Wireless communication has recently received a lot of attention in communication research community. During these improvements, advances in wireless relay networks to increase the transmission rate and coverage are have been more profound than ever before. One Emerging method in relay communications is Physical layer Network Coding (PNC) that is an effective solution to increase the throughput in a two-way relay channel. The basic idea of PNC is to exploit the mixing of signals that occurs naturally when electromagnetic (EM) waves simultaneously transmitted superimpose at the relay. Relay is a middle terminal that cooperates in the transmission of the sources data to the receivers. In particular, at a relay, the simultaneous transmissions by several sources can result in the ambiguity in sources symbols detection. Removing and retrieving the transmitters messages of the relay through physical layer network coding is called mapping. Mapping the relay input signal to unambiguous signal to be sent back to the terminals is the most important challenge in physical layer network coding. Effective mapping results in improved communication parameters, such as rate and reliability. In this thesis, we provide a combination of MSK modulation and mapping to remove the ambiguity of the relay constellation points. Because of orthogonality of the cosine and sine (in-phase and quadrature) components of the MSK, its proper application in the physical layer network coding is beneficial. Compensating for the pathloss effects without the need for additional computations, adaptability to channel conditions and simplicity in implementation, are some of advantages of this mapping technique. Physical layer network coding has been investigated primarily in two-way wireless channels. Due to the increasing number of users and higher rate requirements, in this thesis, we've studied integration of MSK and mapping at the network relay transceiver with the two terminals to attain a two-phase relaying scheme. Simulation results show that this method can be successful to remove the ambiguity and our proposed scheme can improve the BER. These results also show that the proposed scheme outperforms the simple PNC with QPSK modulation and the rotation of constellations. Also, due to the adaptability potential to channel conditions, this method is preferred. Keywords: 1- Physical layer network coding 2-relay 3-mapping 4-MSK