# Plug-In RIS: A Novel Approach to Fully Passive Reconfigurable Intelligent
Surfaces

Mahmoud Raeisi, , Ibrahim Yildirim, , Mehmet C. Ilter, , Majid Gerami, , and
Ertugrul Basar, M. Raeisi, I. Yildirim, and E. Basar are with the
Communications Research and Innovation Laboratory (CoreLab), Department of
Electrical and Electronics Engineering, Koç University, Sariyer, Istanbul
34450, Turkey. (e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>ebasar@ku.edu.tr)I. Yildirim is also with the Faculty of Electrical and
Electronics Engineering, Istanbul Technical University, Istanbul 34469,
Turkey.Mehmet C. Ilter, and M. Gerami are with the Lund Research Center,
Huawei Technologies Sweden AB, Sweden. (e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

This paper presents a promising design concept for reconfigurable intelligent
surfaces (RISs), named plug-in RIS, wherein the RIS is plugged into an
appropriate position in the environment, adjusted once according to the
location of both base station and blocked region, and operates with fixed
beams to enhance the system performance. The plug-in RIS is a novel system
design, streamlining RIS-assisted millimeter-wave (mmWave) communication
without requiring decoupling two parts of the end-to-end channel, traditional
control signal transmission, and online RIS configuration. In plug-in RIS-
aided transmission, the transmitter efficiently activates specific regions of
the divided large RIS by employing hybrid beamforming techniques, each with
predetermined phase adjustments tailored to reflect signals to desired user
locations. This user-centric approach enhances connectivity and overall user
experience by dynamically illuminating the targeted user based on location. By
introducing plug-in RIS’s theoretical framework, design principles, and
performance evaluation, we demonstrate its potential to revolutionize mmWave
communications in limited channel state information (CSI) scenarios.
Simulation results illustrate that plug-in RIS provides power/cost-efficient
solutions to overcome blockage in the mmWave communication system and a
striking convergence in average bit error rate and achievable rate performance
with traditional full CSI-enabled RIS solutions.

###### Index Terms:

Reconfigurable intelligent surface, millimeter wave, energy efficiency,
massive MIMO, 6G.

##  I Introduction

The requirements posed by the next generation of communication networks,
including massive connectivity, ultra-reliability, low latency, and energy
efficiency, necessitate exploring innovative strategies and technologies to
enhance existing communication systems, enabling the deployment of ubiquitous
connected devices. Reconfigurable intelligent surfaces (RISs), a promising
technology that acquired substantial attention from research community, has
emerged as a potential candidate for incorporation into the next-generation
wireless communication networks [1]. By intelligently manipulating incident
signals, RISs enable a smart environment through controlled scattering paths,
significantly improving performance. The RIS-aided virtual channel between the
terminals, making the channel adaptable for boosting communication performance
in various scenarios or circumventing blockages that impede communication, a
common occurrence in millimeter-wave (mmWave) communication systems due to
signal vulnerability to the blockage and severe path loss. These blocked
regions, termed dead zones, can be addressed by properly configuring the RIS
phase shifts based on channel state information (CSI), allowing the RIS to
redirect signals around obstructions and serve users within the dead zones. It
is worth mentioning that CSI acquisition and phase shift configuration are key
limiting factors significantly affecting the RIS design and system
performance. Hence, the following sub-section elaborates on different RIS
designs in the existing literature, mostly focusing on CSI acquisition methods
for RIS phase adjustment [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12].

TABLE I: Comparison among different RIS structures available in the existing
literature and the proposed plug-in RIS.
(Abbreviations: Y = yes; N = no; FP = fully passive; SP = semi-passive; H = high; M = medium; L = low.) | [2] | [3] | [4] | [5] | [6] | [7] | [8] | [9] | [10] | [11] | [12] | Plug-in RIS
---|---|---|---|---|---|---|---|---|---|---|---|---
RIS type: | FP | FP | FP | FP | FP | FP | FP | SP | SP | SP | SP | FP
Channel estimation carries out by: | BS | UE | BS | UE | UE | BS | UE | RIS | RIS | BS/UE | BS/UE | BS
Control link availability: | Y | Y | Y | Y | Y | Y | Y | N | N | Y | Y | N
Implementation complexity: | M | M | H | H | H | M | H | H | H | M | M | L
Signalling overhead: | M | M | H | M | M | M | H | L | L | M | M | L

###  I-A Related Works

Two critical aspects distinguishing RIS deployment are its passive nature and
ease of implementation, as highlighted in [1]. Specifically, it is assumed
that an ideal RIS does not require an external power source and can be easily
adapted for implementation in various environments. By taking these attributes
into account, we classify the existing RIS structures into two main
categories: Fully passive RIS and semi-passive RIS111It is worth mentioning
that there is a type of RIS named active RIS. However, active RIS is not
equipped with baseband components like RF chains; it possesses the added
capability of signal amplification [13]. Accordingly, the channel estimation
method for active RIS is not different from that of fully passive RIS..

####  I-A1 Fully passive RIS

The RIS configuration depends on CSI availability for both the base station
(BS)-RIS and RIS-user equipment (UE) channels, as assumed in most RIS studies
in the literature. In a fully passive RIS setup, where the RIS lacks baseband
processing capability, either the BS or the UE needs to estimate the end-to-
end channel and decouple two parts of it, i.e., BS-RIS and RIS-UE. Numerous
studies in the existing literature have addressed the channel estimation
problem for fully passive RIS systems [2, 3, 4, 5, 6, 7, 8].

In [2], the authors proposed a channel estimation method for passive RIS-
assisted energy transfer systems, assuming that the power beacon manages all
computational tasks due to constraints in UE. In [3], the authors studied
channel estimation in an RIS-assisted mmWave communication system, aiming for
joint active and passive beamforming for single-antenna UEs; nevertheless,
dealing with multi-antenna UEs adds extra computational load for CSI
acquisition and passive phase shift vector optimization. The study of [4]
proposed a two-step channel estimation protocol for acquiring two parts of the
end-to-end channel within a multi-user (MU) mmWave MIMO system, in which the
BS is responsible for channel estimation. Meanwhile, the study of [5] dives
into channel estimation problem within a point-to-point (P2P) RIS-assisted
mmWave communication system. Under the suggested protocol, the UE undertakes
an optimization problem to obtain downlink cascaded channels. Similarly, a
channel estimation algorithm for passive large intelligent metasurfaces (LIM)
is introduced in [6], employing sparse matrix factorization and matrix
completion. In [7], the authors considered UE mobility and proposed a two-time
scale channel estimation framework, leveraging the quasi-static BS-RIS channel
while the RIS-UE is a low-dimensional mobile channel. The study of [8]
investigated channel estimation for broadband RIS-aided mmWave massive MIMO
systems utilizing compressive sensing (CS) method.

This literature review reveals that significant efforts have been made to
estimate the end-to-end channel and separate it into BS-RIS and RIS-UE
components in RIS-assisted mmWave communication systems. It is worth
emphasizing that in fully passive RIS design, channel estimation/decoupling
and optimizing phase shifts are done at one of the endpoints, which
necessitates two key considerations. Firstly, establishing a dedicated control
link is essential to facilitate the transmission of configuration information
from the responsible endpoint to the RIS. Secondly, allocating sufficient
resources to accommodate the computational tasks associated with channel
estimation/decoupling and RIS phase shift optimization at the responsible
endpoint is essential. However, it is worth noting that both of these
requirements have potential drawbacks. Introducing a dedicated control link
can add complexity to the system and potentially increase the overall latency
stemming from reconfiguration latency [14], while allocating substantial
resources, particularly at the UE, may not be a cost/power-efficient solution.
Similarly, if the BS assumes the responsibility for computational tasks,
extending this approach to an MU scenario can significantly elevate system
complexity and overhead, potentially posing challenges to the overall
feasibility of the system.

