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IEEE WIRELESS COMMUNICATIONS LETTERS 1
Beamforming Design for Active IOS Aided NOMA Networks
Hao Luo, Lu Lv, Member, IEEE, Qingqing Wu, Senior Member, IEEE, Zhiguo Ding, Fellow, IEEE,
Naofal Al-Dhahir, Fellow, IEEE, and Jian Chen, Member, IEEE
Abstract—This letter investigates a new active intelligent omni-
surface (IOS) aided non-orthogonal multiple access (NOMA)
network. In particular, simple active devices are introduced into
the IOS to overcome the “double-fading” effect. A sum achievable
rate optimization problem is formulated, where the beamforming
vector at the base station and the active IOS coefficients are jointly
optimized while satisfying the quality of service requirements of
the users. Then, an efficient alternating optimization algorithm
is developed to obtain the stationary point solution. Numerical
results demonstrate the performance advantage of the proposed
active IOS aided NOMA design.
Index Terms—Intelligent omni-surface, simultaneous refraction
and reflection, non-orthogonal multiple access.
I. INTRODUCTION
The intelligent omni-surface (IOS)1, which is capable of
the dual functionality of signal reflection and refraction, has
recently attracted increased attention. Technically, the IOS can
respond to both the electrical and magnetic components of the
incident field, which makes the IOS elements refract and reflect
incident signals simultaneously, thereby achieving full spatial
signal coverage [1], [2]. Furthermore, integrating IOS with non-
orthogonal multiple access (NOMA) increases the flexibility for
communication design, since the use of NOMA can improve
the spectral efficiency and connectivity of IOS networks [3],
[4]. In this context, several latest research has studied the
synergistic integration of IOS and NOMA for enhanced network
performance [5]–[7].
The aforementioned research focused on passive IOS aided
NOMA networks. It is worthy of mentioning that the network
performance with passive IOS is highly limited by the “double-
fading” effect [8]. Although this drawback can be alleviated
by increasing the number of IOS elements to reap the square-
order array gain, implementing such a huge size IOS may
be impractical in an indoor environment or Internet-of-Things
networks. To overcome the “double-fading” limitation, simple
active load impedance is introduced in the reconfigurable intel-
ligent surface (RIS) aided orthogonal multiple access (OMA)
This work was supported by the National Natural Science Foundation of
China under Grants 62271368, 61901313, and 61971320. The work of N. Al-
Dhahir is supported by Erik Jonsson Distinguished Professorship. (Correspond-
ing author: Jian Chen).
Hao Luo, Lu Lv, and Jian Chen are with the School of Telecommunications
Engineering, Xidian University, Xi’an 710071, China (e-mail: 18010500073@s-
tu.xidian.edu.cn; lulv@xidian.edu.cn; jianchen@mail.xidian.edu.cn).
Qingqing Wu is with the Department of Electronic Engineering, Shanghai Jiao
Tong University, Shanghai 200240, China (e-mail: wu.qq1010@gmail.com).
Zhiguo Ding is with the School of Electrical and Electronic Engineer-
ing, The University of Manchester, Manchester M13 9PL, U.K. (e-mail:
zhiguo.ding@manchester.ac.uk).
Naofal Al-Dhahir is with the Department of Electrical and Computer Engi-
neering, The University of Texas at Dallas, Richardson, TX 75080, USA (e-mail:
aldhahir@utdallas.edu).
1The IOS and the simultaneously transmitting and reflecting reconfigurable
intelligent surface (STAR-RIS) have the same signal processing functionality
but with different hardware implementations [1]. Thus, these two terminologies
are interchangeable, and without loss of generality, we use the IOS term in this
work.
networks to amplify the incident signals [9], [10]. In [11], the
received signal-to-noise ratio (SNR) was maximized by jointly
optimizing the receive and reflect beamforming, under the RIS
power budget constraint. In [12], the capacity of an active
RIS aided system was maximized by a joint transmission and
reflection precoding algorithm.
Although existing works have provided a fundamental under-
standing of passive IOS and active RIS aided wireless networks,
the investigation of active IOS aided NOMA networks is still
in the initial stage. Theoretically, an active IOS aided NOMA
network is capable of extending the coverage area of the con-
nected users and improving the flexibility of IOS deployment.
