Grassmannian Constellation Design for Noncoherent MIMO Systems Using Autoencoders

In this letter, we propose an autoencoder (AE) for designing Grassmannian constellations in noncoherent (NC) multiple-input multiple-output (MIMO) systems. To guarantee the properties of Grassmannian constellations, the proposed AE constructs the transmitted symbols following an unitary space-time modulation. It penalizes the difference between input and output symbols in terms of cross entropy during the training, which is regarded as a generic optimization method. The constellations learned by the proposed AE have substantial symbol error rate (SER) performance gains compared to the nonGrassmannian constellations and conventionally constructed Grassmannian constellations in high SNR regime. The resulting Grassmannian constellation of the proposed AE achieves higher diversity than the non-Grassmannian constellation in i.i.d. Rayleigh channels. Moreover, the proposed approach can be adaptive to different channel statistics by training with corresponding channel realizations.