diff --git a/parts/C-classicalDoa.tex b/parts/C-classicalDoa.tex
index e485d2c..fe17bc4 100644
--- a/parts/C-classicalDoa.tex
+++ b/parts/C-classicalDoa.tex
@@ -458,7 +458,7 @@ where $\angle(\cdot)$ denotes the phase angle of a complex number. Finally, the
 \begin{equation}
 \hat{\theta}_k
 =
-\arcsin\!\left(
+\arcsin\left(
 \frac{\lambda_{\mathrm{c}}}{2\pi d}\hat{\mu}_k
 \right),
 \qquad k = 1,\dots,K.
@@ -955,7 +955,7 @@ where $\angle(\cdot)$ denotes the phase angle of a complex number. Finally, the
 \begin{equation}
 \hat{\theta}_k
 =
-\arcsin\!\left(
+\arcsin\left(
 \frac{\lambda_{\mathrm{c}}}{2\pi d}\hat{\mu}_k
 \right),
 \qquad
diff --git a/parts/E-multiSatStaticCrb.tex b/parts/E-multiSatStaticCrb.tex
index 747ea27..8517a86 100644
--- a/parts/E-multiSatStaticCrb.tex
+++ b/parts/E-multiSatStaticCrb.tex
@@ -134,7 +134,7 @@ $\zeta_\ell\in\mathbb C$ 为第 $\ell$ 条链路的未知复干扰系数，$\sig
 \begin{equation}
   [\mathcal I(\boldsymbol\kappa_{\mathrm{stat}})]_{ij}
   =
-  2\Re\!\left\{
+  2\Re\left\{
     \frac{\partial \boldsymbol\mu^{\Herm}(\boldsymbol\kappa_{\mathrm{stat}})}{\partial \kappa_i}
     \mathbf R_n^{-1}
     \frac{\partial \boldsymbol\mu(\boldsymbol\kappa_{\mathrm{stat}})}{\partial \kappa_j}
@@ -237,11 +237,11 @@ $\partial\nu_{\ell_{\mathrm{ref}}}/\partial\beta=0$。若改用别的等价参
 \begin{equation}
   \alpha_\ell^{\mathrm{loc}}
   =
-  \operatorname{atan2}\!\big(u_{\ell,2}^{\mathrm{loc}},u_{\ell,1}^{\mathrm{loc}}\big),
+  \operatorname{atan2}\big(u_{\ell,2}^{\mathrm{loc}},u_{\ell,1}^{\mathrm{loc}}\big),
   \qquad
   \beta_\ell^{\mathrm{loc}}
   =
-  \arcsin\!\big(u_{\ell,3}^{\mathrm{loc}}\big).
+  \arcsin\big(u_{\ell,3}^{\mathrm{loc}}\big).
 \end{equation}
 
 对任意 $x\in\{\alpha,\beta\}$，有
@@ -439,7 +439,7 @@ $\mathbf g_\ell=\mathbf q_\ell\otimes \mathbf a_\ell$
   =
   \sum_{\ell=0}^{L-1}
   \frac{2}{\sigma_{n,\ell}^2}
-  \Re\!\left\{
+  \Re\left\{
     \mathbf J_{\eta,\ell}^{\Herm}\mathbf J_{\eta,\ell}
   \right\},
   \label{eq:A6_Itt}
@@ -448,9 +448,9 @@ $\mathbf g_\ell=\mathbf q_\ell\otimes \mathbf a_\ell$
   \mathcal I_{\eta\psi}
   =
   \begin{bmatrix}
-    \dfrac{2}{\sigma_{n,0}^2}\Re\!\left\{\mathbf J_{\eta,0}^{\Herm}\mathbf J_{\psi,0}\right\}
+    \dfrac{2}{\sigma_{n,0}^2}\Re\left\{\mathbf J_{\eta,0}^{\Herm}\mathbf J_{\psi,0}\right\}
     & \cdots &
-    \dfrac{2}{\sigma_{n,L-1}^2}\Re\!\left\{\mathbf J_{\eta,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
+    \dfrac{2}{\sigma_{n,L-1}^2}\Re\left\{\mathbf J_{\eta,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
   \end{bmatrix},
   \label{eq:A6_Itb}
 \end{equation}
@@ -459,9 +459,9 @@ $\mathbf g_\ell=\mathbf q_\ell\otimes \mathbf a_\ell$
   =
   \operatorname{blkdiag}
   \left(
-    \frac{2}{\sigma_{n,0}^2}\Re\!\left\{\mathbf J_{\psi,0}^{\Herm}\mathbf J_{\psi,0}\right\},
+    \frac{2}{\sigma_{n,0}^2}\Re\left\{\mathbf J_{\psi,0}^{\Herm}\mathbf J_{\psi,0}\right\},
     \ldots,
-    \frac{2}{\sigma_{n,L-1}^2}\Re\!\left\{\mathbf J_{\psi,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
+    \frac{2}{\sigma_{n,L-1}^2}\Re\left\{\mathbf J_{\psi,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
   \right).
