multiple unit-cells with multiple PIN diodes
are combined to form large surfaces. It is challenging to determine the
average percentage of unit-cells that need to be forward-biased to achieve
various functionalities. However, we know that the power requirements of an
RIS are directly proportional to the number of PIN diodes on its surface. The
proportionality constant is the ratio of PIN diodes in the ON state to the
total number of PIN diodes. To simplify and facilitate comparisons, we assume
that this proportionality constant is equal to 1111In reality, the
proportionality constant should be less than 1 because only a fraction of
diodes would be in the ON state for producing typical radiation patterns..

The maximum power requirement of an RIS made consisting of $MN$ unit-cells is
$dMNP_{D}$, where $P_{D}$ is the power used by one PIN diode when forward-
biased (in the ON state). It is apparent that a unit-cell configuration where
$d>n$ is less efficient than one where $d=n$. Additionally, as the value of
$n$ per unit-cell increases, so does the power requirement. The impact of
grouping the unit-cells on power usage would rely on the diode states for each
group. For instance, if we take the 1-bit unit-cell design, all of the unit-
cells in a group would be ON if they received an ON signal. Conversely, if
they receive an OFF signal, all of them would be OFF. The maximum power
requirements, on average, would remain the same. However, grouping simplifies
the control circuit since all of the unit-cells in a group will be in the same
state, based on a single control signal.

Supplying power continuously to an RIS that consists of several hundred unit-
cells operating at very high frequencies can pose a challenge. The power
consumption of RIS per unit area (W/m2) is a crucial factor to consider. In
Table I we have computed these requirements for RIS
$\text{S}_{1}$-$\text{S}_{5}$, assuming that the unit-cells are arranged
uniformly half wavelength apart. The Table also presents the unit-cell
dimensions and design frequencies. For example, RIS-$\text{S}_{1}$ operates at
a frequency of 11.1 GHz, and its power consumption per unit area is 44W/m2.
Suppose we want to use solar panels that produce between 100-200W/m2 during
the sunshine hours. With this assumption, the size of solar panels required to
power up RIS-$\text{S}_{1}$ is less than the size of the RIS. However, these
observations quickly change when we consider higher frequencies (above 30
GHz), because the unit-cell dimensions become small, and the size of solar
panels required to power up the resulting RIS becomes greater than the RIS
size itself.

##  IV Benchmarking Framework - RIS Radiation Patterns and Performance Metrics

In a smart city environment where NLOS situations dominate, we expect RIS to
possess three significant functionalities. These are single beam steering,
multi-beam forming with equal power levels, and multi-beam forming with
different power levels. In the following subsection, we propose a flexible
benchmarking framework that allows us to test these beamforming capabilities
for RIS made from different unit-cell designs under point/planewave source
assumptions (case 1 and case 2).

###  IV-A Benchmark Radiation Patterns

As benchmarks, we determine a set of typical radiation patterns based on NLOS
scenarios. The considered set includes eight radiation patterns, which are
shown in the first column of Figure 5. These radiation patterns are labeled as
$\text{B}_{1}$-$\text{B}_{8}$ for referencing. Radiation patterns
$\text{B}_{1}$ and $\text{B}_{2}$ are used to test the beam steering
capabilities of RIS in a single direction. Radiation patterns $\text{B}_{3}$
(2 beams), $\text{B}_{4}$ (3 beams), $\text{B}_{5}$ (4 beams), $\text{B}_{6}$
(4 beams), and $\text{B}_{7}$ (8 beams) are used to test multi beamforming
capabilities with equal power. Radiation pattern $\text{B}_{8}$ is used to
test the formation of multiple unequal power beams (4 beams). The relative
angles of various beams in these radiation patterns are shown in Figure 5.
These patterns are referred to as the benchmarking patterns in further
discussion. The prominent beams in these benchmarking patterns will be
referred to as the main lobes. The side lobes in all the benchmarking patterns
are desired to be negligible. In our study, the polarization of the incident
EM wave and the operating frequency are assumed to match the design
assumptions of each unit-cell in the original papers. Our proposed framework
is flexible, and more radiation patterns can be included in the benchmarking
set depending on the application scenarios.

