Robust Beamforming with Gradient-based Liquid Neural Network

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.

Robust Continuous-Time Beam Tracking with Liquid Neural Network

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.

Beamforming Inferring by Conditional WGAN-GP for Holographic Antenna Arrays

The beamforming technology with large holographic antenna arrays is one of the key enablers for the next generation of wireless systems, which can significantly improve the spectral efficiency. However, the deployment of large antenna arrays implies high algorithm complexity and resource overhead at both receiver and transmitter ends. To address this issue, advanced technologies such as artificial intelligence have been developed to reduce beamforming overhead. Intuitively, if we can implement the near-optimal beamforming only using a tiny subset of the all channel information, the overhead for channel estimation and beamforming would be reduced significantly compared with the traditional beamforming methods that usually need full channel information and the inversion of large dimensional matrix. In light of this idea, we propose a novel scheme that utilizes Wasserstein generative adversarial network with gradient penalty to infer the full beamforming matrices based on very little of channel information. Simulation results confirm that it can accomplish comparable performance with the weighted minimum mean-square error algorithm, while reducing the overhead by over 50%.

Robust Beamforming for RIS-aided Communications: Gradient-based Manifold Meta Learning

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 lack of 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.

Energy-efficient Beamforming for RISs-aided Communications: Gradient Based Meta Learning

Reconfigurable intelligent surfaces (RISs) have become a promising technology to meet the requirements of energy efficiency and scalability in future six-generation (6G) communications. However, a significant challenge in RISs-aided communications is the joint optimization of active and passive beamforming at base stations (BSs) and RISs respectively. Specifically, the main difficulty is attributed to the highly non-convex optimization space of beamforming matrices at both BSs and RISs, as well as the diversity and mobility of communication scenarios. To address this, we present a greenly gradient based meta learning beamforming (GMLB) approach. Unlike traditional deep learning based methods which take channel information directly as input, GMLB feeds the gradient of sum rate into neural networks. Coherently, we design a differential regulator to address the phase shift optimization of RISs. Moreover, we use the meta learning to iteratively optimize the beamforming matrices of BSs and RISs. These techniques make the proposed method to work well without requiring energy-consuming pre-training. Simulations show that GMLB could achieve higher sum rate than that of typical alternating optimization algorithms with the energy consumption by two orders of magnitude less.