Moreover, existing research has rarely studied how joint trans-
mit beamforming, IOS phase shifts and amplitude adjustment
solutions benefit the network sum rate performance. In fact,
the use of the active IOS not only ameliorates the “double-
fading” effect by signal amplification, but also leads to strong
NOMA inter-user interference and consumes additional power
resources, which calls for an efficient beamforming design for
interference management. Thus, more in-depth investigations
need to be carried out to design and optimize the performance
of an active IOS aided NOMA network.
To fill the above research gap, we investigate the design and
optimization of an active IOS aided NOMA network. The main
contributions are listed as follows.
•A new active IOS aided NOMA design is proposed to over-
come the “double-fading” effect and improve the network
connectivity. In particular, each IOS element is supported
by a set of active load impedances to amplify the incident
signal with low-cost hardware.
•A joint beamforming optimization problem is formulated to
maximize the sum achievable rate of the active IOS aided
NOMA network. Then, an efficient alternating optimization
(AO) algorithm is developed to transform the highly-
coupled non-convex optimization problem into a tractable
form with decoupled optimization variables.
•Numerical results are provided to demonstrate the efficien-
cy of the proposed design. Our results show that with a
relatively small number of IOS elements, the proposed
design achieves a significantly larger sum rate than the
baseline schemes. Furthermore, under the same overall
power budget of the network, the proposed design out-
performs the conventional passive IOS in terms of both
spectrum and energy efficiency.
II. SY ST EM MO DE L AND PRO BL EM FO RM UL ATIO N
Consider an active IOS aided NOMA network2, which con-
sists of a base station (BS) equipped with N-antennas, an active
2In general, the considered system can be applied to outdoor-to-indoor com-
munications, Internet-of-Things network, simultaneous wireless information and
power transfer, and outdoor/indoor environment, and help achieve ubiquitous
connectivity.
IEEE WIRELESS COMMUNICATIONS LETTERS 2
IOS equipped with Mrefracting/reflecting elements, and two
single-antenna users, namely r-user and t-user, respectively. The
r-user is located in the reflection space (i.e., the same side) of
the IOS , while the t-user is located in the refraction space
(i.e., the opposite side) of the IOS. We assume that the direct
communication links between the BS and the users are blocked
by obstacles, such that both the t-user and r-user can only be
served with the aid of the IOS. Let G∈CM×N,hH
t∈C1×M,
hH
r∈C1×Mdenote the channel coefficients from the BS to
the IOS, the IOS to the t-user, and the IOS to the r-user,
respectively. To unleash the full potential of the active IOS, we
assume that the perfect channel state information of all channels
is available at the BS.
1) Active IOS and Signal Models: Different from the passive
IOS [5]–[7], the active IOS can amplify the signal by using
a simple amplifier. To describe this characteristic, we use
amto represent the signal amplification factor of the m-th
element, where m∈M,{1,2. . . , M }. Without loss of
generality, we assume that amcan take any positive value.
The amplitude amplification matrices of the active IOS for
the t-user and r-user are Pt=diag(at,1, at,2, . . . , at,M )and
Pr=diag(ar,1, ar,2, . . . , ar,M). The refraction and reflection
phase matrices of the IOS are Θt=diag(ejθt
1, ejθt
2, . . . , ejθt
M)
and Θr=diag(ejθr
1, ejθr
2, . . . , ejθr
M), where θt
m∈[0,2π)and
θr
m∈[0,2π)denote the refraction and reflection phase shifts of
the m-th element at the IOS, respectively.
To improve the network spectral efficiency, the BS applies the
NOMA principle to communicate with the two users over the
same time/frequency resource [4], and the active IOS operates
in the energy splitting mode to facilitate simultaneous signal re-
fraction and reflection. Let wkand xkdenote the beamforming
vector and transmitted information symbols at the BS for the
k-user, where k∈ {r, t}and E[|xk|2]=1. The signal received
by the k-user is given by
yk=hH
kPkΘkG(wtxt+wrxr) + hH
kPkΘkv+nk,(1)
where v∈CM×1denotes the additive noise incurred by the
active devices of the IOS with v∼ CN (0, σ 2
vIM), and nk∼
CN (0, σ 2
k)denotes the additive white Gaussian noise (AWGN)
at the k-user, respectively.
