Discrete Constraints Research Articles

Joint Active and Passive Beamforming for RIS-Aided MIMO Communications With Low-Resolution Phase Shifts

Practical hardware limitations often impose a reduced number of available phase shifts at the elements of a reconfigurable intelligent surface (RIS). Most works often assume continuous phase-shits at the RIS elements for the transmit and passive beamforming optimization, which can lead to substantial performance loss. Therefore, to harvest the gains of RIS-assisted multi-stream multiple-input multiple-output (MIMO) communications under realistic phase shifts, this letter proposes a problem formulation for the maximization of the achievable rate over the transmit precoder and RIS elements, which avoids an explicit discrete constraint while still incorporating its effect. To efficiently tackle the resulting problem when considering large arrays and RIS panels, an iterative algorithm is derived which comprises a sequence of simple projections. Simulation results demonstrate that the proposed design can be very effective, especially with low-resolution phase-shifts.

Label embedding asymmetric discrete hashing for efficient cross-modal retrieval

Given the exponential growth of multimedia data, how to swiftly and accurately retrieve information has grown in popularity. Among retrieval techniques, supervised hashing stands out due to its low memory footprint and relatively precise accuracy. Prior theoretical studies often inserted high-order tags into binary code learning, treating them as independent entities. Nevertheless, such approaches frequently neglect the latent category correlations revealed by the label information. Additionally, in terms of optimization, some algorithms employ a bit-by-bit scheme, leading to time-consuming, while others adopt a relaxation-based strategy, producing quantization inaccuracy. To address these issues, we formulate a novel, two-step hashing strategy, termed Label Embedding Asymmetric Discrete Hashing (LEADH). In this study, we provide an asymmetric technique to protect the discrete binary code constraints. Compared with the symmetric model, this method significantly reduces time consumption. In particular, a label-binary mutual mapping architecture is specifically recommended. This model can fully explore and utilize multi-label semantic information to provide better discriminative learned binary codes. Furthermore, to minimize quantization errors, an efficient and effective discrete optimization module based on augmented Lagrangian multipliers is elaborately designed. Extensive experimentation and theoretical study support our model’s superiority. Compared to the sub-optimal method, our LEADH achieves an improvement of 2.6%, 1.8%, and 1.1% on Wiki, MIRFlickr, and NUS-WIDE, respectively.

Fast Homotopy for Spacecraft Rendezvous Trajectory Optimization with Discrete Logic

This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods require binary variables and mixed-integer programming (MIP), which is prohibitively slow and computationally expensive. This paper proposes a faster and computationally cheaper algorithm that can produce locally optimal solutions in seconds. This is achieved by blending sequential convex programming and numerical continuation into a single iterative solution process. The algorithm approximates discrete logic constraints with smooth functions and uses a homotopy parameter to control the accuracy of this approximation. The homotopy parameter is updated such that, by the time the algorithm converges, the smooth approximations enforce the exact discrete logic. The effectiveness of this approach is numerically demonstrated for a realistic rendezvous scenario inspired by the Apollo Transposition and Docking maneuver. In less than 15 s of cumulative solver time, the algorithm finds a fuel-minimizing trajectory that obeys the following discrete logic constraints: thruster minimum impulse-bit, range-triggered approach cone, and range- triggered plume impingement. The optimized trajectory uses significantly less fuel than reported NASA design targets.

Unsupervised soft-to-hard hashing with contrastive learning

In order to optimize a binary hash code with deep neural networks, greedy optimization with the discrete constraint relaxation is widely used due to its efficiency. However, noises from skipping gradients may destabilize the optimization in contrastive learning since the noises are superimposed on embedding from two distorted views. To reduce such undesirable impact from the noises, we propose a novel soft-to-hard hashing method by introducing an auxiliary loss in the penultimate block of the model based on the information bottleneck principle, which not only propagates the correlations between positives but also makes the embedding to be non-redundant to the samples in a high-dimensional continuous space. Our method beats the state-of-the-art result on three public datasets and demonstrates how soft code can help greedy back-propagation find a better solution during optimization. Another benefit of our method is that it enables a joint training of unsupervised representational learning and hash code generation, and obtains 5.4% mAP gain over conventional step-by-step training on the CIFAR-10 dataset.

