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# Spectral and Energy Efficiency of IRS-Assisted MISO Communication with Hardware Impairments

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## Abstract

In this letter, we analyze the spectral and energy efficiency of an intelligent reflecting surface (IRS)-assisted multiple-input single-output (MISO) downlink system with hardware impairments. An extended error vector magnitude (EEVM) model is utilized to characterize the impact of radio-frequency (RF) impairments at the access point (AP) and phase noise is considered for the imperfect IRS. We show that the spectral efficiency is limited due to the hardware impairments even when the numbers of AP antennas and IRS elements grow infinitely large, which is in contrast with the conventional case with ideal hardware. Moreover, the performance degradation at high SNR is shown to be mainly affected by the AP hardware impairments rather than the phase noise of IRS. We further obtain in closed form the optimal transmit power for energy efficiency maximization. Simulation results are provided to verify the obtained results.
arXiv:2004.09854v1 [cs.IT] 21 Apr 2020
1
Spectral and Energy Efﬁciency of IRS-Assisted
MISO Communication with Hardware Impairments
Shaoqing Zhou, Wei Xu, Senior Member, IEEE, Kezhi Wang, Member, IEEE,
Marco Di Renzo, Fellow, IEEE, and Mohamed-Slim Alouini, Fellow, IEEE
Abstract
In this letter, we analyze the spectral and energy efﬁciency of an intelligent reﬂecting surface (IRS)-assisted
multiple-input single-output (MISO) downlink system with hardware impairments. An extended error vector mag-
nitude (EEVM) model is utilized to characterize the impact of radio-frequency (RF) impairments at the access
point (AP) and phase noise is considered for the imperfect IRS. We show that the spectral efﬁciency is limited
due to the hardware impairments even when the numbers of AP antennas and IRS elements grow inﬁnitely large,
which is in contrast with the conventional case with ideal hardware. Moreover, the performance degradation at
high SNR is shown to be mainly affected by the AP hardware impairments rather than the phase noise of IRS. We
further obtain the optimal transmit power in closed form for energy efﬁciency maximization. Simulation results are
provided to verify these results.
Index Terms
Intelligent reﬂecting surface, hardware impairments, downlink spectral efﬁciency, energy efﬁciency.
I. INT RO DUC TION
INTELLIGENT reﬂecting surface (IRS) has recently been acknowledged as a promising new tech-
nology to realize spectral-, energy- and cost-efﬁcient wireless communication for the ﬁfth generation
network and beyond [1]. IRS is a planar array consisting of a large number of low-cost reﬂecting elements,
S. Zhou is with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China (e-mail:
sq.zhou@seu.edu.cn).
W. Xu is with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China, and also with
Purple Mountain Laboratories, Nanjing 211111, China (e-mail: wxu@seu.edu.cn).
K. Wang is with the Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne NE1 8ST, U.K.
(e-mail: kezhi.wang@northumbria.ac.uk).
M. Di Renzo is with Universit´e Paris-Saclay, CNRS and CentraleSup´elec, Laboratoire des Signaux et Syst`emes, Gif-sur-Yvette, France.
(e-mail: marco.direnzo@centralesupelec.fr).
M.-S. Alouini is with the Division of Computer, Electrical, and Mathematical Science and Engineering, King Abdullah University of
Science and Technology, Thuwal 23955-6900, Saudi Arabia (e-mail: slim.alouini@kaust.edu.sa).
2
which independently induce phase adjustments on impinging signals to conduct reﬂecting beamforming.
Signiﬁcantly different from existing technologies, IRS reconﬁgures wireless communication environment
between transmitter and receiver via programmable and highly controllable intelligent reﬂection. Moreover,
it avoids active radio-frequency (RF) chains and operates passively for short range coverage enhancement
so that it can be densely deployed in a ﬂexible way with affordable hardware cost and energy consumption.
Traditional communication theories may no longer be applied because the IRS-assisted wireless system
consists of both active and passive components, instead of solely active entities [2]. Researches on channel
estimation, IRS beamforming design and system performance analysis are on the way. Two efﬁcient uplink
channel estimation schemes were proposed in [3] for IRS-assisted multi-user systems with various channel
setups. In [4], transmit precoding and passive IRS phase shifts were jointly optimized for simultaneous
wireless information and power transfer systems. Ergodic spectral efﬁciency of an IRS-assisted massive
multiple-input multiple-output system was characterized in [5] under Rician fading channel. In [6], spectral
efﬁciency of an IRS-aided multi-user system was studied under proportional rate constraints and an
iteratively optimizing solution was proposed with closed-form expressions. Secrecy rate was maximized
in [7] for an IRS-assisted multi-antenna system by alternately optimizing transmitting covariance and IRS
phase shifts. IRS was also shown to be effective in enhancing the performance of cell-edge users [8].
In practice, precise phase control is infeasible at IRS due to hardware limitations and imperfect channel
estimation. Corresponding researches are still in their infancy. Discrete phase shifts were considered for
IRS-assisted multi-user communication in [9], where a hybrid beamforming optimization algorithm was
proposed for sum rate maximization. In addition to non-ideal IRS, the impacts of RF impairments at
transmitter on the performance of an IRS system have not been clear. To capture the aggregate impacts
of various RF impairments, a generalized model named extended error vector magnitude (EEVM) was
proposed in [10] for cellular transmitters.
In this letter, we focus on an IRS-assisted multiple-input single-output (MISO) system with hardware
impairments at both access point (AP) and IRS. Theoretical expression of spectral efﬁciency is derived for
this non-ideal case. We discover that the performance is limited even with increasing numbers of elements
at both the AP and IRS. The impact of phase noise at IRS diminishes at high SNR. Meanwhile, we obtain
a closed-form solution to the optimal power design for maximizing energy efﬁciency. The optimal power
increases with RF impairments.
