Group Sparsity Methods for Compressive Space-Frequency Channel Estimation and Spatial Equalization in Fluid Antenna System

Fluid Antenna System (FAS) unlocks unprecedented flexibility in wireless channel optimization through spatial reconfigurability. However, its practical deployment is hindered by the coupled challenges posed by high-dimensional channel estimation and real-time position optimization. This paper bridges wireless propagation physics with compressed sensing theory to address these challenges through three aspects. First, we establish a group-sparse recovery framework for space-frequency characteristics (SFC) in FAS, formally characterizing leakage-induced sparsity degradation from limited aperture and bandwidth as a structured group-sparsity problem. By deriving dictionary-adapted group restricted isometry property (D-GRIP), we prove tight recovery bounds for a convex $\ell_1/\ell_2$-mixed norm optimization formulation that preserves leakage-aware sparsity patterns. Second, we develop a Descending Correlation Group Orthogonal Matching Pursuit (DC-GOMP) algorithm that systematically relaxes leakage constraints to reduce subcoherence. This approach enables robust FSC recovery with accelerated convergence and superior performance compared to conventional compressive sensing methods like OMP or GOMP. Third, we formulate spatial equalization (SE) as a mixed-integer linear programming (MILP) problem, ensuring optimality through the branch-and-bound method. To achieve real-time implementability while maintaining near-optimal performance, we complement this with a greedy algorithm. Simulation results demonstrate the proposed channel estimation algorithm effectively resolves energy misallocation and enables recovery of weak details, achieving superior recovery accuracy and convergence rate. The SE framework suppresses deep fading phenomena and reduces hardware deployment overhead while maintaining equivalent link reliability.

Holographic MIMO Multi-Cell Communications

Metamaterial antennas are appealing for next-generation wireless networks due to their simplified hardware and much-reduced size, power, and cost. This paper investigates the holographic multiple-input multiple-output (HMIMO)-aided multi-cell systems with practical per-radio frequency (RF) chain power constraints. With multiple antennas at both base stations (BSs) and users, we design the baseband digital precoder and the tuning response of HMIMO metamaterial elements to maximize the weighted sum user rate. Specifically, under the framework of block coordinate descent (BCD) and weighted minimum mean square error (WMMSE) techniques, we derive the low-complexity closed-form solution for baseband precoder without requiring bisection search and matrix inversion. Then, for the design of HMIMO metamaterial elements under binary tuning constraints, we first propose a low-complexity suboptimal algorithm with closed-form solutions by exploiting the hidden convexity (HC) in the quadratic problem and then further propose an accelerated sphere decoding (SD)-based algorithm which yields global optimal solution in the iteration. For HMIMO metamaterial element design under the Lorentzian-constrained phase model, we propose a maximization-minorization (MM) algorithm with closed-form solutions at each iteration step. Furthermore, in a simplified multiple-input single-output (MISO) scenario, we derive the scaling law of downlink single-to-noise (SNR) for HMIMO with binary and Lorentzian tuning constraints and theoretically compare it with conventional fully digital/hybrid arrays. Simulation results demonstrate the effectiveness of our algorithms compared to benchmarks and the benefits of HMIMO compared to conventional arrays.

Affine Frequency Division Multiplexing: Extending OFDM for Scenario-Flexibility and Resilience

Next-generation wireless networks are conceived to provide reliable and high-data-rate communication services for diverse scenarios, such as vehicle-to-vehicle, unmanned aerial vehicles, and satellite networks. The severe Doppler spreads in the underlying time-varying channels induce destructive inter-carrier interference (ICI) in the extensively adopted orthogonal frequency division multiplexing (OFDM) waveform, leading to severe performance degradation. This calls for a new air interface design that can accommodate the severe delay-Doppler spreads in highly dynamic channels while possessing sufficient flexibility to cater to various applications. This article provides a comprehensive overview of a promising chirp-based waveform named affine frequency division multiplexing (AFDM). It is featured with two tunable parameters and achieves optimal diversity order in doubly dispersive channels (DDC). We study the fundamental principle of AFDM, illustrating its intrinsic suitability for DDC. Based on that, several potential applications of AFDM are explored. Furthermore, the major challenges and the corresponding solutions of AFDM are presented, followed by several future research directions. Finally, we draw some instructive conclusions about AFDM, hoping to provide useful inspiration for its development.

