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 non-Grassmannian 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.