arXiv subjects

Zai Yang

Publications and source records attributed to Zai Yang.

At least 19 recordsLinked to original sources

arXiv2026

Deterministic Cramer-Rao Bounds for Coherent Direction-of-Arrival Estimation: Rank Information Versus Coherence Structure

Direction-of-arrival (DOA) estimation is a fundamental problem in array signal processing, for which the Cramer-Rao bound (CRB) serves as a standard performance benchmark under both stochastic and deterministic source models. In multipath environments, the source matrix is of low-rank and, more specifically, exhibits a within-group proportionality structure. Although stochastic CRBs for coherent DOA estimation have been studied, theoretical results for their deterministic counterparts remain limited. This paper aims to bridge this gap. We first derive a tangent-space condition characterizing when structural constraints on the source matrix can strictly reduce the frequency CRB. We then prove that, for uniform linear arrays, imposing only the low-rankness of the source matrix leaves the frequency CRB unchanged, although it reduces the source-matrix CRB whenever the rank constraint is nontrivial, whereas fully exploiting the coherence structure yields a strictly smaller frequency CRB for almost all parameter values under mild conditions. These conclusions are further extended to analytic array manifolds and multidimensional DOA models, with componentwise results established for uniform planar arrays. The results demonstrate that performance gains in DOA estimation arise from the detailed coherence structure rather than low-rankness alone. Numerical experiments are finally provided to validate the theoretical findings.

eess.SP↗

arXiv2026

Jointly Sparse Blind Deconvolution via Riemannian Optimization

Blind deconvolution has been widely applied in system identification and signal processing. While joint sparsity commonly arises in practical scenarios, effectively exploiting this structure to enhance recovery performance remains a challenging and largely open problem. In this paper, we propose a joint-sparsity-promoting optimization problem and develop a Riemannian optimization algorithm for its accurate and efficient solution. We further establish theoretical guarantees that characterize the non-asymptotic relationship between the estimation error and the sample complexity, showing that exploiting joint sparsity can significantly reduce the sample complexity required for successful recovery. Numerical experiments are provided that validate the theoretical results and demonstrate the effectiveness of the proposed approach.

math.OC↗

arXiv2026

Positivity of a Hadamard Product

A notable difference between the ordinary and Hadamard products is that the Hadamard product of two singular positive semidefinite matrices can be nonsingular, and one of the factors can even be indefinite. We present an eigenvalue lower bound for a Hadamard product that depends on the rank, effective condition number, and diagonal entries of one factor, and the smallest eigenvalues of certain principal submatrices of the other factor. We give numerical examples and discuss its applications in array signal processing and matrix time series analysis.

eess.SP↗

arXiv2026

OFDM Waveform Optimization for Bistatic Integrated Sensing and Communications

This paper investigates the design of orthogonal frequency-division multiplexing (OFDM) waveforms for bistatic integrated sensing and communication (ISAC) systems. In the considered framework, an ISAC transmitter jointly optimizes subcarrier assignment and power allocation for a single OFDM waveform that simultaneously supports communication and sensing functionalities. Meanwhile, an ISAC receiver decodes information on communication subcarriers and estimates per-path propagation delays via exploiting pilot symbols on sensing subcarriers. We propose a joint path coefficient and delay estimation (JPCDE) scheme, revealing that the achievable communication data rate (CDR) is determined by the number of communication subcarriers, whereas the delay sensing accuracy is governed by the index distribution of sensing subcarriers. Building on this insight, we formulate an OFDM waveform optimization problem to maximize the CDR subject to sensing-accuracy and power-budget constraints. To solve this problem, we employ a quadratic transform and Lagrangian dual decomposition, which iteratively updates the subcarrier assignment and power allocation variables in closed-form. Our results reveal that a subcarrier is allocated for sensing if and only if its Fisher information gain exceeds the corresponding communication rate loss, while the power allocation for communication subcarriers exhibits a bounded water-filling structure. Simulation results demonstrate that the proposed frameworks substantially outperform existing baselines in both delay estimation accuracy and CDR.