3
II. SY STE M MODE L
A. Signal Model
We consider a MISO downlink system where an IRS consisting of Nreﬂecting elements is deployed
to assist the communication from an M-antenna AP to a single-antenna user. The IRS is triggered
by an attached smart controller connected to the AP. Denote the reﬂection matrix of IRS by Θ=
diag{ζ1e1, ζ2ej θ2,...,ζNeN}, where ζn[0,1] and θn[0,2π)for n= 1,2,...,N are respectively the
amplitude reﬂection coefﬁcient and the phase shift introduced by the nth reﬂecting element. In practice,
each reﬂecting element is usually designed to maximize the signal reﬂection. Without loss of generality,
we set ζn= 1 for all n[11]. The direct link between AP and user is blocked by obstacles, such as buildings
or human body, which is common in the communication at high-frequency bands, like millimeter wave.
Thus it would be better to deploy IRS at positions where line-of-sight (LoS) communication is ensured
for both AP-to-IRS and IRS-to-user links.
Considering the ﬂat-fading model, the channel from the AP to IRS and that from the IRS to user are
respectively denoted by H1and hH
2. Both channels are assumed to be LoS, which are represented by
H1=αaN(φa
r, φe
r)aH
M(φa
t, φe
t),hH
2=βaH
N(ϕa
t, ϕe
t),(1)
where αand βare the corresponding strength of path AP-to-IRS and IRS-to-user, φa
r(φe
r) is the azimuth
(elevation) angle of arrival (AoA) at IRS, φa
t(φe
t) and ϕa
t(ϕe
t) are the azimuth (elevation) angles of
departure (AoD) at AP and IRS, respectively, and aX(ϑa, ϑe)is the array response vector. We consider
uniform square planar array (USPA) with X×Xantennas. The array response vector can be written as
aX(ϑa, ϑe) = [1,...,ej2πd
λ(xsin ϑasin ϑe+ycos ϑe),...,ej2πd
λ((X1) sin ϑasin ϑe+(X1) cos ϑe)]T,(2)
where dand λare the antenna spacing and signal wavelength, and 0x, y < Xare the antenna indices
in the planar. Assume that the AP knows the channel state information (CSI) of both H1and hH
2. Channel
estimation methods for communication with IRS can be found in [11][12].
With the errors caused by imperfect RF chains at AP, we adopt the EEVM in [10] to model the transmit
signal, which can be written as
x=χws+nRF ,(3)
where sis the signal satisfying E[|s|2] = Pwith Pbeing the transmit power budget, wis the nor-
4
malized beamforming vector at AP, χ=diag{χ(1), χ(2),...,χ(M)}with χ(m) = η(m)e(m)for
m= 1,2,...,M representing the RF attenuation and phase rotation of the mth RF chain with |η(m)| ≤ 1,
and nRF = [nRF (1), nRF (2), . . . , nRF (M)]Trepresents the additive distortion noise with covariance matrix
CnRF . The mapping of χand nRF to particular type(s) of RF impairments, e.g., phase noise, I/Q imbalance
and nonlinearity, could be found in [10, Ch. 7]. For notational simplicity, assume that ψ(m)is uniformly
distributed as U[δψ(m), δψ(m)]with δψ(m)[0, π),nRF (m)∼ CN(0, σ2(m)), and the impairments of all
RF chains fall into the same level, i.e., η(m) = η,δψ(m)=δψ,σ(m) = σand CnRF =σ2IM.
Furthermore, there always exist some phase errors at IRS in implementation. The received signal with
phase errors can be modeled as
y=hH
2e
ΘH1x+u=hH
2e
ΘH1χws+hH
2e
ΘH1nRF +u, (4)
where e
Θ=diag{ej˜
θ1, ej˜
θ2,...,ej˜
θN}with ˜
θn=θn+ˆ
θnbeing the practical phase shift of the nth reﬂecting
element, ˆ
θnis the phase noise due to the fact, e.g., only discrete phase shifts are possible at IRS, and uis
the additive noise with zero mean and variance σ2
u. Assume that ˆ
θnis uniformly distributed as U[δˆ
θ, δˆ
θ]
with δˆ
θ[0, π). Since the distortion noise is independent of channel noise, the received SNR is given by
SNR =P|hH
2e
ΘH1χw|2
(hH
2e
ΘH1)CnRF (hH
2e
ΘH1)H+σ2
u
.(5)
Then we have the downlink spectral efﬁciency as
R= log2(1 + SNR).(6)
B. Power Consumption Model
Before we discuss the power consumption, it needs to be emphasized that the IRS does not consume
any transmit power due to its nature of passive reﬂection. The total power consumption is modeled as [13]
PT=µP +PC,(7)
where µ=ν1with νbeing the efﬁciency of transmit power ampliﬁer considering the RF impairments
and PCis the total static hardware power dissipated in all circuit blocks. The establishment of (7) models
well under two assumptions: 1) the transmit ampliﬁer operates within its linear region; and 2) the power
consumption PCdoes not rely on the rate of the communication link. Both assumptions are valid in typical
wireless systems.
5
III. SPECT RAL A ND ENE RGY EFFI CIE NCY ANALYSIS
In this section, we quantitatively analyze the downlink spectral and energy efﬁciency and discover the
impact of hardware impairments at both the AP and IRS. The ideal spectral and energy efﬁciency are
retrieved as a special case of our analysis and it is presented for comparison.
A. Spectral Efﬁciency Analysis
Before analyzing the performance, we need to determine the transmit beamforming of AP and the
reﬂecting beamforming of IRS. Since the hardware impairments are unknown and in order to facilitate
the design in practice, the two parameters, wand Θ, are optimized by treating the hardware as ideal.
