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—The tremendous popularity of internet of things (IoT) applications and wireless devices have prompted a massive increase of indoor wireless traffic. To further explore the potential of indoor IoT wireless networks, creating constructive interactions between indoor wireless transmissions and the built environments becomes necessary. The electromagnetic (EM) wave propagation indoors would be affected by the EM and physical properties of the building material, e.g., its relative permittivity and thickness. In this paper, we construct a new multipath channel model by characterising wall reflection (WR) for an indoor line-of-sight (LOS) single-user multiple-input multipleoutput (MIMO) system and derive its ergodic capacity in closedform. Based on the analytical results, we define the wireless friendliness of a building material based on the spatially averaged indoor capacity and propose a scheme for evaluating the wireless friendliness of building materials. Monte Carlo simulations validate our analytical results and manifest the significant impact of the relative permittivity and thickness of a building material on indoor capacity, indicating that the wireless friendliness of building materials should be considered in the planning and optimisation of indoor wireless networks. The outcomes of this paper would enable appropriate selection of wall materials during building design, thus enhancing the capacity of indoor LOS MIMO communications.
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IEEE INTERNET OF THINGS JOURNAL 1
How Friendly are Building Materials as Reflectors
to Indoor LOS MIMO Communications?
Yixin Zhang, Student Member, IEEE, Chen Chen, Student Member, IEEE, Songjiang Yang, Student Member,
IEEE, Jiliang Zhang, Senior Member, IEEE, Xiaoli Chu, Senior Member, IEEE, Jie Zhang, Senior Member, IEEE
Abstract—The tremendous popularity of internet of things
(IoT) applications and wireless devices have prompted a mas-
sive increase of indoor wireless traffic. To further explore the
potential of indoor IoT wireless networks, creating constructive
interactions between indoor wireless transmissions and the built
environments becomes necessary. The electromagnetic (EM) wave
propagation indoors would be affected by the EM and physical
properties of the building material, e.g., its relative permittivity
and thickness. In this paper, we construct a new multipath
channel model by characterising wall reflection (WR) for an
indoor line-of-sight (LOS) single-user multiple-input multiple-
output (MIMO) system and derive its ergodic capacity in closed-
form. Based on the analytical results, we define the wireless
friendliness of a building material based on the spatially averaged
indoor capacity and propose a scheme for evaluating the wireless
friendliness of building materials. Monte Carlo simulations val-
idate our analytical results and manifest the significant impact
of the relative permittivity and thickness of a building material
on indoor capacity, indicating that the wireless friendliness of
building materials should be considered in the planning and
optimisation of indoor wireless networks. The outcomes of this
paper would enable appropriate selection of wall materials during
building design, thus enhancing the capacity of indoor LOS
MIMO communications.
Index Terms—Building material, wireless friendliness, indoor
communications, EM wave, reflection, LOS, MIMO.
I. INTRODUCTION
Internet of things (IoT) connects numerous heterogeneous
devices, and provides infrastructures for smart buildings [1],
[2], smart grids [3], and smart cities [4]. With the roll-
out of 5G systems and the opening horizon of 6G systems,
cellular networks will provide economical, flexible and reliable
wireless connectivities for IoT devices, e.g., by leveraging
5G massive machine type communication (mMTC) [5] and
6G massive broad bandwidth machine type (mBBMT) [6]
technologies.
It is predicted that 80-96% of wireless data traffic will be
consumed indoors in the future [7]. As a result, indoor wireless
traffic required by IoT is growing at an unprecedented rate.
Notably, physical obstacles like walls would affect the indoor
propagation of electromagnetic (EM) waves. Therefore, indoor
Yixin Zhang, Chen Chen, Songjiang Yang, Jiliang Zhang, and Xiaoli Chu
are with the Department of Electronic and Electrical Engineering, University
of Sheffield, S10 2TN, UK. E-mail: jiliang.zhang@sheffield.ac.uk.
Jie Zhang is with the Department of Electronic and Electrical Engineering,
University of Sheffield, Sheffield, S10 2TN, UK, and also with Ranplan
Wireless Network Design Ltd., Cambridge, CB23 3UY, UK.
This work was supported in part by the European Union’s Horizon 2020
Research and Innovation Programme under Grant 766231 and Grant 752644.
wireless performance should be one of the indispensable
prerequisites when designing buildings [8], [9].
To meet the high data demand and address the capac-
ity crunch in-building, indoor small base stations (BSs) are
usually equipped with large-scale antenna arrays [10], e.g.
consisting of hundreds of antennas, facilitated by multiple-
input multiple-output (MIMO) technology to achieve spatial
multiplexing/diversity gains [11]–[13]. In order to guarantee
a low spatial correlation, the space intervals among antenna
elements of the MIMO antenna array have to be larger
than half wavelength [14], which therefore will increase the
physical dimension of the indoor small BSs and generate
negative weight and visual consequence on a room. Especially
in industrial environment, deploying BSs in the workspace
may increase the risk of accidents.
To avoid any possible negative impact on the functionality
and appearance of a room, a desirable indoor BS deployment
is to integrate MIMO antenna arrays with interior walls [15],
[16], which however will result in non-negligible coupling
between MIMO antenna arrays and building materials [17]–
[19]. Specifically, when an EM wave impinges on a wall
surface, the intensity of the wall reflected wave can be mea-
sured by the reflection coefficient, which depends on the EM
and physical properties of the wall material, i.e., its relative
permittivity and thickness [20]–[25]. The wall reflected EM
waves would be superposed with other EM waves, which
may jointly influence the indoor wireless performance. Hence,
enhancing indoor wireless performance requires a rational
selection and/or design of building materials. In this paper, we
define the wireless friendliness as a new performance metric
of a building material, which is characterised by its relative
permittivity and thickness. A building material with desirable
wireless friendliness would be beneficial to the performance
of indoor wireless networks.
Metamaterials are known as novel artificial structures, which
can be customized to build a programmable EM propaga-
tion environment [26]. The meta-atoms in metamaterials are
software-controlled to firstly capture the signals from the
source and then reflect the signal to the destination actively
or passively [27], [28]. Although metamaterials are expected
to contribute to indoor capacity improvement, they are facing
major challenges such as their design complexity growing
exponentially with the number of meta-atoms. Besides, the
energy efficiency of metamaterial-aided wireless networking
is no better than massive MIMO [29] and relay-supported
transmissions [30].
