Consider a system in which the signal is transmitted from the source to the destination via a relay. The source-relay link and the relay-destination link are assumed to have Rician fading. For such a system, in this paper, we propose a novel non-coherent receiver that detects the signal without knowledge of channel state information (CSI). In addition, we also propose novel receivers for the situation when only partial CSI is available at the destination; that is, channel knowledge of either the source-relay link or the relay-destination link, but not both, is available. These receivers are termed as "half-coherent receivers" because they have the CSI of only one of the two links in the system. These half-coherent receivers can be used in applications in which only the relay can afford additional complexity (e.g., the relay may be a base station) and includes a channel estimation module to acquire channel knowledge of the source-relay link or only the destination includes the channel estimation module to acquire channel knowledge of the relay-destination link. The symbol error rate performances of the proposed receivers for M-ary frequency-shift keying are derived for Rician fading. Numerical results show that considerable performance gains can be achieved by using these new receivers, especially at a low signal-To-noise ratio where the gain is needed most.