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RIS-Aided D2D Communications Relying on Statistical CSI with Imperfect Hardware

Authors:
  • Shanghai Normal University (China)
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Abstract

In this letter, we investigate a reconfigurable intelligent surfaces (RIS)-aided device to device (D2D) communication system over Rician fading channels with imperfect hardware including both hardware impairment at the transceivers and phase noise at the RISs. This paper has optimized the phase shift by a genetic algorithm (GA) method to maximize the achievable rate for the continuous phase shifts (CPSs) and discrete phase shifts (DPSs). We also consider the two special cases of no RIS hardware impairments (N-RIS-HWIs) and no transceiver hardware impairments (N-T-HWIs). We present closed-form expressions for the achievable rate of different cases and study the impact of hardware impairments on the communication quality. Finally, simulation results validate the analytic work.
arXiv:2112.02331v1 [eess.SP] 4 Dec 2021
1
RIS-Aided D2D Communications Relying on
Statistical CSI with Imperfect Hardware
Zhangjie Peng, Tianshu Li, Cunhua Pan, Member, IEEE, Hong Ren, Member, IEEE,
and Jiangzhou Wang, Fellow, IEEE
Abstract—In this letter, we investigate a reconfigurable intelli-
gent surfaces (RIS)-aided device to device (D2D) communication
system over Rician fading channels with imperfect hardware
including both hardware impairment at the transceivers and
phase noise at the RISs. This paper has optimized the phase shift
by a genetic algorithm (GA) method to maximize the achievable
rate for the continuous phase shifts (CPSs) and discrete phase
shifts (DPSs). We also consider the two special cases of no
RIS hardware impairments (N-RIS-HWIs) and no transceiver
hardware impairments (N-T-HWIs). We present closed-form
expressions for the achievable rate of different cases and study the
impact of hardware impairments on the communication quality.
Finally, simulation results validate the analytic work.
Index Terms—Reconfigurable intelligent surface (RIS), hard-
ware impairment, D2D communication, intelligent reflecting
surface (IRS).
I. INTRO DUC TIO N
Reconfigurable intelligent surface (RIS) is a new trans-
mission technology that can configure the radio channel in
a desired manner by optimizing the phase shift of each
reflecting element [1]. Due to their appealing properties of
low power consumption and low cost, RIS-aided wireless
communications have attracted much research attentions [2]–
[5]. Some initial attempts to study RIS-aided communication
systems include RIS-aided full-duplex systems [2], RIS-aided
physical layer security [3], RIS-aided wireless power transfer
[4], RIS-aided mobile edge computing [5], and RIS-aided
multiuser transmission [6]. The cascaded channel estimation
was studied in [7].
(Corresponding author: Cunhua Pan.)
Z. Peng is with the College of Information, Mechanical, and Electrical
Engineering, Shanghai Normal University, Shanghai 200234, China, also
with the National Mobile Communications Research Laboratory, Southeast
University, Nanjing 210096, China, and also with the Shanghai Engineering
Research Center of Intelligent Education and Bigdata, Shanghai Normal
University, Shanghai 200234, China (e-mail: pengzhangjie@shnu.edu.cn).
T. Li is with the College of Information, Mechanical and Electri-
cal Engineering, Shanghai Normal University, Shanghai 200234, China
(e-mail: 1000479056@smail.shnu.edu.cn).
C. Pan is with the School of Electronic Engineering and Computer
Science at Queen Mary University of London, London E1 4NS, U.K.
(e-mail: c.pan@qmul.ac.uk).
H. Ren is with the National Mobile Communications Research Laboratory,
Southeast University, Nanjing 210096, China (e-mail: hren@seu.edu.cn).
J. Wang is with the School of Engineering and Digital Arts, University of
Kent, CT2 7NT Canterbury, U.K. (e-mail: j.z.wang@kent.ac.uk).
D2D communication has received great attention to meet
the rapidly increasing demand for data traffic [8]. In D2D
communication in cellular networks, cellular and D2D users
transmit signals simultaneously using the same spectrum of
cellular users. However, there is a paucity of contributions on
RIS-aided D2D communications. In [9], the authors proposed
to deploy an RIS that can assist pairs of devices in their
communication when the direct links are blocked by high
buildings, plants and walls.