By contrast, the wireless friendliness of concrete as a widely
IEEE INTERNET OF THINGS JOURNAL 2
BS
UE
1
d
LOS
H
WR
H
wall
z
2
d
2
Τ
q
Antenna
Linear array
1
D
ε
1
R
q
2
R
q
q
D
q
D
BS
UE
1
d
LOS
H
WR
H
wall
z
2
d
2
Τ
q
Antenna
Linear array
1
D
ε
1
R
q
2
R
q
q
D
q
D
Fig. 1. The LOS path and the WR path between indoor BS and UE.
used building material has not been sufficiently studied. Most
of the existing works on the EM wave propagation loss through
concrete walls were based on measurements [31]–[33]. As far
as we know, a theoretical analysis of indoor multipath capacity
influenced by the EM and physical properties of concrete is
still missing. As will be shown in the subsequent sections, the
appropriate selection of building materials will increase the
baseline value of indoor capacity. Accordingly, the wireless
performance of building materials should be considered inher-
ently in the design of future smart/green buildings. Hence, it is
of vital importance to build an evaluation scheme to identify
the relationship between the wireless friendliness of a building
material and its EM and physical properties [34].
In this paper, we study the impact of building materials,
especially their relative permittivity and thickness, on the
performance of indoor line-of-sight (LOS) MIMO communi-
cations. To the best of our knowledge, this is the first attempt to
study the indoor capacity from the perspective of wall material
design. The main contributions of this paper are summarized
as follows:
Taking the wall reflection (WR) path into account and
based on distance-dependant Rician fading model, a new
indoor LOS MIMO channel model is proposed.
The marginal probability distribution function (MPDF) of
an unordered squared singular value, the ergodic capacity
of the indoor LOS MIMO channel, and the squared
singular values of its deterministic part are analytically
obtained in closed forms. These analytical expressions
reveal the relationship between the indoor MIMO channel
capacity and the relative permittivity and thickness of the
building material.
We propose a scheme based on spatially averaged indoor
capacity, which can be used to evaluate the wireless
friendliness of building materials and to guide the design
of a wireless-friendly building.
The wireless friendliness performance of building mate-
rials is analysed. The optimal values of the permittivity
and thickness of building materials that maximise the
spatially averaged indoor capacity are obtained for both
the omnidirectional and directional BS antenna arrays.
The analytical results are verified through Monte Carlo
simulations.
The remainder of this paper is organized as follows. Section
II introduces system model for indoor LOS MIMO downlink
transmissions. In Section III, the analytical MPDF of an
unordered squared singular value, the ergodic capacity of an
indoor LOS MIMO channel, and the squared singular values
of its deterministic part are derived in closed forms. Then
a scheme used for evaluating the wireless friendliness of a
building material is proposed in Section IV. The impact of
directional radiation pattern is discussed in Section V. Monte
Carlo simulation results are provided to verify all analytical
results in Section VI. Finally, Section VII concludes this paper.
II. SY ST EM MO DE L
In this section, we introduce a novel system model for
indoor LOS MIMO communications that incorporates the WR
path and the EM and physical properties of the building
material.
We consider indoor LOS MIMO downlink transmissions, as
shown in Fig. 1. In the considered room, one BS is deployed
close to one of the walls and one user equipment (UE) could be
arbitrarily positioned. Since the strength of a WR path from
a wall other than the wall that is closest to the BS will be
dominated by the distance-dependent path loss, the reflected
paths from the other walls would be much weaker than the WR
path from the wall closest to the BS. Hence, the considered
wall refers to the wall closest to the BS hereafter, and the WR
path refers to the wall reflected path from the considered wall.
The BS is deployed in parallel with the considered wall with
a small distance of D1from the wall. The BS and a typical
UE are equipped with NTand NRomnidirectional antennas,
respectively, both in linear arrays with inter-antenna spacing
D. The complex frequency-flat linear channel from the BS to
the typical UE is constructed as
y=Hx +n,(1)
where xCNT×1,yCNR×1denote the transmitted signal
and the received signal, respectively, ndenotes the additive
white Gaussian noise, and His a NR×NTchannel matrix,
[HLOS]nR,nT=µ
4πd1
exp j2πd1
µj2πD
µnRNR1
2cos (θR1+ ∆θ)+nTNT1
2cos θT1 (2)
[HWR]nR,nT=µΓ
4πd2
exp j2πd2
µj2πD
µnRNR1
2cos (θR2+ ∆θ)+nTNT1
2cos θT2 (3)
IEEE INTERNET OF THINGS JOURNAL 3
subject to E[Tr{HH}] = NRNT, where E(·)and Tr{·}
denote the expectation and the trace of a matrix, respectively.
Other than the LOS path, the WR path is taken into account
to capture the impact of building materials on the indoor wire-
less propagation channel. For a certain position in the room,
the LOS path and the WR path are deterministically modelled
by Friis’ formula as NR×NTmatrix HLOS and HWR,
respectively, whose elements are given in (2) and (3) on the
previous page, respectively, in which nT∈ {0,1, ..., NT1}
and nR∈ {0,1, ..., NR1}are the indices of transmit and
receive antenna elements, µdenotes the wavelength of EM
waves in the air, d1and d2denote the length of the LOS
path and the WR path, respectively, θT1and θT2denote the
approximated angle of departure (AoD) of the LOS path and
the WR path at the BS array, respectively, while θR1and
θR2denote the approximated angle of arrival (AoA) of the
LOS path and the WR path at the UE array, respectively, θ
denotes the arbitrary orientation angle of the UE array, where
θT1, θT2, θR1, θR2,θ∈ {0, π},(θR1+ ∆θ)and (θR2+ ∆θ)
denote equivalent AoA of the LOS path and the WR path
at the UE array, respectively, and Γrepresents the equivalent
reflection coefficient of the WR path.
Along the WR path, multiple internal reflections are consid-
ered when the EM wave interacts with the building material.
Using plane wave far-field approximation, the incident angles
of different order reflections are all approximated by α. When
the building material is assumed to be a homogenous dielectric
reflector with relative permittivity εand thickness ζ, the
equivalent reflection coefficient of the WR path is represented
as [20]
Γ = 1exp(j2δ)
1Γ02exp(j2δ)Γ0,(4)
where
δ=2πζ
µpεsin2α, (5)
and the first-order reflection coefficient Γ0represents the
transverse electric (TE) polarisation ΓTE or the transverse
magnetic (TM) polarisation ΓTM of the incident electric field,
respectively, which are given by:
ΓTE =cos αpεsin2α
cos α+pεsin2α,(6)
or
ΓTM =cos αq(εsin2α)2
cos α+q(εsin2α)2
.(7)
For simplicity, HLOS and HWR are merged as one matrix
H1, which can be decomposed as
H1=A1hH
β1hα1+A2hH
β2hα2,(8)
A1=µNTNR
4πd1
e
j2πd1
µ,
A2=µΓNTNR
4πd2
e
j2πd2
µ,
αl= 2πD cos θTl/µ,
βl= 2πD cos (θRl+ ∆θ)/µ,
hαl=
e
jNT
1
2αl
NT
,e
j1NT
1
2αl
NT
, ..., e
jNT
1
2αl
NT
,
hβl=
ejNR1
2βl
NR
,ej1NR1
2βl
NR
, ..., ejNR1
2βl
NR
,
where l∈ {1,2}.
