# SSwsrNet: A Semi-Supervised Few-Shot Learning Framework for Wireless Signal
Recognition

Hao Zhang, , Fuhui Zhou, ,
Qihui Wu, , and Naofal Al-Dhahir  This work was supported by the National
Natural Science Foundation of China under Grant 62031012 and Grant 62222107,
the China Scholarship Council under Grant 202306830108, the Postgraduate
Research & Practice Innovation Program of Jiangsu Province under Grant
KYCX23_0380, and the Interdisciplinary Innovation Fund for Doctoral Students
of Nanjing University of Aeronautics and Astronautics under Grant
KXKCXJJ202302. The work of N. Al-Dhahir was supported by Erik Jonson
Distinguished Professorship at UT-Dallas. (_Corresponding author: Fuhui
Zhou._) Hao Zhang, Fuhui Zhou, and Qihui Wu are with the College of Electronic
and Information Engineering, Nanjing University of Aeronautics and
Astronautics, Nanjing 211106 China. They are also with the Key Laboratory of
Dynamic Cognitive System of Electromagnetic Spectrum Space (Nanjing University
of Aeronautics and Astronautics) and with the Ministry of Industry and
Information Technology, Nanjing, 211106, China (email<EMAIL_ADDRESS><EMAIL_ADDRESS>wuquhui2014@sina.com). Naofal Al-Dhahir is with the
Department of Electrical and Computer Engineering, The University of Texas at
Dallas, Richardson, TX 75080 USA (e-mail: aldhahir@utdallas.edu).

###### Abstract

Wireless signal recognition (WSR) is crucial in modern and future wireless
communication networks since it aims to identify properties of the received
signal. Although many deep learning-based WSR models have been developed, they
still rely on a large amount of labeled training data. Thus, they cannot
tackle the few-sample problem in the practically and dynamically changing
wireless communication environment. To overcome this challenge, a novel
SSwsrNet framework is proposed by using the deep residual shrinkage network
(DRSN) and semi-supervised learning. The DRSN can learn discriminative
features from noisy signals. Moreover, a modular semi-supervised learning
method that combines labeled and unlabeled data using MixMatch is exploited to
further improve the classification performance under few-sample conditions.
Extensive simulation results on automatic modulation classification (AMC) and
wireless technology classification (WTC) demonstrate that our proposed WSR
scheme can achieve better performance than the benchmark schemes in terms of
classification accuracy. This novel method enables more robust and adaptive
signal recognition for next-generation wireless networks.

###### Index Terms:

Wireless signal recognition (WSR), automatic modulation classification (AMC),
wireless technology classification (WTC), few samples, residual shrinkage
unit.

##  I Introduction

WITH the rapidly growing number of devices in wireless communication systems,
spectrum resources are becoming increasingly scarce. To efficiently utilize
spectrum resources, especially the underutilized frequency bands, dynamic
spectrum access (DSA) technology has been introduced for cognitive radio
systems [1, 2]. However, DSA-enabled cognitive radio systems cannot
dynamically avoid interference when sharing spectrum with unlicensed bands.
Therefore, cognitive radios must ensure that they do not interfere with
transmissions from incumbent users. To avoid interference with incumbent
users, it is vital to distinguish their transmissions from those of secondary
users. This can be achieved by signal recognition algorithms that classify
incoming transmissions. In this case, signal recognition can be utilized to
enhance the spectrum efficiency and security of spectrum sharing.

Wireless signal recognition (WSR) involves characterizing the received signals
in non-cooperative communication environments without prior knowledge of the
transmission parameters. WSR has numerous applications across military and
civilian domains, including decoding of intercepted transmissions, adaptive
demodulation, and DSA. Wireless signal recognition can be classified into
several primary applications, including automatic modulation classification
(AMC), wireless technology classification (WTC)/wireless standard
identification (WSI), and radio frequency (RF) fingerprinting identification.
AMC aims to differentiate various modulation types such as amplitude
modulation (AM) and frequency modulation (FM), phase shift keying (PSK), or
quadrature amplitude modulation (QAM), while the objective of WTC is to
recognize the wireless standard of an unidentified signal, such as 4G LTE or
IEEE 802.11. WTC is more challenging than AMC since a wireless standard
typically encompasses multiple modulation types that may vary dynamically
based on factors, such as the channel quality and the transmit scheme.

###  I-A Related Works and Motivations

Wireless signal recognition (WSR) techniques can be categorized into model-
driven (classical) and data-driven methods [3]. Classical WSR predominantly
leverages likelihood-based (LB) methods and feature-based (FB) methods. LB
techniques, such as the average likelihood ratio test (ALRT) [4, 5], the
generalized likelihood ratio test (GLRT) [6], and the hybrid likelihood ratio
test (HLRT) [7] formulate WSR as a hypothesis testing problem by the
likelihood functions, which require known signal-to-noise ratio (SNR) and
frequency offsets. However, these parameters are often unavailable in non-
cooperative conditions, limiting practical LB applicability. FB methods
instead manually extract statistical features, such as moments [8], cumulants
[9], and cyclostationarity from received signals to train classifiers, such as
logistic regression [10], support vector machines [11], and k-nearest
neighbors [12]. However, their performance strongly depends on hand-crafted
features, which are susceptible to noise and have intrinsic limitations.
Overall, although the classical WSR techniques have been widely studied, their
reliance on expert feature engineering and prior channel knowledge constrains
the achievable accuracy and robustness. This has motivated growing interest in
data-driven deep learning approaches that directly learn features from raw
signal samples and channel effects.

Deep learning has made great progress in many areas, especially in computer
vision [13, 14], natural language processing, as well as wireless
communications [3, 15]. Deep learning holds promise for advancing WSR by
learning discriminative features directly from raw signal data in an end-to-
end manner. It can automatically extract features for a classification task
through backpropagation, outperforming hand-crafted features used in the
classical methods. However, the performance of WSR methods based on deep
learning strongly depends on the availability of large labeled datasets, which
can be prohibitively expensive or infeasible to collect in wireless
communication domains. The non-cooperative nature of WSR makes it extremely
challenging to obtain extensive labeled signal data. Firstly, wireless signals
are often transmitted in a non-cooperative manner, which means that labeled
data collection requires extensive time, resources, and expertise. Secondly,
the wireless channel is dynamic and time-varying, which makes it difficult to
collect enough labeled data in a static environment, where the collected data
is effective. Thirdly, the wireless signal is sensitive to the interference,
which makes it difficult to collect data with high-quality labels in a complex
environment, where the label quality will significantly affect the performance
of the model. Therefore, developing deep learning techniques that can learn
from finite labeled examples supplemented by abundant unlabeled data through
semi-supervised or transfer learning is an important research direction.
Recent works have explored leveraging unlabeled samples for data augmentation,
pre-training, and regularization. However, the reliable application of deep
learning for WSR with restricted labeled data remains an open problem.