Active RIS Assisted Rate-Splitting Multiple Access Network: Spectral and Energy Efficiency Tradeoff

With the increasing demand of high data rate and massive access in both ultra-dense and industrial Internet-of-things networks, spectral efficiency (SE) and energy efficiency (EE) are regarded as two important and inter-related performance metrics for future networks. In this paper, we investigate a novel integration of rate-splitting multiple access (RSMA) and reconfigurable intelligent surface (RIS) into cellular systems to achieve a desirable tradeoff between SE and EE. Different from the commonly used passive RIS, we adopt reflection elements with active load to improve a newly defined metric, called resource efficiency (RE), which is capable of striking a balance between SE and EE. This paper focuses on the RE optimization by jointly designing the base station (BS) transmit precoding and RIS beamforming (BF) while guaranteeing the transmit and forward power budgets of the BS and RIS, respectively. To efficiently tackle the challenges for solving the RE maximization problem due to its fractional objective function, coupled optimization variables, and discrete coefficient constraint, the formulated nonconvex problem is solved by proposing a two-stage optimization framework. For the outer stage problem, a quadratic transformation is used to recast the fractional objective into a linear form, and a closed-form solution is obtained by using auxiliary variables. For the inner stage problem, the system sum rate is approximated into a linear function. Then, an alternating optimization (AO) algorithm is proposed to optimize the BS precoding and RIS BF iteratively, by utilizing the penalty dual decomposition (PDD) method. Simulation results demonstrate the superiority of the proposed design compared to other benchmarks.

Hardware-Impaired RIS-Assisted mmWave Hybrid Systems: Beamforming Design and Performance Analysis

Reconfigurable intelligent surface (RIS) has been envisioned as an innovative technology to assist millimeter wave (mmWave) communications. Thanks to both advantages of low hardware cost and low power consumption, the hybrid transceiver structure also becomes an integral component of mmWave systems. However, due to practical limitations of hardware components, the RIS-assisted mmWave communications usually suffer unavoidable hardware impairments (HWIs). In this paper, we aim to minimize the (sum) MSE and maximize the average rate of the hardware-impaired RIS-assisted point-to-point mmWave MIMO system, respectively, by jointly optimizing the hybrid transceiver and RIS reflection coefficients under the realistic discrete phase shift constraints. We firstly consider the single-antenna user case and propose efficient alternating optimization (AO) algorithms to solve the two intractable problems. A binary-oriented exact penalty (BEP) method is developed for the involved discrete optimization, which is able to strike a good trade-off between performance and complexity. Moreover, we analyze the optimality of AO algorithms under the cascaded line-of-sight (LoS) channel condition, and reveal both the MSE floor effect and average rate saturation effect in the high-SNR regime. The above studies are then extended to the general multi-antenna user case, where a low-complexity two-phase scheme with the aim of creating the favorable RIS-cascaded channel in the first phase and enhancing system performance in the second phase is proposed. This two-phase scheme is also demonstrated to attain the optimal performance in the LoS scenario. Numerical results validate our theoretical analysis and illustrate superior performance of the proposed algorithms over various benchmark schemes.

Convergence of a discretization of the Maxwell–Klein–Gordon equation based on finite element methods and lattice gauge theory

AbstractThe Maxwell–Klein–Gordon equations are a set of coupled nonlinear time‐dependent wave equations, used to model the interaction of an electromagnetic field with a particle. The solutions, expressed with a magnetic vector potential, are invariant under gauge transformations. This characteristic implies a constraint on the solution fields that might be broken at the discrete level. In this article, we propose and study a constraint preserving numerical scheme for this set of equations in dimension 2. At the semidiscrete level, we combine conforming Finite Element discretizations with the so‐called Lattice Gauge Theory to design a compatible gauge invariant discretization, leading to preservation of a discrete constraint. Relying on energy techniques and compactness arguments, we establish the convergence of this semidiscrete scheme, without a priori knowledge of the solution. Finally, at the fully discrete level, we propose a compatible explicit time‐integration strategy of leapfrog type. We implement the resulting fully discrete scheme and provide assessment on academic scenarios.

