Edge-caching has received much attention as an efficient technique to reduce delivery latency and network congestion during peak-traffic times by bringing data closer to end users. Existing works usually design caching algorithms separately from physical layer design. In this paper, we analyze edge-caching wireless networks by taking into account the caching capability when designing the signal transmission. Particularly, we investigate multi-layer caching where both base station (BS) and users are capable of storing content data in their local cache and analyze the performance of edge-caching wireless networks under two notable uncoded and coded caching strategies. First, we calculate backhaul and access throughputs of the two caching strategies for arbitrary values of cache size. The required backhaul and access throughputs are derived as a function of the BS and user cache sizes. Second, closed-form expressions for the system energy efficiency (EE) corresponding to the two caching methods are derived. Based on the derived formulas, the system EE is maximized via precoding vectors design and optimization while satisfying a predefined user request rate. Third, two optimization problems are proposed to minimize the content delivery time for the two caching strategies. Finally, numerical results are presented to verify the effectiveness of the two caching methods.