Asymptotic Stochastic Analysis of Partially Relaxed DML

Abstract

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.

Probability of Resolution of G-MUSIC: An Asymptotic Approach

“…This region is typically characterized by a systematic appearance of outliers in the DoA estimates which are caused by merging signal extrema in the spectrum of the DoA estimator. In order to study the probability of resolution of the G-MUSIC technique we follow a similar approach as in [16][17][18] and [19,20] where the probability of resolution of the recently introduced Partially Relaxed Deterministic Maximum Likelihood (PR-DML) algorithm and the conventional Deterministic Maximum Likelihood (DML) as well as the Stochastic Maximum Likelihood (SML) method was derived using tools from Random Matrix Theory (RMT). Whereas the PR-DML, the DML and the SML DoA estimation techniques only involve eigenvalues in the computation of the cost function, the cost function of the G-MUSIC technique also involves eigenvectors and therefore requires a fundamentally new asymptotic stochastic analysis.…”