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

TL;DR

This paper introduces a sparsity-agnostic channel estimation method in the delay-Doppler domain that adaptively detects active supports without prior sparsity knowledge, outperforming fixed-budget approaches.

Contribution

It proposes a novel structured estimator leveraging data-driven support selection via Bayesian information criterion, applicable to waveform-agnostic DD channel estimation.

Findings

High probability exact support recovery demonstrated

Achieves near-oracle channel reconstruction accuracy

Outperforms fixed-budget and sparse Bayesian learning methods

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.