Machine-type communication (MTC) has attracted much attention due to the fact that it provides pervasive connections for billions of MTC devices, forming a basis for the Internet of things. Most works in the literatures on machine-to-machine (M2M) communications focused on media access layer (MAC) layer or other upper layer applications, such as e-health, energy management and entertainment services. On the other hand, physical (PHY) layer plays a pivotal role in M2M communications. To accommodate a large number of MTC devices, M2M should be made efficient enough in terms of its power consumption and spectrum utilisation.