This paper considers a joint scattering environment sensing and data recovery problem in an uplink integrated sensing and communication (ISAC) system. To facilitate joint scatterers localization and multi-user (MU) channel estimation, we introduce a three-dimensional (3D) location-domain sparse channel model to capture the joint sparsity of the MU channel (i.e., different user channels share partially overlapped scatterers). Then the joint problem is formulated as a bilinear structured sparse recovery problem with a dynamic position grid and imperfect parameters (such as time offset and user position errors). We propose an expectation maximization based turbo bilinear subspace variational Bayesian inference (EM-Turbo-BiSVBI) algorithm to solve the problem effectively, where the E-step performs Bayesian estimation of the the location-domain sparse MU channel by exploiting the joint sparsity, and the M-step refines the dynamic position grid and learns the imperfect factors via gradient update. Two methods are introduced to greatly reduce the complexity with almost no sacrifice on the performance and convergence speed: 1) a subspace constrained bilinear variational Bayesian inference (VBI) method is proposed to avoid any high-dimensional matrix inverse; 2) the multiple signal classification (MUSIC) and subspace constrained VBI methods are combined to obtain a coarse estimation result to reduce the search range. Simulations verify the advantages of the proposed scheme over baseline schemes.

With the advancement of wireless communications toward higher user densities and increasingly complex environments, near-field communication has emerged as a critical research focus. Supporting multi-user access in this regime with manageable complexity remains a key challenge, particularly due to the coupling between the spherical wavefront effect and the spatial non-stationarity (SnS) property, which complicates the exploitation of spatial correlation among user channels. To address this, we propose a unified multi-user channel model that incorporates joint support to capture the structured sparsity shared across users. Additionally, we introduce a two-dimensional (2D) Markov prior to model both local sparsity pattern continuity across adjacent grid points and joint burst sparsity in the shared support structure. Based on this, we develop a spatial information-sharing-aided framework that alternately estimates model parameters. Specifically, an inverse-free variational Bayesian inference (IF-VBI) algorithm is employed in the channel estimation module to avoid high-dimensional matrix inversion while enabling information exchange among users via joint support. In the common grid update module, joint updates across users are performed to achieve a full spatial-domain optimum, whereas in the joint visible region (VR) matrix detection module, the user-sharing structure is exploited to decouple and efficiently solve the VR matrix. Simulation results validate the effectiveness of the proposed approach, demonstrating improved estimation accuracy and computational efficiency in multi-user near-field extremely large-scale multiple-input-multiple-output (XL-MIMO) systems.

This work considers a spatially non-stationary channel tracking problem in broadband extremely large-scale multiple-input-multiple-output (XL-MIMO) systems. In the case of spatial non-stationarity, each scatterer has a certain visibility region (VR) over antennas and power change may occur among visible antennas. Concentrating on the temporal correlation of XL-MIMO channels, we design a three-layer Markov prior model and hierarchical two-dimensional (2D) Markov model to exploit the dynamic sparsity of sparse channel vectors and VRs, respectively. Then, we formulate the channel tracking problem as a bilinear measurement process, and develop a novel dynamic alternating maximum a posteriori (DA-MAP) method to solve the problem. DA-MAP contains four core modules: channel estimation module, VR detection module, grid update module, and temporal processing module. Specifically, the first module is an inverse-free variational Bayesian inference (IF-VBI) estimator that avoids computationally intensive matrix inverse in each iteration; the second module is a turbo compressive sensing (Turbo-CS) algorithm that only needs small-scale matrix operations in a parallel fashion; the third module refines the polar-delay domain grid; and the fourth module can process the temporal prior information to ensure high-efficiency channel tracking. Simulation results demonstrate that the proposed method achieves significant improvements in channel tracking performance with low computational overhead.

Integrated sensing and communication (ISAC) has drawn great attention for its capacity to simultaneously support wireless communication and environmental sensing. However, in dynamic ISAC systems, environmental mobility poses critical challenges in both dynamic channel estimation and continuous sensing parameter tracking across multiple time slots under severe Doppler effect. To address these challenges with a unified framework, we propose a novel base station-user cooperative sensing approach for joint dynamic channel estimation and sensing parameter tracking, including target/scatterer locations and actual velocities, which is formulated as a maximum a posterior (MAP) problem. In cases where some moving radar targets also serve as communication scatterers, the spatial overlap induces an underlying partially common sparsity between the location-domain sensing and communication channels. Based on this, we develop a two-dimensional Markov Model (2D-MM) based on dynamic location grids to capture the spatio-temporal correlations and partially common sparsity, thereby enhancing both sensing and communication performance. To alleviate the high-complexity matrix inverse in the E-step of sparse Bayesian inference, we propose a dynamic subspace-constrained variational Bayesian inference (D-SCVBI) algorithm with the aid of prior information obtained from the two-dimensional discrete Fourier transform (2D-DFT) localization and state evolution model. Finally, simulations show that the proposed D-SCVBI algorithm attains remarkable performance gains over various baselines.