Maximum ratio transmission (MRT) is adopted for transmit beamforming, i.e.,
w= (hH
2ΘH1)H/khH
2ΘH1k.(8)
We identify the optimal reﬂecting beamforming of IRS by maximizing the received signal power as
Θopt = arg max
Θ|hH
2ΘH1w|2(a)
= arg max
ΘkhH
2ΘH1k2
= arg max
Θ|aH
N(ϕa
t, ϕe
t)ΘaN(φa
r, φe
r)|2kaH
M(φa
t, φe
t)k2
(b)
= arg max
Θ|X
0x,y<N ,
n=Nx+y+1
ej2πd
λ(xp+yq)+j θn|2,(9)
where (a)is obtained by substituting win (8), (b)makes use of a mapping from the two-dimensional
index (x, y)to the index n,p= sin φa
rsin φe
rsin ϕa
tsin ϕe
t, and q= cos φe
rcos ϕe
t. Observing (9), it is
easy to get the optimal phase shift of the nth reﬂecting element as
θopt
n=2πd
λ(xp +yq),(10)
where x=(n1)/Nand y= (n1) mod N, and ⌊·⌋ represents rounding down the value and
mod means taking the remainder.
Now considering the design of Θopt in (10) and w(Θopt)in (8), we characterize the impacts of both RF
impairments at AP and phase noise at IRS on the downlink spectral efﬁciency in the following Theorem 1.
Theorem 1:The downlink spectral efﬁciency for the massive IRS-assisted MISO with large Mand N
approaches
Ra.s.
log21 + P M N2η2|αβ|2sinc2(δψ)sinc2(δˆ
θ)
MN 2|αβ|2sinc2(δˆ
θ)σ2+σ2
u.(11)
6
Special Case 1: For the ideal system without any impairments, we let η= 1,σ= 0 and δψ=δˆ
θ= 0
in (11). The downlink spectral efﬁciency reduces to
Rideal = log21 + P
σ2
u
MN 2|αβ|2.(12)
Special Case 2: For high SNR, (11) in Theorem 1 can be further simpliﬁed as
Rlog2P+ 2 log2η+ 2 log2sinc(δψ)log2σ2.(13)
Remark 1:It is concluded from (11) that the non-ideal spectral efﬁciency increases with ηwhile
decreases with parameters δψ,σ2and δˆ
θ. The impact of the phase rotation at AP in terms of δψis in
general more signiﬁcant than that of the phase noise at IRS in terms of δˆ
θ.
Remark 2:The spectral efﬁciency in (11) increases with the transmit power approximately in a log-
arithmic manner similar to the ideal case in (12) but with a different scale. Contrary to the ideal case,
the performance is ultimately upper bounded for increasing Mand N, which is R(M, N )¯
R=
log2(1 + η2P
σ2sinc2(δψ)) for all large Mand N.
Remark 3:An interesting observation from (13) is that the spectral efﬁciency at high SNR is merely
limited by the RF impairments at AP rather than the phase noise at IRS, which can be explained from
the perspective that the IRS reﬂecting beamforming simultaneously affects both the desired signal and the
distortion noise under the considerations of hardware impairments at AP and LoS channel. It encourages us
to use cheap IRS with low-resolution phase shifts without much consideration of performance degradation
for large IRS.
B. Energy Efﬁciency Analysis
The energy efﬁciency is deﬁned as the ratio of the spectral efﬁciency to the power consumption, i.e.,
EE ,BR/PTwhere Bis the channel bandwidth. We are interested in the performance at high SNR,
which can be rewritten as
EE =B(log2P+ 2 log2η+ 2 log2sinc(δψ)log2σ2)
µP +PC
.(14)
In the following Theorem 2, we give a closed-form expression of the optimal transmit power maximizing
the EE in (14).
7
SNR (dB)
0 2 4 6 8 10 12 14 16 18 20
0
5
10
15
Ideal analysis in (12)
Ideal simulations
Non-ideal analysis in (11)
Non-ideal approximation in (13)
Non-ideal simulations
Reecting Elements N
0 10 20 30 40 50 60 70 80 90 100
Spectral Eciency (bits/s/Hz)
0
2
4
6
8
10
12
Ideal analysis in (12)
Ideal simulations
Non-ideal analysis in (11)
Non-ideal simulations
σ2= 0.3
σ2= 0.05
σ2= 0.05,
δψ=π/3
¯
R
Fig. 1. Downlink spectral efﬁciency versus SNR and N.
Theorem 2:The optimal transmit power to maximize the energy efﬁciency is the unique solution as
P=µP 1
CW(µ1eCAP1PC),(15)
where W(x)is the Lambert’s W-function and CAP = 2 ln η+ 2 ln sinc(δψ)ln σ2.
Note that for an ideal system without hardware impairments, the optimal transmit power can be similarly
derived as
P
ideal =µP 1
CW(µ1eC1PC),(16)
where C= ln(MN 2|αβ|2)ln σ2
u. We emphasize that the IRS has continuous phase in the ideal case,
which increases the static hardware power consumption of IRS.
Remark 4:For Pin (15) and EE(P)in (14), the optimal transmit power increases with more severe
RF impairments and the corresponding optimal energy efﬁciency decreases.
IV. SIMUL ATION RE SULTS
In this section, simulation results are presented to validate the results in Section III. Assume that
M= 16,N= 64,η= 0.9,δψ=π
18 ,σ2= 0.1,δˆ
θ=π
8,α= 0.1,β= 0.5and µ= 1.1.
