Deterministic Performance Analysis of Subspace Methods for Cisoid Parameter Estimation

TL;DR

This paper provides a deterministic, finite-sample, and finite-SNR performance analysis of ESPRIT and matrix pencil methods for cisoid parameter estimation, introducing a new bound on Vandermonde matrix condition numbers.

Contribution

It introduces a novel deterministic analysis framework and a new upper bound on Vandermonde matrix condition numbers for improved performance assessment.

Findings

Finite-sample performance bounds for ESPRIT and matrix pencil methods.

A new upper bound on Vandermonde matrix condition numbers.

Analysis applicable to nodes inside the unit disk.

Abstract

Performance analyses of subspace algorithms for cisoid parameter estimation available in the literature are predominantly of statistical nature with a focus on asymptotic$-$either in the sample size or the SNR$-$statements. This paper presents a deterministic, finite sample size, and finite-SNR performance analysis of the ESPRIT algorithm and the matrix pencil method. Our results are based, inter alia, on a new upper bound on the condition number of Vandermonde matrices with nodes inside the unit disk. This bound is obtained through a generalization of Hilbert's inequality frequently used in large sieve theory.