Reconfigurable Antenna Multiple Access for 5G
mmWave Systems
Mojtaba Ahmadi Almasi∗ , Hani Mehrpouyan∗, David Matolak∗∗ , Cunhua Pan†, Maged Elkashlan†
∗ Department of Electrical and Computer Engineering, Boise State University, {mojtabaahmadialm,hanimehrpouyan}@boisestate.edu
∗∗ Department of Electrical Engineering, University of South Carolina, {matolak}@cec.sc.edu

arXiv:1803.09918v1 [] 27 Mar 2018

† School of Electronic Engineering and Computer Science, Queen Mary University of London, {c.pan,maged.elkashlan}@qmul.ac.uk

Abstract—This paper aims to realize a new multiple access
technique based on recently proposed millimeter-wave reconfigurable antenna architectures. To this end, first we show that integration of the existing reconfigurable antenna systems with the
well-known non-orthogonal multiple access (NOMA) technique
causes a significant degradation in sum rate due to the inevitable
power division in reconfigurable antennas. To circumvent this
fundamental limit, a new multiple access technique is proposed.
The technique which is called reconfigurable antenna multiple
access (RAMA) transmits only each user’s intended signal at
the same time/frequency/code, which makes RAMA an inter-user
interference-free technique. Two different cases are considered,
i.e., RAMA with partial and full channel state information (CSI).
In the first case, CSI is not required and only the direction
of arrival for a specific user is used. Our analytical results
indicate that with partial CSI and for symmetric channels,
RAMA outperforms NOMA in terms of sum rate. Further, the
analytical result indicates that RAMA for asymmetric channels
achieves better sum rate than NOMA when less power is assigned
to users that experience better channel quality. In the second
case, RAMA with full CSI allocates optimal power to each user
which leads to higher achievable rates compared to NOMA
for both symmetric and asymmetric channels. The numerical
computations demonstrate the analytical findings.

I. I NTRODUCTION
The rapid growth of global mobile data traffic is expected
to be satisfied by exploiting a plethora of new technologies,
deemed as 5th generation (5G) networks. To meet this demand,
millimeter-wave (mmWave) communications operating in the
30 − 300 GHz range is emerging as one of the most promising solutions [1]. The existence of a large communication
bandwidth at mmWave frequencies represents the potential for
significant throughput gains. Indeed, the shorter wavelengths
at the mmWave band allow for the deployment of a large
number of antenna elements in a small area, which enables
mmWave systems to potentially support more higher degrees
of beamforming gain and multiplexing [1]. However, significant path loss, channel sparsity, and hardware limitations are
major obstacles for the deployment of mmWave systems. In
order to address these obstacles, several mmWave systems
have been proposed to date [2]–[4].
An analog beamforming mmWave system is designed in [2]
which uses one radio frequency (RF) chain and can support
only one data stream. Subsequent work considers a hybrid
beamforming mmWave system to transmit multiple streams
This project is supported in part by the NSF ERAS grant award numbers
1642865.

