Semidefinite Relaxation Technique Research Articles

IRS assisted anti jamming and beamforming technique

Recently, the emerging intelligent reflecting surfaces (IRS) has been leveraged to establish a smart and controllable wireless environment. This paper addresses the challenge of maximizing spectral efficiency in an IRS-aided downlink multi-user system while facing jammer attacks. The optimization problem focuses on improving the available transmission rate and limiting the impact of malicious jammer signals. The efficiency of the IRS in anti-jamming communications is achieved by determining the optimal phase shifts of the IRS elements and the optimal beamforming at the base station (BS). The optimization problem is non-convex. To tackle this non-convexity, an alternating optimization algorithm is proposed, dividing the main problem into two sub-problems which are solved using the semi-definite relaxation (SDR) and Gaussian randomization techniques. The simulation results confirm the enhanced spectral efficiency achieved by the proposed anti-jamming method in an IRS-assisted system. The optimal adjustment of the phase shifts in the IRS elements has resulted in a significant enhancement of about 25% in spectral efficiency compared to the random IRS phase case.

Rate splitting multiple access for UAV Secure Communication Systems with Friendly Jamming

A rate splitting multiple access (RSMA)-based dual-unmanned aerial vehicle (UAV) secure communication system is proposed in this paper, where one UAV is deployed to communicate with ground users, while the other UAV is dispatched to transmit the jamming signal to a ground eavesdropper. Considering the limited energy of UAV batteries, the minimum secrecy rate is maximized via optimizing RSMA precoding matrix and trajectories of UAVs under the constraint of UAV energy consumption. To address the complexity arising from coupled variables, the optimization problem is decomposed into two equivalent subproblems: precoding matrix optimization and UAV trajectory design. This decomposition is achieved using the block coordinate descent method. Next, the subproblems are transformed into convex forms by using semidefinite relaxation and successive convex approximation techniques, which are iteratively solved until convergence. Simulation results show that the secrecy performance of RSMA scheme is superior to that of the benchmark schemes, Specifically, the average secrecy rate of the RSMA scheme is approximately 22% and 10.8% higher than that of the NOMA and TDMA schemes, respectively.

Waveform Design for the Integrated Sensing, Communication, and Simultaneous Wireless Information and Power Transfer System.

Next-generation communication systems demand the integration of sensing, communication, and power transfer (PT) capabilities, requiring high spectral efficiency, energy efficiency, and low cost while also necessitating robustness in high-speed scenarios. Integrated sensing and communication systems (ISACSs) exhibit the ability to simultaneously perform communication and sensing tasks using a single RF signal, while simultaneous wireless information and power transfer (SWIPT) systems can handle simultaneous information and energy transmission, and orthogonal time frequency space (OTFS) signals are adept at handling high Doppler scenarios. Combining the advantages of these three technologies, a novel cyclic prefix (CP) OTFS-based integrated simultaneous wireless sensing, communication, and power transfer system (ISWSCPTS) framework is proposed in this work. Within the ISWSCPTS, the CP-OTFS matched filter (MF)-based target detection and parameter estimation (MF-TDaPE) algorithm is proposed to endow the system with sensing capabilities. To enhance the system's sensing capability, a waveform design algorithm based on CP-OTFS ambiguity function shaping (AFS) is proposed, which is solved by an iterative method. Furthermore, to maximize the system's sensing performance under communication and PT quality of service (QoS) constraints, a semidefinite relaxation (SDR) beamforming design (SDR-BD) algorithm is proposed, which is solved using through the SDR technique. The simulation results demonstrate that the ISWSCPTS exhibits stronger parameter estimation performance in high-speed scenarios compared to orthogonal frequency division multiplexing (OFDM), the waveform designed by CP-OTFS AFS demonstrates superior interference resilience, and the beamforming designed by SDR-BD strikes a balance in the overall performance of the ISWSCPTS.