Based on distance-dependant Rician fading model and the
multipath (MP) effect, our channel matrix Hconsists of three
components including the LOS part, the WR part, and the MP
part, which can be presented as
H=s¯
K
1 + ¯
K
¯
H+r1
1 + ¯
KHMP,(9)
where the deterministic matrix ¯
H, including the LOS part and
the WR part, is expressed as
¯
H=H1
kH1kpNRNT,(10)
subject to E[Tr{HH}] = NRNT, with k·k denoting the F-
norm. The MP components are assumed to be independent and
identically distributed zero mean and unit variance complex
Gaussian random variables arranged in the NR×NTmatrix
HMP.¯
Kis the power ratio between the deterministic part ¯
H
and the random part HMP, which can be obtained through
¯
K=KS, (11)
where Kis the distance-dependant Rician factor as a function
of d1defining the power ratio between the LOS part and the
MP part, given by [35, Eq. (5.22)]
K= 8.7+0.051d1(dB),(12)
and
S=kH1k2
kA1k2=
d2
1
d2
2
Γ2+2Md1
NTNRd2
Γ+1
,(13)
β=hH
β2,hH
β1=1
NR
(NR
1)/2
X
q=(NR
1)/2
exp (jq(β1β2)) = sin (πNRD(cos (θR1+ ∆θ)cos (θR2+ ∆θ)) )
NRsin (πD (cos (θR1+ ∆θ)cos (θR2+ ∆θ)) )(16)
α=hhα2,hα1i=1
NT
(NT
1)/2
X
q=(NT
1)/2
exp (jq(α1α2)) = sin (πNTD(cos θT1cos θT2))
NTsin (πD(cos θT1cos θT2))(17)
IEEE INTERNET OF THINGS JOURNAL 4
in which M=
NT
1
P
p=0
NR
1
P
q=0
cos (p(α1α2) + q(β1β2)).
III. ANALYSIS OF ERGODIC CAPACITY
In this section, for an arbitrary position in the room, we
derive the two non-zero squared singular values of H1, the
MPDF of an unordered squared singular value and the ergodic
capacity of an indoor LOS MIMO channel Hin closed forms.
A. The distribution of the squared singular value of channel
For notational convenience, we define m= min{NR, NT}
and n= max{NR, NT}.
Lemma 1: Suppose ϕ1, ϕ2, ..., ϕmare the msquared
singular values of H1, where ϕ1, ϕ2, ..., ϕm2= 0 and
ϕm1, ϕm>0. The two non-zero squared singular values
of H1are computed in closed-form as
ϕm1=kXk2qkXk44|det (X)|2
2,(14)
ϕm=kXk2+qkXk44|det (X)|2
2,(15)
X="A1+A2βα A2βkhαk
A2αkhβkA2khαkkhβk#,
hH
β=hH
β2βhH
β1,
hα=hα2αhα1,
and βand αare given in (16) and (17), respectively [36].
Proof: See Appendix.
Theorem 1: The MPDF of an unordered squared singular
value λof His computed in (18) [37], where the two non-zero
squared singular values of ¯
K¯
Hare given by
φm1=¯
KNRNTϕm1
kH1k2=KNRNTϕm1
kA1k2,(19)
and
φm=¯
KNRNTϕm
kH1k2=KNRNTϕm
kA1k2,(20)
and Di,j is the (i, j)-co-factor of the m×mmatrix Zwhose
(l, k)th entry is given by
(Z)l,k =((nm+k+l2)!,1lm2,
1F1(nm+l,nm+1k)
((nm+l1)!)1,otherwise.(21)
The hypergeometric function 0F1w, z2in (18) is defined in
the series form by
0F1w, z2=
X
s=0
(z)2s
s![w]s
,(22)
and the hypergeometric function 1F1(e, o, g)in (21) is given
by
1F1(e, o, g) =
X
s=0
[e]sgs
[o]ss!,(23)
where [r]t=(r+t1)!
(r1)! .
Proof: Given the channel model in (8)-(13), the channel
matrix His an NR-by-NTnon-central Wishart matrix with
mean q¯
K
1+ ¯
K¯
H. Hence, the MPDF of an arbitrary squared
value of Hcan be found in [37, (3)], which is derived by the
squared singular values of ¯
K¯
H.
Since H1has only two non-zero squared singular values
given in Lemma 1 and the relationship between H1and ¯
H
is given in (10), the two non-zero squared singular values of
¯
K¯
Hare given in (19) and (20), respectively, based on (14)
and (15).
Meanwhile, using [37, Lemma 2], we get
lim
τ0
0F1(nm+1,(¯
K+1)(φi+τi)λ)Ci,j (φi+τi)
m
Q
k<l
((φl+τl)(φk+τk))
=fi(λ)Di,j (φi+τi)
m2
Q
l=1
(l1)!
m
Q
l=m1
φm2
l(φmφm1)
,(24)
where τ={τ1, τ2, ..., τm}is an m-dimensional vector whose
elements are distinct,
fi(λ) = (λi1[nm+ 1]1
i1,1im2,
0F1nm+ 1,¯
K+ 1φiλ,otherwise,
(25)
Di,j is given in (21) and Ci,j in [37, (3)] is the (i, j)-co-
factor of the m×mmatrix Awhose (i, j)th entry is Ai,j =
(nm+j1)!0F1(nm+j, n m+ 1, φi). Since the
Hhas only two non-zero squared values, its MPDF can be
derived as (18) by substituting (24) and (25) into [37, (3)].
B. Closed-form ergodic capacity
Theorem 2: The ergodic capacity at a typical position is
given by (26), where the average signal-to-noise-ratio (SNR)
f(λ) = eφmφm1(¯
K+1)λ
m((nm)!)2λ
m
X
j=1 (¯
K+ 1)λnm+j
(φmφm1)m2(φmφm1)
m3
Q
l=0
l! (nm+l)!
· m2
X
i=1
Di,j ¯
K+ 1λi1+0F1nm+ 1,(¯
K+ 1)φm1λ
(Dm1,j )1+0F1nm+ 1,(¯
K+ 1)φmλ
(Dm,j )1!
(18)
C(ρ) = κ
m
X
j=1 m2
X
i=1
(ϑ1)!
(Di,j )1
ϑ
X
k=1
Eϑk+1 ¯
K+ 1
ρ/NT+
X
p=0 Dm1,j φp
m1+Dm,j φp
m
p! (nm+p)!((τ1)! (nm)!)1
τ
X
k=1
Eτk+1 ¯
K+ 1
ρ/NT!
