Active-RIS-Aided Covert Communications in NOMA-Inspired ISAC Wireless Systems

Next generation wireless systems are envisioned with sensing functionalities that will allow them to achieve high-precision positioning of massive devices and real-time reconstructions of the physical world, which are key enablers for anytime, anywhere, internet of everything (IoE), as well as vehicles networking [1, 2]. With the advancements of massive multiple-input multiple-output (MIMO) schemes, ultra-wide spectral usage, and ultra-high frequency transmission, such as millimeter and terahertz waves, wireless communication systems naturally possess sensing functions with exceptional accuracy and resolution [3]. By co-designing communication and sensing systems together in order to use the same hardware and signal processing platforms, same wireless resources, and unified control modules, collaboration efficiencies can be significantly improved [1]. In this direction, novel concepts of integrated sensing and communication (ISAC) have recently sparked heated discussions, particularly on co-designing of dual-function waveforms [4, 5].

As a promising spectral efficiency (SE)-enhancement technique, non-orthogonal multiple access (NOMA) has been applied to enable ubiquitous high-quality communication and high-resolution sensing in NOMA-inspired ISAC wireless systems [6, 7], which were frequently constrained by limited wireless resources. Through superposition coding at the transmitter and successive interference cancellation (SIC) at the receiver, NOMA-ISAC addressed inter-user interference (IUI) effectively, while additional degrees of freedom (DoF) were introduced by adequate dual-functional beamforming [6]. To simultaneously deliver multicast and unicast messages, common beamforming and transmit power allocation were jointly optimized in NOMA-ISAC wireless systems with the aim of enhancing radar sensing accuracy and achieving extra DoF for communications [7]. Inspired by interference management of NOMA, the dedicated sensing signal (DSS) was partially treated as virtual communication signal and eliminated by SIC at communication receivers [8]. In uplink ISAC systems, a pure-NOMA-based scheme was reported to guarantee the sensing-prior system performance with a fixed communication-to-sensing decoding order [9]. As a step further, a semi-NOMA-based scheme was introduced to provide flexible resource allocation strategies between sensing and communication, which effectively satisfied different objectives of sensing and communication [10].

Due to open and broadcasting natures of wireless propagation, sensitive and privacy information embedded in NOMA-ISAC waveforms was susceptible to interception and eavesdropping [11, 12]. Considering radar target as potential eavesdropper, the authors of [11] exploited artificial jamming and NOMA signal for target detection and eavesdropping prevention. In [12], confidential information of NOMA users was concealed in radar beamforming, in which strong interference was conveyed to damage eavesdropping channels. By using SIC, artificial jamming and sensing interference were eliminated by NOMA users to enhance communication performance [11, 12]. Nevertheless, exposing existences of legitimate transmissions to malicious users brought potential security risks to ISAC systems [13, 14], e.g., exposing only network traffic pattern can lead to sensitive information leakage. Without additional spectrum investments, it is paramount importance to enhance security performance of ISAC systems by resorting to new technologies.

Fortunately, reconfigurable intelligent surface (RIS) provided a promising approach to simultaneously facilitate radar sensing and covert communications [15]. Since RIS possesses ability to manipulate propagation environments intelligently and efficiently, virtual line-of-sight (LoS) links can be created for radar sensing and communication resulting in new DoFs for ISAC optimizations [16, 17, 18]. By controlling reflection amplitude and phase-shift of each element of RIS, the reflected wireless signals can be tuned constructively or destructively, such that signal power in desired directions can be strengthened or weakened [19]. Recently, RIS was utilized to facilitate covert communications in ISAC systems [15] and NOMA systems [20, 21], which provided a higher level of security than conventional physical layer security (PLS) by concealing legitimate transmissions against wardens. Compared to conventional covert communications in NOMA systems, where only the signal of a NOMA public user was utilized as a shield for covert transmissions [22], RIS-aided superposition transmissions hide communication behaviors cost-effectively by leveraging RIS’s phase-shift uncertainties and superposition transmissions of NOMA public and covert users.