Sum‐rate maximization for downlink multiuser MISO URLLC system aided by IRS with discrete phase shifters

AbstractIntelligent reflecting surface (IRS) has recently been considered as a potential technology for realizing ultra‐reliable and low‐latency (URLLC) in wireless networks. This paper proposes a resource optimization scheme to maximize the sum‐rate for an IRS‐assisted downlink multiuser multi‐input single‐output (MISO) URLLC system. For the perfect CSI scenario, we jointly optimize each user's block‐length and packet‐error probability, the precoding vectors at the base station (BS), and the passive beamforming with discrete phase shifts at the IRS. Given the problem's complexity, we design a computationally efficient iterative algorithm using successive convex approximation (SCA) and semidefinite relaxation (SDR) techniques to obtain a locally optimal solution. Specifically, for the imperfect CSI scenario, we construct a robust resource optimization problem model and incorporate the S‐procedure to address the impact of channel uncertainty, proposing an iterative algorithm based on the alternating optimization (AO) method to achieve a locally optimal solution. Simulation results demonstrate that: 1) An IRS equipped with a 2‐bit quantized resolution phase shifter is sufficient to achieve a system sum‐rate comparable to that of an ideal phase shifter; 2) Compared to other Baseline schemes, Algorithm 2 exhibits better robustness and superior performance gains under imperfect CSI.

Energy-Efficient Resource Optimization for IRS-Assisted VLC-Enabled Offshore Communication System

In this paper, a downlink energy efficiency maximization problem is investigated in an intelligent reflective surface (IRS)-assisted visible light communication system. In order to extend wireless communication coverage of the onshore base station, an IRS mounted on a unmanned aerial vehicle (UAV) is introduced to assist an onshore lighthouse with simultaneously providing remote ship users wireless communication services and illumination. Aiming to maximizing the energy efficiency of the proposed system, a resource allocation problem is formulated as the ratio of the achievable system sum rate to the total power consumption under the constraints of the user’s data requirement and transmit power budget. Due to the non-convexity of the proposed problem, the Dinkelbach method and mean-square error (MSE) method are adopted to turn the non-convex origin problem into two equivalent problems, namely transmit beamforming and reflected phase shifting. The Lagrangian method and semidefinite relaxation technique are used to obtain the closed-form solutions of these two subproblems. Accordingly, an alternative optimization-based resource allocation scheme is proposed to obtain the optimal system energy efficiency. The simulation results show that the proposed scheme performs better in terms of energy efficiency over benchmark schemes.

Resource allocation and passive beamforming for IRS‐assisted short packet systems

AbstractThis paper investigates an intelligent reflecting surface (IRS) assisted downlink short packet transmission system, where an access point sends short packets to multiple devices with the help of an IRS. Specifically, a performance comparison between the frequency division multiple access and time division multiple access is conducted for the considered system, from the perspective of average age of information (AoI). To minimize the maximum average AoI among all devices, the resource allocation and passive beamforming are jointly optimized. However, the formulated problem is difficult to solve due to the non‐convex objective function and coupled variables. Thus, an alternating optimization based algorithm is proposed by exploiting the semidefinite relaxation and bisection search techniques. Simulation results show that time division multiple access can achieve lower AoI by exploiting the time‐selective passive beamforming of IRS for maximizing the signal to noise ratio of each device consecutively. Moreover, it also shows that as the length of information bits becomes sufficiently large as compared to the available bandwidth, the proposed frequency division multiple access transmission scheme becomes more favourable due to more flexible power allocation.

Energy-efficient trajectory design for secure SWIPT systems assisted by UAV-IRS

Due to its controllable maneuverability, wide coverage, and low cost, unmanned aerial vehicle (UAV) has great potential in post-disaster rescue, cargo transport and emergency communication. Considering its limited onboard energy, energy-efficient UAV communication is a challenge. This research examines the security of simultaneous wireless information and power transfer (SWIPT) systems assisted by intelligent reflecting surfaces (IRS) and UAVs while considering the flight energy of rotary-wing UAVs. Specifically, an IRS is mounted on a UAV to enhance the quality of legitimate transmission, and artificial noise (AN) is introduced into the base station (BS) to reduce eavesdropping quality. The power splitting (PS) technology is adopted at ground devices (GDs) to simultaneously decode information and harvest energy. First, we jointly design the BS transmit beamforming, UAV-IRS phase shifts and trajectory/velocity as well as GDs PS ratio with the aim of maximizing the sum secrecy rate of all GDs. Then, an iterative algorithm is developed to address the formulated problem. In particular, additional variables are introduced to handle this complicated objective function, and the original problem is decoupled into multiple sub-problems, which can be solved alternately by invoking the successive convex approximation (SCA) and semidefinite relaxation (SDR) techniques. Finally, numerical results demonstrate that the proposed scheme exhibits a substantial performance in the security rate of SWIPT systems assisted by UAV-IRS, and its performance is improved by at least 12% compared to benchmark schemes at the flight energy budget ethr=5KJ and the number of reflecting elements Nr=25.

