  As a promising distributed learning technology, analog aggregation based
federated learning over the air (FLOA) provides high communication efficiency
and privacy provisioning under the edge computing paradigm. When all edge
devices (workers) simultaneously upload their local updates to the parameter
server (PS) through commonly shared time-frequency resources, the PS obtains
the averaged update only rather than the individual local ones. While such a
concurrent transmission and aggregation scheme reduces the latency and
communication costs, it unfortunately renders FLOA vulnerable to Byzantine
attacks. Aiming at Byzantine-resilient FLOA, this paper starts from analyzing
the channel inversion (CI) mechanism that is widely used for power control in
FLOA. Our theoretical analysis indicates that although CI can achieve good
learning performance in the benign scenarios, it fails to work well with
limited defensive capability against Byzantine attacks. Then, we propose a
novel scheme called the best effort voting (BEV) power control policy that is
integrated with stochastic gradient descent (SGD). Our BEV-SGD enhances the
robustness of FLOA to Byzantine attacks, by allowing all the workers to send
their local updates at their maximum transmit power. Under worst-case attacks,
we derive the expected convergence rates of FLOA with CI and BEV power control
policies, respectively. The rate comparison reveals that our BEV-SGD
outperforms its counterpart with CI in terms of better convergence behavior,
which is verified by experimental simulations.
