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.

This paper addresses the problem of estimating Toeplitz covariance matrices from partial entries of randomly quantized samples. To balance the trade-offs among the number of samples, the number of observed entries per sample, and the data resolution, we propose a ruler-based quantized Toeplitz covariance estimator. We derive non-asymptotic upper and lower bounds for the proposed estimator, and analyze the corresponding convergence rates. Our results characterize how sparse observation and coarse quantization affect the performance of the proposed estimator and suggest that reducing data resolution within a certain range has limited impact on estimation accuracy. Numerical experiments are provided to validate the theoretical findings.

The unlimited sampling framework, utilizing modulo analog-to-digital converters (ADCs), has recently been introduced to mitigate the information loss caused by the dynamic range limitations of traditional ADCs. In this paper, we evaluate the noise sensitivity of unlimited sampling in line spectral estimation by deriving the Cramér–Rao bound (CRB) and show that estimation based solely the modulo measurements can be sensitive to noise. To address this issue, we propose integrating the modulo ADC-based unlimited sampling with the sign information of the original signal. We compare the CRBs of different unlimited sampling frameworks and show the benefit of enhanced robustness to noise by the sign-aided approach.

This paper proposes a joint active and passive beamforming design for reconfigurable intelligent surface (RIS)-aided wireless communication systems, adopting a piecewise 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 piecewise 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 piecewise 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 piecewise 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 piecewise near-field model achieves a good trade-off between modeling accuracy and system’s degrees of freedom (DoF).

Bistatic sensing refers to scenarios where the transmitter (illuminating the target) and the sensing receiver (estimating the target state) are physically separated, in contrast to monostatic sensing, where both functions are co-located. In practical settings, bistatic sensing may be required either due to inherent system constraints or as a means to mitigate the strong self-interference encountered in monostatic configurations. A key practical challenge in bistatic radio-frequency radar systems is the synchronization and calibration of the separate transmitter and sensing receiver. In this paper, we are not concerned with these signal processing aspects and take a complementary information-theoretic perspective on bistatic integrated sensing and communication (ISAC). Namely, we aim to characterize the capacity-distortion function—the fundamental tradeoff between communication capacity and sensing accuracy. We consider a general discrete channel model for a bistatic ISAC system and derive a multi-letter representation of its capacity-distortion function. Then, we establish single-letter upper and lower bounds and provide exact single-letter characterizations for degraded bistatic ISAC channels. Numerical examples illustrate the theoretical results, highlighting the benefits of ISAC over separate communication and sensing, as well as the role of leveraging communication to assist sensing in bistatic systems.

This paper focuses on the transmit and receive beamforming design of an integrated sensing and communication system. In particular, a base station transmits waveform for simultaneous downlink multiuser communication as well as radar sensing, and spatial filter is performed for receive echos to reduce the clutter caused by communications users. We use mainlobe ripple control to ensure that this system shows similar sensing performance for any angle in this region. The transmit beamforming design is formulated as an optimization problem to maximize the minimum mainlobe power. The receive beamforming is designed by maximizing the ratio of the minimum beam response in the main lobe region to the maximum beam response in the directions of communication users. Numerical results show that the proposed beamforming scheme can not only guarantees the communication quality, but also utmostly improve the sensing performance.

In direction-of-arrival (DOA) estimation, both stochastic and deterministic priors of source signals have been used to localize more sources than sensors. The stochastic prior refers to uncorrelateness of sources, while the deterministic one includes the constant modulus (CM) property of sources. Existing studies typically exploit one of the two priors. In this paper, we consider the combination of the two priors and present a necessary condition for unique localization of uncorrelated CM sources using a sparse linear array. Our result indicates limited benefits of exploiting both uncorrelated and CM priors in further improving the number of locatable sources.

