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In this paper, we establish for the first time the oracle complexity of a Riemannian inexact augmented Lagrangian (RiAL) method with the classical dual update for solving a class of Riemannian nonsmooth composite problems. By using the Riemannian gradient descent method with a specified stopping criterion for solving the inner subproblem, we show that the RiAL method can find an $\varepsilon$-stationary point of the considered problem with $\mathcal{O}(\varepsilon^{-3})$ calls to the first-order oracle. This achieves the best oracle complexity known to date. Numerical results demonstrate that the use of the classical dual stepsize is crucial to the high efficiency of the RiAL method., Comment: 16 pages, 3 tables

Recently, there has been growing interest in minimax problems on Riemannian manifolds due to their wide applications in machine learning and signal processing. Although many algorithms have been developed for minimax problems in the Euclidean setting, there are relatively few works studying minimax problems on manifolds. In this paper, we develop a flexible Riemannian alternating descent ascent (RADA) algorithmic framework for solving nonconvex-linear minimax problems on Riemannian manifolds. Within this framework, we propose two easy-to-implement yet efficient algorithms that alternately perform one or multiple projected/Riemannian gradient descent steps and a proximal gradient ascent step at each iteration. We show that the proposed RADA algorithmic framework can find both an $\varepsilon$-Riemannian-game-stationary point and an $\varepsilon$-Riemannian-optimization-stationary point of the considered problem within $\mathcal{O}(\varepsilon^{-3})$ iterations, achieving the best-known iteration complexity. We also reveal intriguing similarities and differences between the algorithms developed within our proposed framework and existing algorithms, which provide important insights into why the former outperform the latter. Lastly, we report numerical results on sparse principal component analysis (PCA), fair PCA, and sparse spectral clustering to demonstrate the superior performance of the proposed algorithms., Comment: 39 pages, 5 tables

In this paper, we consider the network slicing (NS) problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and manage network resources to meet diverse quality of service (QoS) requirements. We propose a mixed-integer nonlinear programming (MINLP) formulation for the considered NS problem that can flexibly route the traffic flow of the services on multiple paths and provide end-to-end delay and reliability guarantees for all services. To overcome the computational difficulty due to the intrinsic nonlinearity in the MINLP formulation, we transform the MINLP formulation into an equivalent mixed-integer linear programming (MILP) formulation and further show that their continuous relaxations are equivalent. In sharp contrast to the continuous relaxation of the MINLP formulation which is a nonconvex nonlinear programming problem, the continuous relaxation of the MILP formulation is a polynomial-time solvable linear programming problem, which significantly facilitates the algorithmic design. Based on the newly proposed MILP formulation, we develop a customized column generation (cCG) algorithm for solving the NS problem. The proposed cCG algorithm is a decomposition-based algorithm and is particularly suitable for solving large-scale NS problems. Numerical results demonstrate the efficacy of the proposed formulations and the proposed cCG algorithm., Comment: 16 pages, 10 figs, submitted for possible publication. arXiv admin note: text overlap with arXiv:2110.03915

Consider an integrated sensing and communication (ISAC) system where a base station (BS) employs a full-duplex radio to simultaneously serve multiple users and detect a target. The detection performance of the BS may be compromised by self-interference (SI) leakage. This paper investigates the feasibility of SI cancellation (SIC) through the application of symbol-level precoding (SLP). We first derive the target detection probability in the presence of the SI. We then formulate an SLP-based SIC problem, which optimizes the target detection probability while satisfying the quality of service requirements of all users. The formulated problem is a nonconvex fractional programming (FP) problem with a large number of equality and inequality constraints. We propose a penalty-based block coordinate descent (BCD) algorithm for solving the formulated problem, which allows for efficient closed-form updates of each block of variables at each iteration. Finally, numerical simulation results are presented to showcase the enhanced detection performance of the proposed SIC approach., Comment: Submitted to the 2025 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2025)

We propose and demonstrate a novel method for measuring the polarization direction of a microwave electric field in a single measurement using a Rydberg atom-based mixer with two orthogonally polarized local microwave electric fields. Furthermore, introducing a weak static magnetic field enables the utilization of the Zeeman effect and exploitation of polarization asymmetry. This distinction allows for determining the polarization direction of the microwave field is{\theta}or180{\deg}-{\theta}within the 0 to 180 degree range. This is the first real-time measurement of microwave polarization within 0 to 180 degrees, crucial for microwave sensing and information transmission.

