On the efficiency of transmission strategies for broadcast channels using finite size constellations

In this paper, achievable rates regions are derived for power constrained Gaussian broadcast channel of two users using finite dimension constellations. Various transmission strategies are studied, namely superposition coding (SC) and superposition modulation (SM) and compared to standard schemes such as time sharing (TS). The maximal achievable rates regions for SM and SC strategies are obtained by optimizing over both the joint probability distribution and over the positions of constellation symbols. The improvement in achievable rates for each scheme of increasing complexity is evaluated in terms of SNR savings for a given target achievable rate or/and percentage of gain in achievable rates for one user with reference to a classical scenario.