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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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... l η l e jϑ l p l x + n,(18) 419 where x is the signal transmitted by the source satisfying E |x| 2 = P , with P being the 420 transmit power and n ∼ CN (0, σ 2 N ) denoting the additive white Gaussian noise (AWGN), with 421 zero mean and variance σ 2 N . Furthermore, η l represents the reflection coefficient introduced by the l th illuminated reflective element of the RIS, whilst ϑ l represents the phase shift introduced 423 by the l th illuminated reflective element of the RIS. ...
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We present a simulation framework for evaluating the performance of cooperative reconfigurable intelligent surface (RIS) based systems, which may ultimately deploy an arbitrary number of RISs to overcome adverse propagation-related effects, such as cascaded fading. The physical model underlying the proposed framework considers the (optional) presence of a dominant signal path between the source and RIS, and then between each subsequent stage of the communication link to the destination. Accompanying the dominant signal component is a non-isotropic scattered signal contribution, which accounts for angular selectivity within the cascaded RIS stages between the source and destination. The simulation of the time-correlated scattered signal, reflected by the illuminated reflective elements, is achieved using autoregressive modelling. As a by-product of our analysis, significant insights are drawn which enable us to characterize the amplitude and phase properties of the received signal, and the associated complex autocorrelation functions (ACFs) for the product of multiple Rician channels. For both single and cooperative RIS systems, the outage probability (OP), and important second-order statistics, such as the level crossing rate (LCR) and average outage duration (AOD), are analyzed for a variety of system configurations, accounting for practical limitations, such as phase errors. It is shown that by using multiple RISs cooperatively, the AOD is reduced at a lower signal-to-noise-ratio (SNR) compared to single RIS-assisted transmission under the same operating conditions. Lastly, increased channel variations (i.e., higher maximum Doppler frequencies) are shown to decrease the AOD in the case of absent phase errors; yet, this improvement is not observed when phase errors are present.
... As for the IRS-assisted communication systems, Guo et al. [30] studied the performance of IRS-aided satellite-UAVterrestrial communication systems with HIs, and closed-form expression showed that HIs will increase the outage probability. The spectral and energy efficiency of an IRS-assisted MISO downlink system with HIs was evaluated by Zhou et al. [31], and they demonstrated that HIs restrict the spectral efficiency even when the number of antennas and IRS elements is infinitely large. Boulogeorgos et al. [32] analyzed IRS-assisted UAV systems with mixture-gamma small-scale fading, stochastic disorientation and misalignment, and transceivers HIs, and proved the importance of accurate modeling of these imperfections. ...
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... An IRS is composed of passive reflecting elements made from metasurfaces or mirrors. Typically, these reflecting elements are arranged in a planar surface to independently reflect the incident signals at different angles by different amplitude and/or phase [15].The deployment of IRS in conventional RF networks was shown to enhance performance in terms of spectral and energy efficiency [16]. ...
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... In this regard, RIS-aided multi-user multipleinput single-output (MISO) downlink communication system was studied in [5], [8], [9]. In [10], the authors investigated the spectrum and energy efficiency of a RIS-assisted MISO communication system by adjusting the transmit power and the number of reflecting elements at the RIS. Next, to improve the performance of RISs, the authors in [11] provided an electromagnetic-based communication-theoretic framework. ...
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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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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.
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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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In the intelligent reflecting surface (IRS)-enhanced wireless communication system, channel state information (CSI) is of paramount importance for achieving the passive beamforming gain of IRS, which, however, is a practically challenging task due to its massive number of passive elements without transmitting/receiving capabilities. In this letter, we propose a practical transmission protocol to execute channel estimation and reflection optimization successively for an IRS-enhanced orthogonal frequency division multiplexing (OFDM) system. Under the unit-modulus constraint, a novel reflection pattern at the IRS is designed to aid the channel estimation at the access point (AP) based on the received pilot signals from the user, for which the channel estimation error is derived in closed-form. With the estimated CSI, the reflection coefficients are then optimized by a low-complexity algorithm based on the resolved strongest signal path in the time domain. Simulation results corroborate the effectiveness of the proposed channel estimation and reflection optimization methods.
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In this paper, we investigate secure communication over sparse millimeter-wave (mm-Wave) massive multiple-input multiple-output (MIMO) channels by exploiting the spatial sparsity of legitimate user’s channel. We propose a secure communication scheme in which information data is precoded onto dominant angle components of the sparse channel through a limited number of radio-frequency (RF) chains, while artificial noise (AN) is broadcast over the remaining nondominant angles interfering only with the eavesdropper with a high probability. It is shown that the channel sparsity plays a fundamental role analogous to secret keys in achieving secure communication. Hence, by defining two statistical measures of the channel sparsity, we analytically characterize its impact on secrecy rate. In particular, a substantial improvement on secrecy rate can be obtained by the proposed scheme due to the uncertainty, i.e.“, entropy”, introduced by the channel sparsity which is unknown to the eavesdropper. It is revealed that sparsity in the power domain can always contribute to the secrecy rate. In contrast, in the angle domain, there exists an optimal level of sparsity that maximizes the secrecy rate. The effectiveness of the proposed scheme and derived results are verified by numerical simulations.