For notational convenience, we denote the effective power
gain for the k-user by |ck|2=|hH
kPkΘkGwk|2, and let the
binary variable π(k)denote the NOMA decoding order of the
k-user. Specifically, if the t-user is the strong user with a higher
effective power gain, it first decodes the r-user signal by treating
its own signal as interference, and then removes this signal via
successive interference cancellation (SIC) and decodes its own
signal. While the r-user decodes its own signal directly. In this
case, we have π(t) = 1 and π(r) = 0. Otherwise, π(t) = 0 and
π(r) = 1. Hence, the achievable rate of the k-user is given by
Rk= log21 + |ck|2
σ2
k+|hH
kPkΘk|2σ2
v+π(¯
k)|¯ck|2,(2)
where ¯ck=hH
kPkΘkGw¯
k,¯
k=r, if k=t; and ¯
k=t,
otherwise.
2) Problem Formulation: Our goal is to maximize the sum
achievable rate of the active IOS aided NOMA network. Specif-
ically, the BS beamforming, the IOS beamforming, and the NO-
MA decoding order are jointly optimized, subject to the users’
quality-of-service (QoS) requirements and the power budget at
the BS and IOS. The optimization problem is formulated as3
(P1) max
Pk,Θk,wk,π(k)Rt+Rr(3a)
s.t. Rt≥γ, Rr≥γ, (3b)
∥wt∥2+∥wr∥2≤Pb,(3c)
|PtΘtGwt|2+|PtΘt|2σ2
v
+|PrΘrGwr|2+|PrΘr|2σ2
v≤Pmax
out ,(3d)
(a2
t,m +a2
r,m)(pin
m+σ2
v)≤pm,∀m∈M,(3e)
M
m=1
pm≤Pmax
out ,(3f)
M
m=1
pin
m≤ |Gwt|2+|Gwr|2,(3g)
θr
m, θt
m∈[0,2π),∀m∈M,(3h)
max{at,m, ar,m} ≤ amax
m,∀m∈M,(3i)
|ck|2≥ |c¯
k|2,if π(k) = 1, π(¯
k) = 0,
|ck|2≤ |c¯
k|2,if π(k) = 0, π(¯
k) = 1,(3j)
where γdenotes the minimum achievable rate required by each
user, pmand pin
mdenote the power budget and the incident
signal energy of the m-th element at the active IOS. Constraint
(3b) guarantees the QoS requirements of the users. Constraint
(3c) ensures that the total transmit power for signals xtand xr
is smaller than the transmit power budget Pb. Constraint (3d)
ensures that the power consumption at the active IOS is not
greater than its power budget Pmax
out . Constraint (3e) ensures
that the power consumption of the m-th active IOS element
is not greater than pm. Constraint (3f) ensures that the overall
power consumption of all the elements is not greater than Pmax
out .
Constraint (3g) guarantees that the sum of the incident signal
energy of each element is not greater than the energy of the
signal incident on the active IOS. Constraint (3h) denotes the
phase-shift constraints of the IOS. Constraint (3i) ensures that
the maximum amplification amplitude of each IOS element is
not greater than amax
m. Constraint (3j) guarantees a successful
SIC decoding for NOMA signalling.
Problem (P1) is non-convex and hence difficult to solve.
Particularly, the challenge of problem (P1) lies in the intricately
coupled variables Pt/r,Θt/r and wt/r as well as the non-
convex objective function (3a). In addition, different from the
conventional passive IOS, more optimization variables are in-
volved in problem (P1) as the refraction and reflection matrices
(including amplitude and phase shift coefficients) need to be
optimized simultaneously. Both Pt/r and Θt/r jointly affect the
system performance and are limited by the maximum amplified
power at the active IOS. In the following section, we propose an
efficient iterative algorithm to derive a high-quality suboptimal
solution.
3We highlight that the mathematical formulation of the proposed active IOS
is quite different from the conventional reflection-only RIS. This is because IOS
supports both reflection and refraction simultaneously, such that two coefficient
matrices are used to describe the feature. Moreover, the distribution of reflection
and refraction energy makes the two matrices coupled, i.e., constraints (3d) and
(3e) in (P1), which does not exist in the conventional reflection-only RIS.