Multichannel spectral compressed sensing is a fundamental problem in statistical signal processing. In order to reduce the hardware cost and energy consumption, one-bit multichannel spectral compressed sensing is considered. Inspired by rewighted atomic norm minimization, we propose a new method to solve one-bit spectral compressed sensing and prove that each iteration of the proposed method is weighted atomic norm minimization. A new equivalent form of the weighted atomic norm based on Hankel-Toeplitz model is given in this paper. Numerical simulations are given to demonstrate the superior performance of the proposed method.

We design an algorithm from the perspective of information theory to calculate the capacity region of the Gaussian vector broadcast channel with private messages. For a continuous channel, a common method to approximately calculate its capacity is to apply the Blahut-Arimoto algorithm after discretization. In this work, we derive an equivalent form of the objective function and decouple the coupled variables in the original problem by exploiting the property that a Gaussian distribution is uniquely determined by its mean and variance. And thus develop a Gaussian Blahut-Arimoto algorithm without discretization.

Bistatic Integrated Sensing and Communication (ISAC) systems circumvent the issue of strong self-interference present in monostatic ISAC systems by employing a pair of physically separated sensing transceivers. They maintain the advantage of co-designing radar sensing and communications on shared spectrum and hardware. Motivated by the favorable attributes of bistatic radar, this paper investigates bistatic ISAC. In this setup, a transmitter sends messages to a communication receiver, while a sensing receiver at another location conducts a “decoding-and-estimation” (DnE) operation to obtain the state of the communication receiver. We propose three achievable DnE strategies based on the degree of information decoding at the sensing receiver: blind estimation, partial decoding-based estimation, and full decoding-based estimation. We explore the corresponding rate-distortion regions associated with each strategy. Furthermore, we provide a specific example to illustrate the comparison of the rate-distortion regions among the three DnE strategies and demonstrate the advantage of ISAC over independent communication and sensing.

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 ℓ1norm 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.

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 reweighting 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.

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. To account for the E-UAV state sensing uncertainty and the resulting wiretap channel prediction error, we employ a fully-connected neural network to model the complicated mapping between the state estimation error variance and an upper bound on the channel prediction error, which facilitates the development of a low-complexity suboptimal user scheduling and precoder design algorithm. 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. We reveal that the dual use of artificial noise can improve both sensing and jamming and that navigation is more important for improving the trade-off between sensing and communications than communication resource allocation.

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 structuredmatrix 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.

Channel estimation (CE) plays a key role in recon-figurable intelligent surface (RIS)-aided multiple-input multiple-output (MIMO) systems, while it is challenging due to the passive nature of RIS and the sophisticated cascaded channel structures. In this paper, a partially decoupled atomic norm minimization (PDANM) approach is proposed for the CE in RIS-aided MIMO systems. In particular, PDANM inherits the benefit of atomic norm minimization (ANM) for exploiting the three-dimensional angular structure of the channel in a grid-less manner that achieves a high CE accuracy. Besides, PDANM can partially decouple the differential angles at the RIS from other angular parameters at the base station and user equipment, reducing the computational complexity compared with other ANM-based methods. Numerical simulations illustrate that our proposed approach can significantly reduce the required computational complexity with a slight CE accuracy loss.

We study the spectral super-resolution problem, which concerns the construction of an undamped spectrally sparse signal and its frequencies from its partially revealed entries. We propose a nonconvex method composed of a Hankel-Toeplitz matrix factorization model and a gradient descent algorithm termed as HT-GD. The model is equivalent to an ℓ0norm con-strained problem, which ensures that the all signal structures including the spectral poles lying on the unit circle are exploited. The gradient descent algorithm, consisting of spectral initialization and iterative refinement, is computationally efficient. Numerical results demonstrate that our method out-performs state-of-the-art approaches in terms of accuracy and computational speed.

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$C\frac {\max \left \{{\sigma, \sigma ^{2}}\right \}}{\sqrt {L}}$with overwhelming probability, where$\sigma ^{2}$denotes the Gaussian noise variance,$L$is the number of snapshots and$C$is a coefficient independent of$L$and$\sigma ^{2}$, 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 spatial-smoothing MUSIC are also made. Numerical results are provided corroborating our analysis.

