Zenan Ling

In this paper, we perform asymptotic analyses of the widely used ESPRIT direction-of-arrival (DoA) estimator for large arrays, where the array size N and the number of snapshots T grow to infinity at the same pace. In this large-dimensional regime, the sample covariance matrix (SCM) is known to be a poor eigenspectral estimator of the population covariance. We show that the classical ESPRIT algorithm, that relies on the SCM, and as a consequence of the large-dimensional inconsistency of the SCM, produces inconsistent DoA estimates as $N, T →$∞ with $N/T →c$ ε (0,∞), for both widely- and closely-spaced DoAs. Leveraging tools from random matrix theory (RMT), we propose an improved G-ESPRIT method and prove its consistency in the same large-dimensional setting. From a technical perspective, we derive a novel bound on the eigenvalue differences between two potentially non-Hermitian matrices, which may be of independent interest. Numerical simulations are provided to corroborate our theoretical findings.

Reconfigurable intelligent surface (RIS) is envisioned as a key enabling technology for 6G wireless communications. By configuring the reflection beamforming codebook, RIS focuses signals on target receivers to enhance signal strength. In this paper, we investigate the codebook configuration for both continuous-phase and 1-bit RIS-aided communication systems. We formulate an implicit relationship between user coordinates and the optimal codebook from the perspective of electromagnetic wave propagation mechanisms, and introduce a novel learning-based method, implicit neural representations (INRs), to solve this implicit coordinates-to-codebook mapping problem. Our approach requires only user coordinates, avoiding reliance on explicit channel models. For continuous-phase RIS, we introduce a phase normalization technique to address the periodicity and global phase offset challenges inherent in phase representation. Additionally, for the practical 1-bit RIS scenario, we formulate the codebook configuration as a multi-label classification problem and propose an encoding strategy to reduce codebook dimension, thereby improving learning efficiency. Experimental results from both simulated and real-world datasets demonstrate significant advantages of our unified method across both continuous and 1-bit codebook configurations. The datasets and code are available at: https://github.com/HUSTGSNeRF/Codebook_Inr.

Reconfigurable intelligent surfaces (RISs) have emerged as a promising auxiliary technology for radio frequency imaging. However, existing works face challenges of faint and intricate back-scattered waves and the restricted field-of-view (FoV), both resulting from complex target structures and a limited number of antennas. The synergistic benefits of multi-RIS-aided imaging hold promise for addressing these challenges. Here, we propose a dual-RIS-aided imaging system, Dreamer, which operates collaboratively in complementary modes (reflection-mode and transmission-mode). Dreamer significantly expands the FoV and enhances perception by deploying dual-RIS across various spatial and measurement patterns. Specifically, we perform a fine-grained analysis of how radio-frequency (RF) signals encode scene information in the scattered object modeling. Based on this modeling, we design illumination strategies to balance spatial resolution and observation scale, and implement a prototype system in a typical indoor environment. Moreover, we design a novel artificial neural network with a CNN-external-attention mechanism to translate RF signals into high-resolution images of human silhouettes. Our approach achieves an impressive structural similarity index (SSIM) score 0.83 surpassing state-of-the-art solutions, validating its effectiveness in broadening perception modes and enhancing imaging capabilities. The code to reproduce our results is available at https://github.com/fuhaiwang/Dreamer.

Real-time situational awareness and event analysis are crucial to the security of the modern power grid, which is a complicated nonlinear system and hard to be completely modeled. Massive data is collected but the information hasn't been sufficiently leveraged. To effectively extract the event features, this paper proposes a framework for event detection, localization, and classification in power grids based on semi-supervised learning. Specifically, event detection is realized by invertible neural network (INN), hence to learn complex distributions of real-world measurements in a flexible way. Abundant normal measurements are learned by INN and explicit log-likelihoods then serve as the indicator to distinguish events with adequate sensitivity. Moreover, risks induced by events are assessed and spatial locations are determined. Since the majority of power system events are recorded without labels in practice, a pseudo label (PL) technique is leveraged to classify events with limited labels. The PL-based approach has an enhanced separating capability for events and outperforms other approaches under a low labeling rate. Case studies with simulated data in the IEEE 39-bus system and real-world measurements verify the effectiveness of the proposed framework.