Intelligent reflecting surface (IRS) is an emerging technology to enhance spatial multiplexing in wireless networks. This letter considers the discrete passive beamforming design for IRS in order to maximize the minimum signal-to-interference-plus-noise ratio (SINR) among multiple users in an IRS-assisted downlink network. The main design difficulty lies in the discrete phase-shift constraint. Differing from most existing works, this letter advocates a convex-hull relaxation of the discrete constraints which leads to a continuous reformulated problem equivalent to the original discrete problem. This letter further proposes an efficient alternating projection/proximal gradient descent and ascent algorithm for solving the reformulated problem. Simulation results show that the proposed algorithm outperforms the state-of-the-art methods significantly., Comment: 5 pages

In this paper, the inverse scattering transform for the integrable discrete nonlocal PT symmetric nonlinear Schr\"odinger equation with nonzero boundary conditions is presented. According to the two different signs of symmetry reduction and two different values of the phase difference between plus and minus infinity, we discuss four cases with significant differences about analytical regions, symmetry, asymptotic behavior and the presence or absence of discrete eigenvalues, namely, the existence or absence of soliton solutions. Therefore, in all cases, we study the direct scattering and inverse scattering problem, separately. The Riemann-Hilbert problem is constructed and solved as well as the reconstruction formula of potential is derived, respectively. Finally, combining the time evolution, we provide the dark, bright, dark-bright soliton solutions on the nonzero background in difference cases under the reflectionless condition.

As communication systems advance towards the future 6G era, the incorporation of large-scale antenna arrays in base stations (BSs) presents challenges such as increased hardware costs and energy consumption. To address these issues, the use of one-bit analog-to-digital converters (ADCs)/digital-to-analog converters (DACs) has gained significant attentions. This paper focuses on one-bit multiple-input multiple-output (MIMO) detection in an uplink multiuser transmission scenario where the BS employs one-bit ADCs. One-bit quantization retains only the sign information and loses the amplitude information, which poses a unique challenge in the corresponding detection problem. The maximum-likelihood (ML) formulation of one-bit MIMO detection has a challenging likelihood function that hinders the application of many high-performance detectors developed for classic MIMO detection (under high-resolution ADCs). While many approximate methods for the ML detection problem have been studied, it lacks an efficient global algorithm. This paper fills this gap by proposing an efficient branch-and-bound algorithm, which is guaranteed to find the global solution of the one-bit ML MIMO detection problem. Additionally, a new amplitude retrieval (AR) detection approach is developed, incorporating explicit amplitude variables into the problem formulation. The AR approach yields simpler objective functions that enable the development of efficient algorithms offering both global and approximate solutions. The paper also contributes to the computational complexity analysis of both ML and AR detection problems. Extensive simulations are conducted to demonstrate the effectiveness and efficiency of the proposed formulations and algorithms.

A scenario of ghost imaging with hybrid transform approach is proposed by integrating Hadamard, discrete cosine, and Haar matrices. The measurement matrix is formed by the Kronecker product of the two different transform matrices. The image information can be conveniently reconstructed by the corresponding inverse matrices. In experiment, six hybridization sets are performed in computational ghost imaging. For an object of staggered stripes, only one bucket signal survives in the Hadamard-cosine, Haar-Hadamard, and Haar-cosine hybridization sets, demonstrating flexible image compression. For a handmade windmill object, the quality factors of the reconstructed images vary with the hybridization sets. Sub-Nyquist sampling can be applied to either or both of the different transform matrices in each hybridization set in experiment. The hybridization method can be extended to apply more transforms at once. Ghost imaging with hybrid transforms may find flexible applications in image processing, such as image compression and image encryption., Comment: 5 pages, 4 figures

