ArticlePDF Available

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

Authors:
  • Brunel University of London

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).
REFER ENC E S
[1] S. Dang, O. Amin, B. Shihada, and M.-S. Alouini, “What should 6G be?,” Nat. Electron., vol. 3, no. 1, pp. 20–29,
Jan. 2020.
[2] M. Di Renzo et al., “Smart radio environments empowered by reconfigurable AI meta-surfaces: An idea whose time has
come,” EURASIP J. Wireless Commun. Netw., no. 129, pp. 1–20, May 2019.
[3] B. Zheng, C. You, and R. Zhang, “Intelligent reflecting surface assisted multi-user OFDMA: Channel estimation and
training design,” [Online]. Available: https://arxiv.org/abs/2003.00648v2.
[4] C. Pan et al., “Intelligent reflecting surface aided MIMO broadcasting for simultaneous wireless information and power
transfer, [Online]. Available: https://arxiv.org/abs/1908.04863v4.
[5] Y. Han, W. Tang, S. Jin, C. Wen, and X. Ma, “Large intelligent surface-assisted wireless communication exploiting
statistical CSI,” IEEE Trans. Veh. Technol., vol. 68, no. 8, pp. 8238–8242, Aug. 2019.
[6] Y. Gao, C. Yong, Z. Xiong, D. Niyato, Y. Xiao, and J. Zhao, “Reconfigurable intelligent surface for MISO systems with
proportional rate constraints,” [Online]. Available: https://arxiv.org/abs/2001.10845v1.
[7] H. Shen, W. Xu, S. Gong, Z. He, and C. Zhao, “Secrecy rate maximization for intelligent reflecting surface assisted
multi-antenna communications,” IEEE Commun. Lett., vol. 23, no. 9, pp. 1488–1492, Sep. 2019.
[8] C. Pan, H. Ren, K. Wang, W. Xu, M. Elkashlan, A. Nallanathan, and L. Hanzo, “Multicell MIMO communications
relying on intelligent reflecting surface,” [Online]. Available: https://arxiv.org/abs/1907.10864
[9] B. Di et al., “Hybrid beamforming for reconfigurable intelligent surface based multi-user communications: Achievable
rates with limited discrete phase shifts,” [Online]. Available: https://arxiv.org/abs/1910.14328v1.
[10] T. Schenk, RF Imperfections in High-Rate Wireless Systems: Impact and Digital Compensation. Dordrecht, The
Netherlands: Springer, 2008.
[11] B. Zheng and R. Zhang, “Intelligent reflecting surface-enhanced OFDM: Channel estimation and reflection optimization,”
IEEE Wireless Commun. Lett., Early Access, Dec. 2019.
[12] B. Ning, Z. Chen, W. Chen, and Y. Du, “Channel estimation and transmission for intelligent reflecting surface assisted
THz communications,” [Online]. Available: https://arxiv.org/abs/1911.04719v2.
[13] C. Huang, A. Zappone, G. C. Alexandropoulos, M. Debbah, and C. Yuen, “Reconfigurable intelligent surfaces for energy
efficiency in wireless communication,” IEEE Trans. Wireless Commun., vol. 18, no. 8, pp. 4157–4170, Aug. 2019.
[14] J. Xu, W. Xu, D. W. K. Ng, and A. L. Swindlehurst, “Secure communication for spatially sparse millimeter-wave massive
MIMO channels via hybrid precoding,” IEEE Trans. Commun., vol. 68, no. 2, pp. 887–901, Feb. 2020.
... It allows the system to optimize beamforming and phase shifts accurately. [44]. We design joint beamforming and phase shift using ASTAR-RIS for communication. ...
... The iterative algorithm for solving (26) is given in Algorithm 2. From Algorithm 2, the main complexity of solving (26) lies in solving the phase optimization (32) and (35) and the ASTAR-RIS ON/OFF optimization (44). ...
... According to Algorithm 2, the main complexity of solving (44) lies in solving ASTAR-RIS ON/OFF vector x, which involves the complexity of O L 2 based on (53). Hence, the complexity of solving (44) with Algorithm 2 is O T 2 T 3 L 2 , where T 2 is the number of inner iterations by updating primal variables and dual variables and T 3 is the number of outer iterations by updating the parameter λ. To solve (52) using the gradient method, the complexity at each step is O (L(L + 1)/2) 3 since the dimension of the variables in (52) is O(L(L + 1)/2). ...
