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Reconfigurable Intelligent Surface Configuration
and Deployment in Three-dimensional Scenarios
Bilian Xu, Ting Zhou, Tianheng Xu, and Yuzhen Wang
Shanghai Advanced Research Institute, Chinese Academy of Sciences, China
Email: xubilian2019@sari.ac.cn, zhouting@sari.ac.cn, xuth@sari.ac.cn, wangyuzhen2018@sari.ac.cn
Abstract—The Reconfigurable Intelligent Surface (RIS)
is seen as one of the most prospective technologies for
next-generation networks. RIS can form virtual line-of-sight
(LoS) link during non-line-of-sight (NLoS) transmission to
improve system performance with low power consump-
tion, especially for urban scenarios. In this paper, for an
RIS-aided system, we extend the two-dimensional path-
loss model to a more practical three-dimensional path-
loss model. We further compare the system performance
differences among RIS, relay and single-input single-output
(SISO) systems. We also reveal proper deployment positions
of RIS and derive the number of reflecting elements re-
quired under different constraints. Numerical results verify
the complementarity between RIS and decode-and-forward
(DF) relay. The performance of RIS-aided communication
system can be significantly improved by optimizing RIS
deployment locations and the number of reflecting elements.
Index Terms—Reconfigurable intelligent surface, Three-
dimensional deployment, Numerical configuration
I. INT ROD UC TI ON
The fifth-generation (5G) wireless networks have been
globally promoted commercial deployment [1][2]. Nowa-
days extensive researches have already started on the
sixth-generation (6G) wireless technologies to support
higher requirements, such as energy consumption and
throughput [3]. To keep up with an exponential traffic
growth rate and simultaneously provide ubiquitous con-
nectivity, Reconfigurable Intelligent Surface (RIS) can
become one of the revolutionary candidate technologies
for 6G [4][5]. RIS-aided communication systems can
spontaneously adjust the propagation environment instead
of adapting to the environment. RIS can intelligently
reflect the signal to the target user without amplifying the
signal, so it can improve the signal transmission quality
with low energy consumption.
Currently, optimization problem and analysis problem
are hot RIS research topics. Optimization problems are
mainly to find joint beamforming or phase optimiza-
tion algorithms with lower complexity [6]-[10]. Analysis
problems include performance analysis for the RIS, as
well as comparison between RIS and relays. Ref. [11]
studied the key differences and similarities between RIS
and conventional relays with the plane distance/pathloss
model. In [12], a classic two-dimensional single-input
single-output (SISO) system model was provided and the
number of reflecting elements was discussed. Abdullah et
al. in [13] put forward an average performance analysis
in a hybrid RIS and relay network, which included dif-
ferent hybrid schemes. Nevertheless, the two-dimensional
scenarios in these studies ignore the actual height of
base station, user and RIS. And these researchers seldom
pay attention to the numerical verification between RIS
deployment location and performance gain. Therefore, the
RIS deployment analysis has become an urgent need in
order to more practically guide its applications.
Motivated by the above circumstances, this paper
extends the two-dimensional path-loss model to three-
dimensional urban scenarios. Compared with [12], the
proposed path-loss model can be better applied to practi-
cal scenarios and future mobile communication systems.
Based on the three-dimensional path-loss model, this
paper analyzes the relationship between lateral movement
distance and transmission rate in three systems, i.e.,
decode-and-forward (DF) relay, RIS, and SISO system.
Then we also verify the complementary relationship of
DF relay and RIS at different deployment heights and
plane distances. Our main contributions in this paper are
summarized as follows.
•We extend the traditional two-dimensional path-loss
model to three-dimensional path-loss model. We
design a three-dimensional outdoor urban scenario,
where the path-loss model is more practical for
communication networks.
•We derive the optimal number of reflecting elements
for an RIS system under fixed transmission rate
constraint. It is a closed-form expression which
corresponds to the minimum transmission power.
•We derive the lower bound on the number of re-
flecting elements under fixed transmission power
constraint. This deduction is obtained by comparing
the transmission rates of RIS system with DF relay
system.
•Numerical results provide profound insights into
RIS deployment locations, quantity configurations of
reflecting elements, and relay/RIS performance for
future wireless networks.
