# Planning Mm-Wave Access Networks With Reconfigurable Intelligent Surfaces

Eugenio Moro∗, Ilario Filippini∗, Antonio Capone∗ and Danilo De Donno†
∗ANTLab - Advanced Network Technologies Laboratory, Politecnico di Milano,
Milan, Italy
†Milan Research Center, Huawei Technologies Italia S.r.l, Milan, Italy
Email: $\\{$eugenio.moro, ilario.filippini<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

With the capability to support gigabit data rates, millimetre-wave (mm-Wave)
communication is unanimously considered a key technology of future cellular
networks. However, the harsh propagation at such high frequencies makes these
networks quite susceptible to failures due to obstacle blockages. Recently
introduced Reconfigurable Intelligent Surfaces (RISs) can enhance the coverage
of mm-Wave communications by improving the received signal power and offering
an alternative radio path when the direct link is interrupted. While several
works have addressed this possibility from a communication standpoint, none of
these has yet investigated the impact of RISs on large-scale mm-Wave networks.
Aiming to fill this literature gap, we propose a new mathematical formulation
of the coverage planning problem that includes RISs. Using well-established
planning methods, we have developed a new optimization model where RISs can be
installed alongside base stations to assist the communications, creating what
we have defined as Smart Radio Connections. Our simulation campaigns show that
RISs effectively increase both throughput and coverage of access networks,
while further numerical results highlight additional benefits that the
simplified scenarios analyzed by previous works could not reveal.

##  I Introduction

Current and future mobile radio network generations are challenged to cope
with ever-expanding mobile data demands, spurred by our increasingly connected
society [1].
At the same time, cellular communication systems based on sub-6GHz frequencies
are currently experiencing a bandwidth shortage [2] as they struggle to
deliver the required level of performance.
Millimetre-wave (mm-wave) based cellular communications have been recognized
as the key technology to address both these crucial issues, as they can fulfil
the promise of supporting Gbps demands while also solving the spectrum
scarcity issue [3].
Although its standardization in cellular networks for mobile access began only
recently with 3GPP Release 15, this technology has already been largely
employed in satellite links and cellular backhauling [4] and its limitations
are well known. In particular, mm-waves are affected by harsh propagation
typical of such high frequency that leads to high free space attenuation.
Simultaneously, high penetration losses and poor diffraction mean that any
obstacle crossing the line of sight might easily cause mm-Wave communications
to fail.
While emergent technologies - such as massive MIMO and beamforming - can
effectively compensate for the increased pathloss [5], the problem of blockage
resiliency in mobile access has not encountered the same luck.

Among the candidate technologies that can potentially address the issue above,
the recent emerging concept of Reconfigurable Intelligent Surface (RIS) has
gained extreme popularity among the academic community [6].
RISs are described as quasi-passive planar structures whose electromagnetic
properties can be electronically controlled to manipulate impinging radio
waves in a variety of ways. While an RIS can produce several types of these
electromagnetic manipulations, the ability to reflect and focus impinging
waves in any direction has the potential of transforming these surfaces in
passive relays [7]. This ability is exciting for mm-Wave communications, as an
RIS can increase the blockage resilience by creating an alternative
electromagnetic path. As opposed to active relays, RISs also show
significantly higher energy efficiency [8] and prototypal works [9] have shown
how they can be effectively built with cheap materials. Indeed, part of the
attention that RISs are generating might be well justified by the opportunity
of reducing the cost of deploying and maintaining a resilient wireless access
network as opposed to more traditional and expensive approaches [10].

Theoretical works [11][12][13] have extensively analyzed this particular RIS
configuration from a communication perspective, providing practical
mathematical tools to model the propagation characteristics of such scenarios.
However, these analyses are carried out at the link level with simplified
network scenarios.
In this work, instead, we focus on the planning of large-scale mm-Wave radio
access networks employing intelligent surfaces and, to the best of our
knowledge, it is the first to tackle this challenge. We have employed well-
established coverage planning methods to develop a new mathematical
formulation of the coverage planning problem where both base stations and RISs
can be installed in given locations of an arbitrary geographic area. We have
introduced the concept of Smart Radio Connection (SRC), a logical abstraction
of the well-known concept of the RIS-enabled Smart Radio Environment [14]. An
SRC consists of a radio link assisted by an intelligent surface and, in our
planning model, SRCs can be established alongside traditional connections
between UEs and base stations to increase the coverage and system performance.
Our extensive numerical analysis campaign testifies how the well known point-
to-point benefits of employing RISs do scale well at the system level for
mobile access. Results show that including RISs when planning a radio access
network can simultaneously increase coverage, throughput and blockage
resiliency. Additionally, our results give new interesting insights on the
benefits of employing RISs for coverage planning of mm-wave networks that
could not be noticed in the highly simplified scenarios of related works. In
particular, our model can identify the RIS configurations and the deployment
budget conditions that provide tangible performance advantages when RISs are
considered.

