known, it is reasonable to assume that all the angle-delay domain channel elements are identically distributed, i.e., all the ADCPM elements are equal, in which case the optimal condition in can be achieved when ${\left|\phi_{k}-\phi_{k'}\right|}\geq{N_{\mathrm{g}}}$ for $\forall k\neq k'$, i.e., the extended channels in the delay domain for different UTs are totally separated, which coincides with the conventional PSOPs [@Chi11Training]. For frequency-flat massive MIMO channels, i.e., ${N_{\mathrm{c}}}=1$, the condition in can be achieved when ${{\boldsymbol\Omega}}_{k}\odot{{\boldsymbol\Omega}}_{k'}={\mathbf{0}}$ for $\forall k\neq k'$, i.e., different UTs can share the same pilot when the respective channels have non-overlapping support in the angle domain, which coincides with previous works such as [@You15Pilot; @Yin13coordinated]. In our work, the proposed APSPs exploit the joint angle-delay domain channel sparsity in massive MIMO-OFDM, and are more efficient and general from the pilot overhead point of view.

Channel Prediction with APSPs
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In the previous subsection, we investigated channel estimation during the pilot segment. Directly employing the pilot segment channel estimates in the data segment might not always be appropriate [@Truong13Effects], especially in high mobility scenarios, which are the main focus of the APSPs. In this subsection, we investigate channel prediction during the data segment based on the received pilot signals, 