Transfer-based Adversarial Poisoning Attacks for Online (MIMO-)Deep Receviers
Kunze Wu Weiheng Jiang Dusit Niyato Yinghuan Li Chuang Luo






 
 


Journal of  Class Files, Vol. 14, No. 8, August 2021
Shell et al.: A Sample Article Using IEEEtran.cls for IEEE Journals





Transfer-based Adversarial Poisoning Attacks 
 for Online (MIMO-)Deep Receviers
     Kunze Wu, Weiheng Jiang, Dusit Niyato, Yinghuan Li, and Chuang Luo
  
        
 
 
 
    September 9, 2024
=========================================================================================



§ ABSTRACT 

  Recently, the design of wireless receivers using deep neural networks (DNNs), 
  known as deep receivers, has attracted extensive attention for ensuring reliable communication in complex channel environments. 
  To adapt quickly to dynamic channels, online learning has been adopted to update the weights of deep receivers with over-the-air data (e.g., pilots). 
  However, the fragility of neural models and the openness of wireless channels expose these systems to malicious attacks. 
  To this end, understanding these attack methods is essential for robust receiver design.
  In this paper, we propose a transfer-based adversarial poisoning attack method for online receivers.
  Without knowledge of the attack target, adversarial perturbations are injected to the pilots, poisoning the online deep receiver and impairing its ability to adapt to dynamic channels and nonlinear effects. 
  In particular, our attack method targets Deep Soft Interference Cancellation (DeepSIC)<cit.> using online meta-learning.
  As a classical model-driven deep receiver, DeepSIC incorporates wireless domain knowledge into its architecture. 
  This integration allows it to adapt efficiently to time-varying channels with only a small number of pilots, achieving optimal performance in a multi-input and multi-output (MIMO) scenario.
  The deep receiver in this scenario has a number of applications in the field of wireless communication, which motivates our study of the attack methods targeting it.
  Specifically, we demonstrate the effectiveness of our attack in simulations on synthetic linear, synthetic nonlinear, static, and COST 2100 channels. 
  Simulation results indicate that the proposed poisoning attack significantly reduces the performance of online receivers in rapidly changing scenarios.






  



  Wireless securitys, poisoning attacks, adversarial attacks, model-based deep
  learning, deep receivers, online learning, meta-learning.
 



§ INTRODUCTION


In recent years, the application of deep learning (DL) in designing wireless communication systems has garnered significant interest. 
Researchers have concentrated on employing DL in wireless receivers to enhance communication performance in complex channels 
and to bolster adaptability in dynamic environments
<cit.>. 
However, DL-based wireless applications face vulnerabilities to evasion and data poisoning attacks 
owing to the inherent openness of wireless channels and the fragility of neural models <cit.>. 
Investigating attack methodologies on deep receivers serves to elucidate their response under such threats, 
thereby facilitating the development of secure wireless DL systems, which forms the primary focus of this paper.





 §.§ DL-based Wireless Receivers and Related Applications


Till now, numerous studies have explored DL-based designs for wireless communication systems. 
Most of them utilize an independent DNN to map the input-output relationships of functional modules in communication links. 
Jointly optimizes modules at both the transmitter and receiver by multiple DNNs.
Typically, the applications include DL-based adaptive modulation<cit.>, channel estimation<cit.>, 
channel coding and decoding<cit.>, and modulation recognition<cit.>.
In addition to replacing functional modules in the physical layer, 
various constraints can be integrated into the training process to optimize additional system metrics, 
such as the adjacent channel leakage ratio (ACLR) and peak-to-average power ratio (PAPR) <cit.>,<cit.>.
For the designs of the receiver, lots of work has contributed to enhancing its adaptability to the dynamic channels, 
including training and integrating multiple models with extensive data <cit.> and joint learning 
<cit.>.

However, DL-based wireless designs mentioned above are data-driven methods 
that heavily depend on a substantial amount of training data to improve their generalization capacity. 
Given that deep receivers typically have access to only limited pilots for adaptation, this characteristic poses a significant challenge.
In addition, data-driven designs may suffer from performance degradation 
when faced with data distribution drift caused by dynamic channels<cit.>.
To handle these issues, an online learning based approach has been proposed, involving dataset, training algorithm and deep receivers architecture.
In particular, data augmentation<cit.> and self supervision methods
<cit.>,<cit.> were proposed to to expand  the training data for online adaptation. 
In <cit.> and <cit.>, meta learning was employed to improve the generalization capability.
Furthermore, Model-based deep learning provide a solution for receivers architecture design 
to satisfy the adaptability and data efficiency<cit.>.  
Specifically, the deep receivers were explicitly modelled by incorporating wireless domain knowledge, thereby reducing the dependence on data, 
such as DNN-aided inference<cit.>,<cit.> and deep unfolding
<cit.>. 
In these studies, <cit.> proposed a classic model-based deep receiver, i.e., the DeepSIC, in MIMO scenarios, 
derived from the iterative soft interference cancellation (SIC)<cit.> MIMO detection algorithm. 
It employed DNN instead of each round of interference cancellation and soft detection, 
requiring only a few iterations to achieve extremely low data dependence and optimal performance. 
<cit.> utilized meta-learning to improve the training performance of online DeepSIC,
and the evaluation results indicated that its performance was improved compared with traditional data-driven receiver, 
and it exhibited commendable adaptability to dynamic channels.





 §.§ Security of DL in Wireless Communications


As mentioned earlier, while DL-based transceiver designs can enhance performance, they remain vulnerable to attacks by malicious users.


In particular, attacks on DL-based transceivers are divided into two main categories, i.e., the evasion attacks and data poisoning attacks. 
Evasion attacks, also known as adversarial attacks, manipulates test data to mislead the model<cit.>,<cit.>. 

On the other hand, data poisoning attacks corrupt the training data, affecting the model's performance during testing<cit.>,
<cit.>.

According to extensive literature review, numerous studies on DL-based wireless communication primarily concentrate on evasion attacks.
For instance, <cit.> proposed an adversarial attack method against adaptive modulation.
<cit.> proposed generative adversarial network (GAN)-based method to generate adversarial perturbations for channel received data, 
which can unnoticeably mislead wireless end-to-end autoencoders, 
modulation pattern recognition, and the DL-based symbol detection in orthogonal frequency division multiplexing (OFDM) systems. 
<cit.> reported adversarial perturbations can interfere with gradient-based iterative optimization algorithms in the physical layer.
<cit.> proposed semantic attacks against semantic communication.
Furthermore, adversarial perturbations can also play a role in interpretable (e.g., deep unfolding-based) architectures. 
To illustrate, <cit.> employed transfer-based methods to attack deep sparse coding networks 
and demonstrated that these attacks exert deleterious effects on the various components of deep unfolded-based sparse coding.
Regarding data poisoning attacks, current research primarily focuses on cognitive radio spectrum-aware poisoning <cit.>,<cit.> 
and disrupting distributed wireless federated learning<cit.>.



