# DeepMA: End-to-end Deep Multiple Access for Wireless Image Transmission in
Semantic Communication

Wenyu Zhang, Kaiyuan Bai, Sherali Zeadally, Haijun Zhang, Hua Shao, Hui Ma,
Victor C. M. Leung Wenyu Zhang, Hua Shao, and Hui Ma are with the School of
Intelligence Science and Technology, and the Institute of Artificial
Intelligence, University of Science and Technology Beijing, Beijing, 100083,
China. Emails<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>Bai is with the China Telecom Research Institute,
Beijing, 100096, China. Email<EMAIL_ADDRESS>Zeadally is with
the College of Communication and Information, University of Kentucky,
Lexington, KY 40506 USA. Email<EMAIL_ADDRESS>Zhang is with the
Beijing Advanced Innovation Center for Materials Genome Engineering, Beijing
Engineering and Technology Research Center for Convergence Networks and
Ubiquitous Services, University of Science and Technology Beijing, Beijing
100083, China. E-mail<EMAIL_ADDRESS>C. M. Leung is with the
College of Computer Science and Software Engineering, Shenzhen University,
Shenzhen 518060, China, and also with the Department of Electrical and
Computer Engineering, The University of British Columbia, Vancouver, BC V6T
1Z4, Canada E-mail<EMAIL_ADDRESS>
###### Abstract

Semantic communication is a new paradigm that exploits deep learning models to
enable end-to-end communications processes, and recent studies have shown that
it can achieve better noise resiliency compared with traditional communication
schemes in a low signal-to-noise (SNR) regime. To achieve multiple access in
semantic communication, we propose a deep learning-based multiple access
(DeepMA) method by training semantic communication models with the abilities
of joint source-channel coding (JSCC) and orthogonal signal modulation. DeepMA
is achieved by a DeepMA network (DMANet), which is comprised of several
independent encoder-decoder pairs (EDPs), and the DeepMA encoders can encode
the input data as mutually orthogonal semantic symbol vectors (SSVs) such that
the DeepMA decoders can detect and recover their own target data from a
received mixed SSV (MSSV) superposed by multiple SSV components transmitted
from different encoders. We describe frameworks of DeepMA in wireless device-
to-device (D2D), downlink, and uplink channel multiplexing scenarios, along
with the training algorithm. We evaluate the performance of the proposed
DeepMA in wireless image transmission tasks and compare its performance with
the attention module-based deep JSCC (ADJSCC) method and conventional
communication schemes using better portable graphics (BPG) and Low-density
parity-check code (LDPC). The results obtained show that the proposed DeepMA
can achieve effective, flexible, and privacy-preserving channel multiplexing
process, and demonstrate that our proposed DeepMA approach can yield
comparable bandwidth efficiency compared with conventional multiple access
schemes.

###### Index Terms:

Channel multiplexing, deep learning, multiple access, semantic communication,
wireless image transmission

##  I Introduction

In a conventional communication system, the data processing process mainly
includes the following three parts: source coding for improving transmission
efficiency by reducing the information redundancy of the source data, channel
coding for enhancing the transmitting reliability by using error-check or
error-correcting coding techniques, and signal modulation for improving the
channel resource utilization efficiency by enabling multiple users to transmit
data over a shared physical channel, while transforming the digital signals as
high-frequency waveforms that are suitable for wireless transmission [1].
These processes are conducted by specific and separable functional blocks,
which are designed independently without jointly considering the influences of
other blocks. This separable architecture significantly reduces the design,
development, and maintenance costs of the communication system, but it is
suboptimal from the perspective of end-to-end optimization [2][3].

In recent years, the rapid development of artificial intelligence (AI),
especially deep learning (DL)-based autoencoder models, has enabled us to
achieve the end-to-end semantic communication process by leveraging the
powerful data compression and noise resiliency capability of deep learning
models. A typical semantic communication system (SCS) is mainly composed of a
trainable semantic encoder, a non-trainable noisy physical communication
channel, and a trainable semantic decoder [3][4]. Both semantic encoder and
semantic decoder are realized by using deep learning models, such as
convolution neural networks (CNNs), recurrent neural networks (RNN), and
attention networks. A typical semantic encoder automatically conducts the
joint source-channel coding process to extract the semantic features that are
suitable for transmission over a noisy physical channel. The feature data
contains the semantic contents and channel code of the input data, and in the
physical channel it can be corrupted with noises and interferences after the
transmission process, which may cause semantic distortion to the final
reconstructed result. In accordance with the semantic encoder, a paired
semantic decoder can automatically complete the inference task directly from
the received semantic symbols corrupted by noises or interferences. If the
inference task is recovering the original input data, then the decoder must
perform the channel decoding and source decoding process jointly.

Recent studies [3][5][6][7] have shown that semantic communication can achieve
high communication efficiency and noise resiliency in various data
transmission scenarios, such as video/image transmission [5][8], speech
transmission [6], and text transmission [7]. More specifically, by utilizing
the powerful feature extraction capability of deep learning models, semantic
communication models can achieve a higher data compression ratio compared with
classical data compression methods so that the amount of transmitted data can
be further reduced. Second, deep learning models can be trained with powerful
noise resiliency capability, which enables the semantic communication models
to complete the inference task to obtain high-quality results when there is
some noise and interferences. Semantic encoders and decoders are jointly
trained end-to-end between the source input data at the transmitter and the
final inference result at the receiver. Thus, the source channel encoding and
decoding process are jointly optimized, and it is globally optimal compared
with conventional communication systems with separate functional blocks.
Semantic communication can achieve a relatively stronger noise resiliency in a
low channel signal to noise ratio (SNR) regime, while in conventional
separable communication schemes, the transmission reliability suffers from the
’cliff effect’, i.e., the transmission performance drops sharply when the
channel condition is poor, and even fails to transmit data.

In conventional communications, multiple access (multi-access) is a commonly
used technology that enables multiple users to multiplex the communication
channel without interfering with each other, which is helpful for improving
the utilization efficiency of the channel resources, and typical methodologies
include orthogonal frequency division multiple access (OFDMA) [9], time
division multiple access (TDMA) [10], code division multiple access (CDMA)
[11], and non-orthogonal multiple access (NOMA) [12]. Among them, OFDMA
achieves multiplexing by allocating the dedicated frequency sources to the
user equipments (UEs), and TDMA avoids interference by dividing and allocating
UEs with different transmission timeslot resources. NOMA can support the co-
frequency transmission by using a successive interference cancellation
technique. CDMA is an orthogonal multiple access (OMA) method that can achieve
channel multiplexing by modulating the data bits of multiple users using a set
of orthogonal codes, such that the data can be transmitted over with the same
frequency, and the receiver can recover the data by demodulating the received
data with the same code. CDMA enables multiple UEs to transmit data over a
shared physical channel with the same frequency without worrying about
collisions while protecting the data privacy when the basis code used is
unknown to other UEs, and it has been widely used in conventional
communication systems [1].

As a new communication paradigm, currently, semantic communication research
mainly addresses the deep learning-based joint source-channel coding
(DeepJSCC) problem for point-to-point communication tasks [3] but how to
achieve co-frequency multiple access to enable multiple semantic data streams
to be transmitted simultaneously with the same frequency remains an unexplored
problem. Compared with conventional multiplexing methods, realizing co-
frequency multi-access in semantic communication has the following
differences:

  * •

End-to-end vs separable: Semantic communication achieves end-to-end
communication by leveraging the powerful learning capability of deep learning
models. If we can achieve DeepJSCC and orthogonal modulation in one OMA-
enabled semantic communication model, then there is no need to use the
conventional separable OFDMA or TDMA-based multiple access methods because the
semantic symbols are already orthogonal to each other, and the system
complexity will be significantly reduced.

  * •

Continuous vs binary: Conventional CDMA is only suitable for transmitting bit
data, and it is not suitable for semantic codes with continuous values.
Moreover, from the perspective of bandwidth efficiency, CDMA is not an ideal
choice because its spread spectrum process will significantly decrease the
bandwidth efficiency. Therefore, it is necessary to develop a specific multi-
access method that is suitable for transmitting continuous symbols in semantic
communication systems with high bandwidth efficiency.

  * •

Lossy vs lossless: Conventional communication requires that the transmitted
bit data be lossless, i.e., every bit is correctly transmitted, while semantic
communication is lossy and the received symbols are allowed to be
misinterpreted or distorted to the original transmitted symbols. For CDMA,
when the received codes has error bits, the transmission fails, which is not
compatible to the lossy semantic communication process.

