diff --git a/parts/C-classicalDoa.tex b/parts/C-classicalDoa.tex index fd5ad69..c40251a 100644 --- a/parts/C-classicalDoa.tex +++ b/parts/C-classicalDoa.tex @@ -124,7 +124,7 @@ The \gls{doa} estimates are then obtained by locating the $K$ dominant peaks of \begin{equation} \hat{\theta}_k = -\arg\max_{\theta} +\argmax_{\theta} \widehat{P}_{\mathrm{MVDR}}(\theta), \qquad k=1,\dots,K. \label{eq:mvdr_estimation} @@ -256,7 +256,7 @@ The \gls{doa} estimates are then obtained by locating the $K$ dominant peaks of \begin{equation} \hat{\theta}_k = -\arg\max_{\theta} +\argmax_{\theta} P_{\mathrm{MUSIC}}(\theta), \qquad k=1,\dots,K. \label{eq:music_estimation} @@ -427,7 +427,7 @@ In practice, $\bm{\Psi}$ can be estimated by solving the least-squares problem \begin{equation} \widehat{\bm{\Psi}} = -\arg\min_{\bm{\Psi}} +\argmin_{\bm{\Psi}} \left\| \mathbf{U}_{s,2} - \mathbf{U}_{s,1}\bm{\Psi} \right\|_{\mathrm{F}}^2, @@ -619,7 +619,7 @@ The joint estimates of \gls{doa} and Doppler are then obtained by searching for \begin{equation} (\hat{\theta}_k,\hat{\nu}_k) = -\arg\max_{\theta,\nu} +\argmax_{\theta,\nu} P_{\mathrm{ST\text{-}MUSIC}}(\theta,\nu), \qquad k=1,\dots,K. \label{eq:st_music_estimation} diff --git a/parts/sec3_multiSatSingleUser.tex b/parts/sec3_multiSatSingleUser.tex index 81c5f73..bb2e9f7 100644 --- a/parts/sec3_multiSatSingleUser.tex +++ b/parts/sec3_multiSatSingleUser.tex @@ -224,7 +224,7 @@ \begin{equation} \widehat{\boldsymbol\eta} = - \arg\min_{\boldsymbol\xi,\nu_{\mathrm{ref}}} + \argmin_{\boldsymbol\xi,\nu_{\mathrm{ref}}} \sum_{\ell=0}^{L-1} M_\ell T \log \mathcal E_\ell(\boldsymbol\xi,\nu_{\mathrm{ref}}), @@ -242,7 +242,7 @@ \begin{equation} \widehat{\boldsymbol\eta} = - \arg\max_{\boldsymbol\xi,\nu_{\mathrm{ref}}} + \argmax_{\boldsymbol\xi,\nu_{\mathrm{ref}}} \sum_{\ell=0}^{L-1} \frac{1}{\sigma_\ell} \frac{\left|\mathbf g_\ell^\Herm\tilde{\mathbf y}_\ell\right|^2} diff --git a/parts/sec4_multiSatMultiUser.tex b/parts/sec4_multiSatMultiUser.tex index b2572c7..9a8ee35 100644 --- a/parts/sec4_multiSatMultiUser.tex +++ b/parts/sec4_multiSatMultiUser.tex @@ -152,7 +152,7 @@ $\boldsymbol\Xi\triangleq[\boldsymbol\xi_1,\ldots,\boldsymbol\xi_K]$,$\boldsym \label{eq:sec4_concentrated} \widehat{\boldsymbol\eta}_{\mathrm{mu}} = - \arg\min_{\boldsymbol\Xi,\boldsymbol\nu_{\mathrm{ref}}} + \argmin_{\boldsymbol\Xi,\boldsymbol\nu_{\mathrm{ref}}} \sum_{\ell=0}^{L-1} M_\ell T \log @@ -170,7 +170,7 @@ $\boldsymbol\Xi\triangleq[\boldsymbol\xi_1,\ldots,\boldsymbol\xi_K]$,$\boldsym \begin{equation} \widehat{\boldsymbol\eta}_{\mathrm{mu}} = - \arg\max_{\boldsymbol\Xi,\boldsymbol\nu_{\mathrm{ref}}} + \argmax_{\boldsymbol\Xi,\boldsymbol\nu_{\mathrm{ref}}} \sum_{\ell=0}^{L-1} \frac{1}{\sigma_\ell} \tilde{\mathbf y}_\ell^\Herm diff --git a/parts/sec6_multiFrameCp.tex b/parts/sec6_multiFrameCp.tex index 34c9bf1..05a81f5 100644 --- a/parts/sec6_multiFrameCp.tex +++ b/parts/sec6_multiFrameCp.tex @@ -176,7 +176,7 @@ CP 模型的干扰参数向量为 \begin{equation} \widehat{\boldsymbol\eta} = - \arg\min_{\boldsymbol\xi,\nu_{\mathrm{ref}}} + \argmin_{\boldsymbol\xi,\nu_{\mathrm{ref}}} \min_{\dot\nu_{\mathrm{ref}},\{\chi_\ell\}} \sum_{\ell=0}^{L-1}M_\ell PT\log \mathcal R^{\mathrm{cp,str}}_\ell. \end{equation} @@ -191,7 +191,7 @@ CP 模型的干扰参数向量为 \begin{equation} \widehat{\boldsymbol\eta}_{\mathrm{dyn,rel}} = - \arg\min_{\boldsymbol\xi,\nu_{\mathrm{ref}}} + \argmin_{\boldsymbol\xi,\nu_{\mathrm{ref}}} \min_{\dot\nu_{\mathrm{ref}}} \sum_{\ell=0}^{L-1}M_\ell PT\log \mathcal R^{\mathrm{cp,rel}}_\ell. \end{equation} @@ -201,7 +201,7 @@ CP 模型的干扰参数向量为 \begin{equation} \widehat{\boldsymbol\eta}_{\mathrm{dyn,ip}} = - \arg\min_{\boldsymbol\xi,\nu_{\mathrm{ref}}} + \argmin_{\boldsymbol\xi,\nu_{\mathrm{ref}}} \min_{\dot\nu_{\mathrm{ref}}} \sum_{\ell=0}^{L-1}M_\ell PT\log \mathcal R^{\mathrm{ip}}_\ell. \end{equation} diff --git a/parts/sec7_userPositioning.tex b/parts/sec7_userPositioning.tex index 23e5680..a91b439 100644 --- a/parts/sec7_userPositioning.tex +++ b/parts/sec7_userPositioning.tex @@ -81,7 +81,7 @@ % \begin{equation} \widehat{\boldsymbol\eta}_{\mathrm{pos}} - =\arg\min_{\mathbf p,\nu_{\mathrm{ref}}} + =\argmin_{\mathbf p,\nu_{\mathrm{ref}}} \sum_{\ell=0}^{L-1}M_\ell T\log\mathcal E_\ell(\mathbf p,\nu_{\mathrm{ref}}), \qquad \mathcal E_\ell\triangleq\|\tilde{\mathbf y}_\ell\|_2^2-\frac{\big|\mathbf g_\ell^\Herm\tilde{\mathbf y}_\ell\big|^2}{\|\mathbf g_\ell\|_2^2}.