Deep learning, especially convolutional neural networks (CNNs) and recurrent
neural networks (RNNs) have been extensively studied for WSR. Early work by
O’Shea _et al._[16] adopted a simple two-layer CNN architecture followed by a
softmax classifier. Later, more advanced CNN models were proposed by
incorporating insights from computer vision, such as residual learning in
ResNet [17] to mitigate vanishing gradients when training deep networks.
Direct application of ResNet for AMC yielded limited gains, motivating custom
architectures such as the IQ-ResNet [18] which operates on complex-valued
signals. Other works sought to optimize efficiency through models, such as the
Involutional ResNet [15], balancing accuracy and inference speed. Moreover,
multi-scale convolutional networks have been applied for both AMC and WTC [3,
19]. Meanwhile, RNN architectures including long short-term memory (LSTM) [20]
and gated recurrent units (GRU) [21] have been explored to leverage timing
correlations in signals. However, RNNs entail high training costs and are
often constrained to fewer modulation types. Beyond basic CNNs and RNNs,
researchers have further advanced AMC via techniques, such as feature fusion
[22], adversarial training [23], and joint data and knowledge transfer [24].
The latter work notably combined data-driven learning with expert wireless
knowledge to extract both statistical and deep representations [24]. Recently,
novel MC techniques [25] and efficient networks [26] have been proposed for
WSR to enhance the recognition performance. In summary, while CNNs and RNNs
have driven initial wireless deep learning research, a key limitation that
remains is their reliance on large labeled datasets for training.

For WSR under few-sample conditions, there have been several recent works. As
shown in Fig. 1, these recent works can be classified into three categories,
namely few-sample-based methods, support-data-based methods, and synthetic-
data-based methods. For few-sample-based methods, they only utilize the
labeled data with few samples by using specifically designed architectures and
transfer learning. Li _et al._[27] introduced a neural architecture termed
AMR-CapsNet for AMC that achieves high accuracy under limited training data.
The authors in [28] proposed a transfer learning method for AMC. For support-
data-based methods, the proposed methods are first pre-trained on a specific
dataset named support set to learn the generative learning ability for WSR.
Then, the pre-trained model is trained on the few-sample conditions, namely,
the few-shot learning stage. The support set is often selected from the same
dataset, where the classes cannot appear in the few-shot learning stage. For
WSR, it is not applicable to collect enough additional labeled data to
construct the support set under non-cooperative conditions. Zhou _et al._[29]
proposed a new network, AMC relation network (AMCRN), to boost performance
under few-shot conditions. For synthetic-data-based methods, it is intuitive
to “generate” more labeled data for the training using a generative
adversarial network (GAN). To address the limited availability of labeled
training data for AMC, Zhang _et al._[30] proposed a new few-shot learning
framework by using GAN and SNR augmentation to expand the diversity of the
training set. These works have made impressive progress under the condition of
fewer samples with the help of the few-shot learning. However, these few-shot
learning methods are applicable for the AMC applications, especially under
non-cooperative conditions, where labeled data are difficult to obtain.
Fortunately, there are large amounts of unlabeled data that can be utilized
without any constraints. Moreover, the modulation signals from the system
without labels can be further utilized for improving the classification
performance. Thus, in this research, we investigate using both labeled and
unlabeled data simultaneously to solve the problems of using few samples in
the WSR task.

Figure 1: The structure of a DL-based WSR method. (a) common DL-based method;
(b) few-sample conditions; (c) WSR methods under few-sample conditions.

###  I-B Contributions

The nature of wireless communications, particularly the non-cooperative,
dynamic and open characteristics, makes it extremely challenging to collect
extensive labeled signal data. The few-shot learning can be utilized to
address the challenge of the limited labeled data for WSR by using few-sample
data. However, when training with few samples, the trained model has poor
generalization ability and cannot be applied for other datasets. Moreover,
models may easily overfit the few training data. How to effectively apply few-
shot learning for WSR and improve the generalization ability under few-sample
conditions is a critical issue for WSR. Intuitively, the unlabeled data can be
utilized to improve the classification performance under few-sample conditions
by using semi-supervised learning. However, when the labeled data is limited,
noise in the data may significantly affect the performance of the model and
the model may not be robust to the noise. To mitigate the reliance on large
labeled datasets for deep learning-based WSR, this paper proposes a novel
model termed SSwsrNet by combining a deep residual shrinkage network (DRSN)
with the semi-supervised learning via MixMatch. DRSN is designed to robustly
extract discriminative features from noisy signals. Meanwhile, MixMatch
leverages both labeled and unlabeled data during training to improve the
generalization under limited supervised samples. The key contributions are
developing a tailored deep architecture for wireless feature extraction and
advancing semi-supervised learning for the wireless communications domain.
SSwsrNet provides an important step toward reducing reliance on large labeled
datasets for applying deep neural networks to real-world wireless
applications. The contributions of this paper can be summarized as follows.

  1. 1.

The existing DL-based WSR models cannot simultaneously utilize labeled and
unlabeled data under few-sample conditions. It is the first time that both
labeled and unlabeled data are exploited in the WSR training process for
tackling less samples under few-sample conditions. For few-sample recognition,
we propose a novel SSwsrNet framework with a deep residual shrinkage network
(DRSN) and a modular semi-supervised learning method named MixMatch. DRSN can
learn more discriminative features from noisy signals than the state-of-the-
art DL-based schemes. The semi-supervised learning MixMatch is motivated by
the idea of data augmentation, and it can be flexibly integrated into other
DL-based schemes.

  2. 2.

To learn discriminative features without irrelevant noise information, a deep
residual shrinkage network with residual stacks is proposed for WSR. To enable
the model with the ability to learn deep features without the gradient
exploding problem, the residual stacks constructed by residual shrinkage units
(RSU) with shrinkage block and identity shortcut are developed. The shrinkage
block is designed to learn discriminative features from high-dimensional
tensors by using several convolutional and FC layers. Moreover, soft
thresholding can help the model mitigate the influence of noise from the raw
input signals.

  3. 3.

Extensive simulation results demonstrate the superiority of our proposed WSR
framework SSwsrNet compared with other DL-based WSR schemes in terms of the
classification accuracy. Moreover, the visualized features present the
discriminative and separable representation ability and the superiority of our
proposed WSR framework from another aspect.

The remainder of this paper is organized as follows. Section II provides
background about the wireless signal model and fundamental DL techniques for
WSR. Section III introduces the proposed SSwsrNet framework by combining deep
residual shrinkage networks with modular semi-supervised learning. Section IV
presents experimental results. Finally, Section V concludes the paper. The
list of abbreviations is presented in Table I.

