Interaction of multiplexing gains and power exponents allocation of two‐level superposition coding relaying

A two‐level rate superposition coding relaying (SC‐relaying) scheme is discussed, in which only the relay‐to‐source channel state information feedback (CSF) is considered and, at source, a long power constraint is imposed on the basic signal S 0 and the additional signal S 1 whose multiplexing gains are r 0 and r 1 , respectively. The CSF index is constructed based on the correct decoding of the signal S 0 at relay. For the SC‐relaying scheme, we propose a multilevel iteration constructing rule for the CSF index. With the proposed CSF constructing rule, the allocation method of the power signal‐to‐noise ratio exponents is first obtained by the investigation of the optimal outage exponent of the signal S 0 . Secondly, we obtain the value range of p 11 , p 11 ∈ [1,1∕ r 0 ], by studying the outage exponent lower bound of the signal S 0 , where p 11 denotes the minimum of the power signal‐to‐noise ratio exponent of the signal S . Lastly, to observe the interaction between the multiplexing gains r 0 and r 1 , we discuss the closed‐form solution of the lower bound of the optimal outage exponent for the signal S 1 , through which we find that the multiplexing gain constraint is r 1 ≤ 1 − r 0 p 11 , p 11 ≥ 1. The substantial numerical analyses show that the results in this paper are reasonable.