Article
Full-text available
As the demand for high-speed data transmission grows with the expected emergence of 6G networks and the proliferation of wireless devices, more than traditional wireless infrastructure may be required. Small cell networks (ScNs) integrated with reconfigurable intelligent surfaces (RISs) and multiple-input-multiple-output (MIMO) have emerged as promising solutions to address this issue. However, ScNs have resource allocation limitations, and traditional RISs can only reflect signals in a limited propagation space of 1800180^{0} with fixed reflection properties. This paper proposes a novel approach to overcome these challenges by introducing actively simultaneously transmitting and reflecting (ASTAR)-RISs. Unlike conventional RIS, ASTAR-RISs actively amplify and transmit signals, effectively mitigating the limited propagation challenge and improving signal strength, especially in dense ScNs. This approach enhances the quality of service in complex channel environments by amplifying, on top of reflection, from the macro base station (mBS), improving the overall signal strength, and providing 3600360^{0} flexible propagation space. Furthermore, ASTAR-RIS enables dynamic beam management, significantly improving signal coverage and interference management, which are crucial in dense deployments. In this work, we propose a network architecture where distributed ASTAR-RIS units are deployed to assist small cell mBSs by optimizing signal coverage and enhancing communication performance. ASTAR-RISs dynamically control signal reflection and amplification, complementing the functionality of traditional small-cell BSs in dense network environments. Using the MIMO technique, we design phase shifts for ASTAR elements and develop optimal hybrid beamforming for users at the mBS. We dynamically control the ON/OFF status of the ASTAR-RIS based on active or idle status. We propose an efficient model that ensures fairness of signal-to-noise ratio (SNR) for all users and minimizes overall power consumption while meeting user SNR and phase shift constraints. To this end, we integrate robust beamforming and power allocation strategies, ensuring the system maintains reliable performance even under imperfect channel state information (CSI). We formulate a max-min optimization problem that optimizes the SNR and power consumption, subject to the ON/OFF status, phase shift, and power budget of the ASTAR-RIS. Our proposed method uses an alternating optimization algorithm to optimize the phase shift matrix at the ASTAR-RIS and the hybrid beamforming at the mBS. The approach includes two transmission schemes, and the phase optimization problem is solved using a successive convex approximation method that offers a closed-form solution at each step. Additionally, we use the dual method to determine the optimal ON/OFF status of the ASTAR-RIS. Comprehensive simulations validate the robustness and scalability of our proposed solution, particularly under varying network densities and CSI uncertainties. provides significant performance improvements over 170% compared to traditional RIS schemes.
... In [151], it was shown that RISassisted systems can still achieve the squared SNR scaling law and the linear diversity order scaling as the number of RIS elements grows, although the achievable rate is degraded due to the phase error. The authors of [152] showed that the performance degradation in the high-SNR regime is mainly attributed to the transceiver's hardware impairments rather than the RIS phase noise, since the RIS beamforming simultaneously affects the desired signal and imperfectioninduced noise. Channel impairments due to wet or dirty RIS surfaces may also affect communication performance in practice, although this issue has not been well studied and thus deserves future investigation. ...
... Nearly-passive RISs CSI Acquisition [19], [95], [115], [129]- [142], [153]- [155] Beamforming Design [131], [134], [143]- [147], [149] Hardware Impairments [150]- [152] Multiple RISs [191]- [193] Active RISs ...
Article
To accommodate new applications such as extended reality, fully autonomous vehicular networks and the metaverse, next generation wireless networks are going to be subject to much more stringent performance requirements than the fifth-generation (5G) in terms of data rates, reliability, latency, and connectivity. It is thus necessary to develop next generation advanced transceiver (NGAT) technologies for efficient signal transmission and reception. In this tutorial, we explore the evolution of NGAT from three different perspectives. Specifically, we first provide an overview of new-field NGAT technology, which shifts from conventional far-field channel models to new near-field channel models. Then, three new-form NGAT technologies and their design challenges are presented, including reconfigurable intelligent surfaces, flexible antennas, and holographic multi-input multi-output (MIMO) systems. Subsequently, we discuss recent advances in semantic-aware NGAT technologies, which can utilize new metrics for advanced transceiver designs. Finally, we point out other promising transceiver technologies for future research.
... complex Gaussian random variables that adhere to the distribution of CN(0, 1) [37], [38]. Additionally, using the uniform square planar array (USPA) model, we characterize the LOS routes of the cascaded channel between the RIS and the BS [39]. ...