by exploiting several RF chains [3]. In [4], the concept of
beamspace multi-input multi-output (MIMO) is introduced
where several RF chains are connected to a lens antenna array
via switches. In addition to these systems, non-orthogonal
multiple access (NOMA) has been also considered as another
promising enabling technique for 5G to enhance spectral
efficiency in multi-user scenarios [5], [6]. Unlike orthogonal
multiple access (OMA) techniques that are realized in time,
frequency, or code domain, NOMA is realized in the power
domain [7]. In fact, NOMA performs superposition coding
(SC) in the power domain at the transmitter. Subsequently,
successive interference cancellation (SIC) is applied at the
receiver [8], [9].
In order to serve more users in 5G wireless communications, recently, the integration of NOMA in mmWave
systems, i.e., mmWave-NOMA, has been studied [10]–[14].
The work in [10] designs a random beamforming technique
for mmWave-NOMA systems. The base station (BS) randomly
radiates a directional beam toward paired users. In [11], it
is shown that mismatch between the users’ channel vector
and finite resolution analog beamforming1 simplifies utilizing
NOMA in mmWave-MIMO systems. The work in [12], proposes the combination of beamspace MIMO and NOMA, to
ensure more users can be served with a limited number of RF
chains. As a result, the number of served users is more than the
number of RF chains [12]. In [13], NOMA is studied for hybrid mmWave-MIMO systems. A power allocation algorithm
has been provided in order to maximize energy efficiency.
Newly, a joint power allocation and beamforming algorithm
for NOMA in the analog mmWave systems has been proposed
in [14]. Although the works [10]–[14] have all resulted in
maximizing bandwidth efficiency, this gain has come at the
costs of higher complexity at the receiver and the use of
multiple RF chains or one RF chain along with a large number
of phase shifters and power amplifiers which can be costly at
mmWave frequencies. Hence, in contrast to the prior works,
here, we will propose a new multiple access scheme that takes
advantage of reconfigurable antennas to outperform NOMA,
while at the same requiring one RF chain at the transmitter
and simple receiver structure.
Recently, there has been a new class of reconfigurable
antennas that can support the transmission of multiple radiation beams with one RF chain [15], [16]. The unique
1 Finite resolution analog beamforming is due to the use of a finite number
of phase shifters.

II. S YSTEM M ODEL AND NOMA
In this section, first we introduce the reconfigurable antenna
systems and their properties. Then, NOMA technique for a
BS and multiple users is described. Finally, NOMA for the
reconfigurable antennas is investigated.
A. Reconfigurable antenna systems
A reconfigurable antenna can support multiple reconfigurable orthogonal radiation beams. To accomplish this, a
spherical dielectric lens is fed with multiple tapered slot
antennas (TSAs), as shown in Fig. 1. The combination of each
TSA feed and the lens produces highly directive beams in far
field [15], [16]. That is, each TSA feed generates a beam in
a given direction in the far field. Therefore, a reconfigurable
antenna system is a multi-beam antenna capable of generating
M ≫ 1 independent beams where M is the number of TSA
feeds. Only the feed antennas that generate the beams in the
desired directions need to be excited. To this end, the output
of the RF chain is connected to a beam selection network (see
Fig. 1). The network has one input port that is connected to
the RF chain and M output ports that are connected to the M
TSA feeds [15]. For instance, in Fig. 1, the network selects

(a) RF Transceiver Chain

Spherical
Dielectric Lens

RF Transciever Chain
Mixer

PA

Duplexer

Mixer

LNA

Far-Field
Pencil Beams

Beam Selection
Network

property that distinguishes the system in [15], [16] from prior
art is that the proposed reconfigurable antenna architecture
can support multiple simultaneous orthogonal reconfigurable
beams via one RF chain. Inspired by this class of antennas, this
paper proposes a fresh multiple access technique for mmWave
reconfigurable antenna systems which is called reconfigurable
antenna multiple access (RAMA). We consider a scenario in
which a single BS is equipped with a mmWave reconfigurable
antenna and each beam of the antenna serves one user where
the users are not aligned with the same direction. Given
that the limitation on the RF circuitry of the antenna [15]
results in the division of the transmitted power amongst the
beams, the current state-of-the-art in mmWave-NOMA would
not operate efficiently in such a setting. To enhance the
performance of multiple access schemes in the mmWave band
and also overcome this fundamental limit for reconfigurable
antennas, unlike NOMA, RAMA aims to transmit only the
intended signal of each user. To accommodate this technique,
we will consider two cases, RAMA with partial channel state
information (CSI) and RAMA with full CSI. In the first case,
channel gain information is not required and only the direction
of arrival (DoA) for a specific user is used. Our results
indicate that with partial CSI and for symmetric channels,
RAMA outperforms NOMA in terms of sum rate. Further, the
analytical result indicates that RAMA for asymmetric channels
achieves better sum rate than NOMA when less power is
assigned to a user that experiences a better channel quality. In
the second case, RAMA with full CSI allocates optimal power
to each user which leads to higher achievable rates compared
to NOMA for both symmetric and asymmetric channels. Our
extensive numerical computations demonstrate the analytical
findings.
√
Notations: Hereafter, j = −1. Also, E[·] and | · | denote
the expected value and amplitude value of (·), respectively.

