Probability of Resolution of Partially Relaxed DML an Asymptotic Approach

• Main Authors: Schenck, David, Mestre, Xavier, Pesavento, Marius
• Format: Conference Object
• Language: English
• Published: Zenodo 2019
• Subjects: NO KEYWORDS; DML
• Online Access: https://dx.doi.org/10.5281/zenodo.3673908; https://zenodo.org/record/3673908

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. : Grant numbers : This work was supported in part by the Catalan Government under grant 2017-SGR-01479.