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In this paper, we study efficient channel estimation design for an extremely large-scale intelligent reflecting surface (XL-IRS) assisted multi-user communication systems, where both the base station (BS) and users are located in the near-field region of the XL-IRS. Two unique channel characteristics of XL-IRS are considered, namely, the near-field spherical wavefronts and double-sided visibility regions (VRs) at the BS and users, which render the channel estimation for XL-IRS highly challenging. To address this issue, we propose in this paper an efficient three-step XL-IRS channel estimation method. Specifically, in the first step, an anchor node is delicately deployed near the XL-IRS to estimate the cascaded BS-IRS-anchor channel. Then, an efficient VR detection method is devised to estimate the VR information between the BS and XL-IRS. In this way, only the channels from the visible XL-IRS elements to the BS are estimated, thereby reducing the dimension of the cascaded BS-IRS-users channels to be estimated. Third, by leveraging the common BS-IRS channel, the cascaded channels for all users are consecutively estimated accounting for the VRs of the IRS-user channels. Finally, numerical results are provided to demonstrate the effectiveness of our proposed channel estimation scheme as compared to various benchmark schemes., Comment: 6 pages, 5 figures

This paper investigates joint device identification, channel estimation, and symbol detection for cooperative multi-satellite-enhanced random access, where orthogonal time-frequency space modulation with the large antenna array is utilized to combat the dynamics of the terrestrial-satellite links (TSLs). We introduce the generalized complex exponential basis expansion model to parameterize TSLs, thereby reducing the pilot overhead. By exploiting the block sparsity of the TSLs in the angular domain, a message passing algorithm is designed for initial channel estimation. Subsequently, we examine two cooperative modes to leverage the spatial diversity within satellite constellations: the centralized mode, where computations are performed at a high-power central server, and the distributed mode, where computations are offloaded to edge satellites with minimal signaling overhead. Specifically, in the centralized mode, device identification is achieved by aggregating backhaul information from edge satellites, and channel estimation and symbol detection are jointly enhanced through a structured approximate expectation propagation (AEP) algorithm. In the distributed mode, edge satellites share channel information and exchange soft information about data symbols, leading to a distributed version of AEP. The introduced basis expansion model for TSLs enables the efficient implementation of both centralized and distributed algorithms via fast Fourier transform. Simulation results demonstrate that proposed schemes significantly outperform conventional algorithms in terms of the activity error rate, the normalized mean squared error, and the symbol error rate. Notably, the distributed mode achieves performance comparable to the centralized mode with only two exchanges of soft information about data symbols within the constellation., Comment: This paper has been accepted by IEEE Journal on Selected Areas in Communications

In this paper, a dynamic hybrid active-passive reconfigurable intelligent surface (HRIS) is proposed to further enhance the massive multiple-input-multiple-output (MIMO) system, since it supports the dynamic placement of active and passive elements. Specifically, considering the impact of the hardware impairments (HWIs), we investigate the channel-aware configuration of the receive antennas at the base station (BS) and the active/passive elements at the HRIS to improve the reliability of system. To this end, we investigate the average mean-square-error (MSE) minimization problem for the HRIS-aided massive MIMO system by jointly optimizing the BS receive antenna selection matrix, the reflection phase coefficients, the reflection amplitude matrix, and the mode selection matrix of the HRIS under the power budget of the HRIS. To tackle the non-convexity and intractability of this problem, we first transform the binary and discrete variables into continuous ones, and then propose a penalty-based exact block coordinate descent (BCD) algorithm to solve these subproblems alternately. Numerical simulations demonstrate the great superiority of the proposed scheme over the conventional benchmark schemes., Comment: 5 pages, 2 figures

