Frequency Diverse Array-enabled RIS-aided Integrated Sensing and Communication

Integrated sensing and communication (ISAC) has been envisioned as a prospective technology to enable ubiquitous sensing and communications in next-generation wireless networks. In contrast to existing works on reconfigurable intelligent surface (RIS) aided ISAC systems using conventional phased arrays (PAs), this paper investigates a frequency diverse array (FDA)-enabled RIS-aided ISAC system, where the FDA aims to provide a distance-angle-dependent beampattern to effectively suppress the clutter, and RIS is employed to establish high-quality links between the BS and users/target. We aim to maximize sum rate by jointly optimizing the BS transmit beamforming vectors, the covariance matrix of the dedicated radar signal, the RIS phase shift matrix, the FDA frequency offsets and the radar receive equalizer, while guaranteeing the required signal-to-clutter-plus-noise ratio (SCNR) of the radar echo signal. To tackle this challenging problem, we first theoretically prove that the dedicated radar signal is unnecessary for enhancing target sensing performance, based on which the original problem is much simplified. Then, we turn our attention to the single-user single-target (SUST) scenario to demonstrate that the FDA-RIS-aided ISAC system always achieves a higher SCNR than its PA-RIS-aided counterpart. Moreover, it is revealed that the SCNR increment exhibits linear growth with the BS transmit power and the number of BS receive antennas. In order to effectively solve this simplified problem, we leverage the fractional programming (FP) theory and subsequently develop an efficient alternating optimization (AO) algorithm based on symmetric alternating direction method of multipliers (SADMM) and successive convex approximation (SCA) techniques. Numerical results demonstrate the superior performance of our proposed algorithm in terms of sum rate and radar SCNR.

Channel Estimation for XL-IRS Assisted Wireless Systems with Double-sided Visibility Regions

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.

Massive MIMO-OTFS-Based Random Access for Cooperative LEO Satellite Constellations

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.

Robust Beamforming Design and Antenna Selection for Dynamic HRIS-aided Massive MIMO Systems

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.

Joint Beamforming Optimization and Mode Selection for RDARS-aided MIMO Systems

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.

Dual-Functional MIMO Beamforming Optimization for RIS-Aided Integrated Sensing and Communication

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.

RIS-Aided MIMO Systems with Hardware Impairments: Robust Beamforming Design and Analysis

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.

Neural Operator with Regularity Structure for Modeling Dynamics Driven by SPDEs

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.

Incorporating NODE with Pre-trained Neural Differential Operator for Learning Dynamics

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, learns the dynamics directly from the samples on the trajectory and shows great promise in the scientific field. However, the training of NODE highly depends on the numerical solver, which can amplify numerical noise and be 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 learning dynamics. Specifically, beyond learning directly from the trajectory samples, 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 symbolic functions, and it learns the mapping between the trajectory samples of these functions to their derivatives. We provide theoretical guarantee on that the output of NDO can well approximate the ground truth derivatives by proper tuning the complexity of the library. 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 output by the pre-trained NDO. Experiments on various of dynamics show that our proposed NDO-NODE can consistently improve the forecasting accuracy.

Dynamic of Stochastic Gradient Descent with State-Dependent Noise

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.