The rest of this paper is structured as follows: Sec. II presents some
relevant related works, Sec. III details a baseline mm-wave coverage planning
model that does not include the presence of RISs, Sec. IV describes the
modeling choices that lead us to develop a RIS-aware planning model and
presents the novel mathematical formulation. Finally, Sec. V shows the
simulation setup and the numerical results.

##  II Related Works

Reconfigurable Intelligent Surfaces represent the latest technological
proposition in the domain of propagation waves control [15]. Their use as
passive relays has been proposed in [7], where preliminary link-level
simulations have shown the potential benefits with respect to more traditional
active relaying approaches.
From a communication standpoint, the problem of jointly optimizing the base
station pre-coding and the RIS elements phase shifts has been studied in [11],
where an iterative algorithm addresses the non-convexity challenges. In [12],
a closed-form solution of the same problem is derived exploiting the
characteristic of mm-Wave channels.
Finally, authors of [9] have shown how a prototype RIS can effectively enhance
the coverage of indoor mm-Wave networks.

Historically, the problem of coverage planning has been applied to different
radio access technologies.
However, mm-Wave coverage planning works have only lately appeared in the
literature, given the relatively recent interest. Understandably, these works
have studied the coverage problem with a focus on the network resilience
against blockages.
In particular, authors of [16] study the problem of optimizing the layout of
an mm-Wave access network in a dense urban environment such that the LOS
availability is maximized. A similar analysis is carried out in [17] for mm-
Wave vehicular communication scenarios.
In [18], the coverage planning problem is studied through a network cost
minimization that employs a link availability stochastic model. Finally,
authors of [10] have studied the impact of different network planning
approaches on the blockage resiliency of mm-Wave deployments.
None of the planning works mentioned above has included reconfigurable
intelligent surfaces in their investigations. To the best of the authors’
knowledge, this is the first published work to present such an analysis.

##  III Basic mm-Wave Model

In this section, we give a basic description of a mathematical programming
model for mm-Wave access network coverage planning. Similarly to other
coverage planning works [19, 10], we identify a set $\mathcal{C}$ of candidate
positions (i.e. Candidate Sites, CSs) over a given geographic area where Base
Stations (BS) can be installed. A discrete set of Test Points (TP)
$\mathcal{T}$ represents the traffic/user distribution.
Binary coverage parameter $\Lambda_{t,c}$ captures the propagation
characteristics between TP $t\in\mathcal{T}$ and CS $c\in\mathcal{C}$.
Particularly, $\Lambda_{t,c}=1$ if a radio link between the two positions can
be established and zero otherwise. These parameters are set according to
physical considerations, such as distance, transmission power, receiver
sensitivity, antenna gain, attenuation losses, and more. Additionally,
blockages due to fixed and opaque obstructions between any pair of CS-TP can
be modelled by setting the corresponding coverage parameter to 0.
Given the fixed known position of any potential CS-TP pair, the maximum
achievable downlink bit-rate can be pre-computed according to the transmitter
and receiver characteristics and any propagation model of choice. Indeed,
given the extreme directivity of mm-Wave downlink transmissions that can
strongly limit any interference effect, we can reasonably assume this bit-rate
to be independent of other simultaneous access transmissions [10].
However, a well-known issue of millimetre-based communication is its high
penetration loss and limited diffraction [20], resulting in frequent blockages
due to obstacles transiting across the connection line of sight. Blocked radio
links experience a dramatic reduction in throughput, and this can be taken
into consideration by weighting the maximum achievable bit-rate of each link
with the probability of the link being in a state where such bit-rate is
actually available (i.e., not blocked)111Specific blockage models, such as
[21], express this probability as a decreasing function of the link length,
allowing this quantity to be computed given the CS-TP distances.. Parameter
$R_{t,c}^{\text{BS}}$ denote this expected (blockage-weighted) maximum
throughput between TP $t\in\mathcal{T}$ and BS installed in $c\in\mathcal{C}$.
Similarly, $R^{\text{MIN}}$ identifies the minimum expected throughput that
needs to be guaranteed to each TP for it to be considered as covered. Knowing
the channel states $\mathcal{S}$, their probabilities $p_{s},s\in\mathcal{S}$
and the corresponding achievable rates $r_{s},s\in\mathcal{S}$, these
parameters can be computed according to the following formula:

$R=\sum_{s\in\mathcal{S}}p_{s}r_{s}.$ (1)

Finally, the coverage planning is constrained to a budget value $B$ and
parameter $P_{c}$ describes the cost of installing a BS in a particular CS
$c\in\mathcal{C}$.
The proposed planning model is based on the following decision variables:

  * •

$y_{c}^{\text{BS}}\in\\{0,1\\}$: installation variable equal to 1 if a BS is
installed in site $c\in C$ and 0 otherwise,

  * •

$x_{t,c}\in\\{0,1\\}$: association variable equal to 1 if BS in
$c\in\mathcal{C}$ is assigned for coverage of test point $t\in\mathcal{T}$,

  * •

$\tau_{t,c}^{\text{BS}}\in[0,1]$, time-sharing variable indicating the
fraction of time during which BS in $c\in\mathcal{C}$ transmits to test point
$t\in\mathcal{T}$. This variable allows us to model the BS resource sharing as
a time-sharing process, in accordance to 3GPP Rel. 15 specifications. Note
that the very same notation can be applied if the joint time and sub-carrier
sharing has to be considered.

Given the notation, the parameters and the variables described above, we now
propose a basic MILP (Mixed Integer Linear Programming) formulation of the
coverage planning problem: [2] ∑_t ∈T, c ∈C R_t,c^BS⋅τ^BS_t,c ∑_c ∈Cx_t,c≤1∀t
∈T τ_t,c^BS≤Λ_t,c⋅x_t,c ∀t ∈T, c ∈C ∑_t ∈Tτ_t,c^BS≤y_c^BS∀c ∈C ∑_c ∈C
R_t,c^BS⋅τ_t,c^BS≥R^MIN ∀t ∈T ∑_c ∈CP_c⋅y_c^BS≤B The objective function in (1)
expresses the goal of the planning model: the maximization of the sum-
throughput. A per-user average throughput appears in the sum, which depends on
both the nominal link capacity between BS and TP and the fraction of resources
the BS dedicates to the specific TP. Also, note that we consider this
objective function as one of the very many possible ones. Other approaches,
such as the sum of throughput logarithms, the max-min throughput, etc., can be
easily plugged in with minimal changes to the formulation.
Constraints (III) enforces each TP to be covered at most by 1 BS. Constraint
(III) is such that a BS in $c\in\mathcal{C}$ can transmit to a TP
$t\in\mathcal{T}$ for a strictly positive fraction of time only if such TP is
associated with this particular BS (i.e. $x_{t,c}=1$) and if a radio link can
be established between the two (i.e. $\Lambda_{t,c}=1$).
Constraint (1) has a double function. First, it does not allow any
transmission of strictly positive duration to originate from any BS which has
not been installed. Additionally, it limits to 1 the overall sum of the
fractions of time dedicated for transmissions towards specific TPs for each
installed BS, effectively enforcing a time-based division of BS resources.
Note that this constraint may imply single-beam BS transmissions. However, the
goal of this formulation is not to provide a perfect user throughput figure,
which is usually computed by system-level simulators, but rather to design a
good network layout. The latter can be achieved even with approximated user
throughput models that do not substantially change the optimal deployment. On
top of that, multi-beam antenna patterns remarkably decrease link directivity,
strongly limiting BS coverage. As such, we believe it is reasonable to assume
that most of the downlink transmissions involve one user at a time.
Constraint (1) simply bounds each TP’s throughput to be at least the minimum
throughput $R^{\text{MIN}}$.
Finally, constraint (1) limits the deployment cost to the available planning
budget $B$, with $P_{c}^{\text{BS}}$ indicating the cost of installing a BS in
CS $c\in\mathcal{C}$.