However, most of the existing contributions on D2D com-
munication are based on the assumption of perfect hardware
in the radio frequency chains [10] and the RISs [9]. Existing
studies have shown that hardware impairments adversely affect
the system performance of the multiple-input multiple-output
systems [11], [12]. In addition, an RIS has low hardware cost
[2]–[5], [9], which is prone to hardware imperfections.
Based on above, a natural question is whether we can
use non-ideal low-cost hardware to assist the D2D commu-
nications. Specifically, our contributions are summarized as
follows: 1) We consider an RIS-aided D2D communication
system over Rician fading channels, considering hardware
impairments both at the terminals and at the RISs. We assume
that the hardware impairment is coupling with the transmission
signal at the transceiver. Moreover, the random phase error
caused by the phase noise at the RIS follows the Von Mises
distribution; 2) we present the closed-form expressions for the
achievable rate in the general case of both hardware impair-
ments both at the terminals and at the RISs, which is then
maximized by a genetic algorithm (GA) method. To obtain
more design insights, we also study the two special cases of no
RIS hardware impairments (N-RIS-HWIs) and no transceiver
hardware impairments (N-T-HWIs); 3) we provide simulation
results to verify our derived expressions. In addition, the
exhaustive search method is used to show that our results can
achieve the globally optimal solution.
The rest of the letter is organized as follows. The model
for RIS-aided D2D communication system with hardware
impairments is depicted in Section II. We derive the sum
achievable rate’s expression and maximize it in Section III.
Numerical results are presented in Section IV. And conclusions
are drawn in Section V.
γi=pigT
biΘΦgai
2
K
P
j=1,j6=ipjgT
biΘΦgaj
2
+|gT
biΘΦGaΛηt|2+Υri +σ2
i
.(10)
Rilog2
1+ piαbi αai
εiβi˜
Γi,i+L(εi+βi)+L
(εi+1)(βi+1)
(1 + κr) (1 + κt)
K
P
j=1 pjαbiαaj
εiβj˜
Γi,j +L(εi+βj)+L
(εi+1)(βj+1) piαbiαai
εiβi˜
Γi,i+L(εi+βi)+L
(εi+1)(βi+1) +σ2
i
(13)
2
RN-RIS-HWIs
ilog2
1+ piαbi αai
εiβiΓi,i+L(εi+βi)+L
(εi+1)(βi+1)
(1 + κr) (1 + κt)
K
P
j=1 pjαbiαaj
εiβjΓi,j+L(εi+βj)+L
(εi+1)(βj+1) piαbiαai
εiβiΓi,i+L(εi+βi)+L
(εi+1)(βi+1) +σ2
i
(15)
RIS
1a
g
ai
g
aK
g
bi
g
bK
g
DT
i
DT
K
1
DT
1b
g
Fig. 1. System model for RIS-aided D2D communications.
II. SY S TE M MO DE L
We consider an RIS-aided D2D communication system,
where an RIS assists Kpairs of devices to exchange in-
formation, as shown in Fig. 1. It is assumed that there
are a total of KD2D links in the network, where the
ith single-antenna transmitter (receiver) is denoted by DTi
(DRi) for i= 1,···, K. In the overlay mode, the radio
resources occupied by D2D links are orthogonal to that of
the cellular links, which ensures no interference between
D2D links and cellular links. The RIS includes Lscattered-
reflection elements. And the phase shift matrix is denoted by
Θ=diag(ejθ1,···, e,···, eL), where θis the phase
shift of the th scattered-reflection element.
The channel between DTiand the RIS (the RIS and DRi)
can be written as gai =αaihai ,(1)
gbi =αbihbi ,(2)
where αai and αbi denote the large-scale fading coefficients,
and hai CL×1and hbi CL×1denote Rician fading
channels, which can be expressed as
hai =rεi
εi+ 1hai +r1
εi+ 1 ˜
hai,(3)
hbi =sβi
βi+ 1 hbi +r1
βi+ 1 ˜
hbi,(4)
where εiand βidenote the Rician factors, ˜
hai CL×1and
˜
hbi CL×1are non-line-of-sight components, whose entries
are standard Gaussian random variables with independent and
identical distribution, i.e., CN(0,1), and hai CL×1and
hbi CL×1are line-of-sight (LoS) components. Particularly,
hai and hbi can be written as
hai (ϕa
i, ϕe
i)="1,···, ej2πd
λ(xsin ϕa
isin ϕe
i+ycos ϕe
i),···,
ej2πd
λ((L1)sin ϕa
isin ϕe
i+(L1)cos ϕe
i)
#T
,(5)
hbi (ςa
i, ςe
i)="1,··· , ej2πd
λ(xsin ςa
isin ςe
i+ycos ςe
i),···,
ej2πd
λ((L1)sin ςa
isin ςe
i+(L1)cos ςe
i)
#T
,(6)
where 06x, y 6L1,ϕa
i, ϕe
i(ςa
i, ςe
i)respectively denote
the ith pair of devices’ azimuth and elevation angles of arrival
(angle of departure). We assume d=λ
2in our letter [1].