 §.§ Contribution of This Paper

Unlike previous studies, this paper addresses security threats to online deep receivers. 
Furthermore, we propose a transfer-based adversarial poisoning attack method, 
which can significantly corrupt various online deep receivers even without prior knowledge of the target system.
Specifically,
we focus on online receivers based on model-based deep learning, such as DeepSIC<cit.> and Meta-DeepSIC<cit.>, 
as well as general DNN detectors, including the black-box DNN detector<cit.>,<cit.> 
and the ResNet detector designed based on DeepRX<cit.>.

As previously stated, DeepSIC is a classical model-based deep receiver that can be combined with meta learning for efficient online adaptation.
This design effectively tackles the challenge of limited pilot data in wireless communication scenarios, 
thereby improving the generalization of deep receivers under dynamic channel conditions. 
Moreover, studies on the attack methods for DeepSIC can provide comprehensive insights into deep receiver characteristics and contribute to robust designs. 
Ultimately, this research aids in creating secure and efficient DL-enabled wireless communication systems.



Specifically, the mainly contributions of this paper are summarised as below.


  
  ∙ 
  We highlight a communication system susceptible to malicious user poisoning attacks. 
  We then analyze the vulnerability of the deep receiver based on online learning in the authorization system. 
  From the perspective of malicious users, we further develop an attack utility model and an optimal attack utility decision problem.



  
  ∙ 
  We effectively design a poisoning attack framework and attack perturbation generation method for online learning deep receivers. 
  The fundamental concept is to introduce a poisoned sample into the online training and updating phase of the deep receiver, 
  thereby compromising its performance over time. The poisoning attack framework has two stages. 
  Firstly, malicious users employ joint learning to create a surrogate model, 
  which can be selected from a generic DNN architecture, e.g., feedforward DNNs. 
  Secondly, they generate poisoning perturbation samples based on the surrogate model. 
  The transferability of the poisoning attack makes it work on different types of deep receivers.


  
  ∙We numerically evaluate the effect of the proposed poisoning attack method on four channel models: 
  Linear synthetic channel, nonlinear synthetic channel, static channel, and COST 2100 channel. 
  Simulation results demonstrate that the proposed poisoning attack method impairs the deep receiver's ability to adapt to rapid changes 
  in dynamic channels and to learn from nonlinear effects. 
  Furthermore, deep receivers adapted using meta-learning more severely damaged after poisoning.


The rest of the paper is organized as follows. 
Section II introduces the system and scenario models 
and the attack models of the malicious user.
Section III presents the basic theory of adversarial machine learning, focusing on evasion attacks, data poisoning attacks, 
and the conceptual approaches to attack transferability. 
Section IV details the proposed poisoning attack framework and the method for generating poisoning attack samples for online deep receivers. 
Section V evaluates and analyzes the effectiveness of the proposed poisoning attack method. 
Section VI concludes the paper.




§ SYSTEM AND SCENARIO MODELLING

In this section, we first present the communication system and scenario model under the presence of a malicious poisoning attack user in Section II-A. 
Subsequently, we introduce the operational model of the legitimate receiver based on deep learning in Section II-B. 
Finally, we discuss the detail of malicious user poisoning attack, focusing on pilot poisoning attacks in Section II-C.






 §.§ Communication System Scenario Model


In this paper, we investigate a poisoning attack scenario model for a communication system, as illustrated in Fig. 1. 
This system consists of a pair of legitimate transceivers and a malicious poisoning attack user. 
Both the legitimate transmitter and receiver equip with multiple antennas, denoted as N_tx and N_rx respectively.
We focus on a single-antenna malicious user, as this represents a cost-effective and straightforward approach to conducting attacks.
The data transmission from transceiver to receiver is block-based, as illustrated in Fig. 2. 
The length of one block is L, including L_pilot pilot symbols 
and L_info information symbols, herein, L_info≫ L_pilot.
As shown in Fig. 3, the legitimate receiver utilizes a DL-based architecture for signal receiving and processing. 
It is trained using pilot data and employs the trained deep receiver to decode information data.
For the malicious user, based on the previously collected
pilot data, it launches an attack by  poisoning or disturbing the transmission process of the pilot used by the legitimate user. 
Its objective is to corrupt with the online training and updating of the deep receiver, 
thereby disrupting its information data reception and decoding.





Based on the above illustrated scenario,
defining the transmit symbols by the legitimate transmitter as
𝐬∈ℝ^N_tx, 
and the corresponding modulated symbols as
𝐱∈ℂ^N_tx. 
These modulation symbols are then upconverted, amplified, transmitted through multiple antennas, 
and finally arrived at the receiver.
Let 𝐇∈ℝ^N_rx× N_tx
denote the baseband equivalent channel matrix, and
𝐰∼𝒞 𝒩(0, σ^2  𝐈) 
represent the additive gaussian white noise experienced by the legitimate receiver.
The equivalent baseband signal received by the legitimate receiver, 
in the absence of a malicious user poisoning attack, is
𝐲∈ℂ^N_rx, 
which can be expressed as


    𝐲=𝐇 𝐱+𝐰.



Following that, defining a block of data symbols received by the authorised receiver as 𝐘. 
The received data symbols can then be divided into two parts, denoted as
𝐘_pilot={𝐲_i}_i=1^L_pilot 
and 𝐘_info={𝐲_i}_i=L_pilot+1^L. 








 §.§ Deep Receiver with Online Training




In this paper, 
the online learning based deep receiver is adopted
by the legitimate receiver, as illustrated in Fig. 3.
Here, define the deep receiver as a classifier f_θ 
with model parameter θ. f_θ is trained using a supervised learning approach.
The data used for training is the pilot dataset, which is defined as 
𝒯={𝐘_pilot, 𝐒_pilot}={𝐲_i, 𝐬_i}_i=1^L_pilot. 
Model testing is done with information dataset, which is represented as 
𝒱={𝐘_info, 𝐒_info}={𝐲_i, 𝐬_i}_i=L_pilot+1^L. 
The supervised training loss function is the cross-entropy loss, which is represented as  
ℒ(𝒯 ; θ).  
P̂_θ(·|·) 
denotes the likelihood probability of symbol estimation for deep receivers. 
The deep receiver training objective can be described by 




    θmin{ℒ(𝒯 ; θ)=-∑_(y_i, 𝐱_j) ⊂𝒯logP̂_θ(𝐬_i |𝐲_i)}.