   \label{eq:A6_Ibb}
 \end{equation}
@@ -502,7 +502,7 @@ $\begin{bmatrix}\mathbf g_\ell & j\mathbf g_\ell\end{bmatrix}$。虽然这两个
   =
   2\sum_{\ell=0}^{L-1}
   \frac{1}{\sigma_{n,\ell}^2}
-  \Re\!\left\{
+  \Re\left\{
     \mathbf J_{\eta,\ell}^{\Herm}
     \mathcal P_{\mathbf g_\ell}^{\perp}
     \mathbf J_{\eta,\ell}
@@ -517,7 +517,7 @@ $\begin{bmatrix}\mathbf g_\ell & j\mathbf g_\ell\end{bmatrix}$。虽然这两个
   =
   2\sum_{\ell=0}^{L-1}
   \frac{|\zeta_\ell|^2}{\sigma_{n,\ell}^2}
-  \Re\!\left\{
+  \Re\left\{
     \mathbf D_\ell^{\Herm}
     \mathcal P_{\mathbf g_\ell}^{\perp}
     \mathbf D_\ell
@@ -596,7 +596,7 @@ $\begin{bmatrix}\mathbf g_\ell & j\mathbf g_\ell\end{bmatrix}$。虽然这两个
     \frac{2}{\sigma^2}
     \sum_{\ell=0}^{L-1}
     |\zeta_\ell|^2
-    \Re\!\left\{
+    \Re\left\{
       \mathbf D_\ell^{\Herm}\mathcal P_{\mathbf g_\ell}^{\perp}\mathbf D_\ell
     \right\}.
   \end{equation}
@@ -707,7 +707,7 @@ $\mathbf J_{\psi,\ell}$ 的实参数化二维实子空间与复矩阵 $\mathbf G
   =
   \sum_{\ell=0}^{L-1}
   \frac{2}{\sigma_{n,\ell}^2}
-  \Re\!\big\{\mathbf J_{\eta,\ell}^\Herm\mathbf J_{\eta,\ell}\big\}.
+  \Re\big\{\mathbf J_{\eta,\ell}^\Herm\mathbf J_{\eta,\ell}\big\}.