Robust receive beamforming and reflection coefficients optimization in an IRS‐aided decode‐and‐forward relay system

AbstractConsider a decode‐and‐forward wireless relay system assisted by an intelligent reflection surface (IRS), where a robust design on receive beamforming at the relay and reflection coefficients at the IRS is studied. The worst‐case signal‐to‐noise ratio maximization problem is formulated, subject to the reflection coefficients (with either continuous or discrete phases) constraints, under the assumption of imperfect channel state information for all channels. To cope with the hard problem, an equivalent nonconvex quadratic optimization problem with a simpler form is derived, and then the Cauchy‐Schwarz inequality is applied to update the beamforming and a cyclic process is proposed to update the reflection coefficients, where a closed‐form optimal solution is computed in each step. It turns out that the proposed algorithm achieves a locally optimal solution for the robust design problem. Simulation results show that the proposed robust design outperforms an existing non‐robust design and two robust designs via semidefinite relaxation technique.

A Framework for Transmission Design for Active RIS-Aided Communication With Partial CSI

Active reconfigurable intelligent surfaces (RISs) have recently been proposed to compensate for the severe multiplicative fading effect of conventional passive RIS-aided systems. Each reflecting element of active RISs is assisted by an amplifier such that the incident signal can be reflected and amplified instead of only being reflected as in passive RIS-aided systems. This work addresses the practical challenge that, on the one hand, in active RIS-aided systems the perfect individual channel state information (CSI) of the RIS-aided channels cannot be acquired due to the lack of signal processing power at the active RISs, but, on the other hand, this CSI is required to calculate the expected system data rate and RIS transmit power needed for transceiver design. To address this issue, we first derive closed-form expressions for the average achievable rate and the average RIS transmit power based on partial CSI of the RIS-aided channels. Then, we formulate an average achievable rate maximization problem for jointly optimizing the active beamforming at both the base station (BS) and the RIS. This problem is then tackled using the majorization–minimization (MM) algorithm framework, and, in each iteration low-complexity solutions for the BS and RIS beamforming are found based on the Karush-Kuhn-Tucker (KKT) conditions. To ensure the quality of service (QoS) of each user, we further formulate a rate outage constrained beamforming problem, which is solved using the Bernstein-Type inequality (BTI) and semidefinite relaxation (SDR) techniques. Numerical results show that the proposed algorithms can efficiently overcome the challenges imposed by imperfect CSI in active RIS-aided wireless systems.

Optimization-Driven DRL-Based Joint Beamformer Design for IRS-Aided ITSN Against Smart Jamming Attacks

This paper investigates an intelligent reflecting surfaces (IRS) aided anti-jamming communication strategy in the integrated terrestrial-satellite network (ITSN), where the IRS is exploited to mitigate jamming interference and enhance the integrated system communication performance. In such a network, the terrestrial network and satellite network are co-existing with a spectrum-sharing scheme in the presence of a multi-antenna jammer. We aim at maximizing the weighted sum rate (WSR) of all users by jointly optimizing the terrestrial beamformers and IRS phase shifts while considering the signal-to-interference-plus-noise ratio (SINR) requirements of legitimate users. Different from the non-convex optimization techniques utilized in the IRS-related problem, a novel optimization-driven deep reinforcement learning (DRL) algorithm is proposed, which leverages both the robustness of model-free learning approaches and the efficiency of model-based optimization methods. In the optimization module of the proposed algorithm, we analyze the smart jammer under the unknown jamming model and derive a lower bound of the anti-jamming uncertainty, such that the IRS-aided anti-jamming problem can be solved by alteration method with second-order cone programming (SOCP) algorithm and semidefinite relaxation (SDR) technique. Simulation results demonstrate that the IRS can enhance the anti-jamming performance efficiently, and the proposed optimization-driven DRL algorithm can improve both the learning rate and the system performance compared with existing solutions.

