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Superposition modulation makes it possible for transmitting a node's own data along with its neighbors' relay data in a single time-slot and frequency, which can improve spectral efficiency of cooperative wireless communication system. First, we consider a two-user scenario and propose a design criterion for two-dimensional superposition modulation based cooperative transmission where the users cooperate to transmit their data to a base station. We investigate M-PSK superposition modulation based cooperative scenario for Rayleigh fading channels and thoroughly derive the average symbol error rate (SER) of such system with decode-and-forward relaying. Furthermore, we introduce a design parameter called power allocation ratio (PAR) which can be adaptively changed within the derived limits. We derive SER expressions in terms of the PAR and demonstrate its effect on average SER. Based on analytical and simulation results, we show that the proposed scheme provides reduced SER and increased spectral efficiency per link compared to existing schemes in practical scenarios. Finally, we investigate multi-user scenario, propose an adaptive power allocation scheme for superposition modulation, and confirm that SER is decreased with our proposed scheme.