We study an information-theoretic privacy mechanism design problem, where an agent observes useful data $Y$ that is arbitrarily correlated with sensitive data $X$, and design disclosed data $U$ generated from $Y$ (the agent has no direct access to $X$). We introduce \emph{sparse point-wise privacy leakage}, a worst-case privacy criterion that enforces two simultaneous constraints for every disclosed symbol $u\in\mathcal{U}$: (i) $u$ may be correlated with at most $N$ realizations of $X$, and (ii) the total leakage toward those realizations is bounded. In the high-privacy regime, we use concepts from information geometry to obtain a local quadratic approximation of mutual information which measures utility between $U$ and $Y$. When the leakage matrix $P_{X|Y}$ is invertible, this approximation reduces the design problem to a sparse quadratic maximization, known as the Rayleigh-quotient problem, with an $\ell_0$ constraint. We further show that, for the approximated problem, one can without loss of optimality restrict attention to a binary released variable $U$ with a uniform distribution. For small alphabet sizes, the exact sparsity-constrained optimum can be computed via combinatorial support enumeration, which quickly becomes intractable as the dimension grows. For general dimensions, the resulting sparse Rayleigh-quotient maximization is NP-hard and closely related to sparse principal component analysis (PCA). We propose a convex semidefinite programming (SDP) relaxation that is solvable in polynomial time and provides a tractable surrogate for the NP-hard design, together with a simple rounding procedure to recover a feasible leakage direction. We also identify a sparsity threshold beyond which the sparse optimum saturates at the unconstrained spectral value and the SDP relaxation becomes tight.

This work investigates a multi-user, multi-antenna uplink wireless system, in which multiple users transmit signals to a base station. Prior research has explored the potential for linear growth in spectral efficiency by employing multiple transmit and receive antennas. This gain depends heavily on the quality of channel state information and the number of uncorrelated antennas. However, spatial correlations, arising from closely-spaced antennas and channel aging effects, stemming from the difference between the channel state at pilot and data time instances, can substantially counteract these benefits, and degrade the transmission rate, especially in non-stationary environments. To address these challenges, this work introduces a real-time beamforming framework to compensate for the spatial correlation and channel aging effects. First, a channel estimation scheme leveraging temporal channel correlations and considering mobile device velocity and antenna spacing is developed. Subsequently, an expression approximating the average spectral efficiency, which depends on pilot spacing, pilot and data powers, and beamforming vectors, is obtained. By maximizing this expression, optimal parameters are identified. Numerical results demonstrate the effectiveness of the proposed approach compared to prior works. Interestingly, the optimal pilot spacing remains unaffected by large-scale channel parameters and the velocities of interfering users. The impact of interference components also diminishes with an increasing number of transmit antennas.

The transition toward 6G is pushing wireless communication into a regime where the classical plane-wave assumption no longer holds. Millimeter-wave and sub-THz frequencies shrink wavelengths to millimeters, while meter-scale arrays featuring hundreds of antenna elements dramatically enlarge the aperture. Together, these trends collapse the classical Rayleigh far-field boundary from kilometers to mere single-digit meters. Consequently, most practical 6G indoor, vehicular, and industrial deployments will inherently operate within the radiating near-field, where reliance on the plane-wave approximation leads to severe array-gain losses, degraded localization accuracy, and excessive pilot overhead. This paper re-examines the fundamental question: "Where does the far-field truly begin?" Rather than adopting purely geometric definitions, we introduce an application-oriented approach based on user-defined error budgets and a rigorous Fresnel-zone analysis that fully accounts for both amplitude and phase curvature. We propose three practical mismatch metrics: worst-case element mismatch, worst-case normalized mean square error, and spectral efficiency loss. For each metric, we derive a provably optimal transition distance–the minimal range beyond which mismatch permanently remains below a given tolerance–and provide closed-form solutions. Extensive numerical evaluations across diverse frequencies and antenna-array dimensions show that our proposed thresholds can exceed the Rayleigh distance by more than an order of magnitude. By transforming the near-field from a design nuisance into a precise, quantifiable tool, our results provide a clear roadmap for enabling reliable and resource-efficient near-field communications and sensing in emerging 6G systems.