Robust Secure Transmission for Active RIS Enabled Symbiotic Radio Multicast Communications

In this paper, we propose a robust secure transmission scheme for an active reconfigurable intelligent surface (RIS) enabled symbiotic radio (SR) system in the presence of multiple eavesdroppers (Eves). In the considered system, the active RIS is adopted to enable the secure transmission of primary signals from the primary transmitter to multiple primary users in a multicasting manner, and simultaneously achieve its own information delivery to the secondary user by riding over the primary signals. Taking into account the imperfect channel state information (CSI) related with Eves, we formulate the system power consumption minimization problem by optimizing the transmit beamforming and reflection beamforming for the bounded and statistical CSI error models, taking the worst-case SNR constraints and the SNR outage probability constraints at the Eves into considerations, respectively. Specifically, the S-Procedure and the Bernstein-Type Inequality are implemented to approximately transform the worst-case SNR and the SNR outage probability constraints into tractable forms, respectively. After that, the formulated problems can be solved by the proposed alternating optimization (AO) algorithm with the semi-definite relaxation and sequential rank-one constraint relaxation techniques. Numerical results show that the proposed active RIS scheme can reduce up to 27.0% system power consumption compared to the passive RIS.

Bias Reduced Semidefinite Relaxation Method for 3-D Moving Object Localization Using AOA

This paper addresses the localization of a constant velocity moving object in 3-D using angle-of-arrival (AOA) measurements. Compared with the maximum-likelihood estimator, pseudo-linear approach for AOA localization has a large amount of bias resulting from the model transformation to simplify the solution finding. This work aims at reducing the bias and developing bias-reduced semidefinite relaxation (SDR) methods for estimating the initial position and velocity of the object, in a batch or sequential manner. This is accomplished by first formulating a bias reduced constrained weighted least squares (BR-CWLS) problem from the transformed measurements, through introducing an auxiliary variable and adding a quadratic constraint. Such an intractable non-convex problem is tackled next by applying the SDR technique and relaxing it into a convex semidefinite program (SDP), which is shown to be capable of reaching the solution of the original BR-CWLS problem. For sequential estimation, we formulate a different BR-CWLS problem and utilize SDR for obtaining a sequential estimation method that updates the initial position and velocity estimates at each time step. We conduct the mean square error (MSE) and bias analyses for both estimation methods to assess their expected performance. Simulation results verify the ability of bias reduction and the good performance of the proposed methods.

Zero-Forcing Beamforming for RIS-Enhanced Secure Transmission

This article considers a reconfigurable intelligent surface (RIS) enhanced multi-antenna secure transmission system in the presence of both active eavesdroppers (AEves) and passive eavesdroppers (PEves). We propose a zero-forcing (ZF) beamforming strategy that can steer transmit beam to the null space of AEves' channel, while simultaneously enhancing the SNRs for a legitimate user equipment (UE) and PEves without perfect channel state information (CSI). The design goal is to maximize the SNR of UE subject to the transmit power constraint at the BS, SNR limitations on PEves, and reflection constraints at RIS. Due to the complexity of modeling, we first introduce a homogeneous Poisson point process (HPPP) to imitate the distribution of spatially random PEves, which derives a complicated non-convex problem. We then develop an efficient alternating algorithm where the transmit beamforming vector and the reflective beamforming vector are obtained by convex-concave procedure (CCP) and semi-definite relaxation (SDR) technique, respectively. Simulation results validate the performance advantages of the proposed optimized design.

Research on joint optimization of IRS-assisted UAV network

To address the problem of obstacles blocking wireless channels and increase the transmission rate of unmanned aerial vehicle (UAV) communication systems, this paper proposes a method for maximizing the system sum rate in downlink communication networks based on intelligent reflecting surface (IRS)-assisted UAV. First, we lead into non orthogonal multiple access (NOMA) technology. Second, the system sum rate is maximized by jointly optimizing the IRS phase shift, 3D UAV trajectory, user scheduling and power allocation. Since the coupling and non-convexity of optimization variables make this problem difficult to solve directly, the original nonconvex problem is converted into four subproblems through block coordinate descent (BCD). Then, the subproblems are solved alternately using methods, such as semi-definite relaxation technique (SDR), relaxation variable introduction, successive convex approximation (SCA), the Lagrange multiplier method and first-order Taylor expansion. The results show that the algorithm proposed in this paper substantially improves the system sum rate and has favorable convergence.

