\documentclass[11pt,a4paper]{article}

% packages
\usepackage{xeCJK}
\usepackage{geometry}           % 用于设置上下左右页边距
\geometry{
  left=1.9cm,
  right=1.9cm,
  top=2.54cm,
  bottom=2.54cm
}

\usepackage{indentfirst}
\setlength{\parindent}{2em}

\usepackage{amsmath,amssymb,amsfonts,bm}
\usepackage{array}
\usepackage{longtable}
\numberwithin{equation}{section}
\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}
\DeclareMathOperator*{\diag}{diag}
\DeclareMathOperator*{\maximize}{maximize}
\DeclareMathOperator*{\minimize}{minimize}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\vect}{vec}
\newcommand{\Tran}{\mathsf{T}}
\newcommand{\Herm}{\mathsf{H}}
\newcommand{\diff}{\mathop{}\!\mathrm{d}}
\newcommand{\secref}[1]{第~\ref{#1}~节}
\newcommand{\appref}[1]{附录~\ref{#1}}

\usepackage{arydshln}

\usepackage[
  hidelinks,
  bookmarksopen = true,
  bookmarksnumbered,
  hypertexnames = false,
  colorlinks = true,
  allcolors = blue
  ]{hyperref}

\usepackage{bookmark}

\usepackage[
  backend=biber,
  style=ieee,
  maxcitenames=1,
  mincitenames=1,
  url=false,
  doi=false,
  isbn=false]{biblatex}
% \addbibresource{IEEEabrv.bib}
\addbibresource{ref.bib}

\usepackage[inline]{enumitem}
\setlist[itemize]{itemindent=3em,listparindent=2em,leftmargin=0pt,itemsep=0pt, topsep=0pt, parsep=0pt, partopsep=0pt}
\setlist[enumerate]{itemindent=3em,listparindent=2em,leftmargin=0pt,itemsep=0pt, topsep=0pt, parsep=0pt, partopsep=0pt}

\usepackage[most]{tcolorbox}

\newenvironment{mdquote}{
\begin{tcolorbox}[
  colback=gray!12,
  colframe=gray!40,
  boxrule=0pt,
  left=6pt,
  right=6pt,
  top=6pt,
  bottom=6pt,
  arc=2pt,
  breakable,
  before skip=4pt,
  after skip=4pt
  ]
  \setlength{\parindent}{2em}
  }{
\end{tcolorbox}
}

\usepackage{caption}
\captionsetup[figure]{font=small}

\usepackage{titlesec}
\titlespacing*{\section}{0pt}{*0}{*0}  % 左边缩进 = 0pt，上间距 = 0，下间距 = 0
\titlespacing*{\subsection}{0pt}{*0}{*0}  % 左边缩进 = 0pt，上间距 = 0，下间距 = 0
\titlespacing*{\subsubsection}{0pt}{*0}{*0}  % 左边缩进 = 0pt，上间距 = 0，下间距 = 0

\usepackage[acronym]{glossaries}
\glsdisablehyper%
\setacronymstyle{short-long}
\newacronym{cml}{CML}{Conditional Maximum Likelihood}
\newacronym{crb}{CRB}{Cramér–Rao Bound}
\newacronym{crlb}{CRLB}{Cramér–Rao Lower Bound}
\newacronym{cdml}{CDML}{Concentrated Deterministic Maximum Likelihood}
\newacronym{cpi}{CPI}{Coherent Processing Interval}
\newacronym{csml}{CSML}{Concentrated Stochastic Maximum Likelihood}
\newacronym{dml}{DML}{Deterministic Maximum Likelihood}
\newacronym{doa}{DoA}{Direction-of-Arrival}
\newacronym{ecef}{ECEF}{Earth-centered, Earth-fixed}
\newacronym{eci}{ECI}{Earth-centered Inertial}
\newacronym{efim}{EFIM}{equivalent Fisher information matrix}
\newacronym{esprit}{ESPRIT}{Estimation of Signal Parameters via Rotational Invariant Techniques}
\newacronym{fdoa}{FDOA}{Frequency Difference of Arrival}
\newacronym{fim}{FIM}{Fisher Information Matrix}
\newacronym{leo}{LEO}{Low Earth Orbit}
\newacronym{mle}{MLE}{Maximum Likelihood Estimation}
\newacronym{mse}{MSE}{Mean Square Error}
\newacronym{music}{MUSIC}{MUtiple SIgnal Classification}
\newacronym{pdf}{PDF}{Probability Density Function}
\newacronym{rmse}{RMSE}{Root-Mean Square Error}
\newacronym{sml}{SML}{Stochastic Maximum Likelihood}
\newacronym{tdoa}{TDOA}{Time Difference of Arrival}
\newacronym{ula}{ULA}{Uniform Linear Array}
\newacronym{uml}{UML}{Unconditional Maximum Likelihood}
\newacronym{upa}{UPA}{Uniform Planar Array}

