Over-the-Air Computation on Network Edge for Collaborative Estimation

Parameter estimation is an important task in distributed sensing systems, where data from multiple devices contributes to real-time decision-making. Over-the-air computation (AirComp) provides a new approach for spectrally efficient edge computing in collaborative parameter estimation. In this work, we propose a novel AirComp estimation framework based on the natural aggregation of pre-processed signals from participating agents in wireless multiple access channels. We focus on maximum likelihood estimation of source signal magnitude and time delay, proposing two approaches to complete this task. Our first approach involves a noisy approximation of the joint log-likelihood function (LLF) of agent observations. Our second approach employs noise-whitening to address the effect of pulse shaping. We present four channel compensation schemes to address destructive inter-agent channel interference and derive the corresponding Cramér-Rao lower bound (CRLB) in each scheme. We apply a practical partial phase pre-compensation that achieves nearly the same performance as complete phase compensation, thereby simplifying the conditions of the proposed AirComp estimation in practical deployment.