Pursuing the limit of chirp parameter identifiability: A computational approach

2025/07/02 by Yang, Zai, Ge, Sikai, Wang, Wenlong
#FOS: Electrical engineering #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2507.01286

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≥ 2K when K≥ 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.

Citations

• Gridless Chirp Parameter Retrieval via Constrained Two-Dimensional Atomic Norm Minimization
• Spark Level Sparsity and the ℓ₁ Tail Minimization
• Spark-level sparsity and the ℓ1 tail minimization
• Frequency-Selective Vandermonde Decomposition of Toeplitz Matrices with Applications
• Vandermonde Decomposition of Multilevel Toeplitz Matrices with Application to Multidimensional Super-Resolution
• Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information
• The Theory and Design of Chirp Radars

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