Semidefinite Relaxation Research Articles

Abstract This paper proposes a method for enhancing the security of wireless communication systems aided by multiple reconfigurable intelligent surfaces (RISs). The method considers not only the interactions between multiple RISs and the resulting multi-channel cascades, but also the potential eavesdropping threats to legitimate user communications. To solve the problem of maximizing secrecy rate, this paper proposes an efficient alternating optimization (AO) algorithm. The algorithm achieves joint optimization of base station beamforming and RIS phase shifts by iteratively applying sequential convex approximation (SCA) and semidefinite relaxation (SDR) techniques. The algorithm can effectively transform the complex non-convex optimization problem into a series of subproblems, and then iteratively optimize these subproblems alternately to ultimately obtain a high-quality solution to the original problem. The simulation results show that the multi-RIS aided communication system greatly improves the security performance compared to the single RIS and dual RIS system. Additionally, a comparative evaluation with three other algorithms from the literatures reveals that the proposed method outperforms existing solutions under identical parameter settings, highlighting the superiority of multi-RIS co-optimization in mitigating eavesdropping threats and enhancing information confidentiality. At the same time, we also compare the impacts of real-world situations, such as imperfect channel state information and RIS discrete phase shifts, on the security performance of multi-RIS systems. This reserach provides valuable theoretical guidance and research directions for the future implementation of multi-RIS systems in real-world scenarios.

ABSTRACTAiming to promise timely data delivery and quantify the information freshness of unmanned surface vehicles (USVs), age of information (AoI) is proposed as a novel metric regarding exploring implementations for reconfigurable intelligent surface (RIS)–assisted unmanned aerial vehicle (UAV)–USV multiaccess edge computing network. In this paper, a set of RIS‐carried UAVs serves USVs via time division multiple access; each RIS is capable of delivering a single reflection per USV within its service duration. USV long‐term time‐averaged AoI (AAoI) minimization problem is investigated under USV service duration indicators, UAV‐mounted RIS phase shift vector, terrestrial base station (TBS) beamforming vector, and UAV trajectory constraints. To efficiently solve the formulated problem, Lyapunov framework is applied to decompose the original problem into an array of per‐slot problems, where each of which can be divided into numerous subproblems, for example, TBS beamforming vector subproblem, RIS phase shift subproblem, and the joint UAV trajectories and USV service duration indicator subproblem. Then, each subproblem can be solved using the proposed successive convex approximation, semidefinite relaxation method, and the enhanced differential evolution algorithm iteratively. Consequently, one can efficiently obtain the feasible solution. The proposed solution reduces USV AAoI by up to 55% while maintaining lower UAV power consumption compared with benchmarks. Also, the proposed solution can promise adequate network queue backlogs under typical USV task data size.

We study relaxations of entanglement-assisted quantum channel coding and establish that non-signaling assistance and a natural semi-definite programming relaxation — termed meta-converse — are equivalent in terms of success probabilities. We then present a rounding procedure that transforms any non-signaling-assisted strategy into an entanglement-assisted one and prove an approximation ratio of (1–e−1) in success probabilities for the special case of measurement channels. For fully quantum channels, we give a weaker (dimension dependent) approximation ratio, that is nevertheless still tight to characterize the strong converse exponent of entanglement-assisted channel coding [Li and Yao, IEEE Tran. Inf. Theory (2024)]. Our derivations leverage ideas from position-based coding, quantum decoupling theorems, the matrix Chernoff inequality, and input flattening techniques.

We study correlations in the prepare-and-measure scenario when quantum communication is constrained by photon-number statistics. Such constraints are natural and practical control parameters for semi-device-independent certification in optical platforms. To analyse these scenarios, we show how semidefinite programming relaxations for noncommutative polynomial optimization can be used to bound the set of quantum correlations under restrictions on the photon-number distribution. The practicality of this method is demonstrated by computing optimal performance bounds on several well-known communication tasks. We then apply the method to the certification of semi-device-inpependent random number generation protocols and show how to bound the conditional Shannon entropy. We showcase this versatile tool by improving randomness extraction in established protocols based on coherent states and homodyne measurements.