We plot the downlink spectral efﬁciency in Theorem 1, special cases and by simulations in Fig. 1. Both
non-ideal case in (11) and ideal case in (12) increase with the transmit power but by respective scales.
The simpliﬁed expression in (13) appears to be fairly tight at high SNR.
8
Transmit Power P(dB)
-5 0 5 10 15 20 25
Energy Eciency (bits/s/Joule)
0
0.2
0.4
0.6
0.8
1
1.2
Ideal analysis
Non-ideal analysis
P
Highest point
η= 0.9,δψ=π/18,σ2= 0.1
η= 0.8,δψ=π/18,σ2= 0.1
η= 0.8,δψ=π/4,σ2= 0.1
η= 0.8,δψ=π/4,σ2= 0.15
Fig. 2. Energy efﬁciency versus P.
We further assume SNR = P
σ2= 10 dB. Fig. 1 shows the spectral efﬁciency versus the number of IRS
reﬂecting elements. As the number goes larger, the hardware impairments lead to limited growth of spectral
efﬁciency, which is consistent with Remark 2, while the ideal case continues increasing logarithmically
with the squared number of elements.
In Fig. 2, we give the energy efﬁciency with various degrees of RF impairments. The optimal transmit
power derived in Theorem 2 matches the highest point of the curve well. When the RF impairments become
worse, higher optimal transmit power is required while the corresponding energy efﬁciency decreases. Note
that the ideal case may obtain poorer performance than the non-ideal case because of larger static hardware
power consumption of continuous-phase IRS.
V. CONCLUSION
In this letter, we demonstrate the downlink spectral and energy efﬁciency of an IRS-assisted system
with hardware impairments. The non-ideal spectral efﬁciency is upper bounded for large numbers of AP
antennas and IRS elements. Specially, the impact of imperfect IRS diminishes at high SNR. The optimal
transmit power for maximizing the energy efﬁciency increases as the RF impairments become more severe.
APPEN DIX A
PROO F O F THEO REM 1
Applying (8) and (10), we can rewrite the downlink spectral efﬁciency in (6) as
R= log2 1 + P|hH
2e
ΘH1χ(hH
2ΘH1)H|2/khH
2ΘH1k2
khH
2e
ΘH1k2σ2+σ2
u!
9
R(c)
= log2
1 +
P|αβ|2
N
P
n=1
ejˆ
θn
2
|aH
M(φa
t, φe
t)χaM(φa
t, φe
t)|2
M |αβ|2
N
P
n=1
ejˆ
θn
2
kaM(φt)k2σ2+σ2
u!
= log2
1 +
P η2|αβ|2PM
m=1 e(m)
2PN
n=1 ejˆ
θn
2/M
M|αβ|2PN
n=1 ejˆ
θn
2σ2+σ2
u
,
(17)
where (c)is obtained by substituting the equations hH
2ΘH1=αβNaH
M(φa
t, φe
t)and hH
2e
ΘH1=αβ×
PN
n=1 ejˆ
θnaH
M(φa
t, φe
t).
For large M→ ∞, we have
1
M
M
X
m=1
e(m)
2
(d)
a.s. |E[e(m)]|2(e)
=|E[cos ψ(m)]|2(f)
=sinc2(δψ),(18)
where (d)applies the Strong Law of Large Numbers and the Continuous Mapping Theorem [14] which
indicates that the convergence preserves for continuous matrix functions, (e)uses the symmetry of the odd
function sin ψ(m)for ψ(m)[δψ, δψ],(f)is obtained by substituting the probability density function
of variable ψ(m), i.e., fX(x) = 1
2δψfor x[δψ, δψ], and sinc(x) = sin x
x. Similarly, for large N→ ∞,
we have
1
N
N
X
n=1
ejˆ
θn
2
a.s.
sinc2(δˆ
θ).(19)
Substituting (18) and (19) into (17) completes the proof.
APPEN DIX B
PROO F O F THEO REM 2
By calculating the partial derivative of EE in (14), we have
∂P EE =BP1(µP +PC)µ(ln P+CAP )
(ln 2)(µP +PC)2.(20)
Letting the partial derivative be zero, we have
µP (ln P+CAP 1) = PC,(21)
t=ln P
==µet+CAP 1(t+CAP 1) = eCAP 1PC,
(g)
t=W(µ1eCAP1PC)CAP + 1,(22)
10
where (g)uses the fact the Lambert’s W-function is the inverse function of f(W) = W eW. Now
rearranging (22) yields (15).
The remainder proves that (21) has a unique solution. Deﬁne g(P),µP (ln P+CAP 1). It follows
d
dPg(P) = µ(ln P+CAP)>0. Thus g(P)is monotonically increasing with respect to P, which implies
that equation (21) has at most one solution, which is exactly (15).
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... In [19], the authors designed a task selection strategy and leveraged a RIS to reduce the overall power consumption in green edge interference networks. The authors in [20] investigated the hardware impairments in RIS-assisted multiple-input singleoutput (MISO) broadcast channels (BC), and derived a closed-form solution for maximizing the energy efficiency. However, both [19] and [20] only considered the power consumption of the BS. ...
... The authors in [20] investigated the hardware impairments in RIS-assisted multiple-input singleoutput (MISO) broadcast channels (BC), and derived a closed-form solution for maximizing the energy efficiency. However, both [19] and [20] only considered the power consumption of the BS. Due to the hardware static power consumption of the RISs introduced by phase shifts adjusting, the power consumption of RIS should also be considered when maximizing the energy efficiency of networks, e.g., considering both the power consumption of the BS and that of all RISs. ...