Tapered Slot
Antenna Feeds

Fig. 1. Schematic of the reconfigurable antenna steering multiple beams. The
antenna is composed of a spherical lens fed with a number of tapered slot
antenna feeds. Each feed generates a beam in a given direction in the far
field [15].

only five outputs that are connected to the input ports of five
TSA feeds. Accordingly, the network divides power of the
output signal of the RF chain equally or unequally amongst
five TSA feeds.
It is mentioned that the reconfigurable antennas steer reconfigurable independent beams. This steering is achieved
by selecting the appropriate TSA feed. Also, recall that we
assume that the transmitter has knowledge of the DoA of
the users. Accordingly, by appropriately steering the beams,
the reconfigurable antenna can manipulate the phase of the
received signal at the user terminal. Therefore, steering multiple reconfigurable independent beams and routing the power
amongst those beams are two properties of the reconfigurable
antennas.
B. Review of NOMA
In this paper, we consider the downlink of a single communication cell with a BS in the center that serves multiple users.
The BS and users are provided with a signal omnidirectional
antennas. For simplicity, the number of users is restricted to
two where the users are not aligned with the same direction,
i.e., there is an angle gap between the users.
Let the BS have signals si (i = 1, 2) for User i, where
E[|si |2 ] = 1, with power transmission pi . The sum of pi s, for
i = 1, 2, equals to p. According to the principle of the NOMA
downlink, at the transmitter, s1 and s2 are superposition coded
as
√
√
(1)
x = p 1 s1 + p 2 s2 .
Hence, the received signal at the ith user, for i = 1, 2, is
given by
√
√
yi = xhi + ni ≡ ( p1 s1 + p2 s2 )hi + ni ,
(2)
where hi is the complex channel gain between the BS and User
i, and ni denotes the additive white Gaussian noise with power
σi2 . At the receiver, each user performs the SIC process to
decode the desired signal. The optimal decoding order depends
on the channel gain. Without loss of generality, let us assume
that User 1 have better channel gain, i.e., |h1 |2 /σ12 ≥ |h2 |2 /σ22 ,
which gives p1 ≤ p2 .
After applying SIC, the achievable rate for NOMA for User
i can be determined as

RN = log (1 + p1 |h21 |2 ),
1
2
σ1
(3)
2
2
R2N = log2 (1 + p2 |h22| /σ2 2 ).
p1 |h2 | /σ +1
2

Allocated power to user 1

Power

Allocated power to user 2

Time/Frequency/Code

...,s2, s1

Beam Selection Network

This result indicates that power allocation greatly affects the
achievable rate for each user. For example, an improper power
allocation does now allow User 1 to decode s2 correctly, which
in turn does not allow for the interference from User 2 to be
successfully eliminated.