###  IV-B Performance Metrics

We are interested in quantifying the relative ability of different RISs in
reproducing the benchmarking patterns. To this end, appropriate metrics that
can compare two radiation patterns are required. In this discussion, we will
use the terms ‘achieved radiation pattern’ and ‘reference radiation pattern,’
where achieved radiation pattern means the pattern produced by RIS in response
to a given reference radiation pattern. We develop three performance metrics.
The first metric is the directivity error (DE) which measures the ability of
RIS to reproduce the main lobes of the reference radiation pattern. The second
metric is the normalized mean squared error (NMSE) which quantifies the
accumulative mean square error between the achieved and reference radiation
patterns in all directions. The third metric is the side lobe ratio (SLR)
which quantifies the main lobe to side lobe ratio where the location of the
main lobe is determined from the reference radiation pattern. Please note that
our DE, NMSE, and SLR are comparative metrics, i.e., we use them to check how
closely the achieved radiation pattern matches a reference radiation pattern.
Below we further explain these metrics.

DE: We define DE in the following way:

$\text{DE}=\frac{D_{r}-D_{a}}{D_{r}}.$ (3)

where, $D_{r}$ is the reference directivity value that is determined by
integrating power (square of E-field) over the beam-width of the main lobe in
the reference radiation pattern, while $D_{a}$ is the achieved directivity
value that is determined by integrating power over the starting and ending
angle values obtained from the beam-width of the main lobe of the reference
radiation pattern in the achieved radiation pattern. We calculate the beam-
width of the main lobe using the First null beam-width (FNBW) criteria. Please
note that in both $D_{r}$ and $D_{a}$, starting and ending angles of the main
lobe of the reference radiation pattern are used because the objective is to
reproduce the main lobe of the reference pattern. The value of DE should
generally be positive with a maximum of 1 due to normalization by $D_{r}$. The
DE value of 1 would indicate that the main lobes are not formed in the
intended directions and are in completely different directions (inferior
performance). The negative value of DE would mean that the achieved radiation
pattern is better than the target radiation pattern (this is possible if
benchmarking pattern is not used as a reference radiation pattern).

NMSE: The NMSE is computed as:

$\text{NMSE}=\frac{1}{L}\sum_{\theta,\phi}\bigg{(}\frac{E_{r}(\theta,\phi)}{E_{rmax}}-\frac{E_{a}(\theta,\phi)}{E_{amax}}\bigg{)}^{2}$
(4)

where, $E_{r}(\theta,\phi)$ is the E-field value of reference radiation
pattern and $E_{a}(\theta,\phi)$ is the E-field value of the achieved
radiation pattern at azimuth and elevation angles $\theta$ and $\phi$. We
normalize the E-field values of each radiation pattern by the corresponding
maximum values, i.e., $E_{rmax}$ for the reference radiation pattern values
and $E_{amax}$ for the achieved radiation pattern values. We then average the
squared difference of the normalized E-field values in all directions to
obtain NMSE. In the simulations, we use $L=180\times 360$.

SLR: SLR is computed in dB scale:

$\text{SLR}=10\log_{10}\frac{\text{Power density of intended
lobe}}{\text{Power density of side lobe}}$ (5)

Please note that we determine the intended lobe’s location (starting and
ending angles) from the reference radiation pattern. At these angles, we look
for the power density in the achieved radiation pattern. On the other hand, we
determine the side lobe exclusively from the achieved radiation pattern of RIS
and define it as the most prominent non-intended minor lobe. We are using the
words ‘intended’ because these metrics aim to measure how faithfully a
reference radiation pattern is reproduced. In our set, we also have some
multi-beam (B${}_{3}-\text{B}_{8}$) reference radiation patterns. For such
patterns, we individually compute the SLR for each intended beam according to
(5) and then report their average.

The benchmarking patterns in our set are ideal, with negligible non-intended
lobes. Any RIS of suitable size made from 1-bit or 2-bit unit-cells would
struggle to reproduce these patterns faithfully. Therefore, considering the
benchmarking patterns as reference radiation patterns for the computation of
the quantitative metrics is not an effective way to analyze the relative
performance of S1-S5. To avoid this problem, we can select some appropriate
unit-cell and then make a reference RIS. We refer to such a reference RIS as
$\text{S}_{0}$. We can compute the quantitative metrics with respect to the
radiation patterns produced by $\text{S}_{0}$. Please note that for computing
the performance metrics, the starting and ending angles of the main lobes will
always be those given in the benchmarking patterns, even when we are using the
reference RIS method. With this approach, the values of DE could also become
negative, and it would indicate that the performance of given RIS in producing
the beams in the intended directions, as shown in the benchmarking pattern, is
better than that of S0.

For performance quantification in the next section, we will consider a
reference 2-bit unit-cell whose normalized power radiation pattern $f(\theta)$
will be $\cos(\theta)$ [22, 23]. This response is plotted in Figure 3 as $q=1$
curve. We will assume that this unit-cell is perfectly optimized with
$\Gamma=1$ and the phase differences between any two consecutive diode states
are 90∘. The RIS made from this reference unit-cell will be called
$\text{S}_{0}$, and we will use it to evaluate the performance metrics.

