Hybrid precoder designs for decentralized parameter estimation in millimeter wave (mmWave) sensor networks with perfect and imperfect CSI

Abstract

This work conceives techniques for the design of linear hybrid precoders toward decentralized parameter estimation in a millimeter wave (mmWave) wireless sensor network (WSN). To achieve this objective, a novel system model is proposed for mmWave WSNs, wherein the sensors pre-process their observations using hybrid baseband and radio frequency (RF) precoders, prior to their transmission over a coherent multiple access channel (MAC) to the fusion center (FC). The pertinent combiner is constrained to satisfy the constant signal gain condition, thus ensuring a distortionless estimate at the FC without requiring any additional post-processing. The precoders are designed to achieve the minimum mean square error (MSE) of parameter estimation at the FC. Furthermore, robust precoder designs are also developed to mitigate the effects of imperfect channel state information (CSI) in a mmWave sensor network, which is inevitable due to practical effects such as limited pilot overhead, channel drift, quantization error, among others. Robust designs are presented considering both the probabilistic as well as bounded CSI uncertainty models, which makes the design framework comprehensive since it considers both average and worst case distortion minimization. The centralized MMSE lower bound is also derived to characterize the estimation performance of the proposed schemes. Simulation results are presented to demonstrate the performance of the proposed designs and also verify the analytical propositions.