Millimeter-wave (mmWave) multiple-input multiple-output (MIMO) communication with the advanced beamforming technologies is a key enabler to meet the growing demands of future mobile communication. However, the dynamic nature of cellular channels in large-scale urban mmWave MIMO communication scenarios brings substantial challenges, particularly in terms of complexity and robustness. To address these issues, we propose a robust gradient-based liquid neural network (GLNN) framework that utilizes ordinary differential equation-based liquid neurons to solve the beamforming problem. Specifically, our proposed GLNN framework takes gradients of the optimization objective function as inputs to extract the high-order channel feature information, and then introduces a residual connection to mitigate the training burden. Furthermore, we use the manifold learning technique to compress the search space of the beamforming problem. These designs enable the GLNN to effectively maintain low complexity while ensuring strong robustness to noisy and highly dynamic channels. Extensive simulation results demonstrate that the GLNN can achieve 4.15% higher spectral efficiency than that of typical iterative algorithms, and reduce the time consumption to only 1.61% that of conventional methods.

翻译：毫米波多输入多输出通信结合先进波束赋形技术，是满足未来移动通信日益增长需求的关键使能技术。然而，在大规模城市毫米波MIMO通信场景中，蜂窝信道的动态特性带来了巨大挑战，特别是在复杂性和鲁棒性方面。为解决这些问题，我们提出了一种基于梯度的鲁棒液态神经网络框架，该框架利用基于常微分方程的液态神经元求解波束赋形问题。具体而言，所提出的GLNN框架将优化目标函数的梯度作为输入以提取高阶信道特征信息，并引入残差连接以减轻训练负担。此外，我们采用流形学习技术压缩波束赋形问题的搜索空间。这些设计使GLNN能够在确保对噪声和高动态信道具有强鲁棒性的同时，有效维持低复杂度。大量仿真结果表明，GLNN的频谱效率比典型迭代算法高4.15%，而时间消耗仅为传统方法的1.61%。