Table II: Quantitative results of five RIS S${}_{1}-\text{S}_{5}$, with and
without unit-cell grouping under point source assumptions with the observer in
the far-field (case 1). Best values (smallest in case of DE and NMSE and
largest in case of SLR) are highlighted in bold font, worst values (largest in
case of DE and NMSE and smallest in case of SLR) are highlighted in italic
font.

ID | Grouping | Relative Directivity Error (DE) | Relative Normalized Mean Squared Error (NMSE) | Side Lobe Ratio (SLR) - dB
---|---|---|---|---
|  | $S_{1}$ | $S_{2}$ | $S_{3}$ | $S_{4}$ | $S_{5}$ | $S_{1}$ | $S_{2}$ | $S_{3}$ | $S_{4}$ | $S_{5}$ | $S_{1}$ | $S_{2}$ | $S_{3}$ | $S_{4}$ | $S_{5}$
$\text{B}_{1}$ | No | 0.5 | 0.39 | 0.16 | 1 | 0.94 | 0.1004 | 0.1248 | 0.091 | 0.1131 | 0.0889 | 11.58 | 9.02 | 8.69 | 12.62 | -1.11
$\text{B}_{2}$ | 0.3 | 0.54 | 0.7 | 0.24 | 0.82 | 0.0284 | 0.0459 | 0.0381 | 0.0311 | 0.0516 | 9.96 | 11.01 | 8.86 | 11.62 | 6.27
$\text{B}_{3}$ | 0.22 | 0.29 | 0.47 | 0.18 | 0.91 | 0.0757 | 0.0774 | 0.0919 | 0.0852 | 0.0808 | 8.14 | 8.35 | 8.86 | 8.58 | -0.55
$\text{B}_{4}$ | 0.14 | 0.14 | 0.19 | 0.16 | 1 | 0.1277 | 0.1382 | 0.1288 | 0.1143 | 0.1412 | 9.21 | 2.63 | 7.34 | 9.17 | -2.79
$\text{B}_{5}$ | 0.07 | 0.39 | 0.01 | 0.04 | 1 | 0.1467 | 0.1569 | 0.1414 | 0.1427 | 0.1812 | 5.19 | 1.77 | 5.65 | 4.24 | -2.54
$\text{B}_{6}$ | 0.15 | 0.53 | 0.07 | 0.26 | 1 | 0.137 | 0.1659 | 0.1339 | 0.1359 | 0.1826 | 5.16 | 5.78 | 3.63 | 3.41 | -0.71
$\text{B}_{7}$ | 0.16 | 0.32 | 0.16 | 0.22 | 1 | 0.1995 | 0.2358 | 0.2136 | 0.2255 | 0.305 | -0.65 | -1.73 | -0.26 | 0.91 | -7.26
$\text{B}_{8}$ | 0.06 | 0.42 | 0.01 | 0.24 | 0.79 | 0.1634 | 0.1547 | 0.1623 | 0.143 | 0.1657 | -4.44 | -4.41 | 2.22 | -3.96 | -0.71
$\text{B}_{1}$ | Yes | 0.41 | 0.2 | 1 | 0.14 | 0.83 | 0.1071 | 0.1139 | 0.0961 | 0.0952 | 0.101 | 10.09 | 4.83 | -9.79 | 9.67 | -14.68
$\text{B}_{2}$ | 1 | 0.67 | 1 | 0.8 | 0.8 | 0.0627 | 0.059 | 0.0722 | 0.0528 | 0.0568 | 6.78 | 2.87 | -2 | 7.73 | -7.72
$\text{B}_{3}$ | 0.78 | 0.49 | 1 | 0.65 | 0.85 | 0.0847 | 0.0813 | 0.1005 | 0.0953 | 0.0896 | 3.54 | 3.18 | -4.35 | 7.32 | -11.82
$\text{B}_{4}$ | 0.97 | 0.74 | 1 | 0.73 | 0.69 | 0.1443 | 0.1296 | 0.1298 | 0.1082 | 0.1582 | 0.26 | 0.68 | -1.19 | 3.29 | -12.43
$\text{B}_{5}$ | 0.97 | 0.74 | 1 | 0.7 | 1 | 0.158 | 0.16 | 0.1522 | 0.1552 | 0.1982 | 0.93 | -1.69 | -6.41 | 0.07 | -13.54
$\text{B}_{6}$ | 0.8 | 0.71 | 1 | 0.64 | 0.26 | 0.1606 | 0.1673 | 0.145 | 0.1525 | 0.1836 | 0.34 | -2.08 | -3.27 | 3.21 | -4.23
$\text{B}_{7}$ | 1 | 0.14 | 1 | 0.56 | 0.7 | 0.2252 | 0.2116 | 0.2135 | 0.2137 | 0.3168 | -2.33 | -3.48 | -3.89 | -4.42 | -12.38
$\text{B}_{8}$ | 0.93 | 0.61 | 1 | 0.63 | 1 | 0.1928 | 0.1871 | 0.2205 | 0.1628 | 0.1822 | -7.62 | -3.92 | -1.25 | -5.22 | -0.77

