Super-Resolution for Doubly-Dispersive Channel Estimation

TL;DR

This paper introduces a super-resolution method for estimating doubly-dispersive channel operators in time-varying systems, enabling quick and high-resolution channel identification using sparse linear combinations of atoms.

Contribution

It presents an exact off-the-grid superresolution approach for doubly-dispersive channels, with an adapted algorithm and numerical validation in non-stationary environments.

Findings

The proposed method achieves high-resolution channel estimation.

It outperforms grid refinement and orthogonal matching pursuit algorithms.

Numerical results demonstrate effective performance in radar and wireless scenarios.

Abstract

In this work we consider the problem of identification and reconstruction of doubly-dispersive channel operators which are given by finite linear combinations of time-frequency shifts. Such operators arise as time-varying linear systems for example in radar and wireless communications. In particular, for information transmission in highly non-stationary environments the channel needs to be estimated quickly with identification signals of short duration and for vehicular application simultaneous high-resolution radar is desired as well. We consider the time-continuous setting and prove an exact resampling reformulation of the involved channel operator when applied to a trigonometric polynomial as identifier in terms of sparse linear combinations of real-valued atoms. Motivated by recent works of Heckel et al. we present an exact approach for off-the-grid superresolution which allows to perform the identification with realizable signals having compact support. Then we show how an alternating descent conditional gradient algorithm can be adapted to solve the reformulated problem. Numerical examples demonstrate the performance of this algorithm, in particular in comparison with a simple adaptive grid refinement strategy and an orthogonal matching pursuit algorithm.