A practical barrier to the implementation of cache-aided networks is dynamic and unpredictable user behavior. In dynamic setups, users can freely depart and enter the network at any moment. The shared caching concept has the potential to handle this issue by assigning $K$ users to $P$ caching profiles, where all $\eta_{p}$ users assigned to profile $p$ store the same cache content defined by that profile. The existing schemes, however, cannot be applied in general and are not dynamic in the true sense as they put constraints on the transmitter-side spatial multiplexing gain $\alpha$. Specifically, they work only if $\alpha \leq \min_{p} \eta_{p}$ or $\alpha \geq \hat{\eta}$, where in the latter case, $\gamma$ is the normalized cache size of each user, $\hat{\eta}$ is an arbitrary parameter satisfying $1 \leq \hat{\eta} \leq \max_{p} \eta_{p}$, and the extra condition of $\alpha \geq K\gamma$ should also be met. In this work, we propose a universal caching scheme based on the same shared-cache model that can be applied to any dynamic setup, extending the working region of existing schemes to networks with $\min_{p} \eta_{p} \leq \alpha \leq \hat{\eta}$ and removing any other constraints of existing schemes. We also derive the closed-form expressions for the achievable degrees-of-freedom (DoF) of the proposed scheme and show that it achieves the optimal DoF for uniform user distributions. Notably, it is the first scheme to achieve the optimal DoF of $K\gamma+\alpha$ for networks with uniform user distribution, $\alpha > \hat{\eta}$, and non-integer $\frac{\alpha}{\hat{\eta}}$, without imposing any other constraints. Finally, we use numerical simulations to assess how non-uniform user distribution impacts the DoF performance and illustrate that the proposed scheme provides a noticeable improvement over unicasting for uneven distributions.

翻译：缓存辅助网络在实际部署中面临的一个障碍是用户行为的动态性和不可预测性。在动态场景中，用户可随时离开或加入网络。共享缓存概念通过将$K$个用户分配到$P个缓存配置文件中来应对这一问题，其中分配给配置文件$p$的所有$\eta_{p}$个用户存储由该配置文件定义的相同缓存内容。然而，现有方案无法普遍适用，且并非真正意义上的动态方案，因为它们对发射端空间复用增益$\alpha$施加了约束。具体而言，这些方案仅在$\alpha \leq \min_{p} \eta_{p}$或$\alpha \geq \hat{\eta}$时有效（后者情况下，$\gamma$为每个用户的归一化缓存大小，$\hat{\eta}$为满足$1 \leq \hat{\eta} \leq \max_{p} \eta_{p}$的任意参数），且还需满足$\alpha \geq K\gamma$的额外条件。在本工作中，我们提出了一种基于相同共享缓存模型的通用缓存方案，该方案可适用于任意动态场景，将现有方案的工作区间扩展至$\min_{p} \eta_{p} \leq \alpha \leq \hat{\eta}$的网络，并消除了现有方案的其他约束条件。我们还推导了所提方案可达自由度（DoF）的闭式表达式，并证明其在均匀用户分布下能达到最优DoF。值得注意的是，这是首个在均匀用户分布、$\alpha > \hat{\eta}$且$\frac{\alpha}{\hat{\eta}}$为非整数的情况下，无需施加其他约束即可达到$K\gamma+\alpha$最优DoF的方案。最后，我们通过数值仿真评估非均匀用户分布对DoF性能的影响，并表明所提方案在非均匀分布下相比单播传输能带来显著性能提升。