arXiv subjects

Zai Yang

Publications and source records attributed to Zai Yang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Channel Estimation for RIS-Aided MIMO Systems: A Partially Decoupled Atomic Norm Minimization Approach

Channel estimation (CE) plays a key role in reconfigurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) communication systems, while it poses a challenging task due to the passive nature of RIS and the cascaded channel structures. In this paper, a partially decoupled atomic norm minimization (PDANM) framework is proposed for CE of RIS-aided MIMO systems, which exploits the three-dimensional angular sparsity of the channel. In particular, PDANM partially decouples the differential angles at the RIS from other angles at the base station and user equipment, reducing the computational complexity compared with existing methods. A reweighted PDANM (RPDANM) algorithm is proposed to further improve CE accuracy, which iteratively refines CE through a specifically designed reweighing strategy. Building upon RPDANM, we propose an iterative approach named RPDANM with adaptive phase control (RPDANM-APC), which adaptively adjusts the RIS phases based on previously estimated channel parameters to facilitate CE, achieving superior CE accuracy while reducing training overhead. Numerical simulations demonstrate the superiority of our proposed approaches in terms of running time, CE accuracy, and training overhead. In particular, the RPDANM-APC approach can achieve higher CE accuracy than existing methods within less than 30 percent training overhead while reducing the running time by tens of times.

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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).

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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.

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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.

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arXiv2023

Multichannel Frequency Estimation in Challenging Scenarios via Structured Matrix Embedding and Recovery (StruMER)

Multichannel frequency estimation with incomplete data and miscellaneous noises arises in array signal processing, modal analysis, wireless communications, and so on. In this paper, we consider maximum-likelihood(-like) optimization methods for frequency estimation in which proper objective functions are adopted subject to observed data patterns and noise types. We propose a universal signal-domain approach to solve the optimization problems by embedding the noiseless multichannel signal of interest into a series of low-rank positive-semidefinite block matrices of Hankel and Toeplitz submatrices and formulating the original parameter-domain optimization problems as equivalent structured matrix recovery problems. The alternating direction method of multipliers (ADMM) is applied to solve the resulting matrix recovery problems in which both subproblems of ADMM are solved in (nearly) closed form. The proposed approach is termed as structured matrix embedding and recovery (StruMER). Extensive numerical simulations are provided to demonstrate that StruMER has improved threshold performances in various challenging scenarios, e.g., limited data, low signal-to-noise ratio, impulsive noise, and closely spaced frequencies, as compared with state-of-the-art methods.

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arXiv2023

Direction-of-Arrival Estimation for Constant Modulus Signals Using a Structured Matrix Recovery Technique

This paper addresses the problem of direction-of-arrival (DOA) estimation for constant modulus (CM) source signals using a uniform or sparse linear array. Existing methods typically exploit either the Vandermonde structure of the steering matrix or the CM structure of source signals only. In this paper, we propose a structured matrix recovery technique (SMART) for CM DOA estimation via fully exploiting the two structures. In particular, we reformulate the highly nonconvex CM DOA estimation problems in the noiseless and noisy cases as equivalent rank-constrained Hankel-Toeplitz matrix recovery problems, in which the Vandermonde structure is captured by a series of Hankel-Toeplitz block matrices, of which the number equals the number of snapshots, and the CM structure is guaranteed by letting the block matrices share a same Toeplitz submatrix. The alternating direction method of multipliers (ADMM) is applied to solve the resulting rank-constrained problems and the DOAs are uniquely retrieved from the numerical solution. Extensive simulations are carried out to corroborate our analysis and confirm that the proposed SMART outperforms state-of-the-art algorithms in terms of the maximum number of locatable sources and statistical efficiency.