TABLE I: List of Abbreviations. Abbreviations |  Description
---|---
AM |  amplitude modulation
AMC |  automatic modulation classification
AWGN |  additive white Gaussian noise
DL |  deep learning
DSA |  dynamic spectrum access
DRSN |  deep residual shrinkage network
FB |  feature-based
FC |  fully connected
FM |  frequency modulation
GAN |  generative adversarial network
GAP |  global average pooling
IQ |  in-phase and quadrature
LB |  likelihood-based
LSTM |  long short-term memory
PSK |  phase shift keying
QAM |  quadrature amplitude modulation
RSU |  residual shrinkage unit
SNR |  signal-to-noise ratio
WSR |  wireless signal recognition
WTC |  wireless technology classification

##  II Signal Model

According to the previous work [3], a single antenna is used to receive the
signal. The received signal with the $c$th modulation hypothesis $H_{c}$ can
be expressed as

$H_{c}:x(l)=s_{c}(l)+n(l),l=1,2,\cdots,L,$ (1)

where $c$ denotes the index of the modulation hypothesis. $l$ is the sample
index, while $L$ is the maximum number of samples. Besides, the noise term
$n(l)$ is typically modeled as additive white Gaussian noise (AWGN) with zero
mean and variance $\sigma_{\omega}^{2}$. The signal-to-noise ratio (SNR) is
then defined as $\gamma=|h|^{2}/\sigma_{\omega}^{2}$, where $|h|^{2}$ is the
channel gain.

At the receiver, which has a single antenna, the received data is processed by
sampling and quantizing to obtain the complex-valued raw signal symbols. These
raw signal symbols are then transformed into in-phase (I) and quadrature (Q)
sequences, expressed as

$\textbf{x}^{IQ}=\begin{pmatrix}\Re[x(1),\cdots,x(L)]\\\
\Im[x(1),\cdots,x(L)]\end{pmatrix},$ (2)

where $\Re$ and $\Im$ denote the real and imaginary parts of the signal,
respectively.

After pre-processing, the raw signal symbols are transformed from
$\textbf{x}\in\mathbb{R}^{1\times L}$ to
$\textbf{x}^{IQ}\in\mathbb{R}^{2\times L}$. Then, the outputs are utilized as
the input data of the SSwsrNet framework, and the feature extraction process
can be expressed as

$f_{e}:\textbf{x}^{IQ}\in\mathbb{R}^{2\times
L}\to\textbf{x}_{e}\in\mathbb{R}^{1\times i},$ (3)

where $\textbf{x}_{e}$ denotes the outputs of the feature extractor, and $i$
is the size of the kernel.

The learned features are then classified by the classification module,
comprised of fully connected (FC) layers followed by a softmax classifier. The
final layer consists of an FC layer with the number of neurons equal to the
number of modulation types. Thus, each neuron corresponds to one modulation
type, and the softmax activation function converts the outputs to probability
values representing the likelihood that the input belongs to each candidate
modulation format. The softmax function can be expressed as

$Softmax(z_{i})=\frac{\exp(z_{i})}{\sum_{c=1}^{C}\exp{z_{c}}},$ (4)

where $z_{i}$ is the output of the $i$th neuron, and $C$ is the total number
of neurons, which is equal to the number of classes.

##  III SSwsrNet: Our Proposed WSR Framework

In this section, we describe the details of our proposed SSwsrNet framework
for wireless signal recognition (WSR). First, the overall framework is shown
in Fig. 2. Next, the feature extraction module and the modular semi-supervised
module are introduced, respectively. Finally, training strategies for the
proposed framework are described.

###  III-A Overview of the Proposed SSwsrNet Framework

In this section, we present the details of our proposed SSwsrNet framework. As
illustrated in Fig. 2, the framework of the proposed SSwsrNet comprises four
main components, namely, the input layer, the feature extraction module, the
classification module, and the modular semi-supervised learning module (only
applicable when training). First, in the input layer, the received signal
samples are transformed into in-phase and quadrature (IQ) samples to match the
input requirements of the model. Next, a deep residual shrinkage network
(DRSN) is utilized to extract discriminative features from the input signals.
The DRSN incorporates the proposed residual shrinkage modules to capture
salient features from the raw data. Subsequently, in the classification stage,
the cross-entropy loss (_i.e._ the softmax loss from the final fully connected
(FC) layer) is employed to optimize the model parameters. Furthermore, a
modular semi-supervised learning approach is utilized to enable classification
under few-shot conditions during training. Specifically, the top layer of the
SSwsrNet is meta-trained as low-density separators on an unlabeled dataset to
improve the generalizability of the top layer units. The model is then fine-
tuned on the small labeled dataset.

Figure 2: The structure of the proposed SSwsrNet.

###  III-B Feature Extraction Module

In this work, we propose a DRSN to learn highly discriminative features,
aiming to improve the classification accuracy of WSR. As shown in Fig. 2, the
proposed DRSN consists of three residual stack modules, an FC layer and the
softmax classifier. In DRSN, the residual stack module shares the same
structure as its conventional version in [18]. However, it is more powerful
for capturing accurate information mainly due to the design of the residual
unit. Instead of using two convolutional layers in the original residual unit,
we replace the second convolutional layer with the advanced shrinkage block
[31] to make it more robust to noise. By inheriting both the advantages of the
residual units and shrinkage blocks, the proposed DRSN can learn more accurate
features from the input signals. Firstly, the residual unit can effectively
alleviate the gradient vanishing problem, enabling the network to effectively
capture deeper and more complex features of the input data, improving accuracy
and robustness of information extraction. Secondly, the shrinkage block can
learn more discriminative features from the input signals by adaptively
determining the threshold based on the data, making the process more flexible
and data-driven.

####  III-B1 Residual Stack

To evaluate the efficacy of the proposed residual shrinkage module for WSR,
the residual stack shares the same structure as the original ResNet in [18].
As shown in Fig. 2 (b), the residual stack starts with a convolutional layer
with a $1\times 1$ kernel, which is mainly used to change the channel number
and aggregate information from the previous layer. Then, two residual units
are utilized together to extract the features. Finally, a max-pooling
operation is utilized to decrease the width of the feature maps and to reduce
the computational cost for subsequent layers. In contrast to using a single
residual unit as in [32], the proposed residual stack structure with double
residual units can achieve significant gains in terms of the classification
accuracy. Thus, the elegant structure is adopted to inherit the advantages of
residual units.

####  III-B2 Residual Shrinkage Unit

As illustrated in Fig. 2 (c), the proposed residual shrinkage unit (RSU) is a
modified residual unit incorporating a channel-wise soft thresholding
operation [31]. Specifically, the input feature map $x$ is first flattened
into a 1D vector by using an absolute value operation followed by the global
average pooling (GAP). This vector is then passed through a two-layer FC
network. The second FC layer contains multiple neurons equal to the number of
channels in $x$. The output of this FC network is scaled to the range $(0,1)$
by using a sigmoid activation, given as

$\alpha_{c}=\frac{1}{1+\exp(-z_{c})},$ (5)

where $z_{c}$ denotes the output of the $c$th neuron in the FC layer, and
$\alpha_{c}$ represents the $c$th learned scaling parameter. The threshold for
each channel is then computed as

$\tau_{c}=\alpha_{c}\underset{i,j}{\mathrm{average}}|x_{i,j,c}|,$ (6)

where $\tau_{c}$ represents the threshold for the $c$th channel and $i$, $j$,
and $c$ denote width, height, and channel indexes of the input feature map
$x$, respectively, and $\mathrm{average}$ denotes the average operation. By
stacking multiple RSUs, the model can learn highly discriminative features
through successive nonlinear transformations. The soft thresholding acts as a
shrinkage function within each RSU to suppress noise-related information. The
layered RSUs enable deep feature learning while enhancing the discriminability
of the features.