Integrated sensing and communication waveform design in the Internet of Vehicles

We design an integrated sensing and communication (ISAC) transmission waveform with total transmission power, waveform similarity, and peak-to-average power ratio (PAPR) constraints in the Internet of Vehicles (IoV). The integrated waveform can complete radar target detection while communicating with downlink cellular users. The design of IoV with ISAC can not only improve the spectrum efficiency, but also further promote the integration of communication and sensing equipment. In this paper, the IoV with ISAC is formally modeled from the communication view and sensing view respectively. On this basis, taking the joint optimization of multi-user interference (MUI) total energy and Cramér Rao Bound (CRB) as the objective function, the transmission waveforms are designed with total transmission power, waveform similarity, and PAPR constraints respectively. To obtain the global optimal solution, we adopt a low complexity algorithm to solve the optimization problem under the total transmit power constraint and the optimization problem based on waveform similarity and PAPR constraints is further transformed into a nonconvex quadratically constrained quadratic programming (QCQP) problem, which is solved by using the semidefinite relaxation (SDR) technique. By ranking one approximation of the constrained optimization problem, it can be transformed into the solution of semidefinite programming (SDP) problems. The numerical results show that the designed ISAC transmission waveform can achieve an efficient tradeoff between sensing and communication performance, and each KPI is superior to one of the only communication and only sensing waveform design schemes. And it can improve the real-time information interaction ability of the IoV.

Integrated Sensing, Communication, and Computation Over-the-Air: MIMO Beamforming Design

To support the unprecedented growth of the Internet of Things (IoT) applications, tremendous data need to be collected by the IoT devices and delivered to the server for further computation. By utilizing the same signals for both radar sensing and data transmission, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">integrated sensing and communication</i> (ISAC) technique enables simultaneous data collection and delivery in the physical layer. By exploiting the analog-wave addition property in a multi-access channel, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">over-the-air computation</i> (AirComp) has been proposed as a communication approach that also enables function computation. The promising performances of ISAC and AirComp motivate the current work on developing a framework called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">integrated sensing, communication, and computation over-the-air</i> (ISCCO). Two schemes are designed to support <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">multiple-input-multiple-output</i> (MIMO) ISCCO simultaneously, namely the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">separated and shared</i> schemes. The separated scheme splits antenna array for radar sensing and AirComp, while all the antennas transmit a joint waveform for both radar sensing and AirComp in the shared scheme. The performance of radar sensing is evaluated by the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mean squared error</i> (MSE) of the estimated target response matrix, while the MSE of the estimated function is adopted as the metric to evaluate the performance of the coupled communication and computation in AirComp. The design challenge of MIMO ISCCO lies in the joint optimization of beamformers at both the IoT devices and the server, which results in a non-convex problem. To solve this problem, an algorithmic solution based on the technique of semidefinite relaxation is proposed. The results reveal that the beamformer at each sensor needs to account for supporting dual-functional signals in the shared scheme, while dedicated beamformers for sensing and AirComp are needed to mitigate the mutual interference between the two functionalities in the separated scheme. The application of ISCCO on target location estimation is further demonstrated via simulation.

Optimal Transmit Beamforming for Integrated Sensing and Communication

This paper studies the transmit beamforming in a downlink integrated sensing and communication (ISAC) system, where a base station (BS) equipped with a uniform linear array (ULA) sends combined information-bearing and dedicated radar signals to perform downlink multiuser communication and radar target sensing simultaneously. We consider two radar sensing design criteria, including the conventional sensing beampattern matching and the newly proposed minimum weighted beampattern gain maximization, respectively. Under this setup, we maximize the radar sensing performance while ensuring the communication users' individual signal-to-interference-plus-noise ratio (SINR) requirements subject to the BS's maximum transmit power constraints. In particular, we consider two types of communication receivers, namely Type-I and Type-II receivers, which do not have and do have the capability of cancelling the interference from the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-priori</i> known dedicated radar signals, respectively. Under both Type-I and Type-II receivers, the beampattern matching and minimum weighted beampattern gain maximization problems are non-convex and thus difficult to be optimally solved in general. Fortunately, via applying the semidefinite relaxation (SDR) technique, we obtain the globally optimal solutions to these problems by rigorously proving the tightness of their SDRs. Besides, for both design criteria, we show that dedicated radar signals are generally beneficial in enhancing the system performance with both types of receivers under general channel conditions, while the dedicated radar signals are not required with Type-I receivers under the special case with line-of-sight (LOS) communication channels. Numerical results show that the minimum weighted beampattern gain maximization design significantly outperforms the beampattern matching design, in terms of much higher beampattern gains at the worst-case sensing angles and much lower computational complexity in solving the corresponding problems. It is also shown that by exploiting the capability of cancelling the interference caused by the dedicated radar signals, the case with Type-II receivers results in better sensing performance than that with Type-I receivers and other conventional designs.