Figure 5: Benchmarking radiation patterns $\text{B}_{1}$-$\text{B}_{8}$ and
the radiation patterns obtained by RIS $\text{S}_{1}$-$\text{S}_{5}$ under
point source assumptions (case 1) without unit-cell grouping. The results for
the reference RIS S0 are also shown. The RIS configuration matrix ($40\times
40$) is also reported as a colored image (unit-cell state 1=Blue, 2=Cyan,
3=Yellow, 4=Red). The elevation identifies Beam directions ($\theta$, ranges
between 0∘ and 90∘) and azimuth($\phi$, only takes two values 0∘ and 180∘)
angles. Instead of repeating the two $\phi$ values, $\theta$ and $-\theta$ are
used ($-\theta=\theta_{\phi=180^{\circ}}$).

##  V Benchmark-Based Evaluation Results

In this section, we test the ability of RIS $\text{S}_{1}$-$\text{S}_{5}$ in
reproducing $\text{B}_{1}$-$\text{B}_{8}$. The reference RIS S0 is also used
to reproduce the same benchmarking patterns. Each RIS (including S0) has 40x40
(1600) unit-cells. A commercially available full-wave EM solver (CST) is used
for unit-cell simulations to obtain their radiation responses. We use the
lumped element model (s-parameters) of PIN diodes from Skyworks SMP1340-040LF.
We use the unit-cell data from CST and array factor approximation to simulate
the RIS radiation patterns under point/planewave source assumptions. A genetic
algorithm (GA) implemented in MATLAB determines the optimal configuration
(diode ON/OFF states) of unit-cells on each RIS to generate benchmarking
patterns. The finite-sized RISs with discrete phase controls can fail to
generate the desired radiation patterns exactly. Therefore, in our
simulations, we allow GA to stop after 350 generations because we observe that
there is no significant improvement even if we allow the algorithm to run
longer. When the GA stops, we take the best match. We use the patterns
produced by S0 as reference radiation patterns to compute DE, NMSE, and SLR
metrics.

###  V-A Case 1: Point Source

The qualitative and quantitative results under point source assumptions are
presented in Figure 5 and Table II. The impact of unit-cell grouping to reduce
the control circuit complexity is given in Table II.

