# Unlicensed Spectrum Allocation for LTE and Wi-Fi Coexistence with HAP
## 1 Introduction  
Wireless communication is a continuing trend with the growing number of wireless devices. A wide variety of devices and applications have been introduced as the technology is getting mature and popularized. As a consequence, traffic conveyed over the wireless networks grows explosively. Technology to accommodate the ever-increasing traffic is a pressing yet challenging issue. Unlike wired networks, the radio spectrum for wireless communication is inherently scarce and expensive. Many approaches are studied. One possible solution to ameliorate spectrum utilization is advanced modulation and coding technology. Another exciting alternative is the introduction of novel designs to radio apparatus, such as the work by [PERSON] et al. [1]. Based solely on resonators, their two-element filtering antenna array design had achieved improved transceiving efficiency. However, there are physical limitations to the modulation and coding technology, as well as new radio apparatus designs. As a prospective mechanism, the coexistence of LTE (Long-Term Evolution) and Wi-Fi (wireless fidelity) has received considerable attention for its potential to achieve better spectrum utilization. This study advances the same philosophy and contributes to determining an optimal time ratio for the time-division multiplexing between the LTEand Wi-Fi networks. Symmetric allocation with a duty cycle of 50% cannot be an optimal option. Asymmetric allocation according to the quality of service (QoS) requirements and traffic demands should be considered. As a de facto standard, LTE is an all-IP system with a higher data rate, high-level security, improved spectrum efficiency, lower latency, QoS support, and so forth. LTE was initially designed to operate in the licensed band. To accommodate more traffic, a promising alternative is to allow the LTE to cooperate in the unlicensed band with the Wi-Fi networks. However, there is a fundamental obstacle to this approach. The transmission mechanism of Wi-Fi is intrinsically different from that of LTE. The unlicensed band is already occupied by numerous wireless systems, particularly the Wi-Fi system. LTE adopts a non-contention MAC (media access control) protocol to avoid packet collision among users. It uses the scheduling mechanism in centralized control units, such as eNBs (evolved Node B). The eNBs decide how to allocate resources to users. Each user can utilize the allocated resources to transmit data. On the other hand, Wi-Fi employs the carrier sense multiple access with collision avoidance (CSMA/CA) mechanism to resolve the packet collision problem. CSMA/CA is intrinsically a contention-based MAC protocol for shared, broadcast-based media. In Wi-Fi, when a node has data to transmit, it detects the channel status. If the channel is idle, the node is allowed to transmit data. Otherwise, it will exercise a back-off algorithm waiting for other opportunities to transmit data. Our contributions are threefold. 1. A utility function is defined, and an optimization problem is formulated for the time-division multiplexing between Wi-Fi stations and LTE networks. Then a new scheme is proposed for adequate allocations of spectrum resources utilizing HAPs as bridges. This scheme is peculiarly beneficial to LTE-U (LTE-Unlicensed) systems that plan to maintain the QoS requirements of Wi-Fi users. The proposed scheme can further preserve the access right of Wi-Fi QoS stations (QSTAs). 2. The disadvantages to Wi-Fi users due to the inclusion of LTE users in the unlicensed band for LTE-U can be minimized. It is argued that the Wi-Fi networks would be less advantageous when LTE and Wi-Fi coexist in the same unlicensed band. In recognition of these problems, this study conducts an analytical analysis to determine an optimal ratio for the time-division multiplexing between LTE and Wi-Fi networks, seeking to maximize the total throughput and maintain fairness in the coexistence of Wi-Fi and LTE-U. 3.