Semidefinite Relaxation Research Articles

Robust Transmit Beamforming for Secure Integrated Sensing and Communication

This paper studies a downlink secure integrated sensing and communication (ISAC) system, in which a multi-antenna base station (BS) transmits confidential messages to a single-antenna communication user (CU) while performing sensing on targets that may act as suspicious eavesdroppers. To ensure the quality of target sensing while preventing their potential eavesdropping, the BS combines the transmit confidential information signals with additional dedicated sensing signals, which play a dual role of artificial noise (AN) for degrading the qualities of eavesdropping channels. Under this setup, we jointly design the transmit information and sensing beamforming, with the objective of minimizing the weighted sum of beampattern matching errors and cross-correlation patterns for sensing subject to secure communication constraints. The robust design takes into account the channel state information (CSI) imperfectness of the eavesdroppers in two practical CSI error scenarios. First, we consider the scenario with bounded CSI errors of eavesdroppers, in which the worst-case secrecy rate constraint is adopted to ensure secure communication performance. In this scenario, we present the optimal solution to the worst-case secrecy rate constrained sensing beampattern optimization problem, by adopting the techniques of S-procedure, semi-definite relaxation (SDR), and a one-dimensional (1D) search, for which the tightness of the SDR is rigorously proved. Next, we consider the scenario with Gaussian CSI errors of eavesdroppers, in which the secrecy outage probability constraint is adopted. In this scenario, we present an efficient algorithm to solve the more challenging secrecy outage-constrained sensing beampattern optimization problem, by exploiting the convex restriction technique based on the Bernstein-type inequality, together with the SDR and 1D search. Finally, numerical results show that the proposed designs can properly adjust the information and sensing beams to balance the tradeoffs among communicating with CU, sensing targets, and confusing eavesdroppers, so as to achieve desirable sensing transmit beampatterns while ensuring the CU’s secrecy requirements for the two scenarios.

Covert Ambient Backscatter Communications With Multi-Antenna Tag

This paper presents a unicast beamforming network for covert ambient backscatter communications (AmBC). Different from the prior covert backscatter works using artificial noise or a power-variable RF source, our work achieves covertness by arming the backscatter tag with multiple antennas. The tag uses a subset of its antennas to modulate covert information on backscattered RF signals while using the other antennas to modulate overt message as a cover to hide the covert transmission from the warden. We first derive the warden’s optimum detection threshold to minimize the detection error probability. To fight against the optimum warden, the tag changes impedance matching on each antenna to vary the reflected power and make the reflected overt and covert signals beamforming at space. We derive the optimum beamforming vectors by solving the problems of maximizing the covert rate at the receiver and the detection error probability at the warden, respectively. To address the non-convex constraints, we use semi-definite relaxation (SDR) and obtain near optimal parameters by designing binarySearch algorithms. Numerical results confirm the superiority of our work to the state-of-the-art one, and the existence of tradeoffs between the covert rate and the detection error probability.

Beamforming Design in Short-Packet Transmission for URLLC in Cell-Free Massive MIMO System

Low latency, high reliability, and high data rate are three performance indicators of Ultra-reliable and low latency communication (URLLC) systems, but they are not able to be met simultaneously. Based on the determined latency and reliability requirements, this paper investigates the problem of the weighted sum rate (WSR) in cell-free massive multi-input multi-output (MIMO) system with multiple access points (APs). User-centric access point selection is considered to further reduce the computational complexity for AP used with acceptable performance loss. The transmitting beamforming is designed to mitigate inter-user interference so as to maximize the WSR under the backhaul and transmitting power constraints. Since the proposed problem is non-convex, two algorithms are proposed to solve the problem under the general SINR regime and the high SINR regime, respectively. For the former, we first approximate the objective function with the difference of convex (DC) programming and reformulate the problem into a semi-definite relaxation (SDR) form. Afterward, auxiliary variables are introduced in accordance with the successive convex approximation (SCA) method to further transform the nonconvex problem into a convex one. In the end, the sub-optimal WSR is obtained by iteratively solving a final convex problem. For the latter, the well-known WMMSE method is applied to address the WSR problem. Numerical results demonstrate the efficiency of our proposed algorithm, e.g., the maximum performance gain of the proposed algorithm is about 25% compared to the classical MMSE method. And the user-centric approach achieves 8 times computational complexity reduction with 4% performance loss.

