Massive MIMO systems are typically designed assuming linear power amplifiers (PAs). However, PAs are most energy efficient close to saturation, where non-linear distortion arises. For conventional precoders, this distortion can coherently combine at user locations, limiting performance. We propose a graph neural network (GNN) to learn a mapping between channel and precoding matrices, which maximizes the sum rate affected by non-linear distortion, using a high-order polynomial PA model. In the distortion-limited regime, this GNN-based precoder outperforms zero forcing (ZF), ZF plus digital pre-distortion (DPD) and the distortion-aware beamforming (DAB) precoder from the state-of-the-art. At an input back-off of -3 dB the proposed precoder compared to ZF increases the sum rate by 8.60 and 8.84 bits/channel use for two and four users respectively. Radiation patterns show that these gains are achieved by transmitting the non-linear distortion in non-user directions. In the four user-case, for a fixed sum rate, the total consumed power (PA and processing) of the GNN precoder is 3.24 and 1.44 times lower compared to ZF and ZF plus DPD respectively. A complexity analysis shows six orders of magnitude reduction compared to DAB precoding. This opens perspectives to operate PAs closer to saturation, which drastically increases their energy efficiency.

翻译：大规模MIMO系统通常假设采用线性功率放大器（PA）进行设计。然而，PA在接近饱和区时能效最高，此时会产生非线性失真。对于传统预编码器，这种失真会在用户位置相干叠加，从而限制系统性能。我们提出一种图神经网络（GNN），通过学习信道与预编码矩阵之间的映射关系，利用高阶多项式PA模型最大化受非线性失真影响的总和速率。在失真受限场景下，该基于GNN的预编码器优于迫零（ZF）预编码、ZF结合数字预失真（DPD）以及现有最优的失真感知波束赋形（DAB）预编码器。在输入回退为-3 dB时，所提预编码器相比ZF在双用户和四用户场景下分别使总和速率提升8.60和8.84比特/信道使用。辐射方向图表明，这些增益是通过将非线性失真导向非用户方向实现的。在四用户场景中，为达到固定总和速率，GNN预编码器的总功耗（PA与处理单元）相比ZF及ZF结合DPD分别降低3.24倍和1.44倍。复杂度分析显示，其计算量相比DAB预编码降低六个数量级。这为让PA在更接近饱和区工作开辟了前景，从而大幅提升其能效。