title: Development and Performance Analysis of Direction-of-Arrival Estimators
Creators: name: Schenck, David
Publisher: name: UNSPECIFIED
Year: 2022

description: The problem of determining the angle of incidence of signals on a sensor array under the influence of noise is a long-established research area that enjoys great popularity in sensor array processing and is often referred to as DoA estimation. DoA estimation spans various fields of research, among them not only radar and sonar applications but also biomedical imaging, radio astronomy, seismic exploration, wireless communication, and other fields. Due to the vast amount of applications numerous DoA estimation methods have been proposed in the literature seeking for higher resolution capabilities, improved estimation accuracy and robustness as well as improved computational efficiency. In general, however, a trade-off between estimation accuracy and computational complexity is unavoidable. More recently, a novel class of DoA estimators referred to as Partial Relaxation (PR) framework was introduced. DoA estimators under the PR framework offer excellent estimation accuracy at comparatively low computational cost and are therefore very attractive for use in practice. In the first part of this thesis, we expand the class of PR DoA estimators and propose novel PR estimators that either exploit more prior knowledge about the underlying signal model or estimate the DoAs in an iterative manner or by rooting a polynomial equation. Furthermore, the proposed DoA estimators are very versatile since no particular array geometry is exploited. Simulations show that the proposed DoA estimation methods exhibit improved estimation accuracy especially in difficult scenarios with closely spaced sources, limited data samples and in scenarios with multiple sources while remaining computationally tractable. In the second part of this thesis, we analyze the Root-Mean-Squared-Error (RMSE) behavior of the DoA estimates obtained through the Multiple Signal Classification (MUSIC), the G-MUSIC and the Partially Relaxed Deterministic Maximum Likelihood (PR-DML) approach in the threshold region where both the number of data samples as well as the Signal-to-Noise Ratio (SNR) take moderate values. The threshold region is typically characterized by a systematic appearance of outliers in the DoA estimates which are caused by the incapability of resolving neighboring sources and lead to a total performance breakdown in estimation accuracy. The threshold effect is not captured by standard techniques such as the Cramér-Rao Bound (CRB) and therefore requires an estimator specific analysis. We analyze the asymptotic stochastic behavior of the MUSIC, the G-MUSIC and the PR-DML cost function including the asymptotic first order behavior and the asymptotic second order behavior in the asymptotic regime where both the number of observation as well as the number of data samples increase without bound at the same rate. Furthermore, the derived asymptotic joint distribution of each estimator is used to provide an estimator specific analytical expressions for the probability of resolution. Simulation results show that the proposed asymptotic stochastic analysis as well as the derived probability of resolution is very accurate.