Phase-Only Analog Encoding for a Multi-Antenna Fusion Center

TL;DR

This paper proposes a phase-only encoding scheme for distributed sensors transmitting to a multi-antenna fusion center, optimizing phase parameters to minimize estimation error, with performance close to theoretical bounds.

Contribution

It introduces a semidefinite programming approach for phase optimization in sensor networks, analyzing asymptotic behavior and benefits of multiple antennas.

Findings

Performance close to theoretical bounds.

Large number of sensors with small distance variance shows no benefit from multiple antennas.

Large antennas and low sensor noise reduce estimation error by a factor of M.

Abstract

We consider a distributed sensor network in which the single 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 relax the phase optimization problem to a semidefinite programming problem and the numerical results show that the performance of the proposed method 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 between the sensor nodes and FC is small, multiple antennas do not provide a benefit compared with a single antenna system; when the number of antennas $M$ is large and the measurement 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 $M$.