Thus, we can see that conventional multiple access methods are not the best
choices for semantic communication systems. In particular, conventional CDMA
is actually not applicable in semantic communication due to the differences we
have mentioned above. To achieve co-frequency OMA in semantic communication,
we propose deep learning-based multiple access (DeepMA) to enable lossy and
orthogonal channel multiplexing by exploiting the capabilities of the DL
models. We summarize the main contributions of this work as follows:

  * •

We propose a channel multiplexing-enabled DeepMA network (DMANet), which is
comprised of multiple DeepMA encoder-decoder pairs (EDP), and the EDPs are
trained with the abilities of JSCC and orthogonal signal modulation. Similar
to CDMA, a DMANet can support channel multiplexing by transmitting multiple
orthogonal semantic symbol vectors (SSVs) simultaneously, and the DeepMA
decoders can recover the target data from a received mixed SSV (MSSV)
superposed by several different SSVs. In contrast to CDMA, the orthogonal
modulation process in DeepMA is learned by the model training process, and it
is automatically conducted without the help of an orthogonal basis. DeepMA can
achieve end-to-end and lossy semantic communication for continuous semantic
symbol data with channel multiplexing. In addition, to avoid unnecessary
computation cost, a SSV gate (SSVG) is introduced to conduct the user
detection process to avoid the unnecessary decoding process of undesired data.

  * •

We conducted simulations to evaluate the performance of the proposed DeepMA in
wireless image transmission tasks. First, we developed an attention module and
residual structure-based DeepMA encoder and decoder models, and then trained
the models by using CIFAR10 and ImageNet data. After training, we compare the
peak-signal-to-noise (PSNR) performances of the proposed DeepMA models, ADJSCC
models, and conventional communications schemes that use better portable
graphics (BPG) [13] for source coding and low-density parity-check (LDPC) for
channel coding [2]. We used the ADJSCC model as the reference method for non-
multiplexing semantic transmission to show how the multiple access process
influences the transmission capacity of DeepMA. We used the conventional
multiple access schemes as baselines to demonstrate the performance of our
proposed DeepMA. To demonstrate the performance of the proposed DeepMA, we
first present some illustrative examples to show the mutual orthogonality of
the SSVs, which is also helpful for us to understand why DeepMA can achieve
OMA, and how to use SSV orthogonality to conduct user detection. The
illustrative examples show that a DeepMA decoder can effectively recover the
target image from an MSSV that contains the SSV transmitted from the paired
DeepMA encoder but cannot obtain any useful information if the paired DeepMA
encoder does not send the SSV, showing that the proposed DeepMA can achieve
flexible and privacy-protected multiple access. We compare the (PSNR)
performances achieved by DeepMA, ADJSCC, and conventional BPG+LDPC schemes
with different channel SNR, and the results demonstrate that the proposed can
achieve high-quality recovered images with channel multiplexing, and show that
DeepMA can achieve better noise-resiliency compared with conventional BPG+LDPC
schemes in a very low SNR regime.

We organize the remainder of this paper as follows. Section 2 discusses
related works. Section 3 presents our proposed DeepMA method along with the
training algorithm. Section 4 presents the performance evaluation results on
wireless image transmissions. We also describe the architecture of the DMANet
used. Finally, Section 5 concludes the paper.

_Notation_ : $\mathbb{C}^{n}$ and $\mathbb{R}^{n}$ mean the complex and real
data with total dimensions $n$ respectively.
$x\sim\mathcal{CN}(\mu_{x},\sigma_{x}^{2})$ designates variable $x$ follows a
circularly-symmetric complex Gaussian distribution with mean $\mu_{x}$ and
$\sigma_{x}^{2}$. Variables with bold fonts mean that they are matrices or
vectors. $\mathbf{a}\cdot\mathbf{b}$ means the dot-product of vectors
$\mathbf{a}$ and $\mathbf{b}$. $\mathbf{x}^{*}$ means the conjugate transpose
of complex variable $\mathbf{x}$. Finally, $\mathbb{E}[x]$ means the
expectation value of variable $x$, and $\mathbf{I}$ denotes the identity
matrix.

##  II Related Work

Semantic communication can be used for dealing with a broad range of
intelligent inference tasks over the network [3][14]. These tasks include
answering visual questions [15], image retrieval [16], speech recognition [6],
and video classification [17]. In this paper, we mainly consider the semantic
communication scenario with the goal of recovering the input data at the
receiver, and the data modalities considered can be image/video, speech audio,
and language text. For example, for text data transmission, Farsad et.al [18]
proposed a bidirectional long short-term memory (BLSTM) network to achieve
JSCC. The proposed method achieved a lower word error rate compared with the
traditional gzip and Huffman coding methods. Xie et.al [7] proposed a deep
learning-based semantic communication (DeepSC) system that is built by the
Transformer based semantic encoder/decoder along with a fully connected layer-
based channel encoder/decoder. During the training process, DeepSC maximizes
sentence similarity by using the bilingual evaluation understudy (BLEU) score,
and transfer learning is used for enabling the system to be applicable to
different communication environments. Experimental results obtained
demonstrate that the proposed SCS approach can achieve higher BLEU compared
with traditional communication systems, especially in situations where the
channel SNR is low. In a similar way, the authors of [6] proposed DeepSC for
speech (DeepSC-S) transmission, and the results demonstrated that DeepSC-S
outperforms the traditional speech transmission schemes for both speech
recovery quality and noise-resiliency.

In this paper, we focus on using semantic communication for solving wireless
image transmission tasks, and related works have shown that DeepJSCC methods
can achieve excellent data compression and noise resiliency abilities
[19][20][21][22]. In [5], the authors proposed a DeepJSCC method for wireless
image transmission. Simulation results showed that the proposed DeepJSCC
outperforms the traditional JPEG and JPEG-2000 image compression methods in
low SNR regimes. Compared with traditional digital communication schemes,
DeepJSCC does not suffer from the ’cliff effect’, and it has an strong noise
resiliency capability against the degradation of channel SNR. To further
improve the performance of JSCC, Kurka et.al [23] proposed the use of channel
output feedback to enhance the reliability of the transmission process. The
proposed method can achieve better image reconstruction quality, but it
requires multiple transmissions for one input data. Thus, the communication
efficiency will be reduced. Later, the authors proposed the successive
refinement-based DeepJSCC method to enhance the quality of the reconstructed
images at the receiver [24]. From the perspective of ensemble learning [25],
the performance improvements achieved by the above two methods comes from the
integration of multiple DeepJSCC models with diverse DeepJSCC models and
physical channels, and the quality of the final combined results can be
improved compared with using only one single model [26][27].

The proposed DeepJSCC models above suffer from the SNR adaptation problem,
i.e., a DeepJSCC model can only perform well when the channel SNR is similar
to its training SNR. To achieve the best performance, we need to train several
different DeepJSCC models to cover both low and high SNR regimes. To solve
this problem, Xu et.al [28] proposed an attention-based DeepJSCC (ADJSCC),
which can adaptively adjust the joint source-channel coding process according
to the variation of channel SNR. In a low SNR regime, the attention module can
automatically guide the model to assign more coding resources to the channel
coding process to enhance transmission reliability. On the other hand, in a
high SNR regime, more encoding resources will be assigned to the source coding
process to improve the compression ratio. Simulation results demonstrated that
one ADJSCC model can achieve the best achievable performance of several
DeepJSCC models training with different channel SNRs combined. Therefore,
ADJSCC can greatly reduce the training and deployment cost of Deep learning-
based JSCC models.

Except for the SNR adaptation problem, previous DeepJSCC models were trained
with specific code rates or compression ratios and cannot be changed after
training. To achieve multi-rate transmission, in [29], the authors proposed an
adaptive DeepJSCC model that can automatically adjust its rate using a single
network model. More specifically, in the proposed method the encoder is
divided into two separate models: source encoder and channel encoder, and the
semantic symbols obtained are divided into two parts: the non-selective part
that is always active for transmission, and the selective part that can be
active or inactive for transmission. A policy network is introduced for
determining which selective channel codes are active for transmission
according to the image contents and channel condition. In this way, the
proposed method can support multi-rate transmission for semantic
communication. In the above work, the proposed method cannot achieve an
arbitrary transmission rate, and transmission quality cannot be guaranteed. In
[30], we proposed a predictive and adaptive deep coding (PADC) framework,
which can flexibly adjust compression rates at the same time ensuring the
transmission quality constraint for every single image thereby providing an
effective solution for solving the rate adaptation problem in DeepJSCC.

All the works discussed above focus on the DeepJSCC problem for achieving
point-to-point semantic communication scenario, and the OMA problem has not
been investigated. As such, in this paper, we propose DeepMA to achieve
channel multiplexing and demonstrate that, by leveraging deep learning, we can
obtain effective OMA in semantic communication, and can reap better bandwidth
efficiency compared with conventional multiple access schemes in low SNR
regimes.

Figure 1: The proposed DeepMA framework. Figure 2: DeepMA for wireless D2D,
downlink, and uplink transmissions with channel multiplexing.