RF

Im

Re

C. NOMA for the reconfigurable antennas
8-PSK constellation

Phase
Detector

ej

User 1
0

s1
.5p

0.5p

s2

User 2

TSA feed

Suppose that a BS is equipped with the described recon2. Schematic of the BS for reconfigurable antenna multiple access
figurable antenna system and aims to simultaneously serve Fig.
technique with partial CSI and equal power division amongst the TSA feeds.
two users by using NOMA. The reconfigurable antenna steers It is assumed that the signals s1 and s2 are selected form 8-PSK constellation
two beams by feeding two TSAs. Each TSA serves one user
which is equipped with a single omnidirectional antenna. The
superposition coding of si with allocated power pi is defined A. RAMA with Partial CSI
in (1). Users 1 and 2 receive the following signals as
Let us assume that the BS utilizes a reconfigurable antenna
(
√ √
√
√
and
has partial CSI, i.e., knows the DoA of users. Thus, power
z1 = αxh1 + n1 ≡ α( p1 s1 + p2 s2 )h1 + n1 ,
√
√
√
√
is allocated equally for each user, i.e.,
z2 = 1 − αxh2 + n2 ≡ 1 − α( p1 s1 + p2 s2 )h2 + n2 ,
(4)
p1 = p2 = 0.5p.
(6)
respectively, where factor α ∈ (0, 1) is due to the power
division in the reconfigurable antennas. When α = 0.5,
it means the power is divided equally between two TSAs.
Thus, each user receives only a portion of the power of the
transmitted signal x.
Consider the same order for the channel gains, i.e,
|h1 |2 /σ12 ≥ |h2 |2 σ22 . An error-free SIC process results in the
achievable rate for each user as

RNR = log (1 + αp1 |h2 1 |2 ),
1
2
σ1
(5)
2
2
R2NR = log2 (1 + (1−α)p2 |h22| /σ2 2 ).
(1−α)p1 |h2 | /σ2 +1

Obviously, signal to noise ratio (SNR) for User 1 and signal
to interference plus noise ratio (SINR) for User 2 in (5)
is less than that of the NOMA given in (3). As a result,
combining NOMA with reconfigurable antennas will reduce
the achievable user rate when considering the same channel
gains, power allocation, and noise power. It is noteworthy
that for reconfigurable antenna-NOMA the definition of power
allocation is different from power division. Power allocation
is a strategy which is used in NOMA. While, power division
is one of the properties of the reconfigurable antennas that
divides power of the superposition coded signal among two
TSAs.
In brief, when users are not aligned in the same direction,
the reconfigurable antennas cannot harvest the benefits of
NOMA due to the power division property. Whereas, when
users are located on the same direction, the reconfigurable antenna steers only one beam to serve users which means power
division is not required. In this case, reconfigurable antennaNOMA and NOMA in Subsection II.B achieve identical sum
rate performance.
III. R ECONFIGURABLE A NTENNA M ULTIPLE ACCESS
In this section, a novel multiple access technique for the
reconfigurable antenna systems is proposed. The technique
which we call RAMA takes advantage of the reconfigurable
antenna and directional transmission in mmWave bands.

Our main objective is to suppress inter-user interference. To
this end, we aim to transmit only the intended signal for each
user at the same time/frequency/code blocks. The intended
signals for Users 1 and 2 are s1 and s2 , respectively. Let us
assume that si , for i = 1, 2, is drawn from a phase shift
keying (PSK) constellation and E[|si |2 ] = 1. Accordingly, s2
can be expressed in terms of s1 as
s2 = s1 ej∆θ ,

(7)

where ∆θ denotes the difference between the phases of s1 and
s2 . Similar to (1), the power of the transmitted signal, x, is
assumed to be p.
Unlike NOMA, in RAMA only one of the signals, say s1 ,
is upconverted by the RF chain block and the whole power
p is allocated to that signal before the power division step.
Therefore, x is given by
√
x = ps1 .
(8)
It is clear that the superposition coded signal in (1) and the
signal in (8) carry the same average power p. The proposed
multiple access technique for the signal in (8) is shown in
Fig. 2. The phase detector block calculates the phase difference
between s1 and s2 , ej∆θ . Moreover, as shown in Fig. 2, the
beam selection network selects two TSA feeds as highlighted
with black color based on the users’ DoA. For simplicity, we
call them TSA 1 and TSA 2. The network divides the power
equally between TSA√1 and TSA 2. That is, the signal of TSAs
1 and 2 is given by 0.5ps1 .
The signal intended for TSA 1 is the desired signal for
User 1. To transmit the signal intended for User 2 via TSA
2 we take advantage of the reconfigurable antennas. Thanks
to properties of reconfigurable antennas, signal at each TSA
can independently be rotated with an arbitrary angle. Using
this proper, the beam selection network multiplies the signal
j∆θ
in corresponding to TSA 2 with e√
. This results√ in the
transmitted signal via TSA 2 to be 0.5ps1 ej∆θ = 0.5ps2
which is the desired signal for User 2. Since transmission

