Two-Dimensional Multi-Access Coded Caching with Multiple Transmit Antennas

This work introduces a multi-antenna coded caching problem in a two-dimensional multi-access network, where a server with $L$ transmit antennas and $N$ files communicates to $K1K2$ users, each with a single receive antenna, through a wireless broadcast link. The network consists of $K1K2$ cache nodes and $K1K2$ users. The cache nodes, each with capacity $M$, are placed on a rectangular grid with $K1$ rows and $K2$ columns, and the users are placed regularly on the square grid such that a user can access $r^2$ neighbouring caches in a cyclic wrap-around fashion. For a given cache memory $M$, the goal of the coded caching problem is to serve the user demands with a minimum delivery time. We propose a solution for the aforementioned coded caching problem by designing two arrays: a caching array and a delivery array. Further, we present two classes of caching and delivery arrays and obtain corresponding multi-access coded caching schemes. The first scheme achieves a normalized delivery time (NDT) $\frac{K1K2(1-r^{2\frac{M}{N})}{L+K1K2\frac{M}{N}}$.} The second scheme achieves an NDT $\frac{K1K2(1-r^{2\frac{M}{N})}{L+K1K2r2\frac{M}{N}}$} when $M/N=1/K1K2$ and $L=K1K2-r^2$, which is optimal under uncoded placement and one-shot delivery.