  Recent studies have shown the potential performance gain of Non Uniform
Constellations (NUC) compared to the conventional uniform constellations. NUC
can be a promising candidate in 5G systems to increase the data throughput. In
the literature, NUC is designed for a specific SNR value and propagation
channel. However, in broadcast/multicast services, the received signal by
different users will see independent and different channels. Hence, in this
paper, we focus on the potential gain of NUC when jointly optimized for more
than one propagation channel. In order to assess the gain, we propose an
iterative algorithm to jointly optimize the NUC for different channel
conditions. The resulting constellations are then compared to uniform
constellation and single channel NUC. The simulation results show that the
newly designed constellations outperform the classical single channel NUC
across different channel conditions when the average performance (across
different channels) is considered.