Elaborate multi-task subspace learning with discrete group constraint

In multi-task learning (MTL), multiple related tasks can be learned simultaneously under the shared information to improve the generalization performance. However, most of MTL methods assume that all the learning tasks are related indeed and appropriate for joint learning. In some real situations, this assumption may not hold and further lead to the problem of negative transfer. Therefore, in this paper, we not only focus on researching the problem of robustly learning the common feature structure shared by tasks, but also discriminate with which tasks one task should share. By combining with the idea of subspace learning, we propose an elaborate multi-task subspace learning model (EMTSL) with discrete group structure constraint, which can cluster the learned tasks into a set of groups. By introducing the Schatten p-norm instead of trace norm, our model EMTSL can better approximate the low-rank constraint and also avoid the trivial solution. Furthermore, we design an efficient algorithm based on the re-weighted method to solve the proposed model. In addition, the convergence analysis of our algorithm is given in this paper. Experimental results on both synthetic and real-world datasets demonstrate the superiority of our method.

IRS-Assisted Physical Layer Security in MIMO-NOMA Networks

In this letter, we propose deploying the intelligent reflecting surface (IRS) to enhance the physical layer security in non-orthogonal multiple access (NOMA). The secrecy sum-rate of IRS-assisted multiple-input multiple-output (MIMO) NOMA is maximized in the presence of an eavesdropper. Because of the discrete unit-modulus constraint and the nonconvex property, the secrecy sum-rate maximization problem is hard to solve. We reformulate the original problem into an equivalent parameterized optimization using rotation matrices and apply the particle swarm algorithm for global optimization. Simulation results verify that the performance of the proposed algorithm is close to the secrecy capacity of the channel, realized by exhaustive search, and outperforms other methods like alternating optimization and zero-forcing in terms of complexity and achievable rates.

Weighted Sum-Rate Maximization for STAR-RISs-Aided Networks With Coupled Phase-Shifters

In this letter, we investigate the optimization in a simultaneously transmitting and reflecting reconfigurable intelligent surface-enabled network with a coupled coefficient model, where the transmit beamforming (BF) and the transmitting and reflecting coefficients (TRCs) are jointly designed. Our goal is to maximize the weighted sum rate for multiple users, subject to the discrete coefficient constraint. To solve the nonconcave objective, we develop an alternating optimization method, where the BF can be obtained in a closed form by the bisection method, and the TRCs are solved by the elementwise optimization approach. Simulation results demonstrate the superiority of the proposed algorithm.

Understand-Before-Talk (UBT): A Semantic Communication Approach to 6G Networks

In Shannon theory, semantic aspects of communication were identified but considered irrelevant to the technical communication problems. Semantic communication (SC) techniques have recently attracted renewed research interests in (6G) wireless because they have the capability to support an efficient interpretation of the significance and meaning intended by a sender (or accomplishment of the goal) when dealing with multi-modal data such as videos, images, audio, text messages, and so on, which would be the case for various applications such as intelligent transportation systems where each autonomous vehicle needs to deal with real-time videos and data from a number of sensors including radars. A notable difficulty of existing SC frameworks lies in handling the discrete constraints imposed on the pursued semantic coding and its interaction with the independent knowledge base, which makes reliable semantic extraction extremely challenging. Therefore, we develop a new lightweight hashing-based semantic extraction approach to the SC framework, where our learning objective is to generate one-time signatures (hash codes) using supervised learning for low latency, secure and efficient management of the SC dynamics. We first evaluate the proposed semantic extraction framework over large image data sets, extend it with domain adaptive hashing and then demonstrate the effectiveness of "semantics signature" in bulk transmission and multi-modal data.