... Due to the hardware static power consumption of the RISs introduced by phase shifts adjusting, the power consumption of RIS should also be considered when maximizing the energy efficiency of networks, e.g., considering both the power consumption of the BS and that of all RISs. In addition to the limitation of the power consumption model, [19] and [20] only deployed one RIS in the considered networks. Moving to the power consumption of multiple RISs, the authors in [21] leveraged multiple RISs to maximize the received power for downlink point-to-point millimeter wave communications. ...
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Reconfigurable intelligent surface (RIS) has emerged as a cost-effective and energy-efficient technique for 6G. By adjusting the phase shifts of passive reflecting elements, RIS is capable of suppressing the interference and combining the desired signals constructively at receivers, thereby significantly enhancing the performance of communication In this paper, we consider a green multi-user multi-antenna cellular network, where multiple RISs are deployed to provide energy-efficient communication service to end users. We jointly optimize the phase shifts of RISs, beamforming of the base stations, and the active RIS set with the aim of minimizing the power consumption of the base station (BS) and RISs subject to the quality of service (QoS) constraints of users and the transmit power constraint of the BS. However, the problem is mixed combinatorial and nonconvex, and there is a potential infeasibility issue when the QoS constraints cannot be guaranteed by all users. To deal with the infeasibility issue, we further investigate a user admission control problem to jointly optimize the transmit beamforming, RIS phase shifts, and the admitted user set. A unified alternating optimization (AO) framework is then proposed to solve both the power minimization and user admission control problems. Specifically, we first decompose the original nonconvex problem into several rank-one constrained optimization subproblems via matrix lifting. The proposed AO framework efficiently minimizes the power consumption of wireless networks as well as user admission control when the QoS constraints cannot be guaranteed by all users. Compared with the baseline algorithms, we illustrate that the proposed algorithm can achieve lower power consumption for given QoS constraints. Most importantly, the proposed algorithm successfully addresses the infeasibility issue with a QoS guarantee for active users.
... In order to take advantage of the IRS mentioned above, extensive researches on deploying IRS in various wireless communication systems have been conducted to improve the performance under different metrics. By judiciously adjusting IRS elements, the reflected signals are intelligently elaborated to achieve performance improvement in terms of spectral efficiency [11], energy efficiency [12], transmit power [13], [14], sum-rate [15]- [17], etc., for single-user/multi-user MIMO/multi-input single-output (MISO) [11]- [16], wideband orthogonal frequency division multiplexing (OFDM) [17], or multi-cell systems [18]. In addition, researchers have explored the designs of IRS with low-resolution phase-shift [19] and phase error [20] or under imperfect channel state information (CSI) [21]. ...
... In order to take advantage of the IRS mentioned above, extensive researches on deploying IRS in various wireless communication systems have been conducted to improve the performance under different metrics. By judiciously adjusting IRS elements, the reflected signals are intelligently elaborated to achieve performance improvement in terms of spectral efficiency [11], energy efficiency [12], transmit power [13], [14], sum-rate [15]- [17], etc., for single-user/multi-user MIMO/multi-input single-output (MISO) [11]- [16], wideband orthogonal frequency division multiplexing (OFDM) [17], or multi-cell systems [18]. In addition, researchers have explored the designs of IRS with low-resolution phase-shift [19] and phase error [20] or under imperfect channel state information (CSI) [21]. ...
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Intelligent reflecting surface (IRS) has been regarded as a promising and revolutionary technology for future wireless communication systems owing to its capability of tailoring signal propagation environment in an energy/spectrum/hardware-efficient manner. However, most existing studies on IRS optimizations are based on a simple and ideal reflection model that is impractical in hardware implementation, which thus leads to severe performance loss in realistic wideband/multi-band systems. To deal with this problem, in this paper we first propose a more practical and more tractable IRS reflection model that describes the difference of reflection responses for signals at different frequencies. Then, we investigate the joint transmit beamforming and IRS reflection beamforming design for an IRS-assisted multi-cell multi-band system. Both power minimization and sum-rate maximization problems are solved by exploiting popular second-order cone programming (SOCP), Riemannian manifold, minimization-majorization (MM), weighted minimum mean square error (WMMSE), and block coordinate descent (BCD) methods. Simulation results illustrate the significant performance improvement of our proposed joint transmit beamforming and reflection design algorithms based on the practical reflection model in terms of power saving and rate enhancement.
... Besides, the joint effects of transmitter/receiver RF impairments, oscillator phase noise, and AGC noise can be characterized by the extended error vector magnitude model, where the transmitter/receiver hardware impairment is modeled as the zero-mean Gaussian noise with its variance proportional to the undistorted transmitted/received signal power [211]. The practical IRS channel estimation and passive beamforming designs under the transceiver/IRS hardware impairments have been recently investigated in the literature (see, e.g., [185], [197], [199]- [210], [212]). Specifically, for channel estimation, the authors in [200], [201] proposed a linear-MMSE based cascaded channel estimation scheme, where the transceiver distortions were modeled by the Gaussian distribution and IRS phaseshift errors were modeled by a circular distribution. ...
... Besides, the ergodic and outage capacities of IRS-aided communication systems based on the extended error vector magnitude model were analyzed in [203]- [205], which revealed that the system capacity tends to saturate when the number of reflecting elements exceeds a threshold due to transceiver hardware impairments. Furthermore, the authors in [212] showed that the performance degradation at high SNR is mainly affected by the BS's hardware impairment rather than the phase noise arising from IRS discrete phase-shifts, since the IRS passive beamforming simultaneously affects the desired signal and distortion noise. In [210], the authors considered the effects of the non-linear high power amplifier and showed that the outage capacity can be increased by mitigating the nonlinear distortion via operating the high power amplifier with back-off. ...
