  Machine learning (ML) has attracted a great research interest for physical
layer design problems, such as channel estimation, thanks to its low complexity
and robustness. Channel estimation via ML requires model training on a dataset,
which usually includes the received pilot signals as input and channel data as
output. In previous works, model training is mostly done via centralized
learning (CL), where the whole training dataset is collected from the users at
the base station (BS). This approach introduces huge communication overhead for
data collection. In this paper, to address this challenge, we propose a
federated learning (FL) framework for channel estimation. We design a
convolutional neural network (CNN) trained on the local datasets of the users
without sending them to the BS. We develop FL-based channel estimation schemes
for both conventional and RIS (intelligent reflecting surface) assisted massive
MIMO (multiple-input multiple-output) systems, where a single CNN is trained
for two different datasets for both scenarios. We evaluate the performance for
noisy and quantized model transmission and show that the proposed approach
provides approximately 16 times lower overhead than CL, while maintaining
satisfactory performance close to CL. Furthermore, the proposed architecture
exhibits lower estimation error than the state-of-the-art ML-based schemes.
