arXiv subjects

Zilong Liu

Publications and source records attributed to Zilong Liu.

At least 37 records · Page 2Linked to original sources

arXiv2026

Error Rate Analysis and Low-Complexity Receiver Design for Zero-Padded AFDM

This paper studies the error rate performance and low-complexity receiver design for zero-padded affine frequency division multiplexing (ZP-AFDM) systems. By exploiting the unique ZP-aided lower triangular structure of the time domain (TD) channel matrix, we propose a novel low-complexity minimum mean square error (MMSE) detector and a maximum ratio combining-based TD (MRC-TD) detector. Furthermore, the theoretical bit error rate (BER) performance of both the MMSE and maximum likelihood detectors is analyzed. Simulation results demonstrate that the proposed detectors can achieve identical BER performance to that of the conventional MMSE detector based on matrix inversion while enjoying significantly reduced complexity.

eess.SP↗

arXiv2026

Geographic Bias and Diversity in AI Evaluation

Among the many challenges hindering the responsible development and deployment of AI, arguably none has faced more intense scrutiny than bias in its various forms. This underscores the widespread concerns across AI researchers that model outputs, e.g., from generative AI, may encode structural distributional imbalances (stemming from training data or model design) that may amplify social inequality or introduce systemic distortions across application domains ranging from biodiversity to disaster mitigation. Yet, relatively little work has investigated the geographical nature of bias or developed measurable benchmarks for what it means for (generative) AI to be unbiased. In this chapter, we investigate this issue through a literature review. As foundation models are reshaping the landscape of bias research, we examine work spanning both the pre-generative AI and generative AI periods. First, we identify a range of geographic biases. These biases span from representation bias in the training data and regional disparities in the factual recall of language models to the tendency of generative AI to over-proportionally favor prototypical places (called defaults). Then, we showcase how recent studies address the latter bias by evaluating geographic diversity in the outputs of generative AI across various cognitive levels, parameter settings, and output modalities.

cs.CY↗

arXiv2026

Assessing the Geographic Diversity of AI's Platial Representations in Image Generation

(Gen)AI diversity is not merely an ethical issue. From the perspective of geographic information science (GIScience), it could be interpreted as a function of uncertainty and as a form of cognitive bias, embedded in AI outputs. Recent work has sought to develop information-theoretic diversity measures and apply them to evaluate AI-chatbot outputs in a geographic context. As the AI ecosystem to which we are exposed on a daily basis becomes rapidly multimodal, we believe it is important to examine geographic diversity across various modalities. Focusing on images, this paper aims to fill this research gap. First, we select the GPT and DALL-E models as state-of-the-art examples and point out how assessing their geographic diversity involves various stages, including prompt revision and image generation. Then, taking inspiration from species diversity measures in ecological research, we incorporate similarity weighting into the measurement of geographic diversity. Next, we demonstrate how to evaluate geographic diversity in image generation through a case study. Our analysis reveals several counterintuitive findings. For instance, older models can exhibit greater geographic diversity despite producing lower-quality images, and prompt revision yields greater geographic diversity than image generation. At the same time, we observe explicit model homogeneity underlying the lack of geographic diversity, as the selected models consistently depict the same prototypical geo-specific feature or similar features. This is concerning, as it risks producing stereotypical representations of places.

cs.CY↗

arXiv2026

Toward Low-Altitude Embodied Intelligence: A Sensing-Communication-Computation-Control Closed-Loop Perspective

The rapid growth of the low-altitude economy drives increasingly autonomous unmanned aerial vehicle (UAV) operations, giving rise to low-altitude embodied intelligence (LAEI), in which sensing, communication, computation, and control (SC$^3$) are tightly integrated to enable closed-loop interaction, ensuring timely, effective, and safe responses in complex or unknown environments. This article systematically explores the LAEI networks, from its fundamental architecture to the diverse scenarios that it can support. We examine key enabling techniques that sustain timely information exchange and effective decision feedback within the $\text{SC}^3$ closed loop. A representative low-altitude UAV mission in an unknown urban area is presented as a case study, where the UAV provides communication services and performs environmental sensing to inform closed-loop control, illustrating how coordinated $\text{SC}^3$ capabilities enable efficient and responsive operation. By identifying major challenges and outlining future research directions, this work serves as a cornerstone for developing next-generation low-altitude intelligent systems.

