  Linear hybrid beamformer designs are conceived for the decentralized
estimation of a vector parameter in a millimeter wave (mmWave) multiple-input
multiple-output (MIMO) Internet of Things network (IoTNe). The proposed designs
incorporate both total IoTNe and individual IoTNo power constraints, while also
eliminating the need for a baseband receiver combiner at the fusion center
(FC). To circumvent the non-convexity of the hybrid beamformer design problem,
the proposed approach initially determines the minimum mean square error (MMSE)
digital transmit precoder (TPC) weights followed by a simultaneous orthogonal
matching pursuit (SOMP)-based framework for obtaining the analog RF and digital
baseband TPCs. Robust hybrid beamformers are also derived for the realistic
imperfect channel state information (CSI) scenario, utilizing both the
stochastic and norm-ball CSI uncertainty frameworks. The centralized MMSE bound
derived in this work serves as a lower bound for the estimation performance of
the proposed hybrid TPC designs. Finally, our simulation results quantify the
benefits of the various designs developed.
