# Deep Neural Network-Based Detector for Single-Carrier Index Modulation NOMA

Toan Gian, Vu-Duc Ngo, Tien-Hoa Nguyen, Trung Tan Nguyen, and Thien Van Luong
Toan Gian, Vu-Duc Ngo, and Tien-Hoa Nguyen are with the School of Electrical
and Electronics Engineering, Hanoi University of Science and Technology,
Hanoi, Vietnam. (e-mail<EMAIL_ADDRESS>{hoa.nguyentien,duc.ngovu
<EMAIL_ADDRESS>Tan Nguyen is with the Faculty of Radio-Electronics, Le
Quy Don Technical University, Ha Noi 11355, Vietnam (e-mail:
trungtannguyen@mta.edu.vn).Thien Van Luong is with the Faculty of Computer
Science, Phenikaa University, Hanoi 12116, Vietnam (e-mail:
thien.luongvan@phenikaa-uni.edu.vn).

###### Abstract

In this paper, a deep neural network (DNN)-based detector for an uplink
single-carrier index modulation non-orthogonal multiple access (SC-IM-NOMA)
system is proposed, where SC-IM-NOMA allows users to use the same set of sub-
carriers for transmitting their data modulated by the sub-carrier index
modulation technique. More particularly, users of SC-IM-NOMA simultaneously
transmit their SC-IM data at different power levels which are then exploited
by their receivers to perform successive interference cancellation (SIC)
multi-user detection. The existing detectors designed for SC-IM-NOMA, such as
the joint maximum-likelihood (JML) detector and the maximum likelihood SIC-
based (ML-SIC) detector, suffer from high computational complexity. To address
this issue, we propose a DNN-based detector whose structure relies on the
model-based SIC for jointly detecting both $M$-ary symbols and index bits of
all users after trained with sufficient simulated data. The simulation results
demonstrate that the proposed DNN-based detector attains near-optimal error
performance and significantly reduced runtime complexity in comparison with
the existing hand-crafted detectors.

###### Index Terms:

Non-orthogonal multiple access, NOMA, uplink, successive interference
cancellation, SIC, deep learning, DeepSIC-IM, DNN, bit error rate, runtime
complexity.

##  I Introduction

Wireless technologies have been anticipated to move from the conventional
orthogonal to non-orthogonal solutions to meet requirements of future wireless
networks, such as, ubiquitous coverage, high data rate, low latency, high
transmission reliability and scalability [1], [2]. In particular, using non-
orthogonal multiple access (NOMA) techniques, different users can
simultaneously share the same wireless resources for supporting a massive
number of devices. Moreover, in NOMA, multiple users can transmit data at
different power levels over the same radio resources, which facilitates
successive interference cancellation (SIC) to be effective for detecting the
desired signal. Thus, NOMA is a potential solution to improve spectrum
efficiency, reduce latency and provide high reliability, and facilitate
massive connection compared to the conventional orthogonal multiple access
(OMA) [3].

Index modulation (IM) has been known as an effective solution to provide
trade-off among transmission reliability, spectrum and energy efficiency. In
IM-based systems, information bits are implicitly encoded in indices of
several facilities such as antennas, subcarriers, and spreading codes [4]. For
example, using the indices of active sub-carriers as an additional domain to
the traditional modulated symbols, the orthogonal frequency division
multiplexing with IM (OFDM-IM) was proposed in [3], which significantly
improves the error performance compared with conventional OFDM. Since then,
many efforts have been made in order further improve either the error
performance or spectral efficiency of OFDM-IM, as can be found in [4, 5, 6,
7]. Moreover, the bit error rate (BER), symbol error probability (SEP), and
outage probability of OFDM-IM using different detection types over different
channel state information (CSI) conditions were intensively analyzed in [8, 9,
10, 11], which provide helpful insights into its error performance as well as
impacts of CSI uncertainty.