In this paper, we propose a novel goal-oriented method for identifying stationary Internet of Things (IoT) devices, with the performance robust to the number of inactive devices. We start by formulating a two-dimensional atomic norm minimization problem that captures the angular group-sparsity of the wireless channel. Building on this, we propose a goal-oriented optimization problem that retains only the angular information required to identify active stationary IoT devices. This problem is then reformulated as an equivalent semi-definite programming (SDP) problem, enabling efficient detection of active users. Unlike traditional methods that rely on orthogonal preambles or pilot assignments for joint active user detection and channel estimation, our approach operates without pilots, enabling blind identification of the line-of-sight angles of active stationary devices. Simulation results demonstrate that the proposed method achieves high detection accuracy and low false alarm rates, offering a scalable and robust solution for enabling massive connectivity in future wireless networks.

Integrated sensing and communications (ISAC) is a promising component of 6G networks, fusing communication and radar technologies to facilitate new services. Additionally, the use of extremely large-scale antenna arrays (ELAA) at the ISAC common receiver not only facilitates terahertz-rate communication links but also significantly enhances the accuracy of target detection in radar applications. In practical scenarios, communication scatterers and radar targets often reside in close proximity to the ISAC receiver. This, combined with the use of ELAA, fundamentally alters the electromagnetic characteristics of wireless and radar channels, shifting from far-field planar-wave propagation to near-field spherical wave propagation. Under the far-field planar-wave model, the phase of the array response vector varies linearly with the antenna index. In contrast, in the near-field spherical wave model, this phase relationship becomes nonlinear. This shift presents a fundamental challenge: the widely-used Fourier analysis can no longer be directly applied for target detection and communication channel estimation at the ISAC common receiver. In this work, we propose a feasible solution to address this fundamental issue. Specifically, we demonstrate that there exists a high-dimensional space in which the phase nonlinearity can be expressed as linear. Leveraging this insight, we develop a lifted super-resolution framework that simultaneously performs communication channel estimation and extracts target parameters with high precision.

We propose a novel pilot-free multi-user uplink framework for integrated sensing and communication (ISAC) in mm-wave networks, where single-antenna users transmit orthogonal frequency division multiplexing signals without dedicated pilots. The base station exploits the spatial and velocity diversities of users to simultaneously decode messages and detect targets, transforming user transmissions into a powerful sensing tool. Each user's signal, structured by a known codebook, propagates through a sparse multi-path channel with shared moving targets and user-specific scatterers. Notably, common targets induce distinct delay-Doppler-angle signatures, while stationary scatterers cluster in parameter space. We formulate the joint multi-path parameter estimation and data decoding as a 3D super-resolution problem, extracting delays, Doppler shifts, and angles-of-arrival via atomic norm minimization, efficiently solved using semidefinite programming. A core innovation is multi-user fusion, where diverse user observations are collaboratively combined to enhance sensing and decoding. This approach improves robustness and integrates multi-user perspectives into a unified estimation framework, enabling high-resolution sensing and reliable communication. Numerical results show that the proposed framework significantly enhances both target estimation and communication performance, highlighting its potential for next-generation ISAC systems.

Several previous works have addressed the inherent trade-off between allocating resources in the power and time domains to pilot and data signals in multiple input multiple output systems over block-fading channels. In particular, when the channel changes rapidly in time, channel aging degrades the performance in terms of spectral efficiency without proper pilot spacing and power control. Despite recognizing non-stationary stochastic processes as more accurate models for time-varying wireless channels, the problem of pilot spacing and power control in multi-antenna systems operating over non-stationary channels is not addressed in the literature. In this paper, we address this gap by introducing a refined first-order autoregressive model that exploits the inherent temporal correlations over non-stationary Rician aging channels. We design a multi-frame structure for data transmission that better reflects the non-stationary fading environment than previously developed single-frame structures. Subsequently, to determine the optimal pilot spacing and power control within this multi-frame structure, we develop an optimization framework and an efficient algorithm based on maximizing a deterministic equivalent expression for the spectral efficiency, demonstrating its generality by encompassing previous channel aging results. Our numerical results indicate the efficacy of the proposed method in terms of spectral efficiency gains over the single frame structure.

