Deep-Unfolding Neural-Network Aided Hybrid Beamforming Based on Symbol-Error Probability Minimization

Abstract

In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital (AD) beamforming can be used to attain a high directional gain without requiring a dedicated radio frequency (RF) chain for each antenna element, which substantially reduces both the hardware costs and power consumption. While massive MIMO transceiver design typically relies on the conventional mean-square error (MSE) criterion, directly minimizing the symbol error rate (SER) can lead to a superior performance. In this article, we first mathematically formulate the problem of hybrid transceiver design under the minimum SER (MSER) optimization criterion and then develop an MSER-based iterative gradient descent (GD) algorithm to find the related stationary points. We then propose a deep-unfolding neural network (NN). The iterative GD algorithm is unfolded into a multi-layer structure wherein trainable parameters are introduced to accelerate the convergence and enhance the overall system performance. To implement the training stage, we derive the relationship between adjacent layers' gradients based on the generalized chain rule (GCR). The deep-unfolding NN is developed for both quadrature phase shift keying (QPSK) and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -ary quadrature amplitude modulated (QAM) signals, and its convergence is investigated theoretically. Furthermore, we analyze the transfer capability, computational complexity, and generalization capability of the proposed deep-unfolding NN. Our simulation results show that the latter significantly outperforms its conventional counterpart at a reduced complexity.