Robust Design of IRS-Aided Multi-Group Multicast System With Imperfect CSI

In this paper, the robust design for the intelligent reflective surface (IRS) assisted wireless multi-group multicast system is considered, in which two optimization design problems under two different channel state information (CSI) error models are separately discussed, i.e., the fairness-based problems and the quality-of-service (QoS)-based problems for both the bounded CSI error model and the statistical CSI error model. In order to deal with the non-convex constraints of the considered problems, i.e., bounded CSI error based constraint and statistical CSI error based constraint, S-procedure is adopted to convert the non-convex SINR constraint with bounded CSI error into linear matrix inequalities (LMIs), and the Bernstein-type inequality is utilized to transform the outage probability constraint with statistical CSI error into a second-order cone (SOC) constraint and linear inequalities. Following that, two efficient algorithms based on alternate optimization (AO) are proposed to solve the fairness problems and QoS problems, wherein the semi-definite programming (SDP), penalty convex-concave procedure (CCP) and semi-definite relaxation (SDR) are utilized. Furthermore, we analyze the complexity of the proposed algorithms. Finally, some numerical simulation results are presented to verify the effectiveness of the proposed algorithms, and the impacts of the CSI error and the discrete precision of IRS reflection phase shift on the system performance are analyzed, which provides some insights for the IRS deployment and system robust design.

SLIPT-Enabled Multi-LED MU-MISO VLC Networks: Joint Beamforming and DC Bias Optimization

This paper studies a simultaneous lightwave information and power transfer (SLIPT)-enabled multi-user (MU) multiple input single output (MISO) visible light communication (VLC) network, where multiple user equipments (UEs) are simultaneously allowed to receive information by the photodiode (PD) and harvest energy by the solar panel, respectively. To improve the system spectral efficiency, an achievable sum rate maximization problem is formulated subject to the minimum energy harvesting (EH) requirement of each UE, the total transmit power constraint of the LEDs and the dimming control constraint of the LEDs, by jointly optimizing the beamforming vector and the direct current (DC) bias vector of the LEDs. To be general, the practical non-linear EH model and the information capacity model of the VLC channel are adopted. To solve the non-convex optimization problem, the objective function is equivalently transformed at first by using the epigraph reformulation, and then the transformed problem is relaxed with the semi-definite relaxation (SDR) method. Based on this, an iterative algorithm is designed to approximately obtain the maximal achievable sum rate based on the successive convex approximation (SCA). Simulation results indicate that there exists a non-trivial trade-off between the achievable sum rate and the harvested energy, and that DC bias vector dominates the amount of the harvested energy compared with the beamforming vector. Besides, for a given relatively high EH requirement, the achievable sum rate increases with the increment of the dimming level, especially for relatively small dimming level. Once the dimming level is larger than a specific value, with the increment of the dimming level, more transmit power will be allocated for illumination, resulting in the decrement of the achievable sum rate.

Robust beamforming for dual‐function radar‐communication with imperfect channel state information

AbstractDual‐function radar and communication (DFRC) have recently received significant attention as an effective way to alleviate spectrum congestion and reduce system costs. Joint transmit beamforming plays a critical role in DFRC systems, as it can effectively reduce mutual interference and improve the performance of both the radar and communication systems. This paper investigates the problem of robust beamforming design with imperfect channel state information (CSI) to ensure communication performance while optimizing radar performance. Considering elliptically bounded CSI errors, the objective function is designed to minimize the radar loss function, which is related to the radar transmit beam pattern, subject to worst‐case signal‐to‐interference‐plus‐noise ratio constraints at each user, which ensure fairness between users. An efficient algorithm based on semidefinite relaxation and the S‐procedure is proposed to solve the non‐convex problem. Simulation results are presented to illustrate the effectiveness of the proposed robust beamforming scheme, which can reduce the impact of channel errors.