A Linear Time Algorithm for the Optimal Discrete IRS Beamforming

It remains an open problem to find the optimal configuration of phase shifts under the discrete constraint for intelligent reflecting surface (IRS) in polynomial time. The above problem is widely believed to be difficult because it is not linked to any known combinatorial problems that can be solved efficiently. The branch-and-bound algorithms and the approximation algorithms constitute the best results in this area. Nevertheless, this work shows that the global optimum can actually be reached in linear time on average in terms of the number of reflective elements (REs) of IRS. The main idea is to geometrically interpret the discrete beamforming problem as choosing the optimal point on the unit circle. Although the number of possible combinations of phase shifts grows exponentially with the number of REs, it turns out that there are only a linear number of circular arcs that possibly contain the optimal point. Furthermore, the proposed algorithm can be viewed as a novel approach to a special case of the discrete quadratic program (QP).

DG-integrated stochastic multiyear distribution expansion planning considering fault current-limiting high-temperature superconducting cables

In this paper, the authors present a new stochastic multiyear framework for distribution expansion planning (DEP) that integrates fault current-limiting high-temperature superconducting cables (FCL-HTSCs) and distributed generations (DGs). The proposed framework, from a new perspective, is capable of analyzing and comparing the efficiency of the FCL-HTSCs with other, more generic cables under different short-circuit conditions. The objective function to be minimized isthe net present value of the total investment costs for reinforcing and/or installing substations, feeders, FCL-HTSCs, and DGs, as well as operation and maintenance costs. The framework also considers Kirchhoff’s current and voltage laws, operational limits on equipment capacities, voltage limits, as well as financial and discrete logical constraints. As a comprehensive overview, the authors have developed: (i) a graph-based bi-conditional scheme to ensure radiality requirements and (ii) a multi-horizon fractional information-gap decision theory (MH-FIGDT) to address the stochastic nature of anticipated load demand, power production of the DGs, and a capital expenditure budget. The resulting mixed-integer nonlinear optimization problem is solved by an integer-coded melody search algorithm (ICMSA) empowered with a multi-computational-stage multi-dimensional multiple-homogeneous structure that offers better performance in diversification and exploration. Case studies using the standard 27-node and realistic, large-scale 104-node distribution grids are provided here in order to show the effectiveness of the proposed framework. Based on simulation results, several conclusions can be drawn: (i) the MH-FIGDT critical cost and/or MH-FIGDT critical deviation coefficient chosen by the distribution grid operator play a key role in achieving robust expansion plans against the given uncertainty set; (ii) the incorporation of the FCL-HTSCs into the DEP problem offers a satisfactory compromise between the required amount and capacity of the equipment and total investment costs; (iii) the functionality of the FCL-HTSCs outperforms the generic cables in mitigating feeder congestion and excessive fault currents under normal and short-circuit conditions, respectively; and, (iv) the variations in fault currents caused by rising DG penetration are keep below the nominal interrupt rating of the circuit breakers, which speaks to the suitability of the proposed framework.

Accurate Pseudospectral Optimization of Nonlinear Model Predictive Control for High-Performance Motion Planning

Nonlinear Model Predictive Control (NMPC) is an effective method for motion planning of automated vehicles, but the high computational load of numerical optimization limits its practical application. This paper designs an NMPC based motion planner and presents two techniques, named adaptive Lagrange discretization and hybrid obstacle avoidance constraints, to accelerate the numerical optimization by reducing the optimization variables and simplifying the non-convex constraints. Given the high nonlinearity of vehicle dynamics, the Lagrange interpolation is adopted to convert the state equation of vehicle dynamics and the objective function to ensure a preset accuracy but with less discretization points. An adaptive strategy is then designed to adjust the order of Lagrange polynomials based on the distribution of discretization error. Moreover, a hybrid strategy is presented to construct the constraints for obstacle avoidance by combing the elliptic and linear time-varying methods together. It can ensure driving safety and also make a good balance between computing load and accuracy. The performance of these techniques on accelerating the NMPC based motion planner is validated and analyzed by comparative numerical simulations and experimental tests under various scenarios. Compared with traditional methods, the results show that these techniques improve accuracy and efficiency by 74% and 60%, respectively.

