segment channel estimate in , it can be seen that $$\begin{aligned}
\label{eq:hathkldell}
    {\hat{{\mathbf{H}}}}_{k,\ell+\Delta_{\ell}}=\varrho_{k}\left(\Delta_{\ell}\right){\hat{{\mathbf{H}}}}_{k,\ell}\end{aligned}$$ which indicates that optimal channel estimates during the data segment can be easily obtained via prediction with initial channel estimates obtained during the pilot segment, and the complexity of channel prediction in massive MIMO-OFDM can be further reduced. Similar to , the sum MSE-CP for a given delay $\Delta_{\ell}$ between the data symbol and pilot symbol can be defined as $$\begin{aligned}
\label{eq:epsilonklcp}
  {\epsilon^{\mathrm{CP}}}\left(\Delta_{\ell}\right)
  &\triangleq\sum_{k=0}^{K-1}\sum_{i=0}^{M-1}\sum_{j=0}^{{N_{\mathrm{g}}}-1}
  {{{\mathsf{E}}}\left\{{\left|{\left[{\mathbf{H}}_{k,\ell+\Delta_{\ell}}-{\hat{{\mathbf{H}}}}_{k,\ell+\Delta_{\ell}}\right]_{i,j}}\right|^{2}}\right\}}{\notag\\}&=\sum_{k=0}^{K-1}\sum_{i=0}^{M-1}\sum_{j=0}^{{N_{\mathrm{g}}}-1}
  \Bigg\{{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}
  -\varrho_{k}^{2}\left(\Delta_{\ell}\right){\notag\\}&\qquad\cdot\frac{{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}^{2}}
  {\sum_{k'=0}^{K-1}{\left[{{\boldsymbol\Omega}}_{k'}^{\phi_{k'}-\phi_{k}}\right]_{i,j}}
  +{\frac{1}{{\rho_{\mathrm{tr}}}}}}\Bigg\}.\end{aligned}$$ From , it can be seen that pilot interference will affect channel prediction performance similar to the channel estimation case. However, we will show in the following proposition that such effects can still be eliminated with proper pilot phase shift scheduling.

\[prop:mmsetrscp\] The sum MSE-CP ${\epsilon^{\mathrm{CP}}}\left(\Delta_{\ell}\right)\ \forall\Delta_{\ell}$ is lower bounded by $$\begin{aligned}
\label{eq:varepsiloncp}
  &{\epsilon^{\mathrm{CP}}}\left(\Delta_{\ell}\right)\geq{\varepsilon^{\mathrm{CP}}}\left(\Delta_{\ell}\right){\notag\\}&=\sum_{k=0}^{K-1}\sum_{i=0}^{M-1}\sum_{j=0}^{{N_{\mathrm{g}}}-1}
  \left\{{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}-\varrho_{k}^{2}\left(\Delta_{\ell}\right)\frac{{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}^{2}}{{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}+{\frac{1}{{\rho_{\mathrm{tr}}}}}}\right\}\end{aligned}$$ and the lower bound can be achieved under the condition that, for $\forall k,k'\in{\mathcal{K}}$ and $k\neq k'$, $$\label{eq:condokoudcp}
  \left({\bar{{{\boldsymbol\Omega}}}}_{k,{\left({{N_{\mathrm{c}}}}\right)}}{{\boldsymbol\Pi}}_{{N_{\mathrm{c}}}}^{\phi_{k}}\right)
  \odot\left({\bar{{{\boldsymbol\Omega}}}}_{k',{\left({{N_{\mathrm{c}}}}\right)}}{{\boldsymbol\Pi}}_{{N_{\mathrm{c}}}}^{\phi_{k'}}\right)
  ={\mathbf{0}}.$$

The proof is similar to that of [Proposition \[prop:mmsetrseqcon\]]{}, and is omitted for brevity.

Frame Structure {#subsec:fra_str}
---------------

There exist two typical frame structures for TDD massive MIMO transmission [@Bjornson15Massive]. One type of frame structure (which will be referred to as type-A) 