1 Optimizing the Placement and Beamforming of RIS in Cellular Networks A System-Level Modeling Perspective

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Optimizing the Placement and Beamforming of RIS in

Cellular Networks: A System-Level Modeling Perspective

Pavan Reddy M ., SaiDhiraj Amuru, and Kiran Kuchi

©This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer

be accessible.

Abstract—In this letter, we present in detail the system-

level modeling of reconﬁgurable intelligent surface (RIS)-assisted

cellular systems by considering a 3-dimensional channel model

between base station, RIS, and user. We prove that the optimal

placement of RIS to achieve wider coverage is exactly opposite

to the base station, under the constraint of single RIS in each

sector. We propose a novel beamforming design for RIS-assisted

cellular systems and derive the achievable sum rate in the

presence of ideal, discrete, and random phase shifters at RIS.

Through extensive system-level evaluations, we then show that the

proposed beamforming design achieves signiﬁcant improvements

as compared to the state-of-the-art algorithms.

Index Terms—Beamforming, phase shifters, reconﬁgurable

intelligent surfaces (RIS), and spectral efﬁciency.

I. INTRODUCTION

Reconﬁgurable intelligent surfaces (RIS) is considered a

promising technology for the next generation cellular com-

munications to improve the achievable network capacity and

cellular coverage [1], [2]. RIS consists of a large number of

passive antenna elements (or meta-surfaces) which can reﬂect

the incident ray toward the desired direction. By controlling

the impedance of the meta-surfaces through a passive elec-

tronic circuit, an additional phase shift is introduced into the

reﬂected signal, and thus, the signal is steered in the desired

direction [2]–[5]. This way, RIS helps in achieving improved

signal reception for the users and also providing coverage to

the users who are affected by the signal blockages.

In the existing literature, RIS has been extensively analyzed

and signiﬁcant improvements are demonstrated for single cell

scenario [6]–[8]. In [6], the authors propose a joint beamform-

ing algorithm to maximize the network capacity. In [7], [8],

the authors propose power efﬁcient and sum-rate maximizing

algorithms for RIS-assisted systems. In [9], the authors present

an initial access protocol for RIS aided cellular systems. How-

ever, these works do not consider the multi-cell analysis while

quantifying the achievable gains. Note that only in the multi-

cell analysis, the impact of the inter-cell interference from the

beamformed RIS is captured, and thus, realistically achievable

gains can be understood. Additionally, while performing such

multi-cell analysis, a 3-dimension channel modeling between

the base station (BS), RIS, and user has to be considered to

quantify the achievable gains. However, very few works in the

literature have considered the 3-dimension channel model and

carried out system-level evaluations [10]–[14].

Further, the beamforming at RIS has a signiﬁcant impact on

the achievable gains with RIS-assisted systems [15]. In [10],

Pavan Reddy M. is with WiSig Networks, Hyderabad, India. Kiran Kuchi

and SaiDhiraj Amuru are with the Department of Electrical Engineering,

Indian Institute of Technology Hyderabad, Telangana, India.

(e-mail: pavan@wisig.com, asaidhiraj@ee.iith.ac.in, kkuchi@ee.iith.ac.in).

the authors consider deploying multiple RIS and using random

phase shifters at each RIS. This is a low-complex way to

enhance the network performance but only a few users whose

channel coefﬁcients are aligned with those assigned phase

shifters will observe spectral enhancements. In [1], the authors

consider random phase shift allocation in each time slot and

assume that the users decode the pilot signals transmitted

at the beginning of each slot. Then, the users’ feedback the

channel quality reports to the BS, and the users with the best

instantaneous channel conditions will be scheduled for data

transmission within the rest of the slot. With this approach,

the effective channel observed by each user changes from slot

to slot and BS schedules the data transmissions according

to the channel quality reports to maximize the achievable

capacities. However, this procedure requires a large number

of active users to realize the desired gains, and also, the

feedback from the users within the same time slots is difﬁcult

to realize in practice. Hence, there is a need to consider all

the aforementioned details and design a practically feasible,

low-complex, and yet optimal way of beamforming at RIS.

Motivated by these facts, we present the following key

contributions in this letter.

•We prove that optimal RIS placement (under the con-

straint of single RIS in each sector) to achieve a wider

coverage is exactly opposite to the base station with

boresight of RIS facing the boresight of the base station.

•We propose a novel beamforming design for RIS-assisted

cellular systems and analyze the impact of the selection

of phase shifters on the proposed design. We derive the

achievable sum rates in the presence of ideal, discrete,

and random phase shifters.

•We present the system-level modeling of RIS-assisted cel-

lular systems by considering the 3-dimensional channel

modeling between the BS, RIS, and user. We perform

extensive system-level simulations and show that the

proposed beamforming design signiﬁcantly outperforms

the state-of-the-art algorithms.

II. SYSTEM MODEL

A. Scenario Description

We consider a cellular network with BS, RIS, and users as

shown in Fig. 1. We assume M,N, and Uas the number of

antenna elements at the BS, RIS, and user, respectively, and

formulate the equivalent channel hH

k∈CU×Mbetween the

BS and user kas follows.

k=HH

k+FH

kΘG,(4)

where, [·]Hrepresents Hermitian operation, and G∈CN×M,

F∈CU×N, and H∈CU×Mdenote the channel coefﬁcients

arXiv:2210.03948v2 [cs.IT] 2 May 2023

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1OptimizingthePlacementandBeamformingofRISinCellularNetworks:ASystem-LevelModelingPerspectivePavanReddyM.,SaiDhirajAmuru,andKiranKuchi©ThisworkhasbeensubmittedtotheIEEEforpossiblepublication.Copyrightmaybetransferredwithoutnotice,afterwhichthisversionmaynolongerbeaccessible.AbstractInthisletter,wep...

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