Toward Convergence: A Gradient-Based Multiobjective Method With Greedy Hash for Hyperspectral Unmixing

Multiobjective optimization aims at addressing the conflicting objectives, which has been introduced to improve the performance of sparse hyperspectral unmixing. Recently proposed multiobjective unmixing methods usually employ evolutionary algorithms to improve the unmixing accuracy. However, evolutionary algorithms may suffer the challenge of convergence, in which case the reasonability of the solutions is hard to guarantee. To solve the problem of convergence, in this paper, we present a new gradient-based multiobjective unmixing method, which explores the optimization direction in a theoretically reliable manner. Furthermore, considering the mathematical model of hyperspectral sparse unmixing where sparsity error objective of selected endmembers is discrete, we develop a greedy hash based coding approach which is able to well describe the discrete constraints imposed on endmembers. The major components of the proposed method are a search approach and an update approach. In the search approach, we construct the pareto descent direction via a gradient-based strategy, which contributes to converging to an optimal continuous solution by searching along this direction. In the update approach, we update discrete binary endmember via hash coding under the guidance of greedy principle, which allows our method to handle the problem of discrete objective. The major contribution of the proposed method is designing a new framework that can get the optimal discrete endmembers in a convergent way. Moreover, we provide the theoretical analysis and proof for the convergence. Synthetic and real-world experiments have indicated the advantages of our algorithm when compared with evolutionary multiobjective unmixing methods.

Label Guided Discrete Hashing for Cross-Modal Retrieval

Due to their low storage capacity and fast retrieval speed, hashing techniques have received much attention in cross-modal retrieval. However, there are some issues that need to be further explored. First, some existing hashing methods use the labels to construct the semantic similarity matrix between pairwise data, ignoring the potential manifold structure between heterogeneous data. Second, some existing methods underestimate the importance of multi-label and the gaps between different class labels, making the learned hash codes less discriminative. Third, few of them embed both manifold and balanced structures within the same model, and the relaxation of discrete constraints will lead to an increasing quantization error. To mitigate these problems, this paper proposes a novel supervised hashing method, termed Label Guided Discrete Hashing (LGDH), which simultaneously preserves the comprehensive manifold structure and discriminative balanced codes that are both constructed by label information into Hamming space. We develop a local category distribution of the nearest neighbors, to excavate the underlying manifold structure of heterogeneous data. To maximize the gaps of different categories, a balanced matrix is constructed by labels to generate hash codes with balanced bits. For multi-label data, we also design a novel multi-label manifold and balanced structure matrix to adapt the real-world scenarios. An effective discrete optimization method is used to optimize our proposed objective function instead of the relaxation one. Extensive experiments on three benchmark datasets verify the effectiveness of LGDH. The comparison results demonstrat that LGDH achieves about 2% and 3% improved to different cross-modal tasks on average.