####  I-A2 Semi-passive RIS

Despite extensive endeavors to acquire individual cascaded channels for fully
passive RIS configurations, challenges arise from the inefficient cascaded
channel decoupling process due to the passive nature of RIS elements [9]. In
order to address this issue, semi-passive RIS structure is introduced in [10].
In the semi-passive RIS design, a fraction of RIS elements are connected to
baseband components, enabling the RIS to perform channel estimation through
its integrated baseband components. Consequently, the RIS can accurately
estimate BS-RIS and RIS-UE channels separately and adjust itself without being
controlled by other terminals, i.e., the transmitter (Tx) or the receiver (Rx)
[10]. In [9], the authors proposed an algorithm for semi-passive RIS channel
estimation, leveraging sparsity in both spatial and frequency domains of
mmWave channels. As shown in [9], connecting only $8\%$ of RIS elements to the
baseband components yields more accurate channel estimation than the
considered benchmarks. The study of [11] proposed two practical residual
neural networks to accurately estimate the channel for semi-passive RIS-aided
communication systems. Similarly, the authors in [12] proposed a channel
estimation method for semi-passive RIS-assisted systems based on super-
resolution neural networks. It is worth noting that even though the studies of
[11, 12] exploit semi-passive RIS, a significant portion of the computational
load for channel estimation is carried out by the transceivers to simplify the
RIS structure. Consequently, they inherit some of the drawbacks associated
with both fully passive and semi-passive RIS designs.

Table I provides an overview of the structural characteristics of various RIS
designs discussed above. A notable potential advantage of the semi-passive RIS
design is its reduced reliance on establishing a dedicated control link.
Moreover, this approach eliminates the additional overhead and complexity
imposed on the transceivers, as the RIS efficiently handles the computational
tasks. Nonetheless, the semi-passive RIS configuration deviates from two
fundamental characteristics highlighted previously: The passive nature of the
RIS and its simplicity of implementation. While it is evident that the semi-
passive RIS does not adhere to the passive attribute, it is crucial to
remember that including baseband components introduces a costly and power-
intensive structure, which, in turn, hinders easy and widespread deployment.

###  I-B Motivations and contributions

As summarized in Table I, both fully passive and semi-passive RIS
configurations exhibit drawbacks that pose challenges to their practical
implementation. Based on the existing literature, it becomes evident that
there is a clear and pressing need within academia to create a novel RIS
structure that fulfills the two fundamental attributes emphasized in [1],
which strongly motivates us to introduce a fresh and innovative design, named
plug-in RIS, with the specific aim of simplified deployment and operation
within mmWave communication environments. In this system, the RIS can be
conveniently plugged into the environment to operate with fixed phase shift
profiles, which are adjusted based on the location of the BS and dead zones.
Specifically, initially, the dead zone in the mmWave environment is defined to
the BS (because the BS is initially not aware of which area is the dead zone)
and divided into spatial segments; each spatial segment is considered to be
served via a part of divided RIS, named sub-RIS. Next, we examine the location
of each spatial segment and assign a fixed phase shift profile to the
corresponding sub-RIS. Since both the BS and dead zone have fixed locations,
the sub-RISs are not required to be configured frequently. For activation, the
BS obtains the UE’s spatial segment222This can be achieved by having the BS
transmit a pilot signal across all sub-RISs. The UE, in turn, receives the
pilot signal via the corresponding sub-RIS, and then sends its response back
to the BS through that sub-RIS. Consequently, the BS is able to discern the
spatial segment in which the UE is positioned. and employs beamforming
techniques to illuminate the corresponding sub-RIS, enabling control over
signal reflection towards desired directions and offering a user-centric
approach to enhance wireless communication performance.

Based on the aforementioned motivations, we outline our contributions as
follows:

  * •

Plug-in RIS with standalone operation: In contrast to the fully passive and
semi-passive RIS designs, this study introduces an innovative approach—a plug-
in RIS configuration with standalone operation—for extending communication
coverage in mmWave systems. The proposed structure aligns with key attributes
of RIS technology, such as, its passive nature and ease of implementation. The
plug-in RIS consists of multiple sub-RIS planes, each pre-configured with
fixed phase shifts, intended to cover distinct spatial segments within the
dead zone. Leveraging the high beamforming gain at the Tx in the mmWave
communication systems, only one sub-RIS plane is activated in each
transmission period to establish a virtual link toward the UE. This approach
innovatively integrates the control mechanism within the transmitting beam,
eliminating the necessity for implementing traditional control links and the
associated overheads, which enhances the overall user experience by increasing
the ease of implementation of the RIS in different environments.

  * •

Compatibility with existing end-to-end channel estimation methods: The pre-
configured phase shift design of the suggested plug-in RIS eliminates the
necessity for decoupling two parts of the end-to-end channel, which alleviates
the additional burden of channel decoupling on the participating terminals,
enabling the easy deployment of fully passive RIS in mmWave communication
systems. In other words, in the proposed plug-in RIS, obtaining the
conventional end-to-end channel estimation is enough, and decoupling it into
BS-RIS and RIS-UE channels is not required.

  * •

Reliability analysis: We derive a closed-form expression for the upper bound
of the average bit error rate (ABER) for the proposed plug-in RIS. Our
analytical methodology employs the union-bound and pairwise error probability
(PEP) to validate the precision of our simulation outcomes. Our results
illustrate that these analytical derivations offer a tight upper bound on the
ABER.

  * •

Simulation insights: We conduct exhaustive simulations to evaluate the
performance of the proposed plug-in RIS in terms of ABER, achievable rate,
energy efficiency, and detector complexity. Computer simulation outcomes
indicate that the plug-in RIS exhibits promising effectiveness, showing close
ABER and achievable rate results to the semi-passive design. Moreover, the
plug-in RIS outperforms the benchmark designs in terms of energy efficiency
and detector complexity, highlighting the superiority of our proposed
approach, taking a step forward to the practical implementation of fully
passive RIS.

The rest of this article is organized as follows. Section II outlines the
system, channel, and signal models. The design of the proposed plug-in RIS is
elaborated in Section III. Analytical expression as an upper bound for ABER
performance is derived in Section IV. Simulation results are displayed in
Section V, followed by the conclusion of this study in Section VI.

Notation: In this paper, bold lowercase and uppercase letters denote column
vectors and matrices, respectively. The symbols $(.)^{H}$, $(.)^{T}$,
$(.)^{*}$ $|.|$, $||.||$, and $\operatorname*{diag}(.)$ stand for Hermitian,
transpose, conjugate, absolute value, norm, and diagonalization, respectively.
The operator $\mathbb{E}[.]$ shows the expected value, $\mathcal{R}(.)$
denotes the real component of a complex number, and operator $\circ$
represents the Hadamard (element-wise) product. The notation
$\mathcal{CN}(\mu,\sigma^{2})$ represents the complex Gaussian distribution
with mean $\mu$ and variance $\sigma^{2}$, while $\mathcal{N}(\mu,\sigma^{2})$
denotes the Gaussian distribution with mean $\mu$ and variance $\sigma^{2}$.
The identity matrix of dimension $n$ is represented as $\mathbf{I}_{n}$, while
the vector comprising all zeros and ones of size $n$ is denoted by
$\mathbf{0}_{n}$ and $\mathbf{1}_{n}$, respectively. Additionally,
$\mathcal{U}(a,b)$ indicates a uniform distribution parameterized by $a$ and
$b$. The $Q$-function is denoted and defines as
$Q(x)=\frac{1}{\sqrt{2\pi}}\int_{x}^{\infty}\exp{(-\frac{u^{2}}{2})}du$. It is
worth mentioning that in this paper, the variable $i$ is employed as a local
variable, and its assigned value within each equation is applicable only to
that equation.

##  II System, Channel, and Signal Model

This section describes the system model for the mmWave massive MIMO
communication system aided by the proposed plug-in RIS. Afterward, we present
the utilized channel model and the foundational assumptions supporting our
suggested design. Lastly, we elaborate on the signal model and introduce a
suitable maximum likelihood (ML) detector.

