Phase-only analog encoding for a multi-antenna fusion center

We consider a distributed sensor network in which the sin-gle antenna sensor nodes observe a deterministic unknown parameter and after encoding the observed signal with a phase parameter, the sensor nodes transmit it simultaneously to a multi-antenna fusion center (FC). The FC optimizes the phase encoding parameter and feeds it back to the sensor nodes such that the variance of estimation error can be minimized. We re-lax the phase optimization problem to a semidefinite program-ming (SDP) problem and the numerical results show that the performance of the proposedmethod is close to the theoretical bound. Also, asymptotic results show that when the number of sensors is very large and the variance of the distance be-tween the sensor nodes and FC is small, multiple antennas do not provide a benefit compared with a single antenna system; when the number of antennasM is large and themeasurement noise at the sensor nodes is small compared with the additive noise at the FC, the estimation error variance can be reduced by a factor of M. Index Terms — Distributed sensor network, multi-antenna fusion center, maximum likelihood estimation, phase-only analog encoding, asymptotic estimation error. 1