GAP computes the mean across each channel of the feature map [33]. It is
commonly placed before the final output layer in CNN architectures. By
reducing the spatial dimensions to a single value per channel, GAP drastically
decreases the number of parameters in the subsequent FC layer. This mitigates
overfitting. Additionally, GAP provides spatial invariance, making the learned
feature representations robust to the locations of input patterns. This is
advantageous for handling shifting or impulse noise. Thus, GAP confers the
benefits of overfitting reduction and spatial invariance before
classification.

###  III-C Modular Semi-Supervised Module

For an unlabeled data point $x$, prior work has incorporated the consistency
regularization term

$||\mathrm{p_{model}}(y|\mathrm{Aug}(x);\theta)-\mathrm{p_{model}}(y|\mathrm{Aug}(x);\theta)||^{2}_{2},$
(7)

where $\mathrm{p_{model}}(y|x;\theta)$ denotes the model prediction outputting
a distribution over class labels $y$ for the input $x$ with parameters
$\theta$, and $\mathrm{Aug}(x)$ represents the augmentation for the input $x$.
Since $\mathrm{Aug}(x)$ represents a stochastic augmentation, those two terms
of $\mathrm{p_{model}}(y|\mathrm{Aug}(x);\theta)$ are not identical. MixMatch
[34] employs consistency regularization by leveraging standard data
augmentations for the input signals.

MixMatch combines components from multiple prevailing semi-supervised learning
paradigms into a holistic approach. Given a batch of labeled examples
$\mathcal{X}$ with one-hot encoded labels and an equally-sized batch of
unlabeled examples $\mathcal{U}$, MixMatch generates augmented labeled
examples $\mathcal{X}^{e}$ and unlabeled examples $\mathcal{U}^{e}$ with
predicted “guessed” labels. $\mathcal{X}^{e}$ and $\mathcal{U}^{e}$ are then
used to calculate supervised and unsupervised loss terms, respectively. The
overall loss $\mathcal{L}$ for semi-supervised learning in MixMatch is
generally defined as

$\mathcal{X}^{e},\mathcal{U}^{e}=\mathrm{MixMatch}(\mathcal{X},\mathcal{U},T,K,\alpha),$
(8)

where $H(p,q)$ denotes the cross-entropy between the predict distribution $p$
and the target distribution $q$, and $T$, $K$, and $\alpha$ are
hyperparameters. Algorithm 1 presents the full version of MixMatch, and Fig. 3
illustrates the diagram of the label-guessing process.

Algorithm 1 Given a batch of labeled data $\mathcal{X}$ and a batch of
unlabeled data $\mathcal{U}$, MixMatch generates an expanded set of labeled
examples $\mathcal{X}^{e}$ and an expanded set of unlabeled examples
$\mathcal{U}^{e}$ with predicted labels.

0: Batch of labeled data and corresponding one-hot labels
$\mathcal{X}=((x_{b},p_{b});b\in(1,\cdots,B))$, batch of unlabeled examples
$\mathcal{U}=(u_{b};b\in(1,\cdots,B))$, sharpening temperature $T$, number of
augmentations $K$, Beta distribution parameter $\alpha$ for MixUp;

0: $\mathcal{X}^{e},\mathcal{U}^{e}$.

1: for $b=1$ to $B$ do

2: $\hat{x}_{b}=\mathrm{Aug}(x_{b})$

3: for $k=1$ to $K$ do

4: $\hat{u}_{b,k}=\mathrm{Aug}(u_{b})$

5: end for

6:
$\overline{q}_{b}=\frac{1}{K}\sum_{k}\mathrm{p_{model}}(y|\hat{u}_{b,k};\theta)$

7: $q_{b}=\mathrm{Sharpen}(\overline{q}_{b},T)$

8: end for

9: $\hat{\mathcal{X}}=((\hat{x}_{b},p_{b}),b\in(1,\cdots,B))$

10:
$\hat{\mathcal{U}}=((\hat{u}_{b,k},p_{b}),b\in(1,\cdots,B),k\in(1,\cdots,K))$

11: $\mathcal{W}=\mathrm{Shuffle}(\mathrm{Concat}(\mathcal{\hat{X},\hat{U}}))$

12:
$\mathcal{X}^{e}=(\mathrm{MixUp}(\mathcal{\hat{X}}_{i},\mathcal{W}_{i});i\in(1,\cdots,|\mathcal{\hat{X}}|))$

13:
$\mathcal{U}^{e}=(\mathrm{MixUp}(\mathcal{\hat{U}}_{i},\mathcal{W}_{i+|\mathcal{\hat{X}}|});i\in(1,\cdots,|\mathcal{\hat{U}}|))$

####  III-C1 Data augmentation

Data augmentation is utilized for both the labeled examples $\mathcal{X}$ and
unlabeled examples $\mathcal{U}$. For each labeled example
$x_{b}\in\mathcal{X}$, a transformed version $\hat{x}_{b}$ is generated by
applying a stochastic augmentation function $\hat{x}_{b}=\mathrm{Aug}(x_{b})$
(Algorithm 1, line 2). Similarly, each unlabeled example $u_{b}\in\mathcal{U}$
is augmented $K$ times by drawing $K$ augmented versions
$\hat{u}_{b,k}=\mathrm{Aug}(u_{b}),k\in(1,\dots,K)$ (Algorithm 1, line 4).
Individual augmentations are used to generate a “guessed label” $q_{b}$ for
each $u_{b}$, which includes RandomFlip and RandomSmooth. RandomFlip refers to
the data augmentation method presented in [35], which converts the $I$ or $Q$
part to $-I$ or $-Q$ randomly. RandomSmooth randomly selects several points
and replaces them with the mean of the previous and next values.

####  III-C2 Label guessing

For each unlabeled data $u$ in $\mathcal{U}$, MixMatch generates a pseudo-
label for the data under the prediction mode of the model, which is used in
the unlabeled loss term. The average of the model’s predicted class
distributions across all the $K$ augmentations of $u_{b}$ is computed as

$\overline{q}_{b}=\frac{1}{K}\sum^{K}_{k=1}\mathrm{p_{model}}(y|\hat{u}_{b,k};\theta),$
(9)

in Algorithm 1, line 6. In the consistency regularization methods, data
augmentation is commonly used to create an artificial target for an unlabeled
example.