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arXiv2023

Integrated Sensing, Navigation, and Communication for Secure UAV Networks with a Mobile Eavesdropper

This paper proposes an integrated sensing, navigation, and communication (ISNC) framework for safeguarding unmanned aerial vehicle (UAV)-enabled wireless networks against a mobile eavesdropping UAV (E-UAV). To cope with the mobility of the E-UAV, the proposed framework advocates the dual use of artificial noise transmitted by the information UAV (I-UAV) for simultaneous jamming and sensing to facilitate navigation and secure communication. In particular, the I-UAV communicates with legitimate downlink ground users, while avoiding potential information leakage by emitting jamming signals, and estimates the state of the E-UAV with an extended Kalman filter based on the backscattered jamming signals. Exploiting the estimated state of the E-UAV in the previous time slot, the I-UAV determines its flight planning strategy, predicts the wiretap channel, and designs its communication resource allocation policy for the next time slot. To circumvent the severe coupling between these three tasks, a divide-and-conquer approach is adopted. The online navigation design has the objective to minimize the distance between the I-UAV and a pre-defined destination point considering kinematic and geometric constraints. Subsequently, given the predicted wiretap channel, the robust resource allocation design is formulated as an optimization problem to achieve the optimal trade-off between sensing and communication in the next time slot, while taking into account the wiretap channel prediction error and the quality-of-service (QoS) requirements of secure communication. Simulation results demonstrate the superior performance of the proposed design compared with baseline schemes and validate the benefits of integrating sensing and navigation into secure UAV communication systems.

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arXiv2023

Nonasymptotic Performance Analysis of Direct-Augmentation and Spatial-Smoothing ESPRIT for Localization of More Sources Than Sensors Using Sparse Arrays

Direction augmentation (DA) and spatial smoothing (SS), followed by a subspace method such as ESPRIT or MUSIC, are two simple and successful approaches that enable localization of more uncorrelated sources than sensors with a proper sparse array. In this paper, we carry out nonasymptotic performance analyses of DA-ESPRIT and SS-ESPRIT in the practical finite-snapshot regime. We show that their absolute localization errors are bounded from above by $C_1\frac{\max\{σ^2, C_2\}}{\sqrt{L}}$ with overwhelming probability, where $L$ is the snapshot number, $σ^2$ is the Gaussian noise power, and $C_1,C_2$ are constants independent of $L$ and $σ^2$, if and only if they can do exact source localization with infinitely many snapshots. We also show that their resolution increases with the snapshot number, without a substantial limit. Numerical results corroborating our analysis are provided.

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arXiv2022

Separation-Free Spectral Super-Resolution via Convex Optimization

Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower resolution in the high signal-to-noise (SNR) regime as compared to conventional methods such as ESPRIT. In this paper, we devise a simple weighting scheme in existing atomic norm methods and show that the resolution of the resulting convex optimization method can be made arbitrarily high in the absence of noise, achieving the so-called separation-free super-resolution. This is proved by a novel, kernel-free construction of the dual certificate whose existence guarantees exact super-resolution using the proposed method. Numerical results corroborating our analysis are provided.

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arXiv2022

Nonasymptotic performance analysis of ESPRIT and spatial-smoothing ESPRIT

This paper is concerned with the problem of frequency estimation from multiple-snapshot data. It is well-known that ESPRIT (and spatial-smoothing ESPRIT in presence of coherent sources or given limited snapshots) can locate the true frequencies if either the number of snapshots or the signal-to-noise ratio (SNR) approaches infinity. In this paper, we analyze the nonasymptotic performance of ESPRIT and spatial-smoothing ESPRIT with finitely many snapshots and finite SNR. We show that the absolute frequency estimation error of ESPRIT (or spatial-smoothing ESPRIT) is bounded from above by $C\frac{\max(σ, σ^2)}{\sqrt{L}}$ with overwhelming probability, where $σ^2$ denotes the Gaussian noise variance, $L$ is the number of snapshots and $C$ is a coefficient independent of $L$ and $σ^2$, if and only if the true frequencies can be localized by ESPRIT (or spatial-smoothing ESPRIT) without noise or with infinitely many snapshots. Our results are obtained by deriving new matrix perturbation bounds and generalizing the classical Schur product theorem, which may be of independent interest. Extensions to MUSIC and SS-MUSIC are also made. Numerical results are provided corroborating our analysis.

