Deconstructing the Composite Channel for Beyond Diagonal RIS: Channel Estimation and Beamforming Design

As beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) gain increasing attention in high-frequency wireless communications, accurate and scalable channel-estimation methods become essential. This paper develops a parametric channel-estimation and beamforming framework that deconstructs the composite BD-RIS channel into its generating directional factors, revealing the tensor structure induced jointly by propagation geometry and beyond-diagonal scattering. We propose two tensor-based estimators: Fourth-Order Tucker Channel Estimation (FORTE), which models the partially structured channel as a fourth-order Tucker tensor, and Fourth-Order PARAFAC Channel Estimation (FORPE), which captures the fully structured channel through a fourth-order PARAFAC model. By exploiting partial and full channel geometry, the proposed methods achieve higher estimation accuracy than Least Squares and Block Tucker Kronecker Factorization benchmarks. In particular, FORTE outperforms FORPE due to its more compact representation, attaining an NMSE of about 10^{-4} at 5 dB SNR. In contrast, FORPE provides essentially unique estimates of the composite-channel factor matrices, whereas FORTE identifies their subspaces. The proposed deconstruction also provides a structured representation useful for sensing-oriented parameter extraction and tensor-structured system optimization. Finally, the Tensor Optimization Framework for Beamforming, Combining, and Scattering (TenFormer) achieves spectral efficiency comparable to the benchmark design while significantly reducing computational complexity through parallel tensor-structured optimization.

PARAFAC-Based Time-Varying Channel Estimation for IRS-Aided Communications

This paper proposes a tensor-based parametric channel estimation technique for IRS-assisted communication systems with time-varying channel parameters. We exploit the multidimensional structure of the received signal by developing a $3$rd-order PARAFAC tensor model that is solved by employing the iteratively ALS algorithm. Our simulation results show that the proposed approach provides enhanced performance in terms of NMSE of the concatenated channel compared to the competing solutions by capitalizing on the intrinsic tensor structure of the received signal without increasing the computational complexity of the channel estimation.

Decoupled Delay-Doppler and Angle Estimation in BD-RIS Sensing via Nested Tucker Decomposition

We study single-target localization in a group-connected beyond-diagonal reconfigurable intelligent surface (BD-RIS)-assisted monostatic network with K element groups. We propose a Nested Tensor Factorization and Estimation (NTFE) algorithm that models the received signal as a 3rd-order nested Tucker tensor, decoupling the delay-Doppler and angle domains. The resulting two-stage procedure estimates the target-bearing tensor factors and then extracts the other physical parameters using subspace and closed-form steps. We also analyze identifiability and uniqueness conditions. Simulations show that NTFE exploits the group-connected BD-RIS structure and outperforms state-of-the-art sensing benchmarks.

Multi-Target Estimation via Tensor Decomposition for Beyond Diagonal RIS-Aided Bistatic Sensing

We investigate the performance of beyond-diagonal reconfigurable intelligent surfaces (BD-RIS) for bistatic MIMO multi-target sensing using a two-stage tensor Doppler-delay-angle estimation (TenDAE). The first stage solves a Kronecker sum approximation (KSA) with a rank equal to the number of targets. The second stage employs a nested tensor factorization estimation (NTFE) that exploits the inherent multidimensional structure via two tensor decompositions that are solved in parallel. The first employs a PARAFAC decomposition to extract the targets' angles, and the second uses a nested PARAFAC decomposition to find the targets' delay and Doppler parameters. This two-stage approach decouples acquisition of the angles and delays/Dopplers using either alternating least squares or a higher-order singular value decomposition, followed by a high-resolution subspace technique, such as ESPRIT. We further compare the performance of a BD-RIS with a classical diagonal RIS. For the latter, we solve a Khatri-Rao sum approximation problem rather than the KSA due to the specific structure of the received signal. Notably, our NTFE framework remains blind to the underlying RIS architecture while simultaneously estimating all targets with minimal sensing resources. Additionally, we show that employing a nested-PARAFAC decomposition enables the decoupling of the delay-Doppler and angle domains. We also derive the Cramér-Rao lower bound to further assess the performance of the TenDAE framework. Finally, we numerically evaluate the solutions presented in this paper and demonstrate their efficiency in terms of RMSE compared with state-of-the-art approaches.

Cramér-Rao Bound Analysis of Bistatic ISAC Under Partial Symbol Knowledge and Clutter

Integrated sensing and communication (ISAC) systems rely on communication waveforms to perform sensing tasks, thus making their sensing performance strongly dependent on the level of communication symbol knowledge available to the sensing receivers. However, the existing literature fails to capture this dependency, often relying on full symbol knowledge assumptions. In this paper, we present a Cramer Rao bound (CRB) analysis of a bistatic ISAC network with heterogeneous uplink and downlink illumination and structured clutter. We consider different symbol knowledge regimes by modeling unknown communication symbols as nuisance parameters. Assuming a temporal evolution of the communication channel, we derive a correlation aware channel estimator and an expression for the UEs uplink spectral efficiency (SE). Numerical results show the CRB degradation induced by clutter and symbol uncertainty and how this can affect resource allocation policies. We also show the performance gain of our channel estimator relative to conventional block fading architectures.