The signal transmitted from DTiis given by [11]
xi= ˆxi+ηti ,(7)
where ˆxi∼ CN(0,1) represents the data symbol, ηti
CN 0, κtE|ˆxi|2denotes the impact of impairments in the
transmitter hardware, and κt(0, 1) is the coefficient which
characterizes the impairments at the transmitter.
The RIS’s hardware impairments can take the form of phase
noise because the RIS is a passive device and highly accurate
reflection adjustment is impractical. The phase noise matrix
is denoted by Φ=diag(ej∆θ1,··· , ej∆θ,··· , ej∆θL), for
= 1,2,···, L.∆θis random phase error that follows
the Von Mises distribution with zero mean and concentration
parameter κ∆θ . Additionally, ∆θhas a characteristic function
χ=I1(κ∆θ)
I0(κ∆θ)with Ip(κ∆θ )being the modified Bessel function
of the first kind and order p[12].
We exploit statistical channel state information (CSI), which
varies much slowly than the instantaneous CSI and can be
readily obtained. The signal received at DRiis given by
yi=gT
biΘΦ
K
X
j=1
pjgajxj+ηri +ni
=gT
biΘΦGaΛx +ηri +ni,(8)
where Ga,[ga1,···,gaK ],x,[x1,···, xK]T,pjdenotes
the transmit power of UAj with Λ,diag (p1,···, pK),ηri
CN (0, Υr i)denotes the impact of impairments in the receiver
hardware with Υri =κrEn|gT
biΘΦGaΛx|2o,κr(0, 1)
is the coefficient which characterizes the impairments at the
receiver, and ni∼ CN(0, σ2
i)is the additive white Gaussian
noise at DRi, for i= 1,···, K.
To analyze the achievable rates, we consider the expansion
of (8) as follows
yi=pigT
biΘΦgai ˆxi+
K
X
j=1,j6=i
pjgT
biΘΦgaj ˆxj
+gT
biΘΦGaΛηt+ηri +ni,(9)
where ηt,[ηt1,···, ηtK ]T.
From (9), we obtain the signal-to-interference plus noise
ratio at DRiin (10) shown at the bottom of this page.
Therefore, the achievable rate for DRican be expressed as
Ri=E{log2(1 + γi)},(11)
and the sum achievable rate can be written as
C=
K
X
i=1
Ri.(12)
III. ACHI EVABLE RATE ANA LYS IS
In this section, we first derive an approximate expression for
the sum achievable rate in the following theorem. Then, we
consider two special cases of N-RIS-HWIs and N-T-HWIs.
Finally, we maximize the achievable rate with GA (genetic
algorithm) method.
3
Theorem 1. In a D2D communication system aided by RIS,
the ergodic sum achievable rate of DRican be approximated
as (13), where ˜
Γi,i and ˜
Γi,j can be given by
˜
Γi,h =E
L
X
=1
ej[(θ+∆θ)+πT n,m
i,h ]
2
=L+ 2χ2X
1m<nL
cos θnθm+πT n,m
i,h , h ∈ {i, j}(14)
where Tn,m
i,h = (xnxm)pi,h + (ynym)qi,h, with xz=
(z1)
L,yz= (z1) modL,z∈ {m, n},pi,h =
sin ϕa
isin ϕe
i+ sin ςa
hsin ςe
h, and qi,h = cos ϕe
i+ cos ςe
h.
Proof: See Appendix A.
Corollary 1. Assuming that the RIS hardware is ideal and thus
there is no phase noise, i.e., ∆θ= 0, for i= 1,2,···, N .
