CP-OFDM Achieves Lower Ranging CRB Than Frequency-Spread Waveforms in the Large-Sample Regime

The inherent randomness of communication symbols creates a fundamental tension in Integrated Sensing and Communications (ISAC). On the one hand, they enable data transmission while allowing sensing to fully reuse communication resources. On the other hand, their randomness induces waveform-dependent fluctuations that directly affect sensing accuracy. This paper investigates a foundational question arising from this tradeoff: \textit{How does the modulation waveform affect the ranging Cramér--Rao Bound (CRB) when sensing reuses random data symbols?} We address this question by revealing a structural factorization of the Fisher information matrix (FIM) for joint delay-amplitude estimation, which separates the deterministic Jacobian of the target geometry from the random frequency-domain signal power induced by the data symbols. This structure yields a Jensen-type universal lower bound on the CRB, which is exactly attained by CP-OFDM under PSK constellations. For QAM and broader sub-Gaussian constellations, we develop an asymptotic perturbation analysis of the inverse FIM and prove that, when the number of transmitted symbols $N$ grows large, CP-OFDM achieves a lower ranging CRB than any frequency-spread orthogonal waveform over the almost-sure event where the random FIM is invertible. This superiority is further extended to amplitude estimation and full joint delay-amplitude estimation. We also characterize the local geometry of the stochastic CRB minimization problem over the unitary group. The analysis reveals that CP-OFDM is a stationary point for finite $N$, and its Riemannian Hessian is positive semidefinite for sufficiently large $N$, establishing its asymptotic local optimality. Numerical results confirm that OFDM outperforms representative waveforms including SC, OTFS, and AFDM.

Proximal-Based Generative Modeling for Bayesian Inverse Problems

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we propose a novel proximal-based generative modeling (PGM) framework that rigorously circumvents explicit likelihood evaluation. Our framework is built upon a theoretical equivalence between Gaussian convolution in diffusion processes and Moreau-Yosida regularization in nonsmooth optimization. This enables a new sampling mechanism driven by the proposed Moreau score, which admits a closed-form expression via proximal operators. Moreover, we introduce Moreau score matching to learn the proximal operators that rely solely on samples drawn from the prior distribution. Theoretically, PGM eliminates the early-stopping bias inherent in the score-based diffusion model and achieves non-asymptotic convergence. Experiments demonstrate that PGM significantly surpasses state-of-the-art methods in reconstruction quality and sampling time.

Byzantine-Robust Distributed SGD: A Unified Analysis and Tight Error Bounds

Byzantine-robust distributed optimization relies on robust aggregation rules to mitigate the influence of malicious Byzantine workers. Despite the proliferation of such rules, a unified convergence analysis framework that accommodates general data heterogeneity is lacking. In this work, we provide a thorough convergence theory of Byzantine-robust distributed stochastic gradient descent (SGD), analyzing variants both with and without local momentum. We establish the convergence rates for nonconvex smooth objectives and those satisfying the Polyak-Lojasiewicz condition under a general data heterogeneity assumption. Our analysis reveals that while stochasticity and data heterogeneity introduce unavoidable error floors, local momentum provably reduces the error component induced by stochasticity. Furthermore, we derive matching lower bounds to demonstrate that the upper bounds obtained in our analysis are tight and characterize the fundamental limits of Byzantine resilience under stochasticity and data heterogeneity. Empirical results support our theoretical findings.

Optimal Low-Dimensional Structures of ISAC Beamforming: Theory and Efficient Algorithms

Transmit beamforming design is a fundamental problem in integrated sensing and communication (ISAC) systems. Numerous methods have been proposed to jointly optimize key performance metrics such as the signal-to-interference-plus-noise ratio and Cramér-Rao bound. However, the computational complexity of these methods often grows rapidly with the number of transmit antennas at the base station (BS). To tackle this challenge, we prove a fundamental structural property of the ISAC beamforming problem, i.e., there exists an optimal solution exhibiting a low-dimensional structure. This leads to an equivalent reformulation of the problem with dimension related to the number of users rather than the number of BS antennas, thereby enabling the development of low-complexity algorithms. When applying the interior-point method to the reformulated problem, we achieve up to six orders of magnitude in complexity reduction when the number of antennas exceeds the number of users by an order of magnitude. To further reduce the complexity, we develop a balanced augmented Lagrangian method to solve the reformulated problem. The proposed algorithm maintains optimality while achieving a computational complexity that scales quartically with the number of users. Our simulation results demonstrate that the proposed R-BAL method can achieve a speedup of more than 10000$\times$ over the conventional IPM in massive MIMO scenarios.

An AMP-Based Asymptotic Analysis For Nonlinear One-Bit Precoding

This paper focuses on the asymptotic analysis of a class of nonlinear one-bit precoding schemes under Rayleigh fading channels. The considered scheme employs a convex-relaxation-then-quantization (CRQ) approach to the well-known minimum mean square error (MMSE) model, which includes the classical one-bit precoder SQUID as a special case. To analyze its asymptotic behavior, we develop a novel analytical framework based on approximate message passing (AMP). We show that, the statistical properties of the considered scheme can be asymptotically characterized by a scalar ``signal plus Gaussian noise'' model. Based on this, we further derive a closed-form expression for the symbol error probability (SEP) in the large-system limit, which quantitatively characterizes the impact of both system and model parameters on SEP performance. Simulation results validate our analysis and also demonstrate that performance gains over SQUID can be achieved by appropriately tuning the parameters involved in the considered model.