Beamforming Design for BackCom Assisted NOMA Systems

Backscatter communication (BackCom) assisted non-orthogonal multiple access (NOMA) has received significant attention recently and can be applied to Internet of things (IoT). The BackCom system aims to realize energy cooperation among the devices. NOMA is a well-known technique to enable spectrum cooperation among the devices, which motivates the combination of the two techniques. This work focuses on the beamforming design in BackCom NOMA networks, where an uplink data rate maximization problem is formulated with a constraint to guarantee the downlink user’s quality of service requirements. As the formulated optimization problem is not concave, semidefinite relaxation (SDR) is applied to transform the considered problem into a concave form which can be solved efficiently. Simulation results are provided to demonstrate that the proposed algorithm can achieve superior performance over the considered benchmarking scheme.

New convex approaches to general MVDR robust adaptive beamforming problems

AbstractConsider general minimum variance distortionless response (MVDR) robust adaptive beamforming problems based on the optimal estimation for both the desired signal steering vector and the interference‐plus‐noise covariance (INC) matrix. The optimal robust adaptive beamformer design problem is an array output power maximization problem, subject to three constraints on the steering vector, namely, a (convex or nonconvex) quadratic constraint ensuring that the direction‐of‐arrival (DOA) of the desired signal is separated from the DOA region of all linear combinations of the interference steering vectors, a double‐sided norm constraint, and a similarity constraint; as well as a ball constraint on the INC matrix, which is centered at a given data sample covariance matrix. To tackle the nonconvex problem, a new tightened semidefinite relaxation (SDR) approach is proposed to output a globally optimal solution; otherwise, a sequential convex approximation (SCA) method is established to return a locally optimal solution. The simulation results show that the MVDR robust adaptive beamformers based on the optimal estimation for the steering vector and the INC matrix have better performance (in terms of, e.g., the array output signal‐to‐interference‐plus‐noise ratio) than the existing MVDR robust adaptive beamformers by the steering vector estimation only.

Energy Optimization for IRS-Aided SWIPT Under Imperfect Cascaded Channels

In this paper, intelligent reflecting surface is deployed in simultaneous wireless information and power transfer (SWIPT) system to improve the energy harvesting performance. We investigate the robust beamforming design considering the impact of the imperfect cascaded channels. We maximize the minimum received energy among all energy receivers to ensure fairness, while guaranteeing the worst-case information receivers rate requirement. To address with the coupling effect of multiple variables in the optimization problem, the alternate optimization method is utilized to decouple the optimization problem into two sub-problems, and the successive convex approximation and the semidefinite relaxation methods are used to solve the sub-problems. Simulation results reveal that employing IRS into SWIPT system can enhance the energy harvest performance, Additionally, our proposed two algorithms converges rapidly and can guarantee the robustness of the system.

Distributionally Robust Optimal Power Flow via Ellipsoidal Approximation

This paper proposes a distributionally robust joint chance-constrained AC optimal power flow to manage the risk of operational limits violations which are caused by uncertain renewable generation. By determining the dispatch schedule, this approach can help to decrease the risk of renewable curtailment, load shedding, or emergency redispatch in real-time. To model the proposed approach, the renewable uncertainty is first modeled as a distributionally robust ellipsoidal bound based on the Wasserstein metric. This bound is built upon a limited historical renewable forecast errors dataset without any assumption on the probability distribution of uncertainty. Then, this uncertainty bound is adopted within a semidefinite relaxation of the optimal power flow. The system responses to the renewable generation forecast errors are modeled as linear sensitivities, where all conventional generators are responsible for compensating the impacts of renewable forecast errors. Numerical experiments on IEEE 14-bus and 118-bus systems show the validity and scalability of the proposed method. Furthermore, the effectiveness of the proposed approach in terms of meeting probabilistic guarantees, cost-effectiveness and computational time is also demonstrated in the experiments.

IRS-Enabled Secure G2A Communications for UAV System With Aerial Eavesdropping

As one of the most promising new technologies in the upcoming 6G communication, intelligent reflecting surface (IRS) can significantly improve the reliability of wireless transmission and deal with the security threat in the presence of eavesdroppers by smartly reconfiguring the wireless propagation environment. However, existing research mainly focuses on terrestrial communication networks. In contrast, there is not much research on IRS-aided secure unmanned aerial vehicle (UAV) communication problems, especially for ground-to-air (G2A) communication scenarios with air eavesdroppers that will bring greater security threats. In this article, we consider an IRS-assisted G2A communication network with an altitude-dependent Rician fading channel, where the ground base station (BS) transmits legitimate information to the UAV user in the presence of air eavesdroppers. The transmission power, active and passive beamforming, and UAV 3-D trajectory are jointly optimized to maximize the average secrecy rate. Due to the nonconvexity of the optimization problem, the block coordinate descent method is used to solve it. Specifically, the overall optimization problem is divided into four subproblems, and nonconvex subproblems are solved by successive convex approximation and semidefinite relaxation algorithms. Simulation results show that the proposed alternating optimization algorithm has a good convergence performance and can increase the average secrecy rate by 28% compared with the scenario without IRS assistance.