It follows Φ=IL. The rate of DRion N-RIS-HWIs can be
approximated as (15), where Γi,i and Γi,j can be defined as
Γi,h =L+ 2 X
1m<nL
cos θnθm+πT n,m
i,h , h ∈ {i, j}.(16)
Proof: When Φ=IL, we can use [9, Eq. (20) Eq. (21)],
and write EnhT
biΘhaj
2oand EnhT
biΘhai
2oas
EnhT
biΘhah
2o=εiβhΓi,h +L(εi+βh) + L
(εi+ 1)(βh+ 1) , h ∈ {i, j },
(17)
where Γi,h is defined in (16).
By substituting (17) into (30), we are able to obtain the final
result in (15). This completes the proof.
We aim to solve the achievable rate maximization problem
by optimizing the phase shifts matrix Θin the special case
with only one pair of users, i.e., K= 1. Without loss of
generality, the user pair is referred to as user pair i. We can
rewrite the achievable rate as
RN-RIS-HWIs
i
log2
1+
piαbiαai
(εi+1)(βi+1) (εiβiΓi,i +L(εi+βi)+L)
(κtκr+κt+κr
)piαbiαai
(εi+1)(βi+1)(εiβiΓi,i+L(εi+βi)+L)+σ2
i!.
(18)
The rate depends on the phase shifts matrix Θonly
through the intermediate variable Γi,i. Since Γi,i =
PL
=1 ej[θ+πT n,m
i,h ]
26PL
=1 |ej[θ+πT n,m
i,i ]|2=L2and
Γi,i 0, the optimization problem can be formulated as
follows max
Γi,i
RN-RIS-HWIs
i(19a)
s.t. 06Γi,i 6L2.(19b)
The expression for the first-order derivative of SINRii,i )
with respect to Γi,i is
SINRii,i)
Γi,i
=piαbiαai
(εi+1)(βi+1) εiβiσ2
i
h(κtκr+κt+κr
)piαbiαai
(εi+1)(βi+1) (εiβiΓi,i +L(εi+βi)+L)+ σ2
ii2
>0.(20)
Thus, the optimal design for Θcorresponds to setting Γi,i =
L2, where the optimal phase shifts of all the RIS elements
are given by θ=πT n,m
i,h +C0,, and C0is an arbitrary
constant.
Considering this single-user system with optimal phase
shift, we assume the transmit power is scaled as pi=Eu
L2
and pi=Eu
Lwith L→ ∞. If the transmit power is scaled as
pi=Eu
L2, the rate becomes
RNRISHWIs
i(21)
log2
1+
Euαbiαai εiβi
(εi+1)(βi+1)
(κtκr+κt+κr
)Euαbiαai εiβi
(εi+1)(βi+1) +σ2
i!,as L→ ∞.
If the transmit power is scaled as pi=Eu
L, the rate becomes
RNRISHWIs
ilog2
1+ 1
κtκr+κt+κr,as L→ ∞.(22)
In this case, the achievable rate only depends on the
impairment coefficients at the transceiver when Lgrows into
infinity.
Corollary 2. Assuming that the transceiver hardware is ideal,
i.e., κt=κr= 0. The rate of DRiwith N-T-HWIs can be
approximated as
RN-T-HWIs
i
log2
1+ piαbi αai
εiβi˜
Γi,i+L(εi+βi)+L
(εi+1)(βi+1)
K
P
j=1,j6=ipjαbiαaj
εiβj˜
Γi,j +L(εi+βj)+L
(εi+1)(βj+1) +σ2
i
.(23)
We design the phase shift with one pair of users, the
achievable rate is
RN-T-HWIs
ilog2
1+ piαbiαai
εiβi˜
Γi,i+L(εi+βi)+L
(εi+1)(βi+1)
σ2
i
,(24)
which is a monotonically increasing function of ˜
Γi,i. The
optimal design for Θcorresponds to setting ˜
Γi,i =L2, where
the optimal phase shifts of all the RIS elements are given by
θ=πT n,m
i,h +C1,, and C1is an arbitrary constant.