 \end{equation}
 %
 由于 $\mathbf J_{\psi,\ell}$ 的实子空间等价于 $\mathbf G_\ell$ 的复列空间，关于复增益块的 Schur 补化为对 $\mathbf G_\ell$ 列空间正交补的投影。定义
@@ -730,7 +730,7 @@ $\mathbf J_{\psi,\ell}$ 的实参数化二维实子空间与复矩阵 $\mathbf G
   =
   2\sum_{\ell=0}^{L-1}
   \frac{1}{\sigma_{n,\ell}^2}
-  \Re\!\big\{
+  \Re\big\{
     \mathbf J_{\eta,\ell}^\Herm
     \mathcal P_{\mathbf G_\ell}^\perp
     \mathbf J_{\eta,\ell}
@@ -745,7 +745,7 @@ $\mathbf J_{\psi,\ell}$ 的实参数化二维实子空间与复矩阵 $\mathbf G
   =
   2\sum_{\ell=0}^{L-1}
   \frac{1}{\sigma_{n,\ell}^2}
-  \Re\!\Big\{
+  \Re\Big\{
     \zeta_{\ell,k}^*\zeta_{\ell,k'}\,
     \mathbf D_{\ell,k}^\Herm
     \mathcal P_{\mathbf G_\ell}^\perp
diff --git a/parts/F-timestampErrCrb.tex b/parts/F-timestampErrCrb.tex
index a7c6cc3..8b3097c 100644
--- a/parts/F-timestampErrCrb.tex
+++ b/parts/F-timestampErrCrb.tex
@@ -41,7 +41,7 @@
   =
   \sum_{\ell=0}^{L-1}
   \frac{2}{\sigma_{n,\ell}^2}
-  \Re\!\left\{
+  \Re\left\{
     \frac{\partial\boldsymbol\mu_\ell^\Herm}{\partial\kappa_i}
     \frac{\partial\boldsymbol\mu_\ell}{\partial\kappa_j}
   \right\}.
@@ -66,7 +66,7 @@
   \big[\mathcal I_{\delta\delta}\big]_{\ell\ell'}
   =
   \frac{2}{\sigma_{n,\ell}^2}
-  \Re\!\left\{
+  \Re\left\{
     \frac{\partial\boldsymbol\mu_\ell^\Herm}{\partial\delta_\ell}
     \frac{\partial\boldsymbol\mu_\ell}{\partial\delta_\ell}
   \right\}
@@ -108,16 +108,16 @@ $\mathcal I_{\delta\psi}$ 同样具有按 $\ell$ 的块对角结构：第 $\ell$
     \mathcal I_{\eta\eta}'
     &=
     2\sum_{\ell}\frac{1}{\sigma_{n,\ell}^2}
-    \Re\!\left\{
+    \Re\left\{
       \mathbf J_{\eta,\ell}^\Herm
       \big(\mathbf I-\mathcal P_{\mathbf G_\ell}\big)
       \mathbf J_{\eta,\ell}
     \right\}\big|_{\delta_\ell=0},\\
     \mathcal I_{\delta\delta}'
     &=
-    \operatorname{diag}\!\Big(
+    \operatorname{diag}\Big(
       \tfrac{2}{\sigma_{n,\ell}^2}
-      \Re\!\big\{\mathbf j_{\delta,\ell}^\Herm
+      \Re\big\{\mathbf j_{\delta,\ell}^\Herm
       (\mathbf I-\mathcal P_{\mathbf G_\ell})
       \mathbf j_{\delta,\ell}\big\}\big|_{\delta_\ell=0}
     \Big)_{\ell\neq\ell_{\mathrm{ref}}},\\
@@ -126,7 +126,7 @@ $\mathcal I_{\delta\psi}$ 同样具有按 $\ell$ 的块对角结构：第 $\ell$
     \begin{bmatrix}
       \cdots\quad
       \tfrac{2}{\sigma_{n,\ell}^2}
-      \Re\!\big\{\mathbf J_{\eta,\ell}^\Herm
+      \Re\big\{\mathbf J_{\eta,\ell}^\Herm
       (\mathbf I-\mathcal P_{\mathbf G_\ell})\mathbf j_{\delta,\ell}\big\}\big|_{\delta_\ell=0}
       \quad\cdots
     \end{bmatrix},
