This paper studies an unmanned aerial vehicle (UAV)-enabled multiple access channel (MAC), in which multiple ground users transmit individual messages to a mobile UAV in the sky. We consider a linear topology scenario, where these users locate in a straight line and the UAV flies at a fixed altitude above the line connecting them. Under this setup, we jointly optimize the one-dimensional (1D) UAV trajectory and wireless resource allocation to reveal the fundamental rate limits of the UAV-enabled MAC, under the users individual maximum power constraints and the UAVs maximum flight speed constraints. First, we consider the capacity-achieving non-orthogonal multiple access (NOMA) transmission with successive interference cancellation (SIC) at the UAV receiver. In this case, we characterize the capacity region by maximizing the average sum-rate of users subject to rate profile constraints. To optimally solve this highly non-convex problem, we transform the original speed-constrained trajectory optimization problem into a speed-free problem that is optimally solvable via the Lagrange dual decomposition. It is rigorously proved that the optimal 1D trajectory solution follows the successive hover-and-fly (SHF) structure. Next, we consider two orthogonal multiple access (OMA) transmission schemes, i.e., frequency-division multiple access (FDMA) and time-division multiple access (TDMA). We maximize the achievable rate regions in the two cases by jointly optimizing the 1D trajectory design and wireless resource (frequency/time) allocation. It is shown that the optimal trajectory solutions still follow the SHF structure but with different hovering locations. Finally, numerical results show that the proposed optimal trajectory designs achieve considerable rate gains over other benchmark schemes, and the capacity region achieved by NOMA significantly outperforms the rate regions by FDMA and TDMA.
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