The Internet of Things interconnects billions of devices and forms a vast network where users sporadically transmit short messages through multi-path wireless channels. These channels are characterized by the superposition of a small number of scaled and delayed copies of Dirac spikes. At the receiver, the observed signal is a sum of these convolved signals, and the task is to find the amplitudes, continuous-indexed delays, and transmitted messages from a single signal. This task is inherently ill-posed without additional assumptions on the channel or messages. In this work, we assume the channel exhibits sparsity in the delay domain and that independent and identically distributed random linear encoding is applied to the messages at the devices. Leveraging these assumptions, we propose a semidefinite programming optimization capable of simultaneously recovering both messages and the delay parameters of the channels from only a single received signal. Our theoretical analysis establishes that the required number of samples at the receiver scales proportionally to the sum-product of sparsity and message length of all users, aligning with the degrees of freedom in the lifting-type optimization frameworks. Numerical experiments confirm the efficacy of the proposed method in accurately estimating closely-spaced delay parameters and recovering messages.

We study a multi-task private semantic communication problem, in which an encoder has access to an information source arbitrarily correlated with some latent private data. A user has$L$tasks with priorities. The encoder designs a message to be revealed which is called the semantic of the information source. Due to the privacy constraints the semantic can not be disclosed directly and the encoder adds noise to produce disclosed data. The goal is to design the disclosed data that maximizes the weighted sum of the utilities achieved by the user while satisfying a privacy constraint on the private data. In this work, we first consider a single-task scenario and design the added noise utilizing various methods including the extended versions of the Functional Representation Lemma, Strong Functional Representation Lemma, and separation technique. We then study the multi-task scenario and derive a simple design of the source semantics. We show that in the multi-task scenario the main problem can be divided into multiple parallel single-task problems.

We consider the problem of gridless blind deconvolution and demixing (GB2D) in scenarios where multiple users communicate messages through multiple unknown channels, and a single base station (BS) collects their contributions. This scenario arises in various communication fields, including wireless communications, the Internet of Things, over-the-air computation, and integrated sensing and communications. In this setup, each user's message is convolved with a multi-path channel formed by several scaled and delayed copies of Dirac spikes. The BS receives a linear combination of the convolved signals, and the goal is to recover the unknown amplitudes, continuous-indexed delays, and transmitted waveforms from a compressed vector of measurements at the BS. However, without prior knowledge of the transmitted messages and channels, GB2D is highly challenging and intractable in general. To address this issue, we assume that each user's message follows a distinct modulation scheme living in a known low-dimensional subspace. By exploiting these subspace assumptions and the sparsity of the multipath channels for different users, we transform the nonlinear GB2D problem into a matrix tuple recovery problem from a few linear measurements. To achieve this, we propose a semidefinite programming optimization that exploits the specific low-dimensional structure of the matrix tuple to recover the messages and continuous delays of different communication paths from a single received signal at the BS. Finally, our numerical experiments show that our proposed method effectively recovers all transmitted messages and the continuous delay parameters of the channels with sufficient samples.

