To support various Internet-of-Thing (loT) applica tions involving an enormous number of machine-type devices, deploying LTEILTE-A networks on ISM bands with an exten sive bandwidth has been regarded as a promising solution to enable machine-to-machine (M2M) communications. Designating as licensed-assisted access (LAA) in 3GPP Rel-13, unprecedented challenge of uncontrollable interference from collocated WiFi net works, however, obstructs the state-of-the-art scheduling based radio resource access in LTEILTE-A. To practice LAA, in this paper, we shall derive the optimum radio access scheme for the urgent needs of 3GPP Rel-13 standardization. Observing the LAA-WiFi hidden terminal problem, we analytically derive the optimum number of LAA users randomly accessing a pool of radio resources and the optimum condition for random access, to reach a superior throughput of a LAA network as compared with that of a scheduling based scheme. Our analytic results demonstrate that the conventio...