Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2412.12900

Shift-invariant spaces, bandlimited spaces and reproducing kernel spaces with shift-invariant kernels on undirected finite graphs

Seok-Young Chung·Qiyu Sun
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we introduce the concept of graph shift-invariant space (GSIS) on an undirected finite graph, which is the linear space of graph signals being invariant under graph shifts, and we study its bandlimiting, kernel reproducing and sampling properties. Graph bandlimited spaces have been widely applied where large datasets on networks need to be handled efficiently. In this paper, we show that every GSIS is a bandlimited space, and every bandlimited space is a principal GSIS. Functions in a reproducing kernel Hilbert space with shift-invariant kernel could be learnt with significantly low computational cost. In this paper, we demonstrate that every GSIS is a reproducing kernel Hilbert space with a shift-invariant kernel. Based on the nested Krylov structure of GSISs in the spatial domain, we propose a novel sampling and reconstruction algorithm with finite steps, with its performance tested for well-localized signals on circulant graphs and flight delay dataset of the 50 busiest airports in the USA.

Explore related subjects

eess.SPcs.ITmath.IT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Seok-Young Chung, Qiyu Sun. 2024-12-17. Shift-invariant spaces, bandlimited spaces and reproducing kernel spaces with shift-invariant kernels on undirected finite graphs. https://arxiv.org/abs/2412.12900

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Circulant ADMM-Net for Fast High-resolution DoA Estimation

This paper introduces CADMM-Net and CHADMM-Net, two deep neural networks for direction of arrival estimation within the least-absolute shrinkage and selection operator (LASSO) framework. These two networks are based on a structured deep unfolding of the alternating direction method of multipliers (ADMM) algorithm through the use of circulant as well as Hermitian-circulant matrices. Along with a computational complexity of $\mathcal{O}(N\log(N))$ per layer for the inference, where $N$ is the length of the dictionary $\mathbf{A}$, they additionally exhibit a memory footprint of $N$ and approximately half of $N$ for CADMMNet and CHADMM-Net, respectively, compared with $N^{2}$ for ADMM-Net. Furthermore, these structured networks exhibit a competitive performance against ADMM-Net, LISTA, TLISTA, and THLISTA with respect to the detection rate, the angular root-mean square error, and the normalized mean squared error.

eess.SP↗
arXiv2026

Adaptive Probabilistic Constellation Shaping based on Enumerative Sphere Shaping for FSO Channel with Turbulence and Pointing Errors

Free-space optical (FSO) transmission enables fast, secure, and efficient next-generation communications with abundant spectrum resources. However, atmospheric turbulence, pointing errors, path loss, and atmospheric loss induce random attenuation, challenging link reliability. Adaptive coded modulation technology enhances spectrum utilization and reliability. We propose an adaptive probabilistic constellation shaping (A-PCS) coherent system utilizing enumerative sphere shaping (ESS) for distribution matcher (DM). With PCS-64QAM, the system achieves continuous rate control from conventional QPSK-equivalent to 64QAM spectral efficiency, providing quasi-continuous control with granularities of approximately $0.05$~bits/4D for spectral efficiency and $0.1$~dB for the post-FEC SNR threshold, and a maximum control depth of $12.5$~dB. Leveraging ESS for efficient sequence utilization, it offers higher spectral efficiency and finer control granularity than constant composition distribution matcher (CCDM)-based A-PCS systems. We further model and analyze the FSO channel, presenting calculations and comparisons of outage probability and ergodic capacity under varying turbulence intensities and pointing errors. Results demonstrate 99.999~\% reliability at maximum $σ_\mathrm{R}^2 = 1.02$ and $σ_\mathrm{s} = 0.51~\mathrm{m}$, meeting requirements under severe turbulence and large pointing errors. {Furthermore, under non-ideal delayed channel state information (CSI) feedback conditions, the system adapts to varying turbulence coherence times and feedback delays, with results showing that finer modulation granularity (provided by A-PCS-ESS) enhances immunity to feedback delay, maintaining a performance advantage over conventional adaptive schemes across a range of channel environments and delay values.

eess.SP↗
arXiv2026

Rate-Splitting--Inspired Bistatic OFDM-ISAC

Achieving effective uplink bistatic ISAC over an OFDM waveform gives rise to challenging interference structures. These are mostly due to unequal direct- and echo-path contributions and Doppler-induced ICI, rendering orthogonal resource separation and fixed SIC strategies inadequate. To address this problem, we propose a RS-inspired framework where the transmitter splits each communication message into a robust and a supplementary stream, which are jointly superposed over a sensing signal. Furthermore, we present the design of a staged sensing-communication receiver. Based on this framework, we derive tractable per-subcarrier SINR expressions and establish the relation between sensing accuracy and communication reliability based on the Fisher information. Building on these, we formulate a joint power-allocation problem for SE maximization under sensing-performance and power constraints. The resulting non-convex formulation is solved using convex surrogates and fractional programming. Numerical results demonstrate that, compared to NOMA-inspired baselines, the proposed framework provides more effective IFI management and improved robustness to Doppler-induced ICI.

eess.SP↗