Millimeter-wave (mmWave) technology is increasingly recognized as a pivotal technology of the sixth-generation communication networks due to the large amounts of available spectrum at high frequencies. However, the huge overhead associated with beam training imposes a significant challenge in mmWave communications, particularly in urban environments with high background noise. To reduce this high overhead, we propose a novel solution for robust continuous-time beam tracking with liquid neural network, which dynamically adjust the narrow mmWave beams to ensure real-time beam alignment with mobile users. Through extensive simulations, we validate the effectiveness of our proposed method and demonstrate its superiority over existing state-of-the-art deep-learning-based approaches. Specifically, our scheme achieves at most 46.9% higher normalized spectral efficiency than the baselines when the user is moving at 5 m/s, demonstrating the potential of liquid neural networks to enhance mmWave mobile communication performance.

In integrated ground-air-space (IGAS) wireless networks, numerous services require sensing knowledge including location, angle, distance information, etc., which usually can be acquired during the beam training stage. On the other hand, IGAS networks employ large-scale antenna arrays to mitigate obstacle occlusion and path loss. However, large-scale arrays generate pencil-shaped beams, which necessitate a higher number of training beams to cover the desired space. These factors motivate our investigation into the IGAS beam training problem to achieve effective sensing services. To address the high complexity and low identification accuracy of existing beam training techniques, we propose an efficient hashing multi-arm beam (HMB) training scheme. Specifically, we first construct an IGAS single-beam training codebook for the uniform planar arrays. Then, the hash functions are chosen independently to construct the multi-arm beam training codebooks for each AP. All APs traverse the predefined multi-arm beam training codeword simultaneously and the multi-AP superimposed signals at the user are recorded. Finally, the soft decision and voting methods are applied to obtain the correctly aligned beams only based on the signal powers. In addition, we logically prove that the traversal complexity is at the logarithmic level. Simulation results show that our proposed IGAS HMB training method can achieve 96.4% identification accuracy of the exhaustive beam training method and greatly reduce the training overhead.

Reconfigurable intelligent surface (RIS) has become a promising technology to realize the programmable wireless environment via steering the incident signal in fully customizable ways. However, a major challenge in RIS-aided communication systems is the simultaneous design of the precoding matrix at the base station (BS) and the phase shifting matrix of the RIS elements. This is mainly attributed to the highly non-convex optimization space of variables at both the BS and the RIS, and the diversity of communication environments. Generally, traditional optimization methods for this problem suffer from the high complexity, while existing deep learning based methods are lacking in robustness in various scenarios. To address these issues, we introduce a gradient-based manifold meta learning method (GMML), which works without pre-training and has strong robustness for RIS-aided communications. Specifically, the proposed method fuses meta learning and manifold learning to improve the overall spectral efficiency, and reduce the overhead of the high-dimensional signal process. Unlike traditional deep learning based methods which directly take channel state information as input, GMML feeds the gradients of the precoding matrix and phase shifting matrix into neural networks. Coherently, we design a differential regulator to constrain the phase shifting matrix of the RIS. Numerical results show that the proposed GMML can improve the spectral efficiency by up to 7.31%, and speed up the convergence by 23 times faster compared to traditional approaches. Moreover, they also demonstrate remarkable robustness and adaptability in dynamic settings.