This paper revisits the identity detection problem under the current grant-free protocol in massive machine-type communications (mMTC) by asking the following question: for stable identity detection performance, is it enough to permit active devices to transmit preambles without any handshaking with the base station (BS)? Specifically, in the current grant-free protocol, the BS blindly allocates a fixed length of preamble to devices for identity detection as it lacks the prior information on the number of active devices $K$. However, in practice, $K$ varies dynamically over time, resulting in degraded identity detection performance especially when $K$ is large. Consequently, the current grant-free protocol fails to ensure stable identity detection performance. To address this issue, we propose a two-stage communication protocol which consists of estimation of $K$ in Phase I and detection of identities of active devices in Phase II. The preamble length for identity detection in Phase II is dynamically allocated based on the estimated $K$ in Phase I through a table lookup manner such that the identity detection performance could always be better than a predefined threshold. In addition, we design an algorithm for estimating $K$ in Phase I, and exploit the estimated $K$ to reduce the computational complexity of the identity detector in Phase II. Numerical results demonstrate the effectiveness of the proposed two-stage communication protocol and algorithms., Comment: Submitted to IEEE for possible publication

In this paper, we propose a multi-input multi-output transmit beamforming optimization model for joint radar sensing and multi-user communications, where the design of the beamformers is formulated as an optimization problem whose objective is a weighted combination of the sum rate and the Cram\'{e}r-Rao bound, subject to the transmit power budget. Obtaining the global solution for the formulated nonconvex problem is a challenging task, since the sum-rate maximization problem itself (even without considering the sensing metric) is known to be NP-hard. The main contributions of this paper are threefold. Firstly, we derive an optimal closed-form solution to the formulated problem in the single-user case and the multi-user case where the channel vectors of different users are orthogonal. Secondly, for the general multi-user case, we propose a novel branch and bound (B\&B) algorithm based on the McCormick envelope relaxation. The proposed algorithm is guaranteed to find the globally optimal solution to the formulated problem. Thirdly, we design a graph neural network (GNN) based pruning policy to determine irrelevant nodes that can be directly pruned in the proposed B\&B algorithm, thereby significantly reducing the number of unnecessary enumerations therein and improving its computational efficiency. Simulation results show the efficiency of the proposed vanilla and GNN-based accelerated B\&B algorithms., Comment: Submitted for possible publication

In the first part of this study, a convex-constrained penalized formulation was studied for a class of constant modulus (CM) problems. In particular, the error bound techniques were shown to play a vital role in providing exact penalization results. In this second part of the study, we continue our error bound analysis for the cases of partial permutation matrices, size-constrained assignment matrices and non-negative semi-orthogonal matrices. We develop new error bounds and penalized formulations for these three cases, and the new formulations possess good structures for building computationally efficient algorithms. Moreover, we provide numerical results to demonstrate our framework in a variety of applications such as the densest k-subgraph problem, graph matching, size-constrained clustering, non-negative orthogonal matrix factorization and sparse fair principal component analysis.

This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints, and several types of binary assignment constraints. Capitalizing on the basic principles of concave minimization and error bounds, we study a convex-constrained penalized formulation for general CM problems. The advantage of such formulation is that it allows us to leverage non-convex optimization techniques, such as the simple projected gradient method, to build algorithms. As the first part of this study, we explore the theory of this framework. We study conditions under which the formulation provides exact penalization results. We also examine computational aspects relating to the use of the projected gradient method for each type of CM constraint. Our study suggests that the proposed framework has a broad scope of applicability.