Article
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Intelligent reflecting surface (IRS) has emerged as a key enabling technology to realize smart and reconfigurable radio environment for wireless communications, by digitally controlling the signal reflection via a large number of passive reflecting elements in real time. Different from conventional wireless communication techniques that only adapt to but have no or limited control over dynamic wireless channels, IRS provides a new and cost-effective means to combat the wireless channel impairments in a proactive manner. However, despite its great potential, IRS faces new and unique challenges in its efficient integration into wireless communication systems, especially its channel estimation and passive beamforming design under various practical hardware constraints. In this paper, we provide a comprehensive survey on the up-to-date research in IRS-aided wireless communications, with an emphasis on the promising solutions to tackle practical design issues. Furthermore, we discuss new and emerging IRS architectures and applications as well as their practical design problems to motivate future research.
... are analyzed for both the ideal and non-ideal cases to optimize the SE. With the increase of APs, hardware impairments will affect the noise at the IRS, which impacts the downlink SE [44]. ...
... For example, energy efficiency maximization in IRS assisted systems with suboptimal zero-forcing beamforming was studied in [20]. A closed form solution of the optimal transmit power for EE maximization was given in [24], wherein, an IRS assisted MISO system with hardware impairments was considered. It was shown in [25] that the signal-to-interference plus noise ratio performance in an IRS aided MISO network can be significantly enhanced by jointly optimizing the beamforming vectors at the transmitter and phase shifts at the IRS. ...
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In this paper, we study the performance of an energy efficient wireless communication system, assisted by a finite-element-intelligent reflecting surface (IRS). With no instantaneous channel state information (CSI) at the transmitter, we characterize the system performance in terms of the outage probability (OP) of energy efficiency (EE). Depending upon the availability of line-of-sight (LOS) paths, we analyze the system for two different channel models, viz. Rician and Rayleigh. For an arbitrary number of IRS elements $(N)$, we derive the approximate closed-form solutions for the OP of EE, using Laguerre series and moment matching methods. The analytical results are validated using the Monte-Carlo simulations. Moreover, we also quantify the rate of convergence of the derived expressions to the central limit theorem (CLT) approximations using the \textit{Berry-Esseen} inequality. Further, we prove that the OP of EE is a strict pseudo-convex function of the transmit power and hence, has a unique global minimum. To obtain the optimal transmit power, we solve the OP of EE as a constrained optimization problem. To the best of our knowledge, the OP of EE as a performance metric, has never been previously studied in IRS-assisted wireless communication systems.
... In RIS deployment, wireless signals are transmitted from the transmitter to the receiver at a minimal loss [48,49]. On the other hand, real-time control of the reflection amplitude and phase shift of RISs can present huge implementation issues [50]. In order to address 1 CDF Rain rate due to heavy rain depth Rain rate due to very heavy rain depth Rain rate due to extreme heavy rain depth Figure 1: CDF statistical distribution of rain rates due to different rainfall depth. ...
Article
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Absorption and scattering of propagated microwave radio signals by atmospheric variables, particularly rainfall, remained a major cause of propagation attenuation losses and service quality degradation over terrestrial communication links. The International Telecommunications Union Radio (ITU-R) reports and other related works in the literature provided information on attenuation due to rain and microwave propagation data. Such propagation attenuation information in the tropical region of Nigeria is destitute, especially at lower radio waves transmission frequencies. Therefore, this study addresses this problem by employing 12-year rainfall datasets to conduct realistic prognostic modeling of rain rate intensity levels. A classification of the rainfall data into three subgroups based on the depth of rainfall in the region is presented. Additionally, an in-depth estimation of specific rain attenuation intensities based on the 12-year rainfall data at 3.5 GHz is demonstrated. On average, the three rainfall classes produced rain rates of about 29.27 mm/hr, 73.71 mm/hr, and 105.39 mm/hr. The respective attenuation values are 0.89 dB, 1.71 dB, and 2.13 dB for the vertical polarisation and 1.09 dB, 1.20 dB, and 2.78 dB for the horizontal polarisation at 0.01% time percentage computation. Generally, results indicate that higher rain attenuation of 12% is observed for the horizontal polarisation compared to the vertical polarisation. These results can provide valuable first-hand information for microwave radio frequency planning in making appropriate decisions on attenuation levels due to different rainfall depths, especially for lower frequency arrays.
... M. Jung et al. in [32] proposed the uplink data rate in an LIS-based large antenna-array system where the estimated channel on LIS was subject to estimation errors, interference channels were spatially correlated Rician fading channels, and the LIS experiences hardware impairments which improved reliability and a significantly reduced area for antenna deployment. S. Zhou et al. in [33] analyzed an RIS-assisted multiple input single output (MISO) downlink system with hardware impairments using hybrid beamforming optimization algorithm which improved the energy efficiency (EE). Q. Wu et al. in [34] proposed an RIS-aided cellular network by jointly optimizing the continuous transmit precoding and the discrete reflect phase shifts using both optimal and suboptimal algorithms. ...
