# Covert Communications in Active-RIS-Aided NOMA Systems: Element Grouping or Not?
## 1 Introduction
It was shown that employing a PRIS significantly enhanced the covert communication performance of NOMA systems. Also, ARISs were utilized to maximize the covert communication rate in [30; 31]. Since a large number of the metasurface elements are fabricated on a RIS, different functions could be allocated to different elements, and several element grouping schemes were proposed for RIS-aided wireless communication systems [32; 33; 34]. For example, the incident signal at the grouped PRIS elements could be adjusted to generate the jamming signal in the desired direction [32]. In [33], through element grouping, the incident signal on each PRIS element was amplified for information transmission or modulated into jamming, which effectively improved the PLS performance. On the other hand, using all ARIS elements to reflect the information signal led to certain security risks, whereas using all the ARIS elements to generate the jamming signal led to a decrease in reception quality for legitimate receivers. Therefore, the ARIS's elements were divided into two groups, one working in the reflecting mode and the other in the jamming mode to improve the PLS performance [34]. It was shown that the element grouping scheme effectively improved the minimum secrecy rate among the NOMA users in an ARIS-aided NOMA system, achieving an enlarged channel gain difference between the legitimate and eavesdropping channels [34]. Different from PLS transmissions, proper randomness is needed to balance between the required covertness and legitimate transmission performance in NOMA systems. In particular, the superimposed signal of the NOMA users has already been regarded as a natural shield to conceal covert communication behaviors. When element grouping is applied in ARIS-aided NOMA systems, how to balance the covertness and legitimate transmission performance becomes critical in the presence of the NOMA superimposed signal. Although the element grouping has been investigated for the PLS, the applications of the element grouping in covert communications have never been investigated. Furthermore, although element grouping can improve the secrecy communication performance for the PLS, whether element grouping enhances the covert communication performance is still unknown. To the best of our knowledge, how to employ element grouping to realize covert communications in ARIS-aided NOMA systems has not been tackled. In this work, the impacts of element grouping on covert communication performance are investigated for an ARIS-aided uplink NOMA system. In the element grouping scheme, each element of the ARIS works in at least one mode, i.e., information signal reflection or jamming signal reflection. By adjusting the reflection coefficient and working mode for each element, a trade-off between the covertness and legitimate transmission performance can be optimized. By jointly optimizing the NOMA transmit power, ARIS beamforming, and receive beamforming at the base-station (BS), our design goal is to maximize the covert communication rate. To tackle the intractable optimization problem, we decouple the original problem into three sub-problems of optimizing the NOMA transmit power, ARIS beamforming, and receive beamforming, respectively. We then derive closed-form expression for the sub-problem of the NOMA transmit power optimization. Mixed-integer non-linear programming for element grouping is effectively addressed by an arithmetic and geometric mean (AGM)-based penalized Dinkelbach transform approach. Then, an efficient alternating optimization (AO) algorithm is proposed to solve the formulated non-convex covert communication rate maximization problem [35; 36]. Various simulation results are provided to verify whether element grouping enhances covert communication performance or not. Our work shows that the scheme without element grouping achieves a better covert communication performance than the scheme with element grouping, which is a valuable and novel finding that has never been reported before.