(26)
IEEE INTERNET OF THINGS JOURNAL 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
x (m)
0
1
2
3
4
5
6
7
8
9
10
y (m)
a
b
c
i
d
BS
e
f
g
h
a: (4.50, 1.25)
b: (3.50, 1.25)
c: (2.50, 1.25)
d: (1.50, 1.25)
e: (0.50, 1.25)
f: (0.50, 3.25)
g: (0.50, 5.25)
h: (0.50, 7.25)
i: (0.50, 9.25)
BS: ( 0, 0.0375)
Fig. 2. Cartesian coordinates for a room, e.g. W=L= 10 (m), where the
BS is close to the considered wall and there is an L-shaped route inside.
at each receiver branch is given by
ρ=¯
KkH1k2ρT
¯
K+ 1NRNT
,(27)
in which ρT=Ekxk2.Eknk2refers to the SNR at
transmitter side,
κ=
exp ¯
K+1
SNR/NTφmφm1
ln2 ((nm)!)m1(φmφm1)m2(φmφm1)
m3
Q
l=0
l!
,
(28)
ϑ=nm+j+i1,τ=nm+j+p, and EQ(x) =
R
1exttQdt.
Proof: The ergodic capacity can be derived by taking the
expectation with respect to λas follows [38]
C(ρ) = mElog21 + ρ
NT
λ
=mZ
0
log21 + ρ
NT
λf(λ)dλ,
(29)
where f(λ)is given in (18). The integral over
λin (29) is computed by the series expansion of
0F1nm+ 1,¯
K+ 1φiλin (22) and
Z
0
ln (1 + )λη1eγ λdλ=(η1)!
eγ
$γη
η
X
l=1
Eηl+1 γ
$
(30)
in [39, Appendix A]. Thus, the ergodic capacity at a typical
UE position is given in (26).
IV. WIRELESS FRIENDLINESS EVALUATION SCHEME FOR
BUILDING MATER IA LS
In this section, we investigate how friendly a wall is to
indoor LOS MIMO transmissions. Aiming to quantify the
wireless friendliness of a building material, a reasonable indi-
cator is the expectation of capacity E(C). However, the value
Algorithm 1: An Wireless Friendliness Evaluation
Scheme for a Building Material
Input: ε0,ζ,K,µ,W,L,X,Y,NT,NR,D,D1,ρT
Output: Cavg
1Calculate the step in xaxis: x=W
X;
2Calculate the step in yaxis: y=LD1
Y1;
3Determine the coordinates (x, y)of all sample points :
x=W/2 + (∆x/2) : ∆x:W/2(∆x/2);
y=D1: ∆y:L;
4Determine the BS position located at (0, D1);
5for i= 1; iXdo
6for j= 1; jYdo
7Determine the UE location (xi, yj);
8Calculate d1,d2,θT1,θT2,θR1and θR2,α;
9Calculate Γwith (4)-(7);
10 Constructe Hwith (8)-(13);
11 Derive C(xi, yj)with (26)-(28);
12 Calculate Cavg with (31);
13 return Cavg;
of E(C)cannot be calculated straightforwardly. An alternative
solution is to average the capacity values over dense sample
points inside the room, since the limit of the mean capacity
values over sample points equals E(C)as the sampling density
approaches infinity.
Building a two-dimensional Cartesian coordinate system
inside a W×Lrectangular room as shown in Fig. 2, we take
X×Ysample points spatially evenly distributed throughout the
room. For a UE at the location (xi, yj)where i∈ {1,2, ..., X}
and j∈ {1,2, ..., Y }, its downlink ergodic capacity can be
computed by (26)-(28) and denoted as C(xi, yj)in bit/s/Hz.
The capacity spatially averaged over all sample points, used as
an evaluation indicator for measuring the wireless friendliness
of a building material, is given by
Cavg =1
XY
X
X
i=1
Y
X
j=1
C(xi, yj).(31)
According to [20], a simple expression of relative permit-
tivity εis given by ε=ε01, where the real part and the
imaginary part can be expressed as a function of frequency
f, i.e., ε0=ufvand ε1= 17.98σ/f , where σ=rftis the
conductivity of the building material, and constants u,v,rand
tare compiled in [20, Table III]. In the following, we focus
on the permittivity and thickness of the building material.
Permittivity: The permittivity in this paper refers to the real
part of relative permittivity ε0. The imaginary part is assumed
to be a constant. Note that both εand ε0are unitless.
Thickness: Since the building material in this paper is
assumed to be a homogenous dielectric reflector, the building
material’s thickness of ζequals to that of the wall.
The scheme for evaluating the wireless friendliness of a
building material is given in Algorithm 1. The permittivity ε0
and the thickness ζof a wall material are the inputs, and the
output Cavg is computed following (31) as an indicator of its
wireless friendliness. A higher Cavg indicates that a wall made
IEEE INTERNET OF THINGS JOURNAL 6
wall
z
ε
BS
antenna
b
n
m
n
UE
antenna
Main lobe Back lobe
1
d
2
d
1
D
wall
z
ε
BS
antenna
b
n
m
n
UE
antenna
Main lobe Back lobe
1
d
2
d
1
D
Fig. 3. The impact of the radiation pattern of a directional BS antenna on
the EM propagation along the LOS path and the WR path.
of this kind of material would be more friendly to indoor LOS
MIMO communications.
V. IM PACT O F DIRECTIONAL R AD IATI ON PATT ER N
In this section, we consider each transmit element in the BS
linear array as a directional antenna, as shown in Fig. 3. The
main lobe directivity gain and the back lobe directivity gain
are denoted as νmand νb, respectively, where ν2
m+ν2
b= 2
according to the energy conservation law. Due to the dynamic
attitude of UE, we assume an omnidirectional antenna for the
UE antenna for analytical tractability. The deterministic part
of H1should be rewritten accordingly as
H0
1=νmA1hH
β1hα1+νbA2hH
β2hα2.(32)
The two non-zero squared singular values of H0
1are derived
by replacing Xin (14) and (15) with
X0="νmA1+νbA2βα νbA2βkhαk
νbA2αkhβkνbA2khαkkhβk#.(33)
The ¯
Kin channel model (9)-(13), the squared singular
distribution of channel (18)-(20) and the ergodic capacity (26)-
(28) should all be replaced by K0, where K0=KS0, K is
the Rician factor given by (12), and
S0=
H0
1
2
kA1k2=
d2
1ν2
b
d2
2ν2
m
Γ2+2Md1νb
NTNRd2νm
Γ+1
.(34)
Meanwhile, the ergodic capacity C(ρ0)for directional an-
tenna cases should be derived by the average SNR at each
receiver antenna ρ0, which is given by
ρ0=K0kH0
1k2ρT
(K0+ 1) NRNT
.(35)
The wireless friendliness evaluation scheme for directional
BS antenna arrays is similar to Algorithm I by using (32)-(35).
