## 2 System Model  
We consider a HetNet environment that is illustrated in Figure 1. The network consists of \(I\) SBSs that are distributed by utilizing the homogeneous Poisson point process (PPP)  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Description** \\ \hline \(B\) & Bandwidth \\ \hline \(I\) & Number of small base stations (SBSs) \\ \hline \(D_{c}\) & Content access delay from core network \\ \hline \(|f_{m}|\) & Content size \\ \hline \(D_{b}\) & Delay between SBS and UD \\ \hline \(T_{D}\) & Delay threshold \\ \hline \(D^{\prime}\) & Delay within internet \\ \hline \(P_{in}\) & Interference power \\ \hline \(N_{o}\) & Power spectral density \\ \hline \(c_{i}\) & SBS cache capacity \\ \hline \(|h_{i,n}|^{2}\) & Second-order statistics of Rayleigh fading channel \\ \hline \(\Gamma\) & Signal-to-interference-plus-noise ratio (SINR) \\ \hline \(\gamma\) & Skewness of popularity distribution \\ \hline \(M\) & Total content \\ \hline \(R_{T}\) & Transmission rate \\ \hline \(P_{T}\) & Transmit power \\ \hline \(N\) & Number of sets of UE \\ \hline \hline \end{tabular}
\end{table}
Table 1: Notations.  
with intensity \(\lambda_{SBS}\). A dual-mode transmission system is exploited for SBS transmission. The SBSs are equipped with both \(\upmu\)Wave and mmWave front-ends to improve data services through the cellular links [30]. Furthermore, the network contains \(N\) mobile sets of UE following the independent homogeneous PPP with density \(\lambda_{u}\). The UE sets are represented by the set \(\mathcal{U}=\{1,2,\ldots,N\}\). We consider that UE sets can perform data sharing among themselves via D2D communications. This feature is helpful in alleviating the data traffic burden over the fronthaul. The D2D communications occur on the mmWave spectrum in order to ensure fast data transmission within a limited time period. However, mmWave frequencies are susceptible to path loss and blockages. Therefore, it is assumed that D2D links can be established if any of the UE within D2D range possesses the desired content and there exists a LoS link between the data sender and receiver. We consider a statistical model for both the LoS and NLoS links. The LoS link probability between the content sender and content receiver is \(e^{-\alpha r}\), where \(r\) denotes the length of the LoS link and \(\alpha\) denotes the blockage density. Moreover, the NLoS link probability is \(1-e^{-\alpha r}\)[31].  
Before going into the details of data popularity profile, beamforming, and communication link modeling, the data access procedure is summarized as follows:  
1. Self data offloading: First, the user checks its own cache for the desired content. The request is fulfilled with immediate effect through self data offloading subject to the availability of required content in its own cache.
2. D2D data offloading: If the desired content is not cached locally, then neighboring UE sets within proximity or D2D communication range (\(R_{D2D}\)) are approached. If the requested content is cached by at least one UE, a D2D communication link is established, and the requested content is obtained.
3. SBS data offloading: In case of data access failure through UE caches, the data is demanded from serving SBS. Then, the serving SBS will provide the content to the content demanding UE via mmWave or \(\upmu\)Wave transmission depending on the link probability from its own cache or by fetching from the core network.  
Figure 1: Network scenario. We consider SBSs and UE to be equipped with limited cache resources. Data caching at UE enhances data sharing via D2D communications. Moreover, SBS level caching is also performed to facilitate UE that cannot find its desired content in its own cache or the cache of proximal sets of UE. The concurrent caching at UE and SBS levels substantially minimizes network delay.