In this paper, we consider a decode-forward relay system with a source, a relay, and a destination, where two-layer superposition codes are used at the source and the relay. An equivalent squared minimum distance (ESMD) that determines the error performance is derived by using an upper bound on the pair-wise error probability. Without deriving error probabilities, the error performance level for each of superimposed symbols can be shown in a straightforward manner by the ESMD. An optimal superposition-coded relay scheme and a suboptimal switched-power superposition coding scheme are proposed by improving the ESMD. Closed-form power allocation that maximizes the ESMD for the switched scheme is derived for 2-ary pulse amplitude modulation (PAM). An   $M$  -ary PAM generalization for the switched-power superposition-coded relay scheme is also presented. Simulation results show that significant signal-to-noise ratio gains are achieved in the optimal and switched-power superposition coding strategies for 2-ary and 4-ary PAM over the Rayleigh fading channel.
['Xianglan Jin', 'Hyoung-Nam Kim']
Switched-Power Two-Layer Superposition Coding in Cooperative Decode-Forward Relay Systems