###  II-A System Model

Figure 1: System model for proposed plug-in RIS.

As depicted in Fig. 1, we investigate a P2P mmWave communication system aided
by a set of sub-RIS planes with pre-configured fixed phase shifts333The
proposed plug-in RIS offers easy adaptability to an MU setup in both uplink
and downlink directions. This adaptability is facilitated by its independent
operation and energy-efficient attributes while avoiding an additional
computational load on the transceivers. Users can be categorized into distinct
clusters in an MU scenario based on their spatial segments. Users within the
same segment possess similar angular properties, allowing us to use a fixed
phase shift sub-RIS plane to serve them. However, the realization of such a
scenario necessitates the development of a baseband precoder and combiner
aimed at mitigating interference among users. This aspect exceeds the current
scope of our study and is reserved for future research endeavors.. Due to
propagation loss challenges, the direct BS-UE link is assumed to be blocked,
causing dead zones in the environment; therefore, the sub-RIS planes are
plugged into the surrounding environment to assist UEs located in the dead
zone, ensure constant connectivity and guarantee line-of-sight (LOS) links in
the BS-RIS and RIS-UE channels. Specifically, a dead zone can be covered using
one or more sub-RISs, each covering a distinct spatial segment of the dead
zone with a fixed beam. The set of sub-RISs constitutes the plug-in RIS
entity. During implementation, each sub-RIS is assigned to a spatial segment
in the dead zone; therefore, they are adjusted according to the angular
information of BS and the spatial segments. Specifically, for each spatial
segment, we consider fixed angular information that represents it, and since
this angular information is constant, the sub-RISs are not required to be
adjusted frequently444The BS is typically positioned for maximal environmental
coverage. Nonetheless, mmWave vulnerability to blockages can result in dead
zones in the environment; for example, parallel indoor hallways. Installing an
RIS proves more cost/energy-effective than deploying an extra BS in such a
scenario. Moreover, these dead zones are usually small regions; hence,
employing a plug-in RIS with fixed beams is more cost/energy efficient and
less complex than a usual RIS with a regular phase shift configuration for
covering a wide area.. During the transmission, based on the UE’s location and
with the aid of massive MIMO’s beamforming gain at the BS, the transmitted
beam footprint only activates the corresponding sub-RIS. Both the BS and UE
are equipped with uniform rectangular arrays (URA); $N_{t}$ and $N_{r}$ denote
the number of antenna elements at the BS and UE, respectively. To address
severe path loss while minimizing the need for costly RF chains, analog
beamformers/combiners are employed at the BS/UE. This approach allows a single
RF chain at the BS and UE, supporting a single stream [15]. Our proposed plug-
in RIS comprises $K$ sub-RISs, each containing $M_{k}\ (k=1,\dots,K)$ passive
reflecting elements.

###  II-B Channel Model

In this paper, we adopt the popular Saleh-Valenzuela (SV) channel model for
the BS-RIS and RIS-UE channels as follows [16, 17, 18, 19]:

$\begin{split}\mathbf{G}_{k}=&\sqrt{N_{t}M_{k}}\alpha_{k}\mathbf{a}_{r,ris}(\varphi_{r,ris}^{k},\vartheta_{r,ris}^{k})\mathbf{a}_{t}^{H}(\varphi_{t},\vartheta_{t}),\end{split}$
(1)
$\begin{split}\mathbf{R}_{k}=&\sqrt{M_{k}N_{r}}\beta_{k}\mathbf{a}_{r}(\varphi_{r},\vartheta_{r})\mathbf{a}_{t,ris}^{H}(\varphi_{t,ris}^{k},\vartheta_{t,ris}^{k}),\end{split}$
(2)

where $\mathbf{G}_{k}\in\mathbb{C}^{M_{k}\times N_{t}}$
($\mathbf{R}_{k}\in\mathbb{C}^{N_{r}\times M_{k}}$) is the channel between BS
and $k$-th sub-RIS ($k$-th sub-RIS and UE). The parameter $\alpha_{k}$
($\beta_{k}$) is the LOS channel gain of $\mathbf{G}_{k}$ ($\mathbf{R}_{k}$)
and follows a complex normal distribution $\mathcal{CN}(0,10^{-0.1PL(d)})$,
with $PL(d)$ representing path loss and $d$ indicating the distance between
the associated terminals. The array response (steering) vector is denoted as
$\mathbf{a}(.)$, while $\varphi\in\mathcal{U}(a_{\varphi},b_{\varphi})$ and
$\vartheta\in\mathcal{U}(a_{\vartheta},b_{\vartheta})$ stand for azimuth and
elevation angles, respectively. Specifically, $\varphi_{t}$ ($\vartheta_{t}$)
represents the azimuth (elevation) angle of departure (AoD) at the BS, and
$\varphi_{r}$ ($\vartheta_{r}$) indicates the azimuth (elevation) angle of
arrival (AoA) at the UE; this is while, $\varphi_{t,ris}^{k}$
($\vartheta_{t,ris}^{k}$) shows azimuth (elevation) AoD associated with the
$k$-th sub-RIS, and $\varphi_{r,ris}^{k}$ ($\vartheta_{r,ris}^{k}$) is the
azimuth (elevation) AoA at the $k$-th sub-RIS. Here, it is assumed that each
channel is LOS dominated due to the presence of LOS component [20]. Thus, non-
LOS (NLOS) components are omitted, allowing for a focused investigation of the
proposed plug-in RIS performance. The normalized antenna array response is
defined as follows [15, 20]:

$\mathbf{a}(\varphi,\vartheta)=\frac{1}{\sqrt{N}}[e^{j\mathbf{k}^{T}\mathbf{p}_{0}},e^{j\mathbf{k}^{T}\mathbf{p}_{1}},\dots,e^{j\mathbf{k}^{T}\mathbf{p}_{N-1}}]^{T},$
(3)

where $N$ represents the total number of antenna elements/reflectors at the
corresponding terminal, calculated as $N=N_{x}\times N_{y}$. Here, $N_{x}$
($N_{y}$) refers to the number of antenna elements/reflectors along the
$x$-axis ($y$-axis). The symbol $\mathbf{k}$ denotes the wave number, and
$\mathbf{p}_{n}$ is associated with the structure of the antenna array,
specifying the location of the $n$-th antenna element. We establish
$n=n_{y}N_{x}+n_{x}$, where $0\leq n_{x}\leq N_{x}-1$ ($0\leq n_{y}\leq
N_{y}-1$) represents the location of the antenna element/reflector along the
$x$-axis ($y$-axis). For the URA configuration, the definitions of
$\mathbf{k}$ and $\mathbf{p}_{n}$ are outlined as follows [15, 20]:

$\mathbf{k}=\frac{2\pi}{\lambda}[\sin{\vartheta}\cos{\varphi}\enspace\sin{\vartheta}\sin{\varphi}]^{T},$
(4) $\mathbf{p}_{n}=[n_{x}\delta_{x}\enspace n_{y}\delta_{y}]^{T},$ (5)

where $\delta_{x}$ ($\delta_{y}$) represents the separation between adjacent
antennas/reflectors along the $x$-axis ($y$-axis), and $\lambda$ denotes the
signal wavelength. Note that to calculate the antenna array response for each
terminal, we need to substitute its corresponding $\varphi$ and $\vartheta$
values into (3) and (4). The effective end-to-end channel between the BS and
UE through the $k$-th sub-RIS, denoted as
$\mathbf{H}_{\text{eff},k}\in\mathbb{C}^{N_{r}\times N_{t}}$, can be defined
as follows:

$\mathbf{H}_{\text{eff},k}=\mathbf{R}_{k}\mathbf{\Psi}_{k}\mathbf{G}_{k},$ (6)

where $\mathbf{\Psi}_{k}\in\mathbb{C}^{M_{k}\times M_{k}}$ is the $k$-th sub-
RIS phase shift matrix and define as

$\mathbf{\Psi}_{k}\triangleq\operatorname*{diag}{(e^{j\psi_{1}},e^{j\psi_{2}},\dots,e^{j\psi_{M_{k}}})},$
(7)

where $\psi_{i}$ is the phase shift associated with the $i$-th reflector of
the corresponding sub-RIS. As mentioned earlier, the sub-RISs can be adjusted
using the location of BS and dead zones. Lemma 1 gives a mathematical
expression for sub-RISs phase shift adjustment.

