Asymptotic Stochastic Analysis of Partially Relaxed DML

The Partial Relaxation approach has recently been proposed to solve the Direction-of-Arrival estimation problem [1], [2]. In this paper, we investigate the outlier production mechanism of the Partially Relaxed Deterministic Maximum Likelihood (PR-DML) Direction-of-Arrival estimator using tools from Random Matrix Theory. An accurate description of the probability of resolution for the PR-DML estimator is provided by analyzing the asymptotic stochastic behavior of the PR-DML cost function, assuming that both the number of antennas and the number of snapshots increase without bound at the same rate. The finite dimensional distribution of the PR-DML cost function is shown to be Gaussian in this asymptotic regime and this result is used to compute the probability of resolution.