Synchronization, channel estimation, and multi-user detection (MUD) can be performed in a single shot for a comprehensive grant-free access . The scheme employs compressive sensing by exploiting two sparse phenomena: sparsity in users' activity and sparsity in channel delay spread. The performance of compressive sensing based schemes should be thoroughly studied in a multi-cell environment as the other-cell interference (OCI) may affect the underlying sparsity. In this paper, we provide a performance analysis of the comprehensive grant-free access scheme in a multi-cell environment and showed that OCI would not affect the sparsity of the received signal, and rather can be considered as a dispersed noise, if signature allocation among cells is properly handled. Furthermore, we show the performance & complexity of the receiver in contrast with other multiple measurement vector-based receivers modified for joint & blind channel estimation and (MUD).