  Hybrid transceivers are designed for linear decentralized estimation (LDE) in
a mmWave multiple-input multiple-output (MIMO) IoT network (IoTNe). For a
noiseless fusion center (FC), it is demonstrated that the MSE performance is
determined by the number of RF chains used at each IoT node (IoTNo). Next, the
minimum-MSE RF transmit precoders (TPCs) and receive combiner (RC) matrices are
designed for this setup using the dominant array response vectors, and
subsequently, a closed-form expression is obtained for the baseband (BB) TPC at
each IoTNo using Cauchy's interlacing theorem. For a realistic noisy FC, it is
shown that the resultant mean squared error (MSE) minimization problem is
non-convex. To address this challenge, a block-coordinate descent-based
iterative scheme is proposed to obtain the fully digital TPC and RC matrices
followed by the simultaneous orthogonal matching pursuit (SOMP) technique for
decomposing the fully-digital transceiver into its corresponding RF and BB
components. A theoretical proof of the convergence is also presented for the
proposed iterative design procedure. Furthermore, robust hybrid transceiver
designs are also derived for a practical scenario in the face of channel state
information (CSI) uncertainty. The centralized MMSE lower bound has also been
derived that benchmarks the performance of the proposed LDE schemes. Finally,
our numerical results characterize the performance of the proposed transceivers
as well as corroborate our various analytical propositions.