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.

An Energy-Efficient Optimization Method for High-Speed Rail Communication Systems Assisted by Intelligent Reflecting Surfaces (IRS)

This paper proposes an intelligent reflecting surface (IRS)-assisted energy efficiency optimization algorithm to address the problem of energy efficiency (EE) degradation in high-speed rail communication systems caused by line-of-sight link blockages between base stations and trains. The joint optimization of base station beamforming and IRS phase shifts is formulated as a variable-coupled energy efficiency maximization problem, subject to the base station’s transmission power and the IRS unit’s modulus constraints. This is known to be an NP-hard problem, making it challenging to obtain the global optimal solution. To tackle the issue of optimization variable coupling, an alternating optimization is employed to decompose the original problem into two sub-problems: base station beamforming and IRS phase-shift optimization. The Dinkelbach method is utilized to convert the fractional objective function into a difference form; then, the successive convex approximation (SCA) algorithm is applied to transform non-convex constraints into convex ones, which are solved using CVX. The Riemann conjugate gradient (RCG) algorithm can effectively solve the difficult unit module constraint. Finally, an alternating iterative strategy is employed to converge to a suboptimal solution. Our simulation results demonstrate that the proposed algorithm significantly enhances system efficiency with low computational complexity. Specifically, when the number of IRS reflecting elements is 64, the system’s EE is improved by approximately 12.41%, 35.26%, and 37.96% compared to the semi-definite relaxation algorithm, the random phase shift approach, and no IRS scheme, respectively.

Correlations constrained by composite measurements

How to understand the set of correlations admissible in nature is one outstanding open problem in the core of the foundations of quantum theory. Here we take a complementary viewpoint to the device-independent approach, and explore the correlations that physical theories may feature when restricted by some particular constraints on their measurements. We show that demanding that a theory exhibits a composite measurement imposes a hierarchy of constraints on the structure of its sets of states and effects, which translate to a hierarchy of constraints on the allowed correlations themselves. We moreover focus on the particular case where one demands the existence of a correlated measurement that reads out the parity of local fiducial measurements. By formulating a non-linear Optimisation Problem, and semidefinite relaxations of it, we explore the consequences of the existence of such a parity reading measurement for violations of Bell inequalities. In particular, we show that in certain situations this assumption has surprisingly strong consequences, namely, that Tsirelson's bound can be recovered.

Computation bits enhancement for IRS-assisted multi-UAV wireless powered mobile edge computing systems

Mobile edge computing (MEC) and wireless energy transfer are two important paradigms to improve the computation bits and provide more cost-effective energy for low-power internet of things (IoT) devices. However, the performance of energy transfer and task offloading is significantly affected by propagation loss, and hence the links between IoT devices and transmitters are frequently blocked. To address this issue, in this paper, an intelligent reflecting surfaces (IRS) system is utilized to enhance the energy harvesting and task offloading performances in a multi-unmanned aerial vehicle (UAV)-assisted MEC system. Also, a power beacon (PB) is deployed in the coverage area to provide suitable and stable energy for UAVs via a laser charging system. The sum computation bits of all IoT devices are maximized by jointly optimizing transmit power, time allocation, the phase shift in the energy transfer stage, the phase shift in the task offloading stage, CPU frequency of IoT devices, and UAVs' trajectory. An alternate search method (ASM) is proposed to tackle the non-convexity of the formulated problem in which the closed-form expressions of transmit power, time allocation, the phase shift in the task offloading stage, and CPU frequency are derived. Also, the semidefinite relaxation (SDR) approach and successive convex approximation (SCA) methods are exploited to obtain the phase shifts in the energy transfer stage and UAVs' trajectory via CVX optimizer, respectively. The numerical evaluations confirm the performance gain of the proposed IRS-assisted multi-UAV MEC system compared to existing benchmark designs.