Uncovering the Iceberg in the Sea: Fundamentals of Pulse Shaping and Modulation Design for Random ISAC Signals

Integrated Sensing and Communications (ISAC) is expected to play a pivotal role in future 6G networks. To maximize time-frequency resource utilization, 6G ISAC systems must exploit data payload signals, that are inherently random, for both communication and sensing tasks. This paper provides a comprehensive analysis of the sensing performance of such communication-centric ISAC signals, with a focus on modulation and pulse shaping design to reshape the statistical properties of their auto-correlation functions (ACFs), thereby improving the target ranging performance. We derive a closed-form expression for the expectation of the squared ACF of random ISAC signals, considering arbitrary modulation bases and constellation mappings within the Nyquist pulse shaping framework. The structure is metaphorically described as an ``iceberg hidden in the sea", where the ``iceberg'' represents the squared mean of the ACF of random ISAC signals, that is determined by the pulse shaping filter, and the ``sea level'' characterizes the corresponding variance, caused by the randomness of the data payload. Our analysis shows that, for QAM/PSK constellations with Nyquist pulse shaping, Orthogonal Frequency Division Multiplexing (OFDM) achieves the lowest ranging sidelobe level across all lags. Building on these insights, we propose a novel Nyquist pulse shaping design to enhance the sensing performance of random ISAC signals. Numerical results validate our theoretical findings, showing that the proposed pulse shaping significantly reduces ranging sidelobes compared to conventional root-raised cosine (RRC) pulse shaping, thereby improving the ranging performance.

Distributed Beam Alignment in sub-THz D2D Networks

Devices in a device-to-device (D2D) network operating in sub-THz frequencies require knowledge of the spatial channel that connects them to their peers. Acquiring such high dimensional channel state information entails large overhead, which drastically increases with the number of network devices. In this paper, we propose an accelerated method to achieve network-wide beam alignment in an efficient way. To this aim, we consider compressed sensing estimation enabled by a novel design of pilot sequences. Our designed pilots have constant envelope to alleviate hardware requirements at the transmitters, while they exhibit a "comb-like"' spectrum that flexibly allocates energy only on certain frequencies. This design enables multiple devices to transmit thier pilots concurrently while remaining orthogonal in frequency, achieving simultaneous alignment of multiple devices. Furthermore, we present a sequential partitioning strategy into transmitters and receivers that results in logarithmic scaling of the overhead with the number of devices, as opposed to the conventional linear scaling. Finally, we show via accurate modeling of the indoor propagation environment and ray tracing simulations that the resulting sub-THz channels after successful beamforming are approximately frequency flat, therefore suitable for efficient single carrier transmission without equalization. We compare our results against an "802.11ad inspired" baseline and show that our method is capable to greatly reduce the number of pilots required to achieve network-wide alignment.

Cooperative Multistatic Target Detection in Cell-Free Communication Networks

In this work, we consider the target detection problem in a multistatic integrated sensing and communication (ISAC) scenario characterized by the cell-free MIMO communication network deployment, where multiple radio units (RUs) in the network cooperate with each other for the sensing task. By exploiting the angle resolution from multiple arrays deployed in the network and the delay resolution from the communication signals, i.e., orthogonal frequency division multiplexing (OFDM) signals, we formulate a cooperative sensing problem with coherent data fusion of multiple RUs' observations and propose a sparse Bayesian learning (SBL)-based method, where the global coordinates of target locations are directly detected. Intensive numerical results indicate promising target detection performance of the proposed SBL-based method. Additionally, a theoretical analysis of the considered cooperative multistatic sensing task is provided using the pairwise error probability (PEP) analysis, which can be used to provide design insights, e.g., illumination and beam patterns, for the considered problem.

Analysis of Cross-Domain Message Passing for OTFS Transmissions

In this paper, we investigate the performance of the cross-domain iterative detection (CDID) framework with orthogonal time frequency space (OTFS) modulation, where two distinct CDID algorithms are presented. The proposed schemes estimate/detect the information symbols iteratively across the frequency domain and the delay-Doppler (DD) domain via passing either the a posteriori or extrinsic information. Building upon this framework, we investigate the error performance by considering the bias evolution and state evolution. Furthermore, we discuss their error performance in convergence and the DD domain error state lower bounds in each iteration. Specifically, we demonstrate that in convergence, the ultimate error performance of the CDID passing the a posteriori information can be characterized by two potential convergence points. In contrast, the ultimate error performance of the CDID passing the extrinsic information has only one convergence point, which, interestingly, aligns with the matched filter bound. Our numerical results confirm our analytical findings and unveil the promising error performance achieved by the proposed designs.