eess.SY↗

arXiv2026

Joint Phase Noise and Off-Grid Channel Estimation for AFDM Systems via Sparse Bayesian Learning

In practical affine frequency division multiplexing (AFDM) systems, the intricate coupling of oscillator phase noise (PN) and off-grid fractional shifts traps conventional estimators in a severe high-SNR error floor. To address these challenges, we propose a joint PN and channel estimation method based on sparse Bayesian learning (JPNCE-SBL). Specifically, a reduced-rank subspace projection is first introduced to capture the dominant eigen-energy of the Wiener PN process. Concurrently, a dynamic grid evolution strategy is designed to iteratively eliminate off-grid errors without requiring computationally prohibitive global grid densification. Both components are integrated into a unified Expectation-Maximization (EM) framework, where the channel and PN estimates are jointly updated at each iteration to prevent error propagation. Simulation results demonstrate that JPNCE-SBL significantly outperforms existing benchmarks in both NMSE and BER, closely approaching the perfect channel state information case under practical PN conditions.

eess.SP↗

arXiv2026

On the Scalability of Quasi-Complementary Sequence Sets: Quadratic and Cubic Laws

This work is concerned with the fundamental scaling laws of quasi-complementary sequence sets (QCSSs) by understanding how large the set size (denoted by $M$) can grow with the flock size ($K$) and the sequence length ($N$). We first establish a geometric framework that transforms a QCSS into a complex unit-norm codebook, through which and by exploiting the density thresholds of the codebooks, certain polynomial upper bounds of the QCSS set size are obtained. Sharp quadratic and cubic scaling laws are then introduced. Specifically, we show that asymptotically optimal QCSSs with tightness factor $ρ=1$ satisfy $M \le (1+o(1))K^2N$, while asymptotically near-optimal QCSSs satisfy $M \le (1+o(1))K^3N^2$ for $ρ< {(1+\sqrt{5})}/{2}$. To validate these upper bounds, we further propose explicit additive-character and mixed-character based constructions for QCSSs that achieve $M = K^2N + K$ and $M = K^3N^2 + 2K^2N + K$, respectively, thereby showing that the quadratic and cubic scaling laws are asymptotically tight. Our proposed constructions admit flexible parameter choices, and their maximum correlation estimates are shown to be tight through explicit extremal examples. Additionally, it is conjectured that the cubic scaling law is universal for all $1<ρ\le 2$, i.e., any asymptotically near-optimal QCSSs should satisfy $M \le (1+o(1))K^3N^2$. This identifies a fundamental cubic barrier for QCSS scalability.

math.CO↗

arXiv2026

A Novel Low-Complexity Dual-Domain Expectation Propagation Detection Aided AFDM for Future Communications

This paper presents a dual-domain low-complexity expectation propagation (EP) detection framework for affine frequency division multiplexing (AFDM) systems. By analyzing the structural properties of the effective channel matrices in both the time and affine frequency (AF) domains, our key observation is the domain-specific quasi-banded sparsity patterns, including AF-domain sparsity under frequency-selective channels and time-domain sparsity under doubly-selective channels. Based on these observations, we develop an AF-domain EP (EP-AF) detector for frequency-selective channels and a time-domain EP (EP-T) detector for doubly-selective channels, respectively. By performing iterative inference in the time domain using the Gaussian approximation, the proposed EP-T detector avoids inverting the dense channel matrix in the AF domain. Furthermore, the proposed EP-AF and EP-T detectors leverage the aforementioned quasi-banded sparsity of the AF domain and time domain channel matrices, respectively, to reduce the complexity of matrix inversion from cubic to linear order. Simulation results demonstrate that the proposed low-complexity EP-AF detector achieves nearly identical error rate performance to its conventional counterpart, while the proposed low-complexity EP-T detector offers an attractive trade-off between detection performance and complexity.

eess.SP↗

arXiv2026

A Unified Multicarrier Waveform Framework for Next-generation Wireless Networks: Principles, Performance, and Challenges