Considering the appealing distribution gains of distributed antenna systems (DAS) and passive gains of reconfigurable intelligent surface (RIS), a flexible reconfigurable architecture called reconfigurable distributed antenna and reflecting surface (RDARS) is proposed. RDARS encompasses DAS and RIS as two special cases and maintains the advantages of distributed antennas while reducing the hardware cost by replacing some active antennas with low-cost passive reflecting surfaces. In this paper, we present a RDARS-aided uplink multi-user communication system and investigate the system transmission reliability with the newly proposed architecture. Specifically, in addition to the distribution gain and the reflection gain provided by the connection and reflection modes, respectively, we also consider the dynamic mode switching of each element which introduces an additional degree of freedom (DoF) and thus results in a selection gain. As such, we aim to minimize the total sum mean-square-error (MSE) of all data streams by jointly optimizing the receive beamforming matrix, the reflection phase shifts and the channel-aware placement of elements in the connection mode. To tackle this nonconvex problem with intractable binary and cardinality constraints, we propose an inexact block coordinate descent (BCD) based penalty dual decomposition (PDD) algorithm with the guaranteed convergence. Since the PDD algorithm usually suffers from high computational complexity, a low-complexity greedy-search-based alternating optimization (AO) algorithm is developed to yield a semi-closed-form solution with acceptable performance. Numerical results demonstrate the superiority of the proposed architecture compared to the conventional fully passive RIS or DAS. Furthermore, some insights about the practical implementation of RDARS are provided., Comment: 13 pages, 9 figures. This paper has been submitted to IEEE journal for possible publication

Matrix-variate optimization plays a central role in advanced wireless system designs. In this paper, we aim to explore optimal solutions of matrix variables under two special structure constraints using complex matrix derivatives, including diagonal structure constraints and constant modulus constraints, both of which are closely related to the state-of-the-art wireless applications. Specifically, for diagonal structure constraints mostly considered in the uplink multi-user single-input multiple-output (MU-SIMO) system and the amplitude-adjustable intelligent reflecting surface (IRS)-aided multiple-input multiple-output (MIMO) system, the capacity maximization problem, the mean-squared error (MSE) minimization problem and their variants are rigorously investigated. By leveraging complex matrix derivatives, the optimal solutions of these problems are directly obtained in closed forms. Nevertheless, for constant modulus constraints with the intrinsic nature of element-wise decomposability, which are often seen in the hybrid analog-digital MIMO system and the fully-passive IRS-aided MIMO system, we firstly explore inherent structures of the element-wise phase derivatives associated with different optimization problems. Then, we propose a novel alternating optimization (AO) algorithm with the aid of several arbitrary feasible solutions, which avoids the complicated matrix inversion and matrix factorization involved in conventional element-wise iterative algorithms. Numerical simulations reveal that the proposed algorithm can dramatically reduce the computational complexity without loss of system performance.

Aiming at providing wireless communication systems with environment-perceptive capacity, emerging integrated sensing and communication (ISAC) technologies face multiple difficulties, especially in balancing the performance trade-off between the communication and radar functions. In this paper, we introduce a reconfigurable intelligent surface (RIS) to assist both data transmission and target detection in a dual-functional ISAC system. To formulate a general optimization framework, diverse communication performance metrics have been taken into account including famous capacity maximization and mean-squared error (MSE) minimization. Whereas the target detection process is modeled as a general likelihood ratio test (GLRT) due to the practical limitations, and the monotonicity of the corresponding detection probability is proved. For the single-user and single-target (SUST) scenario, the minimum transmit power of the ISAC transceiver has been revealed. By exploiting the optimal conditions of the BS design, we validate that the BS is able to realize the maximum power allocation scheme and derive the optimal BS precoder in a semi-closed form. Moreover, an alternating direction method of multipliers (ADMM) based RIS design is proposed to address the optimization of unit-modulus RIS phase shifts. For the sake of further enhancing computational efficiency, we also develop a low-complexity RIS design based on Riemannian gradient descent. Furthermore, the ISAC transceiver design for the multiple-users and multiple-targets (MUMT) scenario is also investigated, where a zero-forcing (ZF) radar receiver is adopted to cancel the interferences. Then optimal BS precoder is derived under the maximum power allocation scheme, and the RIS phase shifts can be optimized by extending the proposed ADMM-based RIS design. Numerical simulation results verify the performance of our proposed transceiver designs., Comment: 30 pages, 8 figures, manuscript submitted to IEEE TCOM