is directional in mmWave bands, each user receives only its
intended signal as
(
√
z1 = 0.5ps1 h1 + n1 ,
(9)
√
z2 = 0.5ps2 h2 + n2 .
It is noteworthy that, here, we assume that there is no
interference that is imposed from the signal intended for User
1 on User 2 and vice versa. This assumption is very well
justified since the structure of the proposed lens based slotted
reconfigurable antenna results in very directional beams with
very limited sidelobes. Moreover, due to significant pathloss
and shadowing at mmWave frequencies we do not expect the
signals from the sidelobes to reach the unintended user2 . We
also highlight that in contrast to NOMA, full CSI and the
SIC process are not required at the receiver. Furthermore, in
RAMA power allocation and power division carry the same
concept, such that the routed power for TSA 1 (or 2) is the
same as the allocated power for User 1 (or 2).
The achievable rate of RAMA for each user under equal
power allocation is obtained as

RR,I = log (1 + p|h12|2 ),
1
2
2σ1
(10)
2
R2R,I = log2 (1 + p|h22| ).
2σ2

Let us denote RAMA with partial CSI by RAMA-I. It is
valuable to compare the sum rate of NOMA and RAMA-I. To
this end, we consider two extreme cases as follows. By definiN
tion, sum rate for NOMA and RAMA-I are Rsum
= R1N + R2N
R,I
R,I
R,I
and Rsum = R1 + R2 , respectively, where R1N and R2N
are defined in (3) and R1R,I and R2R,I are defined in (10).
Case I: p|h1 |2 /σ12 = p|h2 |2 /σ22 . In his paper is case is
called symmetric channel [5]. That is, the two users have the
same SNR. In this case, RAMA-I always achieves higher sum
rate than NOMA.
To show this, we calculate the sum rate for NOMA and
RAMA. For NOMA, the sum rate can be calculated as

p2 |h2 |2 /σ22 
p1 |h1 |2 
N
+ log2 1 +
Rsum
= log2 1 +
2
σ1
p1 |h2 |2 /σ22 + 1


p1 |h1 |2 
p2 |h2 |2 /σ22 
(a)
= log2 1 +
1
+
σ12
p1 |h2 |2 /σ22 + 1
2
p2 |h2 |2 
p1 |h1 |
+
= log2 1 +
σ12
σ22
2
p|h|
(b)
= log2 1 + 2 .
(11)
σ

The (a) follows from log2 a + log2 b = log2 ab and the (b)
follows the assumption that |h|2 /σ 2 = |h1 |2 /σ12 = |h2 |2 /σ22
and p1 + p2 = p.
Also, for RAMA-I, we follow the same steps as in NOMA.
Hence, it is obtained as
R,I
Rsum
= log2 1 +

p2 |h|4 
p|h|2
+
.
2
σ
4σ 4

(12)

R,I
N
Since p2 |h|4 /4σ 4 > 0, it gives Rsum
≤ Rsum
.

2 Detail analysis of the impact of sidelobes on inter-user interference in
RAMA is subject of future research.

Case II: p|h1 |2 /σ12 ≥ p|h2 |2 /σ22 . Here, this case is called
asymmetric channel [5]. That is, we assume that the channel
gain for User 1 is stronger than User 2. It can be shown that
for asymmetric channels, RAMA-I achieves higher sum rate
than NOMA when the power isproperly allocated for Users 1
and 23 . To proof this claim, we have
p2 |h2 |2 /σ22
p1 |h1 |2
) + log2 (1 +
)
2
σ1
p1 |h2 |2 /σ22 + 1
p1 |h1 |2
p2 |h2 |2 /σ22 
(a)
= log2 (1 +
)(1 +
)
2
σ1
p1 |h2 |2 /σ22 + 1
(b)
p2 |h2 |2 
p1 |h1 |2
)(1 +
) ,
(13)
≤ log2 (1 +
2
σ1
σ22