Considering this single-user system with optimal phase
shift, we assume the transmit power is scaled as pi=Eu
L2
with L→ ∞. If the transmit power is scaled as pi=Eu
L2, the
rate becomes
RNTHWIs
ilog2
1+ Euαbi αai εiβi
σ2
i(εi+ 1) ( βi+ 1),as L→ ∞.(25)
Due to the first-order derivative of the sum rate with respect
to the phase shift Θis quite hard to obtain, we maximize the
rate with the GA method adopted in [9] by optimizing the
phase shifts. The complexity of the proposed GA algorithm is
Ntn, where Ntis the population size, and nis the number of
generations evaluated. We take into account both continuous
phase shifts (CPSs) and discrete phase shifts (DPSs). In
practice, only a limited number of phase shifts can be used.
We assume that the phase shift of the reflecting elements is
quantized with Bbits when considering DPS, and thus 2B
phase shifts can be chosen for each reflecting element.
IV. NUM ERI CA L RE SU LTS
We evaluate the impact of various parameters on the data
rate performance. We set SNR = pi,εi= 10 dB, κ=κt=κr,
κ∆θ = 4, σ2
i= 1, and ϕa
i=ϕe
iand ςa
i=ςe
iare respectively
set as ϕiand ςiin [9], for i= 1,···, K . Other parameters
are set the same as [9].
4
-10 -5 0 5 10 15 20 25
SNR (dB)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Sum Rate (bits/s/Hz)
N-RIS-HWIs
= 4
= 2
= 1
= 0
simulation
rand scheme ( = 0)
Fig. 2. Sum achievable rate versus SNR with L= 16, K= 6, κ= 0.05,B
= 2.
-10 -5 0 5 10 15 20 25
SNR (dB)
0
0.5
1
1.5
2
2.5
3
3.5
4
Sum Rate (bits/s/Hz)
GA(N-T-HWIs, = 0)
exhaustion (N-T-HWIs, = 0)
GA( = 0.01)
exhaustion( = 0.01)
GA( = 0.05)
exhaustion( = 0.05)
rand scheme
Fig. 3. Sum achievable rate versus SNR with L= 9, K= 2 and B= 2.
In Fig. 2, we depict the rate in (12) versus the SNR obtained
from the approximate expression in (30) and Monte-Carlo
simulations from (11), when L= 16, K= 6, κ= 0.05, B
= 2. The Monte-Carlo simulation results match the analytical
expressions well, which verifies the data rate performance.
Furthermore, the rate with N-RIS-HWIs performs better than
the case with RIS-HWIs. As κ∆θ decreases, the rate decreases.
Additionally, when κ∆θ = 0, the Von Mises distribution de-
generates into the uniform distribution, i.e., ∆θ∼ U[π, π),
for = 1,2,···, L. In this case, the random scheme curve
has the same performance as that of our derived results, which
demonstrate that there is no need to optimize the phase shift.
The phenomenon is consistent with the result in [12].
Fig. 3 shows the sum rate versus the SNR when L= 8, K
= 2, and B= 2. We can reduce the harmful impact of the
T-HWIs by tuning the phase shifts of the RIS. Compared with
the random scheme, the optimal phase shift can achieve higher
rate. It is worth noting that the proposed GA method achieves
similar performance to the exhaustive search, which implies
that our proposed algorithm can achieve almost the globally
optimal solution. Moveover, we observe that different levels of
hardware impairment obtain different rate: the higher the level
of the hardware impairment, the worse the performance of the
rate. The rate with the ideal transceiver hardware (N-T-HWIs,
κ= 0) performs the best, as expected.
Fig. 4 illustrates the rate versus the Rician factor when SNR
= 20 dB and B= 2. In all cases, with different values of L
and K, the rates approach the fixed value as Rician factor
εi→ ∞. This is because the channels are mainly influenced
by LoS component when Rician factor is large.
Fig. 5 shows the sum rate versus B. The figure shows
that, under the condition of DPS, three quantization bits are
-10 0 10 20 30 40 50 60
Rician factor (dB)
0.5
1
1.5
2
2.5
3
3.5
Sum Rate (bits/s/Hz)
= 0.01 (L = 16,K = 4)
= 0.05 (L = 16,K = 4)
= 0.01 (L = 9,K = 2)
= 0.05 (L = 9,K = 2)
simulation
Fig. 4. Sum achievable rate versus Rician factor with B= 2 and SNR = 20
dB.
