A Non-Asymptotic Analysis on the Additional Bias of Capon's Method

The Capon method is one of the classical direction-of-arrival (DOA) estimation methods in array signal processing. The standard analysis of the additional bias of this method is asymptotic, which assumes the number of snapshots K goes to infinity. This paper provides a non-asymptotic analysis for the additional bias by employing some tools from high-dimensional probability and perturbation analysis of optimization problems. We establish upper bounds for the additional bias in both expectation and tail forms, which reveal that the additional bias has an error rate of O(K-^1/2) when the number of snapshots satisfies a certain condition. We demonstrate our results by some numerical experiments.