######  Lemma 1.

The phase shift matrix for the $k$-th sub-RIS can be calculated as follows:

$\mathbf{\Psi}_{k}=\sqrt{M_{k}}\operatorname*{diag}\Big{(}\mathbf{f}_{b,k}\circ{\mathbf{a}_{r,ris}^{*}}(\varphi_{r,ris}^{k},\vartheta_{r,ris}^{k})\Big{)},$
(8)

where $\mathbf{f}_{b,k}$ represents the fixed beam formed by the $k$-th sub-
RIS with azimuth and elevation AoD as $\phi_{b,k}$ and $\theta_{b,k}$,
respectively. $\mathbf{f}_{b,k}$ is expressed as

$\mathbf{f}_{b,k}=[e^{\mathbf{k}^{T}\mathbf{p}_{0}},e^{\mathbf{k}^{T}\mathbf{p}_{1}},\dots,e^{\mathbf{k}^{T}\mathbf{p}_{M_{k}-1}}],$

where $\mathbf{k}$ is calculated as (4) by substituting $\varphi=\phi_{b,k}$
and $\vartheta=\theta_{b,k}$.

###### Proof.

See [18, Section III-C]. ∎

###  II-C Signal Model

In this subsection, we describe the signal model used in this paper. Next, we
represent the ML decoder for the proposed plug-in RIS. As mentioned earlier,
the dead zone is divided into distinct spatial segments based on its geometric
shape. Given that the dead zone’s location remains fixed, the spatial segments
also maintain constant positions. Consequently, each spatial segment is
defined by a pair of unchanging azimuth and elevation angular values. Thus,
sub-RISs are adjusted according to the constant angular information of BS and
spatial segments in order to cover that segment. For starting transmission,
the BS should obtain the CSI, including angular information at the BS and UE.
Since the BS and sub-RISs have fixed positions, the angular information at the
BS is also constant and known to the BS; therefore, after transmitting pilot
signals, the BS can easily find the spatial segment in which the UE is located
and its associated sub-RIS. Furthermore, by estimating end-to-end channel,
both the BS and UE can adjust their analog beamformers/combiners accordingly.
The effective end-to-end channel can be described as (6). Therefore, the
received signal after passing through the combiner is represented as

$y=\sqrt{P}G_{t}G_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}s+\mathbf{f}_{r}^{H}\mathbf{n},$
(9)

where $P$ stands for the transmit power, $G_{i}=g_{e}+10\log_{10}(N_{i})$,
wherein $i\in\\{t,r\\}$, represents the array gain, with $g_{e}$ denoting the
gain of each antenna element [21, 22]. The symbol $s$ corresponds to the
transmitted $\mathcal{M}$-ary symbol, and
$\mathbf{n}\in\mathbb{C}^{N_{r}\times
1}\sim\mathcal{C}\mathcal{N}(0,\sigma^{2})$ is the additive noise component.
Moreover, $\mathbf{f}_{t}\in\mathbb{C}^{N_{t}\times 1}$ denotes the analog
beamformer at the BS, while $\mathbf{f}_{r}\in\mathbb{C}^{N_{r}\times 1}$
represents the analog combiner at the UE. For simplification, continuous phase
shifters are assumed at the BS and UE; thus, analog beamformer/combiner can be
adjusted as $\mathbf{f}_{t}=\mathbf{a}_{t}(\varphi_{t},\vartheta_{t})$ and
$\mathbf{f}_{r}=\mathbf{a}_{r}(\varphi_{r},\vartheta_{r})$. Utilizing the ML
detector at the UE, the estimated symbol is expressed as

$\hat{s}=\operatorname*{arg\,min}_{\forall
s\in\mathcal{S}}|y-\sqrt{P}G_{t}G_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}s|^{2},$
(10)

where $\mathcal{S}$ is the set of $\mathcal{M}$-ary constellation points.

##  III Proposed Plug-in RIS Structure

This section illustrates the structure of the proposed plug-in RIS. In the
plug-in RIS structure, sub-RIS units are placed with appropriate spacing, each
pre-configured to cover a specific spatial segment within a well-known dead
zone. Based on environmental blockage and path loss conditions, the sub-RIS
units can be positioned on either the BS or UE side. The spacing between sub-
RIS units should increase as they are deployed farther from the BS. We
subsequently formulate the minimum spacing between sub-RIS units.
Additionally, in Section V, we illustrate the dead zone spatial segments
through a graphical example using the simulation setup parameters.

Maintaining an appropriate spacing between sub-RIS units is crucial for
reducing power leakage to other segments within the dead zone, which is
particularly beneficial in MU scenarios as it leads to decreased interference.
Leveraging the beamforming gain offered by the massive MIMO antenna array at
the BS, forming a narrow beam precisely directed to a specific spatial area
becomes feasible. This beam’s coverage area, termed footprint, is determined
by the distance from the BS and the emitted signal’s beamwidth. Exploiting
this property of massive MIMO arrays enables the BS to illuminate only the
corresponding sub-RIS based on the UE’s location. In Fig. 1, an illustration
of adjacent sub-RISs separated by $\Delta$ is shown. To establish a closed-
form expression for $\Delta$, we initially define the length of each side of
the sub-RIS along the $i$-axis (where $i\in\\{x,y\\}$) as
$\iota_{i}=M_{i}\delta_{i}$. Note that $M_{i}$ represents the number of
reflectors across the $i$-axis, and for simplicity in notation, we eliminated
the sub-RIS’s index. The footprint of the received beam should exclusively
cover the intended sub-RIS. Assuming uniform spacing between sub-RISs, the
effective footprint diameter (EFD) can be computed as
$\textrm{EFD}=2\Delta+\iota$. Consequently, $\Delta$ can be derived as
follows:

$\Delta=\frac{\textrm{EFD}-\iota}{2}.$ (11)

In order to determine the EFD, we consider half-power beamwidth (HPBW) that
encompasses an effective portion of the radiated power [23]. It is worth
mentioning that an antenna can differentiate between two adjacent sources if
the angular separation between them exceeds half of the first-null beamwidth
(FNBW), which is approximately equivalent to HPBW, i.e.,
$\textrm{HPBW}\approx\frac{\textrm{FNBW}}{2}$ [24]. The HPBW of an antenna
array along the $i$-axis ($i\in\\{x,y\\}$) can be calculated using the
following formula [25]:

$\textrm{HPBW}\approx 0.891\frac{\lambda}{N_{i}\delta_{i}}.$ (12)

######  Lemma 2.

The EFD of the transmitted beam from the Tx at a distance of $d$ can be
computed as follows:

$\textrm{EFD}=2d\times\frac{\sin{(\frac{\textrm{HPBW}}{2})}}{\cos{(\frac{\textrm{HPBW}}{2}+\theta_{0})}},$
(13)

where $\theta_{0}$ represents the angle of the incident signal at the RIS with
respect to the RIS broadside direction.

###### Proof.

See [26, Appendix B]. ∎

Figure 2: EFD versus different amounts of incident angle.

######  Corollary 1.

In the case where $\theta_{0}=0$, indicating that the received beam at the RIS
is perpendicular to the RIS surface, the EFD can be approximated as

$\textrm{EFD}\approx\textrm{HPBW}\times d.$ (14)

###### Proof.

See Appendix A. ∎

Fig. 2 illustrates the precise EFD for various values of $d$ and $\theta_{0}$.
Notably, in Figs. 2 (a) and (b), a distinct pattern emerges: within a limited
range centered around $\theta_{0}=0^{\circ}$, the EFD remains constant; the
extent of this interval diminishes with higher values of $d$. Conversely, as
it is illustrated in Fig 2. (b), adopting a larger antenna array leads to
expanding the interval.

