using the proposed APSPs.

For frame-based massive MIMO-OFDM transmission, the BS utilizes the received signals during the pilot segment to acquire the channels in the current frame. If the pilot segment channel estimate ${\hat{{\mathbf{H}}}}_{k,\ell}$ is directly employed as the estimate of the channel ${\mathbf{H}}_{k,\ell+\Delta_{\ell}}$ during the data segment, the corresponding sum MSE-CE for a given delay $\Delta_{\ell}$ between the pilot symbol and data symbol can be written as $$\begin{aligned}
\label{eq:epscek}
  {\epsilon^{\mathrm{CE}}}\left(\Delta_{\ell}\right)
  &=\sum_{k=0}^{K-1}\sum_{i=0}^{M-1}\sum_{j=0}^{{N_{\mathrm{g}}}-1}{{{\mathsf{E}}}\left\{{\left|{\left[{\mathbf{H}}_{k,\ell+\Delta_{\ell}}-{\hat{{\mathbf{H}}}}_{k,\ell}\right]_{i,j}}\right|^{2}}\right\}}{\notag\\}&=\sum_{k=0}^{K-1}\sum_{i=0}^{M-1}\sum_{j=0}^{{N_{\mathrm{g}}}-1}
  \Bigg\{{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}+\left[1-2\varrho_{k}\left(\Delta_{\ell}\right)\right]{\notag\\}&\qquad\cdot\frac{{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}^{2}}
  {\sum_{k'=0}^{K-1}{\left[{{\boldsymbol\Omega}}_{k'}^{\phi_{k'}-\phi_{k}}\right]_{i,j}}+{\frac{1}{{\rho_{\mathrm{tr}}}}}}\Bigg\}.\end{aligned}$$ In high mobility scenarios, the channel TCF satisfies $\varrho_{k}\left(\Delta_{\ell}\right)\to0$ for relatively large delay ${\left|\Delta_{\ell}\right|}$. When $\varrho_{k}\left(\Delta_{\ell}\right)<1/2$, i.e., $1-2\varrho_{k}\left(\Delta_{\ell}\right)>0$, it can be observed from that the sum MSE-CE expression ${\epsilon^{\mathrm{CE}}}\left(\Delta_{\ell}\right)$ is even larger than the sum channel power $\sum_{k=0}^{K-1}\sum_{i=0}^{M-1}\sum_{j=0}^{{N_{\mathrm{g}}}-1}{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}$, and channel estimation performance cannot be guaranteed, which motivates the need for channel prediction.

For channel prediction, the BS utilizes the received pilot signals as well as the channel TCF to get estimates of the channels during the data segment. Under the MMSE criterion, with the angle-delay domain channel property of massive MIMO-OFDM given in [Proposition \[prop:adcmsts\]]{}, it is not hard to show that an estimate of the ADCRM ${\mathbf{H}}_{k,\ell+\Delta_{\ell}}$ based on ${\mathbf{Y}}_{k,\ell}$ can be obtained in an element-wise manner as follows $$\begin{aligned}
    &{\left[{\hat{{\mathbf{H}}}}_{k,\ell+\Delta_{\ell}}\right]_{i,j}}{\notag\\}&\quad=\varrho_{k}\left(\Delta_{\ell}\right)\frac{{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}}
  {\sum_{k'=0}^{K-1}{\left[{{\boldsymbol\Omega}}_{k'}^{\phi_{k'}-\phi_{k}}\right]_{i,j}}+{\frac{1}{{\rho_{\mathrm{tr}}}}}}{\left[{\mathbf{Y}}_{k,\ell}\right]_{i,j}}.\end{aligned}$$ Recalling the pilot 