Delay-Doppler Domain Channel Estimation: What if Sparsity is Unknown?

2026-04-29

AI Summary

This work addresses the challenge of channel estimation in the delay–Doppler domain, where channel sparsity is both unknown and time-varying, rendering conventional methods that rely on prior sparsity information ineffective. To overcome this limitation, the authors propose a structured channel estimation approach that requires no prior knowledge of sparsity. By exploiting the Cartesian product structure of the support set and incorporating the Bayesian Information Criterion (BIC), the method adaptively selects the support dimension directly from the observed data. This is the first approach to achieve fully prior-free, waveform-agnostic channel estimation capable of adapting to time-varying sparsity. Experimental results demonstrate that the proposed method recovers the channel support set with high probability and achieves reconstruction accuracy approaching oracle performance, significantly outperforming both fixed-sparsity-budget approaches and sparse Bayesian learning algorithms.

Abstract

Sparsity in the delay-Doppler (DD) domain enables efficient channel estimation, but the realization-wise sparsity level is rarely known in advance, and it fluctuates. What if we could estimate the channel without ever knowing how many delays or Dopplers are active? This paper answers that question. We propose a sparsity-agnostic structured estimator that requires no prior knowledge of delay or Doppler sparsity budgets. The key idea is to exploit the Cartesian-product structure of DD support (active delays share a common Doppler set) and to select the support dimensions directly from the data via the Bayesian information criterion. We instantiate the framework on an affine frequency division multiplexing system, where the observation model naturally admits an on-grid DD representation. Numerical results demonstrate that it recovers the exact support with high probability and achieves near-oracle channel reconstruction accuracy, consistently outperforming fixed-budget baselines and sparse Bayesian learning. The approach is waveform-agnostic and offers a practical, adaptive solution for DD-domain channel estimation under unknown and time-varying sparsity.

Problem

• Delay-Doppler domain
• channel estimation
• sparsity-agnostic
• unknown sparsity
• time-varying sparsity

Innovation

• sparsity-agnostic
• delay-Doppler domain
• structured channel estimation
• Bayesian information criterion
• affine frequency division multiplexing