Both dual-functional radar-communication (DFRC) and massive multiple-input multiple-output (MIMO) have been recognized as enabling technologies for 6G wireless networks. This paper considers the advanced waveform design for hardware-efficient massive MIMO DFRC systems. Specifically, the transmit waveform is imposed with the quantized constant-envelope (QCE) constraint, which facilitates the employment of low-resolution digital-to-analog converters (DACs) and power-efficient amplifiers. The waveform design problem is formulated as the minimization of the mean square error (MSE) between the designed and desired beampatterns subject to the constructive interference (CI)-based communication quality of service (QoS) constraints and the QCE constraint. To solve the formulated problem, we first utilize the penalty technique to transform the discrete problem into an equivalent continuous penalty model. Then, we propose an inexact augmented Lagrangian method (ALM) algorithm for solving the penalty model. In particular, the ALM subproblem at each iteration is solved by a custom-built block successive upper-bound minimization (BSUM) algorithm, which admits closed-form updates, making the proposed inexact ALM algorithm computationally efficient. Simulation results demonstrate the superiority of the proposed approach over existing state-of-the-art ones. In addition, extensive simulations are conducted to examine the impact of various system parameters on the trade-off between communication and radar performances., Comment: 17 pages, 11 figures, submitted for possible publication

This paper studies the quality-of-service (QoS) constrained multi-group multicast beamforming design problem, where each multicast group is composed of a number of users requiring the same content. Due to the nonconvex QoS constraints, this problem is nonconvex and NP-hard. While existing optimization-based iterative algorithms can obtain a suboptimal solution, their iterative nature results in large computational complexity and delay. To facilitate real-time implementations, this paper proposes a deep learning-based approach, which consists of a beamforming structure assisted problem transformation and a customized neural network architecture named hierarchical permutation equivariance (HPE) transformer. The proposed HPE transformer is proved to be permutation equivariant with respect to the users within each multicast group, and also permutation equivariant with respect to different multicast groups. Simulation results demonstrate that the proposed HPE transformer outperforms state-of-the-art optimization-based and deep learning-based approaches for multi-group multicast beamforming design in terms of the total transmit power, the constraint violation, and the computational time. In addition, the proposed HPE transformer achieves pretty good generalization performance on different numbers of users, different numbers of multicast groups, and different signal-to-interference-plus-noise ratio targets.

Mathematical optimization is now widely regarded as an indispensable modeling and solution tool for the design of wireless communications systems. While optimization has played a significant role in the revolutionary progress in wireless communication and networking technologies from 1G to 5G and onto the future 6G, the innovations in wireless technologies have also substantially transformed the nature of the underlying mathematical optimization problems upon which the system designs are based and have sparked significant innovations in the development of methodologies to understand, to analyze, and to solve those problems. In this paper, we provide a comprehensive survey of recent advances in mathematical optimization theory and algorithms for wireless communication system design. We begin by illustrating common features of mathematical optimization problems arising in wireless communication system design. We discuss various scenarios and use cases and their associated mathematical structures from an optimization perspective. We then provide an overview of recently developed optimization techniques in areas ranging from nonconvex optimization, global optimization, and integer programming, to distributed optimization and learning-based optimization. The key to successful solution of mathematical optimization problems is in carefully choosing or developing suitable algorithms (or neural network architectures) that can exploit the underlying problem structure. We conclude the paper by identifying several open research challenges and outlining future research directions., Comment: 39 pages, 5 figures, accepted for publication in IEEE Journal on Selected Areas in Communications

Gamma-ray Transient Monitor (GTM) is an all-sky monitor onboard the Distant Retrograde Orbit-A (DRO-A) satellite with the scientific objective of detecting gamma-ray transients ranging from 20 keV to 1 MeV. GTM is equipped with 5 Gamma-ray Transient Probe (GTP) detector modules, utilizing the NaI(Tl) scintillator coupled with a SiPM array. To reduce the SiPM noise, GTP makes use of a dedicated dual-channel coincident readout design. In this work, we firstly studied the impact of different coincidence times on detection efficiency and ultimately selected the 500 ns time coincidence window for offline data processing. To test the performance of GTPs and validate the Monte Carlo simulated energy response, we conducted comprehensive ground calibration tests using Hard X-ray Calibration Facility (HXCF) and radioactive sources, including energy response, detection efficiency, spatial response, bias-voltage response, and temperature dependence. We extensively presented the ground calibration results, and validated the design and mass model of GTP detector. These work paved the road for the in-flight observation and science data analysis., Comment: 15 pages, 25 figures