Living Off the Grid: Continuous Range-Angle Super-Resolution for Near-Field XL-MIMO

Near-field extremely large multiple input multiple output (XL-MIMO) breaks the assumptions that make classical super-resolution effective: the receiver acquires only a limited set of compressed pilot observations, while each propagation path is jointly determined by angle and distance under a spherical-wave model. This invalidates the far-field Vandermonde structure exploited by conventional methods, and many existing near-field formulations remain only gridless by discretizing range and angle and thus inheriting mismatch, coherence, and resolution loss. This paper develops a continuous 2D super-resolution framework for hybrid near-field measurements that avoids range and angle gridding. The key idea is to reparameterize distance through inverse range, which reveals a compact spectral structure for the near-field spherical-wave manifold. Building on this observation, we introduce a panelized weighted fitting strategy that converts the range-dependent Fresnel terms into a stable transform-domain representation, resulting in a lifted mode, in which each continuous range-angle pair is embedded as a structured rank-one atom and the measurement model remains linear under hybrid combining. Recovery is then posed as a 2D atomic norm minimization, with path localization certified through a dual polynomial over the transformed domain. Numerical experiments show exact support recovery in the noiseless setting using only few compressed hybrid measurements. These results establish the proposed inverse-range atomic norm viewpoint as a new gridless foundation for near-field sensing and channel estimation in hybrid XL-MIMO and integrated sensing and communication systems.

Hierarchical Federated Learning with SignSGD: A Highly Communication-Efficient Approach

Hierarchical federated learning (HFL) has emerged as a key architecture for large-scale wireless and Internet of Things systems, where devices communicate with nearby edge servers before reaching the cloud. In these environments, uplink bandwidth and latency impose strict communication limits, thereby making aggressive gradient compression essential. One-bit methods such as sign-based stochastic gradient descent (SignSGD) offer an attractive solution in flat federated settings, but existing theory and algorithms do not naturally extend to hierarchical settings. In particular, the interaction between majority-vote aggregation at the edge layer and model aggregation at the cloud layer, and its impact on end-to-end performance, remains unknown. To bridge this gap, we propose a highly communication-efficient sign-based HFL framework and develop its corresponding formulation for nonconvex learning, where devices send only signed stochastic gradients, edge servers combine them through majority-vote, and the cloud periodically averages the obtained edge models, while utilizing downlink quantization to broadcast the global model. We introduce the resulting scalable HFL algorithm, HierSignSGD, and provide the convergence analysis for SignSGD in a hierarchical setting. Our core technical contribution is a characterization of how biased sign compression, two-level aggregation intervals, and inter-cluster heterogeneity collectively affect convergence. Numerical experiments under homogeneous and heterogeneous data splits show that HierSignSGD, despite employing extreme compression, achieves accuracy comparable to or better than full-precision stochastic gradient descent while reducing communication cost in the process, and remains robust under aggressive downlink sparsification.

On the Impact of Channel Aging and Doppler-Affected Clutter on OFDM ISAC Systems

The temporal evolution of the propagation environment plays a central role in integrated sensing and communication (ISAC) systems. A slow-time evolution manifests as channel aging in communication links, while a fast-time one is associated with structured clutter with non-zero Doppler. Nevertheless, the joint impact of these two phenomena on ISAC performance has been largely overlooked. This addresses this research gap in a network utilizing orthogonal frequency division multiplexing waveforms. Here, a base station simultaneously serves multiple user equipment (UE) devices and performs monostatic sensing. Channel aging is captured through an autoregressive model with exponential correlation decay. In contrast, clutter is modeled as a collection of uncorrelated, coherent patches with non-zero Doppler, resulting in a Kronecker-separable covariance structure. We propose an aging-aware channel estimator that uses prior pilot observations to estimate the time-varying UE channels, characterized by a non-isotropic multipath fading structure. The clutter's structure enables a novel low-complexity sensing pipeline: clutter statistics are estimated from raw data and subsequently used to suppress the clutter's action, after which target parameters are extracted through range-angle and range-velocity maps. We evaluate the influence of frame length and pilot history on channel estimation accuracy and demonstrate substantial performance gains over block fading in low-to-moderate mobility regimes. The sensing pipeline is implemented in a clutter-dominated environment, demonstrating that effective clutter suppression can be achieved under practical configurations. Furthermore, our results show that dedicated sensing streams are required, as communication beams provide insufficient range resolution.

Pilot-to-Data Power Ratio in RIS-Assisted Multiantenna Communication

The optimization of the \gls{pdpr} is a recourse that helps wireless systems to acquire channel state information while minimizing the pilot overhead. While the optimization of the \gls{pdpr} in cellular networks has been studied extensively, the effect of the \gls{pdpr} in \gls{ris}-assisted networks has hardly been examined. This paper tackles this optimization when the communication is assisted by a RIS whose phase shifts are adjusted on the basis of the statistics of the channels. For a setting representative of a macrocellular deployment, the benefits of optimizing the PDPR are seen to be significant over a broad range of operating conditions. These benefits, demonstrated through the ergodic minimum mean squared error, for which a closed-form solution is derived, become more pronounced as the number of RIS elements and/or the channel coherence grow large.

When Near Becomes Far: From Rayleigh to Optimal Near-Field and Far-Field Boundaries

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.