To reduce the entropy of the label distribution under the average prediction
over augmentations $\overline{q}_{b}$, a sharpening function is applied.
Practically, the “temperature” of the categorical distribution is modified,
which is classified as the sharpening operation, given as

$\mathrm{Sharpen}(p,T)_{i}:=p_{i}^{\frac{1}{T}}/\sum_{j=1}^{L}p_{j}^{\frac{1}{T}},$
(10)

where $p$ is the input categorical distribution ($p$ is the average class
distribution over augmentations $\overline{q}_{b}$ in MixMatch, as in
Algorithm 1, line 7) and $T$ denotes the hyperparameter. When $T\to 0$, the
output of $\mathrm{Sharpen}(p,T)$ reaches a Dirac (“one-hot”) distribution.
$q_{b}=\mathrm{Sharpen}(\overline{q}_{b},T)$ is used as an object for the
model’s forecast for augmentation of $u_{b}$, and thus lower-entropy
predictions are generated by the model when the temperature is lower.

Figure 3: Illustration of the label guessing process used in MixMatch.

####  III-C3 MixUp

Both labeled examples and unlabeled examples with predicted labels are
utilized to train the model. A slightly modified version of MixUp is defined
to be compatible with the separate loss terms. For a pair of two examples with
corresponding label distributions $(x_{1},p_{1})$, $(x_{2},p_{2})$,
$(\tilde{x},\tilde{p})$ is computed as

$\displaystyle\lambda$ $\displaystyle\sim\mathrm{Beta}(\alpha,\alpha)$ (11a)
$\displaystyle\tilde{\lambda}$ $\displaystyle=\max(\lambda,1-\lambda)$ (11b)
$\displaystyle\tilde{x}$
$\displaystyle=\tilde{\lambda}x_{1}+(1-\tilde{\lambda})x_{2}$ (11c)
$\displaystyle\tilde{p}$
$\displaystyle=\tilde{\lambda}p_{1}+(1-\tilde{\lambda})p_{2}$ (11d)

where $\alpha$ is a hyperparameter, and Vanilla MixUp sets
$\tilde{\lambda}=\lambda$ directly. Labeled and unlabeled training instances
are mixed within the same mini-batch, and the order of the batch to calculate
individual loss terms should be preserved appropriately. Eq. (11b) is used to
achieve this, which ensures that $\tilde{x}$ is closer to $x_{1}$ than to
$x_{2}$. To implement MixUp, all augmented labeled training examples along
with their ground truth labels are aggregated with unlabeled examples that are
assigned estimated labels, given as

$\displaystyle\mathcal{\hat{X}}$
$\displaystyle=((\hat{x}_{b},p_{b});b\in(1,\cdots,B)),$ (12a)
$\displaystyle\mathcal{\hat{U}}$
$\displaystyle=((\hat{u}_{b,k},q_{b});b\in(1,\cdots,B),k\in(1,\cdots,K)).$
(12b)

Then, these collections are combined by using $\mathrm{Concat}$ operation, and
the result is shuffled by using $\mathrm{Shuffle}$ operation to generate
$\mathcal{W}$, functioning as the input data for MixUp (Algorithm 1, line 11).
For the $i$th labeled example $\mathcal{\hat{X}}_{i}$ and its corresponding
label $\mathcal{W}_{i}$ in the augmented labeled set $\mathcal{\hat{X}}$, the
MixUp augmentation is applied as
$\mathrm{MixUp}(\mathcal{\hat{X}}_{i},\mathcal{W}_{i})$. The output is then
added to the aggregated dataset $\mathcal{X}^{e}$ (Algorithm 1, line 12).
$\mathcal{U}^{e}_{i}=\mathrm{MixUp}(\mathcal{\hat{U}}_{i},\mathcal{W}_{i+|\mathcal{\hat{X}}|})$
for $i\in(1,\cdots,|\mathcal{\hat{U}}|)$ is computed by using the remaining
part of $\mathcal{W}$ that is not utilized in the construction of
$\mathcal{X}^{e}$ (Algorithm 1, line 13). MixMatch transfers $\mathcal{X}$
into $\mathcal{X}^{e}$, a set of labeled examples that are augmented and
MixUp. Similarly, $\mathcal{U}$ is turned into $\mathcal{U}^{e}$, which is a
collection of multiple-augmented unlabeled samples with corresponding guessed
labels.

####  III-C4 Hyperparameters

Since MixMatch incorporates multiple strategies for utilizing unlabeled data,
it brings several hyperparameters, including the sharpening temperature $T$,
number of the unlabeled augmentations $K$, $\alpha$ parameter for Beta in
MixUp, and the unsupervised loss weight $\lambda_{\mathcal{U}}$. In practice,
semi-supervised learning algorithms with multiple hyperparameters can present
difficulties, as cross-validation with small validation sets may not provide
reliable hyperparameter estimates [36, 37]. However, most of the
hyperparameters of MixMatch can be constant and do not need to be tuned during
the training process as indicated in [34]. Thus, we follow the set for all
experiments, where $T=0.5$, $K=2$, $\alpha=0.75$ and
$\lambda_{\mathcal{U}}=75$.

###  III-D Loss Function

The cross-entropy loss is a commonly used objective function for optimization
in multi-class classification models [38]. Compared to the traditional squared
error loss, the cross-entropy loss often results in faster training
convergence since the gradients of the model weights are less likely to
vanish. To compute the cross-entropy loss, the output of the final layer must
first be passed through a softmax function to normalize the predictions to a
probability distribution over the classes, as shown in eq. (13). The per-
sample cross-entropy loss can then be expressed as

$E=-\sum^{C}_{c=1}t_{c}\log(y_{c}),$ (13)

where $t$ is the target output vector and $t_{c}$ is the model’s predicted
probability that a given sample belongs to the class $c$. The parameters of
the model can then be optimized to minimize the cross-entropy loss using
gradient descent over a number of training iterations.

Given the augmented labeled batch $\mathcal{X}^{e}$ and unlabeled batch
$\mathcal{U}^{e}$, the semi-supervised loss function defined in eq. (14a) to
(14c) is utilized for training. The combination of the cross-entropy loss
between labels and model predictions from $\mathcal{X}^{\prime}$, and the
squared L2 loss on predictions and guessed labels from $\mathcal{U}^{e}$, is
expressed in eq. (14c) along with a bias of $\lambda_{\mathcal{U}}$. The L2
loss is commonly utilized for the unlabeled data to gauge predictive
uncertainty due to its bounded nature and reduced sensitivity to incorrect
predictions. Gradient propagation is not performed when computing the guessed
labels.