IEEE WIRELESS COMMUNICATIONS LETTERS 3
III. JOI NT BE AM FO RM IN G DESIGN
In this section, we propose an efficient AO algorithm to
solve problem (P1). Specifically, the BS beamforming is first
optimized for the given active IOS coefficient matrix. Then, the
active IOS amplitude and phase shift matrices are optimized by
fixing the BS beamforming.
A. BS Beamforming Optimization
Since only two users are considered, there are two possible
SIC decoding orders. We calculate the sum achievable rate
of the users in each case separately, and then take the maxi-
mum value as the optimal solution. Without loss of generality,
we consider the decoding order π(t) = 1, π(r)=0as
an example. Denote Sk= (PkΘk)2,HG,Ik=GGHSk,
Hhk,Ik=hkhH
kSk,HG,Ik,hk=GGHSkhkhH
k,∀k∈ {r, t}.
We introduce a slack matrix Wk=wkwH
k,∀k∈ {r, t},
which is rank-one and positive semidefinite. Hence, the SNR
of the t-user and the signal-to-interference-noise ratio (SINR)
of the r-user can be expressed as SNRt=Tr(WtHG,It,ht)
Tr(Hht,It)σ2
v+σ2
t
and
SINRr=Tr(WrHG,Ir,hr)
Tr(WtHG,Ir,hr)+Tr(Hhr,Ir)σ2
v+σ2
r. Then, problem (P1)
with the given IOS coefficient matrix is recast as
(P2) max
Wk
log2(1 + SNRt) + log2(1 + SINRr)(4a)
s.t. log2(1 + SNRt)≥γ, log2(1 + SINRr)≥γ, (4b)
Tr(Wt) + Tr(Wr)≤Pb,(4c)
Tr(WtHG,It) + Tr(St)σ2
v+
Tr(WrHG,Ir) + Tr(Sr)σ2
v≤Pmax
out ,(4d)
Tr(WtHG,It,ht)≥Tr(WrHG,Ir,hr),(4e)
Wk≽0, k ∈ {r, t},(4f)
rank(Wk) = 1, k ∈ {r, t}.(4g)
Since the objective function of problem (P2) is not concave,
by introducing slack variables ζtand ζr, we transform problem
(P2) into
(P3) max
Wk,ζk
log2(1 + ζt) + log2(1 + ζr)(5a)
s.t. SNRt≥ζt,SINRr≥ζr,(5b)
log2(1 + ζt)≥γ, log2(1 + ζr)≥γ, (5c)
(4c) −(4g),(5d)
where ζtand ζrdenote the SNR of the t-user and the SINR
of the r-user, respectively. However, constraint (5b) is still non-
convex. To tackle this, we rewrite constraint (5b) as follows
Tr(WtHG,It,ht)≥Tr(Hht,It)σ2
vζt+σ2
tζt,(6)
Tr(WrHG,Ir,hr)≥Tr(WtHG,Ir,hr)ζr
+Tr(Hhr,Ir)σ2
vζr+σ2
rζr.(7)
Constraint (7) is still non-convex due to the first term in
the right-hand side. Since Tr(WtHG,Ir,hr)and ζrare both
nonnegative, we apply the arithmetic-geometric mean (AGM)
inequality to approximate constraint (7) into a convex form.
Thus, we have
Tr(WrHG,Ir,hr)≥µ1
2Tr2(WtHG,Ir,hr) + 1
2µ1
ζ2
r
+Tr(Hhr,Ir)σ2
vζr+σ2
rζr,(8)
Algorithm 1 Iterative Algorithm for Solving Problem (P4)
1: Initialization: Set n= 1 and initialize µ(0)
1,ω(0)
k,
weig-max,(0)
k;
2: repeat
3: If problem (P4) is feasible, solve the problem, define
ϵ(n)=ϵ(n−1), and update µ(n)
1;
4: Else: define ϵ(n)=1
2ϵ(n−1);
5: Update ωk=min1,λmax(W(0)
k)
Tr(W(0)
k)+ϵ(n);
6: n=n+ 1;
7: until ω(n)
k= 1 and |R(n)−R(n−1) | ≤ δ.
where the equality holds if and only if µ1=ζr
Tr(WtHG,Ir,hr). To
deal with the non-convex rank-one constraint (4g), we utilize
the sequential rank-one constraint relaxation (SROCR) method
to obtain rank-one solutions of problem (P2), as described next.