The rest of the paper is organized as follows. The
system model is introduced in Section II. Section III ex-
pounds three-dimensional path-loss model in the outdoor
urban scenario, then we derive the number of reflecting
elements under different conditions. In Section IV, numer-
978-1-7281-9441-7/21/$31.00 ©2021 IEEE
2021 IEEE International Conference on Communications Workshops (ICC Workshops) | 978-1-7281-9441-7/20/$31.00 ©2021 IEEE | DOI: 10.1109/ICCWorkshops50388.2021.9473592
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Fig. 1. System model.
ical results and the corresponding performance analysis
are exhibited. Finally, we conclude our work in Section
V.
II. SY ST EM M OD EL
As shown in Fig. 1, we consider a SISO system. There
are three deterministic channels in an RIS-aided wireless
communication system with Nreflecting elements, their
channel coefficients represented as hsd ∈C,hsr ∈CN×1,
hrd ∈CN×1.hsd means the channel between base station
and user. The traditional SISO communication system
only contains a direct link, in which the received signal
is expressed as
ySISO =hsd√ps +n, (1)
where prepresents the transmission power, and srep-
resents the signal with unit power information. n∼
NC(0, σ2)means Gaussian white noise.
RIS-aided wireless communication system includes di-
rect links and indirect links. The indirect link assisted by
RIS includes channel hsr between base station and RIS,
channel hrd between RIS and user. On this basis, the
received signal is expressed as
yRIS =hsd +hT
srΘhrd √ps+n,(2)
where hT
srΘhrd =PN
n=1 αnejθn[hsr ]n[hrd]n.
Θ= diag α1ejθ1, . . . , αNejθNdenotes diagonal matrix,
which completely expresses the property of phase
transformation. αn∈[0,1],n= 1, . . . , N .αnrepresents
the fixed amplitude change coefficient caused by n-th
phase shift. We assume that each reflecting element of
RIS scatters the transmission signal to target user with
an approximately constant gain. The subsequent analysis
focuses on communication performance differences
caused by the deployment of RIS. Hence, we assume
αn= 1.θn∈[0,2π],n= 1, . . . , N .θnrepresents the
phase optimized for the phase shift of n-th reflecting
element. When θn= arg (hsd )−arg ([hsr]n[hrd ]n), the
system has the achievable rate.
According to the expression of received signal, the
achievable transmission rate of SISO system is
RSISO =Blog21 + pβsd
σ2.(3)
Then the achievable transmission rate of RIS-aided com-
munication system is expressed as
RRIS =Blog2 1 + p√βsd +Nα√βsrβrd 2
σ2!.(4)
where βsd,βsr and βrd are the channel gains. For brevity,
the notations mean √βsd =|hsd|2,√βsr =|hsr |2,
√βrd =|hrd|2. The channel bandwidth is expressed as
B.σ2means the noise power.
The transmission process of DF relay is divided into
two equal-sized stages, i.e., the source transmits the
signal with the transmission power p1, and the relay
decodes the forwarded signal with the transmission power
p2. The DF relaying system capacity can be expressed
as RDF =1
2Blog21 + min p1βsr
σ2,p1βsd
σ2+p2βrd
σ2.
Suppose p1, p2>0, p =p1+p2
2, when βsd > βsr, RD F <
RSISO is not the main point of our analysis. When
βsd ≤βsr, RD F ≥RRIS may be realized after adjusting
p1, p2. Equations p1βsr
σ2=p1βsd
σ2+p2βrd
σ2and p=p1+p2
2
are combined, the solution is p1=2pβrd
βsr+βr d−βsd , p2=
2p(βsr−βsd )
βsr+βr d−βsd , and then the achievable transmission rate of
DF relay communication system is denoted by [14]-[16]
RDF =1
2Blog21 + 2pβsrβrd
(βsr +βrd −βsd)σ2,(5)
It is worth noting that the transmission power pis equal
in (3)-(5). This setting is convenient to compare the
performance of three communication systems.