Due to “multiplicative fading” effects, reflection link qualities of passive-RIS-aided communications were limited and corresponding capacity gains were negligible. To overcome this limitation, active-RIS was introduced in [23] and [24], which integrated amplifiers into meta-elements to amplify and reflect signals, compensating for substantial path-loss of reflection links and obviating need for complex and power-hungry radio frequency (RF) chains [23]. Owning to the aforementioned benefits, PLS [25] and covert communication performances [26] were improved by optimizing active-RIS reflection beamforming and collaborating with base-station (BS) precoding optimization. In active-RIS-aided multiple-input single-output (MISO) NOMA systems [27], covert rate was maximized subject to the QoS requirements of NOMA public users and the maximum reflection amplitude and power budget of active-RIS.

Recently, active-RIS has been applied to enhance communication quality and sensing capability for ISAC systems in which direct links from BS to potential targets have been blocked [28, 29, 30, 31]. To enhance sensing capability for MIMO-ISAC systems, active-RIS was deployed to shape reflection beampattern towards a point-like target [28]. Different from [28], in which only communication signal was used to achieve dual-function ISAC, DSS was applied in [29] where transmit beamforming and reflection beamfomring were joint optimized to maximize the radar signal-to-noise ratio (SNR). Furthermore, to enhance the non-line-of-sight (NLoS) sensing capability, active-RIS was deployed to assist remote radio heads in cloud radio access networks (C-RANs) to conduct dual-function ISAC [30]. Taking into account target location estimation errors, a hybrid active-passive-RIS was deployed to maximize the minimum sensing beampattern gain while maintaining a pre-defined signal-to-interference-plus-noise ratio (SINR) for each user [31]. The high path-loss was intensively tackled by using active-RIS for ISAC systems, with the aim of not only improving the communication and sensing performances [32, 33, 34], but also enhancing the PLS capabilities [35]. Note that the above active-RIS-aided ISAC contributions, except for [28], have exploited DSS to achieve dual-function ISAC.

Despite the vast research effort that was put on analyzing and optimizing active-RIS empowered wireless systems, how to deploy active-RIS to make the most out of the covert communication for NOMA-ISAC wireless systems is still unknown. Additionally, works in [28, 29, 32, 33, 35, 34] investigated dual-function beamforming with respect to a single target, which was not a typical scenario in practice. Despite multiple targets being considered in [31, 30], the exploited sensing metric, i.e., beampattern gain, was too rough for estimating target parameters. From the perspective of dual-function waveforms, although the usage of DSS and the absence of DSS can improve both the communication and sensing performances, a comprehensive comparison of the impact of the usage of DSS and the absence of DSS on the system performance of active-RIS-aided ISAC systems is missing. In particular, the effects of exploiting DSS in active-RIS-aided NOMA-ISAC systems need to be quantified, especially when DSS is regarded as a part of the NOMA superposition signal. Another question that we need to answer is the following: when active-RIS is deployed to aid covert communications in practical NOMA-ISAC systems, should we apply DSS or not to achieve the enhanced covert communication performance in the presence of multiple targets?

As an attempt to answer the above open questions, we deploy an active-RIS to aid covert communications in a NOMA-ISAC system, where a dual-function BS serves two NOMA users while sensing multiple moving targets. In more detail, one of the NOMA users is a security-required user (covert user) with a high level of covertness and the other is a QoS-required user (public user) with low or no confidentiality requirements. We examine the use of DSS for multi-target sensing and apply the NOMA public user’s signal as the covert medium to hide covert transmissions against warden. Taking into account the realistic assumption of multiple moving targets, we derive Cramér-Rao bound (CRB) to characterize the sensing performance for the considered NOMA-ISAC wireless system. The trade-off between covert communication and multi-target sensing is investigated and the impact of the use of DSS is extrapolated. With the aim of maximizing the covert rate, transmission beamforming and reflection beamforming are jointly optimized, while satisfying the CRB constraint on multi-target estimation and ensuring the covertness level against warden. By involving user scheduling and pairing schemes, the considered NOMA-ISAC system is scalable to accommodate multiple NOMA users.