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arXiv2022

A Robust and Statistically Efficient Maximum-Likelihood Method for DOA Estimation Using Sparse Linear Arrays

A recent trend of research on direction-of-arrival (DOA) estimation is to localize more uncorrelated sources than sensors by using a proper sparse linear array (SLA) and the Toeplitz covariance structure, at a cost of robustness to source correlations. In this paper, we make an attempt to achieve the two goals simultaneously by using a single algorithm. In order to statistically efficiently localize a maximal number of uncorrelated sources, we propose an effective algorithm for the stochastic maximum likelihood (SML) method based on elegant problem reformulations and the alternating direction method of multipliers (ADMM). We prove that the SML is robust to source correlations though it is derived under the assumption of uncorrelated sources. The proposed algorithm is usable for arbitrary SLAs (e.g., minimum redundancy arrays, nested arrays and coprime arrays) and is named as {\em m}aximum-likelihood {\em e}stimation via {\em s}equential {\em A}DMM (MESA). Extensive numerical results are provided that collaborate our analysis and demonstrate the statistical efficiency and robustness of MESA among state-of-the-art algorithms.

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arXiv2022

Robust spectral compressive sensing via vanilla gradient descent

This paper investigates the recovery of a spectrally sparse signal from its partially revealed noisy entries within the framework of spectral compressive sensing. Nonconvex optimization approaches have recently been proposed based on low-rank Hankel matrix completion and projected gradient descent (PGD). The PGD however involves unknown tuning parameters and its theoretical analysis is available only in the absence of noise. In this paper, we propose a hyperparameter-free, vanilla gradient descent (VGD) algorithm and prove that the VGD enables robust recovery of an $N$-dimensional $K$-spectrally-sparse signal from order $K^2 log^2N$ number of noisy samples under coherence and other mild conditions. The above sample complexity increases by factor $logN$ as compared with PGD without noise. Numerical simulations are provided that corroborate our analysis and show advantageous performances of VGD.

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arXiv2021

New Low Rank Optimization Model and Convex Approach for Robust Spectral Compressed Sensing

This paper investigates recovery of an undamped spectrally sparse signal and its spectral components from a set of regularly spaced samples within the framework of spectral compressed sensing and super-resolution. We show that the existing Hankel-based optimization methods suffer from the fundamental limitation that the prior of undampedness cannot be exploited. We propose a new low rank optimization model partially inspired by forward-backward processing for line spectral estimation and show its capability in restricting the spectral poles on the unit circle. We present convex relaxation approaches with the model and show their provable accuracy and robustness to bounded and sparse noise. All our results are generalized from the 1-D to arbitrary-dimensional spectral compressed sensing. Numerical simulations are provided that corroborate our analysis and show efficiency of our model and advantageous performance of our approach in improved accuracy and resolution as compared to the state-of-the-art Hankel and atomic norm methods.

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arXiv2018

On the Sample Complexity of Multichannel Frequency Estimation via Convex Optimization

The use of multichannel data in line spectral estimation (or frequency estimation) is common for improving the estimation accuracy in array processing, structural health monitoring, wireless communications, and more. Recently proposed atomic norm methods have attracted considerable attention due to their provable superiority in accuracy, flexibility and robustness compared with conventional approaches. In this paper, we analyze atomic norm minimization for multichannel frequency estimation from noiseless compressive data, showing that the sample size per channel that ensures exact estimation decreases with the increase of the number of channels under mild conditions. In particular, given $L$ channels, order $K\left(\log K\right) \left(1+\frac{1}{L}\log N\right)$ samples per channel, selected randomly from $N$ equispaced samples, suffice to ensure with high probability exact estimation of $K$ frequencies that are normalized and mutually separated by at least $\frac{4}{N}$. Numerical results are provided corroborating our analysis.