Existing studies related to active intelligent reflecting surface (IRS)-assisted integrated sensing and communication (ISAC) systems generally focus on sensing performance optimization in downlink communication scenarios, and there lacks research that explores the potential of active IRS to boost the communication performance under the sensing performance constraints in more complex uplink communication scenarios. Inspired by the current situation mentioned above, this paper constructs the uplink communication rate maximization problem for active IRS-assisted uplink ISAC system. With the aim of solving the constructed highly non-convex problem involving strong coupling among multiple optimization variables, a joint beamforming and transmit power control strategy is proposed in this paper. The Lagrangian dual transformation and fractional programming methods are first applied to simplify the objective function, and then the optimization variables are solved iteratively by alternating optimization algorithm, maximization-minimization algorithm, and semidefinite relaxation algorithm. Simulation analysis demonstrates that compared to the passive IRS benchmark strategy and the two random configuration strategies, the strategy presented in this paper has the ability to achieve 27.3%, 9.5% and 11.4% user uplink communication rate enhancement ratios, respectively. Additionally, under a fixed total power budget, increasing the maximum transmit power of the dual functional radar-communication base station may impair the communication performance.

The high-proportion integration of renewable energy sources, represented by wind power and photovoltaics, into active distribution networks (ADNs) can effectively alleviate the pressure associated with advancing China’s dual-carbon goals. However, the high uncertainty in renewable energy output leads to increased system voltage fluctuations and localized voltage violations, posing safety challenges. Consequently, research on optimal dispatch for ADNs with a high penetration of renewable energy has become a current focal point. This paper provides a comprehensive review of research in this domain over the past decade. Initially, it analyzes the voltage impact patterns and control principles in distribution networks under varying levels of renewable energy penetration. Subsequently, it introduces optimization dispatch models for ADNs that focus on three key objectives: safety, economy, and low carbon emissions. Furthermore, addressing the challenge of solving non-convex and nonlinear models, the paper highlights model reformulation strategies such as semidefinite relaxation, second-order cone relaxation, and convex inner approximation methods, along with summarizing relevant intelligent solution algorithms. Additionally, in response to the high uncertainty of renewable energy output, it reviews stochastic optimization dispatch strategies for ADNs, encompassing single-stage, two-stage, and multi-stage approaches. Meanwhile, given the promising prospects of large-scale deep reinforcement learning models in the power sector, their applications in ADN optimization dispatch are also reviewed. Finally, the paper outlines potential future research directions for ADN optimization dispatch.

Terahertz (THz) communications and simultaneous wireless information and power transfer (SWIPT) hold the potential to energize battery-less Internet-of-Things (IoT) devices while enabling multi-gigabit data transmission. However, severe path loss, blockages, and rectifier nonlinearity significantly hinder both throughput and harvested energy. Additionally, high-power THz beams pose safety concerns by potentially exceeding specific absorption rate (SAR) limits. We propose a sensing-adaptive power-focusing (APF) framework in which a reconfigurable intelligent surface (RIS) embeds low-rate THz sensors. Real-time backscatter measurements construct a spatial map used for the joint optimisation of (i) RIS phase configurations, (ii) multi-tone SWIPT waveforms, and (iii) nonlinear power-splitting ratios. A weighted MMSE inner loop maximizes the data rate, while an outer alternating optimisation applies semidefinite relaxation to enforce passive-element constraints and SAR compliance. Full-stack simulations at 0.3 THz with 20 GHz bandwidth and up to 256 RIS elements show that APF (i) improves the rate-energy Pareto frontier by 30-75% over recent adaptive baselines; (ii) achieves a 150% gain in harvested energy and a 440 Mbps peak per-user rate; (iii) reduces energy-efficiency variance by half while maintaining a Jain fairness index of 0.999;; and (iv) caps SAR at 1.6 W/kg, which is 20% below the IEEE C95.1 safety threshold. The algorithm converges in seven iterations and executes within <3 ms on a Cortex-A78 processor, ensuring compliance with real-time 6G control budgets. The proposed architecture supports sustainable THz-powered networks for smart factories, digital-twin logistics, wire-free extended reality (XR), and low-maintenance structural health monitors, combining high-capacity communication, safe wireless power transfer, and carbon-aware operation for future 6G cyber-physical systems.