The deep receiver, trained using 𝒯, is used to decode the symbols in 𝒱. 
For the i-th received symbol 𝐲_i, the decoded result is expressed as 𝐬̂_i(𝐲_i ;θ). 
The performance metric of the deep receiver is the symbol error rate (SER), which is defined as 


    S E R(θ)=1/L_info∑_i=L_pilot+1^L 
      Pr(𝐬̂_i(𝐲_i ; θ) ≠𝐬_i) .




 §.§ Modus Operandi of the Malicious User




For the considered system, as mentioned earlier,
there is a malicious user, which aims to corrupt the information
receiving and decoding of the legitimate receiver, 
by poisoning on the pilot data transmission from the transmitter to the receiver.
This is similar to <cit.>.
In particular, the attack process of the malicious user is shown in Fig. 4 and
summarised as below.


  
  * Since the pilot pattern is fixed during transmission, the malicious user can collect pilot data during the communication process between the legitimate transceiver.
  
  * The accumulated pilot data is employed to train a surrogate model 
  that is analogous to the attack target, specifically the authorised deep receiver.
  
  * The malicious user generates the optimal perturbation based on the surrogate model and the transferability of the attack.
  
  * The malicious user injects the channel perturbation.
  The deep receiver will gradually be poisoned until the model fails when it receives the perturbed pilot data used to train the model.


In principle, a poisoning attack perpetrated 
by a malicious user can be conceptualized as a perturbation injection process.
In particular, the perturbation is defined as a vector in the complex space of receiver inputs, denoted as δ∈ℂ^N_rx,
with a poisoning process represented by 𝒫(·). 
For the i-th received symbol 𝐲_i, the corresponding poisoning perturbation is given by δ_i,
and the corresponding poisoned received symbol is given by 𝒫(𝐲_i)=𝐲_i+δ_i.


Therefore, within the context of poisoning attacks on deep receivers, 
the primary challenge for malicious users is to design an optimal perturbation signal structure that maximizes the deep receiver's loss 
on subsequent information symbols or validation sets, 
which will be addressed in the following sections.





§ ADVERSARIAL MACHINE LEARNING THEORY



Before introducing the poisoning attack method for online deep receivers proposed in this paper, 
we briefly discuss the theory of adversarial machine learning.
In particular, we provide a brief overview of the threat model presented in Section III-A, 
including the concepts of the attacker's goal, the attacker's knowledge, and the attacker's capability. 
The aforementioned concepts and definitions facilitate a more comprehensive understanding of the attack method for deep receivers proposed in this paper. 
Subsequently, in Section III-B and Section III-C, the fundamental optimization issues associated with two distinct attack paradigms, 
namely evasion attacks and data poisoning attacks, are briefly elucidated. 
Furthermore, we explain the differences and connections between the two attack paradigms. 
Finally, we analyze the transferability of attack samples in Section III-D, 
and discuss the methods to enhance the transferability of attacks.





 §.§ Threat Model: Attacker's Goal, Knowledge and Capabilities




  §.§.§ Attacker's Goal

As discussed in <cit.>,<cit.>,<cit.>, the objective of the attacker in adversarial machine learning scenarios 
can be categorised according to the form of security threats, including integrity attacks and availability attacks.


  
  ∙ Integrity attacks: The attacker's goal is to tamper the integrity of the target. 
  Specifically, this implies that the attack samples generated by the attacker are only effective in certain parts of the target system, 
  while the remainder of the target system retains its original functionality. 
  For example, an attacker applies a specific adversarial perturbation to an image of a traffic sign 
  in order to circumvent the detection of the visual classifier in an automated vehicle.
  However, at that moment, the visual classifier remains accurately operational for other objects.
  
  
  ∙ Availability attacks: In contrast, availability attacks aim to disrupt the normal functioning of the entire system, 
  rendering it unavailable to legitimate users. 
  



The difference between integrity attacks and availability attacks primarily arises from 
the different focuses of the optimization objectives inherent to the attack models constructed. 
In this paper, the proposed attack method is an availability attack, 
namely the destruction of the usability of all functions of a deep receiver.



  §.§.§ Attacker's Knowledge

The knowledge possessed by the attacker is indicative of the extent to which they are aware of the attack target. 
This knowledge encompasses several key dimensions, as outlined in <cit.>,<cit.>. 
These dimensions include: 
(i) The data utilized for training purposes.
(ii) The architectural design of the target model, the learning algorithms employed during training, 
along with their associated parameters and training hyperparameters.
(iii) The data comprising the test set. 
Based on the combination of these dimensions, two main attack scenarios can be further defined as below:


  
  ∙ White-box attacks: 
  We consider that the attacker has complete knowledge about the attack target. 
  In this context, the attacker will adapt the nature of the attack  
  to align with the specific characteristics of the target to achieve the most effective and impactful outcome.
  
  
  ∙ Black-box attacks: 
  Black box attacks can be further categorized into two main types: 
  Transfer-based attacks and query attacks. In transfer-based attacks, 
  the attacker lacks or only has partial knowledge of the internal workings of the target model.
  The knowledge about the target encompasses the aforementioned dimensions (i), (ii), and (iii).
  In this setting, the attacker is limited to relying on the data they have collected to construct a surrogate model that approximates the target model. 
  This attack is then transferred to the target model by launching a white-box attack on the surrogate model.
  In a black-box query attack, the attacker can query the target's output or confidence level to optimize the attack. 
  Currently, the majority of black-box attacks exploit the transferability for attack purposes 
  <cit.>,<cit.>.
  


The discussion regarding the attacker's knowledge aims to define the scenarios in which attacks are deployed, 
particularly in more practical black-box attacks, which are the focus of this paper. 
Moreover, within the framework of black-box attacks, the transferability of attack samples holds particular significance. 
This will be addressed in greater detail in Section III-D of this paper.



  §.§.§ Attacker's Capability








The attacker's capabilities determine the methods used to influence the attack target and the specific constraints for data manipulation. 
To avoid potential defense filtering mechanisms, the attacker must impose constraints on the manipulated data. 
It is standard practice to add an upper bound of ϵ to the perturbation δ under the p-norm space. 
From the perspective of attack methods<cit.>, 
if the attacker can manipulate data from both the training and testing phases simultaneously, 
which considered as causal attacks and is called data poisoning attacks.
If the attacker can only manipulate the data during the testing phase, this attack is considered exploratory and is called evasion attacks. 
Their difference lies in solving optimization objectives and implementation methods.
This paper focuses on adversarial poisoning attacks in black-box scenarios, 
which can be seen as a synthesis of evasion attacks and data poisoning attacks. 
The specific optimization goals and implementation forms of evasion attacks and data poisoning attacks are described in the following 
Section III-B and Section III-C, respectively.