To the best of our knowledge, this is the first paper investigating covert communications for active-RIS-aided NOMA-ISAC wireless systems in the presence of a warden and multiple moving targets and the first attempt to reveal the impacts of DSS on the covert communication and sensing performances systematically. The key contributions of this paper are summarized as follows:

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  We deploy active-RIS to aid covert communications in a NOMA-ISAC system taking into account two superposition transmission schemes. The first scheme only transmits a NOMA signal without DSS (w/o-DSS scheme), whereas the second scheme transmits NOMA signal with DSS (w-DSS scheme). To precisely measure the sensing performance with respect to multiple moving targets, we exploit CRB as the target sensing metric for both the w/o-DSS and w-DSS schemes. In the w-DSS scheme, both the sensing and communication signals are utilized to not only estimate the parameters of multiple moving targets, but also hide the covert transmission behaviors from the dual-function BS to the NOMA covert user. In the w/o-DSS scheme, although only the signal of the NOMA public user is treated as a shield to achieve low-probability-of-detection covert communications for the NOMA covert user, more transmit power can be allocated to enhance covert communication performance.

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  For both the aforementioned superposition transmission schemes, we formulate the covert rate maximization problems subject to the QoS requirements of the NOMA public user, CRB constraint, power budget constraints at BS and active-RIS, and covertness constraint. We decouple the original non-concave optimization problem into two sub-problems of transmission beamforming optimization at BS and reflection beamforming optimization at active-RIS, respectively, to tackle the optimization variables coupled in the objective and constraints. The resulted rank-one constrained problem of transmission beamforming optimization is solved with the aid of a penalty-term, while the rank-one constrained fractional programming problem of reflection beamforming optimization is solved by exploiting a penalized Dinkelbach transform. Then, we introduce an alternating optimization (AO) algorithm to optimize the transmission and reflection beamforming in an alternating manner.

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  Extensive numerical results clarify the effectiveness of the derived solutions and AO algorithm. It is demonstrated that the active-RIS-aided NOMA-ISAC system outperforms the passive-RIS-aided and without-RIS counterparts in terms of the covert rate and trade-off between communication and sensing performances because active-RIS amplifies the incident signal to obtain additional covert rate gain and allows BS to allocate more transmit power for target sensing. The impacts of DSS on the ISAC system performance are also revealed by the numerical results. Compared to the w-DSS scheme, the w/o-DSS scheme achieves a higher covert rate because more transmit power is available for covert transmissions by omitting DSS, while exploiting only the NOMA signal ensures the required multi-target sensing performance in the considered NOMA-ISAC system.

The remainder of the paper is organized as follows: Section II presents the system model. The covert beamforming design is specified in Section III. Numerical results are illustrated in Section IV. Finally, Section V concludes the paper.

Notations: Throughout the paper, scalars are represented by italic letters, and vectors and matrices are represented by boldfaced lowercase and uppercase letters, respectively. ${\rm{Pr}}\{\cdot\}$ denotes probability, $\mathbb{E}\left\{\cdot\right\}$ denotes the expectation, and $\|\cdot\|$ denotes the Euclidean norm of a complex vector. Superscript $(\cdot)^{T}$, $(\cdot)^{*}$ and $(\cdot)^{H}$ denote vector/matrix transpose, conjugate and Hermitian transpose, respectively. The Hadamard and Kronecker products are denoted by $\odot$ and $\otimes$, respectively. ${\mathbb{C}^{N\times M}}$ and $\mathbb{R}^{N\times M}$ denote the spaces of $N\times M$ complex-valued matrices and real-valued matrices, respectively. $\mathbb{H}^{N}$ represents the set of all $N\times N$ complex Hermitian matrixes. ${\mathbf{A}}\succeq 0$ indicates that $\mathbf{A}$ is a positive semi-definite matrix. The symbols ${\rm{rank}}({\mathbf{A}})$ and ${\rm tr}({\mathbf{A}})$ denote the rank and trace of matrix $\mathbf{A}$, respectively. $\mathbf{0}_{N}$ and $\mathbf{1}_{N}$ denote the $N$-dimensional all-zero and all-ones vectors, respectively. ${{\mathbf{I}}_{N}}$ denote the $N\times N$ identity matrix. The notation $\mathcal{C}\mathcal{N}({\nu,{\sigma^{2}}})$ denotes a circular symmetric complex Gaussian (CSCG) random distribution with mean $\nu$ and variance $\sigma^{2}$.

