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 S0 and the additional signal S1 whose multiplexing gains are r0 and r1, respectively. The CSF index is constructed based on the correct decoding of the signal S0 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 S0. Secondly, we obtain the value range of p11, p11  ∈ [1,1∕r0], by studying the outage exponent lower bound of the signal S0, where p11 denotes the minimum of the power signal-to-noise ratio exponent of the signal S. Lastly, to observe the interaction between the multiplexing gains r0 and r1, we discuss the closed-form solution of the lower bound of the optimal outage exponent for the signal S1, through which we find that the multiplexing gain constraint is r1  ≤ 1 −r0p11, p11  ≥ 1. The substantial numerical analyses show that the results in this paper are reasonable. Copyright © 2011 John Wiley & Sons, Ltd.