Detect-and-avoid (DAA) systems equipped with non-cooperative sensors for unmanned aircraft systems (UAS) beyond visual line-of-sight (BVLOS) operation is of interest to many researchers and industries today. Planning trajectories for UAS DAA in real-time requires fast and efficient trajectory generation algorithms. This thesis presents an airborne radar based non-cooperative DAA system that aims to detect moving obstacles such as aircraft and birds within the collision avoidance threshold and generate the desired trajectory as a resolution advisory for a pilot and UAS control commands. For collision detection, coordinate system transformation with quaternions is applied to process and display the obstacles detected by the airborne radar in the world frame as well as to construct a simulated airborne radar for the software-in-the-loop (SWIL) DAA system simulation. First, a reactive collision cone approach is presented for collision avoidance. In particular, software-in-the-loop simulation with test vectors from the minimum operational performance standards (MOPS) for DAA systems are used for the validation and verification of the system. Then, a non-linear model predictive control (NMPC) that utilizes the differential flatness of the UAV is presented to generate dynamically feasible collision-free trajectories in real-time. In order to overcome the limited performance of this NMPC approach due to the non-convexity of the solution space and high computational complexity, a hierarchical architecture is designed and presented. The efficiency of this approach is achieved by making use of: (i) the idea of global and local planners for the decomposition of trajectory planning and tracking, (ii) the fast analytic collision cone technique for path planning, and (iii) efficient generation of trajectories with minimum snaps as initial guesses for a low-level motion planner. This new DAA system is distributed over a local area network (LAN), which incorporates various design patterns and principles, including multi-threaded object orientation, command query segregation, finite state machine, reader-writer locks, and heartbeat event to address: (i) future demand for on-board and on-cloud computing, (ii) expandability to other unmanned aircraft traffic management (UTM) services, and (iii) system operation and monitoring.