We consider an active-RIS-aided NOMA-ISAC system consisting of a dual-function BS (Alice), an active-RIS, a warden (Willie), a NOMA public user (Grace), a NOMA covert user (Bob), and multiple moving targets indexed by $\mathcal{Q}=\{1,...,Q\}$, as shown in Fig. 1. We assume that Bob has a high-level of confidentiality and Grace only has reliability requirements, which is a realistic assumption in IoE applications. For example, military departments require covert communications in specific scenarios, while weather forecasts have low or no confidential requirements. In the NOMA-ISAC system, Alice is equipped with a uniform linear array (ULA) consisting of $M_{\mathrm{t}}$ transmit antennas and $M_{\mathrm{r}}$ receive antennas with half-wavelength spacing. For simplicity, we assume Alice works in full-duplex mode with perfect self-interference cancellation and $M_{\mathrm{t}}=M_{\mathrm{r}}=M$. Each one of Grace, Bob, and Willie is equipped with a single antenna. The active-RIS consists of $N$ active reflecting elements and is deployed close to the users to assist information communications. We assume that targets fly at low altitudes, which results in strong LoS links from Alice to targets and vice versa, while active-RIS is deployed far away from targets resulting in weak RIS reflection links. Thus, we only consider direct links for target sensing [17, 34, 16]. In addition, Willie keeps monitoring the downlink transmission from Alice to the NOMA users and determining whether Alice is transmitting covert information to Bob. The channel between Alice and node $k$ is denoted by ${{\mathbf{h}}_{ak}}\in{\mathbb{C}^{M\times 1}}$ with $k=g$, $b$, and $w$ standing for Grace, Bob, and Willie, respectively. The Alice-RIS channel and RIS-$k$ channel are denoted by ${{\mathbf{G}}}\in{\mathbb{C}^{N\times M}}$ and ${{\mathbf{h}}_{{rk}}}\in{\mathbb{C}^{N\times 1}}$, respectively. All of the communication channels are assumed to experience Rician fading with the distance-dependent path-loss, e.g., the Alice-RIS channel $\mathbf{G}$ can be obtained as

where $\mathcal{L}_{ar}$ is the distance-dependent path-loss, $\beta_{ar}$ is the Rician factor, $\mathbf{G}^{\text{LoS}}$ denotes the LoS component that is expressed as $\mathbf{G}^{\text{LoS}}=\mathbf{a}_{N}(\theta_{ra})\mathbf{a}_{M}^{H}(\theta_{ar})$, and $\mathbf{G}^{\text{NLoS}}$ denotes the Rayleigh fading component with zero mean and unit variance. Vectors $\mathbf{a}_{M}(\theta_{ar})$ and $\mathbf{a}_{N}(\theta_{ra})$ are the array response vectors of Alice and active-RIS, respectively, which are mathematically given by $\mathbf{a}_{M}(\theta_{ar})=[1,e^{\jmath 2\pi\frac{\delta_{1}}{\lambda}\sin(\theta_{ar})},...,e^{\jmath 2\pi(M-1)\frac{\delta_{1}}{\lambda}\sin(\theta_{ar})}]^{T}$ and $\mathbf{a}_{N}(\theta_{ra})=[1,e^{\jmath 2\pi\frac{\delta_{2}}{\lambda}\sin(\theta_{ra})},...,e^{\jmath 2\pi(N-1)\frac{\delta_{2}}{\lambda}\sin(\theta_{ra})}]^{T}$, respectively, with $\lambda$, $\delta_{1}=\lambda/2$, and $\delta_{2}=\lambda/2$ being the carrier wavelength, adjacent antenna spacing of Alice, and adjacent element spacing of the active-RIS, respectively. The Alice-$k$ and RIS-$k$ channels are independent and identical. Following the works in [20, 21], we assume that Alice possesses statistical knowledge of the channel state information (CSI) of the links involving Willie, along with perfect CSI for the other communication channels. Willie, on the other hand, can attain perfect CSI for its monitoring channels. It is assumed that all channels experience quasi-static block fading, remaining constant within each block. In the rest of this section, two transmission schemes, namely, the w/o-DSS and w-DSS schemes, are respectively presented.

In this section, we focus on the joint optimization of the transmission beamforming and reflection beamforming in the active-RIS-aided NOMA-ISAC system. We firstly formulate the optimization problems when Alice performs the target sensing and communication simultaneously in the two transmission schemes. Then, we present solutions to the formulated optimization problems by designing an AO algorithm for optimizing the transmission beamforming at Alice and reflection beamforming at the active-RIS.