This paper considers cross-layer random access protocol design in the massive machine-type communication (mMTC) scenario. Compared to traditional slotted ALOHA, multi-user detection (MUD) and channel estimation (CE) in the proposed protocol are implemented by compressed sensing technology in isolation, which makes it possible that multiple collided packets can be recovered in one single time slot. The adoption of successive- interference cancellation further enhances the recovery ability. The proposed protocol leads to low signaling overhead and has potential to support the massive uplink connectivity in mMTC. The main factors affecting the performance of MUD and CE are analyzed and a novel low-complexity method is proposed for MUD and CE. Analytical results are given on the data recovery, dynamics of active user equipment number, and packet transmission delay. Numerical results are also provided to investigate the effect of factors on the performance of the proposed protocol.