##  III The Proposed DeepMA

Fig.1 shows the basic framework of DeepMA, wherein the deep coding and
modulation (DCM) processes of a transmitter and a receiver are realized by a
semantic encoder and semantic decoder respectively. More specifically, for the
encoder, except for source encoding and channel encoding, it also conducts
orthogonal signal modulation such that the transmitted SSVs are mutually
orthogonal. Accordingly, the decoder conducts the joint orthogonal signal
demodulation, channel decoding and source decoding processes, such that it can
detect and recover the transmitted data from several superposed SSVs. The
encoders and decoders obtain the DCM abilities from a model training process,
in which the EDPs can automatically learn background knowledge on how to
achieve OMA with different training data and channel conditions. Given
different training data and channel environments, the background knowledge
learned can be different. The transmission quality of DeepMA is jointly
influenced by factors such as semantic ambiguity, model capability, data
compression ratio, and physical channel. In particular, in DeepMA the
transmitted SSVs are mixed at the physical channel, and its main goal is to
achieve OMA to eliminate the influence of other SSVs transmitted from unpaired
encoders. In this section, we will describe the system model, design, and
training algorithm of DeepMA.

###  III-A System Model

In addition to Fig. 1, Fig. 2 shows the system model of the proposed DeepMA in
more detail. We denote the set of transceivers as
$\mathcal{V}=\left\\{(\text{Tx}_{1},\text{Rx}_{1}),\ldots,(\text{Tx}_{N},\text{Rx}_{N})\right\\}$,
in which $\text{Tx}_{i}$ and $\text{Rx}_{i}$ denote the transmitter and
receiver of transceiver $i$ respectively. We construct a DeepMA network
(DMANet) that is composed of $N$ DeepMA encoder-decoder pairs (EDPs), denoted
as
$\mathcal{P}=\left\\{(E_{\phi_{1}},D_{\theta_{1}}),\ldots,(E_{\phi_{N}},D_{\theta_{N}})\right\\}$,
in which $E_{\phi_{i}}$ means the DeepMA encoder model of EDP $i$ is
parameterized by $\phi_{i}$, and $D_{\theta_{i}}$ designates the corresponding
DeepMA decoder network parameterized by $\theta_{i}$. The encoder model
$E_{\phi_{i}}$ and decoder model $D_{\theta_{i}}$ are deployed at the
transmitter $\text{Tx}_{i}$ and receiver $\text{Rx}_{i}$ respectively. When
$N=1$, the DMANet is equivalent to a DeepJSCC network. The deployment of
DeepMA model can be flexible, including the following three scenarios:

  * •

Device-to-device (D2D): Each UE is equipped with one encoder model or decoder
model, and each transmitter or receiver corresponds to one UE.

  * •

Downlink: All encoders are deployed at the base station (BS), and each UE
receiver has a decoder model. Therefore, we have only one transmitter, but
multiple receivers.

  * •

Uplink: All the decoders are deployed at the BS, and each UE transmitter has
an encoder model. Therefore, we have only one receiver, but multiple
transmitters.

We denote $\mathbf{z}_{i}\in\mathbb{C}^{K}$ as the SSV transmitted by
$\text{Tx}_{i}$, and each symbol of SSV $\mathbf{z}_{i}$ experiences an
independent transmission process over through a noisy physical channel. We
consider the AWGN channel and slow Rayleigh fading channel in this paper,
which are two commonly used channel models. In a co-frequency multi-access
scenario, the received signal of $\text{Rx}_{i}$ in AWGN channel case is
formulated as:

$\tilde{\mathbf{z}_{i}}=\sum_{i=1}^{N}\mathbf{z}_{i}+\mathbf{n}_{i},$ (1)

where $\mathbf{n}_{i}\in\mathcal{CN}(0,\sigma_{i}^{2}\mathbf{I})$ denotes the
independent identically distributed (i.i.d) AWGN samples with power
$\sigma_{i}^{2}$. In the slow Rayleigh fading channel case, the transmitted
signals experience independent channel fading processes. We equip each node
with a single antenna, then the channel state information (CSI) among the
transmitters and receivers is denoted by a matrix
$\mathbf{H}\in\mathbb{C}^{N\times N}$, in which $h_{i,j}$ denotes the CSI from
transmitter $\text{Tx}_{i}$ and receiver $\text{Rx}_{j}$. For transceiver $i$,
the CSI from its transmitter to receiver $h_{i,i}$ must be known to the
receiver, but other CSI information is not required to be known to the
receiver.

In the D2D transmission scenario, as Fig.2(a) shows, there are $N$ UEs
transmitting SSVs, and accordingly there are $N$ UEs receiving data, and one
UE transmitter has one and only one paired UE receiver. For SSV
$\mathbf{z}_{i}$, it is transmitted to the corresponding receiver, at the same
time superposed with other SSVs, and corrupted with AWGN, and the mixed SSV
(MSSV) received is:

$\mathbf{z}_{i}^{\text{rev}}=\sum_{k=1}^{N}h_{k,i}\mathbf{z}_{k}+\mathbf{n}_{i}.$
(2)

In the downlink transmission scenario, as Fig.2(b) shows, in the BS, the data
arrived is first encoded as the SSVs by using the DeepMA encoders, then
superposed as the MSSV, and subsequently transmitted to the UEs through the
downlink channel. In this scenario, we can simplify the CSI as
$h_{1,i}=\ldots=h_{N,i}=h^{(i)}$ for $i\in\mathcal{N}$, and the MSSV received
is:

$\mathbf{z}_{i}^{\text{rev}}=h^{(i)}\sum_{k=1}^{N}\mathbf{z}_{k}+\mathbf{n}_{i}.$
(3)

In the uplink transmission scenario, as Fig.2(c) shows, we can also simplify
the CSI as $h_{i,1}=\ldots=h_{i,N}=h_{i}$ for $i\in\mathcal{N}$. In addition,
the AWGN for all RMSSVs are the same, i.e.,
$\mathbf{n}_{1}=\ldots=\mathbf{n}_{N}=\mathbf{n}$. Then we can know the MSSV
received by the BS is:

$\mathbf{z}^{\text{rev}}=\sum_{i=1}^{N}h_{i}\mathbf{z}_{i}+\mathbf{n}.$ (4)

We note that, the SSV transmitting processes defined by equations (3) and (4)
are actually two simplified cases of equation (2). It also worth noting that
in downlink and uplink scenarios, the BS needs to access the data contents
before encoding or after decoding, and this requirement may cause privacy
concerns for the UEs. In this paper, we assume that the BS can protect the
privacy for the transmitted data, and we only focus on the multiple access
problem in DeepMA.

###  III-B Encoding Process

In DeepMA, an encoder of an EDP is a deep learning model that conducts the
JSCC and orthogonal signal modulation process, such that its input data can be
transformed into a SSV that is suitable for wireless transmission with OMA.
More specifically, for EDP $i\in\mathcal{P}$, we denote the input data as
$\mathbf{x}_{i}\in\mathbb{R}^{L}$, and before transmitting, it is encoded as a
$K$-dimensional complex semantic feature data
$\mathbf{y}_{i}\in\mathbb{C}^{K}$ by using its encoder model $E_{\phi_{i}}$,
i.e.,

$\mathbf{y}_{i}=E_{\phi_{i}}(\mathbf{x}_{i},\gamma_{i}),$ (5)

where $\gamma_{i}$ denotes the channel SNR. We note that the transmission
performance of an EDP is also influenced by the channel condition, and the
channel SNR will also be an input data to the encoder. If the semantic feature
$\mathbf{y}_{i}$ is not a vector, it will be reshaped as a vector stream for
the following transmission process. To meet the power constraint,
$\mathbf{y}_{i}$ will be normalized by using the following equation:

$\mathbf{z}_{i}=\sqrt{KP_{z}}\frac{\mathbf{y}_{i}}{\mathbf{y}_{i}^{*}\mathbf{y}_{i}},$
(6)

where $P_{z}>0$ denotes the average transmitting power constraint. In this
paper, we call the above normalized semantic feature as the semantic symbol
vector (SSV). The average power constraint $P_{z}$ can be set to a proper
value that is larger than 0, for example, $P_{z}=1$. After the power
normalization, the SSVs are transmitted to the decoder sides.

In contrast to the SSVs obtained from the encoder in existing DeepJSCC models,
in DeepMA we require the SSVs are mutually orthogonal, as given by:

$\frac{1}{K}\mathbb{E}[\mathbf{z}_{i}^{*}\mathbf{z}_{j}]=\begin{cases}P_{z},&\mbox{if
}i=j\\\ P_{\bot},&\mbox{otherwise}.\end{cases}$ (7)

In the equation above, the value of $P_{\bot}$ is very small and close to 0,
i.e. $P_{\bot}\simeq 0$. The orthogonality above is learned during the
training process of DeepMA, and it will be further illustrated and verified in
the following subsections.