####  V-A1 Performance Without Unit-Cell Grouping

In Figure 5, we present the visual results that show the quality of the
reproduced radiation patterns by each RIS when we individually control the
unit-cells. The performance of S0 is also plotted.
RIS - $\text{S}_{1}$: The visual quality of $\text{B}_{1}$-$\text{B}_{6}$
looks excellent, while that of $\text{B}_{7}$ and $\text{B}_{8}$ is poor.
There are few undesired main lobes in $\text{B}_{6}$, $\text{B}_{7}$ and
$\text{B}_{8}$ as well as several high power side lobes, especially in
$\text{B}_{8}$. However, the value of DE for $\text{B}_{8}$ is very small. The
observations about the excellent quality of radiation patterns are confirmed
by corresponding values of DE, NMSE and SLR in each case, which is either the
best or very close to the best values.
RIS - $\text{S}_{2}$: The visual quality of radiation patterns produced by
$\text{S}_{2}$ looks somewhat poorer to the ones produced by $\text{S}_{1}$.
From Table II, we find out that DE (except for $\text{B}_{1}$) and SLR (except
for $\text{B}_{6}$, $\text{B}_{8}$) values are poor compared to $\text{S}_{1}$
on almost all the benchmarks. From Table I, the control circuit complexity and
power requirements of both $\text{S}_{1}$ and $\text{S}_{2}$ are the same.
Therefore, among optimized 1-bit RISs, $\text{S}_{1}$ comes out as a better
choice than $\text{S}_{2}$ on nearly all the performance metrics under point
source assumption without unit-cell grouping.
RIS - $\text{S}_{3}$: The visual quality of $\text{B}_{1}$-$\text{B}_{6}$
produced by $\text{S}_{3}$ is similar to $\text{S}_{1}$ and better in more
complex benchmarks. Moreover, the quality of $\text{B}_{6}$-$\text{B}_{8}$
looks significantly better than $\text{S}_{1}$ and $\text{S}_{2}$. The
quantitative metrics are also better for several benchmarking patterns. From
Table I, the control circuit complexity of $\text{S}_{3}$ is double while its
function switching rate is half than both $\text{S}_{1}$ and $\text{S}_{2}$.
Since $\text{S}_{3}$ is designed to operate in S-band, its per unit area power
requirements are significantly less than both $\text{S}_{1}$ and
$\text{S}_{2}$. However, the total power requirements of $\text{S}_{3}$ are
the highest among all the RIS because each unit-cell has 5 PIN diodes.
RIS - $\text{S}_{4}$: The visual quality of $\text{B}_{2}$-$\text{B}_{6}$
produced by $\text{S}_{4}$ is similar to $\text{S}_{1}$, $\text{S}_{2}$ and
$\text{S}_{3}$. The quality of $\text{B}_{1}$-$\text{B}_{8}$ looks worse than
$\text{S}_{3}$ and $\text{S}_{1}$ but better than $\text{S}_{2}$. We notice
that DE is not significantly poor, but the performance is effectively degraded
due to higher side lobes and scattering. The control circuit complexity and
power requirements of $\text{S}_{4}$ are double than both $\text{S}_{1}$ and
$\text{S}_{2}$. However, this RIS uses only 2 PIN diodes per unit-cell,
significantly reducing its power requirements compared to $\text{S}_{3}$.
RIS - $\text{S}_{5}$: This surface is made from a 1-bit unoptimized unit-cell.
The visual quality on all the benchmarks is worse than all other RIS. However,
on $\text{B}_{2}$, the main lobes are visible; one is along the desired
direction with two high-power side lobes. The visual quality on
$\text{B}_{1}$-$\text{B}_{8}$ is inferior because there is no correlation
between the target pattern and the pattern produced by $\text{S}_{5}$, i.e.,
$\text{S}_{5}$ is incapable of beam steering except the simple case of very
small angle. The control circuit complexity and power requirements of
$\text{S}_{5}$ are similar to $\text{S}_{1}$ and $\text{S}_{2}$.

In terms of reproducing $\text{B}_{1}$-$\text{B}_{8}$ under point source
assumptions without unit-cell grouping, the overall performance of
$\text{S}_{3}$ is the best, followed by $\text{S}_{1}$, $\text{S}_{4}$,
$\text{S}_{2}$ and $\text{S}_{5}$. Considering control circuit complexity and
power requirements along with the DE, NMSE, and SLR, $\text{S}_{1}$ seems a
better choice. However, in application scenarios where
$\text{B}_{6}$-$\text{B}_{8}$ are mostly required, $\text{S}_{3}$ should be
preferred despite its complexity and power requirements. Finally, if the
application scenario only demands small angle beam steering (such as
$\text{B}_{2}$), we may also use $\text{S}_{5}$ or its slightly more optimized
version.

####  V-A2 Performance With Unit-Cell Grouping

We now consider RIS $\text{S}_{1}$-$\text{S}_{5}$ assuming the unit-cells are
grouped into pairs. This way, the RIS’s complexity, and sensing overhead is
halved. However, the maximum power requirements remain unchanged. The impact
on the resulting RISs’ ability to produce the benchmarking patterns is
quantified in the lower half of Table II. We can see that all metrics show
poorer performance for all the designs. However, the extent to which unit-cell
grouping impacts the performance of each design is different.

When unit-cells are controlled in pairs, the best performance is shown by
$\text{S}_{2}$ followed by $\text{S}_{4}$, $\text{S}_{1}$, $\text{S}_{5}$ and
$\text{S}_{3}$. Please note that the DE value of 1 means that the surface has
failed to produce the main beams in the intended directions. Poor performing
surfaces without grouping ($\text{S}_{2}$, $\text{S}_{4}$, $\text{S}_{5}$) are
observed to be least affected by unit-cell grouping. We should expect small
gains in their performance even if we further increase the RIS size by
increasing the individually controlled unit-cells. On the other hand, the
gains in the performance of $\text{S}_{1}$ and $\text{S}_{3}$ should become
significantly higher with the corresponding increase in the RIS size.
Meanwhile, the choice of beam steering angles and the variation in beam power
levels can significantly raise the required performance criteria for RIS
designers, as we witness in the case of B8.