Next-generation wireless networks require enhanced flexibility, efficiency, and reliability in physical layer waveform design to address the challenges posed by heterogeneous channel conditions and stringent quality-of-service demands. To this end, this paper proposes a unified multicarrier waveform framework that provides a systematic characterization and practical implementation guidelines to facilitate waveform selection for the sixth-generation (6G) mobile networks and beyond. We commence by examining the design principles of the state-of-the-art waveforms, which are categorized into one-dimensional modulation waveforms (e.g., orthogonal frequency division multiplexing (OFDM) and affine frequency division multiplexing (AFDM)) and two-dimensional modulation waveforms (e.g., orthogonal time frequency space (OTFS)). Their inherent resilience against various channel-induced interference is further studied, revealing their distinct suitability in diverse channel conditions. Furthermore, an in-depth performance analysis is presented by comparing their key performance indicators (KPIs), followed by an extensive exploration of these advanced waveforms in various applications. Consequently, this work aims to serve as a pivotal reference for waveform adoption in future 6G standardization and network deployment.

eess.SP↗

arXiv2026

Matched Filtering-Based Channel Estimation for AFDM Systems in Doubly Selective Channels

Affine frequency division multiplexing (AFDM) has recently emerged as an excellent backward-compatible 6G waveform. In this paper, we study matched filtering (MF) assisted channel estimation (CE) for AFDM systems in complex doubly selective channels. By deriving the complete input-output relationship of the continuous-time signal, the inter-chirp-carrier interference, signal-to-interference-plus-noise ratio (SINR), and the effective SINR loss of AFDM, are investigated in discrete affine Fourier transform (DAFT) domain. Further, we propose two low-complexity methods for constructing the channel matrix by taking advantage of its inherent discrete Fourier transform structure and the staircase structure of the piecewise functions in the channel matrix, respectively. It is shown that complexity reduction by at least two orders of magnitude can be achieved for a large number of chirp subcarriers. For the CE problem in doubly selective channels, we introduce an MF assisted CE scheme. This allows us to sequentially estimate the parameters of each path by exploiting the separability and approximate orthogonality of different paths in the DAFT domain, thus leading to significantly reduced complexity. Furthermore, based on generalized Fibonacci search (GFS), an MF-GFS scheme is proposed to avoid significantly redundant computation, which can be extended to typical wide-band systems. Extensive simulation results indicate that the proposed schemes offer superior advantages in terms of their improved communication performance and lower complexity.

eess.SP↗

arXiv2026

Non-Orthogonal Affine Frequency Division Multiplexing for Spectrally Efficient High-Mobility Communications

This paper proposes a novel non-orthogonal affine frequency division multiplexing (nAFDM) waveform for reliable high-mobility communications with enhanced spectral efficiency (SE). The key idea is to introduce a bandwidth compression factor into the AFDM modulator to enable controllable subcarrier overlapping. We first detail the proposed nAFDM transceiver and derive the corresponding input-output signal relationship. Then, an efficient nAFDM signal generation method based on the inverse discrete Fourier transform (IDFT) is proposed, enabling practical implementation using existing inverse fast Fourier transform (IFFT) modules without additional hardware complexity. Next, to characterize the impact of non-orthogonal modulation, we derive a closed-form expression of inter-carrier interference (ICI), showing its dependence on the bandwidth compression factor. To mitigate the resulting interference, we propose a soft iterative detection algorithm and a low-complexity implementation approach that leverages the distribution characteristics of ICI. Simulation results demonstrate that 1) in terms of bit error rate (BER), the proposed nAFDM can achieve near identical BER compared to conventional AFDM, while outperforms other waveform counterparts; 2) nAFDM is capable of striking higher SE compared to other existing waveforms; and 3) the proposed nAFDM achieves an attractive BER vs. SE trade-off, and the proposed soft iterative detection (ID) scheme can attain a trade-off between BER and complexity.

cs.IT↗

arXiv2026

Vehicular Multistatic OTFS-ISAC: A Geometry-Aware Deployment and Kalman-Based Tracking