###  III-C Decoding Process

After the MSSVs are received, the DeepMA decoders conduct the joint orthogonal
signal demodulation, and source-channel decoding processes, and finally obtain
the reconstructed data. Before decoding, we must first compute its recovered
MSSV (RMSSV) to reduce the impact of the wireless channel. For decoder
$D_{\theta_{i}}$, its RMSSV is computed as follows:

$\tilde{\mathbf{z}}_{i}=\frac{\mathbf{z}_{i}^{\text{rev}}}{h_{i,i}}.$ (8)

It is worth noting that in uplink scenario, the MSSV received of all decoders
are the same, i.e.,
$\mathbf{z}_{1}^{\text{rev}}=\ldots=\mathbf{z}_{N}^{\text{rev}}=\mathbf{z}^{\text{rev}}$.

In a multi-access scenario, the RMSSV obtained may not contain the SSV
transmitted from the paired encoder, and it is better to be abandoned because
the decoding process will cause unnecessary computation cost, especially when
the complexity of the decoder model is high. In addition, DeepMA itself has
good data privacy protection ability and a decoder cannot recover the data
transmitted from other unpaired encoders. We present examples to demonstrate
this property in the following section.

Figure 3: User detection using a SSVG.

To classify whether the RMSSV contains the desired SSV component, as Fig. 3
shows, we use a SSV gate (SSVG) to conduct user detection operation by
utilizing the orthogonality of the SSVs. More specifically, we first prepare a
set of reference SSVs samples transmitted from the paired encoder at the
decoder side. We denote the reference SSV samples as
$\mathbf{z}_{1}^{\text{ht}},\ldots,\mathbf{z}_{M}^{\text{ht}}$, then we can
compute the average absolute correlation degree (AACD), denoted as $R_{i}$,
between the RMSSV and reference SSV samples, as given by:

$R_{i}=\frac{1}{KM}\sum_{m=1}^{M}\left|\tilde{\mathbf{z}}_{i}^{*}\mathbf{z}_{m}^{\text{ht}}\right|.$
(9)

When the RMSSV contains a desired SSV component, $R_{i}$ will be a relatively
large value, otherwise it will be a very small value. We note that the
correlation between SSV and AWGN is nearly 0, thus AWGN will not influence the
correlation value obtained by the equation above. In this way, we can use the
thresholding operation to detect the target SSV. Let $R^{\text{th}}>0$ be the
decision threshold, and we can know that, when $R_{i}\geq R^{\text{th}}$, then
the RMSSV contains a target SSV, otherwise it is a non-desired one, and can be
abandoned, as given by:

$\text{decision}=\begin{cases}\text{accept},&\mbox{if }R_{i}\geq
R^{\text{th}}\\\ \text{abandon},&\mbox{otherwise}.\end{cases}$ (10)

If RMSSV $\tilde{\mathbf{z}}_{i}$ is accepted, it will be used to recover the
input data, as given by:

$\tilde{\mathbf{x}}_{i}=D_{\theta_{i}}(\tilde{\mathbf{z}}_{i},\gamma_{i}).$
(11)

In the decoding process above, the DeepMA decoder $D_{\theta_{i}}$ conducts
joint orthogonal demodulation and source-channel decoding processes, such that
the decoder can extract the target SSV and recover the input data from the
RMSSV.

###  III-D DeepMA Training

As we have previously mentioned, DeepMA can be used in D2D, downlink, and
uplink transmission scenarios to achieve co-frequency channel multiplexing. In
the model training process, we recall that the transmission process defined by
equations (3) and (4) are two simplified cases of equation (2), and there is
no need to train specific models for all the three scenarios because a DMANet
trained in the D2D scenario can also be deployed in the uplink and downlink
transmission scenarios.

In DeepMA, each EDP only transmits and recovers its target data
$\mathbf{x}_{i}$, and its loss function is defined as:

$\mathcal{L}(\theta_{i},\phi_{i};\mathbf{x}_{i})=d(\mathbf{x}_{i},\tilde{\mathbf{x}}_{i}),$
(12)

where $d(\mathbf{x}_{i},\tilde{\mathbf{x}}_{i})$ denotes the distortion metric
between the original input $\mathbf{x}_{i}$ and the recovered result
$\tilde{\mathbf{x}}_{i}$. In this paper, we use the mean square error (MSE) as
the distortion metric, and therefore we have
$d(\mathbf{x}_{i},\tilde{\mathbf{x}}_{i})=\|\mathbf{x}_{i}-\tilde{\mathbf{x}}_{i}\|^{2}/L$,
and $L$ denotes the dimension of input data $\mathbf{x}_{i}$. It is worth
noting that the final result $\tilde{\mathbf{x}}_{i}$ is recovered from an
RMSSV that is mixed by the SSVs transmitted by all the DeepMA encoders, as
formulated in equation (2). The loss function of the whole DMANet is quite
simple, and it is set to minimize the average distortions between the input
data and the recovered results of all the EDPs, as given by:

$\displaystyle\mathcal{L}(\Phi,\Theta;\mathbf{X})$
$\displaystyle=\frac{1}{N}\mathcal{L}(\theta_{i},\phi_{i};\mathbf{x}_{i})=\frac{1}{N}\sum_{i=1}^{N}d(\mathbf{x}_{i},\tilde{\mathbf{x}}_{i}),$
(13)

where $\Theta=\left\\{\theta_{1},\ldots,\theta_{N}\right\\}$ and
$\Phi=\left\\{\phi_{1},\ldots,\phi_{N}\right\\}$ denote the parameters of
DeepMA encoders and decoders respectively,
$\mathbf{X}=\left\\{\mathbf{x}_{1},\ldots,\mathbf{x}_{N}\right\\}$ means the
input training data samples. The loss function above enables us to train the
decoders to recover their own target data from a received MSSV in wireless D2D
transmission scenarios. By using a gradient descent algorithm, the parameters
of the whole DMANet can be learned as:

$(\Phi^{*},\Theta^{*})=\text{argmin}_{\Phi,\Theta}\,\,\mathbb{E}_{\mathbf{x}}\left[\mathcal{L}(\Phi,\Theta;\mathbf{X})\right].$
(14)

We note that, except for source-channel coding/decoding, DeepMA encoders and
decoders also will be trained with orthogonal modulation and demodulation
processes, which are key enablers for achieving OMA-based multiple access with
a shared physical channel. In the same way as existing DeepJSCC models, the
proposed DeepMA is also trained in an end-to-end way. One main difference is
that, since we want to achieve co-frequency channel multiplexing, in each
training iteration the input data batch of each EDP must be different, such
that the decoders can be trained with the ability to recover different data
from an RMSSV. More specifically, in each training iteration, we need $N$
different data batches for the $N$ different EDPs. In this way, the decoder of
one EDP will be trained to recover its own data from the received RMSSV, and
ignore the impact of other SSV components transmitted from unpaired encoders.

Algorithms 1 illustrate the process of one training iteration for DMANet-N in
D2D transmission scenarios, in which
$\mathcal{E}_{\Phi}=\left\\{E_{\phi_{1}},\ldots,E_{\phi_{N}}\right\\}$ and
$\mathcal{D}_{\Theta}=\left\\{D_{\theta_{1}},\ldots,D_{\theta_{N}}\right\\}$
denote the DeepMA encoders and decoders respectively. In one training
iteration, we first sample different data batches for different EDPs, then
forward the data batches $\mathbf{x}_{1},\ldots,\mathbf{x}_{N}$ through the
DMANet, and compute the loss by using equation (13), and further compute the
gradients of all model parameters. For the channel model, the CSI and AWGN of
each transmitted SSV are randomly generated such that the channel realizations
are random. Note that the user detection operation is not needed to be
conducted in the training process. At last, the parameters $(\Phi,\Theta)$ of
DMANet can be updated by using the gradients obtained, and one training
iteration is finished. We repeat the training iteration until the loss
achieves convergence.

Algorithm 1 One training iteration for DMANet-$N$.