cs.IT↗

arXiv2026

IGLU: The Integrated Gaussian Linear Unit Activation Function

Activation functions are fundamental to deep neural networks, governing gradient flow, optimization stability, and representational capacity. Within historic deep architectures, while ReLU has been the dominant choice for the activation function, modern transformer-based models increasingly are adopting smoother alternatives such as GELU and other self-gated alternatives. Despite their empirical success, the mathematical relationships among these functions and the principles underlying their effectiveness remains only partially understood. We introduce IGLU, a parametric activation function derived as a scale mixture of GELU gates under a half-normal mixing distribution. This derivation yields a closed-form expression whose gating component is exactly the Cauchy CDF, providing a principled one-parameter family that continuously interpolates between identity-like and ReLU-like behavior via a single sharpness parameter $\sigma$. Unlike GELU's Gaussian gate, IGLU's heavy-tailed Cauchy gate decays polynomially in the negative tail, guaranteeing non-zero gradients for all finite inputs and offering greater robustness to vanishing gradients. We further introduce IGLU-Approx, a computationally efficient rational approximation of IGLU expressed entirely in terms of ReLU operations that eliminates transcendental function evaluation. Through evaluations on CIFAR-10, CIFAR-100, and WikiText-103 across ResNet-20, ViT-Tiny, and GPT-2 Small, IGLU achieves competitive or superior performance on both vision and language datasets against ReLU and GELU baselines, with IGLU-Approx recovering this performance at substantially reduced computational cost. In particular, we show that employing a heavy-tailed gate leads to considerable performance gains in heavily imbalanced classification datasets.

cs.LG↗

arXiv2025

Compressive Toeplitz Covariance Estimation From Few-Bit Quantized Measurements With Applications to DOA Estimation

This paper addresses the problem of estimating the Hermitian Toeplitz covariance matrix under practical hardware constraints of sparse observations and coarse quantization. Within the triangular-dithered quantization framework, we propose an estimator called Toeplitz-projected sample covariance matrix (Q-TSCM) to compensate for the quantization-induced bias, together with its finite-bit counterpart termed the $2k$-bit Toeplitz-projected sample covariance matrix ($2k$-TSCM), obtained by truncating the pre-quantization observations. Under the complex Gaussian assumption, we derive non-asymptotic error bounds of the estimators that reveal a quadratic dependence on the quantization level and capture the effect of sparse sampling patterns through the so-called coverage coefficient. To further improve performance, we propose the quantized sparse and parametric approach (Q-SPA) based on a covariance-fitting criterion, which enforces additionally positive semidefiniteness at the cost of solving a semidefinite program. Numerical experiments are presented that corroborate our theoretical findings and demonstrate the effectiveness of the proposed estimators in the application to direction-of-arrival estimation.

eess.SP↗

arXiv2025

DREAM-B3P: Dual-Stream Transformer Network Enhanced by Feedback Diffusion Model for Blood-Brain Barrier Penetrating Peptide Prediction

Introduction: The blood-brain barrier (BBB) protects the central nervous system but prevents most neurotherapeutics from reaching effective concentrations in the brain. BBB-penetrating peptides (BBBPs) offer a promising strategy for brain drug delivery; however, the scarcity of positive samples and severe class imbalance hinder the reliable identification of BBBPs. Objectives: Our goal is to alleviate class imbalance in BBBP prediction and to develop an accurate, interpretable classifier for BBBP prediction. Methods: We propose DREAM-B3P, which couples a feedback diffusion model (FB-Diffusion) for data augmentation with a dual-stream Transformer for classification. FB-Diffusion learns the BBBP distribution via iterative denoising and uses an external analyzer to provide feedback, generating high-quality pseudo-BBBPs. The classifier contains a sequence stream that extracts structural features from peptide sequences and a physicochemical stream that captures physicochemical features such as hydrophobic surface area, molecular charge, number of rotatable bonds, and polarizability. Combining the two features leads to superior BBBP predictive performance. Results: On a benchmark test set containing equal numbers of BBBPs and non-BBBPs, DREAM-B3P surpasses baseline methods (Deep-B3P, B3Pred, BBPpredict and Augur), improving AUC/ACC/MCC by 4.3\%/17.8\%/14.9\%, respectively, over the second-best method. Conclusion: By integrating feedback diffusion with a dual-stream Transformer classifier, DREAM-B3P effectively mitigates data scarcity and imbalance and achieves state-of-the-art performance.