Figure 6: Benchmarking radiation patterns $\text{B}_{1}$-$\text{B}_{8}$ and
the radiation patterns obtained by RIS $\text{S}_{1}$-$\text{S}_{5}$ under
planewave source assumptions (case 2) without unit-cell grouping. The results
for the reference RIS S0 are also shown. The RIS configuration matrix
($40\times 40$) is also reported as a colored image (unit-cell state 1=Blue,
2=Cyan, 3=Yellow, 4=Red). The elevation identifies Beam directions ($\theta$,
ranges between 0∘ and 90∘) and azimuth($\phi$, only takes two values 0∘ and
180∘) angles. Instead of repeating the two $\phi$ values, $\theta$ and
$-\theta$ are used ($-\theta=\theta_{\phi=180^{\circ}}$). Table III:
Quantitative results of five RIS S${}_{1}-\text{S}_{5}$, with and without
unit-cell grouping under planewave source assumptions with the observer in the
far-field (case 2). Best values (smallest in case of DE and NMSE and largest
in case of SLR) are highlighted in bold font, worst values (largest in case of
DE and NMSE and smallest in case of SLR) are highlighted in italic font.

ID | Grouping | Relative Directivity Error (DE) | Relative Normalized Mean Squared Error (NMSE) | Side Lobe Ratio (SLR) - dB
---|---|---|---|---
|  | $S_{1}$ | $S_{2}$ | $S_{3}$ | $S_{4}$ | $S_{5}$ | $S_{1}$ | $S_{2}$ | $S_{3}$ | $S_{4}$ | $S_{5}$ | $S_{1}$ | $S_{2}$ | $S_{3}$ | $S_{4}$ | $S_{5}$
$\text{B}_{1}$ | No | -0.13 | 0.73 | 1 | 0.15 | 1 | 0.0166 | 0.0138 | 0.014 | 0.0102 | 0.0158 | 0.04 | 0.17 | -8.51 | 14.14 | -14.03
$\text{B}_{2}$ | 0.12 | 0.93 | 0.99 | 0.55 | 1 | 0.01 | 0.0092 | 0.0082 | 0.0049 | 0.0097 | -0.03 | 0.05 | -3.28 | 10.2 | -8.82
$\text{B}_{3}$ | 0.61 | 0.89 | 0.98 | 0.8 | 1 | 0.0119 | 0.0112 | 0.0113 | 0.0074 | 0.0129 | -0.09 | 0.02 | -8.34 | 6 | -12.97
$\text{B}_{4}$ | 0.78 | 0.91 | 0.99 | 0.76 | 0.99 | 0.0117 | 0.0116 | 0.0121 | 0.0083 | 0.0141 | -0.17 | -0.49 | -9.84 | 5.7 | -16.3
$\text{B}_{5}$ | 0.86 | 0.92 | 0.93 | 0.88 | 0.87 | 0.0139 | 0.0142 | 0.0158 | 0.0112 | 0.0184 | -0.14 | -3.38 | -11.79 | 0.98 | -15.62
$\text{B}_{6}$ | 0.6 | 0.52 | 0.84 | 0.75 | 0.88 | 0.0141 | 0.0171 | 0.0119 | 0.0079 | 0.0154 | -1.58 | -3.19 | -8.15 | 2.39 | -6.49
$\text{B}_{7}$ | 0.97 | 0.97 | 0.92 | 0.98 | -0.05 | 0.0185 | 0.0184 | 0.0237 | 0.018 | 0.0259 | -5.68 | -3.29 | -16.15 | -4.74 | -20.78
$\text{B}_{8}$ | 1 | 1 | 1 | 0.99 | 1 | 0.0131 | 0.0131 | 0.0148 | 0.012 | 0.0171 | -4.72 | 3.58 | -1.25 | -6.15 | 5.04
$\text{B}_{1}$ | Yes | 0.16 | 0.74 | 1 | 0.14 | 0.98 | 0.1988 | 0.1553 | 0.3117 | 0.1762 | 0.2235 | -0.19 | -0.264 | -1.958 | 2.704 | -3.088
$\text{B}_{2}$ | 0.13 | 1 | 1 | 0.52 | 1 | 0.2335 | 0.1829 | 0.1096 | 0.0317 | 0.1279 | -0.172 | -0.276 | -0.94 | 1.936 | -1.918
$\text{B}_{3}$ | 0.82 | 1 | 1 | 1 | 1 | 0.1773 | 0.2782 | 0.2049 | 0.0996 | 0.2776 | -0.308 | -0.162 | -1.926 | 1.098 | -2.77
$\text{B}_{4}$ | 1 | 0.95 | 1 | 0.85 | 1 | 0.2178 | 0.0701 | 0.0887 | 0.1299 | 0.3023 | -0.15 | -0.266 | -2.154 | 0.918 | -3.474
$\text{B}_{5}$ | 1 | 1 | 0.99 | 1 | 0.81 | 0.1942 | 0.2579 | 0.2359 | 0.1888 | 0.1287 | -0.292 | -0.848 | -2.578 | -0.018 | -3.288
$\text{B}_{6}$ | 0.72 | 0.69 | 1 | 0.87 | 0.96 | 0.2251 | 0.3974 | 0.1984 | 0.0493 | 0.129 | -0.524 | -0.738 | -1.734 | 0.232 | -1.404
$\text{B}_{7}$ | 0.94 | 1 | 1 | 0.94 | 0.09 | 0.2183 | 0.3955 | 0.1911 | 0.2659 | 0.3232 | -1.328 | -0.926 | -3.334 | -1.164 | -4.384
$\text{B}_{8}$ | 1 | 0.98 | 1 | 1 | 1 | 0.0649 | 0.1213 | 0.2442 | 0.1574 | 0.3597 | -1.236 | 0.424 | -0.368 | -1.43 | 0.88