123456
Number of coding bits B
1
1.5
2
2.5
3
3.5
Sum Rate (bits/s/Hz)
DPSs ( = 0.01,L = 16,K = 4)
DPSs ( = 0.05,L = 16,K = 4)
DPSs ( = 0.01,L = 9,K = 4)
DPSs ( = 0.05,L = 9,K = 4)
CPSs
Fig. 5. Sum achievable rate versus Bwith εi= 10 dB and SNR = 20 dB.
sufficient, which provides useful insight into the engineering
design of systems aided by RISs. In addition, to resolve
the issue caused by imperfect hardware, we can increase the
number of low-cost reflection elements.
V. CO NCL US I ON
In this letter, we investigated an RIS-aided D2D com-
munication system over Rician fading channels, considering
hardware impairments both at the terminals and the RISs. We
considered two special cases of N-RIS-HWIs and N-T-HWIs.
We derived closed-form expressions for the achievable rate of
different cases. The impact of the hardware impairment on the
system performance have been observed. To resolve the issue
caused by imperfect hardware, we can increase the number of
low-cost reflection elements. Additionally, three quantization
bits are sufficient for the DPSs setup, which provides useful
insight into the engineering design of systems aided by RISs.
Moreover, the extension to jointly optimizing power allocation
and the phase shifts of the RIS will be left for our future work.
APP EN D IX A
PROO F OF THE ORE M 1
Using Lemma 1 in [13], Riin (11) is approximated as (23).
Next, we derive EngT
biΘΦgai
2o,EngT
biΘΦgaj
2o,
En|gT
biΘΦGaΛηt|2o, and Υr j . To begin with, we have
EngT
biΘΦgah
2o=αbiαah EnhT
biΘΦhah
2o, h ∈ {i, j}.
(24)
Both En|gT
biΘΦGaΛηt|2oand Υrj contain the terms of
EnhT
biΘΦhai
2oand EnhT
biΘΦhaj
2o. We derive these
items later.
5
Rilog2
1 +
piEngT
biΘΦgai
2o
K
P
j=1,j6=ipjEngT
biΘΦgaj
2o+En|gT
biΘΦGaΛηt|2o+Υri +σ2
i
(23)
Υrj =κrEn|gT
biΘΦGaΛx|2o=κrEngT
biΘΦGaΛ(ˆx +ηt)ˆxH+ηH
tΛHGH
aΦHΘHg
bio
(a)
=κrEngT
biΘΦGaΛEnˆxH+ˆxηH
t+ηtˆxH+ηtηH
toΛHGH
aΦHΘHg
bi
o(b)
=κr(1+ κt)EngT
biΘΦGaΛGH
aΦHΘHg
bi
o(26)
Rilog2
1+
piαbiαai EnhT
biΘΦhai
2o
K
P
j=1,j6=ipjαbi αaj EnhT
biΘΦhaj
2o+ (κtκr+κt+κr)αbi
K
P
j=1 αaj pjE|hT
biΘΦhaj |2+σ2
i
= log2
1+
piαbiαai EnhT
biΘΦhai
2o
(1 + κr) (1 + κt)
K
P
j=1 pjαbiαaj E|hT
biΘΦhaj |2piαbiαaiEnhT
biΘΦhai
2o+σ2
i
(30)
Then, En|gT
biΘΦGaΛηt|2ocan be written as follows
En|gT
biΘΦGaΛηt|2o=κtEgT
biΘΦGaΛGH
aΦHΘHg
bi.
(25)
Υrj also contains the terms of
EgT
biΘΦGaΛGH
aΦHΘHg
bi, which we will derive
later.
Moreover, Υrj is calculated in (26) at the top of this page.
Equality in (a) is obtained because ˆx is independent of both
gbi and Ga;ηtis also independent of both gbi and Ga.
Additionally, equality in (b) uses the following results
EnˆxHo=IK,EηtηH
t=κtIK,(27)
EˆxηH
t=0,EηtˆxH=0.(28)
We can find En|gT
biΘΦGaΛηt|2oand Υrj contain the
item EngT
biΘΦGaΛGH
aΦHΘHg
bio, given by
EngT
biΘΦGaΛGH
aΦHΘHg
bio
(c)
=αbiEnhT
biΘΦHapDaΛpDa
HHH
aΘΦHh
bio
=αbiE
K
X
j=1
αaj pj|hT
biΘΦhaj |2
=
K
X
j=1
αbiαaj pjE|hT
biΘΦhaj |2.(29)
We obtain equality in (c) by defining Da,
diag (αa1,···, αaK ).
