# Optimization of Intelligent-Reflecting-Surface-Enabled Covert Communication in Multi-Sensor Systems
## 1 Introduction  
In the era of the Internet of Things (IoT), the surge in demand for the transmission of sensor information is witnessing exponential growth [1; 2]. Addressing security concerns pertaining to information transmission in multi-sensor environments emerges as a pivotal undertaking [3; 4; 5]. Traditional encryption methodologies and techniques in physical layer security primarily concentrate on protecting the communication content [6; 7]. Nevertheless, the mere protection of communication content no longer suffices to meet contemporary information security requisites [8; 9]. To hide the communication behaviors, covert communication, also known as low probability of detection (LPD) communication, was proposed [10].  
Extensive research has been conducted on covert communication techniques in military communication, with a focus on methods like spread spectrum and frequency-hopping communication [9; 11; 12; 13]. These techniques aim to conceal the existence of communication from vigilant adversaries. However, the theoretical boundaries of covert communication were initially explored in [14], where the square root law (SRL) in additive white Gaussian noise (AWGN) channels was discovered. This seminal discovery was subsequently expanded to various channel models, encompassing binary symmetric channels [15], discrete memoryless channels [16; 17; 18], and multi-user channels [19; 20; 21; 22; 23], among others.  
In this work, we investigate IRS-enabled covert communication in multi-sensor systems, comprising a central processing unit (CPU) and a sensor cluster with \(N\) independent sensors, as shown in Figure 1. [PERSON] utilizes IRS-reflected signals to covertly access one of the sensors, while [PERSON], as the detecting entity, aims to ascertain the presence of covert access. To reduce operational complexity and communication costs, [PERSON] employs the 2-BPSK codebook proposed in [8] for covert communication. The main contributions of this paper are summarized as follows:1. We conducted the first theoretical study on IRS-enabled covert communication in multi-sensor systems with a 2-BPSK codebook. We provided closed-form solutions for the KL divergence and mutual information analysis of the target system.
2. We introduced a gradient descent algorithm, which, when employed, yields optimal initial phase angles for 2-BPSK. This algorithm both ensures covertness and maximizes the transmission rate.
3. We proposed a physical layer optimization method for IRS-enabled covert communication, transforming the multi-parameter optimization problem of transmission amplitude and phase angles into a phase-angle optimization problem. Based on the optimized phase angles, we obtained the optimal transmission amplitude.
4. Through experimental simulations, we validated the effectiveness of the proposed gradient descent algorithm. Comparative analysis with traditional phase angle parameters demonstrated that our optimization method achieves a better covert transmission rate under the same covertness constraints.  
The subsequent sections of this paper are structured as follows. Section 2 introduces related works. In Section 3, the system model of IRS covert communication in multi-sensor systems is introduced. The achievability and the transmission performance analysis of covert communication are provided in Sections 4 and 5. In Section 6, the optimization problem is reformulated and a gradient descent optimization algorithm is proposed to solve the problem. Section 7 provides numerical simulations to verify the effectiveness and superiority of our method. Finally, Section 8 provides the discussion and conclusions of this paper.