vectorization operation. ${\mathbf{F}}_{N}$ denotes the $N$-dimensional unitary discrete Fourier transform (DFT) matrix. ${\mathbf{F}}_{N\times G}$ denotes the matrix composed of the first $G\left(\leq N\right)$ columns of ${\mathbf{F}}_{N}$. ${\mathbf{f}}_{N,q}$ denotes the [$q$th]{} column of the matrix $\sqrt{N}{\mathbf{F}}_{N}$. We further define the permutation matrix ${{\boldsymbol\Pi}}_{N}^{n} \triangleq \left[\begin{IEEEeqnarraybox*}[][c]{,c/c,}
{\mathbf{0}}&{\mathbf{I}}_{N-{\left\langlen\right\rangle_{N}}}\\
{\mathbf{I}}_{{\left\langlen\right\rangle_{N}}}&{\mathbf{0}}\end{IEEEeqnarraybox*}\right]$. The notation $\backslash$ denotes the set subtraction operation.

Outline
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The rest of the paper is organized as follows. In [Section \[sec:massive\_channel\]]{}, we investigate the sparse nature of the massive MIMO-OFDM channel model. In [Section \[sec:one\_tr\]]{}, we propose APSP-CA over one OFDM symbol in massive MIMO-OFDM, including channel estimation and prediction. We investigate the multiple consecutive pilot symbol case in [Section \[sec:mul\_tr\]]{}. Simulation results are presented in [Section \[sec:sim\_res\]]{}, and conclusions are given in [Section \[sec:conc\_pw\]]{}.

Massive MIMO-OFDM Channel Model {#sec:massive_channel}
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In this section, we propose a physically motivated massive MIMO-OFDM channel model, and investigate the inherent channel sparsity property. We consider a single-cell TDD wideband massive MIMO wireless system which consists of one BS equipped with $M$ antennas and $K$ single-antenna UTs. We denote the UT set as ${\mathcal{K}}=\left\{{0,1,\ldots,K-1}\right\}$ where $k\in{\mathcal{K}}$ represents the UT index. We assume that the channels of different UTs are statistically independent. We assume that the BS is 