2D DOA estimation for uniform planar array: A closed-form performance bound framework based on information entropy

The theoretical performance bound plays a pivotal role in parameter estimation by establishing benchmarks for evaluating the asymptotic efficiency of estimators. While the classical Cramér-Rao bound (CRB) in non-Bayesian frameworks maintains strict validity only in asymptotic regions, Bayesian approaches can construct globally tight bounds through prior information but suffer from computational bottlenecks induced by high-dimensional integrals and the absence of explicit expressions. This study proposes a novel entropy error bound (EEB) based on information entropy theory for two-dimensional (2D) joint direction of arrival (DOA) estimation and 1D independent estimation in uniform planar arrays (UPAs). By establishing a normalized differential entropy model under signal-to-noise ratio (SNR) partitioning, we derive closed-form analytical solutions for EEB with explicit expressions. These explicit characteristics quantitatively reveal the impact laws of the number of array elements, the root mean square aperture width, and the number of snapshots on estimation performance. Multi-scenario simulations validate that the proposed EEB maintains global tightness across various SNR conditions, thereby providing a universal performance benchmark for arbitrary parameter estimators.