Market making plays a crucial role in providing liquidity and maintaining stability in financial markets, making it an essential component of well-functioning capital markets. Despite its importance, there is limited research on market making in the Chinese stock market, which is one of the largest and most rapidly growing markets globally. To address this gap, we employ an optimal market making framework with an exponential CARA-type (Constant Absolute Risk Aversion) utility function that accounts for various market conditions, such as price drift, volatility, and stamp duty, and is capable of describing 3 major risks (i.e., inventory, execution and adverse selection risks) in market making practice, and provide an in-depth quantitative and scenario analysis of market making in the Chinese stock market. Our numerical experiments explore the impact of volatility on the market maker's inventory. Furthermore, we find that the stamp duty rate is a critical factor in market making, with a negative impact on both the profit of the market maker and the liquidity of the market. Additionally, our analysis emphasizes the significance of accurately estimating stock drift for managing inventory and adverse selection risks effectively and enhancing profit for the market maker. These findings offer valuable insights for both market makers and policymakers in the Chinese stock market and provide directions for further research in designing effective market making strategies and policies., Comment: 35 pages, 7 figures, 6 tables

Reconfigurable intelligent surface (RIS) has entered the public consciousness as a promising technology for enhancing the performance of future wireless communication systems by dynamically constructing the wireless channels. In this letter, we study a double-RIS aided downlink multi-user multiple-input multiple-output (MIMO) communication system. We investigate the mean-square-error (MSE) minimization problem by jointly optimizing the active transmit beamforming, the receive equalizer and the passive beamforming at each RIS. Different from prior works, for the sake of reducing both communication overhead and signal processing complexity, we assume that the two RISs utilize the common reflection pattern. Under this assumption, the coupling of the variables becomes tighter, thereby making the optimization problem more challenging to solve. To effectively address this issue, we propose a majorization-minimization (MM)-based alternating optimization (AO) algorithm.Numerical results show that in high signal-to-noise ratio (SNR) region, the double-RIS with common reflection pattern can achieve nearly the same performance as that with separate reflection pattern whereas the complexity is only half of the latter. Thus, our proposed design enables an effective tradeoff between the performance and the implementation complexity of the considered system., Comment: 5 pages, 4 figures. This paper has been submitted to IEEE journal for possible publication

Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output (MIMO) system in the presence of transceiver hardware impairments, RIS phase noise and imperfect channel state information (CSI). Joint design of the MIMO transceiver and RIS reflection matrix to minimize the total average mean-square-error (MSE) of all data streams is particularly considered. This joint design problem is non-convex and challenging to solve due to the newly considered practical imperfections. To tackle the issue, we first analyze the total average MSE by incorporating the impacts of the above system imperfections. Then, in order to handle the tightly coupled optimization variables and non-convex NP-hard constraints, an efficient iterative algorithm based on alternating optimization (AO) framework is proposed with guaranteed convergence, where each subproblem admits a closed-form optimal solution by leveraging the majorization-minimization (MM) technique. Moreover, via exploiting the special structure of the unit-modulus constraints, we propose a modified Riemannian gradient ascent (RGA) algorithm for the discrete RIS phase shift optimization. Furthermore, the optimality of the proposed algorithm is validated under line-of-sight (LoS) channel conditions, and the irreducible MSE floor effect induced by imperfections of both hardware and CSI is also revealed in the high signal-to-noise ratio (SNR) regime. Numerical results show the superior MSE performance of our proposed algorithm over the adopted benchmark schemes, and demonstrate that increasing the number of RIS elements is not always beneficial under the above system imperfections., Comment: 16 pages, 6 figures. Accepted by IEEE Transactions on Wireless Communications

In the deep learning era, improving the neural network performance in jet physics is a rewarding task as it directly contributes to more accurate physics measurements at the LHC. Recent research has proposed various network designs in consideration of the full Lorentz symmetry, but its benefit is still not systematically asserted, given that there remain many successful networks without taking it into account. We conduct a detailed study on the Lorentz-symmetric design. We propose two generalized approaches for modifying a network - these methods are experimented on Particle Flow Network, ParticleNet, and LorentzNet, and exhibit a general performance gain. We also reveal that the notable improvement attributed to the "pairwise mass" feature in the network is due to its introduction of a structure that fully complies with Lorentz symmetry. We confirm that Lorentz-symmetry preservation serves as a strong inductive bias of jet physics, hence calling for attention to such general recipes in future network designs., Comment: 16 pages, 7 figures

Stochastic partial differential equations (SPDEs) are significant tools for modeling dynamics in many areas including atmospheric sciences and physics. Neural Operators, generations of neural networks with capability of learning maps between infinite-dimensional spaces, are strong tools for solving parametric PDEs. However, they lack the ability to modeling SPDEs which usually have poor regularity due to the driving noise. As the theory of regularity structure has achieved great successes in analyzing SPDEs and provides the concept model feature vectors that well-approximate SPDEs' solutions, we propose the Neural Operator with Regularity Structure (NORS) which incorporates the feature vectors for modeling dynamics driven by SPDEs. We conduct experiments on various of SPDEs including the dynamic Phi41 model and the 2d stochastic Navier-Stokes equation, and the results demonstrate that the NORS is resolution-invariant, efficient, and achieves one order of magnitude lower error with a modest amount of data.

