Self-Supervised Learning of Graph Neural Networks for Precoding in 1-bit Quantized Large Array Systems

Given the growing number of radio frequency chains in modern large array systems and the move to higher carrier frequencies and larger bandwidths, digital-to-analog converters (DACs) are becoming a bottleneck in terms of hardware complexity and power consumption. In this work, one-bit single-user quantized downlink non-linear precoding is considered. Given the NP-hard nature of this problem, a graph neural network is proposed which directly outputs the precoded symbol vector based on the channel vector and desired transmit symbol. The model is trained in a self-supervised fashion by directly maximizing the achievable rate. In order to overcome the non-differentiability of the loss function a straight-through Gumbel-softmax estimation of the gradients is proposed. The proposed method achieves a three times increase in achievable rate compared to conventional precoding, by transmitting the distortion, resulting from the extreme coarse quantization, in non-user directions.