Wireless communication techniques which use relay nodes, including cooperative communication andphysical-layer network coding, are hot research topics in recent years. However, many researches are basedon coherent decoding, i.e., the receiver has perfect channel information. For rapidly-varying channels, it isdifficult to do channel estimation, so differential encoding at the transmitter and noncoherent decoding atthe receiver is quite important and thus also attracts many research works. Based on these facts, this projectwill research differential encoding on physical-layer network coding, perhaps combined with cooperativecommunication.In the first year, we will focus on the two-step two-way scheme utilizing physical-layer network coding,which is bandwidth efficiency since it only needs one half time compared with the conventional two-waycooperative communication scheme. There are two drawbacks in the research results so far: One is too fewpoints in the used signal constellation which results in low data rate; the other is the decision rule of therelay node using “decode and forward” is too complicated to be realized. In this project, for differentialencoding used in the multiple sources to the relay node, we will try different encoding as well as differentconstellations. For instance, one source uses phase modulation and the other one uses amplitude modulation.By doing so, the error probability and the complexity at the relay would be decreased. In the second year,we plan to apply the differential space-time modulation we proposed before on multiple-relay ormultiple-source physical-layer network coding schemes. In the third year, for physical-layer network codingsystems, we will focus on differential encoding for multiple-symbol differential detection and differentialencoding combined with trellis coding.In these years, we focus on the research of differential encoding and has published several papers in topinternational journals. Based on these experiences, we expect that this project will produce excellentresearch results in the hot topics, cooperative communication and physical-layer network coding.