$\displaystyle\mathcal{L}_{\mathcal{X}}$
$\displaystyle=\frac{1}{|\mathcal{X}^{e}|}\sum_{x,p\in\mathcal{X}^{e}}\mathrm{H}(p,\mathrm{p_{model}}(y|x;\theta)),$
(14a) $\displaystyle\mathcal{L}_{\mathcal{U}}$
$\displaystyle=\frac{1}{L|\mathcal{U}^{e}|}\sum_{u,q\in\mathcal{U}^{e}}||q-\mathrm{p_{model}}(y|u;\theta)||^{2}_{2},$
(14b) $\displaystyle\mathcal{L}$
$\displaystyle=\mathcal{L_{X}}+\lambda_{\mathcal{U}}\mathcal{L_{U}}.$ (14c)

##  IV Experiments

###  IV-A Datasets

Table II illustrates the datasets used for each experiment and the
corresponding results. For AMC, we choose the popular data set
RadioML.2016.04C [16], which is provided by
DeepSig111https://www.deepsig.ai/datasets. The dataset comprises 8 types of
digital signals, namely BPSK, QPSK, 8PSK, QAM16, QAM64, GFSK, CPFSK, and PAM4,
along with 3 types of analog signals which are WBFM, AM-SSB, and AM-DSB. By
the specifications outlined in [27], we opt for a signal-to-noise ratio (SNR)
range of $-6$ dB to $12$ dB with an interval of $2$ dB in our experiment. The
dataset contains a total of $81,030$ samples. The dynamic channel model
hierarchical block, which encompasses frequency offset, sample rate offset,
additive white Gaussian noise (AWGN), multipath, and fading, is utilized for
channel simulation. The signal sequences are aggregated without any
designation of a training or a testing set. To ensure that both the training
set and the testing set adhere to the same data distribution, we adopt the
“hold out” method for selecting distinct samples from the dataset.
Specifically, $20\%$ of the dataset is selected for testing by using a
stratified sampling method. Corresponding ratios (i.e. $3\%$, $5\%$, or
$10\%$) of the dataset are trained with labels, and the remainder is utilized
without labels.

To provide additional evidence of the effectiveness of the proposed approach,
we employ a larger variant of the RadioML dataset, namely RadioML.2016.10A
[16], for supervised learning. This version of the dataset is a more refined
and standardized version of RadioML.2016.04C and includes $220,000$ labeled
data points spanning the same class and SNR range. Specifically, we follow the
settings in our previous works [3, 15].

To conduct wireless technology classification, we utilize the Technology
Recognition (TechRec) dataset 222https://ieee-dataport.org/documents/iq-
signals-captured-lte-wifi-and-dvb-t [39]. This dataset comprises in-phase and
quadrature (IQ) signals captured from multiple wireless technologies (LTE, Wi-
Fi and DVB-T) deployed in varied environments, and is collected over the air
at six distinct locations in Gent, Belgium (UZ, Reep, Rabot, Merelbeke, iGent
and Gentbrugge). Our experiments employ a SNR range of $-6$ dB to $12$ dB,
with an interval of $2$ dB, and the dataset contains a total of $160,800$
samples.

TABLE II: Datasets for Wireless Signal Recognition. Task |  Dataset |  Classes |  Description |  Results
---|---|---|---|---
AMC |  RadioML 2016.10A [16] |  AM-SSB, CPFSK, QPSK, GFSK, PAM4, QAM16, WBFM, 8PSK, QAM64, AM-DSB, BPSK |  $220,000$ samples with a SNR range of [-6:2:12] |  Fig. 4, 6, 7, Table III
AMC |  RadioML 2016.04C [16] |  AM-SSB, CPFSK, QPSK, GFSK, PAM4, QAM16, WBFM, 8PSK, QAM64, AM-DSB, BPSK |  $81,030$ samples with a SNR range of [-6:2:12] |  Fig. 8, 9, 11
WTC |  TechRec [39] |  LTE, Wi-Fi and DVB-T |  $160,800$ samples with a SNR range of [-6:2:12] |  Fig. 5, 10

To train our proposed SSwsrNet framework, we employ the Adam optimization
algorithm with an initial learning rate of $0.001$ over $50$ training epochs.
When training the model under few-sample conditions, the same initial learning
rate is utilized. To assess the performance of various algorithms, model
accuracy is employed as the evaluation metric. Accuracy is defined as the
ratio of correctly predicted observations to the total observations.
Mathematically, it is defined as

$acc=\frac{t}{t+f},$ (15)

where $t$ is the number of correctly predicted observations and $f$ is the
number of wrong observations.

###  IV-B Performance Comparison for AMC

In this subsection, we seek to demonstrate the performance of the proposed
SSwsrNet framework under various conditions. First, we use the RadioML
2016.10A dataset [3] to illustrate the performance of our proposed SSwsrNet
framework under full supervision. Next, we utilize the RadioML 2016.04C
dataset [27] to demonstrate the classification accuracy of our proposed model
under few-sample conditions. The objectives of these experiments are to
illustrate the efficacy of the SSwsrNet approach for both fully-supervised and
few-sample learning settings.

Figure 4: Classification performance comparison among SSwsrNet, AMC-Net[26],
MSNet [3], CNN [16], VGG [18], ResNet [18] and LSTM [40] on RadioML 2016.10A
[16] with $80\%$ data for training and $20\%$ for testing.

As shown in Fig. 4, we compare the performance of our proposed SSwsrNet
framework with several state-of-the-art DL-based AMC methods including
EMC2-Net [25], AMC-Net [26], MSNet [3], CNN [16], VGG [18], ResNet [18], and
LSTM [40]. The network parameters for these models are based on the related
works [3, 16, 18, 40]. To accommodate the input length of 128, only three
layers of the relevant modules are used for VGG and ResNet. Our proposed
SSwsrNet model achieves the superior performance compared to other advanced
DL-based methods, including the recent EMC2-Net [25], AMC-Net [26] and MSNet
[3]. The SSwsrNet achieves over 90% accuracy when SNR is larger than -1 dB,
which is 1 dB more responsive to the EMC2-Net, AMC-Net and MSNet schemes.
Moreover, SSwsrNet reaches an accuracy over 95% when SNR reaches 2 dB, which
is approximately 3% higher than EMC2-Net and AMC-Net, 4% higher than ResNet
and 12% higher than VGG. These results demonstrate the effectiveness of the
SSwsrNet model for AMC.

To further demonstrate the superiority of the proposed SSwsrNet framework, we
compare it with the recently advanced DL-based schemes in terms of the number
of parameters, training and testing time. As shown in Table III, the proposed
SSwsrNet framework achieves the best performance in terms of the accuracy. The
MSNet has the least number of parameters, while it performs worse with higher
training and testing time compared to our proposed SSwsrNet due to its
multiscale structure. VGG can run faster than other models, but it has the
worst performance in terms of the accuracy. Our proposed SSwsrNet achieves a
similar testing speed compared to VGG and less training time than recent works
such as EMC2-Net [25] and AMC-Net [26]. Overall, the proposed SSwsrNet
framework achieves a good balance between the accuracy and the number of
parameters as well as the speed.

