# Semiparametric Stochastic CRB for DOA Estimation in Elliptical Data Model

## TL;DR

This paper investigates the statistical efficiency of DOA estimation algorithms like MUSIC and IAA-APES under complex elliptically symmetric data models, using the semiparametric stochastic CRB as a benchmark.

## Contribution

It introduces a semiparametric framework for evaluating DOA estimators' efficiency considering the CES data model and the density generator as an infinite-dimensional nuisance parameter.

## Key findings

- Analysis of MUSIC and IAA-APES performance relative to SSCRB
- Comparison of covariance matrix estimates in DOA estimation
- Insights into estimator efficiency under CES distribution

## Abstract

This paper aims at presenting a numerical investigation of the statistical efficiency of the MUSIC (with different covariance matrix estimates) and the IAA-APES Direction of Arrivals (DOAs) estimation algorithms under a general Complex Elliptically Symmetric (CES) distributed measurement model. Specifically, the density generator of the CES-distributed data snapshots is considered as an additional, infinite-dimensional, nuisance parameter. To assess the efficiency in the considered semiparametric setting, the Semiparametric Stochastic Cram\'er-Rao Bound (SSCRB) is adopted as lower bound for the Mean Square Error (MSE) of the DOA estimators.