Recently, OFDM-IM has been applied to multi-user communications, particularly
to massive machine-type communications (mMTC), which require massive
connectivity with highly power-efficient transmissions [12]. For example,
aiming at reducing peak to average power ratio (PAPR) inherited from the OFDM
framework, the single-carrier frequency division multiple access (SC-FDMA) was
combined with sub-carrier index modulation in a NOMA manner in [13]. The
resultant scheme called SC-IM-NOMA was demonstrated to achieve higher energy
efficiency and better BER performance than its single-carrier IM-based OMA
counterparts (called SC-IM) proposed in [12], [14]. Note that the SC-IM
schemes proposed in [12] and [14] are based on OMA, in which each user is
allocated a dedicated set of subcarriers for employing SC-IM transmissions to
achieve better BER performance than conventional SC-FDMA. Yet, SC-IM is not
spectrum-efficient compared with SC-IM-NOMA in [13], which allows different
users to use the same set of sub-carriers for SC-IM transmissions. As a
result, SC-IM-NOMA is particularly appropriate for uplink mMTC systems.
However, SC-IM-NOMA, the joint maximum-likelihood (JML) detector and the
combination of maximum likelihood (ML) and SIC methods (ML-SIC), suffers from
high detection complexity compared to both SC-FDMA and SC-IM receivers.
Therefore, our paper appears to tackle this fundamental issue.

In this paper, we propose a deep neural network (DNN)-based detector for the
uplink SC-IM-NOMA system, called DeepSIC-IM, which can significantly reduce
the complexity, while achieving near-optimal BER performance compared with the
existing hand-designed detectors. Consider two uplink NOMA users, we design a
DNN structure for DeepSIC-IM, that relies on the model-based SIC procedure for
jointly detecting both $M$-ary symbols and index bits of both users. More
particularly, the proposed DeepSIC-IM consists of two different DNNs, each is
dedicated for detecting the signal of the corresponding user when fed with the
received signal and the output of the interfering users. Using simulated
dataset, DeepSIC-IM is trained offline to jointly minimize the BERs of both
users. Then, the trained model can be deployed in an online manner with very
low runtime. For this, simulation results are provided to demonstrate that our
DeepSIC-IM detector provides near-optimal BER performance at remarkably lower
runtime complexity than the existing hand-crafted detectors.

We note that deep learning (DL) or DNN techniques have been widely exploited
for enhancing the performance of wireless communication systems. For example,
in [15], a DL-based detector was proposed for OFDM-IM, achieving low runtime
complexity and near-optimal error performance. The channel estimation and
signal detection in OFDM were performed based on DNN in [16]. An application
of DL for downlink NOMA receivers was presented in [17], which, however, only
considers the conventional $M$-ary modulation, without any index modulation. A
number of other DL applications for designing the reliable and low-complexity
transceiver of wireless systems can be found in [18, 19, 20, 21].

The rest of this paper is organized as follows. Section II describes the
system model of SC-IM-NOMA and its existing detection. Section III presents
the proposed DeepSIC-IM structure and its corresponding training process.
Section IV provides simulation results and discussion for BER and runtime
complexity. Finally, Section V concludes the paper.

##  II System Model

Consider an uplink scenario where two users $\left(L=2\right)$,
$l\in\left(1,2\right)$, transmit data bits to the base station (BS) across the
resource block (RB). Gains of channel user 1 to BS and user 2 to BS are
represented as $\left|\mathbf{h}_{1}\right|$ and
$\left|\mathbf{h}_{2}\right|$, respectively. Both of users transmit SC-IM-
based signals to BS with power allocation coefficients of ${P}_{1}$ and
${P}_{2}$, respectively, where $P_{1}>P_{2}$. Each data block takes $b$ bits
from each of $L$ users. Additionally, $N$ and $K$ stand for the total number
of allotted and active subcarriers, respectively. Each SC-IM block transmits a
$b$-bit stream and bits determine the set of $M$-ary modulated symbols that
will be conveyed by $K$ active subcarriers. In this paper, all users use the
same $N$, $K$ and $M$-ary modulation technique. Thus, $b=b^{ind}+b^{sym}$ =
$\left[\log_{2}\left(N,K\right)\right]$ \+ $K$$\log_{2}$$\left(M\right)$ is
the total number of bits transmitted by the $l$-th user in the SC-IM block
[14], [12]. In the IM subblock, the $l$-th user’s initial bits are divided
into two parts. The first $b^{ind}=\log_{2}\left(N,K\right)$ bits are to
select $K$ active indices using either the combinatorial method or the look-up
table [3]. The remaining $b^{sym}=K\log_{2}\left(M\right)$ bits are mapped to
transmitted $M$-ary amplitude/phase modulated (APM) symbols. For example (as
Fig. 1) with $\left(N,K,M\right)=\left(4,2,4\right)$, the transmitted signal
vector, $\mathbf{x}_{l}=\left[x_{l}^{1}\,0\,0\,x_{l}^{2}\right]^{T}$, is made
up by symbols from an $M$-point constellation and zeros associated with the
inactive subcarriers, where $x_{l}^{s}$ stands for the $s$-th symbol of the
$l$-th user, $l={1,2}$. The model can serve a certain number of users since
SC-IM allocates a set of subcarriers to each user. Fig. 1 depicts a sample SC-
IM-NOMA resource mapping for the scenario of two users. Both of users transmit
data over the same RB using NOMA at distinct power levels.

