content(app-C): 经典 DoA 方法补关键引用

附录 C 五个子节原本无引用,对评审属于明显缺陷。补:

- 章首加 Krim/Viberg 1996 与 Van Trees 2002 作为综合性回顾
- C.1 MVDR     → Capon 1969
- C.2 MUSIC    → Schmidt 1986
- C.3 ESPRIT   → Roy & Kailath 1989
- C.4 ST-MUSIC → Wax 1984
- C.5 ST-ESPRIT → 复用 Roy & Kailath + Wax,无单一规范源
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\section{常用 DoA 估计方法}
\label{sec:doa_methods}
本附录汇总 MVDR、MUSIC、ESPRIT 及其空时扩展形式,主要用于补充算法背景。这里的算法记号服务于经典单阵列或空时阵列模型,不改变正文多星主线中 $\boldsymbol\xi$、$\nu_{\mathrm{ref}}$ 和 $\dot\nu_{\mathrm{ref}}$ 的参数分组。
本附录汇总 MVDR、MUSIC、ESPRIT 及其空时扩展形式,主要用于补充算法背景;综合性的子空间方法回顾可参见~\cite{krimTwoDecadesArray1996,vantreesOptimumArrayProcessing2002}。这里的算法记号服务于经典单阵列或空时阵列模型,不改变正文多星主线中 $\boldsymbol\xi$、$\nu_{\mathrm{ref}}$ 和 $\dot\nu_{\mathrm{ref}}$ 的参数分组。
\subsection{MVDR Algorithm}
\subsection{MVDR Algorithm\texorpdfstring{~\cite{caponHighResolutionFrequencyWavenumberSpectrum1969}}{}}
\label{subsec:mvdr}
Consider a narrowband far-field source model impinging on an $M$-element array. The received signal at snapshot $t$ is given by
@@ -115,7 +115,7 @@ The DoA estimates are then obtained by locating the $K$ dominant peaks of the MV
The MVDR algorithm adaptively suppresses interference and noise by minimizing the array output power subject to the distortionless constraint, and thus achieves high-resolution spatial spectrum estimation with improved interference rejection capability.
\subsection{MUSIC Algorithm}
\subsection{MUSIC Algorithm\texorpdfstring{~\cite{schmidtMultipleEmitterLocation1986}}{}}
\label{subsec:music}
Consider the same narrowband far-field array signal model as in \eqref{eq:mvdr_signal_model}. The received signal at snapshot $t$ can be expressed as
@@ -228,7 +228,7 @@ P_{\mathrm{MUSIC}}(\theta),
The MUSIC algorithm achieves high-resolution DoA estimation by exploiting the orthogonality between the array steering vectors and the noise subspace, and has been widely used in subspace-based array signal processing.
\subsection{ESPRIT Algorithm}
\subsection{ESPRIT Algorithm\texorpdfstring{~\cite{royESPRITEstimationSignalParameters1989}}{}}
\label{subsec:esprit}
Consider the same narrowband far-field array signal model as in \eqref{eq:mvdr_signal_model}, i.e.,
@@ -398,7 +398,7 @@ where $\angle(\cdot)$ denotes the phase angle of a complex number. Finally, the
Compared with MUSIC, the ESPRIT algorithm avoids explicit spectral search and directly retrieves the DoA parameters from the rotational invariance structure of the signal subspace, thereby offering lower computational complexity while maintaining high estimation accuracy.
\subsection{Spatio-Temporal MUSIC Algorithm}
\subsection{Spatio-Temporal MUSIC Algorithm\texorpdfstring{~\cite{waxSpatioTemporalSpectralAnalysis1984}}{}}
\label{subsec:st_music}
Consider a narrowband far-field source model observed by an $M$-element array over $T$ temporal samples within each data block. Let $\mathbf{Y}_{\ell} \in \mathbb{C}^{M \times T}$ denote the $\ell$th received data block, where $\ell = 1, \dots, L$. For $K$ uncorrelated sources, the received signal can be written as
@@ -535,7 +535,7 @@ P_{\mathrm{ST\text{-}MUSIC}}(\theta,\nu),
Compared with conventional MUSIC, the spatio-temporal MUSIC algorithm exploits both the spatial array manifold and the temporal Doppler structure, thereby enabling joint angle-Doppler estimation in a unified subspace framework.
\subsection{Spatio-Temporal ESPRIT Algorithm}
\subsection{Spatio-Temporal ESPRIT Algorithm\texorpdfstring{~\cite{royESPRITEstimationSignalParameters1989,waxSpatioTemporalSpectralAnalysis1984}}{}}
\label{subsec:st_esprit}
Consider the same spatio-temporal signal model as in \eqref{eq:st_music_block_model}. For the $\ell$th data block, the received signal matrix is given by