Then the total transmission power of SISO system is
expressed as
PSISO =(2R0/B−1)σ2
βsd
ν+Ps+Pd.(6)
The total transmission power of RIS system is denoted
by [17]
PRIS =2R0/B −1σ2
(√βrd+N α√βsrβrd )2
ν+Ps+Pd+NPe,
(7)
where Ps,Pd,Perepresent the power loss of base station,
user and single reflecting element. The fixed value of
transmission rate is R0.ν∈[0,1], and νsignifies the
efficiency of power amplifier. Then EE(R) = B∗R/P
expresses the energy consumption efficiency [17].
III. PROPOSED METHOD
In this section, we recalculate the path-loss in the three-
dimensional simulation scenario so as to more precisely
analyze the deployment of RIS. Then we analyze the
number of reflecting elements required under different
conditions.
A. Three-Dimensional Path-Loss Model
The original two-dimensional scenarios only consider
the plane distance among base station, user and RIS. The
signal transmission distance depends on its height, which
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Fig. 2. Distance definition of three-dimensional outdoor urban
scenario.
further affects the corresponding path-loss. Therefore, it
is necessary to develop a more accurate three-dimensional
path-loss model.
The 3rd Generation Partner Project (3GPP) defines
a three-dimensional path-loss model for urban outdoor
scenario, i.e., 3GPP UMi Canyon. The analysis in this
paper is based on on this model, which only considers
traditional cellular scenarios. Specailly, base station, user
and RIS/DF relay are located outdoors. For various trans-
mission links in the simulation scenario, the large-scale
fading models are different, i.e., line-of-sight (LoS) and
non-line-of-sight (NLoS) model [18][19].
Fig. 2 shows the distance definition of three-
dimensional outdoor urban scenario. We assume that
d(2D)
sd ,d(2D)
sr and d(2D)
rd represent plane distance. Then
we consider the connection between BS and user as
baseline. The RIS moves parallelly along the baseline.
The distance RIS has moved in the baseline direction is
denoted as d. The vertical distance between RIS deploy-
ment location and the baseline is represented as r, i.e.,
√r2+d2=d(2D)
sd . Then d(3D)
sd ,d(3D)
sr and d(3D)
rd mean
the actual distances in the three-dimensional space.
The symbols hs,hdand hrare used to represent
the antenna heights of base station, user and RIS. The
3GPP UMi Canyon requires that the height range of
user terminal should be limited to hUT ∈(1.5,22.5)m.
In addition, the base station height is also specified
as hs= 10m [18]. In order to facilitate following
calculations, we assume hr= 1.5m [12, 18]. Three
communication links contained in the above scenario are
described subsequently.
Firstly, the actual distance of the LoS link between base
station and RIS transceiver antenna is
d(3D)
sr =q(hs−hr)2+√d2+r22.(8)
When 10m ≤d(2D)
sr ≤d0
sr ≤5000m,and d0
sr =
4(hs−1)(hr−1)fc
C= 36 (hr−1) fc/0.3. The corresponding
channel gain is expressed as
βsr = 32.4 + 21 ∗log10 d(3D)
sr + 20 ∗log10 (fc).(9)
We can get a suitable simulation parameter range through
calculation, i.e., carrier frequency fc= 3GHz, and hr∈
(1.5,14.8)m.
Secondly, the actual distance of the LoS link between
RIS and user is
d(3D)
rd =v
u
u
t(hr−hd)2+ rd(2D)
sd −d2+r2!2
.
(10)
When 10m ≤d(2D)
rd ≤d0
rd, and d0
rd = 2 (hr−1) fc/0.3,
the corresponding channel gain is denoted by
βrd = 32.4 + 21 log10 d(3D)
rd + 20 log10 (fc).(11)
Thirdly, the actual distance of NLoS link between base
station and user is
d(3D)
sd =q(hs−hd)2+ (d(2D)
sd )2.(12)
When 10m ≤d(2D)
sd ≤d0
sd, and d0
sd = 18fc/0.3, the
corresponding channel gain is expressed as
βsd = max P LUMi−NLoS, P L0
UMi−NLoS,(13)
P LUMi−NLoS = 32.4 + 21 log10 d(3D)
sd + 20 log10 (fc)
(14)
and
P L0
UMi−NLoS = 35.3 log10 d(3D)
sd +22.4+21.3 log10 (fc).