Figure 1: Sub-carrier and power allocation of SC-IM-NOMA.

The received signal at the BS over $N$ subcarriers can be represented by

$\mathbf{y}=\sum_{l=1}^{L}\sqrt{P_{l}}\mathbf{h}_{l}\odot\mathbf{x}_{l}+\mathbf{w},$
(1)

where $\odot$ stands for the element-wise multiplication,
$\mathbf{y}=\left[y\left(1\right)\,,\ldots\,,y\left(N\right)\right]^{T}$,
$\mathbf{h}_{l}=\left[{h}_{l}\left(1\right),\ldots,{h}_{l}\left(N\right)\right]^{T}$
is the channel vector,
$\mathbf{x}_{l}=\left[x_{l}\left(1\right)\,,\ldots\,,x_{l}\left(N\right)\right]^{T}$
and $\mathbf{w}=\left[w_{1}\,,\ldots\,,w_{N}\right]^{T}$ is the additive white
Gaussian noise (AWGN) vector, $P_{l}$ is the power for the $l$-th user.

In order to recover transmitted signal, the JML detector and ML-SIC detector
[13] can be employed, which are described in the following.

####  II-1 JML detector

The JML detector performs an exhaustive search to simultaneously recover the
transmitted vector $\mathbf{x}_{l}$ for all $l$-th users. Consider the
scenario of two users, both transmitted vectors $\mathbf{x}_{1}$ and
$\mathbf{x}_{2}$ are recovered simultaneously as follow:

$\left\\{\mathbf{\hat{x}}_{l}\right\\}_{l=1,2}=\underset{\mathbf{x}_{l=1,2}\in\delta}{\text{arg
min}}\left\|\mathbf{y}-\sqrt{P_{1}}\mathbf{h}_{1}\odot\mathbf{x}_{1}-\sqrt{P_{2}}\mathbf{h}_{2}\odot\mathbf{x}_{2}\right\|,$
(2)

where JML checks $\mathbf{y}$ for all possible combinations of transmit
vectors of users, which is denoted by $\mathbf{\delta}$. This detector can
provide the optimal performance at the expense of high computational
complexity, thus, it can be used as a benchmark when designing any low
complexity receiver.

####  II-2 ML-SIC detector

Based on this, the SIC-ML detector of user $l$-th operates in the following
iterative fashion. In the case of 2 users, user 1, which is allocated more
power, will detect its own signal first by treating the interference from the
user 2 as the noise. Using the ML criterion, the estimated signal of user 1 is
determined by

$\hat{\mathbf{x}}_{1}=\underset{\mathbf{x}_{1}\in\mathbf{\delta}}{\text{arg
min}}\left\|\mathbf{y}-\sqrt{P_{1}}\mathbf{h}_{1}\odot\mathbf{x}_{1}\right\|.$
(3)

Then, the contribution of user 1 to $\mathbf{y}$ is eliminated for decoding
the signal of user 2. Explicitly, the symbol of user 2 is recovered using the
ML estimate in which the interfering signal of user 1 is estimated by
$\mathbf{\hat{x}}_{1}$, resulting in

$\hat{\mathbf{x}}_{2}=\underset{\mathbf{x}_{2}\in\mathbf{\delta}}{\text{arg
min}}\left\|\left(\mathbf{y}-\sqrt{P_{1}}\mathbf{h}_{1}\odot\hat{\mathbf{x}}_{1}\right)-\sqrt{P_{2}}\mathbf{h}_{2}\odot\mathbf{x}_{2}\right\|.$
(4)

From the formula (2), (3) and (4), the complexity of the conventional
detectors mentioned above would increase, particularly when having more uplink
NOMA users as well as when the SC-IM-NOMA parameters increase. Motivated by
this issue, we propose a DL-based detector to detect transmitted signals with
competitive performance and low complexity compared to these ML-based
detectors.

