  Recently, the end-to-end training approach for multi-channel ASR has shown
its effectiveness, which usually consists of a beamforming front-end and a
recognition back-end. However, the end-to-end training becomes more difficult
due to the integration of multiple modules, particularly considering that
multi-channel speech data recorded in real environments are limited in size.
This raises the demand to exploit the single-channel data for multi-channel
end-to-end ASR. In this paper, we systematically compare the performance of
three schemes to exploit external single-channel data for multi-channel
end-to-end ASR, namely back-end pre-training, data scheduling, and data
simulation, under different settings such as the sizes of the single-channel
data and the choices of the front-end. Extensive experiments on CHiME-4 and
AISHELL-4 datasets demonstrate that while all three methods improve the
multi-channel end-to-end speech recognition performance, data simulation
outperforms the other two, at the cost of longer training time. Data scheduling
outperforms back-end pre-training marginally but nearly consistently,
presumably because that in the pre-training stage, the back-end tends to
overfit on the single-channel data, especially when the single-channel data
size is small.
