fix(equation): 删去公式中手动 \! 负间距
\arcsin\!\big(、\Re\!\left\{、\mathbf a_\ell\!\big( 等"函数/算子+定界符"
处的手动负间距由 LaTeX 自动排版处理,无需手动加 \!。全文删 39 处。
主文件 \newcommand{\diff}{\mathop{}\!\mathrm{d}} 中的 \! 是微分号标准间距,保留。
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@@ -134,7 +134,7 @@ $\zeta_\ell\in\mathbb C$ 为第 $\ell$ 条链路的未知复干扰系数,$\sig
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\begin{equation}
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[\mathcal I(\boldsymbol\kappa_{\mathrm{stat}})]_{ij}
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=
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2\Re\!\left\{
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2\Re\left\{
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\frac{\partial \boldsymbol\mu^{\Herm}(\boldsymbol\kappa_{\mathrm{stat}})}{\partial \kappa_i}
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\mathbf R_n^{-1}
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\frac{\partial \boldsymbol\mu(\boldsymbol\kappa_{\mathrm{stat}})}{\partial \kappa_j}
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@@ -237,11 +237,11 @@ $\partial\nu_{\ell_{\mathrm{ref}}}/\partial\beta=0$。若改用别的等价参
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\begin{equation}
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\alpha_\ell^{\mathrm{loc}}
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=
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\operatorname{atan2}\!\big(u_{\ell,2}^{\mathrm{loc}},u_{\ell,1}^{\mathrm{loc}}\big),
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\operatorname{atan2}\big(u_{\ell,2}^{\mathrm{loc}},u_{\ell,1}^{\mathrm{loc}}\big),
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\qquad
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\beta_\ell^{\mathrm{loc}}
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=
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\arcsin\!\big(u_{\ell,3}^{\mathrm{loc}}\big).
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\arcsin\big(u_{\ell,3}^{\mathrm{loc}}\big).
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\end{equation}
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对任意 $x\in\{\alpha,\beta\}$,有
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@@ -439,7 +439,7 @@ $\mathbf g_\ell=\mathbf q_\ell\otimes \mathbf a_\ell$
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=
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\sum_{\ell=0}^{L-1}
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\frac{2}{\sigma_{n,\ell}^2}
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\Re\!\left\{
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\Re\left\{
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\mathbf J_{\eta,\ell}^{\Herm}\mathbf J_{\eta,\ell}
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\right\},
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\label{eq:A6_Itt}
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@@ -448,9 +448,9 @@ $\mathbf g_\ell=\mathbf q_\ell\otimes \mathbf a_\ell$
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\mathcal I_{\eta\psi}
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=
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\begin{bmatrix}
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\dfrac{2}{\sigma_{n,0}^2}\Re\!\left\{\mathbf J_{\eta,0}^{\Herm}\mathbf J_{\psi,0}\right\}
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\dfrac{2}{\sigma_{n,0}^2}\Re\left\{\mathbf J_{\eta,0}^{\Herm}\mathbf J_{\psi,0}\right\}
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& \cdots &
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\dfrac{2}{\sigma_{n,L-1}^2}\Re\!\left\{\mathbf J_{\eta,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
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\dfrac{2}{\sigma_{n,L-1}^2}\Re\left\{\mathbf J_{\eta,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
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\end{bmatrix},
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\label{eq:A6_Itb}
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\end{equation}
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@@ -459,9 +459,9 @@ $\mathbf g_\ell=\mathbf q_\ell\otimes \mathbf a_\ell$
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=
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\operatorname{blkdiag}
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\left(
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\frac{2}{\sigma_{n,0}^2}\Re\!\left\{\mathbf J_{\psi,0}^{\Herm}\mathbf J_{\psi,0}\right\},
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\frac{2}{\sigma_{n,0}^2}\Re\left\{\mathbf J_{\psi,0}^{\Herm}\mathbf J_{\psi,0}\right\},
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\ldots,
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\frac{2}{\sigma_{n,L-1}^2}\Re\!\left\{\mathbf J_{\psi,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
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\frac{2}{\sigma_{n,L-1}^2}\Re\left\{\mathbf J_{\psi,L-1}^{\Herm}\mathbf J_{\psi,L-1}\right\}
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\right).
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\label{eq:A6_Ibb}
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\end{equation}
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@@ -502,7 +502,7 @@ $\begin{bmatrix}\mathbf g_\ell & j\mathbf g_\ell\end{bmatrix}$。虽然这两个
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=
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2\sum_{\ell=0}^{L-1}
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\frac{1}{\sigma_{n,\ell}^2}
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\Re\!\left\{
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\Re\left\{
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\mathbf J_{\eta,\ell}^{\Herm}
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\mathcal P_{\mathbf g_\ell}^{\perp}
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\mathbf J_{\eta,\ell}
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@@ -517,7 +517,7 @@ $\begin{bmatrix}\mathbf g_\ell & j\mathbf g_\ell\end{bmatrix}$。虽然这两个
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=
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2\sum_{\ell=0}^{L-1}
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\frac{|\zeta_\ell|^2}{\sigma_{n,\ell}^2}
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\Re\!\left\{
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\Re\left\{
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\mathbf D_\ell^{\Herm}
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\mathcal P_{\mathbf g_\ell}^{\perp}
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\mathbf D_\ell
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@@ -596,7 +596,7 @@ $\begin{bmatrix}\mathbf g_\ell & j\mathbf g_\ell\end{bmatrix}$。虽然这两个
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\frac{2}{\sigma^2}
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\sum_{\ell=0}^{L-1}
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|\zeta_\ell|^2
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\Re\!\left\{
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\Re\left\{
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\mathbf D_\ell^{\Herm}\mathcal P_{\mathbf g_\ell}^{\perp}\mathbf D_\ell
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\right\}.
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\end{equation}
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@@ -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
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=
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\sum_{\ell=0}^{L-1}
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\frac{2}{\sigma_{n,\ell}^2}
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\Re\!\big\{\mathbf J_{\eta,\ell}^\Herm\mathbf J_{\eta,\ell}\big\}.
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\Re\big\{\mathbf J_{\eta,\ell}^\Herm\mathbf J_{\eta,\ell}\big\}.
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\end{equation}
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%
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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
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@@ -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
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=
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2\sum_{\ell=0}^{L-1}
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\frac{1}{\sigma_{n,\ell}^2}
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\Re\!\big\{
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\Re\big\{
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\mathbf J_{\eta,\ell}^\Herm
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\mathcal P_{\mathbf G_\ell}^\perp
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\mathbf J_{\eta,\ell}
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@@ -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
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=
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2\sum_{\ell=0}^{L-1}
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\frac{1}{\sigma_{n,\ell}^2}
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\Re\!\Big\{
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\Re\Big\{
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\zeta_{\ell,k}^*\zeta_{\ell,k'}\,
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\mathbf D_{\ell,k}^\Herm
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\mathcal P_{\mathbf G_\ell}^\perp
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