  Over-the-air computation (AirComp) has recently been identified as a
prominent technique to enhance communication efficiency of wireless federated
learning (FL). This letter investigates the impact of channel state information
(CSI) uncertainty at the transmitter on an AirComp enabled FL (AirFL) system
with the truncated channel inversion strategy. To characterize the performance
of the AirFL system, the weight divergence with respect to the ideal
aggregation is analytically derived to evaluate learning performance loss. We
explicitly reveal that the weight divergence deteriorates as
$\mathcal{O}(1/\rho^2)$ as the level of channel estimation accuracy $\rho$
vanishes, and also has a decay rate of $\mathcal{O}(1/K^2)$ with the increasing
number of participating devices, $K$. Building upon our analytical results, we
formulate the channel truncation threshold optimization problem to adapt to
different $\rho$, which can be solved optimally. Numerical results verify the
analytical results and show that a lower truncation threshold is preferred with
more accurate CSI.