##  III  Proposed DeepSIC-IM Detector

In this section, the structure of the proposed DeepSIC-IM detector and its
training procedure are presented.

###  III-A Structure of proposed DeepSIC-IM

Figure 2: The proposed DeepSIC-IM DNN structure.

The structure of DeepSIC-IM is illustrated in Fig. 2. Assume that the channel
state information (CSI) is perfectly known at the receiver and considered as
input of the decoder, along with the received signal $\mathbf{y}$. Hence, the
well-known zero-forcing (ZF) equalizer is employed to get an equalized
received signal vector as
$\mathbf{\bar{y}}=\mathbf{y}\odot\mathbf{h}^{-1}_{1}$. Particularly, the
complex vectors $\mathbf{\bar{y}}_{R}$ and $\mathbf{\bar{y}}_{I}$ are
transformed into an $2N$-dimensional real vector
$\mathbf{z}=\left[\mathbf{\bar{y}}_{R},\mathbf{\bar{y}}_{I}\right]$, as shown
in Fig. 2, where $\mathbf{\bar{y}}_{R}$, $\mathbf{\bar{y}}_{I}$ are real and
imaginary parts of $\mathbf{\bar{y}}$.

TABLE I: Parameters of DNN 1 and DNN 2 with $\left(N,K,M\right)=\left(4,1,4\right)$ Parameter | DNN 1 | DNN 2
---|---|---
Input size |  $2N+\left(l-1\right)2^{b}$= 8 |  $2N+\left(l-1\right)2^{b}$= 24
Output size |  $2^{b}$= 16 |  $2^{b}$= 16
FC layer | 3 | 3
Hidden Nodes | 32-64 | 128-256

The input of the $l$-th DNN block includes both $\mathbf{z}$ and the output of
the previous $l-1$ DNN blocks, namely $\mathbf{\text{s}}_{l}$. More
specifically, those elements are concatenated to form an input vector of the
size $\left[2N+\left(l-1\right)2^{b}\right]$. Due to the complexity of each
signal being different (the signal detection for $l$-th user will be more
difficult than that for $\left(l-1\right)$-th user), each DNN to detect each
signal will have a different number of nodes, as shown in Table I.

The proposed decoder of each user has three nonlinear FC layers. At the hidden
layer, either the rectifier linear unit (Relu),
$f_{\text{Relu}}\left(x\right)=\text{max}\left(0,x\right)$, or the hyperbolic
tangent (Tanh) function, $f_{\text{Tanh}}(x)\,=\,\frac{1-e^{-2x}}{1+e^{-2x}}$,
can be used as the activation function. The decoder generates an output
probability vector $\mathbf{\hat{u}}_{l}$ with the Softmax layer as the output
layer. The output vector $\mathbf{\hat{u}}_{l}$ of each DNN with size
$\left[2^{b}\right]$ can be given by

$\mathbf{\hat{u}}_{l}=f_{\text{Softmax}}\left(\mathbf{W}_{3}f_{\text{Relu}}\left(\mathbf{W}_{2}f_{\text{Relu}}\left(\mathbf{W}_{1}\mathbf{\mathbf{s}}_{l}+\mathbf{b}_{1}\right)+\mathbf{b}_{2}\right)+\mathbf{b}_{3}\right),$
(5)

where $\mathbf{\text{W}}_{1}$, $\mathbf{\text{b}}_{1}$,
$\mathbf{\text{W}}_{2}$, $\mathbf{\text{b}}_{2}$ and $\mathbf{\text{W}}_{3}$,
$\mathbf{\text{b}}_{3}$ denote the weights and biases of the first, second and
third FC layers, respectively, $\mathbf{s}_{l}$ is the input vector of the
$l$-th DNN, which is represented by
$\mathbf{s}_{l}=\left[\mathbf{z},\mathbf{\hat{u}}_{1},\ldots,\mathbf{\hat{u}}_{l-1}\right]$.
Finally, we get the vector $\bar{\mathbf{u}}_{l}$ based on the largest entry
of $\hat{\mathbf{u}}_{l}$. Then, the information prediction will be
calculated.