##  IV Modelling Reconfigurable Intelligent Surfaces

Figure 1: Example of SRC with RIS orientation and lines of sight angles.

In our modelling efforts, RISs behave as passive beamformers, focusing the
impinging radio waves in specific directions and creating what is often
identified as a Smart Radio Environment. In this way, a proper configuration
of the RIS can actively assist the communication between a transmitter-
receiver pair by increasing the Signal to Noise Ratio (SNR) at the receiver
[7]. Following the same rationale, we introduce the novel concept of Smart
Radio Connection (SRC): a triplet that comprises one transmitter (i.e. the
BS), one receiver (i.e. the UE located in a specific TP) and a smart surface
configured to assist this specific communication222While it is possible for
multiple RIS to be configured to assist a single TX-RX pair [11], in this work
we focus on up to one surface per SRC.. Any SRC is then modeled as a tuple
$<t,d,r>$, where $t\in\mathcal{T}$ denotes the TP, $d\in\mathcal{C}$ denotes
the BS installation site and $r\in\mathcal{C}$ denotes the RIS installation
site, as the example pictured in Figure 1 shows.
The problem of jointly optimizing the transmitter pre-coding and the RIS
elements’ phase shifts in a SRC is generally not convex [11]. However, the
inherent characteristics of a mm-Wave channel allow for significant
simplifications and an optimal closed form expression of the average received
power can be derived. In this work, we consider the average SRC channel gain
expression developed in [12] for mm-Wave communication, which we propose here
in a compact form:

$\gamma=f(\mathbf{h}_{B,R},\mathbf{h}_{R,P})+f^{\prime}(\mathbf{h}_{B,R},\mathbf{h}_{R,P},\mathbf{h}_{B,P})+f^{\prime\prime}(\mathbf{h}_{B,P}),$
(2)

where $\mathbf{h}_{B,R}$ is the channel between the BS and the RIS,
$\mathbf{h}_{R,P}$ is the channel between the RIS and the TP,
$\mathbf{h}_{B,P}$ is the channel between the BS and the TP and
$f,f^{\prime},f^{\prime\prime}$ are proper functions.
The contribution of the RIS to the SRC channel gain is linearly separable from
the contribution of the traditional direct link, meaning that the increment in
SRC link capacity with respect to unassisted communication is directly
dependent only on the terms
$f(\mathbf{h}_{B,R},\mathbf{h}_{R,P})+f^{\prime}(\mathbf{h}_{B,R},\mathbf{h}_{R,P},\mathbf{h}_{B,P})$.
It follows that, by knowing the relative positions of the three components of
a SRC, as well as the state probability of each channel, the performance of
any SRC can be completely characterized. Indeed, we define
$R_{t,d,r}^{\text{SRC}}$ as the expected (blockage-weighted) throughput when
BS in $d\in\mathcal{C}$ transmits to TP $t\in\mathcal{T}$, while being
assisted by RIS in $r\in\mathcal{C}$.
In general, a RIS can be part of many SRCs, and we assume an instantaneous
reconfiguration of the reflecting elements when the surface switches between
different SRCs. However, we allow each surface to assist up to 1 TX-RX pair at
a time, meaning that the RIS sharing takes the form of a time-sharing process.
We are fully aware that the previous assumptions may represent some though
technological challenges for RIS hardware manufacturers. However, we believe
them to be consistent with a realistic technological maturity level that needs
to be considered from the beginning if we want to investigate the potential
benefits of RIS development. For instance, a similar evolution occurred in
literature to beamforming reconfiguration assumptions.
Similarly to what happens for uniform linear antenna arrays, RISs are expected
to present a limited array field of view [9]. We consider this by defining a
RIS orientation, coinciding with the vector normal to the surface. For a given
orientation, the lines of sight of the base stations/test points of all SRCs
which the RIS is assigned to have to fall inside the surface field of view. In
this work, we define a horizontal field of view angle $D$ and we discard the
vertical field of view333It usually has a limited impact on the network
layout, however, if needed, a vertical field of view can be easily included in
the model.
Finally, our proposed model maintains generality by not forcing any BS-TP pair
to be RIS-assisted. However, including both SRCs and traditional direct-link
radio connections in a planning model was found to require a cumbersome number
of additional variables and constraints. We worked around this issue by
including an additional candidate site $\tilde{c}$ where a fake RIS is always
installed. This particular RIS has no cost, no time-sharing limitation and
360° field of view, but grants no additional throughput performance to any
assisted BS-TP pair. After an optimal solution is found, a post-processing
operation changes any SRC including the fake RIS into a traditional unassisted
BS-TP communication. This way, we could maintain a leaner formulation by
modelling SRCs only, while avoiding any loss of generality.
According to the previously described modeling choices, the following
variables were needed to extend the mm-Wave coverage planning model presented
in sec. III:

  * •

$y_{c}^{\text{RIS}}\in\\{0,1\\}$: RIS installation variable, equal to 1 if a
RIS is installed in site $c\in\mathcal{C}$ and 0 otherwise,

  * •

$s_{t,d,r}\in\\{0,1\\}:$ SRC activation variable, equal to 1 if RIS in
$r\in\mathcal{C}$ is assigned to assist the communication between BS in
$d\in\mathcal{C}$ and TP $t\in\mathcal{T}$,

  * •

$\tau_{t,d,r}^{\text{SRC}}\in[0,1]:$ SRC time sharing variable, indicating the
fraction of time during which BS in $d\in\mathcal{C}$ transmits to TP
$t\in\mathcal{T}$ aided by a RIS installed in $r\in\mathcal{C}$,

  * •

$\phi_{r}\in[0,2\pi]:$ azimuth of RIS installed in CS $r\in\mathcal{C}$
computed with respect to a reference direction.

We are now ready to introduce the coverage planning model extended to include
Reconfigurable Intelligent Surfaces: [3] ∑_t ∈T, d ∈C, r ∈C
R_t,d,r^SRC⋅τ^SRC_t,d,r y_c^BS+y_c^RIS≤1∀c ∈C y_~c^RIS≥1 ∑_d ∈C, r
∈Cs_t,d,r≤1∀t ∈T τ_t,d,r^SRC≤Λ_t,d,r⋅s_t,d,r∀t ∈T, d,r ∈C ∑_t ∈T, r
∈Cτ_t,d,r^SRC≤y_d^BS∀d ∈C ∑_t ∈T, d ∈Cτ_t,d,r^SRC≤y_r^RIS∀r ∈C∖{~r} ∑_d ∈C, r
∈CR_t,d,r^SRC⋅τ^SRC_t,d,r≥R^MIN∀t ∈T ϕ_r≥Φ^A_r,t - D/2 - 2π(¬s_t,d,r)∀t ∈T,
d,r ∈C: r ≠~c ϕ_r≤Φ^A_r,t + D/2 + 2π(¬s_t,d,r)∀t ∈T, d,r ∈C: r ≠~c ϕ_r≥Φ^B_r,d
- D/2 - 2π(¬s_t,d,r)∀t ∈T, d,r ∈C: r ≠~c ϕ_r≤Φ^B_r,d + D/2 + 2π(¬s_t,d,r)∀t
∈T, d,r ∈C: r ≠~c ∑_c ∈C∖{~c}(P_c^BS⋅y_c^BS \+ P_c^RIS⋅y_c^RIS)≤B Objective
function (2) is of the sum-throughput type. Constraint (IV) makes sure that a
BS and a RIS cannot be installed in the same candidate site, while (2) forces
the installation of the fake surface. Constraint (IV) allows for up to 1 SRC
to be active for each TP, meaning that each $t\in\mathcal{T}$ is covered by up
to 1 BS and up to 1 RIS. In (IV-2) the BS and RIS time sharing is enforced. In
particular, a strictly positive transmission duration is allowed only if the
SRC is active, if both BS and RIS are installed and if a radio connection
between the three network components can be established444Note that, while the
coverage parameter $\Lambda_{t,d}$ has been extended to also include a third
index representing the RIS CS, its rationale remains unchanged.. Constraints
(IV-IV) force the RIS azimuth to be such that the lines of sight of any
associated BS and TP all fall inside its field of view. Parameters
$\Phi_{r,t}^{\text{A}}$ and $\Phi_{r,d}^{\text{B}}$ indicate the angle between
a reference vector originating from RIS $r\in\mathcal{C}$ and the connected TP
$t\in\mathcal{T}$ and BS $d\in\mathcal{C}$ lines of sight, respectively. The
reader can find an illustration in Figure 1. Note that $\neg
s_{t,d,r}=(1-s_{t,d,r})$. Finally, we have introduced a RIS cost parameter
$P_{c}^{\text{RIS}}$ in the budget constraint (2).

