Trainable Projected Gradient Detector for Massive Overloaded MIMO Channels: Data-Driven Tuning Approach

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 <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is larger than that of receive antennas <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">$m n$ </tex-math></inline-formula> 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. The numerical simulations show that the proposed detector achieves a comparable detection performance to those of the existing algorithms for the massively overloaded MIMO channels, e.g., the state-of-the-art IW-SOAV detector, with a lower computation cost.

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