Substituting EFD into (11), sub-RISs inter-spacing, i.e., $\Delta$, can be
calculated as

$\Delta=\frac{\textrm{HPBW}\times d-\iota}{2}.$ (15)

Notably, $\Delta$ defines the minimum distance that needs to be maintained
between two neighboring sub-RIS units to mitigate power leakage to the other
spatial segments.

##  IV Theoretical Analysis

In this section, we begin by presenting a mathematical expression to validate
the accuracy of our ABER simulation results. Following that, we provide
expressions for computing the detector’s complexity for both plug-in and semi-
passive RIS designs.

###  IV-A ABER Theoretical Upper Bound

Obtaining ABER involves calculating the pairwise error probability (PEP),
which denotes the likelihood of detecting $\hat{s}$ when transmitting $s^{*}$.
Initially, we consider the channel as a known entity for both cascaded
channels. This allows us to express the conditional PEP (CPEP) as follows:

$\begin{split}\mathcal{P}(s^{*}\rightarrow\hat{s}|\alpha_{k},\beta_{k})=&\mathcal{P}(|y-\sqrt{P}G_{t}G_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}s^{*}|^{2}\\\
&>|y-\sqrt{P}G_{t}G_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}\hat{s}|^{2}).\end{split}$
(16)

######  Lemma 3.

The mathematical expression for CPEP is as

$\begin{split}\mathcal{P}(s^{*}\rightarrow&\hat{s}|\alpha_{k},\beta_{k})\\\
&=Q\Big{(}\frac{\sqrt{P}G_{t}G_{r}|\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}(s^{*}-\hat{s})|^{2}}{\sqrt{2}\sigma||\mathbf{f}_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}(s^{*}-\hat{s})||}\Big{)}.\end{split}$
(17)

###### Proof.

See Appendix B. ∎

Lemma 3 provides a closed-form expression for the CPEP. To compute the
unconditional PEP (UPEP), we take the expectation of CPEP over a sufficient
number of channel realizations, denoted as
$\mathrm{UPEP}=\mathbb{E}[\mathrm{CPEP}]$. Furthermore, to establish an upper
bound for the ABER, we utilize the union-bound approach as follows:

$\textrm{ABER}\leq\frac{1}{\eta\mathcal{M}}\sum_{s^{*}}\sum_{\hat{s}}E_{b}(s^{*}\rightarrow\hat{s})\textrm{UPEP},$
(18)

where $E_{b}(s^{*}\rightarrow\hat{s})$ is the total number of erroneous bits
and $\mathcal{M}$ is the order of $\mathcal{M}$-ary constellation.

###  IV-B Detector Complexity

This subsection discusses the computation of detector complexity for our
suggested plug-in RIS and semi-passive RIS designs. Both designs employ the
same detector as given in (10), but the main difference lies in obtaining
$\mathbf{H}_{\text{eff}}$. In the semi-passive RIS design, $\mathbf{G}$ and
$\mathbf{R}$ are computed separately, and the phase shift matrix
$\mathbf{\Psi}$ is also calculated by the RIS in each transmission period. The
detector then uses these matrices to calculate $\mathbf{H}_{\text{eff}}$,
affecting the detector’s complexity. However, in the plug-in RIS design,
$\mathbf{H}_{\text{eff}}$ is directly acquired without the need for separate
calculations of $\mathbf{G}$, $\mathbf{R}$, and $\mathbf{\Psi}$ due to the
pre-adjusted sub-RIS configuration. Considering this point, we compute each
RIS systems’s detector complexity as follows. In this subsection, for the sake
of notation simplicity, we show the number of RIS/sub-RIS elements engaged in
the communication with $M$; hence, the index of sub-RISs has been ignored.

  1. 1.

Semi-passive RIS: To compute $\mathbf{H}_{\text{eff}}$, the detector
calculates $\mathbf{\Psi}\mathbf{G}$, involving $\sim M^{2}N_{t}$ operations.
Subsequently, $\mathbf{R}\mathbf{\Psi}\mathbf{G}$ demands $\sim N_{r}MN_{t}$
operations. Thus, for computing $\mathbf{H}_{\text{eff}}$, $\sim
M^{2}N_{t}+N_{r}MN_{t}$ operations are needed. Moreover,
$\mathbf{H}_{\text{eff}}\mathbf{f}_{t}$ entails $\sim N_{r}N_{t}$ operations,
and obtaining $\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff}}\mathbf{f}_{t}$ takes
$\sim N_{r}$ operations. With this procedure repeated $\mathcal{M}$ times, the
detector’s complexity is
$\mathcal{O}(\mathcal{M}(M^{2}N_{t}+N_{r}MN_{t}+N_{t}N_{r}+N_{r}))$. However,
by neglecting the lower-order terms $N_{t}N_{r}+N_{r}$, the complexity of the
semi-passive RIS detector can be simplified to
$\sim\mathcal{O}(\mathcal{M}MN_{t}(M+N_{r}))$.

  2. 2.

Plug-in RIS: In the plug-in RIS design, the detector has direct access to
$\mathbf{H}_{\text{eff}}$ as explained earlier. Thus, in the initial step, it
computes $\mathbf{H}_{\text{eff}}\mathbf{f}_{t}$, requiring $\sim N_{r}N_{t}$
operations. Following this, to calculate
$\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff}}\mathbf{f}_{t}$, the detector
performs $\sim N_{r}$ operations. This process is repeated $\mathcal{M}$
times, resulting in a detector complexity of order
$\mathcal{O}(\mathcal{M}(N_{r}N_{t}+N_{r}))$. By omitting the lower-order term
$N_{r}$, the plug-in RIS complexity can be simplified to
$\sim\mathcal{O}(\mathcal{M}N_{r}N_{t})$.

The complexity analysis conducted for both the semi-passive and plug-in RIS
detectors demonstrates that the semi-passive RIS detector is more
computationally complex, which is numerically shown in Section V-E.

##  V Illustrative Results

This section evaluates the proposed plug-in RIS using four performance
metrics: ABER, achievable rate, energy efficiency (EE), and detector
complexity. We also validate the ABER performance of the plug-in RIS via the
theoretical upper bound. The assessment is conducted in practical scenarios,
both indoors (office) and outdoors (street canyon), implementing RIS at the BS
and UE sides, respectively. The effectiveness of the plug-in RIS is compared
with two benchmarks: semi-passive RIS [10, 9] and blind RIS [27]555In [27],
the blind RIS suggests setting all RIS elements’ phase shifts to zero.
However, to enhance the performance of the blind RIS in the mmWave
communication systems, we set random phase shift adjustments to increase
diversity.. It is worth noting that semi-passive RIS has been proposed in the
literature as a practical approach that eliminates the need for cascaded
channels decoupling [9]. On the other hand, in the blind RIS configuration,
the phase adjustments occur fully randomly; accordingly, there is no necessity
for cascaded channel decoupling or control link establishment. Hence, the
semi-passive RIS and blind RIS are two suitable candidates for benchmarking
within the scope of this paper.

Figure 3: Indoor office scenario for BS-side RIS implementation [28].

###  V-A Simulation Setup

In this subsection, we describe two wireless communication scenarios to
evaluate the performance of the proposed plug-in RIS in enhancing coverage.
These scenarios have also presented in [28] as practical options for RIS
implementation.

  1. 1.

Indoor Office (BS-side RIS): The first scenario involves an indoor environment
with two parallel hallways, as illustrated in Fig. 3. In practical situations,
the BS is optimally installed to cover maximum areas, but due to mmWave
vulnerability to blockage, certain spots and zones become challenging to
cover, for instance, one of the parallel hallways in this scenario. Instead of
deploying additional costly and inefficient BS, the RIS can be implemented to
extend coverage to these dead zones. Here, the distance between the BS (RIS)
and the RIS (UE) is $2.5\ m$ ($10\ m$).

