A phase offset estimation algorithm for superimposed signals based on full-rank pilots in over-the-air computation

Over-the-air computation (OAC) is a new technique for fast computation using the superposition property of wireless channels. In an OAC system, the fusion center(FC), as the receiver, receives only a superimposed signal made up of multiple sending signals. This makes it challenging to perform phase offset estimation at the FC. The existing algorithms use the reference signals by FC broadcast to perform phase offset estimation at the transmitting nodes and pre-compensate for the offsets. However, in practice, the uplink and downlink are not perfectly reciprocal. This leads to residual phase offsets in the received superimposed signal and consequently reduces the computational accuracy of the OAC. This paper presents a phase offsets estimation algorithm based on full-rank pilots for the first time to address this issue. The phase offsets estimator for superimposed signal is deduced by designing the full-rank pilots and constructing the maximum likelihood function. The proposed algorithm can estimate the phase offsets of each sending signal directly from the superimposed signals at the FC, which can cope with the phase offsets introduced by the imperfect channel reciprocity. Experiments show that the proposed algorithm has a high estimation accuracy and effectively improves the computation accuracy of the OAC system.