1: Input: Training dataset $\mathbf{X}$, transmitting power $P_{z}$, channel
SNRs $\gamma_{1},\ldots,\gamma_{N}$, learning rate $\eta$;

2: Output: Model parameters $(\Theta,\Phi)$ of DMANet-N;

3: Transmitters:

4: for each DeepMA encoder $E_{\phi_{i}}\in\mathcal{E}_{\Phi}$:

5: Sample a different training data batch $\mathbf{x}_{i}$ from $\mathbf{X}$;

6: Compute SSV $\mathbf{y}_{i}\leftarrow
E_{\phi_{i}}(\mathbf{x}_{i},{\color[rgb]{0,0,0}\gamma_{i}})$;

7: Power normalization
$\mathbf{z}_{i}\leftarrow\sqrt{KP_{z}}\frac{\mathbf{y}_{i}}{\mathbf{y}_{i}^{*}\mathbf{y}_{i}}$;

8: end for each

9: Channel:

10: Randomly generate CSI matrix $\mathbf{H}=[h_{i,j}]_{N\times N}$, in which
$h_{i,j}\sim\mathcal{CN}(0,1)$;

11: for each transceiver $i\in\mathcal{N}$:

12: Compute AWGN power $\sigma_{i}^{2}=\frac{P_{z}}{10^{(\gamma_{i}/10)}}$;

13: Randomly generate AWGN
$\mathbf{n}_{i}\sim\mathcal{CN}(0,\sigma_{i}^{2}\mathbf{I})$;

14: end for each

15: Receivers:

16: for each DeepMA decoder $D_{\theta_{i}}\in\mathcal{D}_{\Theta}$:

17: Receive MSSV
$\mathbf{z}_{i}^{\text{rev}}=\sum_{k=1}^{N}h_{k,i}\mathbf{z}_{k}+\mathbf{n}_{i}$;

18: Compute RMSSV
$\tilde{\mathbf{z}}_{i}\leftarrow{\mathbf{z}_{i}^{\text{rev}}}/{h_{i,i}}$;

19: Recover data $\tilde{\mathbf{x}}_{i}\leftarrow
D_{\theta_{i}}(\tilde{\mathbf{z}}_{i},{\color[rgb]{0,0,0}\gamma_{i}})$;

20: end for each

21: Compute loss
$\mathcal{L}(\Phi,\Theta;\mathbf{X})\leftarrow\frac{1}{N}\sum_{i=1}^{N}d(\mathbf{x}_{i},\tilde{\mathbf{x}}_{i})$;

22: Update model parameters by gradient descent:
$\Theta\leftarrow\Theta-\eta\triangledown_{\Theta}\mathcal{L}(\Phi,\Theta;\mathbf{X}),\Phi\leftarrow\Phi-\eta\triangledown_{\Phi}\mathcal{L}(\Phi,\Theta;\mathbf{X}).$

##  IV DeepMA for Wireless Image Transmission

In this section, we evaluate the performance of the proposed DeepMA by
conducting simulations on DeepMA-enabled wireless image transmission tasks.
First, we describe the architecture of the DMANet used and the experimental
settings. Next, we describe the SSV orthogonality to explain why DeepMA can
achieve channel multiplexing and how to use SSV orthogonality to conduct user
detection, at the same time showing its flexibility and privacy properties.
Finally, we present the performance evaluation results, along with their
analysis.

Figure 4: Network architecture of one EDP of the DMANet used.

###  IV-A Network Architecture

Fig. 4 shows the architecture of the DMANet used for image transmission with
channel multiplexing ability. First, we normalize the input image with a value
range [0, 1], and then passes it through the DeepMA encoder to obtain the SSV.
The DeepMA encoder is used for conducting the joint source-channel coding and
orthogonal signal modulation process, which is achieved by four residual
convolutional blocks (RCBs) and three attention feature blocks (AFBs). The
RCBs are used for extracting the image features by using convolutional
operations, and the AFB is used for adjusting the image features obtained by
the RCBs. In AFB, we first compute the channel-wise mean (CWM) values of the
image features. By using the CWM and channel SNR information, we use a simple
fully connection (FC) network to predict the importance weights of the feature
channels and automatically adjust the learned features with the weights
obtained. The authors of [28] provide more detailed introduction of AFB. In
each RCB, we use the generalized normalization transformation (GDN) as the
normalization layer, which has been demonstrated effective in density modeling
and image compression tasks [31][32]. The RCB is designated as $m\times
n\times c\,\,|\downarrow s$, where $m,n,c,s$ correspond to the height, width,
output channel number, and downsampling stride length respectively of the
convolutional layer used. When the stride length is $s=1$, then the shape of
the output data is the same as the shape of the input data. When the stride
length is $s=2$, the height and weight of the output data is half of the input
data. For the channel number $c$, the maximum channel number is $256$, and in
the first RCB, the channel number is $128$, which is helpful for reducing
memory space when the input image is large. In the last RCB, the channel
number $c$ is used for adjusting the data compression ratio, and a relatively
larger value of $c$ produces a better image recovery quality, but the
transmission efficiency will be reduced. We denote $H$ and $W$ as the height
and width of the input image respectively because we have three downsampling
operations with $s=2$. Then we know the shape of the output data of the last
RCB which is ${H}/{8}\times{W}/{8}\times c$. In this way, we define the
bandwidth efficiency performance as the following symbol per pixel (SPP)
metric:

$\text{SPP}(c)=\frac{{H}/{8}\times{W}/{8}\times c}{H\times W}=\frac{c}{64}.$
(15)

After the reshape operation, we transform the image feature as a
$K$-dimensional complex SSV, and we can know $K=\frac{HW}{128}$. We note that
a complex semantic symbol is composed of two real semantic features.
Accordingly, we define complex SPP (CSPP) metric as follows:

$\text{CSPP}(c)=\frac{c}{128}.$ (16)

We observe that $\text{SPP}(c)=2\text{CSPP}(c)$. For DMANet-N, it can support
at most $N$ transmissions simultaneously. Therefore the achievable minimal
CSPP (MinSCPP) is:

$\text{MinCSPP}(c,N)=\frac{c}{128N}.$ (17)

For example, if we set $c=128$, for an ADJSCC model or one EDP, the CSPP is 1,
and for DMANet-2, the MinCSPP is 0.5. In this paper, when the MinCSPP of a
DeepMA model is equal to the CSPP of an ADJSCC model, we say that their
achievable code rates are the same.

The DeepMA decoder is used for conducting the joint signal filtering and
channel-source decoding process to recover the original input image with the
RMSSV obtained. Like the DeepMA encoder, the architecture of a DeepMA decoder
is composed of four residual transpose convolutional blocks (RTCB) and three
AFBs. The main difference between RTCB and RCB is that RTCB uses a
transconvolution operation for reconstructing the image and uses an inverse
GDN (IGDN) operation for feature normalization. Accordingly, since we want to
recover the original image from the RMSSVs received, in the last three RTCBs,
we use three upsampling operations with stride length $s=2$ to ensure the size
of the recovered image is the same as the original input image. Finally, we
denormalize the output image as 8-bit integer pixels within the range [0,
255].

###  IV-B Simulation Settings

We evaluated the performances of our proposed DeepMA on CIFAR100 [33] and
Kodak24 [34] data transmission tasks with channel multiplexing, and we also
tested the performance of the state-of-the-art ADJSCC model for non-
multiplexing transmissions. For an EDP model and an ADJSCC model, when the
model architecture and the achievable code rates are the same, we expect that
ADJSCC will achieve better performance compared with the DeepMA model because
achieving orthogonal modulation and filtering will incur additional model
encoding and decoding resources, and the used model resource for joint source-
channel coding will be reduced. Note that model resources in this paper means
the black-box computation process of the model. We used the following
simulation settings in our performance evaluation tests:

CIFAR100 data transmission: In this test, we will use CIFAR10 [35] data as the
training data and validation data, and then test the transmission performance
on CIFAR100 test data. Both CIFAR10 and CIFAR100 contain 60000 color image
samples with size $32\times 32$, in which 5000 images are training samples,
and the remaining 1000 images are test samples. We will first train the
semantic communication models by using CIFAR10 training data, and at the end
of each training epoch, we validate the performance of the current model using
the CIFAR10 test data. We implement DMANet and the ADJSCC models in the
Pytorch environment, the batch size per EDP is set as 64. The initial learning
rate is set as $\eta=5\times 10^{-4}$. After 100 epochs and 200 epochs, it is
decreased as $\eta=1\times 10^{-4}$ and $\eta=5\times 10^{-5}$ respectively.
The maximal number of training epochs is set as 400. In each training epoch,
we first update the model by training data, then evaluate the performance of
the model on the validation data. If the achieved performance is better than
the best performance previously achieved, we save the model as the final
model, otherwise, the final model will not be updated. After training, we use
CIFAR100 test data to test the transmission performance of the proposed DeepMA
and ADJSCC models.

Kodak24 data transmission: In this test, we used the ImageNet [36] data to
train the DeepMA and ADJSCC models pretrained on the CIFAR10 data. Since the
model is previously trained on small-scale CIFAR10 data, the training time and
the number of ImageNet training samples used can be reduced. The original
ImageNet data has more than one million color images, and in this paper we
only used ImageNet validation dataset as the training data and validation
data, in which the first 45000 images are used as training samples and the
remaining 5000 images are used as the validation dataset. The image size of
ImageNet can be different, thus we set the input image size to $128\times 128$
by using the center-crop operation. As pretrained models are used, the
training epochs on ImageNet data are not required to be too large, and we set
the maximal epoch number to 200. We set the initial learning rate to
$\eta=1\times 10^{-4}$, and then gradually decreasing to $5\times 10^{-5}$,
$1\times 10^{-5}$, and $1\times 10^{-6}$ at the 100th, 160-th, and 190-th
epochs respectively. In the same way with the CIFAR10 data training process,
at the end of each training epoch, we tested the performance of the models
obtained on the validation data, and if the performance is better than the
best performance previously achieved, we updated the final model, otherwise,
the final model remains unchanged. After model training, we use the Kodak24
data to test the performance of the model obtained. The Kodak24 data is
composed of 24 color images with size $768\times 512$, and it is a widely used
benchmark for evaluating the image quality of image reconstruction tasks.
Since the number of images is quite limited, we therefore used the average
performance on 100 tests to avoid performance fluctuation caused by the
uncertain SSV transmission process.