  2. 2.

Street Canyon (UE-side RIS): For the second scenario, we consider a street
canyon environment, shown in Fig. 4, where the BS is installed on the rooftop
of one building on one side of the street. UEs positioned along the same side
of the street experience signal deficiency owing to their placement within the
dead zone. While an alternative could involve deploying another BS on top of a
building on the opposite side of the street, adopting RIS proves to be a more
cost/energy-effective way to cover the dead zone. In this scenario, we assume
that the distance between the BS (RIS) and the RIS (UE) is $20\ m$ ($10\ m$).

Figure 4: Street canyon scenario for UE-side RIS implementation.

This paper considers a limited and well-known dead zone [28], as depicted in
Figs. 3 and 4, which leads to an assumption that the elevation AoD of the sub-
RISs is constrained within a limited range. Consequently, we consider that the
azimuth and elevation AoDs of the sub-RISs are
$\varphi_{t,ris}\in\mathcal{U}[-\pi,\pi]$ and
$\vartheta_{t,ris}\in\mathcal{U}[-\pi/16,\pi/16]$, respectively. With such
assumptions and by adopting a sub-RIS of size $10\times 10$, the sub-RIS can
cover a circular area with a diameter of $4\ m$ which is located $10$ m away
from the sub-RIS. Furthermore, given the fixed position of BS and sub-RISs, we
can align the sub-RISs optimally with the BS [20] to meet the desired minimum
sub-RISs separation requirements. Based on our discussion in Section III and
as given in Fig. 2 (a), we assume that
$\varphi_{t},\varphi_{r,ris}\in\mathcal{U}[-\pi,\pi]$ and
$\vartheta_{t},\vartheta_{r,ris}\in\mathcal{U}[-\pi/3,\pi/3]$, considering the
BS is equipped with a $10\times 10$ antenna array. In other words, we assume
that if the incident angle $\theta_{0}$ is confined to an interval of
$[-\pi/3,\pi/3]$, the EFD remains constant666It is worth mentioning that
different antenna arrays’ and RISs’ sizes, and the use of beam widening
techniques, as discussed in [29], can lead to the definition of different AoD
and AoA intervals at the terminals. Nevertheless, these aspects are beyond the
scope of this paper and are left for future research directions.. We can
consider the maximum amount of EFD in this interval to calculate $\Delta$.

Figure 5: The variations of sub-RIS inter-spacing ($\Delta$) with respect to
different BS antenna array sizes for different distances and sub-RIS sizes.

Fig. 5 depicts sub-RIS inter-spacing versus different system parameters. As
shown in Fig. 5, with increasing BS antenna array size, the minimum spacing
among sub-RISs $\Delta$ decreases due to narrower beams emitted through BS. On
the other hand, with increasing the distance between BS and RIS, the EFD
increases, which means that the sub-RISs inter-space should be increased to
avoid power leakage to the non-targeted sub-RISs. Nevertheless, since the RIS
is a passive device, we can increase the number of reflecting elements in each
sub-RIS to decrease $\Delta$. This is specifically feasible in the proposed
plug-in RIS since increasing the number of elements does not entail more
complexity in the system. It is worth emphasizing that since the sub-RISs in
the plug-in RIS exploit fixed beams, only traditional end-to-end channel
estimation is enough, and cascaded channel decoupling is not required in the
practical plug-in RIS system, resulting in significant complexity reduction in
comparison with semi-passive and fully passive RIS structures, which allows us
to easily increase the number of reflectors in the plug-in RIS structure. Fig.
5 shows that with increasing the sub-RIS size, the sub-RISs inter-space
decreases. Note that in this paper, we consider BS antenna array and sub-RISs
of size $10\times 10$ to prevent high computational burden in the computer
simulations, since in the computer simulations, we need to construct the
cascaded channels separately for the sake of analysis.

As depicted in Fig. 6, various segments within the receive dead zone are
represented in polar coordinates for both two and four divisions. The fixed
beam orientation for each segment and several potential UE positions within
the dead zone are also illustrated in Fig. 6. It is worth mentioning that the
information given in Fig. 6 is used for plug-in RIS configuration and dead
zone segmentation in this paper. Specifically, for two and four spatial
segments, $(\phi_{b,i},\theta_{b,i})\in\\{(\pi/2,\pi/32),(-\pi/2,\pi/32)\\}$
and
$(\phi_{b,i},\theta_{b,i})\in\\{(\pi/4,\pi/32),(3\pi/4,\pi/32),(-\pi/4,\pi/32),(-3\pi/4,\pi/32)\\}$,
respectively. As the number of segments increases, the average distance
between the UE positions and the corresponding fixed beam orientations
decreases; consequently, the UEs can receive signals via more favorable beams,
which enhances overall system performance. It is important to mention that
although Fig. 6 shows dead zone division only along the azimuth angle, such
division can also be applied along the elevation angle. However, for clarity
and simplicity, we have opted not to illustrate more complex divisions in the
figures.

Figure 6: Dead zone divisions, fixed beams, and possible UE positions for (a) two segments and (b) four segments. TABLE II: Simulation parameters. | Parameter |  Description |  Value
---|---|---
$f_{c}$ |  Carrier frequency |  $28$ GHz
$B$ |  Bandwidth |  $100$ MHz
$N_{t}$ |  BS antenna array size |  $10\times 10$
$N_{r}$ |  UE antenna array size |  $1$
$\delta_{x}=\delta_{y}$ |  Antenna element separation |  $\lambda/2$
Noise PSD |  Noise power spectral density |  $-174$ dBm
$g_{e}$ |  Antenna element gain |  $0$ dBi
$\varphi_{t}$ ($\varphi_{r,ris}$) |  Azimuth Tx AoD (RIS AoA) |  $\mathcal{U}[-\pi,\pi]$
$\varphi_{t,ris}$ |  Azimuth RIS AoD |  $\mathcal{U}[-\pi,\pi]$
$\vartheta_{t}$ ($\vartheta_{r,ris}$) |  Elevation Tx AoD (RIS AoA) |  $\mathcal{U}[-\pi/3,\pi/3]$
$\vartheta_{t,ris}$ |  Elevation RIS AoD |  $\mathcal{U}[-\pi/16,\pi/16]$
$(\phi_{b,k},\theta_{b,k})$ |  Azimuth and elevation AoD for a two sub-RIS system |  $\\{(\frac{\pi}{2},\frac{\pi}{32})$,$(-\frac{\pi}{2},\frac{\pi}{32})\\}$
$(\phi_{b,k},\theta_{b,k})$ |  Azimuth and elevation AoD for a four sub-RIS system |  $\\{(\frac{\pi}{4},\frac{\pi}{32})$,$(\frac{3\pi}{4},\frac{\pi}{32})$, $(-\frac{\pi}{4},\frac{\pi}{32})$,$(-\frac{3\pi}{4},\frac{\pi}{32})\\}$
$P_{\text{PA}}$ |  Power amplifier power consumption |  $20$ mW [30]
$N_{\text{rf}}$ |  Number of RF chain |  $1$
$M_{\text{active}}$ |  Number of RIS active elements |  $0.08\times M$ [9]
$P_{\text{PS}}$ |  Phase shifter power consumption |  $30$ mW [30]
$P_{\text{RF-chain}}$ |  RF chain power consumption |  $40$ mW [31, 30]
$P_{\text{BB}}$ |  Baseband processor power consumption |  $200$ mW [31, 30]
$P_{\text{LNA}}$ |  Low noise amplifier power consumption |  $20$ mW [31, 30]
$P_{\text{PA\\_RIS}}$ |  RIS element power consumption |  $10$ mW [10]
$FOM_{W}$ |  Walden’s figure-of-merit |  $46.1$ fJ/conversion-step [10]
Indoors |  $(a,b)$ |  Path loss parameters |  $(32.4,1.73)$ [32]
$d_{BR}$ |  Distance between BS and RIS |  $2.5\ m$
$d_{RU}$ |  Distance between RIS and UE |  $10\ m$
Outdoors |  $(a,b)$ |  Path loss parameters |  $(32.4,2.1)$ [32]
$d_{BR}$ |  Distance between BS and RIS |  $20\ m$
$d_{RU}$ |  Distance between RIS and UE |  $10\ m$

The carrier frequency is designated as $28$ GHz, and the path loss model is
employed as follows [32]:

$PL(d)=a+10b\log_{10}{(d)}+20\log_{10}{(f_{c})},$ (19)

where the values of $a$ and $b$ are given in Table II. The analysis assumes a
noise power spectral density (PSD) of $-174$ dBm/Hz, with a bandwidth ($B$) of
$100$ MHz [20]. This results in a noise power calculation of $\sigma^{2}=-94$
dBm [20]. The antenna gain of each element is considered to be $g_{e}=0$ dBi,
signifying the utilization of omnidirectional antennas for every element. The
assumed values for system parameters are summarized in Table II.

