In order to meet the Quality of Experience (QoE) requirements of mobile users and the Quality of Service (QoS) concerns for new high-performance, innovative services, Multiaccess Edge Computing (MEC), Software Defined Mobile Networks (SDMN), and Cloud Radio Access Networks (C-RAN) are being introduced to the next generation of wireless networks in order to boost performance and to deliver Quality of Service (QoS). It is essential for mobile operators to allocate their available resources efficiently as telecom networks become increasingly complex, traffic continues to rise, and users demand faster bitrate speeds. In this paper, we investigate how to allocate resources appropriately across a wireless network enabled by MEC, SDMN, and C-RAN technology to deliver high quality adaptive video streams. We propose the Backhaul-Aware CrossLayer Bitrate Allocation (BACLBA) algorithm, which utilizes information from higher layers regarding traffic patterns and desired video quality to maximize HTTP Video Adaptive Streaming (HAS) users' QoE and reduce the backhaul traffic by caching the popular videos on MEC servers. We solve a mixed-integer nonlinear programming problem that considers the limitations of radio resource availability, storage and transcoding capacities of MEC servers. BACLBA is designed to maximize users' QoE by minimizing the deviation between the achievable throughput at the MAC layer and the allocated bit rate for video frames at the application layer. Furthermore, it reduces the backhaul traffic by caching popular video content on MEC servers. Compared to a baseline scheme, our algorithm achieves a 20.50% higher system utilization rate, a 10.44% higher video quality, and a 50.33% reduction in backhaul traffic.