TABLE I
MAI N SIM UL ATION A SS UMP TI ON
Parameter name Parameter value
Frequency f(GHz) 6
Room width W(m) 10
Room length L(m) 10
Inter-antenna spacing D=µ/2(m) 0.025
The distance from BS to wall D1(m) 0.0375
Number of BS antennas NT4
Number of UE antennas NR4
Samples along room xaxis X100
Samples along room yaxis Y100
VI. NUMERICAL RESULTS
In this section, we present and analyse the numerical
results for both omnidirectional and directional BS antenna
arrays to present a comprehensive understanding of the impact
of building materials as reflectors on indoor LOS MIMO
communications. Subsection A-C show the results for the
omnidirectional BS antenna array, while Subsection D shows
the results for the directional BS antenna array.
The parameters used in the simulations are given in Table I.
The incident wave is assumed to be TE polarised. The trans-
mission power of the BS is assumed to be equally allocated
to every transmit antenna element. The BS is deployed at
point (0, D1) and its antenna array is deployed parallel to the
considered wall. In the Monte Carlo simulations, the ergodic
capacity at point (xi, yj)is computed by
Csim (xi, yj)=Elog2det I+ρ
NT
HH.(36)
A. The ergodic capacity for a specific sample point
In this subsection, we take three points, i.e. (0.3, 0.25), (4.5,
8.0) and (-2.5, 0.55), as examples to verify the correctness of
analytical expression of (18)-(20) and (26)-(28). The Rician
factor Kof the three points is computed by (12) accordingly.
Fig. 4 depicts the MPDF of an unordered squared singular
value of the LOS MIMO channel. It is found that the MPDF
becomes more concentrated as Kis reduced, which reveals
that the squared singular values of matrix Hare more evenly
distributed and thus results in a larger ergodic capacity.
Fig. 5 shows the ergodic capacity versus the transmit
SNR. The ergodic capacity increases when the transmit SNR
increases. Meanwhile, a larger Kleads to a lower ergodic
capacity under the same transmit SNR due to the less con-
centrated MPDF of an unordered squared singular value of
channel matrix H.
From the results for θbeing 0 and π/2in Fig. 4 and Fig.
5, respectively, we can see that θhas a limited impact on the
MPDF of an unordered squared singular value and the ergodic
capacity of indoor LOS MIMO channel. This is because β
in (16) is hardly affected by θ. When θincrease from 0
to π,βis always very close to 1. As a result, the squared
singular values of Hderived by (14)-(15) will not change
much with θ. Consequently, the MPDF of an unordered
squared singular value in (18)-(20) and the ergodic capacity
in (26)-(28) of Hwill stay nearly constant for varying θ.
IEEE INTERNET OF THINGS JOURNAL 7
0 5 10 15 20
0
0.05
0.1
0.15
0.2
0.25
0.3
MPDF
13.18 13.2 13.22
0.0404
0.0406
0.0408
Fig. 4. The MPDF of an unordered squared singular value at three points,
for ζ= 0.2,ε= 5.31 j0.5861f0.1905 [20, Table III]. Markers represent
simulation values while red solid lines and blue dash lines represent analytical
values when θ= 0 and θ=π/2, respectively.
55 60 65 70 75 80 85 90 95
T (dB)
0
10
20
30
40
50
60
70
Ergodic capacity (bit/s/Hz)
87.67 87.672
31.76
31.765
Fig. 5. Relationship between ergodic capacity and transmit SNR at three
points, for ζ= 0.2,ε= 5.31 j0.5861f0.1905. Markers represent
simulation values while red solid lines and blue dash lines represent analytical
values when θ= 0 and θ=π/2, respectively.
Therefore, due to the space limitation, all the numerical results
hereinafter are conducted when θ= 0.
B. The ergodic capacity distribution in a square room
To verify the accuracy of the evaluation indicator Cavg in
(31) and the usefulness of Algorithm 1, the ergodic capacity
at different positions is studied in this subsection.
a b c d e f g h i
Point
0
1
2
3
4
5
6
7
8
9
Ergodic Capacity (bit/s/Hz)
T=50dB No WR
T=60dB No WR
T=50dB WR
T=60dB WR
Fig. 6. Ergodic capacity at the points for L-shaped route, for ζ= 0.2,
ε= 5.31 j0.5861f0.1905. Markers represent simulation values while
both the solid and dash lines represent analytical values.
Fig. 7. Ergodic capacity distribution in the 10 m ×10 m square room, for
ρT= 60 dB, ζ= 0.2,ε= 5.31 j0.5861f0.1905. Markers represent
simulation values while the lines represent analytical values.
We design a L-shaped route that includes some typical UE
positions in the square room, as shown in Fig. 2. The ergodic
capacities from point a to j along this route, in the presence
or absence of WR path, are shown in Fig. 6. The dash lines
illustrate the results taking into account the WR path. From
point a to e, we observe an increase in capacity as the UE is
approaching the BS except for point d, where the slump in
ergodic capacity is due to the power cancellation caused by
IEEE INTERNET OF THINGS JOURNAL 8
Fig. 8. The ergodic capacity difference between our proposed channel and the
Rician channel, for ρT= 60 dB, ζ= 0.2,ε= 5.31j0.5861f0.1905 . The
positive/negative difference indicates constructive/destructive interference.
3.5 4 4.5 5 5.5 6 6.5 7 7.5
Permittivity
2.58
2.6
2.62
2.64
2.66
2.68
2.7
2.72
2.74
2.76
Spatially averaged capacity (bit/s/Hz)
Thickness=0.1
Thickness=0.15
Thickness=0.2
Simulations
Fig. 9. Impact of wall permittivity on spatially averaged capacity for the
omnidirectional BS antenna array for ρT= 60 dB.
the destructive combination of the LOS path and the WR path.
When the UE moves from point e to i, the capacity declines.
This is different from the ergodic capacity under the Rician
fading model without considering the WR path that would
monotonically decrease with an increasing UE-BS distance,
as shown by the solid lines in Fig. 6.
The spatial distribution of the ergodic capacity in a square
room using our proposed model is shown in Fig. 7. It is
observed that the ergodic capacity is not a monotonic function
of the UE-BS distance. This phenomenon can be attributed
0.1 0.15 0.2 0.25 0.3
Thickness (m)
2.6
2.62
2.64
2.66
2.68
2.7
2.72
Spatially averaged capacity (bit/s/Hz)
Permittivity=4.5
Permittivity=5.5
Permittivity=6.5
Simulations
Fig. 10. Impact of wall thickness on spatially averaged capacity for the
omnidirectional BS antenna array for ρT= 60 dB.
Fig. 11. The composite impact of permittivity and thickness on spatially
averaged capacity for the omnidirectional BS antenna array for ρT= 60 dB.
to the constructive and destructive interference between the
EM waves along the LOS path and the WR path. The length
difference in O(λ)leads to the great changes of the amplitude
and phase of the superposed EM wave arriving at the UE.