##  V Results

In this section, we numerically analyze the previously described models when
applied to different instances. Such instances are characterized by parameters
that vary according to the specific result or property intended to be
highlighted. However, some assumptions will be valid throughout the entire
section unless otherwise stated.
We consider scenarios where the BS employs several uniform linear antenna
arrays, such that the BS field of view is 360°. We assume 64 antennas per
array and a transmit power of $30dBm$. The receiver’s antenna is assumed to be
omnidirectional, and RX sensitivity is set to $-78dBm$.
Given that the size of the reflecting surface is directly related to the
system performance [22], we show results for both $10^{4}$ and $10^{5}$
reflecting elements in each RIS. These are compatible with surface sizes of
about $50\text{x}50cm$ (i.e. small RIS) and $150\text{x}150cm$ (i.e. large
RIS), respectively, since the reflecting elements need around $\lambda/2$
spacing [23]. Additionally, RIS field of view is set to 120°.
Carrier frequency is set to $28GHz$ and both propagation and blockage models
are taken from [21]. According to this model, the expected throughput
decreases with the link-length, as longer links incur in higher blockage
probabilities.
The received power of SRCs has been computed with the formula derived in [12]
and summarized by Eq. 2. Traditional direct communication received powers have
been computed using the same formula, but discarding the RIS contributions,
without loss of generality.
Maximum achievable bit-rates are computed according to realistic modulation
and coding schemes, like those specified by IEEE 802.11ad standard [24].
In each instance, 52 CSs and 32 TPs are randomly but uniformly scattered on a
$400\text{x}300m$ area.
The default planning budget is set to $10.6$. BS cost is set to 1, while large
and small RIS costs are set to $0.1$ and $0.05$, respectively.
For any given set of parameters, numeric results have been computed by
averaging on 30 random instances of TP and CS positions.
We have used MATLAB to generate each instance and CPLEX to find an optimal
solution.

Figure 2: Mean TP throughput varying $R^{\text{MIN}}$

The first result we intend to analyze is the performance in terms of expected
throughput experienced at the test points for different values of
$R^{\text{MIN}}$.
Figure 2 shows this value averaged over all TPs, for $R^{\text{MIN}}$ spanning
from $0Mbps$ to $800Mbps$, with $100Mbps$ increments.
We note how, independently on the RIS size, the basic planning model is
outperformed by the model that includes intelligent surfaces for any value of
$R^{\text{MIN}}$.
Additionally, larger surfaces perform better than their smaller versions, and
the performance difference between the 3 cases grows with the minimum
guaranteed throughput. This suggests that the well studied link-level benefits
of employing RIS in mm-Wave communication scale well also at system-level.
Finally, the model without RIS becomes unfeasible when
$R^{\text{MIN}}>600Mbps$, while optimal solutions can still be found for both
RIS sizes. This shows how re-configurable surfaces allow mm-Wave radio access
networks to go beyond the coverage capabilities of traditional networks when a
larger minimum guaranteed throughput is required.

(a) Mean TP throughput

(b) Active sites

Figure 3: Budget variations, from $5$ to $35$ units with $4$ units increments.
Figure 4: Average TP-CS distances when varying budget.

