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



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
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
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.
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:
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:
K. Wang is with the Department of Computer and Information Sciences, Northumbria University, Newcastle upon Tyne NE1 8ST, U.K.
M. Di Renzo is with Universit´e Paris-Saclay, CNRS and CentraleSup´elec, Laboratoire des Signaux et Syst`emes, Gif-sur-Yvette, France.
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:
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.
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
r, φe
t, φe
t, ϕe
where αand βare the corresponding strength of path AP-to-IRS and IRS-to-user, φa
r) is the azimuth
(elevation) angle of arrival (AoA) at IRS, φa
t) and ϕa
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-
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
ΘH1nRF +u, (4)
where e
θ1, ej˜
θN}with ˜
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
with δˆ
θ[0, π). Since the distortion noise is independent of channel noise, the received SNR is given by
ΘH1)CnRF (hH
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.
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
We identify the optimal reflecting beamforming of IRS by maximizing the received signal power as
Θopt = arg max
= arg max
= arg max
t, ϕe
r, φe
t, φe
= arg max
0x,y<N ,
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
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
log21 + P M N2η2|αβ|2sinc2(δψ)sinc2(δˆ
MN 2|αβ|2sinc2(δˆ
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
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
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 )¯
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
In the following Theorem 2, we give a closed-form expression of the optimal transmit power maximizing
the EE in (14).
SNR (dB)
0 2 4 6 8 10 12 14 16 18 20
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)
Ideal analysis in (12)
Ideal simulations
Non-ideal analysis in (11)
Non-ideal simulations
σ2= 0.3
σ2= 0.05
σ2= 0.05,
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
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
ideal =µP 1
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.
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
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.
Transmit Power P(dB)
-5 0 5 10 15 20 25
Energy Eciency (bits/s/Joule)
Ideal analysis
Non-ideal analysis
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.
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.
Applying (8) and (10), we can rewrite the downlink spectral efficiency in (6) as
R= log2 1 + P|hH
= log2
1 +
t, φe
t, φe
M |αβ|2
= log2
1 +
P η2|αβ|2PM
m=1 e(m)
n=1 ejˆ
n=1 ejˆ
where (c)is obtained by substituting the equations hH
t, φe
t)and hH
n=1 ejˆ
t, φe
For large M , we have
a.s. |E[e(m)]|2(e)
=|E[cos ψ(m)]|2(f)
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
Substituting (18) and (19) into (17) completes the proof.
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,
t=W(µ1eCAP1PC)CAP + 1,(22)
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
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).
[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:
[4] C. Pan et al., “Intelligent reflecting surface aided MIMO broadcasting for simultaneous wireless information and power
transfer, [Online]. Available:
[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:
[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:
[9] B. Di et al., “Hybrid beamforming for reconfigurable intelligent surface based multi-user communications: Achievable
rates with limited discrete phase shifts,” [Online]. Available:
[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:
[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.
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One of the main challenges facing optical wireless communication (OWC) systems is service disconnection in high blockage probability scenarios where users might lose the line of sight (LoS) connection with their corresponding access points (APs). In this work, we study the deployment of passive reflecting surfaces referred to as Intelligent Reflecting Surfaces (IRSs) in indoor visible light communication (VLC) to boost users signal to noise ratio (SNR) and ensure service continuity. We formulate an optimization problem to allocate APs and the mirrors of IRSs to users such that the sum rate is increased. The results show a 35% increase in the sum rate of the IRS-aided OWC system compared to the sum rate achieved by only considering the LoS channel components. The results also shows that the deployment of IRSs improves the sum rate under LoS blockage.
... 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. ...
The reconfigurable intelligent surface (RIS) has been recognized as an essential enabling technology for sixth-generation (6G) mobile communication networks. An RIS comprises a large number of small and low-cost reflecting elements whose parameters can be dynamically adjusted with a programmable controller. Each of these elements can effectively reflect a phase-shifted version of the incident electromagnetic wave. By configuring the wave phases in real time, the propagation environment of the information-bearing signals can be dynamically manipulated to enhance communication reliability, boost transmission rate, expand cellular coverage, and strengthen communication security. In this study, we provide an overview on RIS-assisted wireless communications. Specifically, we elaborate on the state-of-the-art enabling techniques for the RIS technology as well as their corresponding substantial benefits from the perspectives of RIS reflection and RIS modulation. With these benefits, we envision the integration of RISs into emerging applications for 6G. In addition, communication security is of unprecedented importance in future 6G networks with ubiquitous wireless services in multifarious verticals and areas. We highlight potential contributions of RISs to physical-layer security, in terms of secrecy rate and secrecy outage probability, exemplified by a typical case study from both theoretical and numerical aspects. Finally, we discuss challenges and opportunities on the deployment of RISs in practice to motivate future research.
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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.
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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.
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.
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.
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.
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.
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.