###  IV-C Performance Evaluation Metrics

To evaluate the quality of the images recovered, we used peak signal-to-noise
ratio (PSNR) [37] as the performance metric, and it is defined as:

$\text{PSNR}=10\log_{10}\frac{\text{MAX}^{2}}{\text{MSE}},$ (18)

where MSE is the mean-squared error between the original input image and the
image recovered, and MAX means the allowable peak pixel value of the images.
Since the images used is 8-bit per pixel, the signal peak value is
$\text{MAX}=2^{8}-1=255$. A higher PSNR means better quality of the recovered
image because the MSE becomes lower. In one DeepMA model, the PSNR performance
results of the EDPs can be slightly different from each other. Thus, we used
the average value of the PSNRs of all EDPs as the PSNR performance of a
DMANet.

During the transmission process, the channel SNR may significantly affect the
quality of the image recovered, and the channel SNR of EDP $i$ is defined as:

$\gamma_{i}=10\log_{10}\frac{P_{z}}{\sigma_{i}^{2}},$ (19)

where $P_{z}$ denotes the average transmitting power of the SSV $\mathbf{z}$,
and as we have mentioned before we set $P_{z}=2P_{0}=2$. With a given channel
SNR $\gamma_{i}$ and transmitting power $P_{z}$, we can compute the
corresponding noise power $\sigma_{i}^{2}=10^{(-\gamma_{i}/10)}P_{z}$. Then,
we can randomly generate the AWGN samples for each symbol of the MSSV
received. With the randomly generated channel CSI matrix and AWGN noise
samples, we can create random channels with given channel SNRs.

(a) Kodim22, $\mathbf{x}_{1}$, EDP $(E_{\phi_{1}},D_{\theta_{1}})$

(b) Kodim23, $\mathbf{x}_{2}$, EDP $(E_{\phi_{2}},D_{\theta_{2}})$

(c) Kodim24, $\mathbf{x}_{3}$, EDP $(E_{\phi_{3}},D_{\theta_{3}})$

(d)
$\mathbf{z}_{1}^{\text{rev}}=\sum_{i=1}^{3}(h_{i,1}\mathbf{z}_{i}+\mathbf{n}_{1})$,
33.53dB

(e)
$\mathbf{z}_{2}^{\text{rev}}=\sum_{i=1}^{3}(h_{i,2}\mathbf{z}_{i}+\mathbf{n}_{2}),D_{\theta_{2}}$,
36.47dB

(f)
$\mathbf{z}_{3}^{\text{rev}}=\sum_{i=1}^{3}(h_{i,3}\mathbf{z}_{i}+\mathbf{n}_{3}),D_{\theta_{3}}$,
35.01dB

(g)
$\mathbf{z}_{1}^{\text{rev}}=h_{1,1}\mathbf{z}_{1}+\mathbf{n}_{1},D_{\theta_{1}}$,
33.54dB

(h)
$\mathbf{z}_{2}^{\text{rev}}=h_{2,2}\mathbf{z}_{2}+\mathbf{n}_{2},D_{\theta_{2}}$,
36.35dB

(i)
$\mathbf{z}_{3}^{\text{rev}}=h_{3,3}\mathbf{z}_{3}+\mathbf{n}_{3},D_{\theta_{3}}$,
35.06dB

(j)
$\mathbf{z}_{1}^{\text{rev}}=\sum_{i=2}^{3}(h_{i,1}\mathbf{z}_{i}+\mathbf{n}_{i}),D_{\theta_{1}}$

(k) $\mathbf{z}_{2}^{\text{rev}}=\sum_{i=1,i\neq
2}^{3}(h_{i,2}\mathbf{z}_{i}+\mathbf{n}_{i}),D_{\theta_{2}}$

(l)
$\mathbf{z}_{3}^{\text{rev}}=\sum_{i=1}^{2}(h_{i,3}\mathbf{z}_{i}+\mathbf{n}_{i}),D_{\theta_{3}}$

Figure 5: Examples of the images reconstructed by DMANet-3 for wireless image
transmission with slow Rayleigh fading channel, we set MinCSPP to 0.5, and the
channel SNRs of EDPs $(E_{\phi_{1}},D_{\theta_{1}})$,
$(E_{\phi_{2}},D_{\theta_{2}})$ and $(E_{\phi_{3}},D_{\theta_{3}})$ to 8 dB,
12 dB, and 16 dB respectively.

###  IV-D Illustrative Examples of DMANet-3

In this subsection, we present some image examples reconstructed by DMANet-3
for the D2D wireless image transmission scenario. Fig. 5 shows the example
images, in which subfigures (a)-(c) are the three original input images, and
subfigures (d)-(l) are the reconstructed images obtained with different
RMSSVs. The three example images used are kodim22, kodim23, and kodim24, and
they are denoted as $\mathbf{x}_{1}$, $\mathbf{x}_{2}$, and $\mathbf{x}_{3}$
respectively. We transmitted three images independently by three different
transmitters, and the EDPs used for $\mathbf{x}_{1}$, $\mathbf{x}_{2}$, and
$\mathbf{x}_{3}$ are $(E_{\phi_{1}},D_{\theta_{1}})$,
$(E_{\phi_{2}},D_{\theta_{2}})$, and $(E_{\phi_{3}},D_{\theta_{3}})$
respectively. The corresponding normalized SSVs of the three images are
$\mathbf{z}_{1}$, $\mathbf{z}_{2}$, and $\mathbf{z}_{3}$. We set the channel
to a slow Rayleigh fading channel, and we set the channel SNRs of the three
paths to 8dB, 12dB, and 16dB. Using the settings above, we conducted the
following three tests:

Test 1: Channel multiplexing. In this test, the wireless channel is
multiplexed by the three transceivers, and the received MSSV of the receiver
$k$ is
$\mathbf{z}_{k}^{\text{rev}}=\sum_{i=1}^{3}(h_{i,k}\mathbf{z}_{i}+\mathbf{n}_{k})$.
We then can compute the RMSSV of $D_{\theta_{1}}$, $D_{\theta_{2}}$, and
$D_{\theta_{3}}$ as: $\tilde{\mathbf{z}}_{1}=\mathbf{z}^{\text{rev}}/h_{1}$,
$\tilde{\mathbf{z}}_{2}=\mathbf{z}^{\text{rev}}/h_{2}$, and
$\tilde{\mathbf{z}}_{3}=\mathbf{z}^{\text{rev}}/h_{3}$ respectively. Finally,
we can obtain the final reconstructed images as:
$\tilde{\mathbf{x}}_{1}=D_{\theta_{1}}(\tilde{\mathbf{z}}_{1})$,
$\tilde{\mathbf{x}}_{2}=D_{\theta_{2}}(\tilde{\mathbf{z}}_{2})$, and
$\tilde{\mathbf{x}}_{3}=D_{\theta_{3}}(\tilde{\mathbf{z}}_{3})$, and
subfigures (d)-(f) plot the results obtained. Visually, we can observe that
the recovered images are the same as their original input images. More
precisely, the PSNRs of three recovered images $\tilde{\mathbf{x}}_{1}$,
$\tilde{\mathbf{x}}_{2}$, and $\tilde{\mathbf{x}}_{3}$ are 35.53 dB, 36.47 dB,
and 35.01 dB respectively, which demonstrate that DMANet3 can achieve the
channel multiplexing process while at the same time yields good image
reconstruction quality.

Test 2: Dedicated communication. In this test, the channel is dedicated to
only one EDP. In other words, only one transmitter transmits data at a one-
time slot. In this scenario, the SSVs received from the receivers
$D_{\theta_{1}}$, $D_{\theta_{2}}$, and $D_{\theta_{3}}$ are
$\mathbf{z}_{1}^{\text{rev}}=h_{1}\mathbf{z}_{1}+\mathbf{n}_{1}$,
$\mathbf{z}_{2}^{\text{rev}}=h_{2}\mathbf{z}_{2}+\mathbf{n}_{2}$, and
$\mathbf{z}_{3}^{\text{rev}}=h_{3}\mathbf{z}_{3}+\mathbf{n}_{3}$ respectively,
and the subfigures (g)-(i) show the corresponding reconstructed images. We
observe that the PSNRs of the reconstructed images $\tilde{\mathbf{x}}_{1}$,
$\tilde{\mathbf{x}}_{2}$, and $\tilde{\mathbf{x}}_{3}$ are 33.54 dB, 36.35 dB,
and 35.06 dB respectively, which show that DMANet can recover the results in a
dedicated communication scenario. It is also worth noting that the quality of
the images recovered is the same as in the previous channel multiplexing
scenario. These results show that, in the channel multiplexing scenario, the
undesired SSVs received by one EDP decoder do not affect the final
reconstructed result. This is because these SSVs are mutually orthogonal, and
the decoders can automatically filter out the non-desired SSVs. In this way,
we note that DeepMA can work in a flexible way to support both multiplexing
and non-multiplexing transmissions.