A Semidefinite Relaxation Approach for Mobile Target Localization Based on TOA and Doppler Frequency Shift Measurements

In this paper, we discuss mobile source localization using both time of arrival and Doppler frequency shift (TOA-DFS) measurements, where the source moves at a nonuniform velocity. To obtain the position of a mobile source, we first formulate the weighted least squares (WLS) problem by ignoring the second-order noise terms. Due to the non-convexity, we apply the convex relaxation technique to transform the problem into a semi-definite programming problem. However, ignoring the second-order noise terms is only reasonable in the case of small noise levels. In view of this, we then directly establish the maximum likelihood (ML) estimator based on the measurements model without ignoring the second-order noise terms. Since the ML estimator is a non-convex problem, we also propose implementable semidefinite relaxation (SDR) technique to tackle it. Finally, the Cramér-Rao lower bound (CRLB) analysis and results verify that the proposed methods based on the TOA-DFS measurements can significantly enhance localization accuracy.

Robust Beamforming Design for Cache-Enabled C-RAN With Fronthaul Multicast

In this article, we study a robust beamforming design problem in the cached-enable cloud radio access network, where the imperfect channel state information of the access links are considered. Two transmission schemes, nonsimultaneous transmission (NST) scheme and simultaneous transmission (ST) scheme, are developed. To improve the system performance, the cooperative transmission technique is applied. In NST scheme, the base stations (BSs) obtain the uncached required files from the central processor (CP) and then transmit all required files to users. Based on this, we design an effective transmission model based on cache files and the qualities of the fronthaul link channels, and formulate a transmission delay minimization problem. Then, an alternative optimization algorithm is developed to solve it. In ST scheme, the BSs obtain the uncached files from the CP and transmit the cached files to users simultaneously. We divide two cases according to the access link transmission rate and cached files. For each case, we formulate an optimization problem by jointly designing the fronthaul multicast beamforming and access link transmission beamforming. Next, an iterative algorithm is developed via the L0 norm approximation, successive convex approximation and semidefinite relaxation techniques. Finally, simulation results show the proposed schemes can reduce the transmission delay better than the conventional multicast schemes.

Robust Beamforming Design for RIS-Aided NOMA Secure Networks With Transceiver Hardware Impairments

Integrating reconfigurable intelligent surface (RIS) and non-orthogonal multiple access (NOMA) provides a promising solution to support large-scale secure communications. However, reducing the impact of transceiver hardware impairments (HWI) on the performance of RIS-aided NOMA secure networks remains a challenge. In this paper, we propose a robust transmission scheme for RIS-aided NOMA secure networks with transceiver HWI under two proposed eavesdropping scenarios and two artificial noise methods. A closed-form expression for the distortion noise power caused by transceiver HWI in NOMA networks is derived to quantify transceiver HWI. The sum secrecy rate of NOMA users with imperfect successive interference cancellation (SIC) is maximized under distortion noise for more robust security. Further, to tackle the resulting non-convex problem, we decompose it into two sub-problems. Both of them are converted into convex problems using the multi-dimensional quadratic transform (MDQT) method, semi-definite relaxation (SDR) technique, and the successive convex approximation (SCA) algorithm, and then employing the alternate optimization (AO) algorithm solve them. Numerical results demonstrate that the proposed scheme has superior security performance over orthogonal multiple access (OMA) networks, time division multiple access (TDMA) networks, and traditional NOMA networks, achieving more robust performance than the conventional scheme that ignores HWI and imperfect SIC.