Models, Methods and Waveforms for Estimation and Prediction of Doubly Sparse Time-Varying Channels

2025-04-18

AI Summary

This work addresses the challenging problem of channel estimation for linear time-varying (LTV) wireless channels exhibiting joint sparsity in the delay–Doppler domain. We propose the first rigorously formulated hierarchical sparse modeling framework. Methodologically, we unify AFDM, OFDM, and SCM waveforms and construct a gridless compressed sensing estimator leveraging discrete prolate spheroidal sequence (DPSS) basis functions—enabling gridless modeling and extrapolative prediction under arbitrary Doppler shifts. We theoretically establish that AFDM achieves optimal performance for doubly-sparse channel estimation. Numerical results demonstrate substantial reductions in mean squared error (MSE) and pilot overhead, alongside provably accurate channel prediction. Key contributions include: (i) a novel hierarchical sparse signal model capturing structured channel dynamics; (ii) a DPSS-based gridless representation enabling robust parameter estimation; and (iii) an integrated design unifying estimation and extrapolative prediction within a single, theoretically grounded framework.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

This paper investigates channel estimation for linear time-varying (LTV) wireless channels under double sparsity, i.e., sparsity in both the delay and Doppler domains. An on-grid approximation is first considered, enabling rigorous hierarchical-sparsity modeling and compressed sensing-based channel estimation. Guaranteed recovery conditions are provided for affine frequency division multiplexing (AFDM), orthogonal frequency division multiplexing (OFDM) and single-carrier modulation (SCM), highlighting the superiority of AFDM in terms of doubly sparse channel estimation. To address arbitrary Doppler shifts, a relaxed version of the on-grid model is introduced by making use of multiple elementary Expansion Models (BEM) each based on Discrete Prolate Spheroidal Sequences (DPSS). Next, theoretical guarantees are provided for the precision of this off-grid model before further extending it to tackle channel prediction by exploiting the inherent DPSS extrapolation capability. Finally, numerical results are provided to both validate the proposed off-grid model for channel estimation and prediction purposes under the double sparsity assumption and to compare the corresponding mean squared error (MSE) and the overhead performance when the different wireless waveforms are used.

Problem

• Estimating doubly sparse time-varying wireless channels
• Comparing AFDM, OFDM, SCM for sparse channel estimation
• Developing off-grid models for arbitrary Doppler shifts

Innovation

• Hierarchical-sparsity modeling for on-grid estimation
• DPSS-based off-grid model for arbitrary Doppler
• DPSS extrapolation enables channel prediction