Test 3: Cross decoding. In this test, a DeepMA encoder does not send any SSV
to the channel, but its paired DeepMA decoder tries to recover the image from
the received MSSVs transmitted from other unpaired DeepMA encoders. For
example, we try to recover the result of
$\mathbf{z}^{\text{rev}}=\sum_{i=2}^{3}(h_{i}\mathbf{z}_{i}+\mathbf{n}_{i})$
by using the DeepMA decoder $D_{\theta_{1}}$, and subfigure (j) shows the
result obtained. We observe that the image obtained is pure black, and all the
pixels are 0. Subfigures (k)(l) show similar results. From these results, we
conclude that a DeepMA decoder can only recover images from the MSSVs
containing the SSV component transmitted by the paired DeepMA encoder,
otherwise, nothing useful can be obtained. Therefore, a DeepMA model itself
can therefore achieve good privacy protection.

###  IV-E SSV Orthogonality

TABLE I: Correlation matrix of the three complex SSVs | $\mathbf{z}_{1}$ | $\mathbf{z}_{2}$ | $\mathbf{z}_{2}$
---|---|---|---
$\mathbf{z}_{1}$ | 2 | $2.32\times 10^{-5}$ | $2.04\times 10^{-5}$
$\mathbf{z}_{2}$ | $2.32\times 10^{-5}$ | 2 | $9.55\times 10^{-5}$
$\mathbf{z}_{3}$ | $2.04\times 10^{-5}$ | $9.55\times 10^{-5}$ | 2
TABLE II: Correlation matrix of the three real SSVs | $\mathbf{v}_{1}$ | $\mathbf{v}_{2}$ | $\mathbf{v}_{2}$
---|---|---|---
$\mathbf{v}_{1}$ | 1 | $-8.01\times 10^{-6}$ | $1.02\times 10^{-5}$
$\mathbf{v}_{2}$ | $-8.01\times 10^{-6}$ | 1 | $-4.77\times 10^{-5}$
$\mathbf{v}_{3}$ | $1.02\times 10^{-5}$ | $-4.77\times 10^{-5}$ | 1

We have seen that DeepMA achieves a flexible, effective, and secure
communication process with channel multiplexing. The reason why DeepMA can be
so powerful is because the DeepMA model can achieve an orthogonal signal
modulation process, such that the recovered results of one decoder will not be
influenced by other SSVs sent from the unpaired encoders. In this subsection,
we provide an example to demonstrate the orthogonality of the SSVs. In this
test, we used the environment settings as the test used in subfigures
5(d)(e)(f). To quantify the orthogonality, we first define the correlation
metric between complex SSVs $\mathbf{z}_{i}$ and $\mathbf{z}_{j}$ as follows:

$R_{z}(\mathbf{z}_{i},\mathbf{z}_{j})=\frac{1}{K}\mathbb{E}[\mathbf{z}_{i}^{*}\mathbf{z}_{j}],$
(20)

We can see that when $i=j$, the correlation metric above is equal to the
average signal power of the SSV, i.e.,
$R(\mathbf{z}_{i},\mathbf{z}_{j})=P_{z}$. As we have mentioned before, in this
paper, we set $P_{z}=2$. We compute the correlation matrix of the SSVs
obtained from the DMANet3 on kodim22, kodim23, and kodim24, and Table I
presents the results. We can observe that, for $i,j\in\left\\{1,2,3\right\\}$,
when $i\neq j$, the value of $R(\mathbf{z}_{i},\mathbf{z}_{j})$ are very close
to zero, which means that the three SSVs $\mathbf{z}_{1}$, $\mathbf{z}_{2}$,
and $\mathbf{z}_{3}$ are orthogonal to each other. Next, we transform the
$K$-dimensional complex SSVs as $2K$-dimensional real SSVs as follows:
$\mathbf{v}_{i}=[\text{Re}(\mathbf{z}_{i});\text{Im}(\mathbf{z}_{i})]$, then
we can define the correlation metric between real SSVs $\mathbf{v}_{i}$ and
$\mathbf{v}_{j}$ as follows:

$R_{v}(\mathbf{v}_{i},\mathbf{v}_{j})=\frac{1}{2K}\langle\mathbf{v}_{i},\mathbf{v}_{j}\rangle,$
(21)

where $\langle\mathbf{v}_{i},\mathbf{v}_{j}\rangle$ means the inner product of
$\mathbf{v}_{i}$ and $\mathbf{v}_{j}$. According to the above definition, we
can expect that
$R_{z}(\mathbf{z}_{i},\mathbf{z}_{j})=2R_{v}(\mathbf{v}_{i},\mathbf{v}_{j})$.
Accordingly, we compute the correlation matrix of the three real SSVs, and
Table II shows the result obtained. Again, we observe that the three real SSVs
$\mathbf{v}_{1}$, $\mathbf{v}_{2}$, and $\mathbf{v}_{3}$ are orthogonal to
each other. We note that the SSVs are not strictly orthogonal to each other,
as we can see the average inner product of two different real SSVs is only
close to zero, but not equal to zero.

Figure 6: AACD examples in user detection.

The results above show the mutual orthogonality of the transmitted SSVs. Next
we show how to use AACD defined in equation (9) to conduct the user detection
process. Recall that the AACD quantifies the correlation between the RMSSV
received and reference SSVs. Again, we use the same three images as the
examples and test the AACDs with increasing channels SNRs in different
scenarios. In each test, when transmitting one image, the SSVs of the other
two images are used as the references for computing the AACD. Since the
channel uncertainty has an impact on the AACD values, we get results for 100
repeats. Fig. 6 shows the results obtained, and we have the following
observations:

  * •

Unpaired transmission: In this test, the decoder of one EDP receives a MSSV
data transmitted from other two unpaired encoders, and we observe that the
AACD distributions remains stable with a mean value 0.0103 and a standard
deviation 0.0070, which are very small.

  * •

Paired transmission: In this test, we only has one EDP transmit data, and we
observe that, due to the impact of AWGN, the AACD values increases when the
channel’s SNR increases. In a very low SNR regime (e.g., 0dB), the mean value
and standard deviation are about 0.067 and 0.0083 respectively, which are
quite distinct compared with the unpaired transmission scenario. We observe
that, by using only two reference SSVs, we can achieve an effective user
detection process.

From the results above, we note that joint source-channel encoding and
orthogonal modulation processes are conducted in the DeepMA encoder, and the
SSVs obtained are orthogonal to each other, which enable different
transceivers to transmit data over a shared physical channel without causing
mutual interferences. In addition, as we have mentioned before, by using the
SSV orthogonality, we can use the AACD defined in equation (9) for solving the
user detection problem in DeepMA, and then only execute the decoding process
when the paired encoder transmits data.

Figure 7: Comparison of the PSNR performances of DeepMA and ADJSCC on CIFAR100
data in the AWGN channel case.

Figure 8: Comparison of the PSNR performances of DeepMA and ADJSCC on CIFAR100
data in the slow Rayleigh fading channel case.

###  IV-F Results on CIAFR100 Data

In this subsection, we evaluate the PSNR performances of the proposed DeepMA
and ADJSCC models on CIFAR100 data transmissions. Our main goal is to
demonstrate that the proposed DeepMA can achieve effective channel
multiplexing in wireless transmission scenarios, and at the same time show how
the number of EDPs influences the performance of a DeepMA model. In a general
D2D communication scenario, the SNRs of the transceivers can be different. To
control the channel SNR and improve the legibility of the results, we set the
SNRs of all transceivers to be the same. As aforementioned, downlink and
uplink transmissions are two simplified of D2D transmissions, and we will test
the performances of the D2D transmission case, and results of uplink and
downlink transmission will not be presented due to the space limit.

