Intelligent Reflecting Surface Aided Secure Communication with Federated Learning

Applying federated learning into the covert communication can not only ensure the communication reliability, but also reduce the probability of enemy detection. The use of airspace resources is an e ff ective way to achieve covert communication. However, most of the existing works on the airspace covert communication represented by MIMO need to adapt to the channel state and cannot improve the channel, resulting in the performance bottleneck of covert communication. The intelligent reflective surface (IRS) provides a new perspective for the covert communication by flexibly adjusting the reflection phase shift of the incident signal and intelligently configuring the wireless channel. However, the potential of IRS in the covert communication is far from being fully exploited. To solve this issue, this paper firstly performs a comprehensive literature review on the secure communication with the aid of federated learning, and then gives some challenges on the secure communication in poor channel state. In further, this paper provides some solutions to the challenges on the secure communication, where some results are provided to show the advantages. The research results have important theoretical and practical significance for forming a new research paradigm of airspace intelligent and controllable covert communication and promoting the application and popularization of covert communication in various fields of security.


Introduction
With the rapid development and wide popularity of 5G, there is an unprecedented concern about the security of wireless communications [1]. The importance of information security cannot be overstated, and in some special wireless communication scenarios with highsecurity levels, the exposure of the communication process poses incalculable risks and losses. Moreover, preventing the wireless signal from being illegally detected is often more critical than mere information security [2].
The recent emergence of covert communications, which aims to hide the act of communication * Corresponding author. Email: 19bwlu@stu.edu.cn itself from political parties, i.e. to achieve a low detection probability of communication, provides a new way of thinking to solve the problem of privacy and security of wireless communications [3]. Covert communications are in common demand in military and civilian applications, for example, covert communications in vehicles to evade location trails and conceal military activities to counter enemy reconnaissance [4]. Covert communication is even more useful in the field of defence and national security. With electromagnetic space becoming the main battlefield of international information confrontation, intelligence departments of various countries are competing to establish electromagnetic reconnaissance and monitoring systems for the right to control electromagnetism [5]. Covert communication can help secretly transmit wireless signals to avoid close monitoring by other countries and provide an important guarantee for seizing the high ground of information confrontation and electromagnetic power [6]. It can be seen that covert communication has a very wide range of applications, from small civilian privacy to national security. Therefore, the study of covert communication technology has important and far-reaching strategic significance. Fig. 1 illustrates a typical model of a wireless covert communication system, where Alice, the sender, wishes to transmit a message covertly to Bob, the target user, and Willie, the listener, listens to the wireless signal in real-time and attempts to detect the communication from Alice to Bob [7]. However, stealth is often gained at the expense of spectral efficiency. For example, Alice needs to minimise the transmit power to achieve high stealth, but this will inevitably reduce Bob's signal reception quality, leading to a reduction in the system's frequency harmonic efficiency [8][9][10]. How to achieve a good balance between high spectral efficiency and low detection probability is the core problem facing covert communication.
With the increasing scarcity of frequency and harmonic resources, the exploitation of airspace resources has become an effective way to achieve and enhance covert communications [11,12]. Singleantenna transceivers have extremely limited airspace freedom, which makes it difficult to reconcile the conflict between the system's frequency-harmonic efficiency and its stealthiness [13,14]. Another implementation of MIMO, distributed node collaboration, can also help improve covert communications by using collaborating nodes to relay signals or to take turns for the target signal transmission. Traditionally, the wireless channel is considered to be uncontrollable. Significant improvement in covert communication often comes at the cost of significant increase in the system cost and implementation complexity, such as the use of large-scale MIMO to enhance covert communication, which requires the configuration of a large number of RF links. This can lead to a dramatic increase in the system power consumption, hardware overhead, and lead to a dramatic increase in system power, hardware overhead and redundancy. It is imperative to find new cost-effective technologies to achieve a breakthrough in covert communication performance.
Fortunately, intelligent reflecting surface (IRS) provides a new way of thinking for covert communication. The intelligent and controllable nature of the IRS airspace has greatly enriched the exploitation of airspace resources and is naturally beneficial for covert communications [15,16]. Therefore, there is a great need to introduce IRS into the covert communication system to achieve a significant breakthrough in covert communication performance. It is worth noting that due to the passive reflection characteristics, IRS needs to be combined with traditional airspace technologies for covert communication, of which MIMO technology should be preferred. This is because MIMO offers more freedom in the airspace than single-antenna transceivers, providing significant improvements in spectral efficiency, energy efficiency and covert performance, while at the same time MIMO does not introduce additional system overhead due to complex operations such as synchronisation and information sharing between nodes as in the case of distributed node collaboration. Fig. 2 depicts the system model of an IRSassisted MIMO stealth communication, where an IRS with a large number of passive reflectors under system control flexibly constructs a reflection path from Alice to Bob and Willie by adjusting the reflection phase shift of the incident signal from Alice and combining the MIMO direct path to assist Alice in stealth communication.

