To efficiently utilize the scarce wireless resource, the random access scheme has been attaining renewed interest primarily in supporting the sporadic traffic of a large number of devices encountered in the Internet of Things (IoT). In this paper we investigate the performance of slotted ALOHA -- a simple and practical random access scheme -- in connection with the grant-free random access protocol applied for user-centric cell-free massive MIMO. More specifically, we provide the expression of the sum-throughput under the assumptions of the capture capability owned by the centralized detector in the uplink. Further, a comparative study of user-centric cell-free massive MIMO with other types of networks is provided, which allows us to identify its potential and possible limitation. Our numerical simulations show that the user-centric cell-free massive MIMO has a good trade-off between performance and fronthaul load, especially at low activation probability regime.
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