Integrated sensing and communication (ISAC) is a promising paradigm for next-generation vehicular networks, yet existing orthogonal frequency-division multiplexing (OFDM)-based designs suffer from limited spatial diversity and severe sensitivity to Doppler and multipath effects. While orthogonal time-frequency space (OTFS) modulation offers robustness under high mobility, the impact of spatial node deployment in multistatic OTFS-ISAC has remained largely unexplored. This paper presents the first geometry-aware multistatic OTFS-ISAC framework, in which a triangulation-based cooperative sensing approach is developed for joint target localization and velocity estimation. Closed-form expressions for the localization error covariance are derived under general receiver topologies, revealing that maximizing the triangulation area is fundamental to minimizing estimation error. This leads to a near-optimal deployment strategy based on orthogonal receiver placement and its equivalence to multi-antenna architectures with cubic-order error reduction. To enable reliable tracking of moving targets, a correlated random walk (CRW)-based Kalman filter (KF) framework is integrated into multistatic OTFS-ISAC for active sensing and ISAC. Numerical results demonstrate significant reductions in localization root-mean-square error (RMSE) and communication bit error rate (BER), highlighting the effectiveness of geometry-aware, KF-assisted multistatic OTFS-ISAC in dynamic vehicular environments.

cs.NI↗

arXiv2026

Optimally Deployed Multistatic OTFS-ISAC Design With Kalman-Based Tracking of Targets

This paper studies orthogonal time-frequency space (OTFS) modulation aided multistatic integrated sensing and communication (ISAC) in vehicular networks, whereby its delay-Doppler robustness is exploited for enhanced communication and high-resolution sensing. We present a triangulation-based deployment framework combined with Kalman filtering (KF) that enables accurate target localization and velocity estimation. In addition, we assess the ISAC performance in the multistatic topology to determine its effectiveness in the dynamic environment. Further, a suboptimal placement strategy for the multistatic receivers is devised to reduce the targets' localization error. Numerical results demonstrate significant reductions in the sensing error and bit error rate (BER) performances.

cs.NI↗

arXiv2026

Hybrid Rate-Splitting and Sparse Code Multiple Access (RS-SCMA): Design and Performance

This paper proposes, for the first time, a hybrid multiple access framework that integrates the principles of rate-splitting (RS) and sparse code multiple access (SCMA) in an SISO downlink scenario. The proposed scheme, termed RS-SCMA, unifies the powerful interference management capability of rate-splitting multiple access (RSMA) with the near-optimal multiuser detection of SCMA. A key feature of RS-SCMA is a tunable splitting factor $α$, which governs the allocation between the generic $M$-ary modulated common messages and SCMA-encoded private messages. This enables dynamic control over the fundamental trade-off between system sum-rate, bit error rate (BER), and the overloading factor. We develop novel transmitter and receiver architectures based on soft successive interference cancellation (SIC), incorporating message passing algorithm (MPA) detection and soft-symbol reconstruction. Furthermore, a unified analytical expression for the achievable sum-rate is derived as a function of the splitting factor $α$. The performance of the proposed RS-SCMA system is evaluated in terms of both BER and sum-rate. Simulation results confirm the superiority of RS-SCMA over conventional SCMA and multi-carrier RSMA, demonstrating its scalability and robustness even in the presence of channel estimation errors.

eess.SP↗

arXiv2026

OTFS-based Integrated Positioning and Communication Systems with Low-Resolution ADCs

This paper proposes a two-phase orthogonal time frequency space (OTFS)-based integrated positioning and communication (IPAC) framework under realistic low-resolution analog-to-digital converters (ADCs). In the uplink phase, the positioning signal is used to estimate channel parameters, which are subsequently used to determine the user's position. The spatial smoothing-multiple signal classification algorithm is introduced to estimate the angle-of-arrival, whereas an iterative interference cancellation scheme is conceived for the remaining parameters' estimation. The corresponding Cramer-Rao lower bounds of channel parameters and user position are also derived. During the downlink communication phase, the estimated parameters are exploited to improve beamforming at the base station. Simulation results evaluate the impact of ADC quantizer resolutions. Specifically, it is shown that enhanced downlink bit error rate performance can be achieved with improved uplink positioning, while the use of low-resolution ADCs induces noticeable performance degradation in the OTFS-IPAC system.