A novel algorithm was proposed for solving the max-cut problem, which seeks to identify the cut with the maximum weight in a given graph. Our technique is based on the bundle approach, applied to a newly formulated semidefinite relaxation. This research establishes the theoretical convergence of our approximation technique and presents the numerical results obtained on several large-scale graphs from the BiqMac library, specifically with 100, 250, and 500 nodes. The resulting performance was compared with that produced by two alternative semidefinite programming-based approximation methods, namely the BiqMac and BiqBin solvers, by comparing the CPU time and the number of function calls. The primary objective of this work was to enhance the scalability and computational efficiency in solving the max-cut problem, particularly for large-scale graph instances. Despite the development of numerous approximation algorithms, a persistent challenge lies in effectively handling problems with a large number of constraints. Our algorithm addresses this by integrating a novel semidefinite relaxation with a bundle-based optimization framework, achieving faster convergence and fewer function calls. These advancements mark a meaningful step forward in the efficient resolution of NP-hard combinatorial optimization problems.

Abstract Unmanned aerial Vehicle (UAV) enabled wireless powered communication network (WPCN) often experience poor energy delivery on the downlink and restricted data rates on the uplink. We tackle these issues by deploying an intelligent reflecting surface (IRS) and a clustered non-orthogonal multiple access (NOMA) scheme within a UAV-assisted WPCN. A sum-throughput maximization is posed that simultaneously determines the UAV’s flight trajectory, IRS phase configuration, user transmit powers, and slot-time division. The resulting non-convex program is split into three manageable blocks and addressed through an alternating framework that leverages semidefinite relaxation and successive convex approximation. Simulations demonstrate sizable throughput improvements over conventional designs.

This paper investigates a multi-input single-output (MISO) wireless information and power transfer (SWIPT) communication system based on intelligent reflecting surfaces (IRS) for multiple users. The system includes a base station with a multi-antenna array that simultaneously transmits energy and data to single-antenna users, where users communicate through power splitting (PS) technology. This approach simultaneously processes data reception and energy collection, introducing new energy efficiency metrics aiming to achieve equilibrium between transmission rate and power harvesting capacity. Through the joint optimization of the base station’s active beamforming, IRS passive beamforming, and PS proportion of users. Considering the problem’s nonlinear complexity, our approach initially constructs the minimum upper bound to derive a fractional function, which leads to a fractional function that can be effectively tackled utilizing the Dinkelbach algorithm. Thereafter, a cyclic resolution approach is used to solve two subproblems separately. For the first subproblem, upper bound minimization and semi-definite relaxation are employed; for the second subproblem, a block coordinate descent search method is used to improve system efficiency. Numerical trials confirm our methodology’s superior performance compared to benchmark algorithms, with energy efficiency improved by 13% when compared to systems without IRS.

In this paper, we investigate a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-assisted non-orthogonal multiple access (NOMA) communication system where the STAR-RIS is mounted on an unmanned aerial vehicle (UAV) with adjustable altitude. Due to severe blockages in urban environments, direct links from the base station (BS) to users are assumed unavailable, and signal transmission is realized via the STAR-RIS. We formulate a joint optimization problem that maximizes the system sum rate by jointly optimizing the UAV’s altitude, BS beamforming vectors, and the STAR-RIS phase shifts, while considering Rician fading channels with altitude-dependent Rician factors. To tackle the maximum achievable rate problem, we adopt a block-wise optimization framework and employ semidefinite relaxation and gradient descent methods. Simulation results show that the proposed scheme achieves up to 22% improvement in achievable rate and significant reduction in bit error rate (BER) compared to benchmark schemes, demonstrating its effectiveness in integrating STAR-RIS and UAV in NOMA networks.