Crucial points of the proposed scheme structure can be described as follows.
First, the length of input and output of DeepSIC-IM is determined by system
parameters such as $N$, $K$ and $M$. This will make the complexity of the
proposed scheme highly dependent on each of the three aforementioned
indicators. Intuitively, when the number of transmitted $b$-bit increases, we
need a number of nodes large enough to guarantee a predetermined performance.
Therefore, the number of nodes of the $l$-th DNN (denoted by
$\mathcal{O}_{l}$) must be carefully chosen to obtain the desired performance
for each system configuration. The value of $\mathcal{O}_{l}$ must be
sufficiently large to ensure a predetermined performance. In addition, we can
attain a promising trade-off between the detection accuracy and the model
complexity by adjusting value of $\mathcal{O}_{l}$.

###  III-B Training Procedure

Before implementing the proposed DeepSIC-IM technique, the DNN model with the
collected data from simulation need to be trained. Initially, various $b$-bit
sequences will be randomly created for $L$ users and transformed into the
matching vector $\mathbf{x}_{l}$. The one-hot vectors $\mathbf{u}_{l}$ are
generated first to create $L$ sets of one-hot labels for $L$ users, while
noise vectors are randomly generated. At the receiver, $\mathbf{y}$ and
$\mathbf{h}_{1}$ are pre-processed to obtain the vector $\mathbf{z}$, which is
then combined with the output of the previous $l-1$ DNN blocks to provide the
input for the $l$-th DNN block $\mathbf{s}_{l}$. The mean square error (MSE)
cost function which is adopted to measure the difference between the
estimation vector $\mathbf{\hat{u}}_{l}$ and its true value vector
$\mathbf{u}_{l}$, as follows:

$\mathcal{L}\left(\mathbf{u}_{l},\hat{\mathbf{u}_{l}};\mathbf{\theta}_{l}\right)=\sum_{l=1}^{L}\frac{1}{b}\left\|\mathbf{u}_{l}-\hat{\mathbf{u}}_{l}\right\|^{2},$
(6)

where $\theta_{l}=\left\\{\mathbf{W}_{i},\mathbf{b}_{i}\right\\}_{i=1,2,3}$
are the weights and biases of the $l$-th DNN user model, $\mathbf{u}_{l}$ is
the collection of one hot vector corresponding to $b$ bits trained offline and
$\mathbf{\hat{u}}_{l}$ is the output vector of the $l$-th DNN. Model
parameters are updated for the batches randomly picked up from data samples,
using the stochastic gradient descent (SGD) algorithm as follows

$\theta^{+}:=\theta-\eta\nabla\mathcal{L}\left(\mathbf{u}_{l},\mathbf{\hat{u}}_{l};\theta\right),$
(7)

where $\eta$ is learning rate. In our training, we use the adaptive moment
estimation (Adam) optimizer, a sophisticated updating technique built on SGD.
The signal to noise ratio (SNR) training (denoted as $\lambda_{train}$), which
has a significant impact on the performance of the training model, will be
chosen to suit the model as closely as possible. For instance, if
$\lambda_{train}$ train is too small, the training will not account for the
influence of noise, which will result in poor generalization of the trained
model. Choosing a suitable $\lambda_{train}$ for achieving the desired
performance will be presented in detail in the simulations.

##  IV Simulation results

This section presents simulation results to demonstrate the performance of our
DeepSIC-IM compared to the existing schemes, including JML and ML-SIC
detectors, in terms of both BER and runtime complexity.

TABLE II: A summary of simulation parameters Parameter | Value
---|---
Number of users $L$ | 2
Parameters of index modulation ($N$, $K$, $M$) | 4,1,4
Gains of channel $\mathbf{h}_{1}$, $\mathbf{h}_{2}$ |  $\left[2,2,2,2\right]$, $\left[1,1,1,1\right]$
Power allocation coefficient $P_{1}$,$P_{2}$ | 2,1
Hidden nodes of DNN 1 | 32-64
Hidden nodes of DNN 2 | 128-256
Activation for hidden layers of DNN 1 | Tanh
Activation for output layers of DNN 1, 2 | Softmax
Activation for hidden layers of DNN 2 | Relu
Training SNR $\lambda_{train}$ | 16, 18, 20, 22, 24 dB
Learning rate $\eta$ | 0.001
Batch size | 200
Number of training epochs | 500
Training data size | $2\times 10^{6}$
Testing data size | $10^{6}$
Optimizer | Adam [22]

###  IV-A Parameter Setting

In Table II, we summarize the SC-IM-NOMA system parameters as well as the DNN
model parameters, which are used for conducting simulations in this section.
For example, we train our DeepSIC-IM with 500 epochs, each contains $10^{4}$
samples, where the batch size is 200 samples. During training, data samples
are randomly generated for each batch. Therefore, we have a total of $2\times
10^{6}$ different data samples for training, while the testing size is
$10^{6}$ samples. The learning rate $\eta$ is set to be 0.001.

