Radio access design for fifth generation (5G) mobile communications is diverse, and has seemingly contradictory requirements, ranging from high spectral efficiency in enhanced mobile broadband (eMBB) communications to sub-millisecond radio access latency in ultra-reliable and low latency communication (uRLLC), in addition to support of massive connectivity in machine-type communication (mMTC). With the envisioned adoption of machine-type communication, such as in auto-generated software update/reconfiguration, network command, and mobile autonomous reporting (MAR) in the Internet of Things (IoTs), new random and medium access techniques should be considered. Aiming at providing immediate channel access, grant-free random access (GF-RA), in which users transmit data, including control signaling in a single shot, without waiting for radio resource assignment, has received significant attention in recent years. Our objective in this project, is to design a grant-free random access GF-RA, including one shot channel estimation and synchronization, which supports massive connectivity while reducing access delay time and control signal overhead. Our-approach includes non-orthogonal multiple access (NOMA)-based channel access, compressive-sensing based joint channel-estimation, synchronization and multi-user detection.