Fig. 8 plots the ergodic capacity difference between our
proposed channel model based on (8)-(13) and the Rician
fading channel model. The position with a positive/negative
difference corresponds to a location that experiences the
constructive/destructive interference between the EM waves
along the LOS path and the WR path. We can see that the
IEEE INTERNET OF THINGS JOURNAL 9
0 5 10 15 20
0
0.05
0.1
0.15
0.2
0.25
0.3
MPDF
Fig. 12. The MPDF of an unordered squared singular value at three points,
for ζ= 0.2,ε= 5.31 j0.5861f0.1905. Markers represent simulation
values while lines represent analytical values.
positions suffering from the destructive interference appear
in certain directions, along which the Fabry-P´
erot resonance
phenomenon of EM waves is observed.
Concluded from Fig. 6-8, the impact of the WR path
that characterises the EM and physical properties of building
materials on indoor ergodic capacity is non-trivial, which
cannot be ignored in indoor LOS MIMO communications.
C. The impact of wall permittivity and thickness on spatially
averaged capacity
In order to identify a wall material with desirable wireless
friendliness, the relationship between the evaluation indicator
named spatially averaged capacity Cavg and the key parame-
ters, i.e., the permittivity ε0and the thickness ζof building
materials is shown in this subsection.
Fig. 9 and Fig. 10 plot the spatially averaged capacity as
a function of the permittivity and the thickness of building
materials, respectively. In Fig. 9, as the permittivity increases
from 3.5 to 7.5, the envelope of each spatially averaged
capacity curve presents a upward trend. The variation in the
spatially averaged capacity becomes more significant with the
increase of the permittivity. In Fig. 10, for a given permittivity,
as the wall thickness increases, the spatially averaged capacity
first fluctuates with it under a decreasing envelope and grad-
ually converges to a constant value when the thickness goes
beyond 0.25 m. We observe quite severe fluctuations of the
spatially averaged capacity at relatively small wall-thickness
values. That is because the reflection coefficient amplitude
fluctuates more severely when the wall is thinner. It should
be highlighted that a tiny lapse in the wall permittivity or the
thickness would bring about changes in the spatially averaged
capacity of up to 0.19 bits/s/Hz.
55 60 65 70 75 80 85 90 95
T (dB)
0
10
20
30
40
50
60
70
Ergodic capacity (bits/s/Hz)
Fig. 13. Relationship between ergodic capacity and transmit SNR at three
points, for ζ= 0.2,ε= 5.31 j0.5861f0.1905. Markers represent
simulation values while lines represent analytical values.
a b c d e f g a b
Point
0
1
2
3
4
5
6
7
8
9
Ergodic Capacity (bit/s/Hz)
T=50dB No WR
T=60dB No WR
T=50dB WR
T=60dB WR
Fig. 14. Ergodic capacity at the points for L-shaped route, for ζ= 0.2,
ε= 5.31 j0.5861f0.1905. Markers represent simulation values while
both the solid and dash lines represent analytical values.
The composite impact of the building material’s permittivity
and thickness on the spatially averaged capacity is illustrated
in Fig. 11. When the permittivity and the thickness are
configured in the range from 1.5 to 7.5 and from 0.1 to
0.25 m, respectively, we observe that the optimal parameter
pair of [ε0,ζ] resulting in the highest spatially averaged
capacity of 2.763 bits/s/Hz is [6.92, 0.1], while the worst
pair resulting in the lowest spatially averaged capacity of
2.415 bits/s/Hz is [1.50, 0.1]. We can conclude that certain
combinations of the wall thickness and permittivity values lead
IEEE INTERNET OF THINGS JOURNAL 10
3.5 4 4.5 5 5.5 6 6.5 7 7.5
Permittivity
2.96
2.97
2.98
2.99
3
3.01
3.02
3.03
3.04
3.05
3.06
Spatially averaged capacity (bit/s/Hz)
Thickness=0.1
Thickness=0.15
Thickness=0.2
Simulations
Fig. 15. Impact of wall permittivity on spatially averaged capacity for the
directional BS antenna array for ρT= 60 dB.
to peak values of the spatially averaged capacity, which can
be more than 14.4% higher than the lowest spatially averaged
capacity values associated with some combinations of the wall
thickness and permittivity values that should be avoided during
the selection and/or design of building materials.
D. Analysis for directional BS antenna array
In this subsection, Fig. 12-17 depict the numerical results
for the directional BS antenna array. The main lobe directivity
gain and the back lobe directivity gain are assumed as νm=
p1/3and νb=p5/3, respectively.
Fig. 12 and Fig. 13 are plotted for the same three sample
points shown in Fig. 4 and Fig. 5, i.e. (0.3, 0.25), (4.5, 8.0)
and (-2.5, 0.55). It is found in Fig. 12 that the MPDF of an
unordered squared singular value of the LOS MIMO chan-
nel becomes more concentrated and that the largest squared
singular value of the LOS MIMO channel becomes larger,
when compared with the omnidirectional BS antenna array
in Fig. 4. Moreover, the difference between the MPDF under
different Rician factor Kbecomes less substantial. In Fig. 13,
the ergodic capacity shows an increasing trend with the rise of
transmit SNR. When comparing the red lines in Fig. 5 with the
red lines in Fig. 13, the ergodic capacity under the directional
BS antenna array is shown to be larger than that under the
omnidirectional BS antenna array.
Given the same 9 points along the L-route drawn in Fig. 2,
Fig. 14 shows similar results from Fig. 6. Even though there is
less change in ergodic capacity in the presence or absence of
the WR path compared with the omnidirectional BS antenna
array, it still appears some positions that suffer destructive
interference, such as point d.
With regards to the impact of the wall permittivity and
thickness on spatially averaged capacity, significant variation
up to 0.093 bits/s/Hz can be observed from Fig. 15 and Fig.
0.1 0.15 0.2 0.25 0.3
Thickness (m)
2.97
2.98
2.99
3
3.01
3.02
3.03
Spatially averaged capacity (bit/s/Hz)
Permittivity=4.5
Permittivity=5.5
Permittivity=6.5
Simulations
Fig. 16. Impact of wall thickness on spatially averaged capacity for the
directional BS antenna array for ρT= 60 dB.
Fig. 17. The composite impact of permittivity and thickness on spatially
averaged capacity for the directional BS antenna array for ρT= 60 dB.
16. In Fig. 17, it is found that the optimal wall parameter pair
of [ε0,ζ] leading to the highest spatially averaged capacity
of 3.057 bits/s/Hz is [6.84, 0.10], while the worst pair leading
to the lowest spatially averaged capacity of 2.887 bits/s/Hz
is [1.50, 0.10]. The 5.9% difference in the spatially averaged
capacity generated by the certain combinations of the wall
permittivity and thickness is worthy to be considered.
The results above indicate that for directional BS antenna
arrays, the EM and physical properties of building materials
will definitely exert a substantial influence on a room’s wire-
less performance.
