Delay-Doppler Domain Channel Estimation: What if Sparsity is Unknown?
It addresses the practical problem of unknown and time-varying sparsity in delay-Doppler channel estimation for wireless communications, offering an adaptive solution.
This paper proposes a sparsity-agnostic structured estimator for delay-Doppler domain channel estimation that requires no prior knowledge of the sparsity level. The method recovers exact support with high probability and achieves near-oracle reconstruction accuracy, outperforming fixed-budget baselines and sparse Bayesian learning.
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.