Advantages and challenges of IRS-based MIMO covert communication system
Theoretically, the deep integration of IRS and MIMO enables fuller exploitation and utilisation of airspace resources, where the advantages are reflected in at least the following two aspects.
(1) Refinement and efficiency of airspace resource utilisation: IRS's airspace reconfiguration capability and MIMO's airspace high-resolution capability enable 2 EAI Endorsed Transactions on Mobile Communications and Applications 01 2023 -06 2023 | Volume 7 | Issue 4 | e2 IRS and MIMO to complement each other's strengths, allowing for fine-grained. In particular, the IRS can be controlled by controlling each reflecting element independently to change the phase of the incident signal and collaboratively generate a fine reflected beam. At the same time, the IRS reflected signal and the MIMO direct signal can be superimposed constructively to achieve signal enhancement for the target user and zero trapping for the listener respectively, thus significantly improving the system spectral efficiency and effectively reducing the probability of detection.
(2) Diversity and flexibility of covert communication strategies: IRS's low profile, low power consumption, low cost and other excellent characteristics determine its high flexibility and superior compatibility with existing covert communication technologies and systems. The IRS and MIMO cascade form a virtual massive MIMO, which can be used to take advantage of the ultra-high airspace splitting capabilities of massive MIMO to achieve fixed-point energy focusing, thus significantly enhancing covert communication performance. IRS and MIMO can also work together to create uncertainty in the airspace characteristics, which can interfere with the listening party's detection judgement. The time-frequency resources can be combined to further enhance covert communications. In addition, the IRS can also be used on a large scale to give full play to the group intelligence of the IRS to assist in achieving low detection probability communications in complex scenarios such as ultra-long-range high and obstacledense environments.
At the same time, IRS-based MIMO covert communication faces more than one challenge, including the following.
(1) The challenges posed by the uncertainty of the wireless channel for robust airspace exploitation. The time-varying nature of the wireless channel and the channel measurement inaccuracy inevitably result in uncertainty in the channel state information (CSI). This CSI uncertainty is particularly significant for joint IRS and MIMO systems. On one hand, the highly directional beams formed by IRS and MIMO are nonband dependent on CSI, and the MIMO transmitted signal and IRS reflection phase shift are designed to mismatch with CSI. On the other hand, the IRS does not have the signal processing capability, so the negative impact of the CSI uncertainty is transmitted "unreservedly" step by step, resulting in a serious deterioration in the system performance. It is therefore critical to design robust covert communication methods that minimise the negative effect of CSI uncertainty when exploiting the airspace resources. Considering that CSI uncertainty can also have an impact on the listening party, one can also consider exploiting or creating uncertainty to turn it into a favourable resource for covert communication.
(2) The challenge posed by the strong coupling of high-dimensional variables for efficient parameter design. To guarantee a certain level of concealment while maximising the information transmission rate of the system, i.e. the concealment rate, it is often necessary to jointly optimise two high-dimensional matrix variables, namely the MIMO signal covariance matrix and the IRS phase shift matrix. However, due to the auxiliary mechanism of IRS passive reflections, the two optimisation variables form a complex coupling of additivity and multiplicity in the objective function of the steganographic rate.
(3) The challenge of intelligent covert communication posed by active listening means. Its passive reflection feature reduces the cost and complexity of the system while inadvertently facilitating the listening party, who has the opportunity to actively use the reflection function of the IRS to enhance its listening effect. For example, the listener can actively transmit an interfering signal, which will inevitably be reflected by the IRS and interfere with the target user's signal demodulation, when the sender needs to increase the transmission power to ensure the reliability of the communication, thus increasing the risk of exposure and facilitating the listener's detection. The listener can also configure a dedicated IRS to assist in the listening process by designing the IRS reflections to be phaseshifted, thus improving detection performance. To effectively counteract the diverse active listening tactics of the listener, more intelligent covert communication schemes need to be tailored, taking into account the game of policy and parameter design between the transmitter and listener.
As we can see above, the traditional channel adaptation-based airspace covert communication technology has reached a bottleneck, and IRS has achieved an important leap from airspace "adaptation" to "reconfiguration" in the form of low-cost wireless communication technology, providing a breakthrough into the performance bottleneck of covert communication. The organic combination of IRS and MIMO presents new opportunities and challenges for covert communications, and its potential for covert communications has yet to be exploited. The potential for covert communication is still unexplored and unexploited. Therefore, it is necessary to integrate the advantages of IRS and MIMO to enable covert communications, actively explore more efficient and intelligent means of airspace development and advantages to significantly improve the performance of covert communications, and vigorously promote the research and development of covert communications.
Based on the above understanding, this paper intends to fully exploit the combined high airspace splitting and reconfiguration capabilities of IRS and MIMO, and focus on the key technology of IRS-enabled MIMO 3 EAI Endorsed Transactions on Mobile Communications and Applications 01 2023 -06 2023 | Volume 7 | Issue 4 | e2 covert communication. The research work has important scientific and theoretical significance and practical application value. In terms of scientific theories, the research results fully reveal the mechanism of IRS and MIMO combined for covert communication, explore a novel and effective theoretical method for covert communication. The research results are expected to break the limitations of the traditional airspace-adapted covert communication framework and lead to the formation of a new paradigm of airspace-oriented intelligent and controllable covert communication research. In terms of practical applications, the research results will have a positive impact and promote the popularization of covert communication applications in civil, military and national defence security areas by systematically and thoroughly examining covert communication scenarios and problems of different levels of complexity and formulating practical covert communication technology.