N
Rsum
= log2 (1 +

where p1 and p2 are allocated power for Users 1 and 2, respectively. Also, the (a) follows from log2 a + log2 b = log2 ab,
and the (b) is a result of p1 |h2 |2 /σ22 > 0 . Using (13) and
R,I
N
(10), the inequality Rsum
≤ Rsum
holds when the following
condition follows
(1 +

p1 |h1 |2
p2 |h2 |2
p|h1 |2
p|h2 |2
)(1
+
)
≤
(1
+
)(1
+
).
σ12
σ22
2σ12
2σ22
(14)

Obviously, for p1 /p ∈ (0, 0.5] the inequality holds which
indicates that User 1 should have lower power than User
2. Although this range is not tight, it gives a considerable
insight. This result implies that with proper power allocation in
NOMA, RAMA-I attains higher sum rate. However, RAMA-I
may not achieve user fairness when channel gain of one of
the users is significantly greater than that of other user. In this
case, the allocated power for user with strong channel gain
should be far less than other user and equal power allocation
would not lead to user fairness.
B. RAMA with full CSI
Assume that full CSI is available at the BS. Furthermore, the
BS can unequally allocate the power between two users. For
signals s1 and s2 that are chosen from a QAM constellation
and E[|si |2 ] = 1, the relationship between two arbitrary signals
selected from the constellation is given by
s2 = s1 s̄ej∆θ

(15)

where s̄ denotes |s2 |/|s1 |. For RAMA with full CSI, the
transmitted signal is defined as
p
p
(16)
x = p′ s1 ≡ ( p1 + p2 s̄2 )s1 ,

which obviously has the same average power as the signal in
(1). It is assumed that p1 and p2 are the allocated power for
User 1 and User 2, respectively. For simplicity, we consider
that our power allocation strategy is exactly the same as
NOMA. Fig. 3 depicts the schematic of the reconfigurable
antenna for the RAMA. The phase detector and s̄ calculator
blocks calculate ej∆θ and s̄, respectively. The beam selection
network first selects two suitable TSA feeds, TSA 1 and TSA
2 which are highlighted with black color in Fig. 3, based on
3 To achieve user fairness in NOMA, when |h |2 /σ 2 ≥ |h |2 /σ 2 we have
1
2
2
1
p1 ≤ p2 [5].

•

Power

Allocated power to User 1
Allocated power to User 2

...,s2, s1

Beam Selection Network

Time/Frequency/Code

RF

Im

Re

16-QAM constellation

Calculator
Phase
Detector

User 1
s1
√p 1
√p2 s

2

User 2

TSA feed

ejΔθ

RAMA technique is not an alternative for NOMA. When
users are aligned in the same direction, RAMA would
be combined with one of OMA or NOMA. Accordingly,
the users located on the same direction are considered
as a cluster. Each cluster will be served via RAMAOMA or RAMA-NOMA. Integration of RAMA with
other multiple access techniques is beyond the scope of
this paper.

Fig. 3. Schematic of the BS for reconfigurable antenna multiple access
technique regarding full CSI and unequal power allocation. It is assumed
that signals s1 and s2 are chosen from 16-QAM constellation.