It is noteworthy that in this paper the system performance analysis is carried
out using two and four sub-RIS configurations. During each transmission
period, only one sub-RIS is used while the rest remain idle. On the other
hand, the semi-passive RIS utilizes all implemented elements for maximum
performance. In other words, the plug-in RIS uses only a portion of deployed
elements, potentially sacrificing passive beamforming gain compared to the
semi-passive RIS. However, the semi-passive RIS employs baseband components to
estimate the cascaded channels and adjust its phase shifts autonomously, while
the proposed plug-in RIS remains fully passive. Therefore, the plug-in RIS
offers a favorable trade-off between system performance and
EE/cost/complexity. Likewise, for the blind RIS, all implemented elements are
engaged in each transmission cycle.

###  V-B Examining ABER Performance and Theoretical Validation

This subsection displays simulation results for the ABER performance of the
proposed plug-in RIS. We further verify these results via the analytical upper
bound derived in Lemma 3. Here, we utilize a $10\times 10$ RIS for the semi-
passive RIS structure to match the passive beamforming gain with the proposed
plug-in RIS in each transmission period (since in each transmission period,
only one sub-RIS of size $10\times 10$ is used). In contrast, for the blind
RIS design, we consider RIS sizes of $20\times 10$ and $20\times 20$ to
highlight the superiority of the plug-in RIS over blind RIS.

As depicted in Fig. 7, our simulations closely align with the upper bound,
confirming the accuracy of the conducted simulations for both indoor office
and street canyon scenarios. Notably, we utilized a binary phase shift keying
(BPSK) signaling scheme for this simulation. Fig. 7 illustrates a substantial
performance improvement exhibited by the proposed plug-in RIS when compared
with the blind RIS design, even though the blind RIS configuration considered
here offers a larger beamforming gain due to its bigger size. Additionally,
results in Fig. 7 reveal that adopting a plug-in RIS with two sub-RISs results
in roughly $9$ dB higher ABER compared to the semi-passive RIS. On the other
hand, employing four sub-RISs leads to performance enhancement, causing only a
$2$ dB ABER degradation compared to the semi-passive RIS in both scenarios. It
is important to recall that each sub-RIS corresponds to a segment within the
dead zone, as shown in Fig. 6. Therefore, increasing the number of sub-RISs is
equivalent to increasing the number of segments. Consequently, when we
increase the sub-RISs from two to four, the ABER performance improves by about
$7$ dB because the UE has more chance to receive a stronger signal. These
outcomes underline the efficacy of the proposed plug-in RIS structure, which
proves to be more cost-effective than the semi-passive alternative with a few
degradations in ABER.

Figure 7: ABER performance analysis for (a) the BS-side RIS-aided system in
the indoor office environment, (b) the UE-side RIS-aided system in the street
canyon environment.

###  V-C Analysis of Achievable Rate Performance

In this subsection, we examine the achievable rate performance of the proposed
plug-in RIS and compare it with benchmarks. For this subsection, alongside the
RIS sizes explored in the previous subsection, we consider an RIS of size of
$10\times 10$ for the blind RIS scheme. The achievable rate can be calculated
as

$R=\mathbb{E}[\log_{2}(1+\textrm{SNR})],$ (20)

where SNR stands for signal-to-noise ratio and can be calculated as follows:

$\textrm{SNR}=\frac{|\sqrt{P}G_{t}G_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}|^{2}}{\sigma^{2}}.$
(21)

Fig. 8 depicts the plug-in RIS performance in terms of achievable rate
compared to the two considered benchmark schemes. Similar to the ABER
performance, the plug-in RIS exhibits satisfactory achievable rate performance
compared to the two benchmark schemes under consideration. Compared with the
blind RIS configuration, our novel plug-in RIS configuration significantly
improves the achievable rate performance. Likewise, similar to the ABER
performance outcomes, even larger-scale blind RIS configurations, which
provide more significant beamforming gains, fail to reach the achievable rate
performance offered by the plug-in RIS configuration. In comparison to the
semi-passive RIS, the proposed plug-in RIS shows a performance degradation of
$5$ dB with $2$ sub-RISs. This degradation decreases to $2$ dB when using $4$
sub-RISs, demonstrating the impact of higher SNR at the UE due to increased
segments in the dead zone.

Computer simulation results in this subsection emphasize the effectiveness of
our plug-in RIS compared to the benchmarks. While the plug-in RIS may not
outperform the semi-passive RIS, its cost-effective passive design merits
consideration.

Figure 8: Achievable rate performance for (a) the BS-side RIS-aided system in
the indoor office environment, (b) the UE-side RIS-aided system in the street
canyon environment.

###  V-D Energy Efficiency Analysis

In this subsection, we focus on the strength point of the plug-in RIS design,
which is its EE. We also highlight the trade-offs between EE and
ABER/achievable rate. The EE is computed as follows:

$\eta_{EE}=\frac{R\times B}{P_{c}}\ \text{bits/Joule},$ (22)

where $P_{c}$ signifies the power consumption within the system and can be
determined as follows [10]:

$P_{c}=P_{\text{Tx}}+P_{\text{Rx}}+P_{\text{RIS}},$ (23)

where $P_{i}$ ($i\in\\{\text{Tx, Rx, RIS}\\}$) denotes the power consumption
of the respective terminal and can be calculated as follows [30, 31]:

$\begin{split}P_{\text{Tx}}=P+N_{t}&P_{\text{PA}}+N_{\text{rf}}(N_{t}P_{\text{PS}}+P_{\text{RF-
chain}}+2P_{\text{DAC}})+P_{\text{BB}},\end{split}$ (24)
$\begin{split}P_{\text{Rx}}=N_{r}P_{\text{LNA}}&+N_{\text{rf}}(N_{r}P_{\text{PS}}+P_{\text{RF-
chain}}+2P_{\text{ADC}})+P_{\text{BB}},\end{split}$ (25)
$P_{\text{RIS(Passive)}}=MP_{\text{PA\\_RIS}},$ (26)
$\begin{split}P_{\text{RIS(Semi\\_Passive})}=&MP_{\text{PA\\_RIS}}+M_{\text{active}}(P_{\text{LNA}}\\\
&+P_{\text{RF-chain}}+2P_{\text{ADC(RIS)}})+P_{\text{BB}},\end{split}$ (27)

where $M$ represents for number of RIS/sub-RIS elements engaged in the
communication and $P_{\text{ADC}}$ ($P_{\text{DAC}}$) is the consumption power
of analog-to-digital (ADC) (digital-to-analog (DAC)) converter at the receive
(transmit) terminal and can be computed as follows [10, 31]:

$P_{\text{ADC}}=P_{\text{DAC}}=FOM_{W}\times f_{s}\times 2^{b},$ (28)

where $FOM_{W}$ corresponds to Walden’s figure-of-merit for assessing ADC
power efficiency, the variable $f_{s}$ stands for the Nyquist sampling
frequency, while $b$ represents the ADC resolution bits. Our assumption
employs $FOM_{W}=46.1$ fJ/conversion-step for a $100$ MHz bandwidth [10]. We
utilize ADCs with $1$ bit and $4$ bits resolution for the semi-passive RIS [9]
and transceivers [31], respectively. We also consider $8\%$ of elements in the
semi-passive RIS being connected to baseband components as suggested in [9].
All other parameters align with those defined in Table II.

