## 2 System Model
### Channel Model  
We adopt the standard spatial channel model [46]. Accordingly, a channel vector \(h_{l,f}\) for slot \(l\) in frame \(f\), is obtained by sampling the continuous-time multipath vector channel impulse response  
\[h_{l,f}(\tau)=\sum_{d=1}^{D}\sqrt{\Omega_{d,f}}a_{d,f}g(\tau-\tau_{d,f})\text {exp}(-j2\pi\gamma_{d,f}t_{l}), \tag{4}\]which is the sum of contributions from \(D\) paths. In (4), the waveform \(g(\tau)\) is given by the convolution of the transmitted waveform and the matched filter at the receiver. Furthermore, the contribution of the \(d\)-th path depends on the average power \(\Omega_{d,f}\), the path delay \(\tau_{d,f}\), the \(N_{T}N_{R}\times 1\) spatial vector \(a_{d,f}\), the Doppler frequency \(\gamma_{d,f}\), and the starting wall-clock time of the \(l\)-th slot \(t_{l}\). The average power \(\Omega_{d,f}\), path delays \(\tau_{d,f}\), spatial vector \(a_{d,f}\), and Doppler frequency \(\gamma_{d,f}\) are constant within one frame because they depend on large-scale geometric features of the propagation environment. However, they may change over frames following Clause 7.6.3.2 (Procedure B) in [46]. The number of paths is assumed without loss of generalization to be the same for all frames \(f\) because one can set \(\Omega_{d,f}=0\) for frames with a smaller number of paths.  
In [46], the spatial vector \(a_{d,f}\) has a structure that depends on field patterns and steering vectors of the transmit and receive antennas, as well on the polarization of the antennas. Mathematically, the entry of the spatial vector \(a_{d,f}\) corresponding to the receive and transmit antenna element \(n_{R}\) and \(n_{T}\) can be modeled as [46]  
\[[a_{d,f}]_{n_{R}+(n_{T}-1)N_{R}}=\mathbf{F}_{rx,n_{R}}(\theta_{d, f,ZOA},\phi_{d,f,AOA})^{T}\mathbf{M}_{d,f}\] \[\cdot\mathbf{F}_{tx,n_{T}}(\theta_{d,f,ZOD},\phi_{d,f,AOD})\exp \left(-\frac{j2\pi l\lambda_{d,f,n_{T}}}{\lambda_{0}}\right), \tag{5}\]  
where \(\mathbf{F}_{rx,n_{R}}(\cdot,\cdot)\) and \(\mathbf{F}_{tx,n_{T}}(\cdot,\cdot)\) are the \(2\times 1\) field patterns, \(\theta_{d,f,ZOA}\), \(\phi_{d,f,AOA}\), \(\theta_{d,f,ZOD}\), and \(\phi_{d,f,AOD}\) are the zenith angle of arrival (ZOA), azimuth angle of arrival (AOA), zenith angle of departure (ZOD), and azimuth angle of departure (AOD) (in degrees), \(\lambda_{0}\) is the wavelength (in m) of the carrier frequency, \(l_{d,f,n_{R},n_{T}}\) is the length of the path (in m) between the two antennas, and \(\mathbf{M}_{d,f}\) is the polarization coupling matrix defined as  
\[\mathbf{M}_{d,f}=\left(\begin{array}{cc}\exp\left(j\Phi_{d,f}^{\phi\phi} \right)&\sqrt{1/\kappa_{d,f}}\exp\left(j\Phi_{d,f}^{\phi\phi}\right)\\ \sqrt{1/\kappa_{d,f}}\exp\left(j\[PERSON]_{d,f}^{\phi\phi}\right)&\exp\left(j\[PERSON]_{ d,f}^{\phi\phi}\right)\end{array}\right), \tag{6}\]  
with random initial phase \(\Phi_{d,f}^{(\cdot,\cdot)}\sim U(-\pi,\pi)\) and log-normal distributed cross polarization power ratio (XPR) \(\kappa_{d,f}>0\)[46].  
In order to obtain the \(S\times 1\) vector \(h_{l,f}\), we sample the continuous-time channel \(h_{l,f}(\tau)\) in (4) at Nyquist rate \(1/T\) to obtain \(W\) discrete-time \(N_{R}N_{T}\times 1\) channel impulse response  
\[h_{l,f}[w]=h_{l,f}((w-1)T) \tag{7}\]  
for \(w=1,\ldots,W\). Following [41], the channel vector \(h_{l,f}\in\mathcal{C}^{N_{R}N_{T}W\times 1}\) is obtained by concatenating the \(W\) channel vectors \(h_{l,f}[w]\) for \(w=1,\ldots,W\) as  
\[h_{l,f}=[h_{l,f}[1],\ldots,h_{l,f}[W]]^{\top}. \tag{8}\]