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arXiv2017

Frequency-Selective Vandermonde Decomposition of Toeplitz Matrices with Applications

The classical result of Vandermonde decomposition of positive semidefinite Toeplitz matrices, which dates back to the early twentieth century, forms the basis of modern subspace and recent atomic norm methods for frequency estimation. In this paper, we study the Vandermonde decomposition in which the frequencies are restricted to lie in a given interval, referred to as frequency-selective Vandermonde decomposition. The existence and uniqueness of the decomposition are studied under explicit conditions on the Toeplitz matrix. The new result is connected by duality to the positive real lemma for trigonometric polynomials nonnegative on the same frequency interval. Its applications in the theory of moments and line spectral estimation are illustrated. In particular, it provides a solution to the truncated trigonometric $K$-moment problem. It is used to derive a primal semidefinite program formulation of the frequency-selective atomic norm in which the frequencies are known {\em a priori} to lie in certain frequency bands. Numerical examples are also provided.

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arXiv2017

Sparse Methods for Direction-of-Arrival Estimation

Direction-of-arrival (DOA) estimation refers to the process of retrieving the direction information of several electromagnetic waves/sources from the outputs of a number of receiving antennas that form a sensor array. DOA estimation is a major problem in array signal processing and has wide applications in radar, sonar, wireless communications, etc. With the development of sparse representation and compressed sensing, the last decade has witnessed a tremendous advance in this research topic. The purpose of this article is to provide an overview of these sparse methods for DOA estimation, with a particular highlight on the recently developed gridless sparse methods, e.g., those based on covariance fitting and the atomic norm. Several future research directions are also discussed.

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arXiv2016

Exact Joint Sparse Frequency Recovery via Optimization Methods

Frequency recovery/estimation from discrete samples of superimposed sinusoidal signals is a classic yet important problem in statistical signal processing. Its research has recently been advanced by atomic norm techniques which exploit signal sparsity, work directly on continuous frequencies, and completely resolve the grid mismatch problem of previous compressed sensing methods. In this work we investigate the frequency recovery problem in the presence of multiple measurement vectors (MMVs) which share the same frequency components, termed as joint sparse frequency recovery and arising naturally from array processing applications. To study the advantage of MMVs, we first propose an $\ell_{2,0}$ norm like approach by exploiting joint sparsity and show that the number of recoverable frequencies can be increased except in a trivial case. While the resulting optimization problem is shown to be rank minimization that cannot be practically solved, we then propose an MMV atomic norm approach that is a convex relaxation and can be viewed as a continuous counterpart of the $\ell_{2,1}$ norm method. We show that this MMV atomic norm approach can be solved by semidefinite programming. We also provide theoretical results showing that the frequencies can be exactly recovered under appropriate conditions. The above results either extend the MMV compressed sensing results from the discrete to the continuous setting or extend the recent super-resolution and continuous compressed sensing framework from the single to the multiple measurement vectors case. Extensive simulation results are provided to validate our theoretical findings and they also imply that the proposed MMV atomic norm approach can improve the performance in terms of reduced number of required measurements and/or relaxed frequency separation condition.

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arXiv2016

Vandermonde Decomposition of Multilevel Toeplitz Matrices with Application to Multidimensional Super-Resolution

The Vandermonde decomposition of Toeplitz matrices, discovered by Carathéodory and Fejér in the 1910s and rediscovered by Pisarenko in the 1970s, forms the basis of modern subspace methods for 1D frequency estimation. Many related numerical tools have also been developed for multidimensional (MD), especially 2D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds for multilevel Toeplitz matrices in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided when the matrix rank is lower than the dimension of each Toeplitz block. A numerical method for searching for a decomposition is also proposed when the matrix rank is higher. The new results are applied to studying MD frequency estimation within the recent super-resolution framework. A precise formulation of the atomic $\ell_0$ norm is derived using the Vandermonde decomposition. Practical algorithms for frequency estimation are proposed based on relaxation techniques. Extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared to the existing atomic norm and subspace methods.

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