eess.SP↗

arXiv2026

Zak-Transform-Induced Optimal Sequences and Their Applications in OTFS

This paper introduces a novel finite Zak transform (FZT)-aided framework for constructing multiple zero-correlation zone (ZCZ) sequence sets with optimal correlation properties. Specifically, each sequence is perfect with zero auto-correlation sidelobes, each ZCZ sequence set meets the Tang-Fan-Matsufuji bound with equality, and the maximum inter-set cross-correlation of multiple sequence sets meets the Sarwate bound with equality. Our study shows that these sequences can be sparsely expressed in the Zak domain through properly selected index and phase matrices. Particularly, it is found that the maximum inter-set cross-correlation beats the Sarwate bound if every index matrix is a circular Florentine array. Several construction methods of multiple ZCZ sequence sets are proposed, demonstrating both the optimality and high flexibility. {Additionally, it is shown that excellent synchronization performance can be achieved by the proposed sequences in orthogonal-time-frequency-space (OTFS) systems.

cs.IT↗

arXiv2026

An Explicit Upper Bound of Generalized Quadratic Gauss Sums and Its Applications for Asymptotically Optimal Aperiodic Polyphase Sequence Design

This work is motivated by the long-standing open problem of designing asymptotically order-optimal aperiodic polyphase sequence sets with respect to the celebrated Welch bound. Attempts were made by Mow over 30 years ago, but a comprehensive understanding to this problem is lacking. Our first key contribution is an explicit upper bound of generalized quadratic Gauss sums which is obtained by recursively applying Paris' asymptotic expansion and then bounding it by leveraging the fast convergence property of the Fibonacci zeta function. Building upon this major finding, our second key contribution includes four systematic constructions of order-optimal sequence sets with low aperiodic correlation and/or ambiguity properties via carefully selected Chu sequences and Alltop sequences. For the first time in the literature, we reveal that the full Alltop sequence set is asymptotically optimal for its low aperiodic correlation sidelobes. Besides, we introduce a novel subset of Alltop sequences possessing both order-optimal aperiodic correlation and ambiguity properties for the entire time-shift window.

cs.IT↗

arXiv2026

Doppler-Resilient LEO Satellite OFDM Transmission with Affine Frequency Domain Pilot

Orthogonal frequency division multiplexing (OFDM) based low Earth orbit (LEO) satellite communication system suffers from severe Doppler shifts, while {the Doppler-resilient affine frequency-division multiplexing (AFDM) transmission suffers from significantly high processing complexity in data detection}. In this paper, we explore the channel estimation gain of affine frequency (AF) domain pilot to enhance the OFDM transmission under high mobility. Specifically, we propose a novel AF domain pilot embedding scheme for satellite-ground downlink OFDM systems for capturing the channel characteristics. By exploiting the autoregressive (AR) property of adjacent channels, a long short-term memory (LSTM) based predictor is designed to replace conventional interpolation operation in OFDM channel estimation. Simulation results show that the proposed transmission scheme significantly outperforms conventional OFDM scheme in terms of bit error rate (BER) under high Doppler scenarios, thus paving a new way for the design of next generation non-terrestrial network (NTN) communication systems.

eess.SP↗

arXiv2026

PartImageNet++ Dataset: Enhancing Visual Models with High-Quality Part Annotations

To address the scarcity of high-quality part annotations in existing datasets, we introduce PartImageNet++ (PIN++), a dataset that provides detailed part annotations for all categories in ImageNet-1K. With 100 annotated images per category, totaling 100K images, PIN++ represents the most comprehensive dataset covering a diverse range of object categories. Leveraging PIN++, we propose a Multi-scale Part-supervised recognition Model (MPM) for robust classification on ImageNet-1K. We first trained a part segmentation network using PIN++ and used it to generate pseudo part labels for the remaining unannotated images. MPM then integrated a conventional recognition architecture with auxiliary bypass layers, jointly supervised by both pseudo part labels and the original part annotations. Furthermore, we conducted extensive experiments on PIN++, including part segmentation, object segmentation, and few-shot learning, exploring various ways to leverage part annotations in downstream tasks. Experimental results demonstrated that our approach not only enhanced part-based models for robust object recognition but also established strong baselines for multiple downstream tasks, highlighting the potential of part annotations in improving model performance. The dataset and the code are available at https://github.com/LixiaoTHU/PartImageNetPP.

cs.CV↗