This paper aims to facilitate the integration of integrated sensing and communication (ISAC) and symbiotic radio (SR), which studies a reconfigurable intelligent surface (RIS)-assisted ISAC-SR system in single-user and multi-user scenarios. In the ISAC-SR system, a base station (BS) transmits the downlink signal to the user while sensing multiple targets. The RIS reflects the BS signal by adjusting its reflection coefficient and embeds its data for user transmission. We aim to maximize the communication rate of RIS by optimizing the transmit beamformers and RIS phase shift matrix while meeting the minimum quality of service (QoS) requirement for BS data transmission and targets sensing. Due to the non-convexity of the formulated problem, in the single-user case, we develop an alternating optimization (AO) algorithm using a semidefinite relaxation (SDR) and the Dinkelbach method to transform it into a convex problem. In the multi-user case, we leverage SDR and successive convex approximation (SCA) to obtain a suboptimal solution and prove that a rank-one solution is guaranteed. Numerical results validate the effectiveness of our proposed schemes.

In existing UAV communication systems incorporating active reconfigurable intelligent surfaces (ARIS), hardware impairments (HIs) in transceivers and thermal noise from active units are frequently overlooked. This oversight leads to signal distortion at user terminals and excessive system power consumption. To address these challenges, this study proposes a solution to enhance signal transmission quality by jointly optimizing the dynamic topology of an ARIS and the average achievable rate (AAR) for users. Firstly, to mitigate inter-element interference in the ARIS, a hybrid genetic algorithm (HGA) is proposed. This algorithm integrates the global search capability of genetic algorithms with the local optimization efficiency of the tabu search algorithm (TSA) to iteratively derive the optimal dynamic topology matrix for the ARIS. Secondly, to maximize the AAR by increasing received signal power, fractional programming with quadratic transformation is combined with semidefinite relaxation and successive convex approximation to tackle the highly coupled multi-variable non-convex fractional programming problem. This approach transforms subproblems into single-variable convex optimizations. Finally, an alternating iterative method is employed to solve the convex subproblems, yielding a suboptimal solution. The simulation results demonstrate that the proposed UAV-ARIS dynamic topology optimization scheme improves the system AAR by 27–130% and energy efficiency by 19–32% compared with conventional schemes, while ensuring flexible deployment and high energy efficiency.

Integrated sensing and communication (ISAC) can improve the energy harvesting (EH) efficiency of simultaneous wireless information and power transfer (SWIPT)-assisted IoT networks by enabling precise energy harvest. However, the transmit power is increased in the hybrid system due to the fact that the sensing signals are required to be transferred in addition to the communication data. This paper aims to tackle this issue by formulating an optimization problem to minimize the transmit power of the base station (BS) under a nonlinear EH model, considering the coexistence of power-splitting users (PSUs) and time-switching users (TSUs), as well as the beamforming vector associated with PSUs and TSUs. A two-layer algorithm based on semi-definite relaxation is proposed to tackle the complexity issue of the non-convex optimization problem. The global optimality is theoretically analyzed, and the impact of each parameter on system performance is also discussed. Numerical results indicate that TSUs are more prone to saturation compared to PSUs under identical EH requirements. The minimal required transmit power under the nonlinear EH model is much lower than that under the linear EH model. Moreover, it is observed that the number of TSUs is the primary limiting factor for the minimization of transmit power, which can be effectively mitigated by the proposed algorithm.

We implement a bootstrap method that combines stationary state conditions, thermal inequalities, and semidefinite relaxations of matrix logarithm in the ungauged one-matrix quantum mechanics, at finite rank N as well as in the large N limit, and determine finite temperature observables that interpolate between available analytic results in the low and high temperature limits respectively. We also obtain bootstrap bounds on thermal phase transition as well as preliminary results in the ungauged two-matrix quantum mechanics.

