Machine-type communication (MTC) devices usually have low-data rate, and in some applications, latency is critical. In long-term evolution, establishing a connection requires a relatively complex handshaking procedure. Such an approach is suitable for a system serving only a few high-activity users, but it becomes cumbersome for MTC traffic, where large amounts of low-activity users intermittently transmit a small number of packets. We propose a random access channel (RACH)-based scheme for the future 5G system that allows MTC users to send small packets within the random access burst. Device activity detection, channel estimation, authentication, and data decoding are performed simultaneously from the same access burst. In addition to the inherent reduction in energy consumption, the scheme eliminates the signaling overhead and creates more resources for data transmission. We have constructed an analytical framework for the detection performance of a multiple-input-multiple-output receiver in a frequency-selective channel. This has been validated with simulations, and results show that a one-shot correlate-and-cancel algorithm is sufficient for activity detection and channel estimation when the base station either employs multiple receive antennas or schedules multiple resource blocks for MTC RACH.