  Massive multiple-input multiple-output (MIMO) is a key technology used in
fifth-generation wireless communication networks and beyond. Recently, various
MIMO signal detectors based on deep learning have been proposed. Especially,
deep unfolding (DU), which involves unrolling of an existing iterative
algorithm and embedding of trainable parameters, has been applied with
remarkable detection performance. Although DU has a lesser number of trainable
parameters than conventional deep neural networks, the computational
complexities related to training and execution have been problematic because
DU-based MIMO detectors usually utilize matrix inversion to improve their
detection performance. In this study, we attempted to construct a DU-based
trainable MIMO detector with the simplest structure. The proposed detector
based on the Hubbard--Stratonovich (HS) transformation and DU is called the
trainable HS (THS) detector. It requires only $O(1)$ trainable parameters and
its training and execution cost is $O(n^2)$ per iteration, where $n$ is the
number of transmitting antennas. Numerical results show that the detection
performance of the THS detector is better than that of existing algorithms of
the same complexity and close to that of a DU-based detector, which has higher
training and execution costs than the THS detector.