@@ -196,10 +196,10 @@ $\boldsymbol\delta$ 在导频自相关半宽 $T_{\mathrm{ac}}$ 处的非线性
   \mathcal I_{\mathrm e}^{(\mathrm{stat})}(\boldsymbol\eta_{\mathrm{stat}})
   =
   \frac{2|\zeta_0|^2}{\sigma_{n,0}^2}
-  \Re\!\big\{\mathbf D_0^\Herm\mathcal P_{\mathbf g_0}^\perp\mathbf D_0\big\}
+  \Re\big\{\mathbf D_0^\Herm\mathcal P_{\mathbf g_0}^\perp\mathbf D_0\big\}
   +
   \frac{2|\zeta_1|^2}{\sigma_{n,1}^2}
-  \Re\!\big\{\mathbf D_1^\Herm\mathcal P_{\mathbf g_1}^\perp\mathbf D_1\big\}\bigg|_{\delta_1=0},
+  \Re\big\{\mathbf D_1^\Herm\mathcal P_{\mathbf g_1}^\perp\mathbf D_1\big\}\bigg|_{\delta_1=0},
 \end{equation}
 %
 其中 $\mathbf D_\ell$ 沿用 \eqref{eq:A6_Dl} 定义，$\delta_1=0$ 处求值即得到完全相干情形的 \gls{efim}。
@@ -225,7 +225,7 @@ $\boldsymbol\delta=[\delta_1]$ 退化为标量，\eqref{eq:F2_jdelta} 中
   \frac{2|\zeta_1|^2}{\sigma_{n,1}^2}
   \big\|\mathbf a_1(\boldsymbol\xi)\big\|_2^2
   \cdot
-  \Re\!\big\{(\dot{\mathbf q}_1^{\,\mathrm{te}})^\Herm\mathcal P_{\mathbf q_1}^\perp\dot{\mathbf q}_1^{\,\mathrm{te}}\big\},
+  \Re\big\{(\dot{\mathbf q}_1^{\,\mathrm{te}})^\Herm\mathcal P_{\mathbf q_1}^\perp\dot{\mathbf q}_1^{\,\mathrm{te}}\big\},
 \end{equation}
 %
 其中 $\mathcal P_{\mathbf q_1}^\perp=\mathbf I_T-\mathbf q_1\mathbf q_1^\Herm/\|\mathbf q_1\|^2$。化简利用了 Kronecker 内积关系 $(\mathbf u_1\otimes\mathbf v_1)^\Herm(\mathbf u_2\otimes\mathbf v_2)=(\mathbf u_1^\Herm\mathbf u_2)(\mathbf v_1^\Herm\mathbf v_2)$，并把空间部分因式 $\|\mathbf a_1\|^2$ 提出。
@@ -237,7 +237,7 @@ $\boldsymbol\delta=[\delta_1]$ 退化为标量，\eqref{eq:F2_jdelta} 中
   \mathbf v'_{\eta\delta,1}
   =
   \frac{2}{\sigma_{n,1}^2}
-  \Re\!\Big\{
+  \Re\Big\{
     \zeta_1^*\mathbf D_1^\Herm
     \big(\mathbf I-\mathcal P_{\mathbf g_1}\big)
     \big[\zeta_1\,\dot{\mathbf q}_1^{\,\mathrm{te}}\otimes\mathbf a_1\big]
diff --git a/parts/H-userPositionCrb.tex b/parts/H-userPositionCrb.tex
index 3780aa6..a5bb538 100644
--- a/parts/H-userPositionCrb.tex
+++ b/parts/H-userPositionCrb.tex
@@ -56,7 +56,7 @@ Doppler 部分，由 $\nu_\ell=\nu_{\mathrm{ref}}+\Delta\nu_\ell(\mathbf p)$ 与
 \begin{equation}
   \mathcal I_{\mathrm e}(\boldsymbol\eta_{\mathrm{pos}})
   =2\sum_{\ell=0}^{L-1}\frac{|\zeta_\ell|^2}{\sigma_{n,\ell}^2}
-  \Re\!\big\{(\mathbf D_\ell^{\mathrm{pos}})^\Herm\mathcal P_{\mathbf g_\ell}^\perp\mathbf D_\ell^{\mathrm{pos}}\big\}\in\mathbb R^{4\times4}.
+  \Re\big\{(\mathbf D_\ell^{\mathrm{pos}})^\Herm\mathcal P_{\mathbf g_\ell}^\perp\mathbf D_\ell^{\mathrm{pos}}\big\}\in\mathbb R^{4\times4}.