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.

Near-Field Integrated Sensing and Communications

A near-field integrated sensing and communications (ISAC) framework is proposed, which introduces an additional distance dimension for both sensing and communications compared to the conventional far-field system. In particular, the Cramer-Rao bound for the near-field joint distance and angle sensing is derived, which is minimized subject to the minimum communication rate requirement of each user. Both fully digital antennas and hybrid digital and analog antennas are investigated. For fully digital antennas, a globally optimal solution of the ISAC waveform is obtained via semidefinite relaxation. For hybrid antennas, a high-quality solution is obtained through two-stage optimization. Numerical results demonstrate the performance gain introduced by the additional distance dimension of the near-field ISAC over the far-field ISAC.

Energy-Efficient Optimization in Distributed Massive MIMO Systems for Slicing eMBB and URLLC Services

The fifth generation (5G) communication system aims to support diverse services such as enhanced mobile broadband (eMBB) and ultra-reliable and low-latency communication (URLLC). In order to enable the coexistence of eMBB and URLLC services on a common physical infrastructure, network slicing incorporated in the distributed massive multiple-input multiple-output (DM-MIMO) system is regarded as a promising solution. In this paper, a non-orthogonal slicing scheme is proposed to improve the spectral efficiency, and the short packet transmission is adopted for URLLC to meet the low latency requirement. Through a joint optimization of beamforming and remote radio unit (RRU) selection, we investigate the energy efficiency (EE) maximization problem for the downlink DM-MIMO system. The formulated problem is a mixed integer nonlinear program (MINLP) that we solve by applying some efficient approaches, such as the Dinkelbach method, the reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula> -norm and difference of convex (DC) programming. By combining these approaches in one iteration, a double-loop procedure based on semi-definite relaxation (SDR) and successive convex approximation (SCA) is employed to find the suboptimal solution of the problem. Simulation results show that the proposed scheme significantly improves the EE of the DM-MIMO system and efficiently manages resource allocation.

Passive Reflection Optimization for IRS-Aided Multicast Beamforming With Discrete Phase Shifts

Intelligent reflecting surface (IRS) can bring promising advantages to enhance the communication system performance by reconfiguring wireless channels dynamically. The design of passive IRS reflection has attracted high attention and most existing works have considered continuous phase shift for IRS reflection. However, this is difficult to realize in practice due to hardware limitations and discrete phase shifts are applied for practical IRSs instead. In this letter, the information multicast beamforming problem in an IRS-aided multi-user system is considered, where the minimum receive signal-to-noise-ratio among the users is maximized by optimizing the IRS reflections with discrete phase shifts. By leveraging semi-definite relaxation (SDR) and gradient descent/ascent (GDA), two solutions are presented with high/low computational complexity, respectively. Simulation results show the efficacy of the proposed GDA-based algorithm as compared to the SDR-based and other benchmark schemes.

Source Localization by Frequency Measurements in Unknown Signal Propagation Speed Environments

Signal propagation speed may not be available in practical localization scenarios. This paper addresses both the moving and stationary source localization problems by using frequency measurements when the signal propagation speed is unavailable. The task is fulfilled by exploiting the Doppler frequency shift coming from the relative motion between the source and a network of mobile sensors. Owing to the complicated nonlinear measurement model and the absence of the knowledge about signal propagation speed, it is difficult to conduct localization. To address this problem, we first transform the measurement model to a tractable form, from which to formulate a constrained weighted least squares (CWLS) problem. Afterwards, we propose two methods to solve the non-convex CWLS problem. The first method relaxes the CWLS problem into a semidefinite programming (SDP) problem by applying semidefinite relaxation (SDR). The second method adopts the alternating estimation procedure by utilizing the prior information about the nominal value of the signal propagation speed. Two subproblems are formulated and solved in an alternate manner, one in estimating the source position and velocity by applying SDR and the other the signal propagation speed by an explicit expression. Furthermore, we conduct the mean square error (MSE) analysis to show that the CWLS solution is able to reach the Cramér-Rao lower bound (CRLB) performance. Simulation results validate the expected performance of the proposed methods.