###  V-B Case 2: Planewave Source

The qualitative and quantitative results under planewave source assumptions
are presented in Figure 6 and Table III. In this case, the number of unit-cell
control states greatly impacts the performance.

####  V-B1 Performance Without Unit-Cell Grouping

The qualitative results without unit-cell grouping are shown in Figure 6,
while the corresponding quantitative results are presented in the upper half
of Table III.
RIS - $\text{S}_{1}$: We can observe that the RIS can reproduce the main
lobes, but there are non-intended side lobes in every radiation pattern
produced by $\text{S}_{1}$. These side lobes are called ‘quantization lobes.’
They generally appear in RISs made from 1-bit unit-cells due to more
pronounced phase rounding quantization effects [24, 25]. The RIS can reproduce
the main lobes; therefore, the DE values are very good in four out of eight
benchmarking patterns ($\text{B}_{1}$-$\text{B}_{3}$, $\text{B}_{5}$), but
NMSE is very bad compared to the best NMSE obtained for RIS $\text{S}_{4}$ in
the same tests. The side lobe level of $\text{S}_{1}$ is close to 0 or
negative in some cases, showing that the scattering level is close to the main
lobes.
RIS - $\text{S}_{2}$: This 1-bit RIS also produces quantization lobes. We can
observe that main lobes are wider compared to $\text{S}_{1}$. On quantitative
metrics, except $\text{B}_{6}$, the performance of $\text{S}_{2}$ is generally
poor and NMSE is very close to $\text{S}_{1}$ in all the tests. The side lobes
are close to the main lobes or even greater in magnitude than the main lobes
making the SLR values close to 0 or negative.
RIS - $\text{S}_{3}$: There are no quantization lobes in the radiation
patterns produced by $\text{S}_{3}$. The main lobes also look narrow and
focused. However, the RIS could not form the main lobes in the intended
directions. The starting and ending angles of the main lobes in the
benchmarking and the achieved radiation patterns are very close to each other
but there is no overlap due to narrow beams formed by $\text{S}_{3}$. Thus,
the DE and SLR values are extremely poor because although beam steering is
prominent but it is not in the intended directions. On the other hand, NMSE
values are relatively good and second best in two cases ($\text{B}_{2}$ and
$\text{B}_{3}$).
RIS - $\text{S}_{4}$: The visual quality of the radiation patterns produced by
$\text{S}_{4}$ also looks good, and the quantization lobes are also missing.
The overall performance of $\text{S}_{4}$ is significantly better in all the
benchmark tests. The RIS can produce the main lobes with low side lobe levels.
Moreover, the main lobes are wide as compared to $\text{S}_{3}$ and the
starting and ending angles of the main lobes in the benchmarking and the
achieved radiation patterns overlap. Therefore, the DE values are better than
$\text{S}_{3}$ but relatively worse than $\text{S}_{1}$ on multiple benchmarks
under planewave source assumptions. However, the values of NMSE and SLR in all
benchmark tests are significantly better (often the best) than $\text{S}_{1}$
and $\text{S}_{3}$.
RIS - $\text{S}_{5}$: This RIS consists of an un-optimized 1-bit unit-cell,
and it is evident that the surface has entirely failed in almost all the
benchmarking patterns. The visual quality is the worst because the RIS lacks
the beam steering capability under planewave source assumption. The
quantitative values of $\text{S}_{5}$ are also the worst on all the
benchmarking patterns. In $\text{B}_{7}$, the DE is close to 0, but NMSE and
SLR are still the worst. The better value of DE occurs because $\text{B}_{7}$
has eight beams, and high scattering can at least satisfy some intended
directions. Still, poor performance becomes evident when the error of
unintended directions is considered through NMSE and SLR values. The same is
true for $\text{B}_{8}$ where SLR is good, but the other two metrics are the
worst.

