Pursuing the limit of chirp parameter identifiability: A computational approach

TL;DR

This paper establishes the fundamental limits for uniquely identifying multiple chirp signals from samples, introduces a novel optimization-based algorithm for parameter estimation, and demonstrates its effectiveness through theoretical and empirical validation.

Contribution

It provides the first necessary and sufficient condition for chirp parameter identifiability and proposes a new algorithm that achieves this bound.

Findings

The minimum number of samples needed is at least twice the number of chirps.

The proposed algorithm successfully identifies parameters at the theoretical lower bound.

The algorithm outperforms existing methods in numerical experiments.

Abstract

In this paper, it is shown that a necessary condition for unique identifiability of $K$ chirps from $N$ regularly spaced samples of their mixture is $N\geq 2K$ when $K\geq 2$. A necessary and sufficient condition is that a rank-constrained matrix optimization problem has a unique solution; this is the first result of such kind. An algorithm is proposed to solve the optimization problem and to identify the parameters numerically. The lower bound of $N=2K$ is shown to be tight by providing diverse problem instances for which the proposed algorithm succeeds to identify the parameters. The advantageous performance of the proposed algorithm is also demonstrated compared with the state of the art.