σ2

respectively.
It is straightforward to show that RAMA with full CSI,
denoted by RAMA-II, achieves higher sum rate than NOMA
R,II
N
irrespective of their channel condition. That is, Rsum
≤ Rsum
R,II
R,II
R,II
where Rsum = R1 +R2 . Further, RAMA-II considers user
fairness the same as NOMA.
The following remarks are in order:
•

•

•

RAMA-I significantly reduces system overhead. In highly
dense networks where the number of users is much larger
than two, it is reasonable to serve users with RAMAI. This is because RAMA-I does not require the BS to
know full CSI and only users’ direction information is
necessary.
RAMA-I implemented by PSK constellation is very
simple in practice. The beam selection network divides
the power equally by using a simple power divider and
the received signal is interference-free. The later is also
preserved for RAMA-II. Indeed, RAMA-I with QAM
constellations is operational if power is divided properly.
RAMA-II needs an optimal power allocation strategy. In
Subsection III.B it is pointed out that power allocation
strategy for NOMA is adopted for RAMA-II. However, this strategy may not be efficient in reconfigurable
antenna systems with full CSI. It is because NOMA
considers the interference and the minimum achievable
rate for each user to allocate the power [5]. Whereas,
for RAMA-II the interference is removed which leads to
designing a better power allocation strategy.

20

20

NOMA
RAMA

10

5

0
-10

NOMA, p 1 /p = 1/4
NOMA, p 1 /p = 1/2

15

Sum rate (bits/s/Hz)

respectively. Accordingly, the achievable rate for user 1 and
user 2 is obtained as

RR,II = log (1 + p1 |h21 |2 ),
1
2
σ1
(18)
2
R2R,II = log2 (1 + p2 |h22 | ),

This section evaluates the performance of the proposed multiple access technique by using numerical computations, where
the analytical findings will also be verified. Transmission in
mmWave bands can be done through both line-of-sight and
non line-of-sight paths. Here, for the sake of simplicity, we
will consider Rayleigh fading channels.
Figure 4.(a) represents sum rate versus symmetric channel
plot for NOMA and RAMA-I. It is clear that RAMA-I
achieves better sum rate than NOMA. This is because the user
achievable rate for NOMA is limited due to the interference
from other users, which degrades the sum rate. At symmetric
channels, the interference in NOMA is severe and as a result
leads to a considerable sum rate gap compared to the RAMA
technique which is an inter-user interference-free technique.
This result verifies our claim in Case I Subsection III.A.
Figure 4.(b) illustrates sum rate performance versus asymmetric channel gains for RAMA-I and various power allocation schemes for NOMA. The aim of this simulation is to support our analytical finding in Case II Subsection III.A. When (p|h1 |2 /σ12 )/(p|h2 |2 /σ22 ) is not large
enough, RAMA-I outperforms NOMA for all power allocation
schemes since the channel is similar to a symmetric channel.
By increasing (p|h1 |2 /σ12 )/(p|h2 |2 /σ22 ) channel satisfies the
condition in Case II Subsection III.A. At high region of
(p|h1 |2 /σ12 )/(p|h2 |2 /σ22 ), for p1 /p ≤ 1/2, e.g., p1 /p = 1/2
and p1 /p = 1/4, sum rate of RAMA-I is always better than
NOMA which is consistent with Case II. For p1 /p = 3/4 and
large channel gain difference, NOMA has a little better sum
rate. This is because much more power is allocated to User 1
which can nearly achieve maximum sum rate. However, in this
condition NOMA does not consider user fairness. In contrast,

Sum rate (bits/s/Hz)

the users’ DoA information. Then, it divides the signal in (16)
√
√
into p1 s1 and p2 s1 s̄ regarding the obtained CSI and the
√
power allocation strategy. The signal for User 1, p1 s1 , is
ready to transmit from TSA 1. For User 2, the intended signal
√
√
is built by multiplying p2 s1 s̄ by ej∆θ which yields p2 s2 .
Hence, the interference-free received signals for Users 1 and
2 are attained as
(
√
z 1 = p 1 s1 + n1 ,
(17)
√
z 2 = p 2 s2 + n2 ,

IV. N UMERICAL C OMPUTATIONS

NOMA, p 1 /p = 3/4

15

RAMA-I, p 1 /p = 1/2

10

5

0
0

10
2

20
2

30

0

20

40

|h 1 | = |h 2 | (dB)

(p|h 1 | 2 / 21 )/(p|h 2 | 2 / 22 ) (dB)

(a)

(b)

60

Fig. 4. Sum rate comparison between NOMA and RAMA-I for (a) symmetric
channel and (b) symmetric channel.