 §.§ Evasion Attacks

The evasion attacks are implemented by constructing adversarial samples whose objective is to induce a catastrophic misclassification in the testing phase of the DNN. 
This is achieved by identifying the blind spots of the DNN and introducing carefully crafted tiny perturbations to the input, as illustrated in Fig. 5(a). 
The construction of adversarial samples arises from the observation that the deeper features and outputs of a classifier can undergo notable alterations 
when the inputs undergo slight directional changes. Gradient-based optimizers <cit.>,<cit.> are capable of readily identifying these directions, 
which exert an influence on the DNN. 
Accordingly, the methodology for the construction of adversarial samples can be expressed as follows: 
In the case of a given target model and inputs, 
the gradient of the objective function is employed to direct the application of minor perturbations to the input data to maximise the loss incurred by the input. 
This process can therefore be conceptualised as a single-layer optimization problem.
Specifically, 𝐲 denotes the model input, 𝐬 denotes the labels corresponding 
to 𝐲, and 𝐲^' denotes the adversarial samples after the adversarial perturbation is added. 
The adversarial perturbation δ=𝐲^'-𝐲_p has an upper bound of ϵ>0, 
and the optimal adversarial sample obtained after optimization is 𝐲^*. 
θ denotes the parameters of the classifier f_θ. For the classification task, 
the cross-entropy loss function ℒ(𝐲^', 𝐬 ; f_θ) is defined. 
Thus, finding the optimal adversarial samples constitutes the following optimization problem


    𝐲^* ∈𝐲^'maxℒ(𝐲^', 𝐱 ; θ) , such that δ=𝐲^'-𝐲_p ≤ϵ.





 §.§ Data Poisoning Attacks


The optimization goal of the data poisoning attack is to poison the target with poisoned training data to degrade its test performance, 
which is shown in Fig. 5(b). 
Similar to the production of adversarial samples, in the production of poisoning samples, 
the perturbation δ is applied to each sample in the training set at p-norm and does not exceed the upper bound ϵ>0. 
Specifically, the test set 𝒱 and the training set 𝒯 are defined, 
as well as the poisoned training set 𝒫(𝒯) after applying the perturbation to the data set. 
Furthermore, θ^* denotes the optimal poisoning parameter of the target classifier with respect to the parameter θ. 
Thus, the poisoning attack can be modelled as a dual optimization problem as follows:


    max _𝒫ℒ(𝒱 ; θ^*) , and θ^* ∈minℒ(𝒫(𝒯) ; θ).


Herein, firstly, the inner layer optimization involves the standard model training process. 
In this process, the attacker uses the poisoned data to train the target model by minimizing the empirical loss ℒ(𝒫(𝒯); θ) 
to obtain the optimal poisoned parameter θ^*. Secondly, based on the obtained θ^*, 
the attacker maximizes the loss ℒ(𝒱; θ^*) on the test set. 
Note that solving this optimization problem directly is often very difficult, 
and it is more common practice to approximate this maximization process through gradient optimization of δ.







  §.§.§ Adversarial Samples as Poisoning Attacks

As previously stated in Section III-B and Section III-C, 
although both adversarial sample construction for evasion attacks and data poisoning attack sample construction 
can be attributed to the gradient-based optimization framework, 
the goals achieved by constructing perturbations for these two types of attacks are different. 

Recently, however, researchers have discovered that adversarial samples are also highly effective for poisoning DNNs, 
a phenomenon known as Adversarial Poisoning <cit.>,<cit.>. 
In this case, the poisoning attack optimization problem (<ref>eq:5) can also be uniformly expressed 
in the form of the adversarial sample attack optimization problem (<ref>eq:4) in Section III-B. 
<cit.> provides a method for creating adversarial poisoning samples to obtain optimal poisoning results. 
Additionally, <cit.> shows that antipoisoning attacks can also cause serious harm to the meta-learner in a white-box attack setting. 
Compared with the dual optimization process of the poisoning attack method in (<ref>eq:5), 
using adversarial samples as poisoning attack samples is more convenient and practically feasible. 
This is also the basis for the poisoning attack method proposed in this paper.



 §.§ Transferability of Attacks



  §.§.§ Why Can Attacks Be Transferred?

The concept of attack transferability means that the attack generated for one model can be used against another in a black-box attacks scenario. 
This phenomenon has been observed and demonstrated in various studies, as referenced in <cit.>. 
Given that the approach outlined in this paper can be classified as a black-box attack, 
it is essential that the attack samples demonstrate the capacity for transferability. 

<cit.> presented an upper bound on the loss theory that arises when black-box transfer occurs. 
Define f_φ as the surrogate model with parameter φ, 
f_θ as the target model with parameter θ, and ℒ(𝐲, 𝐬, φ) as the loss of the input 𝐲 
in f_φ against the label 𝐬. 
In consideration of the transferability of evasion attacks (poisoning attacks also take the same form), 
the optimal adversarial sample, denoted as 𝐲^* is obtained by solving (<ref>eq:4) on f_φ, 
with the corresponding optimal perturbation, denoted as δ^*.
To illustrate, consider the sphere space with p=2 and radius denoted as ϵ. 
The optimal adversarial perturbation obtained on f_φ can be expressed in (<ref>) as follows:



    δ^*=ϵ∇_𝐲ℒ(𝐲, 𝐬, φ)/∇_𝐲ℒ(𝐲, 𝐬, φ)_2.



As a result, the loss of 𝐲 on the target model, denoted as ℒ(𝐲, 𝐬, θ). 
Define Δℒ as the increase in loss of the input 𝐲^* compared to the input 𝐲 on the target model. 
The upper bound of  Δℒ on the target model can be described by 


    Δℒ=ϵ∇_𝐲ℒ(𝐲, 𝐬, φ)^⊤/∇_𝐲ℒ(𝐲, 𝐬, φ)_2∇_𝐲ℒ(𝐲, 𝐬, θ) ≤ϵ∇_𝐲ℒ(𝐲, 𝐬, θ)_2.


The left-hand side of the inequality in (<ref>) represents the loss in the black-box attack scenario, 
while the right-hand side represents the loss in the white-box attack scenario. 
In the white-box attack scenario, i.e., f_φ = f_θ, inequalities in (<ref>) becomes an equality.
The attack achieves its upper bound and has optimal attack effect.
Therefore, the effectiveness of the attack when the attack sample is transferred from the surrogate model to the target model 
is influenced by two factors: The intrinsic adversarial vulnerability of the target model (right-hand side of the inequality in (<ref>)) 
and the complexity of the surrogate model used to optimize the attack (left side of the inequality in (<ref>)).

