  Hybrid precoder and combiner designs are conceived for decentralized
parameter estimation in millimeter wave (mmWave) multiple-input multiple-output
(MIMO) wireless sensor networks (WSNs). More explicitly, efficient pre- and
post-processing of the sensor observations and received signal are proposed for
the minimum mean square error (MMSE) estimation of a parameter vector. The
proposed techniques exploit the limited scattering nature of the mmWave MIMO
channel for formulating the hybrid transceiver design framework as a multiple
measurement vectors (MMV)-based sparse signal recovery problem. This is then
solved using the iterative appealingly low-complexity simultaneous orthogonal
matching pursuit (SOMP). Tailor-made designs are presented for WSNs operating
under both total and per-sensor power constraints, while considering ideal
noiseless as well as realistic noisy sensors. Furthermore, both the Bayesian
Cramer-Rao lower bound and the centralized MMSE bound are derived for
benchmarking the proposed decentralized estimation schemes. Our simulation
results demonstrate the efficiency of the designs advocated and verify the
analytical findings.