TABLE III: The number of parameters and speed for different DL-based schemes. Model |  Parameters |  Training (s/epoch) |  Testing (s/epoch) |  Accuracy
---|---|---|---|---
CNN [16] |  13,130,579 |  3.31 |  0.45 |  75.85%
VGG [18] |  160,536 |  1.46 |  0.21 |  74.97%
LSTM [40] |  2,298,379 |  2.46 |  0.31 |  80.65%
ResNet [18] |  180,619 |  2.57 |  0.48 |  84.98%
EMC2-Net [25] |  282,372 |  3.52 |  0.35 |  86.46%
AMC-Net [26] |  466,144 |  4.29 |  0.35 |  85.41%
MSNet [3] |  74,955 |  2.95 |  0.32 |  86.90%
SSwsrNet |  90,915 |  2.56 |  0.25 |  88.88%

###  IV-C Performance Comparison for WTC

In this subsection, to demonstrate the performance of our proposed SSwsrNet
for different WSR tasks, simulations are conducted using the dataset TechRec
[39] on the fully supervised situation. As shown in Fig. 5, we compare the
proposed SSwsrNet with the recent advanced models including MSNet [19], VGG
[18], ResNet [18], and LSTM [40]. We observe that the proposed SSwsrNet
achieves the best performance in terms of accuracy compared to other advanced
DL-based WTC schemes, including the powerful model MSNet. The SSwsrNet can
achieve over $80\%$ $acc$ when SNR is larger than $0$dB, which is $1$ dB more
sensitive than the advanced MSNet and ResNet scheme. Moreover, SSwsrNet can
reach an accuracy over $90\%$ when SNR reaches $4$ dB, which is $2$ dB more
sensitive than VGG and CNN. In terms of the overall classification accuracy,
SSwsrNet achieves 82.66% in all three classes over a wider range of SNRs,
which is 1.5% higher than MSNet and ResNet, and about 5% higher than VGG and
CNN.

Figure 5: Classification performance comparison among SSwsrNet, MSNet-WTC
[19], CNN [16], VGG [18], ResNet [18] and LSTM [40] on TechRec [39] with
$80\%$ data for training and $20\%$ for testing.  Figure 6: Classification
performance over layers on RadioML 2016.10A [16] with $80\%$ training data.

Figure 7: The training process over layers on RadioML 2016.10A[16]. (a) test
loss; (b) test accuracy.

Figure 8: The impact of the proportion of the labeled training samples on
classification accuracy under different models for AMC using RadioML 2016.04C
[16]. (a) $10\%$; (b) $5\%$; (c) $3\%$.

Figure 9: Classification accuracy of modulation signals by SSwsrNet under few
samples with $5\%$ labeled data. (a) SNR=$-4$ dB, (b) SNR=$12$ dB.

###  IV-D Ablation Study

As demonstrated in the previous works [41, 18], the network depth influences
the classification performance of the DL-based models. Thus, we perform an
ablation study on the depth of the proposed SSwsrNet. As suggested in [18], a
constant channel number of $32$ is adopted for the SSwsrNet, and the
evaluation is applied to the dataset of RadioML 2016.10A [16] with $80\%$ of
the data for training. As presented in Fig. 6, the performance achieved with
different numbers of residual stacks used in the SSwsrNet is given, as well as
the corresponding network parameters. It is evident that the SSwsrNet with
three layers of residual stacks can achieve the best accuracy among all the
number sets. SSwsrNet with two layers of residual stacks has the least network
parameters, but its performance is about $2\%$ percent compared to that with
three layers in terms of accuracy. To further demonstrate the effectiveness of
the SSwsrNet with four layers of residual stacks, we visualize the test loss
and test accuracy during the training process. As shown in Fig. 7 (a) and (b),
SSwsrNet with four and five layers of residual stacks causes the over-fitting
problem mainly due to their deep architectures with numerous network
parameters. Moreover, SSwsrNet with four layers of residual stacks can achieve
comparable performance compared to that with three layers. However, four
layers bring more trainable parameters and are hard to be trained. Thus, the
proposed SSwsrNet is equipped with three layers of residual stacks to reach a
balance between accuracy and network parameters.

###  IV-E Performance Comparison Under Few-sample Conditions

In this subsection, we demonstrate the effectiveness of the proposed semi-
supervised learning method for WSR under few-sample conditions. To this end,
we further investigate the classification accuracy of other network
architectures, including CNN[16], LSTM[40], CNN-LSTM [27], GRU[21], ResNet
[18], and AMR-CapsNet [27], under few-sample settings using the RadioML
2016.04C dataset as in [27]. As shown in Fig. 8 (a), when $10\%$ of the
dataset is used for training, the classification accuracy of our proposed
framework SSwsrNet is close to $95\%$ as the SNR increases. When $5\%$ of the
labeled dataset is used for training, the classification accuracy of CNN
fluctuates around $80\%$ and AMR-CapsNet can achieve 85% accuracy when the SNR
is greater than 0 dB, while the classification accuracy of SSwsrNet continues
to improve by nearly $95\%$. When using $3\%$ of the labeled training data,
the classification accuracy of most network structures for modulation signals
fluctuates between $60\%$ and $70\%$ and AMR-CapsNet can achieve 80% accuracy.
In contrast, the classification accuracy of SSwsrNet fluctuates around $92\%$.
When the SNR is $12$ dB, the classification accuracy is close to $95\%$.

As shown in Fig. 9, $5\%$ of the labeled data ($4,050$ samples) and $75\%$ of
the unlabeled data are used to train the SSwsrNet framework, while the
remaining data is utilized for model evaluation. We employ a confusion matrix
to analyze the performance of modulation signal classification under different
SNRs. As it can be seen from Fig. 9 (a), at a SNR of $-4$ dB, the model cannot
accurately identify the distinguishing characteristics of the modulation
signals due to noise, resulting in deviations in determining the signal
modulation types. With increasing SNR, the classification accuracy
significantly improves for most modulation signals, with most classes
achieving over $95\%$ accuracy. However, in line with [27], 8PSK, AM-DSB, and
WBFM exhibit lower accuracy. As the SNR increases to $2$ dB in Fig. 9 (b), the
performance of 8PSK and AM-DSB improves significantly, though WBFM accuracy
remains relatively low. Overall, these results demonstrate that the proposed
SSwsrNet framework achieves good performance for AMC, especially at higher
SNRs.

Figure 10: The impact of the proportion of training samples on classification
accuracy under different models for WTC using TechRec [39]. (a) $10\%$; (b)
$5\%$; (c) $3\%$; (d) $1\%$.

Next, we further illustrate the effectiveness of the proposed SSwsrNet and
semi-supervised learning method for WTC under limited training data
conditions. In Fig. 8, we compare the proposed SSwsrNet with the recent
advanced models including MSNet [19], VGG [18], ResNet [18], and LSTM [40]
under different few sample conditions. As shown in Fig. 8 (a), when using
$10\%$ of the labeled training dataset, the classification accuracy of our
proposed scheme SSwsrNet approaches $90\%$ as the SNR increases, while the
classification accuracy of the other advanced DL-based is under 85%. When
$5\%$ of the labeled dataset is used for training, the classification accuracy
of MSNet fluctuates around $83\%$ and when the SNR is greater than $4$ dB,
while the classification accuracy of SSwsrNet continues to improve by nearly
$85\%$. When using $3\%$ of labeled training data, the classification accuracy
of most network structures shows similar performance as the labeled data is
$5\%$. This is because the amount of labeled data is still quite small.
Moreover, we train the models in an extreme few-sample condition with only
$1\%$ of labeled data (about $1,286$ samples). As shown in Fig. 10 (d),
training with only $1.3K$ samples, MSNet, ResNet, VGG, and CNN suffer severe
overfitting, with worse performance when SNR increases. In contrast, the
proposed SSwsrNet with semi-supervised learning can achieve over $80\%$
classification accuracy when SNR is larger than 6dB, which is much better than
the compared models.