q-bio.QM↗

arXiv2025

Quotient Manifold Optimization for Spectral Compressed Sensing

Spectral compressed sensing involves reconstructing a spectral-sparse signal from a subset of uniformly spaced samples, with applications in radar imaging and wireless channel estimation. By fully exploiting the signal structures, this problem is formulated as a rank-constrained semidefinite program subject to Hankel-Toeplitz structural constraints in our previous work. To further enhance computational efficiency, this paper proposes a quotient-manifold-based optimization framework that leverages the underlying Riemannian geometry in a matrix factorization space. Specifically, we establish an equivalence between spectral-sparse signals and matrix equivalence classes under the action of the real orthogonal group, where each class member corresponds to a rank-constrained positive-semidefinite Hankel-Toeplitz structured matrix. The associated quotient manifold geometry--including the Riemannian metric, horizontal space, retraction, and vector transport--is rigorously derived. Based on these results, we develop a Riemannian conjugate gradient descent algorithm, where each iteration is efficiently implemented using fast Fourier transforms (FFTs) by exploiting the Hankel and Toeplitz structures. Extensive numerical experiments demonstrate the superior performance of the proposed algorithm in both computational speed and accuracy compared to state-of-the-art methods.

math.OC↗

arXiv2025

Extended AB Algorithms for Bistatic Integrated Sensing and Communications Systems

Integrated sensing and communication (ISAC) is pivotal for next-generation wireless networks, rendering the computation of rate-distortion trade-off in ISAC systems critically important. In this paper, we propose the extended Arimoto-Blahut (AB) algorithms to calculate the rate-distortion trade-off in bistatic ISAC systems, which overcome the limitation of existing AB algorithms in handling non-convex constraints. Specifically, we introduce auxiliary variables to transform non-convex distortion constraints into linear constraints, prove that the reformulated linearly-constrained optimization problem maintains the same optimal solution as the original problem, and develop extended AB algorithms for both squared error and logarithmic loss distortion metrics based on the framework of AB algorithm. Numerical results validate the effectiveness of the proposed algorithm.

cs.IT↗

arXiv2025

Pursuing the limit of chirp parameter identifiability: A computational approach

In this paper, it is shown that a necessary condition for unique identifiability of $K$ chirps from $N$ regularly spaced samples of their mixture is $N\geq 2K$ when $K\geq 2$. A necessary and sufficient condition is that a rank-constrained matrix optimization problem has a unique solution; this is the first result of such kind. An algorithm is proposed to solve the optimization problem and to identify the parameters numerically. The lower bound of $N=2K$ is shown to be tight by providing diverse problem instances for which the proposed algorithm succeeds to identify the parameters. The advantageous performance of the proposed algorithm is also demonstrated compared with the state of the art.

eess.SP↗

arXiv2025

Channel Knowledge Map-assisted Dual-domain Tracking and Predictive Beamforming for High-Mobility Wireless Networks

