Universal Multi-Stage Precoding with Monomial Phase Rotation for Full-Diversity M2M Transmission

Machine-to-machine (M2M) communications have been considered as an important application to connect a massively large number of different devices in networks. In particular for M2M wireless networks, low latency and high reliability are of great importance. To fulfill the requirements, a diversity technique exploiting limited resources is proposed in this paper for short-message transmissions. The proposed method uses multiple stages of fast unitary transforms and diagonal phase rotations to achieve full- diversity gain. A monomial phase rotation is also proposed to facilitate an optimization of the precoding matrix. It is verified that the proposed four-stage precoding provides universal diversity gain irrespective of channel selectivity in time and frequency, without changing monomial parameters. In addition, it is shown that the four-stage precoding based on the discrete Haar transform (DHT) achieves a full diversity while the computational complexity is significantly reduced from a log- linear order to a linear order compared to the other unitary transforms such as the discrete Fourier transform (DFT).