Unmanned Aerial Vehicle (UAV) aided communication has the potential to provide on-demand wireless services and improve the outdoor link throughput. Applications for UAVs are rapidly growing with the development of Internet of Things. Because of limited battery energy, the UAVs need time-limited spectrum access to complete data transmission. Hence there are two challenges for the UAV-based communication: 1) Spectrum-efficient design; 2) Energy-efficient design. In this paper, we investigate the optimization of spectrum efficiency (SE) and energy efficiency (EE) for cognitive UAV network based on location information. Because of high mobility, the cognitive radio (CR) based UAVs operate on different frequency bands that vary with time and space. Thus, one spectrum band that is available in one region may not be necessarily available in another region. Based on location information of the primary transmitter and the UAV, we propose a hybrid mode in which the sensing performance and UAV's transmit power can be adjusted simultaneously to satisfy the outage constraint of the primary user. The multi-objective optimization theory is used to solve the tradeoff between SE and EE. The UAV's transmit power, sensing time and sensing threshold are optimized jointly to solve the tradeoff problem. To further improve the SE and EE performance, we propose a multi-frame combined sensing scheme, in which multiple frames are bundled together. Simulation results are provided to show the SE-EE tradeoff design, to validate the effectiveness of the proposed hybrid mode, and to show the advantages of the multi-frame combined sensing scheme in EE performance. INDEX TERMS UAV, spectrum efficiency, energy efficiency, cognitive radio, multi-frame combined sensing. I. INTRODUCTION Recently, Unmanned Aerial Vehicles (UAVs) have attracted much attention due to their wide use in many applications. Examples of the applications include: military operations, fire control, tracking and surveillance, wilderness search and many others [1]. The UAVs are equipped with cameras, sensors and communication equipment, which can be used for reconnoitering and monitoring purposes. With the advantages of high maneuverability and flexibility, the UAVs are widely The associate editor coordinating the review of this manuscript and approving it for publication was Shihao Yan. used to assist the wireless devices on the ground [2]. UAV plays an important role in high-speed 5G wireless network. The network connection can be expanded from ground to air and various services can be provided for hot spots in different locations. Compared with terrestrial communication, UAV-assisted communication has the advantages of rapid deployment, high mobility and low operating costs [3]. Unlike traditional cellular networks, the UAVs can be used as mobile base stations such that the wireless services can be provided with no infrastructure constraint [4]. The UAV-assisted wireless network has attracted much attention by the academia and industry since it can alleviate urgent