This paper introduces a novel channel knowledge map (CKM)-assisted dual-domain tracking and predictive beamforming scheme for high-mobility wireless networks. The central premise is that the CKM integrates both the coordinate and beam domains, thereby enabling tracking in one domain via treating the other domain's input as priors or measurements. In the coordinate domain (C-Domain), an extended Kalman filter (EKF) is employed to predict and track the state (i.e., location and velocity) of a moving communication receiver across time slots under both line-of-sight (LoS)-present and LoS-absent conditions, where the CKM provides a prior mapping from multipath channel parameters to potential target locations. In the beam domain (B-Domain), the updated location of the receiver is fed back to CKM to offer a priori information of angle of arrival (AoA) variations, which are incorporated to establish beam transition models for effective beam tracking, depending on the angular variation situation of each path. Then, we analyze the Cram\'er-Rao Bound (CRB) for AoA estimation for each path in the considered system and propose a jointly predictive beamforming and power allocation design to minimize AoA estimation errors, directly enhancing multipath beam tracking accuracy and indirectly improving target tracking performance. Simulation results demonstrate that the proposed scheme achieves significant improvements in both target and beam tracking performance compared to the state-of-the-art approaches, particularly in AoA tracking of non-line-of-sight (NLoS) paths, highlighting the potential gain of CKM in facilitating both target and beam tracking in high-mobility communications.

eess.SP↗

arXiv2025

Gaussian Arimoto-Blahut Algorithm for Capacity Region Calculation of Gaussian Vector Broadcast Channels

This paper is concerned with the computation of the capacity region of a continuous, Gaussian vector broadcast channel (BC) with covariance matrix constraints. Since the decision variables of the corresponding optimization problem are Gaussian distributed, they can be characterized by a finite number of parameters. Consequently, we develop new Blahut-Arimoto (BA)-type algorithms that can compute the capacity without discretizing the channel. First, by exploiting projection and an approximation of the Lagrange multiplier, which are introduced to handle certain positive semidefinite constraints in the optimization formulation, we develop the Gaussian BA algorithm with projection (GBA-P). Then, we demonstrate that one of the subproblems arising from the alternating updates admits a closed-form solution. Based on this result, we propose the Gaussian BA algorithm with alternating updates (GBA-A) and establish its convergence guarantee. Furthermore, we extend the GBA-P algorithm to compute the capacity region of the Gaussian vector BC with both private and common messages. All the proposed algorithms are parameter-free. Lastly, we present numerical results to demonstrate the effectiveness of the proposed algorithms.

cs.IT↗

arXiv2024

UAV-Enabled Secure ISAC Against Dual Eavesdropping Threats: Joint Beamforming and Trajectory Design

In this work, we study an unmanned aerial vehicle (UAV)-enabled secure integrated sensing and communication (ISAC) system, where a UAV serves as an aerial base station (BS) to simultaneously perform communication with a user and detect a target on the ground, while a dual-functional eavesdropper attempts to intercept the signals for both sensing and communication. Facing the dual eavesdropping threats, we aim to enhance the average achievable secrecy rate for the communication user by jointly designing the UAV trajectory together with the transmit information and sensing beamforming, while satisfying the requirements on sensing performance and sensing security, as well as the UAV power and flight constraints. To address the non-convex nature of the optimization problem, we employ the alternating optimization (AO) strategy, jointly with the successive convex approximation (SCA) and semidefinite relaxation (SDR) methods. Numerical results validate the proposed approach, demonstrating its ability to achieve a high secrecy rate while meeting the required sensing and security constraints.

cs.IT↗

arXiv2024

Bit Efficient Toeplitz Covariance Estimation

This paper addresses the challenge of Toeplitz covariance matrix estimation from partial entries of random quantized samples. To balance trade-offs among the number of samples, the number of entries observed per sample, and the data resolution, we propose a ruler-based quantized Toeplitz covariance estimator. We derive non-asymptotic error bounds and analyze the convergence rates of the proposed estimator. Our results show that the estimator is near-optimal and imply that reducing data resolution within a certain range has a limited impact on the estimation accuracy. Numerical experiments are provided that validate our theoretical findings and show effectiveness of the proposed estimator.

eess.SP↗

arXiv2024

Low-Complexity Algorithms for Multichannel Spectral Super-Resolution

This paper studies the problem of multichannel spectral super-resolution with either constant amplitude (CA) or not. We propose two optimization problems based on low-rank Hankel-Toeplitz matrix factorization. The two problems effectively leverage the multichannel and CA structures, while also enabling the design of low-complexity gradient descent algorithms for their solutions. Extensive simulations show the superior performance of the proposed algorithms.