We have shown how intelligent surfaces effectively augment the coverage while
also increasing the TP experienced throughput. In the following results, we
further expand the analysis of the latter in order to establish the efficacy
of RISs in boosting the raw network performance.
We set $R^{\text{MIN}}=100Mbps$ and let $B$ span from around $6$ units to
around $36$ units with increments of $4$ units. Note that $B=36$ is equivalent
to an infinite budget since it allows the installation of the maximum number
of BSs and RISs given the other parameters.
Figure 3a shows the impact of the available budget on the experienced TP
throughput, while in Figure 3b we have plotted the variations in the number of
active sites where either BSs or RISs are installed.
Interestingly, the number of active sites where RISs are installed - dotted
and dashed blue curves in Figure 3b \- decreases as the budget increases from
$4$ until around $16$ units, independently on the RIS size. For the same
values of $B$, the number of installed base stations increases.
Optimal solutions for lower budgets seem to favour a relatively larger number
of RIS installations, which is reduced when BSs substitute RISs as more budget
becomes available. However, while still being able to provide adequate
coverage levels, the larger count of RISs has little impact on performance
boosting for such low values of $B$, as Figure 3a testifies.
Indeed, this figure shows that a budget of 20 units or more is needed in order
to experience a more substantial raw performance boost, which also coincides
with an increased installed RISs count. The suggestion is that the sites where
to install intelligent surfaces are chosen to increase coverage for lower
values of $B$, while, as the budget increases, additional RISs are installed
to increase the throughput.
We confirm this by showing the average TP-RIS distances - dashed and dotted
blue curves - against the budget variations in Figure 4. Here is indeed
evident how these distances decrease at first, as the budget increases,
testifying that RISs are installed closer and closer to TPs in order to
decrease the probability of blockage and thus guarantee a better coverage.
However, when $B\geq 32$ units, the average distances abruptly increase
together with the average RIS installation count. Note indeed that only up to
$32$ BSs can be installed (i.e. one per TP), leaving the remaining budget to
be spent entirely on RIS installations.
This behaviour indirectly shows how RISs are most effective in boosting the
radio access network performance when a portion of the planning budget can be
dedicated to their installation or, in other words, when the BSs have been
already installed. This is arguably an exciting result, as it suggests that
intelligent surfaces might be quite effective in boosting the performance of
mm-Wave access networks that have been already deployed.

We conclude this section by providing additional comments on Figure 4.
Consider the solid black line and both the dashed and dotted red lines. These
represent the average optimal TP-BS distance for the model without RISs (solid
black), the average optimal TP-BS distance in SRCs with small RIS size (dashed
red) and the same quantity for larger RIS size (dotted red).
In general, we can expect SRCs to be more robust against blockages because
multiple lines of sight need to be interrupted at the same time for the
connection to fail.
This concept becomes evident when comparing the 3 curves above, as they show
how base stations belonging to SRCs can be placed further away from the test
points without reducing the blockage-weighted throughput as opposed to BS-TP
distances found by solving the base model. Additionally, SRCs allow for a more
efficient BS resource sharing, since on average more TPs are in the coverage
range of each BS.
As mentioned in Section IV, the RIS-aware model still allows for any TP to be
covered by a traditional connection if such a choice is optimal. In this
regard, the dashed and dotted black curves in Figure 4 show how those TPs
which are covered through a traditional connection are, on average, remarkably
closer to the assigned BS with respect to the test points involved in SRCs.
This confirms that optimal TP-RIS assignments are chosen such that TPs which
are further away from base stations are prioritized, while also suggesting
that a heuristic approach based on such policy might yield satisfying results.

##  VI Conclusion

To study the effect of RISs on large-scale mm-Wave access networks, we have
developed a new mathematical formulation for the coverage planning problem
that includes reconfigurable surfaces. In our models, RIS can be installed in
given candidate sites of a geographic area to assist the communication between
base stations and test points, effectively creating what we call a Smart Radio
Connection. We have also formulated a baseline model where the coverage
planning does not consider the presence of RISs. Our simulation campaigns show
how RISs can effectively increase both performance and throughput of access
networks. Numerical results also highlight the impact of the planning budget
on the KPIs above. In particular, we have shown how RISs can offer better
coverage even for relatively low budget values, while increasingly noticeable
throughput gains are obtained for larger values. Finally, our analysis on the
optimal distances between base stations, RISs and test points have shown which
RIS positioning policies are the most effective. The study of different
planning objectives, more complex deployment scenarios and more refined
channel models might be subject of future works.

## Acknowledgment

The research in this paper has been carried out in the framework of Huawei-
Politecnico di Milano Joint Research Lab. The Authors acknowledge Huawei Milan
research center for the collaboration.

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