The rank-one constraint rank(W(n)
k) = 1 at the n-th iteration
is replaced by a linear inequality as
weig-max,(n−1)
kW(n)
kweig-max,(n−1)
k≥ω(n−1)
kTr(W(n)
k),(9)
where ω(n−1)
k∈[0,1] denotes the trace ratio parameter of Wk
at the (n−1)th iteration, which gradually increases from 0 to
1. weig-max,(n−1)
i∈CN×1denotes the eigenvector of the largest
eigenvalue of W(n−1)
kwith the parameter ω(n−1)
k. The iterative
convex problem at the n-th iteration is given by
(P4) max
Wk,ζk
log2(1 + ζt) + log2(1 + ζr)(10a)
s.t. (4c) −(4e),(5c),(6),(8),(9).(10b)
Note that problem (P4) can be efficiently solved by using
standard convex optimization solvers, e.g., CVX. The iterative
algorithm for problem (P4) is summarized in Algorithm 1,
where δdenotes the convergence accuracy.
B. Active IOS Beamforming Optimization
By fixing the BS beamforming vectors and the decoding
order, we optimize the active IOS coefficients. We denote
fk= (ak,1ejθk
1, ak,2ejθk
2, . . . , ak,M ejθk
M)H, and introduce a
slack matrix Fk=fkfH
k, k ∈ {r, t}, which is rank-one and
positive semidefinite. Then, denote Hhk=hkhH
k,HG,wk=
GwkwH
kGH,∀k∈ {r, t}. Then, the SNR of the t-user and the
SINR of the r-user can be expressed as SNR′
t=Tr(FtHhtHG,wt)
Tr(FtHht)σ2
v+σ2
t
and SINR′
r=Tr(FrHhrHG,wr)
Tr(FrHhrHG,wt)+Tr(FrHhr)σ2
v+σ2
r. Therefore, the
optimization problem (P1) is reformulated as
(P5) max
Fk,pm,P in
m
log2(1 + SNR′
t) + log2(1 + SINR′
r)(11a)
s.t. log2(1 + SNR′
t)≥γ, log2(1 + SINR′
r)≥γ, (11b)
Tr(FtHG,wt) + Tr(Ft)σ2
v+
Tr(FrHG,wr) + Tr(Fr)σ2
v≤Pmax
out ,(11c)
(F(m,m)
t+F(m,m)
r)≤pm
pin
m+σ2
v
,∀m∈M,(11d)
M
m=1
pin
m≤Tr(HG,wt) + Tr(HG,wr),(11e)
F(m,m)
k≤(amax
m)2,∀m∈M, k ∈ {r, t},(11f)
Fk≽0, k ∈ {r, t},(11g)
IEEE WIRELESS COMMUNICATIONS LETTERS 4
rank(Fk) = 1, k ∈ {r, t},(11h)
Tr(FtHhtHG,wt)≥Tr(FrHhrHG,wr),(11i)
(3f).(11j)
Then, we again introduce auxiliary variables ζtand ζrwhich
denote the SNR of the t-user and the SINR of the r-user,
respectively, and problem (P5) is transformed into
(P6) max
Fk,ζk,pm,P in
m
log2(1 + ζt) + log2(1 + ζr)(12a)
s.t. SNR′
t≥ζt,SINR′
r≥ζr,(12b)
log2(1 + ζt)≥γ, log2(1 + ζr)≥γ, (12c)
(11c) −(11i),(3f).(12d)
However, constraints (11d) and (12b) are still non-convex due
to the complicated fractional form and the coupled variables.