Article
Full-text available
The rapid and low-power configuration capabilities of Reconfigurable Intelligent Surfaces (RISs) have made them an attractive option for future wireless networks in terms of energy efficiency. They have the ability to greatly increase connection and facilitate low-latency communications. However, because RIS-based systems often have a large number of RIS unit elements and unique hardware constraints, accurate and low-overhead channel estimate remains a crucial challenge. In this study, we offer a channel estimation framework and concentrate on the uplink of a multi-user multiple-input multiple-output (MU-MIMO) communication system driven by RIS. Our primary goal is to enhance the achievable rate and system capacity. We derive a closed-form deterministic expression for the uplink achievable rate under practical scenarios where channel state information (CSI) is not directly known and must be estimated. In contrast to previous studies assuming perfect CSI, our approach incorporates the channel estimation process, leading to a more realistic performance assessment. Extensive simulations validate the tightness of our derived expression compared to the actual achievable rate across various system parameters (with discrepancies typically within 2-5%). The results highlight the significant impact of RIS on system performance enhancement, even with imperfect CSI. Our findings provide crucial insights into the deployment and optimization of RIS-assisted multi-user wireless networks, underscoring their potential for substantial improvements in rate and capacity.
... Assume the RIS is on the xoy-plane shown in Fig. 1, and , the realization number is 5000, and Doppler effect is ignored. 6 We employ cos(⋅) as the NF pixel gain function in this paper. 7 While M = 200 is sufficient to demonstrate the benefits of the RIS [12], we choose a larger value for M in this study to ensure a typical NF scenario [3] and to obtain more compelling Monte Carlo results. ...
Conference Paper
Full-text available
Near-field reconfigurable intelligent surfaces (RISs) are unlocking promising potentials for the next generation of communications. Different from prior works that separately address phase shifts with errors and phase-dependent amplitudes (PDAs) in the RIS pixel hardware, this paper jointly studies power losses (PLs) caused by these two impairment factors. We propose three different pixel reflection models to accommodate different practical scenarios and derive their approximated upper bounds on the PL. It is important to note that neglecting uncertainties in the PDA may lead to an overestimation of the performance improvement offered by the RIS, thereby explaining the discrepancy between analytical and measurement results in several previous studies. Numerical simulations verify the correctness of the theoretical results.
Article
This study proposes a two-timescale transmission scheme for extremely large-scale reconfigurable intelligent surface aided (XL-RIS-aided) massive multi-input multi-output (MIMO) systems in the presence of visibility regions (VRs). The beamforming of base stations (BSs) is designed based on rapidly changing instantaneous channel state information (CSI), while the phase shifts of RIS are configured based on slowly varying statistical CSI. Specifically, we first formulate a system model with spatially correlated Rician fading channels and introduce the concept of VRs. Then, we derive a closed-form approximate expression for the achievable rate and analyze the impact of VRs on system performance and computational complexity. Then, we solve the problem of maximizing the minimum user rate by optimizing the phase shifts of RIS through an algorithm based on accelerated gradient ascent. Finally, we present numerical results to validate the performance of the considered system from different aspects and reveal the low system complexity of deploying XL-RIS in massive MIMO systems with the help of VRs.
Article
Full-text available
The increasing demand for efficient and reliable wireless communication has driven interest in Intelligent Reflecting Surfaces (IRS). This study introduces a novel 3D stochastic geometry model for IRS-assisted communication, uniquely integrating Uniform Rectangular Arrays (URA) as transmitters to evaluate the impact of hardware impairments (HWI) on spectral efficiency (SE) and outage probability. Unlike prior works, this study incorporates realistic system constraints, including phase noise, amplifier nonlinearities, and channel state information errors, into a comprehensive 3D framework. Our findings reveal that distortion noise resulting from HWI reduces SE by up to 45% while increasing IRS elements and optimizing URA configurations can mitigate these effects. This work establishes a benchmark for advancing IRS-assisted communication by addressing practical deployment challenges and offering insights critical for next-generation wireless networks.