IEEE INTERNET OF THINGS JOURNAL 11
VII. CONCLUSIONS AND FUT UR E WORKS
In this paper, we firstly construct a new indoor LOS MIMO
downlink channel model by considering the impact of building
materials on indoor wireless performance. Then, the MPDF
of the squared singular value and the ergodic capacity of the
indoor LOS MIMO channel and the squared singular value
of its deterministic part are obtained in closed forms. On
this basis, a scheme for evaluating the wireless friendliness
of building materials is provided. The analytical results are
verified through Monte Carlo simulations conducted in the
6 GHz band. Numerical results demonstrate that building
materials as reflectors have to be well selected or designed
to avoid the risk of reducing indoor wireless performance,
because a minor discrepancy in the configuration of the relative
permittivity and thickness of the wall material might cause
over 14.4% losses in indoor capacity.
This work is the first attempt to investigate how indoor
capacity is influenced by the EM and physical properties
of building materials, which has laid a solid foundation of
wireless friendliness evaluation of indoor built environments.
In future works, there are some extensive research directions
worthy of in-depth study, including but not limit to: 1) Multi-
layer building materials: It is of great necessity to analyse
both single-layer and multi-layer building materials. One of
the challenges is that the analytical relationship between the
indoor MIMO capacity and the EM and physical properties of
multi-layer building materials is hard to find due to the non-
closed-form reflection coefficients [20]. Moreover, the optimal
configuration of multi-layer materials would be formulated
into a multi-variate optimisation problem, the complexity of
which would increase with the number of layers. 2) Millimetre
wave (mmWave): MmWave bands have been a promising
candidate for 5G and B5G wireless network, which has been
widely studied in both theoretical and experimental study. The
propagation mechanism for sub-6 GHz bands and mmWave
bands are substantially different due to the orders of magnitude
change in the wavelength [10], [15], [40]. Hence, the work
extending to mmWave bands should start from the accurate
and tractable modelling of indoor mmWave propagation. An-
other scheme is required to evaluate the wireless friendliness
of building materials at mmWave bands. 3) Experimental
validation: It is critical to verify the numerical results of
the proposed channel model and the evaluation scheme with
experimental results. A comprehensive measurement campaign
will be held in future work.
APPENDIX: PRO OF O F LEMMA 1
Since two deterministic components including the LOS path
and the WR path are considered in our model as shown in (8),
it is obvious that H1has two non-zero singular values. The
singular value decomposition of deterministic part H1can be
given as
H1=BHXA,(37)
where
B=hβ1hβ/khβkT,
A=hα1hα/khαkT,
X= 1 ∆β
0khβk! A10
0A2! 1 0
αkhαk!.
Initially using Gram-Schmidt process, hα1and hH
β1are or-
thonormalized with hα/khαkand hH
β.khβk, respectively,
which means that BHB=Iand AHA=I.
Then Xcan be simplified as a 2×2matrix, with four
elements given in (14). Assuming Xcould be decomposed as
X=PH ϕm10
0ϕm!Q,(38)
where PHP=Iand QHQ=I, then ϕm1and ϕmare two
squared singular values of matrix X. Hence we obtain
H1=(PB)H ϕm10
0ϕm!QA.(39)
Here it is interesting to find that ϕm1and ϕmare the two
squared singular values of H1as well, since (PB)HPB =I
and (QA)HQA=I.
Therefore, the two non-zero squared singular values of H1,
i.e. ϕm1and ϕm, can be easily obtained by conducting
singular value decomposition to low dimensional matrix X,
as given in (14) and (15), respectively.
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Yixin Zhang received the B.Eng. degree from Bei-
jing University of Posts and Telecommunications,
Beijing, China, in 2017. She is currently pursuing
the Ph.D. degree in the Department of Electronic and
Electrical Engineering at the University of Sheffield,
Sheffield, UK. Her research interests include electro-
magnetic wave propagation, wireless channel mod-
elling, MIMO antenna configurations, and indoor
wireless networks.
Chen Chen received the B.Eng. degree from East
China University of Science and Technology, Shang-
hai, China, in 2018. He is currently pursuing his
Ph.D. degree in Wireless Communications at the
University of Sheffield, UK. His current research
interests include millimeter wave networks, green
networks, stochastic geometry and machine learning.
Songjiang Yang received the B.Eng. degree with
class one honours in electronic and communication
engineering from the University of Sheffield, U.K.,
in 2017, where he is currently pursuing the Ph.D. de-
gree. His research interests include millimetre wave
channel modelling and millimetre wave wireless
communications.
Jiliang Zhang (M’15, SM’19) received the B.E.,
M.E., and Ph.D. degrees from the Harbin Institute
of Technology, Harbin, China, in 2007, 2009, and
2014, respectively. He was a Postdoctoral Fellow
with Shenzhen Graduate School, Harbin Institute
of Technology from 2014 to 2016, an Associate
Professor with the School of Information Science
and Engineering, Lanzhou University from 2017 to
2019, and a researcher at the Department of Electri-
cal Engineering, Chalmers University of Technology,
Gothenburg, Sweden from 2017 to 2018. He is now
a Marie Curie Research Fellow at the Department of Electronic and Electrical
Engineering, The University of Sheffield, Sheffield, UK. His current research
interests include, but are not limited to wireless channel modelling, modulation
system, relay system, wireless ranging system, vehicular communications,
ultra-dense small cell networks, neural dynamic, and smart environment
modelling.
IEEE INTERNET OF THINGS JOURNAL 13
Xiaoli Chu is a Professor in the Department of Elec-
tronic and Electrical Engineering at the University
of Sheffield, UK. She received the B.Eng. degree in
Electronic and Information Engineering from Xi’an
Jiao Tong University in 2001 and the Ph.D. degree
in Electrical and Electronic Engineering from the
Hong Kong University of Science and Technology
in 2005. From 2005 to 2012, she was with the
Centre for Telecommunications Research at Kings
College London. Xiaoli has co-authored over 150
peer-reviewed journal and conference papers. She is
co-recipient of the IEEE Communications Society 2017 Young Author Best
Paper Award. She co-authored/co-edited the books “Fog-Enabled Intelligent
IoT Systems”(Springer 2020), “Ultra Dense Networks for 5G and Be-
yond”(Wiley 2019), “Heterogeneous Cellular Networks: Theory, Simulation
and Deployment”(Cambridge University Press 2013), and “4G Femtocells:
Resource Allocation and Interference Management”(Springer 2013). She is
Senior Editor for the IEEE Wireless Communications Letters, Editor for
the IEEE Communications Letters, and received the IEEE Communications
Letters Exemplary Editor Award in 2018. She was Co-Chair of Wireless
Communications Symposium for IEEE ICC 2015, Workshop Co-Chair for
IEEE GreenCom 2013, and has co-organized 8 workshops at IEEE ICC,
GLOBECOM, WCNC, and PIMRC.
Jie Zhang has held the Chair in Wireless
Systems at the Department of Electronic and
Electrical Engineering, University of Sheffield
(www.sheffield.ac.uk) since Jan. 2011.