The multi-user linearly-separable distributed computing problem is considered here, in which N servers help to compute the real-valued functions requested by K users, where each function can be written as a linear combination of up to L (generally non-linear) subfunctions. Each server computes a fraction γ of the subfunctions, then communicates a function of its computed outputs to some of the users, and then each user collects its received data to recover its desired function. Our goal is to bound the ratio between the computation workload done by all servers over the number of datasets.To this end, we here reformulate the real-valued distributed computing problem into a matrix factorization problem and then into a basic sparse recovery problem, where sparsity implies computational savings. Building on this, we first give a simple probabilistic scheme for subfunction assignment, which allows us to upper bound the optimal normalized computation cost as $\gamma \leq \frac{K}{N}$ that a generally intractable ℓ0-minimization would give. To bypass the intractability of such optimal scheme, we show that if these optimal schemes enjoy $\gamma \leq - r\frac{K}{N}W_{ - 1}^{ - 1}\left( { - \frac{{2K}}{{eNr}}} \right)$ (where W−1(•) is the Lambert function and r calibrates the communication between servers and users), then they can actually be derived using a tractable Basis Pursuit ℓ1-minimization. This newly-revealed connection opens up the possibility of designing practical distributed computing algorithms by employing tools and methods from compressed sensing.

Resource allocation and multiple access schemes are instrumental for the success of communication networks, which facilitate seamless wireless connectivity among a growing population of uncoordinated and non-synchronized users. In this paper, we present a novel random access scheme that addresses one of the most severe barriers of current strategies to achieve massive connectivity and ultra reliable and low latency communications for 6G. The proposed scheme utilizes wireless channels' angular continuous group-sparsity feature to provide low latency, high reliability, and massive access features in the face of limited time-bandwidth resources, asynchronous transmissions, and preamble errors. Specifically, a reconstruction-free goal oriented optimization problem is proposed which preserves the angular information of active devices and is then complemented by a clustering algorithm to assign active users to specific groups. This allows to identify active stationary devices according to their line of sight angles. Additionally, for mobile devices, an alternating minimization algorithm is proposed to recover their preamble, data, and channel gains simultaneously, enabling the identification of active mobile users. Simulation results show that the proposed algorithm provides excellent performance and supports a massive number of devices. Moreover, the performance of the proposed scheme is independent of the total number of devices, distinguishing it from other random access schemes. The proposed method provides a unified solution to meet the requirements of machine-type communications and ultra reliable and low latency communications, making it an important contribution to the emerging 6G networks.

This work presents a novel framework for random access (RA) in crowded scenarios of massive multiple-input multiple-output (MIMO) systems. A huge portion of the system resources is dedicated as orthogonal pilots for accurate channel estimation which imposes a huge training overhead. This overhead can be highly mitigated by exploiting intrinsic angular domain sparsity of massive MIMO channels and the sporadic traffic of users, i.e., few number of users are active to send or receive data in each coherence interval. Besides, the continuous-valued angles of arrival (AoA) corresponding to each active user are alongside each other forming a specific cluster. To exploit these features in this work, we propose a blind clustering algorithm based on super-resolution techniques that not only detects the spatial features of the active users but also provides accurate channel estimation. Specifically, an off-grid atomic norm minimization is proposed to obtain the AoAs and then a clustering-based approach is employed to identify which AoAs correspond to which active users. After active user detection, an alternating-based optimization approach is performed to obtain the channels and transmitted data. Simulation results demonstrate the effectiveness of our approach in AoA detection as well as data recovery which indeed provides a high performance spatial-based RA in crowded massive MIMO systems.

In this letter, we consider a multiple-input single-output (MISO) linear time-varying system whose output is a superposition of scaled and time-frequency shifted versions of inputs. The goal of this letter is to determine system characteristics and input signals from the single output signal. More precisely, we want to recover the continuous time-frequency shift pairs, the corresponding (complex-valued) amplitudes and the input signals from only one output vector. This problem arises in a variety of applications such as radar imaging, microscopy, channel estimation and localization problems. While this problem is naturally ill-posed, by constraining the unknown input waveforms to lie in separate known low-dimensional subspaces, it becomes tractable. More explicitly, we propose a semidefinite program which exactly recovers time-frequency shift pairs and input signals. We prove uniqueness and optimality of the solution to this program. Moreover, we provide a grid-based approach which can significantly reduce computational complexity in exchange for adding a small gridding error. Numerical results confirm the ability of our proposed method to exactly recover the unknowns.