(15)
B. Optimal Number of Reflecting Elements
Based on the above three-dimensional path-loss model,
when the RIS plays an aided role independently, we
derive the optimal numerical configuration of reflecting
elements. It is subsequently derived by optimizing the
transmission power of the RIS. The second derivative of
(7) is
d2PRIS
dN2=(2R0/B−1)σ2
ν
6βsrβrd
(√βsd+N α√βsrβrd )4.(16)
The numerical result of (16) above is always greater than
zero, thus PRIS(N)is convex function.
Then the first derivative of (7) is
dPRIS
dN=(2R0/B−1)σ2
ν
(−2√βsrβrd )
(√βsd+N α√βsrβrd )3+Pe.(17)
We let dPRIS
dN= 0, the solution of Ncan be regarded
as the optimal number of reflecting elements required by
RIS at the minimum power. The optimal solution of N
obtained in this paper is
N(3D)
opt =3
r2
ν
3
s2R0/B −1σ2
Peβsrβrd −sβsd
βsrPrd
.(18)
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TABLE I: Simulation Parameters [12, 13, 18]
Parameters Values
Transmission power (P) 20 dBm
Transmission rate (R0) 6.5 bit/s/Hz
Carrier frequency (fc) 3 GHz
RIS deployment height (hr)2,6,8,10 m
Distance between BS and user (dsd) 100 m
Phase amplification coefficient (α) 1
Power amplification efficiency (ν) 0.5
Gaussian white noise power (σ2) 94 dBm
Bandwidth (B) 10 MHz
Base station height (hs) 10 m
User height (hd) 1.5 m
Vertical distance between RIS and BS (r) 10 m
Hardware power loss for BS (Ps) 5 dBm
Hardware power loss for user (Pd) 5 dBm
Hardware power loss for reflecting element (Pe) 0.8 dBm
C. Minimum Number of Reflecting Elements
We assume that RIS and DF relay work together in
the above three-dimensional scenario. In order to ensure
that the RIS effectively assists the communication system,
we derive a lower bound for the numerical configuration
of reflecting elements. It is derived by comparing their
achievable rates. Specifically, the value of Nrequired by
RIS is derived when the achievable rate of RIS system
is higher than DF relay system. When the indirect link
has more communication advantages, RRIS >RDF can
be calculated by (4) and (5),
N(3D)
min >sσ2
PRIS r1 + 2PDF βsr βrd
(βsr+βrd −βsd )σ2−1−√βsd
√βsrβrd
.
(19)
It is worth noting that the numerical result in the right
part of (19) may not be an integer, but the actual value
of Nshould be an integer. Therefore, in the subsequent
analysis, N(3D)
min is equal to the smallest integer greater
than the numerical result on the right.
IV. SIMULATION RESULTS AND PERFORMANCE
ANA LYSIS
In this section, the performance of RIS system is
revealed by numerical analysis. In addition, we compare
the transmission performance of DF relays, SISO and RIS
systems at different deployment heights. Specifically, the
following will compare the performance gain change for
different RIS deployment locations, optimal number of
reflecting elements, and minimum number of reflecting
elements. Related parameters are also shown in Table
I. Unless otherwise specified, all parameters are set to
the values in Table I by default, whereas the settings in
each figure take precedence wherever applicable. Then
numerical results are shown in Fig. 3-5.
Fig. 3 illustrates the relationship between transmission
rate and RIS lateral deployment distance d. We can
see that both DF relay system and RIS system have
higher transmission rates than SISO system during the
movement. Then, we observe the RIS/DF movement
from two aspects. First, we observe the results of plane
Fig. 3. The function relationship between achievable rate Rand
distance d.
(a) Optimal solution of N versus achievable rate.
(b) Energy efficiency versus achievable rate.
Fig. 4. The optimal number of reflecting elements N(3D)
opt and
energy efficiency EE with different achievable rate R.
movement. The communication advantage of DF relay
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gradually increases as it moves away from base station.
It has the best performance where the relay is located
at d= 50m. During the same movement, the RIS curve
has the opposite tendency. The BS-side and user-side RIS
in general outperforms other counterparts in terms of the
achievable rate. When d > 100m, the throughput of the
relay system and RIS system is reduced, but the relay
system is superior to the RIS system. Second, we observe
the results of the deployment height changes. When RIS
is located close to user, an RIS deployed at 2m has a
higher throughput than other optional heights. It should
be noted that 2m is closest to the user height hd= 1.5m.
