Probability of Resolution of Partially Relaxed DML an Asymptotic Approach

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. Instead of applying a single source
approximation to multi-source estimation criteria, which is the case for the MUSIC algorithm, the conventional beamformer, or
the Capon beamformer, the Partial Relaxation approach accountsfor the existence of multiple sources using a non-parametric
modification of the signal model. In this paper, an accurate description of the probability of resolution for the PR-DML
estimator is provided by analyzing the asymptotic 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.