Deep learning methods have been increasingly adopted to study jets in particle physics. Since symmetry-preserving behavior has been shown to be an important factor for improving the performance of deep learning in many applications, Lorentz group equivariance - a fundamental spacetime symmetry for elementary particles - has recently been incorporated into a deep learning model for jet tagging. However, the design is computationally costly due to the analytic construction of high-order tensors. In this article, we introduce LorentzNet, a new symmetry-preserving deep learning model for jet tagging. The message passing of LorentzNet relies on an efficient Minkowski dot product attention. Experiments on two representative jet tagging benchmarks show that LorentzNet achieves the best tagging performance and improves significantly over existing state-of-the-art algorithms. The preservation of Lorentz symmetry also greatly improves the efficiency and generalization power of the model, allowing LorentzNet to reach highly competitive performance when trained on only a few thousand jets. Code and models are available at \url{https://github.com/sdogsq/LorentzNet-release}., Comment: 22 pages, 3 figures, and 7 tables

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential equations, is popular in learning dynamics recently due to its robustness to irregular samples and its flexibility to high-dimensional input. However, the training of NODE is sensitive to the precision of the numerical solver, which makes the convergence of NODE unstable, especially for ill-conditioned dynamical systems. In this paper, to reduce the reliance on the numerical solver, we propose to enhance the supervised signal in the training of NODE. Specifically, we pre-train a neural differential operator (NDO) to output an estimation of the derivatives to serve as an additional supervised signal. The NDO is pre-trained on a class of basis functions and learns the mapping between the trajectory samples of these functions to their derivatives. To leverage both the trajectory signal and the estimated derivatives from NDO, we propose an algorithm called NDO-NODE, in which the loss function contains two terms: the fitness on the true trajectory samples and the fitness on the estimated derivatives that are outputted by the pre-trained NDO. Experiments on various kinds of dynamics show that our proposed NDO-NODE can consistently improve the forecasting accuracy with one pre-trained NDO. Especially for the stiff ODEs, we observe that NDO-NODE can capture the transitions in the dynamics more accurately compared with other regularization methods., Comment: 19 pages, 12 figures, 4 tables

Stochastic gradient descent (SGD) and its variants are mainstream methods to train deep neural networks. Since neural networks are non-convex, more and more works study the dynamic behavior of SGD and the impact to its generalization, especially the escaping efficiency from local minima. However, these works take the over-simplified assumption that the covariance of the noise in SGD is (or can be upper bounded by) constant, although it is actually state-dependent. In this work, we conduct a formal study on the dynamic behavior of SGD with state-dependent noise. Specifically, we show that the covariance of the noise of SGD in the local region of the local minima is a quadratic function of the state. Thus, we propose a novel power-law dynamic with state-dependent diffusion to approximate the dynamic of SGD. We prove that, power-law dynamic can escape from sharp minima exponentially faster than flat minima, while the previous dynamics can only escape sharp minima polynomially faster than flat minima. Our experiments well verified our theoretical results. Inspired by our theory, we propose to add additional state-dependent noise into (large-batch) SGD to further improve its generalization ability. Experiments verify that our method is effective.

The potential of deploying large-scale antenna arrays in future wireless systems has stimulated extensive research on hybrid transceiver designs aiming to approximate the optimal fully-digital schemes with much reduced hardware cost and signal processing complexity. Generally, this hybrid transceiver structure requires a joint design of analog and digital processing to enable both beamsteering and spatial multiplexing gains. In this paper, we develop various weighted mean-square-error minimization (WMMSE) based hybrid transceiver designs over multiple-input multiple-output (MIMO) interference channels at both millimeter wave (mmWave) and microwave frequencies. Firstly, a heuristic joint design of hybrid precoder and combiner using alternating optimization is proposed, in which the majorization-minimization (MM) method is utilized to design the analog precoder and combiner with unit-modulus constraints. It is validated that this scheme achieves the comparable performance to the WMMSE fully-digital solution. To further reduce the complexity, a phase projection-based two-stage scheme is proposed to decouple the designs of analog and digital precoder combiner. Secondly, inspired by the fully-digital solutions based on the block-diagonalization zero-forcing (BD-ZF) and signal-to-leakage-plus-noise ratio (SLNR) criteria, low-complexity MMbased BD-ZF and SLNR hybrid designs are proposed to well approximate the corresponding fully-digital solutions. Thirdly, the partially-connected hybrid structure for reducing system hardware cost and power consumption is considered, for which the MM-based alternating optimization still works. Numerical results demonstrate the similar or superior performance of all the above proposed schemes over the existing benchmarks., Comment: 13 pages, 8 figures