4
3
2
OMA
NOMA
RAMA-II

1
0
0

2

4

Achievable rate for User 1 (bits/s/Hz)

Achievable rate for User 2 (bits/s/Hz)

Achievable rate for User 2 (bits/s/Hz)

5

1
0.8
0.6
0.4
0.2

OMA
NOMA
RAMA-II

0
0

5

10

Achievable rate for User 1 (bits/s/Hz)

(a)

(b)

Fig. 5. Achievable rate region of user 1 and 2 for (a) symmetric channel
with p|hi |2 /σi2 = 15 dB for i = 1, 2 and (b) asymmetric channel with
p|h1 |2 /σ12 = 30 dB and p|h2 |2 /σ22 = 0 dB.

equal power is allocated for the users in RAMA-I and they
cannot exploit maximum sum rate.
Figure 5 shows achievable rate region of two users for
OMA, NOMA, and RAMA-II. OMA in downlink transmission
is assumed to be implemented by OFDMA technique where
R1O = βlog2 (1 + p1 |h1 |2 /βσ12 ) and R2O = (1 − β)log2 (1 +
p2 |h2 |2 /(1 − β)σ22 ) are achievable rate for Users 1 and 2 with
the bandwidth of β Hz assigned to User 1 and (1 − β) Hz
assigned to User 2 [5].
In Fig. 5.(a), channel is assumed to be symmetric where its
gain is set to p|hi |2 /σi2 = 15 dB for i = 1, 2. The achievable
rate region for OMA and NOMA are identical. The region
for RAMA-II is much wider than that for OMA and NOMA
because RAMA-II neither suffers from inter-user interference
nor divides the bandwidth among users. For instance, when
User 2 achieves rate 2.5 bits/s/Hz, achievable rate of User 1
for RAMA-II with channel gain information is approximately
twice higher than that for OMA and NOMA. Notice that when
total power is allocated to either user, all three techniques are
able to achieve maximum rate for that user.
The achievable sum rate of asymmetric channel for
p|h1 |2 /σ12 = 30 dB and p|h2 |2 /σ22 = 0 dB has been
represented in Fig. 5.(b). From the figure it is clear that for
OMA, NOMA and RAMA-II only User 1 achieves maximum
sum rate when whole power is allocated to that user. However,
NOMA achieves wider rate region than OMA as expected.
Interestingly, the achievable rate region for RAMA-II is greater
than NOMA. As an example, when we want that User 1
to achieve 8 bits/s/Hz, User 1 can reach 0.68 bits/s/Hz and
0.8 bits/s/Hz with NOMA and RAMA-II, respectively. This is
because the achievable rate of User 2 in NOMA is affected by
the interference term from User 1 due to using superposition
coding at transmitter and SIC process at receiver. Whereas, in
RAMA-II, User 1 does not impart interference on User 2. In
other words, the gap between NOMA and RAMA-II reflects
the impact of inter-user interference on NOMA.
V. C ONCLUSION
In this paper, we propose a new multiple access technique
for mmWave reconfigurable antennas in order to simultaneously support two users by using a single BS in downlink.

First, we show that NOMA is not suitable technique for
serving the users for the reconfigurable antenna systems. Then,
by wisely using the properties of reconfigurable antennas, a
novel multiple access technique called RAMA is designed
by assuming partial CSI and full CSI. The proposed RAMA
provides mmWave reconfigurable antenna system with an
inter-user interference-free user serving. That is, the users with
higher allocated power do not required to decode signals of
other users. It is shown that for symmetric channels RAMAI outperforms NOMA for an arbitrary p1 in terms of sum
rate. Also, for asymmetric channels RAMA-I demonstrates
better sum rate performance if approximately more than half
of the power is allocated to User 2. Further, RAMA-II always
achieves higher sum rate than NOMA. Numerical computations support our analytical investigations.
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