\title{DoA 与 Doppler 估计}
\author{Josh Gao}
\date{\today}

\linespread{1.5}
\allowdisplaybreaks[4]
\setlength{\abovedisplayskip}{0pt}
\setlength{\belowdisplayskip}{0pt}

\begin{document}

\maketitle

\begin{abstract}
  使用通信信号估计来波方向与 Doppler 参数，是通信感知一体化和低轨卫星协作感知中的基础问题。
  本文以学习笔记的方式记录这一问题的递进路径：每节只沿一个维度推进模型，其余维度保持最简形态。
  正文从多快拍单阵列确定信号 \gls{doa} 估计出发，依次引入 Doppler、多星几何，并以多用户与星间时间戳误差两节给出后续方向所需的模型接口与初步分析；随后转入多帧连续相位结构，最后以从全局方向到用户三维位置的输出参数化收尾，为多星协作定位等拓展方向提供模型接口。
  正文仅写到集中似然的最终形式与 \gls{efim} 的 Schur complement 表达式，详细矩阵代入与逐步化简见附录。
  附录按``是否共享推导框架''组织：单阵列三种 \gls{crb} 合并为\appref{sec:singleArrayCrb}，多星静态模型为\appref{sec:A6_multiArrayStatDetDoaDopplerCrb}，时间戳误差 \gls{fim} 分析为\appref{sec:timestampErrCrb}，多帧动态模型的连续/独立相位对比为\appref{sec:multiFrameCrb}，用户三维位置 \gls{crb} 为\appref{sec:userPositionCrb}。
\end{abstract}

\input{parts/preface.tex}
\input{parts/sec1_singleArrayDoa.tex}
\input{parts/sec2_singleArrayDoaDoppler.tex}
\input{parts/sec3_multiSatSingleUser.tex}
\input{parts/sec4_multiSatMultiUser.tex}
\input{parts/sec5_timestampError.tex}
\input{parts/sec6_multiFrameCp.tex}
\input{parts/sec7_userPositioning.tex}
% \input{parts/sec8_beamforming.tex}        % 预留，本次不展开

\appendix
\renewcommand{\thesection}{\texorpdfstring{\Alph{section}}{附录 \Alph{section}}}
\titleformat{\section}{\normalfont\Large\bfseries}{附录~\thesection}{1em}{}
\titlespacing*{\section}{0pt}{*0}{*0}
\renewcommand{\thesubsection}{\Alph{section}.\arabic{subsection}}
\renewcommand{\thesubsubsection}{\Alph{section}.\arabic{subsection}.\arabic{subsubsection}}
\renewcommand{\theequation}{\Alph{section}.\arabic{equation}}

\newpage
\input{parts/A-symbolIndex.tex}
\newpage
\input{parts/B-mathBackground.tex}
\newpage
\input{parts/C-classicalDoa.tex}
\newpage
\input{parts/D-singleArrayCrb.tex}
\newpage
\input{parts/E-multiSatStaticCrb.tex}
\newpage
\input{parts/F-timestampErrCrb.tex}
\newpage
\input{parts/G-multiFrameCrb.tex}
\newpage
\input{parts/H-userPositionCrb.tex}

\newpage
\renewcommand*{\bibfont}{\footnotesize}
\printbibliography

\end{document}