Pulse Shaping for Random ISAC Signals: The Ambiguity Function Between Symbols Matters

Integrated sensing and communications (ISAC) has emerged as a pivotal enabling technology for next-generation wireless networks. Despite the distinct signal design requirements of sensing and communication (S&C) systems, shifting the symbol-wise pulse shaping (SWiPS) framework from communication-only systems to ISAC poses significant challenges in signal design and processing This paper addresses these challenges by examining the ambiguity function (AF) of the SWiPS ISAC signal and introducing a novel pulse shaping design for single-carrier ISAC transmission. We formulate optimization problems to minimize the average integrated sidelobe level (ISL) of the AF, as well as the weighted ISL (WISL) while satisfying inter-symbol interference (ISI), out-of-band emission (OOBE), and power constraints. Our contributions include establishing the relationship between the AFs of both the random data symbols and signaling pulses, analyzing the statistical characteristics of the AF, and developing algorithmic frameworks for pulse shaping optimization using successive convex approximation (SCA) and alternating direction method of multipliers (ADMM) approaches. Numerical results are provided to validate our theoretical analysis, which demonstrate significant performance improvements in the proposed SWiPS design compared to the root-raised cosine (RRC) pulse shaping for conventional communication systems.

OFDM Achieves the Lowest Ranging Sidelobe Under Random ISAC Signaling

This paper aims to answer a fundamental question in the area of Integrated Sensing and Communications (ISAC): What is the optimal communication-centric ISAC waveform for ranging? Towards that end, we first established a generic framework to analyze the sensing performance of communication-centric ISAC waveforms built upon orthonormal signaling bases and random data symbols. Then, we evaluated their ranging performance by adopting both the periodic and aperiodic auto-correlation functions (P-ACF and A-ACF), and defined the expectation of the integrated sidelobe level (EISL) as a sensing performance metric. On top of that, we proved that among all communication waveforms with cyclic prefix (CP), the orthogonal frequency division multiplexing (OFDM) modulation is the only globally optimal waveform that achieves the lowest ranging sidelobe for quadrature amplitude modulation (QAM) and phase shift keying (PSK) constellations, in terms of both the EISL and the sidelobe level at each individual lag of the P-ACF. As a step forward, we proved that among all communication waveforms without CP, OFDM is a locally optimal waveform for QAM/PSK in the sense that it achieves a local minimum of the EISL of the A-ACF. Finally, we demonstrated by numerical results that under QAM/PSK constellations, there is no other orthogonal communication-centric waveform that achieves a lower ranging sidelobe level than that of the OFDM, in terms of both P-ACF and A-ACF cases.

Resource Allocation Design for Next-Generation Multiple Access: A Tutorial Overview

Multiple access is the cornerstone technology for each generation of wireless cellular networks and resource allocation design plays a crucial role in multiple access. In this paper, we present a comprehensive tutorial overview for junior researchers in this field, aiming to offer a foundational guide for resource allocation design in the context of next-generation multiple access (NGMA). Initially, we identify three types of channels in future wireless cellular networks over which NGMA will be implemented, namely: natural channels, reconfigurable channels, and functional channels. Natural channels are traditional uplink and downlink communication channels; reconfigurable channels are defined as channels that can be proactively reshaped via emerging platforms or techniques, such as intelligent reflecting surface (IRS), unmanned aerial vehicle (UAV), and movable/fluid antenna (M/FA); and functional channels support not only communication but also other functionalities simultaneously, with typical examples including integrated sensing and communication (ISAC) and joint computing and communication (JCAC) channels. Then, we introduce NGMA models applicable to these three types of channels that cover most of the practical communication scenarios of future wireless communications. Subsequently, we articulate the key optimization technical challenges inherent in the resource allocation design for NGMA, categorizing them into rate-oriented, power-oriented, and reliability-oriented resource allocation designs. The corresponding optimization approaches for solving the formulated resource allocation design problems are then presented. Finally, simulation results are presented and discussed to elucidate the practical implications and insights derived from resource allocation designs in NGMA.