math.OC↗

arXiv2024

RIS-aided MIMO Beamforming: Piece-Wise Near-field Channel Model

This paper proposes a joint active and passive beamforming design for reconfigurable intelligent surface (RIS)-aided wireless communication systems, adopting a piece-wise near-field channel model. While a traditional near-field channel model, applied without any approximations, offers higher modeling accuracy than a far-field model, it renders the system design more sensitive to channel estimation errors (CEEs). As a remedy, we propose to adopt a piece-wise near-field channel model that leverages the advantages of the near-field approach while enhancing its robustness against CEEs. Our study analyzes the impact of different channel models, including the traditional near-field, the proposed piece-wise near-field and far-field channel models, on the interference distribution caused by CEEs and model mismatches. Subsequently, by treating the interference as noise, we formulate a joint active and passive beamforming design problem to maximize the spectral efficiency (SE). The formulated problem is then recast as a mean squared error (MSE) minimization problem and a suboptimal algorithm is developed to iteratively update the active and passive beamforming strategies. Simulation results demonstrate that adopting the piece-wise near-field channel model leads to an improved SE compared to both the near-field and far-field models in the presence of CEEs. Furthermore, the proposed piece-wise near-field model achieves a good trade-off between modeling accuracy and system's degrees of freedom (DoF).

cs.IT↗

arXiv2024

A Robust Super-resolution Gridless Imaging Framework for UAV-borne SAR Tomography

Synthetic aperture radar (SAR) tomography (TomoSAR) retrieves three-dimensional (3-D) information from multiple SAR images, effectively addresses the layover problem, and has become pivotal in urban mapping. Unmanned aerial vehicle (UAV) has gained popularity as a TomoSAR platform, offering distinct advantages such as the ability to achieve 3-D imaging in a single flight, cost-effectiveness, rapid deployment, and flexible trajectory planning. The evolution of compressed sensing (CS) has led to the widespread adoption of sparse reconstruction techniques in TomoSAR signal processing, with a focus on $\ell _1$ norm regularization and other grid-based CS methods. However, the discretization of illuminated scene along elevation introduces modeling errors, resulting in reduced reconstruction accuracy, known as the "off-grid" effect. Recent advancements have introduced gridless CS algorithms to mitigate this issue. This paper presents an innovative gridless 3-D imaging framework tailored for UAV-borne TomoSAR. Capitalizing on the pulse repetition frequency (PRF) redundancy inherent in slow UAV platforms, a multiple measurement vectors (MMV) model is constructed to enhance noise immunity without compromising azimuth-range resolution. Given the sparsely placed array elements due to mounting platform constraints, an atomic norm soft thresholding algorithm is proposed for partially observed MMV, offering gridless reconstruction capability and super-resolution. An efficient alternative optimization algorithm is also employed to enhance computational efficiency. Validation of the proposed framework is achieved through computer simulations and flight experiments, affirming its efficacy in UAV-borne TomoSAR applications.

eess.SP↗

arXiv2024

Multichannel Frequency Estimation with Constant Amplitude via Convex Structured Low-Rank Approximation

We study the problem of estimating the frequencies of several complex sinusoids with constant amplitude (CA) (also called constant modulus) from multichannel signals of their superposition. To exploit the CA property for frequency estimation in the framework of atomic norm minimization (ANM), we introduce multiple positive-semidefinite block matrices composed of Hankel and Toeplitz submatrices and formulate the ANM problem as a convex structured low-rank approximation (SLRA) problem. The proposed SLRA is a semidefinite programming and has substantial differences from existing such formulations without using the CA property. The proposed approach is termed as SLRA-based ANM for CA frequency estimation (SACA). We provide theoretical guarantees and extensive simulations that validate the advantages of SACA.

math.OC↗