Robust Hybrid Transceiver Designs for Linear Decentralized Estimation in mmWave MIMO IoT Networks in the Face of Imperfect CSI

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 mean squared error (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 receiver 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 MSE minimization problem is nonconvex. 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.