Cooperative Transmission of mobiles has been seen as an attractive solution to enhance network robustness. In the other word, network coding has been receiving more and more attentions for its ability to save power and improve the throughput of wireless network. In our paper, we consider an example of physical network coding in the wireless cooperative network, which consists of two source nodes, A and B and a common destination node D. In the first time slot, node A transmits its packet a to the node D and B where a is modulated based on the constellation map Mi. In the second time slot, node B transmits its packet b to D and A where b is modulated based on the constellation map M2. Then in the third time slot, source node A and B transmit the network-coded packet c = a ⊕ b to node D at the same time where c is modulated based on the constellation map M3 in the node A and M4 in the node B. The criterion in the optimal design of the constellation maps (Mi, M2, M3, M4) has been introduced in our research. Example by 4-PAM (Pulse Amplitude Modulation), it is proved by simulation result that almost 1 dB gain could be get if the optimal design has been chosen.
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