The right-hand side of the inequality in (<ref>) shows that a more vulnerable target model has a larger upper bound on the loss, 
represented by ϵ||∇_𝐲ℒ(𝐲, 𝐬, θ)||_2. 
The intrinsic complexity of the model measures the learning algorithm's ability to fit the training data. 
More complex models, like those without regularization or those prone to overfitting,
have more complex parameter spaces and rugged loss landscapes, making them sensitive to input perturbations and susceptible to attacks.
For robust models with smaller upper loss bounds, a successful attack requires a higher perturbation limit, 
reducing the likelihood of bypassing the system's monitoring.
This demonstrates the impact of the intrinsic adversarial vulnerability of the target model on transferability of attacks.

The complexity of the surrogate model used to optimize the attack depends on two main factors: 
The gradient alignment between the surrogate and the target, 
and the variance magnitude of the surrogate model's loss function.
These factors are particularly relevant for the left-hand side of the inequality in (<ref>).
When the surrogate has better gradient alignment with the target, 
such as the gradient cosine similarity used in <cit.>,
attack samples from the surrogate model exhibit better transferability. 
This is reflected in ∇_𝐲ℒ(𝐲, 𝐬, φ)^⊤∇_𝐲ℒ(𝐲, 𝐬, θ), 
as shown on the left-hand side of the inequality in (<ref>). 
Additionally, a surrogate model with low variance leads to a more stable optimization process, 
producing attack samples effective across different target models. 
In contrast, a large variance leads to an unstable optimization process, leading to attack samples may not match the target model, resulting in failure. 
Intuitively, on the left-hand side of the inequality in (<ref>), high variance of the loss function increases the corresponding denominator term 
||∇_𝐲ℒ(𝐲, 𝐬, φ)||_2, 
which results in smaller upper bounds on the achievability of the transfer.



  §.§.§ Related Work of Transfer-based Attacks

In summary, when designing transfer-based methods in black-box attacks scenario, one can approach from two perspectives: 
The inherent adversarial vulnerability of the target model and the complexity of optimizing the surrogate model.


  
  ∙ For the former, certain assumptions about the target model are typically necessary to model the attack objective. 
  For example, one might assume the existence of unstable common vulnerabilities in the integrated model as discussed in <cit.>. 
  In this scenario, more robust constraints can be applied to the optimization target, 
  or an optimization algorithm with strong generalization ability <cit.>,<cit.> can be used to optimize the attack samples, 
  making the transfer attack more effective. 
  However, the intrinsic adversarial vulnerability of unknown target is often difficult to identified directly.
  
  
  ∙ 
  For the latter, typical approaches include using integration-based surrogate model <cit.>, 
  self-integration method based on diverse regularizations <cit.>, and data augmentation <cit.>. 
  <cit.> mentioned that alternating different training paradigms (e.g., unsupervised and self-supervised models) as surrogate models 
  when generating poisoning attack samples can improve the transferability.
  These methods aim to develop more generalized and robust surrogate models, 
  which are then optimized to obtain more effective and transferable attack samples. 
  










§ A POISONING ATTACK FRAMEWORK 
 FOR ONLINE DEEP RECEIVERS




As mentioned earlier, in the scenarios discussed in this paper, legitimate deep receivers adapt to fast-varying wireless channels by utilizing pilot and updating model parameters using online learning methods.
However, this online update mechanism, aimed at adapting to local channel variations, faces the threat of sample input poisoning. 

In the attack framework of the malicious user, the legitimate online deep receiver becomes the target model,
which is updated online to adapt to local variations in the channel for better local performance.
However, this process is inherently not robust and the local adaptation can result in overfitting <cit.>.
From this point onwards, the attack target of this paper is similar to <cit.>, 
which causes catastrophic forgetting of the target by constructing poisoned samples.
According to the analysis of attack transferability in Section III-D, 
this overfitting is the source of the target model's intrinsic adversarial vulnerability.
This implies that a malicious user can effectively attack the target model by optimizing a surrogate model and generating corresponding adversarial perturbations.

Therefore, this section proposes a poisoning attack framework targeting online deep receivers. 
The core idea is to poison the model training and updating phases, resulting in a poisoned model after a certain period, leading to performance degradation.
Specifically, based on the behavioral patterns of malicious users described in Section II-C, 
the poisoning attack framework and the method for generating the poisoning attack samples can be refined into  below three steps, as illustrated in Fig. 7.


  
  * The malicious user collects communication data (e.g., pilot) from the wireless channel and produces a joint learning dataset. 
  This dataset is used to train a surrogate model for attacking the target (the legitimate deep receiver).
  
  * The malicious user optimization solution (<ref>eq:4) generates an adversarial perturbation based on the surrogate model.
  
  * The malicious user injects the adversarial perturbation onto the channel, causing the deep receiver to receive the poisoned pilot. 
  Consequently, the deep receiver undergoes online learning with the perturbed pilot, resulting in the model being poisoned and deactivated.


The specific details of Steps 1 and 2 are detailed in the following Sections IV-A to IV-C.



 §.§ Surrogate Model Selection

As discussed earlier in Section III-D regarding attack transferability, 
black-box attacks require the malicious user to consider the degree of gradient alignment between the surrogate model and the target model to ensure the attack's generalization. 
To achieve this, it is important to avoid using surrogate models that are overly specialized for specific problems. 
This strategy ensures consistent compatibility with various types of deep receivers, 
thereby enhancing the attack's overall effectiveness. 
Consequently, this paper adopts a generic DNN architecture, e.g., feedforward neural networks, as the surrogate model for the attack, as illustrated in Step 1 of Fig. 6.



 §.§ Joint Learning for Training of Surrogate Models

From the perspective of a malicious user, 
it is essential to select a suitable surrogate model architecture similar to the target model 
and to effectively train and optimize the surrogate model.
In the proposed attack framework, joint learning is used to train the surrogate model. 
This approach utilizes data collected under various channel conditions to train the DNN, 
enabling it to adapt to dynamic channels <cit.>.

It is important to note that, 
unlike legitimate communicating parties that have to use online learning methods to adapt to time-varying wireless channels, 
the malicious user has preparation time to eavesdrop communications and collect large samples to train a robust model. 
Furthermore, the use of joint learning, instead of channel state information as input or online learning <cit.>, 
addresses the issue of attack generality at the data level, avoiding over-specialized surrogate models in black-box attack transfers, 
as previously discussed in Section IV-A.
Finally, in terms of training effectiveness, joint learning meets the data volume requirements of deep learning, 
making the surrogate model more robust compared to the target model using online learning. 
This results in attack patterns with more stable and effective attack results.
Conversely, the robust learning process of the target model mitigates the impact of poisoning. 
To demonstrate this, we will adjust the pilot size in Section V-E.