   \label{eq:H_efim}
 \end{equation}
 %
diff --git a/parts/sec1_singleArrayDoa.tex b/parts/sec1_singleArrayDoa.tex
index c3de2e2..c7a9730 100644
--- a/parts/sec1_singleArrayDoa.tex
+++ b/parts/sec1_singleArrayDoa.tex
@@ -155,7 +155,7 @@ $M$ 元阵列在第 $t$ 个快拍的接收向量记为
   \qquad
   \widehat\sigma(\bm\Theta)
   =
-  \frac{1}{M}\tr\!\left[\left(\mathbf I_M-\mathcal P_{\mathbf A}\right)\widehat{\mathbf R}\right],
+  \frac{1}{M}\tr\left[\left(\mathbf I_M-\mathcal P_{\mathbf A}\right)\widehat{\mathbf R}\right],
 \end{equation}
 %
 其中
@@ -176,7 +176,7 @@ $\mathcal P_{\mathbf A}$ 是导向矩阵列空间的正交投影算子，将贯
   \widehat{\bm\Theta}_{\mathrm{CDML}}
   =
   \argmin_{\bm\Theta}
-  \tr\!\left[\left(\mathbf I_M-\mathcal P_{\mathbf A(\bm\Theta)}\right)\widehat{\mathbf R}\right].
+  \tr\left[\left(\mathbf I_M-\mathcal P_{\mathbf A(\bm\Theta)}\right)\widehat{\mathbf R}\right].
 \end{equation}
 %
 也即把 $\bm\Theta$ 的来向估计等价为最小化投影残差能量。集中似然的逐步矩阵代入与对应的 \gls{crb}/\gls{fim} 推导见附录~\ref{sec:det_doa_crb}。
diff --git a/parts/sec2_singleArrayDoaDoppler.tex b/parts/sec2_singleArrayDoaDoppler.tex
index eec1fd1..a6884e0 100644
--- a/parts/sec2_singleArrayDoaDoppler.tex
+++ b/parts/sec2_singleArrayDoaDoppler.tex
@@ -112,7 +112,7 @@ $\mathbf b_{\mathrm{st},k}$ 的 Kronecker 结构把空间维度的 $\mathbf a(\b
   \tilde{\mathbf y},
 \end{equation}
 %
-其中 $\mathcal P_{\mathbf B_{\mathrm{st}}}\triangleq\mathbf B_{\mathrm{st}}\!\left(\mathbf B_{\mathrm{st}}^\Herm\mathbf B_{\mathrm{st}}\right)^{-1}\mathbf B_{\mathrm{st}}^\Herm$ 为空时字典列空间的投影算子。
+其中 $\mathcal P_{\mathbf B_{\mathrm{st}}}\triangleq\mathbf B_{\mathrm{st}}\left(\mathbf B_{\mathrm{st}}^\Herm\mathbf B_{\mathrm{st}}\right)^{-1}\mathbf B_{\mathrm{st}}^\Herm$ 为空时字典列空间的投影算子。
 对 $\boldsymbol\zeta$ 与 $\sigma$ 的闭式消元过程与第~\ref{sec:det_doa_est} 节的单阵列 \gls{doa} 完全平行，详细矩阵代入见附录~\ref{sec:det_doa_doppler_crb}。
 
 若 Doppler 本身不感兴趣、仅作为干扰参数，可先做 profile 处理：
diff --git a/parts/sec3_multiSatSingleUser.tex b/parts/sec3_multiSatSingleUser.tex
index 65533de..3fc5a30 100644
--- a/parts/sec3_multiSatSingleUser.tex
+++ b/parts/sec3_multiSatSingleUser.tex
@@ -70,11 +70,11 @@
 \begin{equation}
   \alpha_\ell^{\mathrm{loc}}
   =
-  \operatorname{atan2}\!\big(u^{\mathrm{loc}}_{\ell,2},u^{\mathrm{loc}}_{\ell,1}\big),
+  \operatorname{atan2}\big(u^{\mathrm{loc}}_{\ell,2},u^{\mathrm{loc}}_{\ell,1}\big),
   \qquad
   \beta_\ell^{\mathrm{loc}}
   =
-  \arcsin\!\big(u^{\mathrm{loc}}_{\ell,3}\big).
+  \arcsin\big(u^{\mathrm{loc}}_{\ell,3}\big).