The new paradigm of wirelessly powered two-tier heterogeneous networks (HetNets) is considered in this paper. Specifically, the femtocell base station (FBS) is powered by a power beacon (PB) and transmits confidential information to a legitimate femtocell user (FU) in the presence of a potential eavesdropper (EVE) and a macro base station (MBS). In this scenario, we investigate the secrecy beamforming design under three different levels of FBS-EVE channel state information (CSI), namely, the perfect, imperfect and completely unknown FBS-EVE CSI. Firstly, given the perfect global CSI at the FBS, the PB energy covariance matrix, the FBS information covariance matrix and the time splitting factor are jointly optimized aiming for perfect secrecy rate maximization. Upon assuming the imperfect FBS-EVE CSI, the worst-case and outage-constrained SRM problems corresponding to deterministic and statistical CSI errors are investigated, respectively. Furthermore, considering the more realistic case of unknown FBS-EVE CSI, the artificial noise (AN) aided secrecy beamforming design is studied. Our analysis reveals that for all the above cases both the optimal PB energy and FBS information secrecy beamformings are of rank-1. Moreover, for all considered cases of FBS-EVE CSI, the closed-form PB energy beamforming solutions are available when the cross-tier interference constraint is inactive. Numerical simulation results demonstrate the secrecy performance advantages of all proposed secrecy beamforming designs compared to the adopted baseline algorithms., Comment: 31 pages, 8 figures

Wireless powered sensor networks (WPSNs) have emerged as a key development towards the future self-sustainable Internet of Things (IoT) networks. To achieve a good balance between self-sustainability and reliability, partially WPSNs with a mixed power solution are desirable for practical applications. Specifically, most of the sensor nodes are wireless powered but the key sensor node adopts traditional wire/battery power for reliability. As a result, this paper mainly investigates optimal design for the partially WPSNs in which simultaneous wireless information and power transfer (SWIPT) is adopted in the downlink. Two scenarios with space division multiple access (SDMA) and time division multiple access (TDMA) in the uplink are considered. For both the SDMA-enabled and TDMA-enabled partially WPSNs, joint design of downlink beamforming, uplink beamforming and time allocation is investigated to maximize the uplink sum rate while guaranteeing the quality-of-service (i.e., satisfying the downlink rate constraint) at the key sensor node. After analyzing the feasibility of uplink sum rate maximization problems and the influence of the downlink rate constraint, semi-closed-form optimal solutions for both SDMA-enabled and TDMA-enabled WPSNs are proposed with guaranteed global optimality. Complexity analysis is also provided to justify the advantage of the proposed solutions in low complexity. The effectiveness and optimality of the proposed optimal solutions are finally demonstrated by simulations., Comment: 14 pages

We propose a comprehensive framework exploiting the polarization sensitive array (PLA) to improve the physical layer security of wireless communications. More specifically, the polarization difference among signals is utilized to improve the secrecy rate of wireless communications, especially when these signals are spatially indistinguishable. We firstly investigate the PLA based secure communications for point-to-point wireless systems from the perspectives of both total power minimization and secrecy rate maximization. We then take a step further to apply the PLA based secure beamforming designs to relaying networks. The secrecy rate maximization for relaying networks is discussed in detail under both the perfect channel state information and the polarization sensitive array pointing error. In the later case, a robust scheme to achieve secure communications for relaying networks is proposed. Simulation results show that the proposed PLA based algorithms achieve lower total power consumption and better security performance compared with the conventional scalar array designs, especially under challenging environments where all received signals at destination are difficult to be distinguished from the spatial domain., Comment: 36 Pages, 14 Figures, IEEE Transactions on Information Forensics and Security