Specifically, as illustrated in Step 2 of Fig. 6, the malicious user deploys joint learning to train a DNN (i.e., the surrogate model) 
utilizing a substantial quantity of communication data (e.g., pilot) amassed from authorised transceivers. 
The objective is for this DNN to learn a mapping that is applicable to the majority of channel states, 
reflecting the input-to-output mapping relationship of the authorised deep receivers (i.e., the target model). 
The data that is jointly learned comprises two categories: 
Communication data under disparate channel distribution conditions and communication data under varying signal-to-noise ratio (SNR) conditions within the same channel.
Finally, to produce effective adversarial poisoning samples, 
malicious user need to consider suitable attack generation methods based on the surrogate model, as detailed in Section IV-C.




 §.§ Adversarial Poisoning Attack Samples Generation




Once the optimized surrogate model has been obtained, the malicious user generates the necessary poisoning attack samples 
in order to execute the attack. 
As illustrated in Step 2 of Fig. 6, we employ the projected gradient descent (PGD) algorithm <cit.>, 
to generate the adversarial poisoning attack perturbations discussed in Section III-C. 
The whole algorithmic flow of generating perturbations is shown in Algorithm 1,
and summarised as below.


  
  * Obtain the pilot dataset 𝒯_pilot≡{𝐲, 𝐬}. 
  Then, within an interval [-ϵ, +ϵ] defined by the upper bound of the p-norm constraints, 
  use uniformly distributed sampling to generate a randomly initialized perturbation vector δ.

  
  * Superimpose the δ  on the pilot data. 
  The perturbed data should then be fed into the surrogate model f_φ to calculate the attack loss.
  
  
  * δ updates in the gradient direction of loss with step size γ,
  and 𝐲 + γδ remains within the specified upper bound I_max, and lower bound I_min.
  
  
  * The Step 2 and Step 3 iteratively repeat the Q rounds to obtain poisoned pilot data with the optimal attack perturbation.




Once the iteration is complete, the optimal perturbation will be applied to the current block's pilot to generate the poisoned pilot dataset, denoted as 𝒫(𝒯). 
This dataset will then be received by the deep receiver and poisoned during the training and updating of the model, as illustrated in Step 3 of Fig. 6. 






§ NUMERICAL EVALUATIONS

In this section, we conduct a numerical evaluation of the proposed poisoning attack method aimed at disrupting the online adaptation process of the deep receiver.
We first provide provides an overview of the parameter settings employed in 
the simulation experiments in Sections V-A to V-D. 
These parameters include the channel models, the deep receivers, the online training methods and the poisoning attack method, which are all evaluated in this paper. 
Subsequently, the simulation results for our evaluated deep receivers are presented under the following conditions: 
A linear time-varying synthetic channel, a nonlinear time-varying synthetic channel, a linear static synthetic channel, and the time-varying COST 2100 channel (Section V-E). 
Finally, the experimental results of the proposed attack method under the four channel settings are summarised and discussed in Section V-F.



 §.§ Evaluated Channel Models



The deep receiver operates on a discrete memoryless MIMO channel.
The number of transmitting and receiving antennas is set to N_t x=N_r x=4. 
The experimental evaluation channel model comprises synthetic channels <cit.> 
and COST 2100 channels <cit.>. 
Fig. 7 illustrates the four channel tapping coefficients for a randomly selected user in a multiuser system over 100 blocks of data transmission.




In the context of linear channels, the input-output relationship is expressed by the (<ref>) given in Section II-A. 
In the context of a nonlinear channel model <cit.>, the input-output relationship is represented by 

    𝐲=tanh (k(𝐇 𝐱+𝐰)),
 
where the tanh (·) function is used to simulate the non-linear variations in the transceiver process 
due to non-ideal hardware, with the parameter k=0.5.



 §.§ Evaluated Deep Receivers



















We consider three deep receiver architectures in the evaluated network architecture: Namely, 
the model-based deep receiver DeepSIC <cit.>, the black-box DNN detector <cit.>,<cit.>, 
and the ResNet detector designed based on DeepRX <cit.>.The relevant details are as follows:



  
  ∙ DeepSIC: 
  SIC estimates and cancels the interfering signals at each iteration to revise previous estimates, 
  while DeepSIC unfolds the SIC iterative process and replaces it with a sub-neural network to improve the performance of each iteration. 
  The function of each sub-neural network is to enhance the reliability of the present estimation 
  by utilizing the received symbols and the preceding iteration's output confidence. 
  This design enables DeepSIC to attain high reliability even with a limited number of training data<cit.>. 
  Furthermore, DeepSIC presented in this paper incorporates 3 iterations, resulting in a total of 3 × N_t x sub-networks. 
  In this configuration, each sub-network is a two-layer fully connected layer network. 
  The first layer has a dimension of (N_r x + N_t x - 1) × 64, 
  and the second layer has a dimension of 64 × |S|, where |S| is the size of the set of symbols to be transmitted. 
  For example, |S| = 4 when using QPSK transmission. 
  The activation function employed in the initial layer of each subnetwork is ReLU, 
  while the second layer utilizes softmax classification.
  
  ∙ Black-box DNN Detector: 
  The black-box DNN architecture comprises four fully-connected layers and a softmax classification header. 
  The input and output dimensions are N_r x× 60,60 × 60,60 × 60 and 60 ×|S|^N_tx, 
  respectively, for each layer of the network.
  
  ∙ ResNet Detector: 
  The ResNet detector employed in this paper consists of 10 layers of residual blocks, 
  with each block comprising two convolutional layers that use 3×3 kernels, 
  one-pixel padding on both sides, and no bias terms, with a ReLU activation function in between. Each convolutional layer is followed by 2D batch normalization.




 §.§ Online Training Methods






The objective of this paper is to present an attack strategy, which attacks online adaptation of the deep receivers. 
Consequently, the focus is on the deep receiver's online training, with the parameter configurations illustrated in Table I.
The parameter settings for online training come from <cit.>.
Upon receipt of a data block, the deep receiver is only able to utilize a subset of the data block for training, 
like pilot symbols, specifically L_pilot = 200.
Then the deep reciver predicts the subsequent L_info = 50000 symbols. 
In the experiment, a total of 100 data blocks were transmitted, 
with the transmitted data being QPSK modulated, i.e., the user-transmitted symbols 𝐬 were mapped to the set 
C={( ±1/√(2), ±1/√(2))}^4. 
Furthermore, the deep receivers are trained using the Adam optimizer<cit.>.
The training epochs are 300. 
The initial learning rate η is set to 5 × 10^-3  for ResNet detector, black-box DNN detector and DeepSIC. 
Additionally, online training is performed for different architectural receivers, 
which were implemented in the following two cases:

  
  ∙ Online learning: 
  Based on the adaptation to the pilot data from the previous data block, the deep receiver trains 
  and updates the current model using the limited pilot symbols received in the current data block.
  
