  Millimeter wave multiple-input multiple-output (mmWave-MIMO) systems with
small number of radio-frequency (RF) chains have limited multiplexing gain.
Spatial path index modulation (SPIM) is helpful in improving this gain by
utilizing additional signal bits modulated by the indices of spatial paths. In
this paper, we introduce model-based and model-free frameworks for beamformer
design in multi-user SPIM-MIMO systems. We first design the beamformers via
model-based manifold optimization algorithm. Then, we leverage federated
learning (FL) with dropout learning (DL) to train a learning model on the local
dataset of users, who estimate the beamformers by feeding the model with their
channel data. The DL randomly selects different set of model parameters during
training, thereby further reducing the transmission overhead compared to
conventional FL. Numerical experiments show that the proposed framework
exhibits higher spectral efficiency than the state-of-the-art SPIM-MIMO methods
and mmWave-MIMO, which relies on the strongest propagation path. Furthermore,
the proposed FL approach provides at least 10 times lower transmission overhead
than the centralized learning techniques.