With the dominance of digital imaging systems, we are often dealing with discrete-domain samples of an analog image. Due to physical limitations, all imaging devices apply a blurring kernel on the input image before taking samples to form the output pixels. In this paper, we focus on the reconstruction of binary shape images from few blurred samples. This problem has applications in medical imaging, shape processing, and image segmentation. Our method relies on representing the analog shape image in a discrete grid much finer than the sampling grid. We formulate the problem as the recovery of a rank r matrix that is formed by a Hankel structure on the pixels. We further propose efficient ADMM-based algorithms to recover the low-rank matrix in both noiseless and noisy settings. We also analytically investigate the number of required samples for successful recovery in the noiseless case. For this purpose, we study the problem in the random sampling framework, and show that with O(r log4(n1n2)) random samples (where the size of the image is assumed to be n1 x n2) we can guarantee the perfect reconstruction with high probability under mild conditions. We further prove the robustness of the proposed recovery in the noisy setting by showing that the reconstruction error in the noisy case is bounded when the input noise is bounded. Simulation results confirm that our proposed method outperform the conventional total variation minimization in the noiseless settings.

This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to success as the number of measurements increases. In fact, in large dimensions, TV minimization succeeds in recovering the gradient-sparse signal with high probability when the number of measurements exceeds a certain threshold; otherwise, it fails almost certainly. Obtaining a closed-form expression that approximates this threshold is a major challenge in this field and has not been appropriately addressed yet. In this work, we derive a tight lower-bound on this threshold in case of any random measurement matrix whose null space is distributed uniformly with respect to the Haar measure. In contrast to the conventional TV phase transition results that depend on the simple gradient-sparsity level, our bound is highly affected by generalized notions of gradient-sparsity. Our proposed bound is very close to the true phase transition of TV minimization confirmed by simulation results.

In this letter, we consider the problem of recovering analysis-sparse signals from under-sampled measurements when some prior information about the support is available. We incorporate such information in the recovery stage by suitably tuning the weights in a weighted L1-analysis optimization problem. Indeed, we try to set the weights such that the method succeeds with minimum number of measurements. For this purpose, we exploit the upper-bound on the statistical dimension of a certain cone to determine the weights. Our numerical simulations confirm that the introduced method with tuned weights outperforms the standard L1-analysis technique.

We study the problem of reconstructing a block-sparse signal from compressively sampled measurements. In certain applications, in addition to the inherent block-sparse structure of the signal, some prior information about the block support, i.e., blocks containing non-zero elements, might be available. Although many block-sparse recovery algorithms have been investigated in the Bayesian framework, it is still unclear how to incorporate the information about the probability of occurrence into regularization-based block-sparse recovery in an optimal sense. In this letter, we bridge between these fields by the aid of a new concept in conic integral geometry. Specifically, we solve a weighted optimization problem when the prior distribution about the block support is available. Moreover, we obtain the unique weights that minimize the expected required number of measurements. Our simulations on both synthetic and real data confirm that these weights considerably decrease the required sample complexity.

Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and it has become standard to replace it with an upper-bound. To ensure that this technique is suitable, [1] has introduced an upper-bound on the gap between the statistical dimension and its approximation. In this work, we first show that the error bound in [1] in some low-dimensional models such as total variation and ℓ1analysis minimization becomes poorly large. Next, we develop a new error bound which significantly improves the estimation gap compared to [1]. In particular, unlike the bound in [1] that fails in some settings with overcomplete dictionaries, our bound exhibits a decaying behavior in such cases.

This letter considers the use of total variation (TV) minimization in the recovery of a given gradient sparse vector from Gaussian linear measurements. It has been shown in recent studies that there exists a sharp phase transition behavior in TV minimization for the number of measurements necessary to recover the signal in asymptotic regimes. The phase-transition curve specifies the boundary of success and failure of TV minimization for large number of measurements. It is a challenging task to obtain a theoretical bound that reflects this curve. In this letter, we present a novel upper bound that suitably approximates this curve and is asymptotically sharp. Numerical results show that our bound is closer to the empirical TV phase-transition curve than the previously known bound obtained by Kabanava.