 \end{equation}
 %
 第 $\ell$ 颗卫星的阵列导向矢量统一定义为
@@ -82,7 +82,7 @@
 \begin{equation}
   \mathbf a_\ell(\boldsymbol\xi)
   \triangleq
-  \mathbf a_\ell\!\big(\alpha_\ell^{\mathrm{loc}},\beta_\ell^{\mathrm{loc}}\big)
+  \mathbf a_\ell\big(\alpha_\ell^{\mathrm{loc}},\beta_\ell^{\mathrm{loc}}\big)
   \in\mathbb C^{M_\ell\times 1},
 \end{equation}
 %
diff --git a/parts/sec6_multiFrameCp.tex b/parts/sec6_multiFrameCp.tex
index e24e979..19490a5 100644
--- a/parts/sec6_multiFrameCp.tex
+++ b/parts/sec6_multiFrameCp.tex
@@ -126,8 +126,8 @@ $\chi_\ell$ 为第 $\ell$ 颗卫星在参考时刻的\emph{公共相位}，由
   \zeta_{\ell,p}^{\mathrm{ip}}
   \mathbf a_\ell(\boldsymbol\xi)
   s_p(t)
-  \exp\!\left\{
-    j\!\left[
+  \exp\left\{
+    j\left[
       \bar\nu_{\ell,p}t+\frac{1}{2}\dot\nu_\ell t^2
     \right]
   \right\}
@@ -228,7 +228,7 @@ CP 模型的干扰参数向量为
 \begin{equation}
   \mathcal I_{\mathrm{e}}
   =
-  2\Re\!\left\{
+  2\Re\left\{
     \bar{\mathbf J}_{\eta}^{\Herm}
     \mathcal P^{\perp}_{\bar{\mathbf J}_{\psi}}
     \bar{\mathbf J}_{\eta}
diff --git a/parts/sec7_userPositioning.tex b/parts/sec7_userPositioning.tex
index b6d9f8f..09e3d46 100644
--- a/parts/sec7_userPositioning.tex
+++ b/parts/sec7_userPositioning.tex
@@ -23,15 +23,15 @@
 \begin{equation}
   \mathbf u_\ell^{\mathrm{loc}}(\mathbf p)=\boldsymbol\Omega_\ell^\Tran\mathbf u_\ell(\mathbf p),
   \qquad
-  \alpha_\ell^{\mathrm{loc}}=\operatorname{atan2}\!\big(u^{\mathrm{loc}}_{\ell,2},u^{\mathrm{loc}}_{\ell,1}\big),
+  \alpha_\ell^{\mathrm{loc}}=\operatorname{atan2}\big(u^{\mathrm{loc}}_{\ell,2},u^{\mathrm{loc}}_{\ell,1}\big),
   \qquad
-  \beta_\ell^{\mathrm{loc}}=\arcsin\!\big(u^{\mathrm{loc}}_{\ell,3}\big),
+  \beta_\ell^{\mathrm{loc}}=\arcsin\big(u^{\mathrm{loc}}_{\ell,3}\big),
 \end{equation}
 %
 并据此代入与第~\ref{subsec:single_arr_array_model} 小节完全相同的 \gls{ula}/\gls{upa} 阵列导向模板，得到本地导向矢量
 %
 \begin{equation}
-  \mathbf a_\ell(\mathbf p)\triangleq\mathbf a_\ell\!\big(\alpha_\ell^{\mathrm{loc}}(\mathbf p),\beta_\ell^{\mathrm{loc}}(\mathbf p)\big)\in\mathbb C^{M_\ell\times1}.
+  \mathbf a_\ell(\mathbf p)\triangleq\mathbf a_\ell\big(\alpha_\ell^{\mathrm{loc}}(\mathbf p),\beta_\ell^{\mathrm{loc}}(\mathbf p)\big)\in\mathbb C^{M_\ell\times1}.
 \end{equation}
 %
 也即\emph{每阵列内部仍是平面波模型，阵列导向 $\mathbf a_\ell$ 的形式一字不改}；变的只是``本地角由 $\mathbf p$ 而非 $\boldsymbol\xi$ 诱导''。