# Wireless Covert Communication with Polarization Dirty Constellation
## 1 Introduction  
The proliferation of 5G and other wireless communication technologies has given rise to a broad range of multi-modal sensors, which have accelerated the process of social information [1; 2]. However, the majority of IoT devices are susceptible to hacking and compromise. Given that eavesdroppers can intercept wireless communication signals, confidential information is at risk. This poses a significant threat to communication security. To ensure the privacy of user data, several approaches have been proposed to transmit noisy or incomplete data, which can impact the performance of some IoT applications [3]. As a result, it is crucial to transmitting information secretly without detection or interception, known as wireless covert communication.  
Wireless covert channels, modern information-hiding technology in the wireless communication domain, conceal the transmission process of information that requires secrecy during typical wireless communication. Even if an eavesdropper intercepts the communication signal, it is impossible to differentiate it from standard wireless communication. The fundamental theory and performance limits of covert communication in AWGN channels are discussed in Ref. [4]. The authors established that a maximum of \(\mathcal{O}(\sqrt{n})\) bits can be transmitted to the receiver reliably without being detected by the detector. Researchers have subsequently analyzed the covert communication capacity in multiple scenarios with unfavorable factors for eavesdroppers. These include the transmitter [5; 6], receiver [7; 8; 9], and additional nodes [10; 11]. Covert communication techniques include artificial additional signal noise, artificial coding domain error, and insertion of additional signal bands, among others. The research in this field has been extended to other communication scenarios, such as relay communication [12; 13], multi-antenna [14; 15], and broadcast communication [16; 17; 18], etc.  
In the realm of covert communication, numerous techniques have been proposed to transmit confidential information without being detected [19] while some countermeasures to detect or localize covert communication entity has also been put forward [20]. However, achieving the theoretical covert rate of \(\mathcal{O}(\sqrt{n})\) under detection remains a challenging task. With the growing demand for 5G, polar codes have emerged as a promising solution that can achieve the Shannon capacity for channel coding [21]. Therefore, it is imperative to investigate the potential of polar codes in the context of covert communication. To this end, our main contributions are listed as follows.  
* We present a novel wireless covert channel that integrates polar code and dirty constellations, which, to the best of our knowledge, has not been proposed before.
* We employ two distinct decoding techniques, to enhance the reliability of the system and provide solutions for low-computational power scenarios.
* We conduct experiments on a wireless covert channel testbed to evaluate the performance of our proposals. The results show that the proposed wireless covert channel can obtain better reliability and undetectability.  
The remainder of this paper is structured as follows. In Section 2, we present a summary of the system model and related works. The fundamental principles of our scheme are elaborated in Section 3. In Section 4, we provide a detailed description of our wireless covert channel. Section 5 presents the experimental results obtained from our proposed method. Lastly, in Section 6, we conclude this paper.