of antennas $M\to\infty$, elements of the ADCRM ${\mathbf{H}}_{k,\ell}$ satisfy $$\begin{aligned}
\label{eq:exbhk}
  &{{{\mathsf{E}}}\left\{{\left[{\mathbf{H}}_{k,\ell+\Delta_{\ell}}\right]_{i,j}}{\left[{\mathbf{H}}_{k,\ell}\right]_{i',j'}}^{*}\right\}}{\notag\\}&\qquad=\varrho_{k}\left(\Delta_{\ell}\right){\delta\left(i-i'\right)}{\delta\left(j-j'\right)}\cdot{\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}\end{aligned}$$ where ${{\boldsymbol\Omega}}_{k}$ is given in .

See [Appendix \[app:prop\_adcmsts\]]{}.

[Proposition \[prop:adcmsts\]]{} shows that, for massive MIMO-OFDM channels, different elements of the ADCRM ${\mathbf{H}}_{k,\ell}$ are approximately mutually statistically uncorrelated, which lends the ADCRM in its physical interpretation. Specifically, different elements of the ADCRM correspond to the channel gains for different incidence angles and delays, which can be resolved in massive MIMO-OFDM with a sufficiently large antenna array aperture. Note that ${\left[{{\boldsymbol\Omega}}_{k}\right]_{i,j}}$ corresponds to the average power of ${\left[{\mathbf{H}}_{k}\right]_{i,j}}$, and can describe the sparsity of the wireless channels in the angle-delay domain. Hereafter we will refer to ${{\boldsymbol\Omega}}_{k}$ as the angle-delay domain channel power matrix (ADCPM) of UT $k$. The dimension of the ADCPM ${{\boldsymbol\Omega}}_{k}$ is much smaller than that of the SFCCM ${\mathbf{R}}_{k}$, and most elements in ${{\boldsymbol\Omega}}_{k}$ are approximately zero due to the channel sparsity. In addition, ${{\boldsymbol\Omega}}_{k}$ is composed of the variances of independent angle-delay domain channel elements, and thus can be estimated in an element-wise manner. Therefore, in practice there will be enough resources for one to obtain an estimate of ${{\boldsymbol\Omega}}_{k}$ with guaranteed accuracy. In the rest of the paper, we will assume that the 