Positioning and sensing, as critical enablers for emerging applications, can be further empowered by multi-band fusion technology. In this paper, a two-stage framework utilizing position-domain joint stochastic particle variational Bayesian inference (PD-JSPVBI) is proposed to address the key challenges in time-of-arrival (TOA)-based direct position determination. Unlike existing works focusing on multi-band delay estimation or single-band direct positioning, our unified framework enables joint target localization directly from multi-station, multiband signals. The algorithm integrates prior information and resolves spatial coordinate coupling via a novel two-dimensional particle-based variational approximation, significantly improving estimation efficiency. Additionally, a joint estimation mechanism is introduced to synchronously optimize positioning parameters (e.g., target coordinates) and non-ideal factors (e.g., timing synchronization errors, random initial phases) within a unified variational framework. Simulation results validate the proposed algorithm's superiority, outperforming conventional cascaded architectures by eliminating error propagation and leveraging multi-band coherence. The proposed solution offers a promising pathway for high-precision direct positioning systems.

We investigate a joint scattering environment sensing, channel estimation, and data recovery problem in an uplink integrated sensing and communication (ISAC) system. Based on a three-dimensional (3D) location-domain sparse channel model, the joint problem is formulated as a bilinear sparse recovery problem with a dynamic position grid and imperfect parameters. We propose an expectation maximization based bilinear subspace variational Bayesian inference (EM-BiSVBI) algorithm to solve the problem effectively, where the E-step performs Bayesian estimation of the the location-domain sparse channel and transmitted data, and the M-step refines the dynamic position grid and learns the imperfect factors via gradient update. In particular, the BiSVBI algorithm in the E-step avoids the high-dimensional matrix inverse by a subspace constrained approach while ensuring convergence to a stationary solution of the Kullback-Leibler divergence minimization problem. Simulations verify the advantages of the proposed method over baselines.

We investigate a joint visibility region (VR) detection and channel estimation problem in extremely large-scale multiple-input-multiple-output (XL-MIMO) systems, where nearfield propagation and spatial non-stationary effects exist. In this case, each scatterer can only see a subset of antennas, i.e., it has a certain VR over the antennas. A novel alternating maximum a posteriori (MAP) framework is developed for high-accuracy VR detection and channel estimation, which consists of three basic modules: a channel estimation module, a VR detection module, and a grid update module. Specifically, the first module is a low-complexity inverse-free variational Bayesian inference (IF-VBI) algorithm that avoids the matrix inverse via minimizing a relaxed Kullback-Leibler (KL) divergence. The second module is an expectation propagation (EP) algorithm that can recover binary VRs. And the third module refines polar-domain grid parameters via gradient ascent. Simulations demonstrate the superiority of the proposed algorithm in both VR detection and channel estimation.

This paper considers an intelligent unmanned cluster system, where edge nodes need to communicate with a cluster head to collaborate on certain tasks, posing higher requirements for accurate channel estimation and localization of edge nodes. To achieve this, we propose a joint channel estimation and cooperative localization scheme by fusing the pilot signals and location prior information (LPI). In particular, we propose a mixed location-delay domain channel model, where the dominant channel paths are modeled using the nodes' locations, while the others are modeled using a delay-domain sparse channel prior. In this way, LPI is directly exploited to achieve high-accuracy channel estimation with limited pilot overhead. In turn, the more accurate channel estimation results are exploited to achieve cooperative localization among nodes. By combining the turbo approach and the expectation-maximization (EM) method, we propose a LPI-aided EM-based turbo compressive sensing (EM-Turbo-CS) algorithm that updates the location-delay domain channel coefficients and location/delay parameters alternately to achieve high-precision channel estimation and node localization with limited pilot overhead. Finally, the feasibility and superiority of the proposed scheme are verified through simulations.

