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（mmWave）多输入多输出（MIMO）通信技术结合先进的波束赋形技术，是满足未来移动通信日益增长需求的关键推动力。然而，大规模城市场景中毫米波MIMO通信信道具有动态特性，尤其在复杂度和鲁棒性方面带来了巨大挑战。为解决这些问题，我们提出一种基于梯度的稳健液态神经网络（GLNN）框架，该框架利用常微分方程驱动的液态神经元求解波束赋形问题。具体而言，所提GLNN框架以优化目标函数的梯度作为输入，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能够在保持低复杂度的同时，对噪声和高度动态信道具备强鲁棒性。大量仿真结果表明，与典型迭代算法相比，GLNN的频谱效率可提升4.15%，而时间消耗仅为传统方法的1.61%。