  This paper presents a deep learning-aided iterative detection algorithm for
massive overloaded multiple-input multiple-output (MIMO) systems where the
number of transmit antennas $n$ is larger than that of receive antennas $m$.
Since the proposed algorithm is based on the projected gradient descent method
with trainable parameters, it is named the trainable projected
gradient-detector (TPG-detector). The trainable internal parameters, such as
the step-size parameter, can be optimized with standard deep learning
techniques, i.e., the back propagation and stochastic gradient descent
algorithms. This approach is referred to as data-driven tuning, and ensures
fast convergence during parameter estimation in the proposed scheme. The
TPG-detector mainly consists of matrix-vector product operations whose
computational cost is proportional to $m n$ for each iteration. In addition,
the number of trainable parameters in the TPG-detector is independent of the
number of antennas. These features of the TPG-detector result in a fast and
stable training process and reasonable scalability for large systems. Numerical
simulations show that the proposed detector achieves a comparable detection
performance to those of existing algorithms for massive overloaded MIMO
channels, e.g., the state-of-the-art IW-SOAV detector, with a lower computation
cost.