To deal with this, we rewrite (12b) as follows
Tr(FtHhtHG,wt)≥(Tr(FtHht)σ2
v+σ2
t)ζt,(13)
Tr(FrHhrHG,wr)≥(Tr(FrHhrHG,wt)
+Tr(FrHhr)σ2
v+σ2
r)ζr,(14)
and apply the AGM inequality to approximate them into
2Tr(FtHhtHG,wt)≥((Tr(FtHht)σ2
v+σ2
t)µ2)2
+ (ζt/µ2)2,(15)
2Tr(FrHhrHG,wr)≥((Tr(FrHhrHG,wt)
+Tr(FrHhr)σ2
v+σ2
r)µ3)2+ (ζr/µ3)2,(16)
((F(m,m)
t+F(m,m)
r)µ4)2+ ((pin
m+σ2
v)/µ4)2≤2pm.(17)
where equalities hold µ2=ζt/(Tr(FtHht)σ2
v+σ2
t),µ3=
ζr/(Tr(FrHhrHG,wt) + Tr(FrHhr)σ2
v+σ2
r), and µ4=
(pin
m+σ2
v)/(F(m,m)
t+F(m,m)
r). To tackle the non-convex
rank-one constraint (11h), we again apply the SROCR method
to obtain rank-one solutions of problem (P5). The relaxed rank-
one constraint at the n-th iteration is given by
feig-max,(n−1)
kF(n)
kfeig-max,(n−1)
k≥f(n−1)
kTr(F(n)
k).(18)
Finally, we obtain the iterative convex program at the n-th
iteration as follows
(P7) max
Fk,ζk,pm,P in
m
log2(1 + ζt) + log2(1 + ζr)(19a)
s.t. (11c),(11e),(11f),(11i),(12c),(3f),(15) −(18).
(19b)
The iterative algorithm for solving problem (P7) is similar to
Algorithm 1 and hence is omitted. The overall AO algorithm
for solving problem (P1) is given in Algorithm 2.
C. Convergence and Complexity Analysis
The AO algorithm in each iteration obtains the optimal
solution, implying that the algorithm generates a non-decreasing
objective function. In addition, due to the BS and active IOS
power budget, the objective function has an upper bound, which
ensures the convergence of the algorithm.
For problem (P4), the complexity with the interior-point
method is O(Ia(2N2+ 2)3.5), where 2N2+ 2 is the number of
the variables, and Iais number of iterations needed for solving
(P4). Similarly, the complexity for solving (P7) is O(Ib(2M2+
Algorithm 2 AO Algorithm for Solving Problem (P1)
1: Initialization: Set l= 1 and initialize µ(0)
1,µ(0)
2,µ(0)
3,
µ(0)
4,P(0)
t,P(0)
r,Θ(0)
t,Θ(0)
r,ω(0)
k,weig-max,(0)
k,f(0)
k, and
feig-max,(0)
k;
2: repeat
3: Solve problem (P4) by fixing P(l−1)
t,P(l−1)
r,Θ(l−1)
t, and
Θ(l−1)
t;
4: Solve problem (P7) by fixing w(l)
tand w(l)
r;
5: l=l+ 1;
6: until |R(l)−R(l−1)| ≤ δ.
10 15 20 25 30 35 40 45 50 55
0
2
4
6
8
10
12
Fig. 1. Sum achievable rate versus the BS transmit power with N= 4,
M= 32,Pmax
out = 10 dBm, and amax
m= 10.
2M+2)3.5). Hence, the overall complexity of the AO algorithm
is O(2IAO(Ia(2N2+2)3.5+Ib(2M2+2M+2)3.5)), where IAO
denotes the number of alternating iterations.
IV. NUMERICAL RES ULT S
We provide numerical results to quantify the performance of
the proposed design. A two-dimensional network topology is
considered, where the BS is located at (0,0) meters and the IOS
is located at (50,0) meters. Two users are randomly distributed
on both sides of the IOS with a radius of 5 meters centered in
the IOS. Similar to [8], the channels are assumed to be Rician
fading channels, where the path loss at the reference distance
is −30 dB and the other parameters are set the same as [8].
Fig. 1 plots the sum achievable rate of the active IOS aided
NOMA network versus the BS transmit power, where the rates
of the conventional OMA and the passive IOS schemes are
also plotted for comparison. In the OMA scheme, the two users
are served using the non-overlapped time slots with optimized
time allocation. We observe that the proposed active IOS aided
NOMA design achieves the highest sum achievable rate among
all the schemes in the moderate transmit power region, thus
demonstrating the performance benefits of our proposed design.