  ∙ Online meta-learning: 
  According to <cit.>, <cit.>, the meta-learning framework is employed to facilitate adaptation to the channel. 
  In particular, the pilot data from 5 data blocks is accumulated each time, after which meta-learning is 
  performed on the accumulated data in order to obtain the meta-learning weights of the deep receiver. 
  Subsequently, the aforementioned meta-learning weights are employed in an online learning process involving the pilot data of the current block.


Unless otherwise stated,
the deep receivers are trained using online learning, 
including black-box DNN detector, ResNet detector, and DeepSIC. 
Only online meta-learning DeepSIC receiver, 
i.e., Meta-DeepSIC, is trained using online meta-learning methods.





 §.§ Attacker's Configuration





The attack samples are designed based on the gradient of the surrogate model, 
and joint learning is performed on the surrogate model based on the collected pilot dataset. 
In the joint learning configuration, the black-box DNN detector, presented in Section V-B, is employed as the surrogate model. 
This model has three times the number of parameters compared to a single sub-network of DeepSIC. 
The parameter configurations for joint learning are referenced in <cit.>. 
In particular, a linear time-varying synthetic channel model is employed to generate the channel data for joint learning.
The training data is generated under the condition of an SNR of 2 dB to 16 dB with an interval of 2 dB, 
and the SNR used for generation is represented as SNR_sur.
In this manner, L_sur=5000 training pilot symbols are generated at each SNR value, and the surrogate model is trained in accordance with this procedure. 

Moreover, the poisoning samples are optimized iteratively using the PGD algorithm. 
In this context, the adversarial poisoning attack samples are created with reference to the settings in <cit.>, 
and the adversarial poisoning samples at this specific parameter configuration are the most toxic. 
The iteration step size is set to γ = 0.01, 
the iterations of PGD is Q = 250, and the upper bound ϵ of the perturbation under the constrained norm p = 2 is set to 0.3. 
The maximum and minimum values of the received symbol magnitude are denoted as I_max and I_min, respectively, 
and I_max =  max {𝐲} = -I_min.
The attack samples are presented in Fig. 8 and Fig. 9, respectively. 
The two subfigures in Fig. 8 represent the real and imaginary parts of the original and poisoned received symbols, respectively. 
Fig. 9 presents the original and poisoned received symbols in a constellation diagram. 












 §.§ Numerical Results under Four Channel Models

This section presents the results of an experimental investigation into the efficacy of the proposed poisoning attack method in the context of various channel models. 
Specifically, the effectiveness of the method is evaluated under the following scenarios: 
Linear time-varying synthetic channels, nonlinear time-varying synthetic channels, linear static synthetic channels, and time-varying COST 2100 channels. 
For black-box DNN detector, a white-box poisoning attack is launched against this architecture receiver since its architecture is the same as the surrogate model. 
For the ResNet detector, we implement transfer poisoning attacks in black box scenarios. 
As the DeepSIC comprises multiple sub-networks, it is not feasible to utilize its gradient information directly in the design of poisoning attack samples. 
It is therefore anticipated that the attack perturbations designed on the surrogate model will transfer the poisoning effect to DeepSIC. 
Consequently, a transfer-based poisoning attack is executed on DeepSIC.




  §.§.§ Linear Time-varying Synthesis Channel Results






Firstly, Fig. 10 evaluates the effectiveness of the proposed poisoning attack method under a linear time-varying synthetic channel.
 
Fig. 10(a) illustrates the results of 100 data transmission blocks, 
with the cumulative SER calculated on a block-wise basis over five repetitions at an SNR of 14 dB. 
It can be observed that the Meta-DeepSIC, which combines the model-based method and the meta-learning, 
is more effective in capturing the time-varying characteristics of the wireless channel in the absence of a poisoning attack. 
Consequently, it achieves a superior SER performance in comparison to the black-box DNN detector, ResNet detector and the DeepSIC. 
However, the Meta-DeepSIC is also more susceptible to poisoning attacks than the DeepSIC.
This finding aligns with the conclusions presented in <cit.>. 
Furthermore, the proposed black box poisoning attack significantly impacts the ResNet detector. 
Since this method targets the black-box DNN detector through a white-box attack approach, the black-box DNN detector performs the worst after poisoning.


Fig. 10(b) illustrates the results of the 100-block data transmission experiment, 
with the SER averaged across the same five repetitions under varying SNR conditions. 
It can be observed that the proposed poisoning attack is effective for ResNet detector, black-box DNN detector and DeepSIC at different SNRs. 
In particular, the SER performance of the poisoned DeepSIC exhibits a degradation of approximately 0.67 dB compared to that of the normal DeepSIC at an SNR of 10 dB.
Similarly, the SER performance of the poisoned Meta-DeepSIC is seen to deteriorate by approximately 0.91 dB in comparison to that of the normal Meta-DeepSIC. 
Additionally, it is observed that the SER of the black-box DNN detector exhibits an increase of approximately 0.5 dB, 
and the SER of the ResNet detector exhibits an increase of approximately 0.68 dB.
As the SNR increases, the impact of the attack becomes increasingly pronounced. 
The deterioration in the SER performance of the poisoned DeepSIC and Meta-DeepSIC reaches 1.37 dB and 2.0 dB, respectively, at SNR = 15 dB.




  §.§.§ Non-linear Time-varying Synthetic Channels Results


Secondly, Fig. 11 evaluates the effectiveness of the proposed poisoning attack methodology under a nonlinear time-varying synthetic channel.
The experimental configuration are consistent with those depicted in Fig. 10. 
It can be observed that the proposed poisoning attack method results in a more pronounced poisoning effect in the nonlinear time-varying synthetic channel 
environment than in the linear time-varying synthetic channel. 
In particular, the proposed poisoning attack method has a detrimental impact on the SER performance of the ResNet detector, the black-box DNN detector, 
DeepSIC, and Meta-DeepSIC, with an SER performance deterioration of 0.93 dB, 0.53 dB, 1.35 dB, and 1.42 dB, respectively, at SNR = 10 dB. 
Similarly, as the SNR increases, the attack effect becomes more pronounced, 
with the SER performance deterioration of the four receiver architectures reaching 1.13 dB, 0.71 dB, 2.74 dB, and 3.09 dB, respectively, at SNR = 15 dB.