For many practical applications in wireless communications, we need to recover a structured sparse signal from a linear observation model with dynamic grid parameters in the sensing matrix. Conventional expectation maximization (EM)-based compressed sensing (CS) methods, such as turbo compressed sensing (Turbo-CS) and turbo variational Bayesian inference (Turbo-VBI), have double-loop iterations, where the inner loop (E-step) obtains a Bayesian estimation of sparse signals and the outer loop (M-step) obtains a point estimation of dynamic grid parameters. This leads to a slow convergence rate. Furthermore, each iteration of the E-step involves a complicated matrix inverse in general. To overcome these drawbacks, we first propose a successive linear approximation VBI (SLA-VBI) algorithm that can provide Bayesian estimation of both sparse signals and dynamic grid parameters. Besides, we simplify the matrix inverse operation based on the majorization-minimization (MM) algorithmic framework. In addition, we extend our proposed algorithm from an independent sparse prior to more complicated structured sparse priors, which can exploit structured sparsity in specific applications to further enhance the performance. Finally, we apply our proposed algorithm to solve two practical application problems in wireless communications and verify that the proposed algorithm can achieve faster convergence, lower complexity, and better performance compared to the state-of-the-art EM-based methods.

Future wireless networks are envisioned to provide ubiquitous sensing services, driving a substantial demand for multi-dimensional non-convex parameter estimation. This entails dealing with non-convex likelihood functions containing numerous local optima. Variational Bayesian inference (VBI) provides a powerful tool for modeling complex estimation problems and leveraging prior information, but poses a long-standing challenge on computing intractable posterior distributions. Most existing variational methods depend on specific distribution assumptions for obtaining closed-form solutions, and are difficult to apply in practical scenarios. Given these challenges, firstly, we propose a parallel stochastic particle VBI (PSPVBI) algorithm. Due to innovations like particle approximation, added updates of particle positions, and parallel stochastic successive convex approximation (PSSCA), PSPVBI can flexibly drive particles to fit the posterior distribution with acceptable complexity, yielding high-precision estimates of the target parameters. Furthermore, additional speedup can be obtained by deep-unfolding this algorithm. Specifically, superior hyperparameters are learned to dramatically reduce iterations. In this PSPVBI-induced deep-unfolding network, some techniques related to gradient computation, data sub-sampling, differentiable sampling, and generalization ability are also employed to facilitate the practical deployment. Finally, we apply the learnable PSPVBI (LPSPVBI) to solve two important positioning/sensing problems over wireless networks. Simulations indicate that the LPSPVBI algorithm outperforms existing solutions.

This paper considers an integrated sensing and communication system, where some radar targets also serve as communication scatterers. A location domain channel modeling method is proposed based on the position of targets and scatterers in the scattering environment, and the resulting radar and communication channels exhibit a two-dimensional (2-D) joint burst sparsity. We propose a joint scattering environment sensing and channel estimation scheme to enhance the target/scatterer localization and channel estimation performance simultaneously, where a spatially non-stationary Markov random field (MRF) model is proposed to capture the 2-D joint burst sparsity. An expectation maximization (EM) based method is designed to solve the joint estimation problem, where the E-step obtains the Bayesian estimation of the radar and communication channels and the M-step automatically learns the dynamic position grid and prior parameters in the MRF. However, the existing sparse Bayesian inference methods used in the E-step involve a high-complexity matrix inverse per iteration. Moreover, due to the complicated non-stationary MRF prior, the complexity of M-step is exponentially large. To address these difficulties, we propose an inverse-free variational Bayesian inference algorithm for the E-step and a low-complexity method based on pseudo-likelihood approximation for the M-step. In the simulations, the proposed scheme can achieve a better performance than the state-of-the-art method while reducing the computational overhead significantly.

This paper considers an integrated sensing and communication system, where some radar targets also serve as communication scatterers. A location domain channel modeling method is proposed based on the position of targets and scatterers in the scattering environment, and the resulting radar and communication channels exhibit a partially common sparsity. By exploiting this, we propose a joint scattering environment sensing and channel estimation scheme to enhance the target/scatterer localization and channel estimation performance simultaneously. Specifically, the base station (BS) first transmits downlink pilots to sense the targets in the scattering environment. Then the user transmits uplink pilots to estimate the communication channel. Finally, joint scattering environment sensing and channel estimation are performed at the BS based on the reflected downlink pilot signal and received uplink pilot signal. A message passing based algorithm is designed by combining the turbo approach and the expectation maximization method. The advantages of our proposed scheme are verified in the simulations.