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LoRa, due to its advantage of long-range communication capability, is promising for Internet of Things (IoT) and space-air-ground communications. However, the conventional MAC protocol used with LoRa is classified as an Aloha-based algorithm, which leads to drastic decrease in throughput when a huge amount of end-devices try to access the network. To achieve stable and high throughput of LoRa, we propose a design to combine the distributed queueing (DQ) and in-band-full-duplex (IBFD) technologies. The usage of DQ mechanism is benefit for fast collision resolution, while the IBFD-enabled gateway helps to reduce the heavy control overhead of DQ. The designs of access procedure and frame structure are discussed in detail. The outage probability and average throughput are evaluated under imperfect self-interference cancelation. Also, a mathematical programming method is developed to optimize the spreading factor and code rate. Numerical results show that our proposal gains an extra enhancement of 1.83-fold in throughput. [ABSTRACT FROM AUTHOR]