To reveal the mystery behind deep neural networks (DNNs), optimization may offer a good perspective. There are already some clues showing the strong connection between DNNs and optimization problems, e.g., under a mild condition, DNN's activation function is indeed a proximal operator. In this paper, we are committed to providing a unified optimization induced interpretability for a special class of networks—equilibrium models, i.e., neural networks defined by fixed point equations, which have become increasingly attractive recently. To this end, we first decompose DNNs into a new class of unit layer that is the proximal operator of an implicit convex function while keeping its output unchanged. Then, the equilibrium model of the unit layer can be derived, we name it Optimization Induced Equilibrium Networks (OptEq). The equilibrium point of OptEq can be theoretically connected to the solution of a convex optimization problem with explicit objectives. Based on this, we can flexibly introduce prior properties to the equilibrium points: 1) modifying the underlying convex problems explicitly so as to change the architectures of OptEq; and 2) merging the information into the fixed point iteration, which guarantees to choose the desired equilibrium point when the fixed point set is non-singleton. We show that OptEq outperforms previous implicit models even with fewer parameters.

We revisit the weight initialization of deep residual networks (ResNets) by introducing a novel analytical tool in free probability to the community of deep learning. This tool deals with the limiting spectral distribution of non-Hermitian random matrices, rather than their conventional Hermitian counterparts in the literature. This new tool enables us to evaluate the singular value spectrum of the input-output Jacobian of a fully connected deep ResNet in both linear and nonlinear cases. With the powerful tool of free probability, we conduct an asymptotic analysis of the (limiting) spectrum on the single-layer case, and then extend this analysis to the multi-layer case of an arbitrary number of layers. The asymptotic analysis illustrates the necessity and university of rescaling the classical random initialization by the number of residual units L, so that the squared singular value of the associated Jacobian remains of order O(1), when compared with the large width and depth of the network. We empirically demonstrate that the proposed initialization scheme learns at a speed of orders of magnitudes faster than the classical ones, and thus attests a strong practical relevance of this investigation.

The online monitoring data in distribution networks contain rich information on the running states of the networks. By leveraging the data, this paper proposes a spatio-temporal correlation analysis approach for anomaly detection and location in distribution networks. First, spatio-temporal matrix for each feeder line in a distribution network is formulated and the spectrum of its covariance matrix is analyzed. The spectrum is complex and exhibits two aspects: 1) bulk, which arises from random noise or fluctuations and 2) spikes, which represents factors caused by anomaly signals or fault disturbances. Then, by connecting the estimation of the number of factors to the limiting empirical spectral density of covariance matrices of residuals, the spatio-temporal parameters are accurately estimated, during which free random variable techniques are used. Based on the estimators, anomaly indicators are designed to detect and locate the anomalies by exploring the variations of spatio-temporal correlations in the data. The proposed approach is sensitive to the anomalies and robust to random fluctuations, which makes it possible for detecting early anomalies and reducing false alarming rate. Case studies on both synthetic data and real-world online monitoring data verify the effectiveness and advantages of the proposed approach.

Synchronized measurements of a large power grid enable an unprecedented opportunity to study the spatial-temporal correlations. Statistical analytics for those massive datasets start with high-dimensional data matrices. Uncertainty is ubiquitous in a future's power grid. These data matrices are recognized as random matrices. This new point of view is fundamental in our theoretical analysis since true covariance matrices cannot be estimated accurately in a high-dimensional regime. As an alternative, we consider large-dimensional sample covariance matrices in the asymptotic regime to replace the true covariance matrices. The self-adjoint polynomials of large-dimensional random matrices are studied as statistics for big data analytics. The calculation of the asymptotic spectrum distribution (ASD) for such a matrix polynomial is understandably challenging. This task is made possible by a recent breakthrough in free probability, an active research branch in random matrix theory. This is the very reason why the work of this paper is inspired initially. The new approach is interesting in many aspects. The mathematical reason may be most critical. The real-world problems can be solved using this approach, however.