Explicit Entropy Error Bound for DOA Estimation in Nested Array

Among the numerous DOA estimation bounds, the Cramér-Rao bound (CRB) is only tight in the asymptotic region. The Bayesian bound, by incorporating <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information, provides a globally tight bound but often incurs high computational complexity due to high-dimensional integration. In contrast, the existing globally tight entropy error bound (EEB) with low complexity is only applicable to assessing DOA estimation under single snapshot scenarios. In this paper, we derive an explicit EEB tailored for evaluating DOA estimation in multi-snapshot scenarios with nested arrays. Furthermore, the derivation can be extended to multi-snapshot parameter estimation scenarios with other sparse linear arrays (SLAs) and uniform linear arrays (ULAs). The derived explicit EEB reveals the relationship between DOA estimation performance and the number of snapshots, SNR, array aperture width, and total number of elements. Simulation results demonstrate that, compared to CRB, the derived EEB exhibits significant advantages in assessing and predicting the performance of multi-snapshot DOA estimation.