RIS-Enhanced Information-Decoupled Symbiotic Radio Over Broadcasting Signals

This paper studies a reconfigurable intelligent surface (RIS)-enhanced decoupled symbiotic radio (SR) system in which a primary transmitter delivers common data to multiple primary receivers (PRs), while a RIS-based backscatter device sends secondary data to a backscatter receiver (BRx). Unlike conventional SR, the BRx performs energy detection and never decodes the primary signal, thereby removing ambiguity and preventing exposure of the primary payload to unintended receivers. In this paper, we formulate the problem as the minimization of the transmit power subject to a common broadcast rate constraint across all PRs and a bit error rate (BER) constraint at the BRx. The problem is nonconvex due to the unit-modulus RIS constraint and coupled quadratic forms. Leveraging a rate-balanced reformulation and a monotonic BER ratio characterization, we develop a low-complexity penalty-based block coordinate descent algorithm with closed-form updates. Numerical results show fast convergence of the proposed algorithm and reduced power consumption of the considered RIS-enhanced information-decoupled SR system over conventional SR baselines.

Duality-Based Fixed Point Iteration Algorithm for Beamforming Design in ISAC Systems

In this paper, we investigate the beamforming design problem in an integrated sensing and communication (ISAC) system, where a multi-antenna base station simultaneously serves multiple communication users while performing radar sensing. We formulate the problem as the minimization of the total transmit power, subject to signal-to-interference-plus-noise ratio (SINR) constraints for communication users and mean-squared-error (MSE) constraints for radar sensing. The core challenge arises from the complex coupling between communication SINR requirements and sensing performance metrics. To efficiently address this challenge, we first establish the equivalence between the original ISAC beamforming problem and its semidefinite relaxation (SDR), derive its Lagrangian dual formulation, and further reformulate it as a generalized downlink beamforming (GDB) problem with potentially indefinite weighting matrices. Compared to the classical DB problem, the presence of indefinite weighting matrices in the GDB problem introduces substantial analytical and computational challenges. Our key technical contributions include (i) a necessary and sufficient condition for the boundedness of the GDB problem, and (ii) a tailored efficient fixed point iteration (FPI) algorithm with a provable convergence guarantee for solving the GDB problem. Building upon these results, we develop a duality-based fixed point iteration (Dual-FPI) algorithm, which integrates an outer subgradient ascent loop with an inner FPI loop. Simulation results demonstrate that the proposed Dual-FPI algorithm achieves globally optimal solutions while significantly reducing computational complexity compared with existing baseline approaches.

A Unified Distributed Algorithm for Hybrid Near-Far Field Activity Detection in Cell-Free Massive MIMO

A great amount of endeavor has recently been devoted to activity detection for massive machine-type communications in cell-free multiple-input multiple-output (MIMO) systems. However, as the number of antennas at the access points (APs) increases, the Rayleigh distance that separates the near-field and far-field regions also expands, rendering the conventional assumption of far-field propagation alone impractical. To address this challenge, this paper establishes a covariance-based formulation that can effectively capture the statistical property of hybrid near-far field channels. Based on this formulation, we theoretically reveal that increasing the proportion of near-field channels enhances the detection performance. Furthermore, we propose a distributed algorithm, where each AP performs local activity detection and only exchanges the detection results to the central processing unit, thus significantly reducing the computational complexity and the communication overhead. Not only with convergence guarantee, the proposed algorithm is unified in the sense that it can handle single-cell or cell-free systems with either near-field or far-field devices as special cases. Simulation results validate the theoretical analyses and demonstrate the superior performance of the proposed approach compared with existing methods.

Asymptotic Analysis of Nonlinear One-Bit Precoding in Massive MIMO Systems via Approximate Message Passing

Massive multiple-input multiple-output (MIMO) systems employing one-bit digital-to-analog converters offer a hardware-efficient solution for wireless communications. However, the one-bit constraint poses significant challenges for precoding design, as it transforms the problem into a discrete and nonconvex optimization task. In this paper, we investigate a widely adopted ``convex-relaxation-then-quantization" approach for nonlinear symbol-level one-bit precoding. Specifically, we first solve a convex relaxation of the discrete minimum mean square error precoding problem, and then quantize the solution to satisfy the one-bit constraint. To analyze the high-dimensional asymptotic performance of this scheme, we develop a novel analytical framework based on approximate message passing (AMP). This framework enables us to derive a closed-form expression for the symbol error probability (SEP) at the receiver side in the large-system limit, which provides a quantitative characterization of how model and system parameters affect the SEP performance. Our empirical results suggest that the $\ell_\infty^2$ regularizer, when paired with an optimally chosen regularization parameter, achieves optimal SEP performance within a broad class of convex regularization functions. As a first step towards a theoretical justification, we prove the optimality of the $\ell_\infty^2$ regularizer within the mixed $\ell_\infty^2$-$\ell_2^2$ regularization functions.

Distributed Activity Detection for Cell-Free Hybrid Near-Far Field Communications

A great amount of endeavor has recently been devoted to activity detection for massive machine-type communications in cell-free massive MIMO. However, in practice, as the number of antennas at the access points (APs) increases, the Rayleigh distance that separates the near-field and far-field regions also expands, rendering the conventional assumption of far-field propagation alone impractical. To address this challenge, this paper considers a hybrid near-far field activity detection in cell-free massive MIMO, and establishes a covariance-based formulation, which facilitates the development of a distributed algorithm to alleviate the computational burden at the central processing unit (CPU). Specifically, each AP performs local activity detection for the devices and then transmits the detection result to the CPU for further processing. In particular, a novel coordinate descent algorithm based on the Sherman-Morrison-Woodbury update with Taylor expansion is proposed to handle the local detection problem at each AP. Moreover, we theoretically analyze how the hybrid near-far field channels affect the detection performance. Simulation results validate the theoretical analysis and demonstrate the superior performance of the proposed approach compared with existing approaches.