Figs. 7 and 8 show the PSNR performance results obtained with increasing
channel SNRs. In all tests, the network architecture of the ADJSCC model used
is the same as the EDP models of the DMANets used. For the ADJSCC model, we
evaluated the PSNR performances with two code rates, namely CSPP=0.25 and
CSPP=0.5, and the corresponding output channels of the encoder model are 32
and 64. For a DMANet-$N$ model, we also have $32N$ and $64N$. It is worth
noting that, for one EDP, its CSPP is $N$ times the MinCSPP of DMANet-$N$,
i.e., CSPP=$N\times$MinCSPP. We denote the two code choices as
$\alpha=\left\\{0.25,0.5\right\\}$, and from the two figures, we observe that,
when the bandwidth efficiencies are the same, the proposed DMANet can even
achieve higher PSNRs when the channel SNR is not very high, but the PSNR
performances of ADJSCC can be higher when channel SNR is high. These results
first demonstrate that the proposed DeepMA method can achieve an effective OMA
process and a stronger transmission ability than ADJSCC models for point-to-
point transmission in a low SNR regime. One plausible reason is because when
the bandwidth efficiency of ADJSCC and DMANet-$N$ are the same, the code
length of DMANet-$N$ is $N$ times than the SSV of ADJSCC, and therefore incurs
more total code resources on the channel coding process. In addition, in the
training process, an EDP is trained with the ability to recover data from the
interferences of other EDPs, which may be helpful for further enhancing the
noise-resiliency capability of the EDPs. When the channel SNR is very high
(e.g., 25 dB), the impact of noises is quite limited, and the code resources
will be mainly used for the source coding process. However, the DMANet also
needs to allocate more resources to the orthogonal modulation process, and
therefore its remaining source coding resources will be lower than ADJSCC, and
the PSNR performance achieved will be relatively lower.

Next, we compare the PSNRs achieved by the DMANet models with different
numbers of EDPs. We denote the $\text{PSNR}^{(N)}$ as the PSNR performance of
the DMANet-$N$ model, and let $\text{PSNR}^{(1)}$ be the PSNR of the ADJSCC
model. Then, from Fig. 7, we can see that, in the low SNR regime, the PSNR
performance rank is
$\text{PSNR}^{(1)}>\text{PSNR}^{(2)}>\ldots>\text{PSNR}^{(5)}$, while in the
high SNR regime, the PSNR performance rank is
$\text{PSNR}^{(1)}<\text{PSNR}^{(2)}<\ldots<\text{PSNR}^{(5)}$. Possible
reasons could include: with the increasing EDN number $N$, the code length of
a DAMNet model becomes larger, and it is trained with a stronger ability for
dealing with more complex interferences. It also can be possible that the
DMANet model has more total channel coding resources which increase the noise-
resiliency ability. When the channel SNR is high, the average source coding
resources reduce because model resources for orthogonal modulation increase,
and the source coding performance decreases. The results in Fig. 8 are the
same as those in Fig. 7 when the EDP number is smaller than 4. We observe
that, in Fig. 8(a), the performance of DeepMA-$5$ is significantly lower than
ADJSCC and other DeepMA schemes. Similarly, in Fig. 8(b), the performance of
DeepMA-$4$ and DeepMA-$5$ are lower than the other schemes. This result again
shows that achieving the orthogonal modulation and demodulation process
requires non-negligible model resources, especially as the EDP number
increases. From these results, we can conclude that, in a complex fading
channel case, a too-large EDP number may cause a negative impact on the
transmission performance, and it is not suggested to use a too large EDP
number to avoid significant performance loss.

Figure 9: Comparison of the PSNR performances of DeepMA, ADJSCC, and
conventional BPG+LDPC-based transmission schemes achieved on the Kodak24 data
in the AWGN channel case.

Figure 10: Comparison of the PSNR performances of DeepMA, ADJSCC, and
conventional BPG+LDPC-based transmission schemes achieved on the Kodak24 data
in the slow Rayleigh fading channel case.

###  IV-G Results on Kodak24 Data

In this subsection, we compare the PSNR performances of ADJSCC and the
proposed DeepMA method achieved on the kodak24 data, whose resolution is much
higher than the CIFAR100 data. For a fair comparison, in each test, the
architecture of a used ADJSCC model is the same with one EDP of a DeepMA
model, and the CSPP of the ADJSCC model is equal to the MinCSPP of the DeepMA
model. Except for ADJSCC and DeepMA models, we also evaluated the performance
of conventional wireless communications schemes that use BPG and LDPC codecs
to achieve source coding and channel coding respectively. BPG is a well-known
image [13] codec based on discrete Fourier transform and intra-frame encoding,
and it can achieve better image compression performance compared with the JPEG
and the JPEG2000 standard [13]. For LDPC, we used the channel coding scheme
used in IEEE 802.11n protocol [38]. We set the code block length to 1296, and
we evaluated the performance of the following three code combinations
$(648,648)$, $(864,432)$, and $(972,324)$, and the corresponding code rates
are 1/2, 2/3, and 3/4 respectively. In general, a relatively larger code rate
increases the transmission efficiency but decreases the noise resiliency
capability. For the conventional communications scheme, the term
$\text{LDPC}(R)$ means that the code rate of the LDPC code is $R$, and
$R\in\left\\{1/2,2/3,3/4\right\\}$. For signal modulation, we tested the
following 3 modulation orders: 4QAM, 16QAM, and 64QAM, and the corresponding
number of bits per symbol is 2, 4, and 6 respectively. We note that the
modulation order also significantly influences transmission efficiency and
reliability. A relatively larger modulation order means a higher transmission
efficiency and a lower transmission reliability. For conventional multiple
access schemes, we assume that the OFDMA and TDMA schemes are used, and we
equally allocate the frequency or timeslot resources to the UEs, such that the
code length of each UE in the transmission is the same as each other. The
proposed DeepMA can support co-frequency transmission, while OFDMA and TDMA
cannot do so because they must allocate dedicated transmission resources for
each UE. We did not compare the performance to CDMA-based multiple access
schemes, because CDMA uses orthogonal basis codes to represent 1-bit data, and
this digital coding process will greatly reduce the transmission bandwidth
efficiency. Given the same bandwidth efficiency, the PSNR performances
achieved with CDMA-based multiple access will be much lower than OFDMA and
TDMA.

Figs. 9 and 10 show the results obtained in the case of the AWGN channel and
the slow Rayleigh fading channel cases. In a general D2D communication
scenario, the SNRs of the transceivers can be different. Similar to the
results in Figs. 7 and 8, we can observe that, compared with ADJSCC, in both
AWGN and slow Rayleigh fading channels, the proposed DeepMA can achieve higher
PSNR performances in the low SNR regime (e.g., 5dB in Fig. 9(a)), but lower
PSNR performances in a high SNR regime (e.g., 24dB in Fig. 9(b)). In addition,
we can also see that, in the slow Rayleigh fading channel case, a high EDP
number will decrease the PSNR performance. We have explained the reasons for
these results in the previous subsection, and we do not repeat the
explanations here.

Finally, we compare the PSNR performances of the proposed DeepMA, ADJSCC, and
conventional BPG+LDPC-based transmission schemes. We observe from, Figs. 9 and
10, that the performances of conventional schemes suffered from the cliff
effect. Moreover, when the channel SNR is very low, e.g., lower than 0dB, the
conventional schemes used even fail to transmit data. On the contrary, for
both ADJSCC and the proposed DeepMA, the cliff effect does not exist, and they
can still transmit data even when the channel SNR is very low. These results
highlight the noise-resilience ability of ADJSCC and DeepMA. However, except
for a very low SNR regime, the results obtained show that both ADJSCC and the
proposed DeepMA cannot achieve better PSNR performances compared with
conventional schemes. When MinCSPP is 0.25, conventional LDPC+BPG schemes with
64QAM can achieve much higher PSNR than DeepMA. This performance gap becomes
much smaller when the MinCSPP is 0.5, and we note that DeepMA can achieve
closer performance to conventional schemes. These results show that DeepMA
still needs more effective deep learning models and training methods to
improve its ability. However, in this work, our main goal is to demonstrate
the effectiveness of DeepMA rather than achieving higher transmission
performance than conventional BPG+LDPC schemes in all situations. In future
work, we can explore the design of a more powerful network architecture to
improve the transmission performance of the proposed DeepMA model.

##  V Conclusion

In this paper, we have proposed DeepMA for achieving OMA-based channel
multiplexing in semantic communication systems. We formulated the DeepMA
models for D2D, downlink, and uplink wireless communication scenarios, and we
illustrated their training algorithm. We demonstrated the performance of the
proposed DeepMA model on wireless image transmission tasks, and we presented
the network architecture of the models used. We trained the ADJSCC and DeepMA
models by using both low-resolution and small-scale CIFAR10 data and high-
resolution and large-scale ImagNet data, and we evaluated the PSNR
performances by using the CIFAR100 data and the kodak24 data. The results
obtained show that the proposed DeepMA method can achieve effective, flexible,
and privacy-preserved multiple access, and also showed that achieved
orthogonal signal modulation will reduce performance compared with an ADJSCC
model with the same encoding and decoding resources.

## Acknowledgment

We thank the anonymous reviewers for their valuable comments which helped us
improve the content and presentation of this paper.

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