Similarly, when the RIS is located near base station and
hr= 10m, the RIS has more communication advantages.
Based on phenomenons in Fig. 3 above, we know that
both RIS and relay systems can enhance the performance
of traditional SISO system. In a three-dimensional out-
door urban scenario, the linear distance changes in inverse
proportion to achievable rates. In terms of deployment
on a two-dimensional plane, RIS should be deployed on
the BS-side or the user-side. In terms of the deployment
height of the three-dimensional space, the deployment
height of RIS should match the deployment position in
the two-dimensional plane. Its height should be closer
to the counterpart of stronger link to maximize RIS
support. Furthermore, RIS signal applied to improve the
quality and reduce the power requirements in short-
distance communications. The DF relay is suitable for
extending the signal transmission distance. The RIS and
the DF relay complement each other to better improve
the signal transmission quality.
Fig. 4 describes the optimal number of reflecting ele-
ments/energy efficiency versus rate when the RIS system
is deployed at d= 90m. From Fig. 4(a), we can observe
that the RIS system is simplified to the SISO system
when N(3D)
opt = 0. As the deployment height increases, the
corresponding zero point in Fig. 4(a) moves gradually to
the right. The height difference between user-RIS and user
decreases, the energy efficiency of user-RIS increases.
In Fig. 4(b), the energy efficiency of the SISO system
fluctuates with the improvement of rate, under the optimal
numerical configuration of reflecting elements and given
transmission power. When R > 3.2bit/s/Hz, the energy
efficiency of the SISO system decreases rapidly. This
curve trend verifies that the rate of SISO system is
increasing at the expense of reducing energy efficiency.
However, the energy efficiency of the RIS system has
increased over a period of time, which proves the low
energy consumption advantage of RIS. After comparing
Fig. 4(a) and Fig. 4(b), RIS energy efficiency also begins
to be higher than SISO system when the optimal number
of reflecting elements is gradually greater than zero. The
reason is that the RIS aided link is insufficient to improve
system-level spectral efficiency in this case. When the
energy efficiency of the RIS is gradually greater than that
of the SISO system, N(3D)
opt >0, and the deployment of
Fig. 5. The function relationship between the minimal number of
reflecting elements N(3D)
min and distance d. The minimal number
of reflecting elements calculated by comparing DF relay rate
with RIS system.
RIS comes into effect.
Fig. 5 illustrates the function relationship between N
and dwith the defination of (19). The movement of
the RIS is divided into two processes. First, 10m 6
d6100m,the RIS gradually moves away from the
base station and approaches the user. When the RIS
is in the middle, the RIS has the highest demand for
reflecting elements to make up for the weak transmission
performance. Second, 100m 6d6120m, the RIS further
keeps away from base station and user. The transmission
rate gradually decrease again, and the Nrequired by the
system correspondingly increases over again. In the three-
dimensional scenarios, the numerical configuration of the
RIS reflecting elements is also one of the emphases to
more efficient applications. When the RIS works with the
DF relay to assist the communication system, the numer-
ical configuration also takes into account the minimum
value, which is derived by comparing their achievable
rates.
V. C ONCLUSIONS
This paper has investigated and analyzed the deploy-
ment of RIS under the three-dimensional scenario, and
has compared it with the relay and SISO systems. The
numerical results confirmed a more practical deployment
principle for RIS, in which both the plane position and
deployment height are considered. The plane deployment
of RIS should be on the BS-side or the user-side, and the
deployment height of the RIS should be close to the other
side of the shorter link. This paper also has derived the
numerical configuration of the reflecting elements, which
can provide meaningful theoretical guidance for the RIS
works alone or with the DF relay.
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ACK NOW LE DG EM EN T
This work was supported in part by the National
Key Research and Development Program of China
(2018YFB1802300), National Natural Science Founda-
tion of China (Nos. 61801461 and 61801460), and the
Shanghai Municipality of Science and Technology Com-
mission Project (Nos. 20JC1416500 and 18DZ2203900).
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