###  IV-F Model Generalization

Figure 11: Classification performance comparison with models with the proposed
semi-supervised learning method MixMatch using $5\%$ labeled data trained on
RadioML 2016.04C [16].

To demonstrate the generalization of the proposed semi-supervised learning for
other DL-based AMC methods under few-sample conditions, we exploit the
MixMatch for several DL-based methods including MSNet [3], ResNet [18], and
CNN [16]. As shown in Fig. 11, we trained all the models by using 5% labeled
data from RadioML 2016.04C. The results demonstrate that the proposed SSwsrNet
achieves the best performance among all the models under few-sample
conditions, with an improvement of +5.39% over it without MixMatch (_i.e._ ,
DRSN in isolation). SSwsrNet without MixMatch can still achieve the best
performance among all the models including MSNet, CNN, and ResNet. Moreover,
the proposed semi-supervised learning MixMatch can help the conventional DL-
based methods such as MSNet, ResNet and CNN perform better under few-sample
conditions. For example, MSNet with MixMatch can achieve an improvement of
$+3.77\%$ over it without MixMatch, achieving about $85\%$ accuracy when SNR
is larger than $0$ dB. ResNet suffers from severe over-fitting problems under
few-sample conditions, and it can achieve comparable performance with the help
of MixMatch. CNN can achieve about $90\%$ accuracy when SNR is larger than $2$
dB, which is over $10\%$ higher than its original performance.

To further demonstrate the effectiveness of the proposed semi-supervised
learning for AMC under few-sample conditions, we evaluate the generalization
ability in different datasets. Labeled data from RadioML 2016.04C and
unlabeled data from RadioML 2016.10A are used for training together. As shown
in Table. II, the labeled data for training and testing is adopted from
RadioML 2016.04C with $4,010$ samples and $16,170$ samples, and the unlabeled
data is brought from RadioML 2016.10A with $88,000$ samples. The comparison is
presented in Fig. 12, where “SSwsrNet-Combined” represents the result of
training with different datasets. The combined training can not reach a better
performance than that from the same dataset. However, the proposed SSwsrNet
under few-sample conditions and combined learning from another dataset can
still achieve a promising performance compared to other DL-based methods.
Specifically, SSwsrNet-Combined can reach over $85\%$ $acc$ when SNR is larger
than $-2$ dB, which is about $4$ dB sensitive than the recent few-shot
learning scheme AMC-Cap [27]. Moreover, when SNR reaches $12$ dB, SSwsrNet-
Combined can obtain a comparable performance compared to SSwsrNet, reaching
about $92.7\%$ in terms of accuracy. Fig. 13 presents the confusion matrices
of SSwsrNet-Combined and AMC-Cap [27] under a low SNR of $-4$ dB. Our proposed
SSwsrNet can achieve a better performance compared to the AMC-Cap under few-
sample conditions with the help of unlabeled data from other datasets.
Specifically, $7$ classes in SSwsrNet can achieve an accuracy of $80\%$, while
there are only $2$ classes in AMC-Cap. Moreover, the confusion between classes
of AMC-Cap is larger than the proposed SSwsrNet.

Figure 12: Classification performance comparison of model generalization using
different datasets.

Figure 13: The confusion matrices of (a) SSwsrNet-Combined and (b) AMC-Cap
[27] under $5\%$ of labeled data of RadioML 2016.04C [16].

##  V Conclusion

In this paper, a novel SSwsrNet framework was proposed by utilizing a deep
residual shrinkage network (DRSN) and a modular semi-supervised learning
method to address the limited training data issue faced by existing wireless
signal recognition (WSR) methods due to the dynamic wireless communication
environment. A novel modular semi-supervised learning method is proposed that
leverages both labeled and unlabeled data during the model training.
Simulation results demonstrated that the proposed framework outperforms
benchmark methods in terms of classification accuracy. Additionally, the
impacts of network parameters and the effectiveness of the semi-supervised
learning approach on the achievable performance were comprehensively
investigated. Our proposed SSwsrNet framework can provide meaningful insights
for designing DL-based methods addressing WSR with limited labeled data.

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|  Hao Zhang (Graduate Student Member, IEEE) received the master’s degree from
the School of Information Engineering, Nanchang University, China, in 2020. He
is currently pursuing the Ph.D. degree in the College of Electronic and
Information Engineering, Nanjing University of Aeronautics and Astronautics,
Nanjing, China. His research interests focus on machine learning, deep
learning, wireless communication, and signal processing.
---|---
|  Fuhui Zhou (Senior member, IEEE) is currently a Full Professor at Nanjing
University of Aeronautics and Astronautics. He is an IEEE Senior Member. His
research interests focus on cognitive radio, cognitive intelligence, knowledge
graph, edge computing, and resource allocation. He was awarded as IEEE ComSoc
Asia-Pacific Outstanding Young Researcher and Young Elite Scientist Award of
China and URSI GASS Young Scientist. He serves as an Editor of IEEE
Transactions on Communications, IEEE Systems Journal, IEEE Wireless
Communications Letters, IEEE Access and Physical Communications.
---|---
|  Qihui Wu (Fellow, IEEE) received the B.S. degree in communications
engineering, the M.S. and Ph.D. degrees in communications and information
systems from the Institute of Communications Engineering, Nanjing, China, in
1994, 1997, and 2000, respectively. From 2003 to 2005, he was a Postdoctoral
Research Associate with Southeast University, Nanjing, China. From 2005 to
2007, he was an Associate Professor with the College of Communications
Engineering, PLA University of Science and Technology, Nanjing, China, where
he was a Full Professor from 2008 to 2016. Since May 2016, he has been a Full
Professor with the College of Electronic and Information Engineering, Nanjing
University of Aeronautics and Astronautics, Nanjing, China. From March 2011 to
September 2011, he was an Advanced Visiting Scholar with the Stevens Institute
of Technology, Hoboken, USA. His current research interests span the areas of
wireless communications and statistical signal processing, with emphasis on
system design of software defined radio, cognitive radio, and smart radio.
---|---
|  Naofal Al-Dhahir (Fellow, IEEE) is Erik Jonsson Distinguished Professor &
ECE Associate Head at UT-Dallas. He earned his PhD degree from Stanford
University and was a principal member of technical staff at GE Research Center
and AT&T Shannon Laboratory from 1994 to 2003. He is co-inventor of 43 issued
patents, co-author of over 575 papers and co-recipient of 7 IEEE best paper
awards. He is an IEEE Fellow, AAIA Fellow, received 2019 IEEE COMSOC SPCC
technical recognition award, 2021 Qualcomm faculty award, and 2022 IEEE COMSOC
RCC technical recognition award. He served as Editor-in-Chief of IEEE
Transactions on Communications from Jan. 2016 to Dec. 2019. He is a Fellow of
the US National Academy of Inventors and a Member of the European Academy of
Sciences and Arts.
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