  Caching at base stations is a promising technology to satisfy the increasing
capacity requirements and reduce the backhaul loads in future wireless
networks. Careful design of random caching can fully exploit the file
popularity and achieve good performance. However, previous works on random
caching scheme usually assumed single antenna at BSs and users, which is not
the case in practical multi-antenna networks. In this paper, we consider the
analysis and optimization in the cache-enabled multi-antenna networks with
limited backhaul. We first derive a closed-form expression and a simple tight
upper bound of the successful transmission probability, using tools from
stochastic geometry and a gamma approximation. Based on the analytic results,
we then consider the area spectrum efficiency maximization by optimizing design
parameters, which is a complicated mixed-integer optimization problem. After
analyzing the optimal properties, we obtain a local optimal solution with lower
complexity. To further simplify the optimization, we then solve an asymptotic
optimization problem in the high user density region, using the upper bound as
the objective function. Numerical simulations show that the asymptotic optimal
caching scheme achieves better performance over existing caching schemes. The
analysis and optimization results provide insightful design guidelines for
random caching in practical networks.