System Model
Consider the IRS-based MIMO covert communication system shown in Fig.2,   Willie sets the detection threshold to λ. IfP W ≤ λ, we can consider H 0 holds, and vice versa for H 1 . Consider H 0 and H 1 with equal prior probabilities, i.e., P {H 0 } = P {H 1 } = 0.5, and the detection error probability can be defined as ξ ≜ P FA + P MD where P FA ≜ P P W > λ|H 0 = P σ 2 w > λ and P MD ≜ P P W ≤ λ|H 1 = P P w + σ 2 w ≤ λ represent the probability of a false alarm and the probability of missed detection, respectively. Considering the uncertainty of the noise at Willie due to the change in the electromagnetic environment, the probability of false alarm and the probability of missed detection are based on bounded uncertainty. Based on the bounded uncertainty model, the probability density function of the noise power σ 2 w is expressed as,

Concealed Detection Issues
where ρ ≥ 1 is the noise uncertainty coefficient. It is important to note that this noise uncertainty will have an important impact on the analysis of detection performance and the subsequent optimisation of parameters.
In this study, the concealment rate is used as the core metric. According to (1), the concealment rate Ω can be expressed as, This study proposes to jointly design the MIMO signal covariance matrix R and the IRS phase shift matrix Q. The basic idea is to tailor the design to different levels of CSI knowledge and to make the best use of the already available information.

Global CSI known
Consider the problem of maximizing the concealed rate when Alice's global CSI is known, which is described as, Constraint (6a) indicates that the Alice transmit power cannot exceed P , (6b) represents the concealed constraint that the detection error probability ξ cannot fall below the threshold 1 − ϵ, and (6c) represents the unit modulus constraint on the IRS reflection phase shift coefficient.
To solve the above optimization problem, the detection error probability ξ needs to be expressed analytically. Combined with the noise uncertainty model of equation (4), the detection error probability ξ(λ) under the given detection threshold λ can be calculated as, Consider the robust design and assume that Willie can always use the optimal detection threshold λ * to obtain the minimum detection error probability ξ * = ξ(λ). We can obtain the closed-form expression of the optimal detection threshold λ * and the minimum detection error probability ξ * by taking the derivative of equation (7) to λ. We can observe that ξ * is a monotone decreasing function of Willie's signal receiving power P W . Therefore, the hidden constraint (6b) can be transformed into the following constraint on P W , where κ is equal to (1 − ϵ), representing the maximum allowable signal power leaked to Willie. As the optimization variables R and Q present a complex coupling relationship in the objective function (6) and hidden constraint (6b), we can adopt the idea of alternate optimization to design R and Q. First, fix Q, and we can find that the original problem degenerates into a convex problem about R, and the closed-form solution of the optimal R can be derived. Then, given R, the optimization problem about Q is a typical nonconvex problem due to the existence of the constraint (6c) on the unit modulus of the elements in Q. In this case, optimization methods such as maximizing the lower bound of the objective function or using continuous convex approximation can be used to solve the subproblem. The optimal R * and Q * can be obtained through the iterative solution of the above two subproblems. Fig. 3-5 show the results of secrecy outage probability with federate learning, where the transmit power P varies from 0dB to 20dB. In particular, Fig. 3 is associated with one IRS unit, where the detailed  numerical data in given in Table 1; Fig. 4 is associated with two IRS units, where the detailed numerical data in given in Table 2; Fig. 5 is associated with three IRS units, where the detailed numerical data in given in Table 3. From the three figures and tables, one can see that proposed scheme is better than the zero-forcing (ZF) and maximal ratio combing (MRC) schemes, as it can efficiently exploit the spatio-temporal resources provided by multiple antennas and IRS units, through the federated learning.

Conclusions
To     review on the secure communication with the aid of federated learning, and then listed some key challenges on the secure communication in poor channel state. In further, this paper provided some solutions to the challenges on the secure communication, where some results were provided to show the advantages coming from the IRS technology. The research results in this paper can provide some important theoretical and practical guidance for the system design and optimization on the future network and security.