DOA estimation with sparse linear arrays has been extensively studied, with an emphasis on localizing more sources than sensors. A critical assumption in previous studies however is that the sources are all uncorrelated. In this paper, we present an algorithm that is shown to be able to localize more sources than sensors in presence of correlated or coherent sources without the knowledge of the source coherence structure. Our algorithm is generalized from our recently proposed rank-constrained ADMM approach to maximum likelihood estimation for uncorrelated sources with a uniform linear array.

Spatial smoothing is a common preprocessing scheme for subspace methods that resolves their sensitivity to coherent sources. The source resolvability problem of spatial-smoothing-based subspace methods has been extensively investigated using different analysis techniques. In this paper, a unified Hadamard product technique is provided to recover these results. This is done by answering a long-standing question in linear algebra as to under what conditions the Hadamard product of two singular positive-semidefinite matrices is positive definite.

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 (log K) (1 + L/1 log N) 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 4/N. Numerical results are provided corroborating our analysis.

The authors have recently proposed two kinds of gridless sparse methods for direction of arrival (DOA) estimation that exploit joint sparsity among snapshots and completely resolve the grid mismatch issue of previous grid-based sparse methods. One is based on covariance fitting from a statistical perspective and termed as the gridless SPICE (GL-SPICE, GLS); the other uses deterministic atomic norm optimization which extends the recent super-resolution and continuous compressed sensing framework from the single to the multi-snapshot case. In this paper, we unify the two techniques by interpreting GLS as atomic norm methods in various scenarios. As a byproduct, we are able to provide theoretical guarantees of GLS for DOA estimation in the case of limited snapshots.

This paper concerns the line spectral estimation problem within the recent super-resolution framework. The frequencies of interest are assumed to follow a prior probability distribution. To effectively and efficiently exploit the prior information, we devise a weighted atomic norm approach that is physically sound and can be formulated as convex programming like the standard atomic norm method. Numerical simulations are provided to demonstrate the superior performance of the proposed approach in accuracy and speed compared to the state-of-the-art.

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 1-D frequency estimation. Many related numerical tools have also been developed for multidimensional (MD), especially 2-D, 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 study the 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 the relaxation techniques. Extensive numerical simulations are provided to demonstrate the effectiveness of these algorithms compared with the existing atomic norm and subspace methods.

The super-resolution theory developed recently by Candès and Fernandes-Granda aims to recover fine details in a sparse frequency spectrum from coarse scale information. The theory was then extended to the cases of compressive samples and/or multiple measurement vectors. However, the existing atomic norm (or total variation norm) techniques succeed only if the frequencies are sufficiently separated, prohibiting commonly known high resolution. In this paper, a reweighted atomic-norm minimization (RAM) approach is proposed which iteratively carries out atomic norm minimization (ANM) with a sound reweighting strategy that enhances sparsity and resolution. It is demonstrated analytically and via numerical simulations that the proposed method achieves high resolution with application to DOA estimation.

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 multi-dimensional (MD), especially 2D, frequency estimation; however, a fundamental question has remained unresolved as to whether an analog of the Vandermonde decomposition holds in the MD case. In this paper, an affirmative answer to this question and a constructive method for finding the decomposition are provided under appropriate conditions. The new result is also used to study MD frequency estimation from compressive data within the recent super-resolution framework. A systematic approach is proposed and a numerical simulation is provided to demonstrate its effectiveness compared to the existing atomic norm method.

This paper focuses on the problem of source localization using time-difference-of-arrival (TDOA) measurements in both 2-D and 3-D spaces. Different from existing studies where the variance of TDOA measurement noises is assumed to be independent of the associated source-to-sensor distances, we consider the more realistic model where the variance is a function of the source-to-sensor distances, which dramatically complicates TDOA-based source localization. After formulating the distance-dependent noise model, we prove that using the extra information about the source location in the functional variance improves the estimation accuracy of TDOA-based source localization, but contributes little under a sufficiently small noise level. Further, we theoretically analyze the problem of optimal sensor placement, and derive the necessary and sufficient conditions for optimizing localization performance under different circumstances. Then, a localization scheme based on the iteratively reweighted generalized least squares (IRGLS) method is proposed to efficiently exploit the extra source location information. Finally, a simulation analysis confirms our theoretical studies, and shows that the performance of the proposed localization scheme is comparable to the Cramer-Rao lower bound (CRLB) given moderate TDOA measurement noises.

Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex-valued. We study the popular recovery method ofl1-regularized least squares or LASSO. While several studies have shown that LASSO provides desirable solutions under certain conditions, the precise asymptotic performance of this algorithm in the complex setting is not yet known. In this paper, we extend the approximate message passing (AMP) algorithm to solve the complex-valued LASSO problem and obtain the complex approximate message passing algorithm (CAMP). We then generalize the state evolution framework recently introduced for the analysis of AMP to the complex setting. Using the state evolution, we derive accurate formulas for the phase transition and noise sensitivity of both LASSO and CAMP. Our theoretical results are concerned with the case of i.i.d. Gaussian sensing matrices. Simulations confirm that our results hold for a larger class of random matrices.

The sparse signal recovery in standard compressed sensing (CS) requires that the sensing matrix is exactly known. The CS problem subject to perturbation in the sensing matrix is often encountered in practice and has attracted interest of researches. Unlike existing robust signal recoveries with the recovery error growing linearly with the perturbation level, this paper analyzes the CS problem subject to a structured perturbation to provide conditions for stable signal recovery under measurement noise. Under mild conditions on the perturbed sensing matrix, similar to that for the standard CS, it is shown that a sparse signal can be stably recovered by ℓ1minimization. A remarkable result is that the recovery is exact and independent of the perturbation if there is no measurement noise and the signal is sufficiently sparse. In the presence of noise, largest entries (in magnitude) of a compressible signal can be stably recovered. The result is demonstrated by a simulation example.

The phase transition is a performance measure of the sparsity-undersampling tradeoff in compressed sensing (CS). This letter reports our first observation and evaluation of an empirical phase transition of thel1minimization approach to the complex valued CS (CVCS), which is positioned well above the known phase transition of the real valued CS in the phase plane. This result can be considered as an extension of the existing phase transition theory of the block-sparse CS (BSCS) based on the universality argument, since the CVCS problem does not meet the condition required by the phase transition theory of BSCS but its observed phase transition coincides with that of BSCS. Our result is obtained by applying the recently developed ONE-L1 algorithms to the empirical evaluation of the phase transition of CVCS.

In this paper, recently developed ONE-L1 algorithms for compressed sensing are applied to complex-valued signals and sampling matrices. The optimal and iterative solution of ONE-L1 algorithms enables empirical investigation and evaluation of the sparsity-undersampling tradeoff of ℓ1minimization of complex-valued signals. A remarkable finding is that, not only there exists a sharp phase transition for the complex case determining the behavior of the sparsity-undersampling tradeoff, but also this phase transition is different and superior to that for the real case, providing a significantly improved success phase in the transition plane.

Compressed sensing (CS) enables the reconstruction of MR images from highly under-sampled k-space data via a constrained ℓ1-minimization problem. However, existing convex optimization techniques to solve such a constrained optimization problem suffer from slow convergence rate when dealing with data of a large size. On the other hand, many iterative thresholding techniques improve the convergence rate but at the cost of accuracy. In this work, we present a new iterative optimization technique to efficiently solve the constrained ℓ1optimization without compromising the accuracy of the solution. The key idea is to expand the sensing matrix into an orthonormal matrix, which casts the ℓ1constrained optimization into an equivalent convex optimization problem that can be exactly solved by the joint application of augmented Lagrange multipliers (ALM) method and alternating direction method (ADM). The proposed algorithm, dubbed as One - ℓ1, provides much faster convergence rate without compromising the reconstruction accuracy, when compared with commonly used optimization techniques, such as nonlinear conjugate gradient (NCG) method, as demonstrated with both phantom and in-vivo MR experiments.