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Sixth generation (6G) internet of things (IoT) networks will modernize the applications and satisfy user demands through implementing smart and automated systems. Intelligence-based infrastructure, also called reconfigurable intelligent surfaces (RISs), have been introduced as a potential technology striving to improve system performance in terms of data rate, latency, reliability, availability, and connectivity. A huge amount of cost-effective passive components are included in RISs to interact with the impinging electromagnetic waves in a smart way. However, there are still some challenges in RIS system, such as finding the optimal configurations for a large number of RIS components. In this paper, we first provide a complete outline of the advancement of RISs along with machine learning (ML) algorithms and overview the working regulations as well as spectrum allocation in intelligent IoT systems. Also, we discuss the integration of different ML techniques in the context of RIS, including deep reinforcement learning (DRL), federated learning (FL), and FL-deep deterministic policy gradient (FL-DDPG) techniques which are utilized to design the radio propagation atmosphere without using pilot signals or channel state information (CSI). Additionally, in dynamic intelligent IoT networks, the application of existing integrated ML solutions to technical issues like user movement and random variations of wireless channels are surveyed. Finally, we present the main challenges and future directions in integrating RISs and other prominent methods to be applied in upcoming IoT networks. <br
... M. Jung et al. in [32] proposed the uplink data rate in an LIS-based large antenna-array system where the estimated channel on LIS was subject to estimation errors, interference channels were spatially correlated Rician fading channels, and the LIS experiences hardware impairments which improved reliability and a significantly reduced area for antenna deployment. S. Zhou et al. in [33] analyzed an RIS-assisted multiple input single output (MISO) downlink system with hardware impairments using hybrid beamforming optimization algorithm which improved the energy efficiency (EE). Q. Wu et al. in [34] proposed an RIS-aided cellular network by jointly optimizing the continuous transmit precoding and the discrete reflect phase shifts using both optimal and suboptimal algorithms. ...
Preprint
Sixth generation (6G) internet of things (IoT) networks will modernize the applications and satisfy user demands through implementing smart and automated systems. Intelligence-based infrastructure, also called reconfigurable intelligent surfaces (RISs), have been introduced as a potential technology striving to improve system performance in terms of data rate, latency, reliability, availability, and connectivity. A huge amount of cost-effective passive components are included in RISs to interact with the impinging electromagnetic waves in a smart way. However, there are still some challenges in RIS system, such as finding the optimal configurations for a large number of RIS components. In this paper, we first provide a complete outline of the advancement of RISs along with machine learning (ML) algorithms and overview the working regulations as well as spectrum allocation in intelligent IoT systems. Also, we discuss the integration of different ML techniques in the context of RIS, including deep reinforcement learning (DRL), federated learning (FL), and FL-deep deterministic policy gradient (FL-DDPG) techniques which are utilized to design the radio propagation atmosphere without using pilot signals or channel state information (CSI). Additionally, in dynamic intelligent IoT networks, the application of existing integrated ML solutions to technical issues like user movement and random variations of wireless channels are surveyed. Finally, we present the main challenges and future directions in integrating RISs and other prominent methods to be applied in upcoming IoT networks.
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Reconfigurable intelligent surface (RIS) is a candidate technology for future wireless networks. It enables to shape the wireless environment to reach massive connectivity and enhanced data rate. The promising gains of RIS-assisted networks are, however, strongly depends on the accuracy of the channel state information. Due to the passive nature of the RIS elements, channel estimation may become challenging. This becomes most evident when physical imperfections or electronic impairments affect the RIS due to its exposition to different environmental effects or caused by hardware limitations from the circuitry. In this paper, we propose an efficient and low-complexity tensor-based channel estimation approach in RIS-assisted networks taking different imperfections into account. By assuming a short-term model in which the RIS imperfections behavior, modeled as unknown amplitude and phase shifts deviations, is non-static with respect to the channel coherence time, we formulate a closed-form higher order singular value decomposition based algorithm for the joint estimation of the involved channels and the unknown impairments. Furthermore, the identifiability and computational complexity of the proposed algorithm are analyzed, and we study the effect of different imperfections on the channel estimation quality. Simulation results demonstrate the effectiveness of our proposed tensor-based algorithm in terms of the estimation accuracy and computational complexity compared to competing tensor-based iterative alternating solutions.
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Intelligent reflecting surface (IRS) has emerged as a promising technique for wireless communication networks. By dynamically tuning the reflection amplitudes/phase shifts of a large number of passive elements, IRS enables flexible wireless channel control and configuration and thereby enhances the wireless signal transmission rate and reliability significantly. Despite the vast literature on designing and optimizing assorted IRS-aided wireless systems, prior works have mainly focused on enhancing wireless links with single signal reflection only by one or multiple IRSs, which may be insufficient to boost the wireless link capacity under some harsh propagation conditions (e.g., indoor environment with dense blockages/obstructions). This issue can be tackled by employing two or more IRSs to assist each wireless link and jointly exploiting their single as well as multiple signal reflections over them. However, the resultant double-/multi-IRS-aided wireless systems face more complex design issues as well as new practical challenges for implementation compared to the conventional single-IRS counterpart, in terms of IRS reflection optimization, channel acquisition, as well as IRS deployment and association/selection. As such, a new paradigm for designing multi-IRS cooperative passive beamforming and joint active/passive beam routing arises, which calls for innovative design approaches and optimization methods. In this article, we give a tutorial overview of multi-IRS-aided wireless networks, with an emphasis on addressing the new challenges due to multi-IRS signal reflection and routing. Moreover, we point out important directions worthy of research and investigation in the future.
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An intelligent reflecting surface (IRS) is invoked for enhancing the energy harvesting performance of a simultaneous wireless information and power transfer (SWIPT) aided system. Speciﬁcally, an IRS-assisted SWIPT system is considered, where a multi-antenna aided base station (BS) communicates with several multi-antenna assisted information receivers (IRs), while guaranteeing the energy harvesting requirement of the energy receivers (ERs). To maximize the weighted sum rate (WSR) of IRs, the transmit precoding (TPC) matrices of the BS and passive phase shift matrix of the IRS should be jointly optimized. To tackle this challenging optimization problem, we ﬁrst adopt the classic block coordinate descent (BCD) algorithm for decoupling the original optimization problem into several subproblems and alternatively optimize the TPC matrices and the phase shift matrix. For each subproblem, we provide a low-complexity iterative algorithm, which is guaranteed to converge to the Karush-Kuhn-Tucker (KKT) point of each subproblem. The BCD algorithm is rigorously proved to converge to the KKT point of the original problem. We also conceive a feasibility checking method to study its feasibility. Our extensive simulation results conﬁrm that employing IRSs in SWIPT beneﬁcially enhances the system performance and the proposed BCD algorithm converges rapidly, which is appealing for practical applications.