####  V-B2 Performance With Unit-Cell Grouping

When we group the unit-cells in pairs, the performance of all the RISs under
planewave source assumptions further decreases. As shown in the bottom half of
Table III RISs $\text{S}_{1}$ and $\text{S}_{2}$ consisting of 1-bit unit-
cells shows degraded performance on all the metrics as compared to RISs
$\text{S}_{3}$ and $\text{S}_{4}$ consisting of 2-bit unit-cells. The
performance of RIS $\text{S}_{5}$ is still the worst. The distinction between
1-bit and 2-bit unit-cell and the effect of unit-cell radiation response are
more prominent in dictating RIS beam steering capability under planewave
source assumptions. Optimizing unit-cell in terms of producing maximally apart
phase shifts in different control states also becomes crucial in obtaining
good performance.

###  V-C Discussion and Comparison

In Figure 7, we present the visual quality of the radiation pattern produced
by $\text{S}_{1}$ (1-bit unit-cell) while reproducing the benchmarking pattern
$\text{B}_{4}$ under point/planewave source assumptions and without/with unit-
cell grouping in pairs. We can see that we obtain the best result under the
point source assumption without grouping, which means that all the 1600 1-bit
unit-cells on the RIS have a separate control. On the other hand, when we
control the unit-cells in pairs, under point source assumptions, the ability
of the surface to reproduce the given pattern is severely degraded with a
significant scattering of power in all directions. Under planewave source
assumptions and without unit-cell grouping, the quantization lobes are visible
along with all the desired main lobes. When the unit-cells are grouped in
pairs to reduce the control circuit overhead, the performance degrades under
planewave source assumption.

In Figure 8, we present the visual quality of the radiation pattern produced
by $\text{S}_{3}$ (2-bit unit-cell) while reproducing the benchmarking pattern
$\text{B}_{4}$ under point/planewave source assumptions and without/with unit-
cell grouping in pairs. Under the point source assumption, without unit-cell
grouping, the three beams are visible. In this case, the scattering level in
the unintended directions is relatively less compared to the radiation pattern
generated by $\text{S}_{1}$. When we group the unit-cells in pairs, the
performance significantly degrades under the point source assumption, and it
becomes equally bad, as we observe in $\text{S}_{1}$. Under planewave source
assumptions and without unit-cell grouping, the performance of $\text{S}_{3}$
is comparable to the point source case with two out of three main lobes
visible. Unlike $\text{S}_{1}$, there are no quantization lobes. Finally, with
grouping and planewave source assumptions, $\text{S}_{3}$ loses its beam
steering capability and cannot form any of the major lobes.

The interplay of unit-cell design, grouping for control circuit complexity
reduction, the number of diode control states on each unit-cell, the unit-cell
radiation response, the power requirements of the RIS control circuit, and the
radiation pattern generation capabilities of RIS under point/planewave source
assumptions is evident from these results. Our benchmarking framework,
metrics, and these observations would help the research community make
appropriate design choices and tradeoffs to achieve the desired far-field
beamforming performance in different smart city application scenarios.

Figure 7: Radiation patterns generated by $\text{S}_{1}$ (1-bit unit-cell)
while reproducing the benchmarking pattern $\text{B}_{4}$ under
point/planewave source assumptions and without/with unit-cell grouping in
pairs. Figure 8: Radiation patterns generated by $\text{S}_{3}$ (2-bit unit-
cell) while reproducing the benchmarking pattern $\text{B}_{4}$ under
point/planewave source assumptions and without/with unit-cell grouping in
pairs.

##  VI Conclusion

We conducted a detailed analysis of the performance aspects of RISs composed
of various unit-cell designs. We developed a benchmarking framework that
included radiation patterns commonly required in smart city environments and
presented performance metrics to quantify RIS radiation pattern generation
capabilities relative to the benchmarking patterns, control circuit
complexity, and power requirements for point/planewave source assumptions.
Using the framework, we tested and compared five different RISs
($\text{S}_{1}$-$\text{S}_{5}$) made up from five different unit-cell designs.
The unit-cells on these surfaces were first individually controlled and later
in groups. The proposed framework can be handy for choosing unit-cells from
existing designs in various application settings and source type assumptions.
We can also use the framework to determine the usefulness of future designs
and their most viable applications. With the help of our proposed framework,
we can also determine the optimal group size for the best tradeoff that favors
ease of implementation and reduces the channel sensing overhead. A better
understanding of the unit-cell- and surface-level RIS design interplay could
lead to better strategies for system-level performance enhancement in RIS-
assisted communications.

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