In recent years, Internet of Things (IoT) technology has emerged and gradually sprung up. As the needs of large-scale IoT applications cannot be satisfied by the fifth generation (5G) network, wireless communication network needs to be developed into the sixth generation (6G) network. However, with the increasingly prominent security problems of wireless communication networks such as 6G, covert communication has been recognized as one of the most promising solutions. Covert communication can realize the transmission of hidden information between both sides of communication to a certain extent, which makes the transmission content and transmission behavior challenging to be detected by noncooperative eavesdroppers. In addition, the integrated high altitude platform station (HAPS) terrestrial network is considered a promising development direction because of its flexibility and scalability. Based on the above facts, this article investigates the covert communication in an integrated HAPS terrestrial network, where a constant power auxiliary node is utilized to send artificial noise (AN) to realize the covert communication. Specifically, the covert constraint relationship between the transmitting and auxiliary nodes is derived. Moreover, the closed-form expressions of outage probability (OP) and effective covert communication rate are obtained. Finally, numerical results are provided to verify our analysis and reveal the impacts of critical parameters on the system performance.

The Internet of Things (IoT) is an information carrier based on the Internet and traditional telecommunication networks, which allows all ordinary physical objects that can be independently addressed to form an interconnected network. Nowadays, because the demand for large-scale IoT can not be satisfied by the fifth generation (5G) terrestrial mobile communication, the sixth generation (6G) terrestrial mobile communication development is becoming the general trend. Moreover, over recent years, high altitude platform station (HAPS) has been considered a critical part of the next-generation wireless communication networks for its high altitude, large capacity, flexible communication services, lower communication delay, and smaller terrestrial receiving antenna [

However, the openness of wireless communication and the broad coverage of the HAPS beam will lead to a series of security problems, such as channel monitoring, information eavesdropping, and malicious interruption. Generally, many traditional security policies focus on preventing the extraction of information, such as coding encryption or physical layer security technology using information theory. Popovic et al. [

Nevertheless, preventing transmission from being perceived is considered a more direct and effective measure. Compared with the above means, covert communication has more advantages than other security policies, which can prevent transmission content and behavior from being detected by non-cooperative eavesdroppers to solve the problem of information security fundamentally. Based on this, many scientists and engineers have focused on the research of covert communication. Covert communication was first cited in military communications by Prescott et al. [

Inspired by the works mentioned above, this article considers an integrated HAPS terrestrial network with one constant power auxiliary node, a terrestrial eavesdropper, a HAPS as the transmitter, and a terrestrial user as the receiver. Moreover, all nodes are equipped with a single omnidirectional antenna and operate in half-duplex mode. Specifically, the significant contributions of this paper are summarized below:

Firstly, considering the single-user scenario, a novel integrated HAPS terrestrial covert communication network structure is established, and a constant power auxiliary node assists the covert communication between HAPS and the user.

Secondly, considering the actual situation of signal transmission, such as rainfall attenuation and free path loss, the statistical characteristics of the channel are given. In addition, the covert constraints on universal significance are derived.

Thirdly, based on the above, the closed expression of outage probability (OP) under this covert communication network is deduced to obtain more in-depth insights and laws. Furthermore, the index to measure the covert performance named effective covert communication rate is given.

Finally, the numerical simulation results are given further to analyze key parameters’ impact on system covert performance. Moreover, the observation results are analyzed in detail.

As shown in

In order to get close to realistic transmission scenarios, the impacts of rain attenuation, free space loss, and antenna gain are considered in this system. Thus, the channel coefficient between

In

Moreover, we assume that the channels within the system experience standard SR fading, which means that the channel gain of each time slot remains unchanged but varies independently from one-time slot to another. Based on the above, it can be considered that the

Besides, following the general assumptions in covert communication theory [

Regarding a given maximum correct detection probability

Similarly, the received signal of

In our model, only a single auxiliary node is considered, and the energy detection method is adopted by

The

Therefore, the error detection of

On the above foundation, the requirements of covert communication can be expressed as

Furthermore, since the probability density functions of

According to the weak law of large numbers and some mathematical steps, when

Similarly, when

By means of

Moreover, the sufficient conditions of

With the help of

Then, the following formula can be obtained as

Hence, the average error detection of

In conclusion,

In this section, the statistical properties of SR fading are provided. On this basis, the exact expression of OP for the covert communication in this integrated HAPS terrestrial network is obtained. Besides, we derive the closed-form expression of the effective covert communication rate to measure the system’s covert communication performance.

Firstly, the probability distribution function (PDF) and cumulative distribution function (CDF) of SR fading are obtained. From [

Under the situation that

According to

From

OP can well evaluate the performance of the system, and in this paper we define the OP as the probability of the instantaneous capacity for any node lower than its excepted capacity. When

Assuming that the default coding rate of

By substituting

Furthermore, the final expression of OP can be derived as

Effective covert communication rate is also a momentous and more intuitive index in the covert communication system, defined as the average ratio of practical transmission information to the transmission time from transmitter to the receiver under all fading conditions. Finally, the effective covert communication rate

Furthermore, the final expression of the effective covert communication rate is given by

In this section, the critical constraint relationship of average SNR between the transmitting node and the auxiliary node, and the effective covert communication rate of the considered system are proved through MC simulations. In general, we set

Frequent heavy shadowing (FHS):

Average shadowing (AS):

Infrequent light shadowing (ILS):

This article systematically investigated the covert constraint and effective performance of covert communication in the integrated HAPS terrestrial networks, which utilized an auxiliary node with constant power. In particular, the covert constraint relationship between the transmitting node and the auxiliary node was discussed. Furthermore, the exact expressions of OP and effective covert communication rate were derived. According to numerical results, we found that the power of the transmitting node and auxiliary node under the covert constraint had a linear relationship. Secondly, the tightening of the covert constraint caused the deterioration of the achievable effective covert communication rate. Thirdly, there was an optimal preset coding rate to obtain the maximum effective covert communication rate. In addition, we knew that it was difficult for the

Thanks to all the authors for their contributions to this paper. The authors would like to thank the anonymous reviewers for their insightful suggestions that helped us improve this paper’s quality.

Recalling the transmission model, under the condition of

Due to the weak law of large number and

Further, for

Moreover, for

When

Therefore, at this time, for

Hence, when

Similarly, under the condition of

Based on the previous

Moreover, due to

Therefore, according to the scenario all we consider and the probability density distribution curve of

Namely,