In this work we propose an approach to construct a fully asynchronous unsourced random access communications (URA) system. Besides the common URA features such as the absence of the user identification information in the packet and the decoding oriented to receiving the content of the messages, there is no limitation on the user transmission timing. The active users can transmit their packet any time on demand. The proposed system belongs to the class of preamble-payload URA formats. Contrary to the typical role of the preamble to serve as a temporary user identification, the preamble serves for the purpose of timing acquisition. The proposed system also employs a very small pool of preambles to resolve collisions of packets transmitted simultaneously.We provide a performance analysis and simulation results for the proposed system and demonstrate that for a wide range of signal-to-noise ratios (SNR)s the supported numbers of active users are close to the numbers of users supported by a slotted URA system counterpart.

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