He is also Founder, Board Chairman and Chief
Scientific Officer (CSO) of Ranplan Wireless
(www.ranplanwireless.com), a public company listed
on Nasdaq OMX. Ranplan Wireless produces a
suite of world leading indoor and the only joint
indoor–outdoor 5G/4G/WiFi network planning and
optimization tools suites including Ranplan Profes-
sional and Collaboration-Hub, which are being used by the world’s largest
mobile operators and network vendors across the globe.
Along with his students and colleagues, he has pioneered research in small
cell and heterogeneous network (HetNet) and published some of the landmark
papers and books on these topics, widely used by both academia and industry.
Prof. Zhang published some of the earliest papers on using social media
network data for proactive network optimisation. Since 2010, he and his
team have developed ground-breaking work in modelling and designing
smart built environments considering both wireless and energy efficiency. His
Google scholar citations are in excess of 7000 with an H-index of 35.
Prior to his current appointments, he studied and worked at Imperial
College London, Oxford University, University of Bedfordshire, and East
China University of Science and Technology, reaching the rank of a Lecturer,
Reader and Professor in 2002, 2005 and 2006 respectively.
... In order to predict the impact of a wall that is closest to the BS on the indoor wireless performance, we proposed wireless friendliness as a new performance metric of a wall in [26], where we also developed an approach to evaluating the wireless friendliness of a wall by adopting the indoor spatially averaged capacity of a multipath channel as a metric, which is a function of and is affected by the BS transmission power. Note that the capacity of the two-ray channel comprising of the line-of-sight (LOS) path and the wall reflection (WR) path [18], [27] and the capacity of a multipath channel that incorporates other multipath components in addition to the LOS path and the WR path have the same monotonicity, which can be proven using the results in [28]. ...
... As will be shown in Section II, by leveraging the logarithmic sum or logarithmic product of the eigenvalues of the two-ray channel, the influence of the BS transmission power on a wall's wireless friendliness can be removed. Consequently, compared with the metric in [26], the three new metrics proposed herein no longer require the calculation of the following four parameters: the BS transmit SNR, the power ratio of the LOS and WR paths to the other multipath components, and the two eigenvalues of the two-ray channel, which facilitates a faster and simpler approach to evaluating a wall's wireless friendliness. ...
... In this article, we investigate how the transverse dimension (equal to the length or width of a room), longitudinal dimension (thickness), and dielectric properties (relative permittivity and conductivity) of the wall closest to the BS affect the indoor LOS MIMO downlink transmissions in a rectangular room, which may have various room sizes, aspect ratios, and distances between the BS and its closest wall. Given that the wall closest to the BS would exert a much greater impact on the received signal strength than the other walls due to the dominating distance-dependent path loss over the much weaker reflection gain [26], in this article, we focus on the wireless friendliness evaluation of the wall closest to the BS. For brevity, the wall closest to the BS in a room is referred to as the wall hereafter. ...
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Indoor base stations (BSs) equipped with multiple-input multiple-output (MIMO) antenna arrays are commonly deployed in the vicinity of a wall. The wireless friendliness of the wall, determined by the intrinsic electromagnetic (EM) and physical properties of the wall material, significantly influences the indoor wireless performance and thus needs to be thoroughly considered during building design. In this article, for a rectangular room with a BS deployed near one of the walls, by deriving the asymptotic expression of lower-bound indoor wireless capacity of a UE location-specific channel, we reveal that the impact of the BS transmission power and that of the wall material properties on the lower-bound indoor capacity can be decoupled. More specifically, in our derived lower-bound indoor wireless capacity, the properties of the wall material are captured by the logarithmic eigenvalue summation (LES) and logarithmic eigenvalue product (LEP), which are both independent of the BS transmit signal-to-noise ratio (SNR). To simplify the wireless-friendliness evaluation of a wall by leveraging such decoupling, we derive both the LES and LEP in closed forms for a UE location-specific channel, and define the spatially averaged LES, the spatially averaged LEP, and the upper-bound outage probability (all over the room of interest) as new metrics for fast evaluating the wireless friendliness of the wall closest to the BS. Numerical results verify the effectiveness of the three proposed metrics and reveal the crucial impact of room settings and wall materials on the indoor capacity. The proposed approach will enable architects and civil engineers to quickly select building materials according to their wireless friendliness.
... A popular solution is to integrate the AP with an interior wall of the building [7]. In this sense, the interactions between the indoor electromagnetic wave (EM) propagation and the interior wall should not be neglected in the deployment of indoor APs [8], [9]. ...
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Indoor access points (APs) with large-scale antenna arrays would commonly be deployed in the vicinity of a wall, where wall reflection (WR) affects the indoor electromagnetic (EM) wave propagation. In this paper, we investigate the effects of WR on the per-antenna power distribution of a transmit uniform linear array (ULA) adopting a zero-forcing (ZF) precoder. A new channel model is constructed to characterise the impact of both the line-of-sight (LOS) path and the WR path on indoor millimetre wave (mmWave) multi-user (MU) multiple-input multiple-output (MIMO) downlink transmissions. Specifically for the dual user equipment (UE) scenario, the ZF precoding matrix is analytically obtained and verified through simulations. The effects of WR on the per-antenna power distribution of the ZF-precoded ULA, in terms of the normalized power distribution and maximum power ratio (MPR), are evaluated through the comparisons between our proposed channel model and the pure LOS channel model. Our analytical and numerical results reveal the impact of AP configurations (the number of antennas and the AP-wall distance), multi-user spatial distribution (the angle of departure (AoD) and length of the LOS path for each user), and wall parameters (permittivity and thickness) on the power distribution across the ZF-precoded ULA. It is found that the effects of WR will exacerbate the uneven power distribution across the ZF-precoded ULA.
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The authors regret the errors in [1, eqs. (13), (27), (34), and (35)] . The corrections for these equations are given as follows:
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To avoid negative visual and weight impact of antenna arrays in indoor multiple-input multiple-output (MIMO) systems, the antenna arrays can be integrated in building materials. In this letter, we model building materials integrated with antenna arrays and develop an approach that can characterize and evaluate their wireless performance using a ray-tracing model that incorporates multipath propagation from line-of-sight (LOS), reflected, and other paths. The approach comprises the following: 1) Using the effective transmission coefficient to characterize the electromagnetic (EM) coupling between the antenna array and the building material with which it is integrated; 2) Taking the spatially averaged capacity as a performance metric to quantify wireless performance of integrated materials; 3) Optimizing integrated materials’ wireless performance by tuning their conductivity, permittivity, thickness and integration depth; and 4) Comparing wireless performance between optimized and unoptimized integrated materials. Our numerical results show that the spatially averaged capacity varies with different material property settings, indicating that integrated materials should be carefully designed to enhance their wireless performance.
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