A High-Dimensional Sparse Hashing Framework for Cross-Modal Retrieval

In recent years, many achievements have been made in improving the performance of supervised cross-modal hashing. However, it remains an open issue on how to fully explore the data information to achieve fine-grained retrieval performance. Most methods employ logical labels or a binary similarity matrix to supervise the hash learning, losing a lot of useful information. From another point of view, the low expressiveness of dense hash code severely limits its preservation of fine-grained data information. With this motivation, in this paper, we propose a high-dimensional sparse hashing framework for cross-modal retrieval, i.e., High-dimensional Sparse Cross-modal Hashing, HSCH for short. It leverages not only high-level semantic labels but also low-level multi-modal features to construct a fine-grained similarity. In particular, based on two well-designed rules, i.e., multi-level and prioritized, it is able to avoid semantic conflicts. Additionally, it leverages the strong power of high-dimensional sparse hash codes to preserve the fine-grained similarity. Then, it efficiently solves the sparse and discrete constraints of sparse hash codes through an efficient discrete optimization algorithm. In light of this, it is much more efficient and scalable to large-scale datasets. More importantly, the computational complexity of HSCH in the retrieval phase is as efficient as those naive hashing methods that use dense hash codes. Moreover, to support online learning scenarios, this paper also extends HSCH into an online version, i.e., HSCH_on. Extensive experiments on three benchmark datasets demonstrate the superiority of our framework compared with some state-of-the-art cross-modal hashing approaches in terms of both accuracy and efficiency.

Stochastic Augmented Projected Gradient Methods for the Large-Scale Precoding Matrix Indicator Selection Problem

In this paper, we consider the large-scale precoding matrix indicator (PMI) selection problem at the receiver in wireless communications. The selection is based on the channel capacity of the PMI matrix in a pre-designed codebook. The quality of the PMI matrix is essential in achieving higher spectral efficiency. We first derive two novel formulations including a partial permutation-matrix model and an indicator-vector model for the original problem. The discrete constraints in the formulations make the problem NP-hard. Then we propose a stochastic projected gradient method augmented by block coordinate descent under various strategies. We show that the algorithms terminate in finite steps and produce sufficient descent at each iteration when the step size is chosen properly. Extensive experiments demonstrate that our proposed algorithms are able to find better PMI matrices more efficiently compared to the existing methods.

Distributed Q-Learning Algorithm for Dynamic Resource Allocation With Unknown Objective Functions and Application to Microgrid.

Dynamic resource allocation problem (DRAP) with unknown cost functions and unknown resource transition functions is studied in this article. The goal of the agents is to minimize the sum of cost functions over given time periods in a distributed way, that is, by only exchanging information with their neighboring agents. First, we propose a distributed Q -learning algorithm for DRAP with unknown cost functions and unknown resource transition functions under discrete local feasibility constraints (DLFCs). It is theoretically proved that the joint policy of agents produced by the distributed Q -learning algorithm can always provide a feasible allocation (FA), that is, satisfying the constraints at each time period. Then, we also study the DRAP with unknown cost functions and unknown resource transition functions under continuous local feasibility constraints (CLFCs), where a novel distributed Q -learning algorithm is proposed based on function approximation and distributed optimization. It should be noted that the update rule of the local policy of each agent can also ensure that the joint policy of agents is an FA at each time period. Such property is of vital importance to execute the ε -greedy policy during the whole training process. Finally, simulations are presented to demonstrate the effectiveness of the proposed algorithms.

Discrete Joint Semantic Alignment Hashing for Cross-Modal Image-Text Search

Supervised cross-modal image-text hashing has aroused extensive concentrations in comprehending the correspondence between vision and language for data search tasks. Existing methods learn the compact hash codes by leveraging a given image-text data pairs or supervised information to explore such correspondence. However, they still confront obvious drawbacks. First, there is no engagement between multiple semantic information that yields the suboptimal search performance. Second, most of them adopt continuous relaxation strategy by discarding the discrete constraints, which results in large binary quantization errors. To deal with these problems, we propose a novel supervised hashing method, termed Discrete Joint Semantic Alignment Hashing (DJSAH). Specifically, it builds a connection between semantics (a.k.a. class labels and pairwise similarities) by the joint semantic alignment learning. And thus the high-level discriminative semantics can be preserved into the hash codes. Besides, a well-designed discrete optimization algorithm with linear computation and memory cost is developed to reduce the information loss of the hash codes with no need for relaxation. Extensive experiments and analyses on three benchmark datasets validate the superiority of the proposed DJSAH against several state-of-the-art hashing methods.