This is because in the proposed design, the elements of the active
IOS can refract and reflect the incident signal simultaneously to
make a full use of the communication time resource, which
is not possible in the OMA scheme. As compared to the
passive IOS scheme, our proposed active IOS architecture can
additionally amplify the incident signal to boost the receiving
quality of the users, which yields a superior rate performance.
However, as the transmit power increases, the sum achievable
rate increase of the active IOS system becomes slower, and
when the transmit power is sufficiently large, the sum achievable
rate saturates. The reason is that when the transmit power is
large enough, the active IOS elements cannot fully amplify the
IEEE WIRELESS COMMUNICATIONS LETTERS 5
5 10 15 20 25
0
1
2
3
4
5
6
Fig. 2. Sum achievable rate versus the number of
the IOS elements with N= 4 and Pb= 45 dBm.
10 15 20 25 30 35 40 45 50 55
0
2
4
6
8
10
12
14
16
Fig. 3. Sum achievable rate versus the overall power
budget.
10 15 20 25 30 35 40 45 50 55
0
0.05
0.1
0.15
0.2
0.25
0.3
Fig. 4. Energy efficiency versus the overall power
budget.
incident signal due to the limitation on its maximum power
consumption.
Fig. 2 shows the sum achievable rate achieved by the different
schemes versus the number of IOS elements. It can be seen that
the sum achievable rate of the active IOS aided NOMA design
increases slower than that of the passive IOS counterpart, due
to the reduced power scaling order in the presence of additive
noise with active components. With a small number of IOS
elements, the active IOS can achieve superior performance over
the passive IOS, due to the fact that the active IOS is able to
amplify the incident signal to achieve the performance gain.
We also observe from the figure that the increase of the sum
achievable rate achieved by the proposed design is much faster
than that achieved by the OMA scheme. The reason is that
our proposed scheme can exploit the whole transmission time
to fully exploit the beamforming gain provided by the active
IOS, whilst the OMA scheme can use only a portion of the
beamforming gain. However, the OMA scheme can achieve a
better performance than the NOMA scheme with a small number
of the IOS elements. Since the OMA scheme enjoys inter-user
interference-free transmission, and interference dominates the
performance when the number of IOS elements is small.
Fig. 3 illustrates the sum achievable rate versus the overall
power budget. For the passive IOS, the overall power budget is
the BS transmit power. For the active IOS, the overall power
budget is optimized to balance the power budget between the
BS and the active IOS for sum achievable rate improvement.
Similar performance enhancement of the proposed design over
the baseline schemes can be seen from the figure. The active IOS
aided OMA scheme outperforms the passive IOS aided NOMA
scheme, since active IOS can provide sufficient amplification
gain. In addition, by increasing the overall power budget, the
sum achievable rate of the proposed design is also increased.
This implies that our scheme preferentially uses the overall
power budget for the maximum power consumption of the
active IOS, such that the active IOS can always amplify the
signal to its maximum to benefit the performance. We also
compare the performance of the proposed system with three
baseline schemes, i.e., random phase (RP), random phase and
amplitude (RPA), and two reflection-only active RISs with each
having M
2elements. Fig. 3 shows that RP and RPA scheme
loses some performance due to the fact that it cannot always
strengthen SINR at users. The active RIS scheme achieves the
worst performance. Since the conventional RIS cannot exploit
the adjustable numbers of reflection and refraction elements to
enhance the signal strength and mitigate inter-user interference.
Fig. 4 plots the energy efficiency (EE) versus the overall
power budget, where the EE is defined as Rt+Rr
Pmax . It can be seen
that the proposed active IOS aided NOMA scheme achieves the
highest EE. The reason is that the active IOS can amplify the
incident signal to obtain amplification gain, and the NOMA
scheme can make full use of the communication time and
increase the sum rate.
V. CONCLUSION
We proposed a new design of an active IOS aided NOMA
network. An efficient AO algorithm was developed to optimize
the BS and the IOS beamforming to improve the sum achievable
rate. Simulation results were presented to demonstrate the
effectiveness of the active IOS aided NOMA network and obtain
useful design insights.
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