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Large intelligent surface (LIS)-assisted wireless communications have drawn attention worldwide. With the use of low-cost LIS on building walls, signals can be reflected by the LIS and sent out along desired directions by controlling its phases, thereby providing supplementary links for wireless communication systems. In this study, we evaluate the performance of an LIS-assisted large-scale antenna system by formulating a tight approximation of the ergodic capacity and investigate the effect of the phase shifts on the ergodic capacity in different propagation scenarios. In particular, we propose an optimal phase shift design based on the ergodic capacity approximation and statistical channel state information. Furthermore, we derive the requirement on the quantization bits of the LIS to promise an acceptable capacity degradation. Numerical results show that using the proposed phase shift design can achieve the maximum ergodic capacity, and a 2-bit quantizer is sufficient to ensure capacity degradation of no more than 1 bit/s/Hz.
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The adoption of a Reconfigurable Intelligent Surface (RIS) for downlink multi-user communication from a multi-antenna base station is investigated in this paper. We develop energy-efficient designs for both the transmit power allocation and the phase shifts of the surface reflecting elements, subject to individual link budget guarantees for the mobile users. This leads to non-convex design optimization problems for which to tackle we propose two computationally affordable approaches, capitalizing on alternating maximization, gradient descent search, and sequential fractional programming. Specifically, one algorithm employs gradient descent for obtaining the RIS phase coefficients, and fractional programming for optimal transmit power allocation. Instead, the second algorithm employs sequential fractional programming for the optimization of the RIS phase shifts. In addition, a realistic power consumption model for RIS-based systems is presented, and the performance of the proposed methods is analyzed in a realistic outdoor environment. In particular, our results show that the proposed RIS-based resource allocation methods are able to provide up to 300% higher energy efficiency, in comparison with the use of regular multi-antenna amplify-and-forward relaying.
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To achieve the full passive beamforming gains of intelligent reflecting surface (IRS), accurate channel state information (CSI) is indispensable but practically challenging to acquire, due to the excessive amount of channel parameters to be estimated which increases with the number of IRS reflecting elements as well as that of IRS-served users. To tackle this challenge, we propose in this paper two efficient channel estimation schemes for different channel setups in an IRS-assisted multiuser broadband communication system employing the orthogonal frequency division multiple access (OFDMA). The first channel estimation scheme, which estimates the CSI of all users in parallel simultaneously at the access point (AP), is applicable for arbitrary frequency-selective fading channels. In contrast, the second channel estimation scheme, which exploits a key property that all users share the same (common) IRS-AP channel to enhance the training efficiency and support more users, is proposed for the typical scenario with line-of-sight (LoS) dominant user-IRS channels. For the two proposed channel estimation schemes, we further optimize their corresponding training designs (including pilot tone allocations for all users and IRS time-varying reflection pattern) to minimize the channel estimation error. Moreover, we derive and compare the fundamental limits on the minimum training overhead and the maximum number of supportable users of these two schemes. Simulation results verify the effectiveness of the proposed channel estimation schemes and training designs, and show their significant performance improvement over various benchmark schemes.
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In this paper, we study the reconfigurable intelligent surface (RIS) based downlink multi-user system where a multi-antenna base station (BS) sends signals to various users assisted by the RIS reflecting the incident signals of the BS towards the users. Unlike most existing works, we consider the practical case where only the large-scale fading gain is required at the BS and a limited number of phase shifts can be realized by the finite-sized RIS. To maximize the sum rate, we propose a hybrid beamforming scheme where the continuous digital beamforming and discrete RIS-based analog beamforming are performed at the BS and the RIS, respectively. An iterative algorithm is designed for beamforming and theoretical analysis is provided to evaluate how the size of RIS influences the achievable rate. Simulation results show that the RIS-based system can achieve a good sum-rate performance by setting a reasonable size of RIS and a small number of discrete phase shifts.
Conference Paper
This paper investigates the spectral efficiency (SE) in reconfigurable intelligent surface (RIS)-aided multiuser multiple-input single-output (MISO) systems, where RIS can reconfigure the propagation environment via a large number of controllable and intelligent phase shifters. In order to explore the SE performance with user proportional fairness for such a system, an optimization problem is formulated to maximize the SE by jointly considering the power allocation at the base station (BS) and phase shift at the RIS, under nonlinear proportional rate fairness constraints. To solve the non-convex optimization problem, an effective solution is developed, which capitalizes on an iterative algorithm with closed-form expressions, i.e., alternatively optimizing the transmit power at the BS and the reflecting phase shift at the RIS. Numerical simulations are provided to validate the theoretical analysis and assess the performance of the proposed alternative algorithm. Index Terms-Reconfigurable intelligent surface (RIS), transmit power, phase shift, fairness, proportional rate constraint.
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We investigate transmission optimization for intelligent reflecting surface (IRS) assisted multi-antenna systems from the physical-layer security perspective. The design goal is to maximize the system secrecy rate subject to the source transmit power constraint and the unit modulus constraints imposed on phase shifts at the IRS. To solve this complicated non-convex problem, we develop an efficient alternating algorithm where the solutions to the transmit covariance of the source and the phase shift matrix of the IRS are achieved in closed form and semi-closed forms, respectively. The convergence of the proposed algorithm is guaranteed theoretically. Simulations results validate the performance advantage of the proposed optimized design.