Preprint
Full-text available
Reconfigurable Intelligent Surfaces (RISs) are a promising technique for enhancing the performance of Next Generation (NextG) wireless communication systems in terms of both spectral and energy efficiency, as well as resource utilization. However, current RIS research has primarily focused on theoretical modeling and Physical (PHY) layer considerations only. Full protocol stack emulation and accurate modeling of the propagation characteristics of the wireless channel are necessary for studying the benefits introduced by RIS technology across various spectrum bands and use-cases. In this paper, we propose, for the first time: (i) accurate PHY layer RIS-enabled channel modeling through Geometry-Based Stochastic Models (GBSMs), leveraging the QUAsi Deterministic RadIo channel GenerAtor (QuaDRiGa) open-source statistical ray-tracer; (ii) optimized resource allocation with RISs by comprehensively studying energy efficiency and power control on different portions of the spectrum through a single-leader multiple-followers Stackelberg game theoretical approach; (iii) full-stack emulation and performance evaluation of RIS-assisted channels with SCOPE/srsRAN for Enhanced Mobile Broadband (eMBB) and Ultra Reliable and Low Latency Communications (URLLC) applications in the worlds largest emulator of wireless systems with hardware-in-the-loop, namely Colosseum. Our findings indicate (i) the significant power savings in terms of energy efficiency achieved with RIS-assisted topologies, especially in the millimeter wave (mmWave) band; and (ii) the benefits introduced for Sub-6 GHz band User Equipments (UEs), where the deployment of a relatively small RIS (e.g., in the order of 100 RIS elements) can result in decreased levels of latency for URLLC services in resource-constrained environments.
Preprint
Full-text available
In this paper, we investigate a reconfigurable intelligent surface (RIS)-aided multiuser full-duplex secure communication system with hardware impairments at transceivers and RIS, where multiple eavesdroppers overhear the two-way transmitted signals simultaneously, and an RIS is applied to enhance the secrecy performance. Aiming at maximizing the sum secrecy rate (SSR), a joint optimization problem of the transmit beamforming at the base station (BS) and the reflecting beamforming at the RIS is formulated under the transmit power constraint of the BS and the unit modulus constraint of the phase shifters. As the environment is time-varying and the system is high-dimensional, this non-convex optimization problem is mathematically intractable. A deep reinforcement learning (DRL)-based algorithm is explored to obtain the satisfactory solution by repeatedly interacting with and learning from the dynamic environment. Extensive simulation results illustrate that the DRL-based secure beamforming algorithm is proved to be significantly effective in improving the SSR. It is also found that the performance of the DRL-based method can be greatly improved and the convergence speed of neural network can be accelerated with appropriate neural network parameters.
Article
Full-text available
Intelligent reflecting surfaces (IRSs) constitute a disruptive wireless communication technique capable of creating a controllable propagation environment. In this paper, we propose to invoke an IRS at the cell boundary of multiple cells to assist the downlink transmission to cell-edge users, whilst mitigating the inter-cell interference, which is a crucial issue in multicell communication systems. We aim for maximizing the weighted sum rate (WSR) of all users through jointly optimizing the active precoding matrices at the base stations (BSs) and the phase shifts at the IRS subject to each BS’s power constraint and unit modulus constraint. Both the BSs and the users are equipped with multiple antennas, which enhances the spectral efficiency by exploiting the spatial multiplexing gain. Due to the nonconvexity of the problem, we first reformulate it into an equivalent one, which is solved by using the block coordinate descent (BCD) algorithm, where the precoding matrices and phase shifts are alternately optimized. The optimal precoding matrices can be obtained in closed form, when fixing the phase shifts. A pair of efficient algorithms are proposed for solving the phase shift optimization problem, namely the Majorization-Minimization (MM) Algorithm and the Complex Circle Manifold (CCM) Method. Both algorithms are guaranteed to converge to at least locally optimal solutions. We also extend the proposed algorithms to the more general multiple-IRS and network MIMO scenarios. Finally, our simulation results confirm the advantages of introducing IRSs in enhancing the cell-edge user performance.
Article
Full-text available
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.
Article
Full-text available
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.
Article
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.
Article
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.
Article
The standardization of fifth generation (5G) communications has been completed, and the 5G network should be commercially launched in 2020. As a result, the visioning and planning of 6G communications has begun, with an aim to provide communication services for the future demands of the 2030s. Here, we provide a vision for 6G that could serve as a research guide in the post-5G era. We suggest that human-centric mobile communications will still be the most important application of 6G and the 6G network should be human centric. Thus, high security, secrecy and privacy should be key features of 6G and should be given particular attention by the wireless research community. To support this vision, we provide a systematic framework in which potential application scenarios of 6G are anticipated and subdivided. We subsequently define key potential features of 6G and discuss the required communication technologies. We also explore the issues beyond communication technologies that could hamper research and deployment of 6G. This Perspective provides a vision for sixth generation (6G) communications in which human-centric mobile communications are considered the most important application, and high security, secrecy and privacy are its key features.
Article
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.
Article
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.