  §.§.§ Linear Static Synthetic Channels Results


Fig. 12 presents an evaluation of the efficacy of 
the proposed poisoning attack method in the context of a linear static synthetic channel.
Similarly, the experimental scenario and parameter configuration are consistent with those depicted in Fig. 10. 
It can be observed that the performance of DeepSIC and Meta-DeepSIC is essentially indistinguishable in this case. 
Furthermore, the lack of diverse data renders the black-box DNN detector unsuitable for adapting to the channel environment. 
Meanwhile, compared to the black box DNN detector, 
the ResNet detector that performed better in the first two channel environments performed the worst in the static channel model.
The poisoning effect of the ResNet detector has lost its reference significance.
In particular, in this scenario with an SNR of 10 dB, the proposed poisoning attack method results in an SER performance 
degradation of 0.08 dB, 0.71 dB, and 0.72 dB for the black-box architecture receiver, the DeepSIC receiver, and the Meta-DeepSIC receiver, respectively. 
As with the preceding scenario, the impact of the attack is more pronounced as the SNR increases. 
At an SNR of 15 dB, the SER performance degradation for the three receiver architectures is 0.06 dB, 1.05 dB, and 1.07 dB, respectively.





  §.§.§ Time-varying COST 2100 Channels Results


The efficacy of the proposed poisoning attack method is subsequently assessed under the time-varying COST 2100 channel, 
with the experimental results illustrated in Fig. 13. The experimental configuration is identical to that of the linear time-varying synthetic channel. 
Concurrently, the surrogate model is trained on the joint channel data based on the time-varying linear channel model. 
As illustrated in the Fig. 13, 
the proposed poisoning attack method is not only effective for receivers with different architectural depths and different online training scenario settings, 
but also adaptable to different channel environments. 
In this channel environment and with an SNR of 10 dB, the poisoning attack results in a deterioration of SER performance for the ResNet detector, 
the black-box DNN detector, DeepSIC, and Meta-DeepSIC of up to 0.12 dB, 0.25 dB, 0.61 dB, and 0.78 dB, respectively. 
At an SNR of 15 dB, the deterioration of SER performance for the four receiver architectures is up to 0.04 dB, 0.23 dB, 2.11 dB, and 1.36 dB, respectively.





  §.§.§ The Impact of Pilot Size on Poisoning




The online learning of deep receivers is influenced by the training data, i.e., the pilot size L_pilot. 
Larger pilot sizes generally enhance performance, leading to more stable learning and reduced overfitting.
To explore the impact of overfitting on the poisoning effect, 
Fig. 14 examines the influence of pilot size in a linear time-varying synthetic channel at an SNR of 14 dB.
The results show that as L_pilot increases, 
the effectiveness of poisoning attacks diminishes. 
Specifically, when comparing L_pilot=200 with L_pilot=1000, 
the poisoning effects on the ResNet detector, black-box DNN detector, DeepSIC, and Meta-DeepSIC are reduced by 0.34 dB, 0.74 dB, 0.14 dB, and 0.34 dB, respectively.
However, Larger pilot sizes cannot alleviate the poisoning effects on meta-learning methods, and the poisoned Meta-DeepSIC still performs worse than DeepSIC.




 §.§ Discussion of Results

The experimental results demonstrate that the poisoning attack method devised in this paper is effective in four distinct channel environments. 
Nevertheless, the precise impact of these attacks varies depending on the specific channel environment. 
In light of the aforementioned experimental results, the following inferences can be drawn.

As illustrated in Fig.11, the poisoning effect observed in the nonlinear time-varying synthetic channel is markedly higher than in the other three cases. 
The performance of the deep receivers subjected to a poisoning attack is severely degraded and approaches failure in this channel environment. 
This suggests that the poisoning attack is capable of impeding the deep receiver's ability to adapt to the rapid changes in the channel's effects 
and to learn the nonlinear effects.

Secondly, the experimental results for the linear time-varying synthetic channel and the COST 2100 channel corroborate the preceding conclusion from disparate vantages.
In comparison to the synthetic channel, the tap coefficients of the COST 2100 channel demonstrate greater long-term variance, 
while exhibiting a relatively flat profile in the short term (for instance, between two blocks).
As shown in Fig. 13(a), the impact of poisoning attacks consistently reduces receiver performance over an extended period in the COST 2100 channel, 
indicating a sustained but limited exacerbation. 
In contrast, in the linear time-varying synthetic channel undergoing significant changes over time, 
the poisoning attack has a more pronounced effect on the receiver's performance. 
This indicates that the attack has a impact on the deep receiver's capacity to track long-term channel alterations and 
a more pronounced disruptive effect on short-term rapid adaptation.
Notably, as shown in Fig. 14, a larger pilot size can mitigate the adverse effects of poisoning attacks, but this means more spectrum resources are consumed.




Finally, from the perspective of the deep receiver, Meta-DeepSIC, which incorporates a meta-learning approach,
demonstrates optimal performance when utilizing limited pilot data, particularly in scenarios where channel variations occur rapidly. 
Furthermore, this learning capability demonstrates efficacy in nonlinear channel environments, 
while increased sensitivity to poisoned samples results in a more pronounced deterioration 
in performance than that observed for DeepSIC in fast-varying channels.
In scenarios characterised by slow-varying or static channels,  
the performance of Meta-DeepSIC and DeepSIC, with or without poisoning attacks, is more consistent than in fast-varying channel conditions. 
This is corroborated by the data presented in Fig. 12 and Fig. 13.



In conclusion, the attack method devised in this paper primarily impedes the receiver's ability to learn rapid channel changes and non-linear effects 
in the short term, resulting in a decline in performance. The poisoning effect is particularly pronounced in the context of Meta-DeepSIC 
when combined with meta-learning techniques. This conclusion highlights the security risks associated with the design of wireless receivers using 
online and online meta-learning methods, particularly in environments characterised by rapid channel changes and non-linear effects, where the system is particularly susceptible 
to poisoning attacks.



§ CONCLUSION

This paper proposes a transfer-based adversarial poisoning attack method for online deep receivers without the knowledge of the target. 
The fundamental concept is to corrupt the online training and updating phases of deep receivers 
in such a way that the model becomes compromised after a designated period of training, 
resulting in a decline in performance. 
The poisoning attack framework and the generation of poisoning attack samples comprise two steps. 
Initially, the malicious user acquires the surrogate model through the joint learning method. 
Subsequently, the poisoning attack perturbations are generated based on the surrogate model to poisoning the pilot. 
Simulation experiments on the proposed poisoning attack method under varying channel models demonstrate that 
it disrupts the adaptation of dynamic channls and learning of nonlinear effects.
Meanwhile, the proposed attack can be effective against both model-based deep learning architectures and typical DNN-based receiver architectures.

Meta-DeepSIC demonstrates optimal performance in fast-varying channels. 
However, it is particularly susceptible to poisoning attack samples, resulting in a notable decline in performance. 
It is therefore recommended that future research should concentrate on the development of efficient, robust and secure deep receiver architectures 
that are capable of defending against potential attacks, 
such as poisoning purification before learning or reducing the impact after poisoning<cit.>,
with a view to furthering the application of deep learning in wireless transceiver design and deep receiver deployment.














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