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Millimeter wave multiple-input multiple-output (mmWave-MIMO) systems withsmall number of radio-frequency (RF) chains have limited multiplexing gain.Spatial path index modulation (SPIM) is helpful in improving this gain byutilizing additional signal bits modulated by the indices of spatial paths. Inthis paper, we introduce model-based and model-free frameworks for beamformerdesign in multi-user SPIM-MIMO systems. We first design the beamformers viamodel-based manifold optimization algorithm. Then, we leverage federatedlearning (FL) with dropout learning (DL) to train a learning model on the localdataset of users, who estimate the beamformers by feeding the model with theirchannel data. The DL randomly selects different set of model parameters duringtraining, thereby further reducing the transmission overhead compared toconventional FL. Numerical experiments show that the proposed frameworkexhibits higher spectral efficiency than the state-of-the-art SPIM-MIMO methodsand mmWave-MIMO, which relies on the strongest propagation path. Furthermore,the proposed FL approach provides at least 10 times lower transmission overheadthan the centralized learning techniques.

Federated Dropout Learning for Hybrid Beamforming With Spatial Path Index Modulation In Multi-User mmWave-MIMO Systems