Figure 9: Energy efficiency comparison for (a) the BS-side RIS-aided system in
the indoor office environment, (b) the UE-side RIS-aided system in the street
canyon environment.

As illustrated in Fig. 9, the plug-in RIS performs better than both benchmarks
in indoor and outdoor scenarios. The performance of the plug-in RIS improves
as the number of sub-RISs increases, benefiting from higher SNR and the power-
efficient nature of passive elements. Essentially, increasing the number of
sub-RISs allows for increasing the number of segments within the dead zone.
Consequently, each segment becomes smaller, leading to improved received SNR
and better $\eta_{EE}$. On the contrary, increasing the number of elements in
the semi-passive RIS negatively affects EE and leads to performance
deterioration. It is important to note that although enlarging the RIS size in
the semi-passive RIS configuration increases received SNR due to enhanced
beamforming gain, it also involves more baseband components in the RIS
structure, resulting in higher power consumption. In this case, power
consumption primarily impacts EE performance and leads to decreased EE.

In the case of the blind RIS, different behaviors are observed in two
scenarios. In the indoor scenario, increasing the number of elements does not
improve EE. Fig. 9 (a) shows that increasing the dimension of the blind RIS
reduces EE due to the dominant effect of power consumption by passive
elements. In contrast, in the outdoor scenario, increasing the number of
elements from $10\times 10$ to $20\times 10$ leads to positive effects on
beamforming gain, but power consumption also increases proportionally,
resulting in no change in EE. However, a larger RIS size in the outdoor
scenario, i.e., $20\times 20$, repeats the indoor scenario’s behavior, with
power consumption becoming dominant and causing EE degradation. It is worth
mentioning that a notable EE performance gap exists between blind RIS and the
proposed plug-in RIS, primarily due to the enhanced SNR provided by the plug-
in RIS without a proportional increase in power consumption.

###  V-E Detector Complexity

Figure 10: Detector complexity comparison as a function of (a) number of
transmit antennas, $N_{t}$, and number of RIS elements, $M$, (b) number of
transmit antennas, $N_{t}$, and constellation order, $\mathcal{M}$.

The detector complexity for different numbers of transmit antennas, RIS
elements, and constellation orders is depicted in Fig. 10. As shown in Fig. 10
(a), it is evident that the plug-in RIS’s detector exhibits significantly
lower computational complexity compared to the semi-passive RIS’s detector. It
is worth noting that the increase in the number of RIS elements ($M$) has a
more significant impact on the complexity of the semi-passive RIS detector
compared to the increase in the number of antennas ($N_{t}$); this is
attributed to the quadratic relationship between $M$ and the detector
complexity in the semi-passive detector expression, while the plug-in RIS
design remains unaffected by the increase in $M$. Note that in Fig. 10 (a), we
have considered $\mathcal{M}=2$. Fig. 10 (b) further illustrates how
variations in $N_{t}$ and $\mathcal{M}$ affect detector complexity while
maintaining a constant number of RIS elements ($M=100$), emphasizing the
superiority of the proposed plug-in RIS over semi-passive RIS design.

##  VI Conclusion

This paper has introduced a practical RIS structure, the plug-in RIS, for
mmWave communication systems to enhance coverage to the dead zones. The plug-
in RIS operates passively, cleverly integrating the control mechanism within
the transmitted beam to the RIS, eliminating the need for conventional
reliable control links. It also relaxes the channel estimation process by
eliminating complex cascaded channel decoupling, a common challenge in RIS-
assisted systems. In this approach, dead zones are divided into segments, each
served by a dedicated sub-RIS with a fixed beam. Computer simulation results
have shown that deploying four sub-RISs causes only slight degradation in ABER
and achievable rates, making fully passive operation feasible. We have also
compared the EE of the plug-in RIS with benchmarks. While the semi-passive RIS
slightly outperforms the plug-in RIS in terms of ABER and achievable rate, its
EE performance is worse than the proposed plug-in RIS due to active baseband
components. Besides, the plug-in RIS detector exhibits superior complexity
performance compared to the semi-passive RIS thanks to the conventional
channel estimation mechanism.

In summary, our plug-in RIS proves to be a compelling solution, performing
closely to the semi-passive RIS regarding ABER and achievable rate
performances, surpassing the benchmarks in terms of EE performance and
detector complexity, and addressing challenges in mmWave systems. Unlike
traditional RIS designs, plug-in RIS allows simultaneously serving multiple
UEs within the same spatial segment. Nonetheless, such a scenario requires
careful interference mitigation design, which remains a topic for future
research endeavors.

##  Appendix A Proof of Corollary 1

By substituting $\theta_{0}=0$ into (13), we can simplify it as:

$\textrm{EFD}=2d\times\tan(\frac{\textrm{HPBW}}{2}).$ (29)

On the other hand, the tangent function can be expanded using the MacLaurin
series as follows:

$\tan(x)=x+\frac{x^{3}}{3}+\frac{2x^{5}}{15}+\dots;\ \ \textrm{if}\ \
|x|<\frac{\pi}{2},$ (30)

whereas when $x$ is of a small magnitude, it can be approximated as
$\tan(x)\approx x$. Note that $\frac{\textrm{HPBW}}{2}$ becomes relatively
small when implementing a massive MIMO array at the BS. Consequently, the
approximation formula remains applicable here, and we can further simplify
(29) to (14).

##  Appendix B Proof of Lemma 3

By exploiting [20, equation (24)] and after some mathematical manipulations,
(16) can be updated as

$\begin{split}\mathcal{P}(s^{*}\rightarrow&\hat{s}|\alpha_{k},\beta_{k})=\mathcal{P}(|\sqrt{P}G_{t}G_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}(s^{*}-\hat{s})|^{2}\\\
&+2\mathcal{R}\\{\sqrt{P}G_{t}G_{r}\mathbf{n}^{H}\mathbf{f}_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}(s^{*}-\hat{s})<0\\}).\end{split}$
(31)

As the elements of $\mathbf{n}^{H}$ follows a complex normal distribution with
variance $\sigma^{2}$, its real component also conforms to a normal
distribution with variance $\frac{\sigma^{2}}{2}$, represented as
$\mathcal{R}\\{\mathbf{n}^{H}\\}\sim\mathcal{N}(\mathbf{0}_{N_{r}},\frac{\sigma^{2}}{2}\mathbf{I}_{N_{r}})$.
Consequently, we can readily express:

$\begin{split}\mathcal{R}\\{A\mathbf{n}^{H}\\}+\mu\mathbf{1}_{N_{r}}^{H}\sim\mathcal{N}(\mu\mathbf{1}_{N_{r}},\frac{A^{2}\sigma^{2}}{2}\mathbf{I}_{N_{r}}),\end{split}$
(32)

where
$A=2\sqrt{P}G_{t}G_{r}||\mathbf{f}_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}(s^{*}-\hat{s})||$
and
$\mu=|\sqrt{P}G_{t}G_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}(s^{*}-\hat{s})|^{2}$;
accordingly, (31) can be calculated as

$\begin{split}\mathcal{P}(s^{*}\rightarrow&\hat{s}|\alpha_{k},\beta_{k})=Q(\sqrt{2}\frac{\mu}{A\sigma})\\\
&=Q(\frac{\sqrt{P}G_{t}G_{r}|\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}(s^{*}-\hat{s})|^{2}}{\sqrt{2}\sigma||\mathbf{f}_{r}\mathbf{f}_{r}^{H}\mathbf{H}_{\text{eff},k}\mathbf{f}_{t}(s^{*}-\hat{s})||}).\end{split}$
(33)

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