Constellation Design for Multiuser Non-Coherent Massive SIMO Based on DMPSK Modulation

Non-coherent (NC) schemes combined with massive antenna arrays are proposed to replace traditional coherent schemes in scenarios which require an excessive number of reference signals, since NC approaches avoid channel estimation and equalization. Differential $M$ -ary phase shift keying is one of the most appealing NC schemes due to its implementation simplicity in realistic scenarios. However, the analytical constellation design for multiuser scenarios is intractable, as discussed in this paper. We propose to solve this problem by using optimization techniques relying on evolutionary computation. We design two approaches, namely Gaussian-approximated optimization and Monte-Carlo based optimization. They can provide both individual constellations for each user equipment and a bit mapping policy to minimize the bit error rate. We perform a complexity analysis and propose strategies for its reduction. We propose a set of constellations for different number of users and constellation sizes, and evaluate the link-level performance of some illustrative examples to verify that our solutions outperforms the existing ones. Finally, we show via simulations that NC outperforms the coherent schemes in high mobility and/or low signal-to-noise ratio scenarios.