We note that in this work we only consider fixed channels for both users, as
shown in Table II. For varying or random fading channels, we may have to use
some advanced training techniques, such as feed-forward error correction
(FEC)-aided online labeling [17]. We consider such the extension as our future
work. Furthermore, throughout extensive experiments, we discovered that user 1
would prefer the Tanh activation function, while user 2 would prefer the Relu
activation function, for better BER performance, as shown in Table II.

###  IV-B BER Performance

Figure 3: BER performance of DeepSIC-IM for user 1 trained at various training
SNRs $\lambda_{train}$. The training setting is described in Table II. Figure
4: BER performance of DeepSIC-IM for user 2 trained at various training SNRs
$\lambda_{train}$. The training setting is described in Table II.

The BER performance of user 1 and user 2 using the proposed DeepSIC-IM trained
at various training SNRs is illustrated in Fig. 3 and Fig. 4, respectively. It
is shown from both figures that the BER performance achieved by DeepSIC-IM for
both users varies with respect to the training SNR, especially at high testing
SNRs. It is also observed that our proposed DeepSIC-IM tends to achieve the
best BER for the two users when the training SNR is between 18 and 20 dB.
Therefore, in the following, we will use a training SNR of 18 dB for training
DeepSIC-IM to compare with the baseline.

Figure 5: BER comparison between the proposed DeepSIC-IM and baselines with
training SNR $\lambda_{train}$ = 18dB. The training setting is described in
Table II.

Fig. 5 compares the BER performance among the proposed DeepSIC-IM detector,
JML and ML-SIC detector, where both users are considered, and our scheme is
trained at 18 dB. It is shown from Fig. 5 that the proposed learning detector
attains BER performance very close to that of the JML and ML-SIC detectors.
For example, at the BER of $10^{-2}$, the SNR gap between the proposed
detector, JML and ML-SIC is negligible with less than 0.4 dB and 0.3 dB,
respectively, while our detector requires much lower runtime complexity than
its counterpart, as shown in the following subsection.

###  IV-C Runtime Complexity

We now measure the runtime for detecting each sample of the proposed DeepSIC-
IM, JML and ML-SIC detectors. In particular, we convert the DeepSIC-IM model
that was trained using the Tensorflow library to MATLAB. To ensure a fair
comparison, the JML and ML-SIC detectors are also run on MATLAB on the same
computer. The obtained complexity for the three detectors measured in seconds
is compared in Table III. It is show from this table that the proposed
learning detector demands much less runtime than both the JML and ML-SIC
detectors. More particularly, the runtime of our DeepSIC-IM is 7 and 3 times
less than that of the JML and ML-SIC, respectively, which clearly validates
the advantage of the proposed detector in terms of runtime complexity.

TABLE III: Complexity comparison among DeepSIC-IM, JML and ML-SIC $(N,K,M)$ | JML | ML-SIC | DeepSIC-IM
---|---|---|---
(4,1,4) | $7.65\times 10^{-4}$ | $3.31\times 10^{-4}$ | $1.14\times 10^{-4}$

##  V Conclusions

In this paper, we proposed the DeepSIC-IM detector for the SC-IM-NOMA system.
In particular, we designed a novel DNN structure for SC-IM-NOMA that includes
several DNN blocks, each used for detecting the transmitted signal of the
corresponding user, where its input data is made up of the pre-processed
received signal and the output of the interfering users. Once trained with
simulated dataset, our proposed method can be deployed for detecting data bits
in an online manner with very low runtime. Our simulation results demonstrated
that the proposed DeepSIC-IM detector achieves near-optimal BER performance at
remarkably lower runtime complexity compared to the existing ML-based
detectors. Although we only consider two uplink NOMA users in this work, the
extension of DeepIM-SIC for more users is straightforward. In the future, we
plan to extend the proposed DeepSIC-IM to time-varying channels, where the
channel coding-aided online training technique in [17] is helpful.

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