Substituting (24), (25), (26) and (29) into (23), we obtain
(30). Employing the results of [9, Eq. (20) Eq. (21)] one
obtains
EnhT
biΘΦhah
2o=εiβh˜
Γi,h +L(εi+βh) + L
(εi+ 1)(βh+ 1) , h ∈ {i, j },
(31)
where ˜
Γi,h is defined by
˜
Γi,h=L+2 X
1m<nL
Encos h(θn+∆θn)(θm+∆θm) + πT n,m
i,h io.
(32)
With the help of
Encos h(θn+∆θn)(θm+∆θm) + πT n,m
i,h io
=χ2cos hθnθm+πT n,m
i,h i,(33)
˜
Γi,h can be further given in (14).
By substituting (31) into (30), we are able to obtain the final
result in (13). The proof of theorem 1 is completed.
REF ERE NC E S
[1] C. Pan et al., “Reconfigurable intelligent surfaces for 6G systems:
Principles, applications, and research directions,IEEE Commun. Mag.,
vol. 59, no. 6, pp. 14–20, Jun. 2021.
[2] Z. Peng, Z. Zhang, C. Pan, L. Li, and A. L. Swindlehurst, “Multiuser
full-duplex two-way communications via intelligent reflecting surface,
IEEE Trans. Signal Process., vol. 69, pp. 837–851, Jan. 2021.
[3] 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.
[4] C. Pan et al., “Intelligent reflecting surface aided MIMO broadcasting
for simultaneous wireless information and power transfer,” IEEE J. Sel.
Areas Commun., vol. 38, no. 8, pp. 1719–1734, Aug. 2020.
[5] T. Bai, C. Pan, Y. Deng, M. Elkashlan, A. Nallanathan, and L. Hanzo,
“Latency minimization for intelligent reflecting surface aided mobile
edge computing,IEEE J. Sel. Areas Commun., vol. 38, no. 11, pp.
2666–2682, Nov. 2020.
[6] Z. Yang, W. Xu, C. Huang, J. Shi, and M. Shikh-Bahaei, “Beamforming
design for multiuser transmission through reconfigurable intelligent
surface,IEEE Trans. Commun., vol. 69, no. 1, pp. 589–601, Jan. 2021.
[7] B. Zheng and R. Zhang, “Intelligent reflecting surface-enhanced OFDM:
Channel estimation and reflection optimization,” IEEE Wireless Com-
mun. Lett., vol. 9, no. 4, pp. 518–522, Apr. 2020.
[8] J. Lee and J. H. Lee, “Performance analysis and resource allocation
for cooperative D2D communication in cellular networks with multiple
D2D pairs,” IEEE Commun. Lett., vol. 23, no. 5, pp. 909–912, May
2019.
[9] Z. Peng, T. Li, C. Pan, H. Ren, W. Xu, and M. D. Renzo, “Analysis
and optimization for RIS-aided multi-pair communications relying on
statistical CSI,” IEEE Trans. Veh. Technol., vol. 70, no. 4, pp. 3897–
3901, Apr. 2021.
[10] N. Serafimovski et al., “Practical implementation of spatial modulation,”
IEEE Trans. Veh. Technol., vol. 62, no. 9, pp. 4511–4523, Nov. 2013.
[11] A. Afana and S. Ikki, “Analytical framework for space shift keying mimo
systems with hardware impairments and co-channel interference,” IEEE
Commun. Lett., vol. 21, no. 3, pp. 488–491, Mar. 2017.
[12] A. Papazafeiropoulos, C. Pan, P. Kourtessis, S. Chatzinotas, and J. M.
Senior, “Intelligent Reflecting Surface-assisted MU-MISO Systems
with Imperfect Hardware: Channel Estimation, Beamforming Design,”
2021. [Online]. Available: https://arxiv.org/abs/2102.05333v1
[13] Q. Zhang, S. Jin, K.-K. Wong, H. Zhu, and M. Matthaiou, “Power
scaling of uplink massive MIMO systems with arbitrary-rank channel
means,” IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp. 966–981,
Oct. 2014.
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