A Semidefinite Relaxation for Sums of Heterogeneous Quadratic Forms on the Stiefel Manifold

Semi-definite relaxation based beamforming design for double-RIS aided MISO system with limited feedback

ABSTRACTThis paper investigates the application of intelligent reflecting surfaces (IRS) in secure wireless communication under multi‐user and multi‐eavesdropper scenarios, focusing on addressing the challenges posed by imperfect channel state information (CSI). In this context, multiple users receive confidential information via a multi‐antenna access point (AP), while the eavesdroppers' channels may be stronger than the legitimate communication channels and exhibit spatial correlation. To improve secure communication efficiency, a unified optimization method is introduced, combining AP signal direction adjustments and IRS reflection control to boost the confidentiality rate of authorized communication pathways. Considering the challenges of imperfect CSI and the presence of multiple users and eavesdroppers, the paper employs alternating optimization and semidefinite relaxation (SDR) methods, combined with an iterative hybrid optimization (IHO) algorithm, to solve the optimization problem and obtain high‐quality suboptimal solutions. Simulation outcomes reveal that the suggested approach markedly enhances confidentiality rates in multi‐user and multi‐eavesdropper scenarios compared to traditional benchmark models, effectively mitigating the impact of imperfect CSI.

Abstract We study the optimization landscape of a smooth nonconvex programme arising from synchronization over the two-element group $\mathbf{Z}_{2}$, that is, recovering $z_{1}, \dots , z_{n} \in \{\pm 1\}$ from (noisy) relative measurements $R_{ij} \approx z_{i} z_{j}$. Starting from a max-cut-like combinatorial problem, for integer parameter $r \geq 2$, the nonconvex problem we study can be viewed both as a rank-$r$ Burer–Monteiro factorization of the standard max-cut semidefinite relaxation and as a relaxation of $\{ \pm 1 \}$ to the unit sphere in $\mathbf{R}^{r}$. First, we present deterministic, non-asymptotic conditions on the measurement graph and noise under which every second-order critical point of the nonconvex problem yields exact recovery of the ground truth. Then, via probabilistic analysis, we obtain asymptotic guarantees for three benchmark problems: (1) synchronization with a complete graph and Gaussian noise, (2) synchronization with an Erdős–Rényi random graph and Bernoulli noise and (3) graph clustering under the binary symmetric stochastic block model. In each case, we have, asymptotically as the problem size goes to infinity, a benign nonconvex landscape near a previously established optimal threshold for exact recovery; we can approach this threshold to arbitrary precision with large enough (but finite) rank parameter $r$. In addition, our results are robust to monotone adversaries.

A wireless-powered communication network (WPCN) provides sustainable power solutions for energy-intensive Internet of Things (IoT) devices in remote or inaccessible locations. This technology is particularly beneficial for applications in smart transportation and smart cities. Nevertheless, WPCN experiences performance degradation due to severe path loss and inefficient long-range energy and information transmission. To address the limitation, this paper investigates an intelligent reflecting surface (IRS)-enhanced multi-cell WPCN integrated with non-orthogonal multiple access (NOMA). The emerging IRS technology mitigates propagation losses through precise phase shift adjustments with symmetric reflective components. Asymmetric resource utilization in symmetric downlink and uplink transmissions is crucial for optimal throughput and quality of service. Alternative iterations are employed to optimize time allocation and IRS phase shifts in both downlink and uplink transmissions. This approach allows for the attainment of maximum sum throughput. Specifically, the phase shifts are optimized using two algorithms called semidefinite relaxation (SDR) and block coordinate descent (BCD). Our simulations reveal that integrating the IRS into multi-cell NOMA-WPCN enhances user throughput. This surpasses the performance of traditional multi-cell WPCN. In addition, the coordinated deployment of multiple hybrid access points (HAPs) and IRS equipment can expand communications coverage and network capacity.