  Recently, machine learning-based channel estimation has attracted much
attention. The performance of machine learning-based estimation has been
validated by simulation experiments. However, little attention has been paid to
the theoretical performance analysis. In this paper, we investigate the mean
square error (MSE) performance of machine learning-based estimation. Hypothesis
testing is employed to analyze its MSE upper bound. Furthermore, we build a
statistical model for hypothesis testing, which holds when the linear learning
module with a low input dimension is used in machine learning-based channel
estimation, and derive a clear analytical relation between the size of the
training data and performance. Then, we simulate the machine learning-based
channel estimation in orthogonal frequency division multiplexing (OFDM) systems
to verify our analysis results. Finally, the design considerations for the
situation where only limited training data is available are discussed. In this
situation, our analysis results can be applied to assess the performance and
support the design of machine learning-based channel estimation.
